Sustainable polymer compositions and methods

Abstract

In one aspect, the present invention encompasses compositions of sustainable polycarbonate polymers, methods of producing such polymers, and methods for evaluating whether certain constituents of a polymer chain are derived from biomass or a fossil carbon source.

Claims

1. A polymer composition comprising aliphatic polycarbonate polyols having a structure P1: ##STR00252## wherein: R.sup.1, R.sup.2, R.sup.3, and R.sup.4 are, independently at each occurrence in the polymer chain, selected from the group consisting of: —H; and an optionally substituted group selected from C.sub.1-30 aliphatic, and C.sub.6-14 aryl; 3- to 12-membered heterocycle, and 5- to 12-membered heteroaryl, where two or more of R.sup.1, R.sup.2, R.sup.3, and R.sup.4 can be taken together with intervening atoms to form one or more optionally substituted 3- to 12-membered rings, optionally containing one or more heteroatoms; the radiocarbon content of carbon atoms at positions labeled α is lower than the radiocarbon content of carbon atoms at positions labeled β; Y is, at each occurrence, independently —H, a reactive group, or a site of attachment to chain-extending moieties or isocyanates; n is, at each occurrence, independently an integer from about 2 to about 50; is a covalent bond or a multivalent moiety; and x and y are each independently an integer from 0 to 6, where the sum of x and y is between 2 and 6.

2. The polymer composition according to claim 1, comprising polymer chains characterized in that the carbon atoms at positions labeled α have a percent Modern Carbon (pMC) value measured according to ASTM D6866-16 (Method B) that is lower than a pMC value of the carbon atoms at positions labeled β.

3. The polymer composition according to claim 2, wherein the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 50, less than about 20, less than about 10, less than about 5, or less than about 1.

4. The polymer composition according to claim 3, wherein the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of 0.

5. The polymer composition according to claim 2, wherein the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of greater than about 75, greater than about 80, greater than about 85, greater than about 90, greater than about 95, greater than about 100, or greater than about 105.

6. The polymer composition according to claim 5, wherein the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 100.

7. The polymer composition according to claim 1, wherein the % biobased carbon is greater than about 40%, 50%, 60%, 70%, 80%, or 90%.

8. The polymer composition according to claim 1, wherein the % biobased carbon is less than about 80%, 70%, 60%, 50%, 40%, 30%, 20%, or 10%.

9. The polymer composition according to claim 1, wherein the % biobased carbon is between about 40% and about 80%, between about 40% and about 60%, or between about 60% and about 80%.

10. The polymer composition according to claim 1, derived from biobased epoxides selected from the group consisting of ethylene oxide, propylene oxide, epoxides derived from natural oils, epoxides derived from fatty acids, epoxides derived from fatty alcohols, and mixtures of any two or more of these.

11. The polymer composition according to claim 1, derived from biobased epoxides selected from the group consisting of ethylene oxide and propylene oxide.

12. The polymer composition according to claim 1, comprising aliphatic polycarbonates, wherein the aliphatic polycarbonates are characterized in that, on average in the composition, the percentage of carbonate linkages is 90% or greater.

13. The polymer composition according to claim 1, wherein the polymer composition has a number average molecular weight (Mn) of greater than about 20,000 g/mol.

14. The polymer composition according to claim 1, wherein the polymer composition has a number average molecular weight (Mn) of less than about 20,000 g/mol.

15. A method comprising steps of: a) fermenting carbohydrate derived from biomass to produce biobased ethanol; b) converting the biobased ethanol to a biobased epoxide; and c) copolymerizing carbon dioxide sequestered from a fossil carbon source with the biobased epoxide to produce a polymer composition of claim 1.

16. A method comprising steps of: a) treating a polymer composition of claim 1 to liberate a cyclic carbonate of formula: ##STR00253## b) treating the cyclic carbonate to liberate carbon atoms labeled α as CO.sub.2, and carbon atoms labeled β as an epoxide of formula: ##STR00254## and c) measuring the radiocarbon content of the CO.sub.2 comprising carbon atoms labeled α, and the epoxide comprising carbon atoms labeled β.

17. The method according to claim 16, further comprising the step of separating the CO.sub.2 from the epoxide.

18. The method according to claim 16, wherein the radiocarbon content is measured according to ASTM D6866-16 (Method B).

19. The method according to claim 16, further comprising the steps of: e) using the measured radiocarbon content to confirm that the carbon atoms at the positions labeled α are derived from a fossil carbon source by having a pMC value measured according to ASTM D6866-16 (Method B) of less than about 1, less than about 0.1, or less than about 0.03; and f) using the measured radiocarbon content to confirm that the carbon atoms at the positions labeled β are derived from a biobased feedstock by having a pMC value measured according to ASTM D6866-16 (Method B) of at least about 95, at least about 99, or at least about 100.

20. The polymer composition of claim 1, comprising aliphatic polycarbonate polyols having a structure P2b: ##STR00255##

21. The polymer composition of claim 1, comprising aliphatic polycarbonate polyols having a structure Q7a′: ##STR00256## wherein R.sup.q is at each occurrence in the polymer chain independently —H or —CH.sub.3; R.sup.a is —H, or —CH.sub.3; and q and q′ are independently an integer from about 0 to about 40.

22. The polymer composition according to claim 1, wherein the polymer composition has an number average molecular weight (Mn) between about 500 and about 5,000 g/mol.

Description

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

(1) I. Polymer Compositions with Biobased and Fossil-Based Carbon

(2) A. Polymer Compositions

(3) In one aspect, the present invention provides polymer compositions that are both biobased and fossil-carbon sequestering. In some embodiments, the invention encompasses polymer compositions whose manufacture sequesters CO.sub.2 produced from a fossil carbon source, and utilizes biobased feedstocks as constituents of the polymer chain.

(4) In certain embodiments, a provided polymer composition comprises aliphatic polycarbonate polymers with biobased and fossil-based carbon. In certain embodiments, such provided polymer compositions comprise aliphatic polycarbonate polyols. In some embodiments, aliphatic polycarbonate polyols are derived from the copolymerization of one or more epoxides and carbon dioxide. Examples of aliphatic polycarbonate polyols derived from epoxides and CO.sub.2 are disclosed in PCT Publication No. WO 2010/028362 the entirety of which is incorporated herein by reference.

(5) In certain embodiments, the present invention provides a polymer composition comprising polymer chains having repeating units with a structure:

(6) ##STR00005##
wherein: R.sup.1, R.sup.2, R.sup.3, and R.sup.4 are, independently at each occurrence in the polymer chain, selected from the group consisting of: —H; and an optionally substituted group selected from C.sub.1-30 aliphatic, and C.sub.6-14 aryl; 3- to 12-membered heterocycle, and 5- to 12-membered heteroaryl, where two or more of R.sup.1, R.sup.2, R.sup.3, and R.sup.4 can be taken together with intervening atoms to form one or more optionally substituted 3- to 12-membered rings, optionally containing one or more heteroatoms; and the radiocarbon content of carbon atoms at positions labeled α is lower than the radiocarbon content of carbon atoms at positions labeled β.

(7) In some embodiments, R.sup.1 is —H. In some embodiments, R.sup.1 is optionally substituted C.sub.1-20 aliphatic. In some embodiments, R.sup.1 is optionally substituted C.sub.1-15 aliphatic. In some embodiments, R.sup.1 is optionally substituted C.sub.1-10 aliphatic. In some embodiments, R.sup.1 is optionally substituted C.sub.1-6 aliphatic. In some embodiments, R.sup.1 is optionally substituted C.sub.1-6 aliphatic. In some embodiments, R.sup.1 is methyl. In some embodiments, R.sup.1 is ethyl. In some embodiments, R.sup.1 is —CH.sub.2OR.sup.g where R.sup.g is selected from the group consisting of C.sub.1-6 acyl, C.sub.1-4 aliphatic, and optionally substituted aryl. In some embodiments, R.sup.1 is optionally substituted C.sub.6-14 aryl. In some embodiments, R.sup.1 is optionally substituted phenyl.

(8) In some embodiments, R.sup.2 is —H. In some embodiments, R.sup.2 is optionally substituted C.sub.1-20 aliphatic. In some embodiments, R.sup.2 is optionally substituted C.sub.1-15 aliphatic. In some embodiments, R.sup.2 is optionally substituted C.sub.1-10 aliphatic. In some embodiments, R.sup.2 is optionally substituted C.sub.1-6 aliphatic. In some embodiments, R.sup.2 is optionally substituted C.sub.1-4 aliphatic. In some embodiments, R.sup.2 is methyl. In some embodiments, R.sup.2 is ethyl. In some embodiments. R.sup.2 is —CH.sub.2OR.sup.g where R.sup.g is selected from the group consisting of C.sub.1-6 acyl, C.sub.1-8 aliphatic, and optionally substituted aryl. In some embodiments, R.sup.2 is optionally substituted C.sub.6-14 aryl. In some embodiments, R.sup.2 is optionally substituted phenyl.

(9) In some embodiments, R.sup.3 is —H. In some embodiments, R.sup.3 is optionally substituted C.sub.1-20 aliphatic. In some embodiments, R.sup.3 is optionally substituted C.sub.1-15 aliphatic. In some embodiments, R.sup.3 is optionally substituted C.sub.1-10 aliphatic. In some embodiments, R.sup.3 is optionally substituted C.sub.1-6 aliphatic. In some embodiments, R.sup.3 is optionally substituted C.sub.1-4 aliphatic. In some embodiments, R.sup.3 is methyl. In some embodiments, R.sup.3 is ethyl. In some embodiments, R.sup.3 is —CH.sub.2OR.sup.g where R.sup.g is selected from the group consisting of C.sub.1-6 acyl, C.sub.1-8 aliphatic, and optionally substituted aryl. In some embodiments, R.sup.3 is optionally substituted C.sub.6-14 aryl. In some embodiments, R.sup.3 is optionally substituted phenyl.

(10) In some embodiments, R.sup.4 is —H. In some embodiments, R.sup.4 is optionally substituted C.sub.1-20 aliphatic. In some embodiments, R.sup.4 is optionally substituted C.sub.1-6 aliphatic. In some embodiments, R.sup.4 is optionally substituted C.sub.1-10 aliphatic. In some embodiments, R.sup.4 is optionally substituted C.sub.1-6 aliphatic. In some embodiments, R.sup.4 is optionally substituted C.sub.1-4 aliphatic. In some embodiments, R.sup.4 is methyl. In some embodiments, R.sup.4 is ethyl. In some embodiments, R.sup.4 is —CH.sub.2OR.sup.g where R.sup.g is selected from the group consisting of C.sub.1-6 acyl, C.sub.1-8 aliphatic, and optionally substituted aryl. In some embodiments, R.sup.4 is optionally substituted C.sub.6-14 aryl. In some embodiments, R.sup.4 is optionally substituted phenyl.

(11) In some embodiments, each of R.sup.1, R.sup.2, R.sup.3, and R.sup.4 are —H. In some embodiments, one of R.sup.1, R.sup.2, R.sup.3, and R.sup.4 is methyl, and the remaining three are —H.

(12) In some embodiments, polymer composition comprising polymer chains having repeating units with a structure:

(13) ##STR00006##

(14) In some embodiments, polymer composition comprising polymer chains having repeating units with a structure:

(15) ##STR00007##

(16) In some embodiments, polymer composition comprising polymer chains having repeating units with a structure:

(17) ##STR00008##
where R.sup.g is as defined above and in the embodiments herein.

(18) In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is lower than the radiocarbon content of carbon atoms at positions labeled β.

(19) In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 5% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 10% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 15% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 20% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 25% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 30% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 35% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 40% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 45% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 50% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 55% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 60% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 65% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 70% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 75% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 80% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 85% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 90% lower than the radiocarbon content of carbon atoms at positions labeled β. In some embodiments, the radiocarbon content of carbon atoms at positions labeled α is at least 95% lower than the radiocarbon content of carbon atoms at positions labeled β.

(20) In some embodiments, a polymer composition comprises polymer chains characterized in that the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) that is lower than a pMC value of the carbon atoms at positions labeled β.

(21) In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 50. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 45. In some embodiments, the carbon atoms at positions labeled α have a pMC value of less than about 40. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 35. In some embodiments, the carbon atoms at positions labeled α have a pMC value of less than about 30. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 25. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 20. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 15. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 10. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 5. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 1. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 0.1. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of less than about 0.01. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 0.

(22) In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of between about 0 and about 10. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of between about 0 and about 1. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of between about 0 and about 0.1. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of between about 0 and about 0.01. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of between about 0 and about 5. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of between about 5 and about 10.

(23) In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 50. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 45. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 40. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 35. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 30. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 25. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 20. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 15. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 10. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 5. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 1. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 0.1. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 0.01. In some embodiments, the carbon atoms at positions labeled α have a pMC value measured according to ASTM D6866-16 (Method B) of about 0.

(24) In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of greater than about 75. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of greater than about 80. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of greater than about 85. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of greater than about 90. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of greater than about 95. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of greater than about 100. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of greater than about 105.

(25) In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of between about 75 and about 107.5. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of between about 85 and about 107.5. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of between about 95 and about 107.5. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of between about 105 and about 107.5. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of between about 75 and about 100. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of between about 75 and about 85. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of between about 85 and about 105. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of between about 95 and about 105.

(26) In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 75. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 80. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 85. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 90. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 95. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 100. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 105. In some embodiments, the carbon atoms at positions labeled β have a pMC value measured according to ASTM D6866-16 (Method B) of about 107.5.

(27) In some embodiments, a polymer composition comprises greater than about 10% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 20% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 30% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 40% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 50% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 60% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 70% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 80% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 90% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 95% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 98% biobased carbon content. In some embodiments, a polymer composition comprises greater than about 99% biobased carbon content.

(28) In some embodiments, a polymer composition comprises less than about 90% biobased carbon content. In some embodiments, a polymer composition comprises less than about 80% biobased carbon content. In some embodiments, a polymer composition comprises less than about 70% biobased carbon content. In some embodiments, a polymer composition comprises less than about 60% biobased carbon content. In some embodiments, a polymer composition comprises less than about 50% biobased carbon content. In some embodiments, a polymer composition comprises less than about 400% biobased carbon content. In some embodiments, a polymer composition comprises less than about 30% biobased carbon content. In some embodiments, a polymer composition comprises less than about 20% biobased carbon content. In some embodiments, a polymer composition comprises less than about 10% biobased carbon content.

(29) In some embodiments, a polymer composition comprises between about 10% and about 90% biobased carbon content. In some embodiments, a polymer composition comprises between about 20% and about 90% biobased carbon content. In some embodiments, a polymer composition comprises between about 30% and about 90% biobased carbon content. In some embodiments, a polymer composition comprises between about 40% and about 90% biobased carbon content. In some embodiments, a polymer composition comprises between about 50% and about 90% biobased carbon content. In some embodiments, a polymer composition comprises between about 10% and about 80% biobased carbon content. In some embodiments, a polymer composition comprises between about 10% and about 70% biobased carbon content. In some embodiments, a polymer composition comprises between about 10% and about 60% biobased carbon content. In some embodiments, a polymer composition comprises between about 10% and about 50% biobased carbon content. In some embodiments, a polymer composition comprises between about 20% and about 80% biobased carbon content. In some embodiments, a polymer composition comprises between about 30% and about 70% biobased carbon content. In some embodiments, a polymer composition comprises between about 40% and about 60% biobased carbon content. In some embodiments, a polymer composition comprises between about 45% and about 55% biobased carbon content. In some embodiments, a polymer composition comprises between about 45% and about 65% biobased carbon content. In some embodiments, a polymer composition comprises between about 50% and about 70% biobased carbon content. In some embodiments, a polymer composition comprises between about 60% and about 80% biobased carbon content. In some embodiments, a polymer composition comprises between about 70% and about 80% biobased carbon content. In some embodiments, a polymer composition comprises between about 65% and about 85% biobased carbon content. In some embodiments, a polymer composition comprises between about 75% and about 85% biobased carbon content. In some embodiments, a polymer composition comprises between about 65% and about 75% biobased carbon content. In some embodiments, a polymer composition comprises between about 55% and about 65% biobased carbon content.

(30) In some embodiments, all of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source, and all of the carbon atoms at the positions labeled β are derived from a biobased epoxide.

(31) In some embodiments, at least about 50% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 60% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 70% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 80% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 90% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 95% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 96% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 97% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 98% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 99% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source. In some embodiments, at least about 99.5% of the carbon atoms at the positions labeled α are derived from CO.sub.2 sequestered from a fossil carbon source.

(32) In some embodiments, at least about 50% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 60% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 70% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 80% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 90% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 95% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 96% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 97% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 98% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 99% of the carbon atoms at the positions labeled β are derived from a biobased epoxide. In some embodiments, at least about 99.5% of the carbon atoms at the positions labeled β are derived from a biobased epoxide.

(33) In some embodiments, biobased epoxides are selected from the group consisting of ethylene oxide, propylene oxide, epoxides derived from natural oils, epoxides derived from fatty acids, epoxides derived from fatty alcohols, epoxides derived from terpenes, and mixtures of any two or more of these. In some embodiments, biobased epoxides are selected from the group consisting of ethylene oxide, propylene oxide, glycidol ethers, glycidol esters, and limonene oxide. In some embodiments, biobased epoxides are ethylene oxide or propylene oxide. In some embodiments, biobased epoxides are ethylene oxide. In some embodiments, biobased epoxides are propylene oxide. In some embodiments, biobased epoxides are limonene oxide.

(34) In some embodiments, a biobased epoxide is an epoxide derived from a terpene. In some embodiments, a biobased epoxide derived from a terpene is selected from the group consisting of limonene oxide and α-pinene oxide.

(35) In some embodiments, a biobased epoxide is an epoxide derived from plant oils. In some embodiments, a biobased epoxide derived from plant oils is selected from the group consisting of 1,4-cyclohexadiene, cyclohexene, methyl-9,10-epoxystearate, and 18-hydroxy-9,10-epoxyoctadecanoate.

(36) In some embodiments, a biobased epoxide is an epoxide derived from glycerol. In some embodiments, a biobased epoxide derived from glycerol is selected from the group consisting of glycidol, glycidol ethers, glycidol esters, and epichlorohydrin. In certain embodiments where the epoxide comprises a glycidol ether or ester, such ethers and esters are derived by combining glycidol with a biobased alcohol or carboxylic acid respectively (or a reactive derivative of such a biobased alcohol or carboxylic acid).

(37) In some embodiments, biobased epoxides include epoxides derived from naturally occurring materials such as epoxidized resins or oils. Examples of such epoxides include, but are not limited to: Epoxidized Soybean Oil; Epoxidized Linseed Oil; Epoxidized Octyl Soyate; Epoxidized PGDO; Methyl Epoxy Soyate; Butyl Epoxy Soyate; Epoxidized Octyl Soyate; Methyl Epoxy Linseedate; Butyl Epoxy Linseedate; and Octyl Epoxy Linseedate. These and similar materials are available commercially from Arkema Inc. under the trade name Vikoflex®. Examples of such commercially available Vikoflex® materials include Vikoflex 7170 Epoxidized Soybean Oil, Vikoflex 7190 Epoxidized Linseed, Vikoflex 4050 Epoxidized Octyl Soyate, Vikoflex 5075 Epoxidized PGDO, Vikoflex 7010 Methyl Epoxy Soyate, Vikoflex 7040 Butyl Epoxy Soyate, Vikoflex 7080 Epoxidized Octyl Soyate, Vikoflex 9010 Methyl Epoxy Linseedate, Vikoflex 9040 Butyl Epoxy Linseedate, and Vikoflex 9080 Octyl Epoxy Linseedate.

(38) In certain embodiments, polymer chains comprise aliphatic polycarbonate polymers derived from fossil-based carbon dioxide and one or more epoxides, wherein at least one of the epoxides is a biobased epoxide. In certain embodiments, aliphatic polycarbonate chains comprise a copolymer of fossil-based carbon dioxide and biobased ethylene oxide. In certain embodiments, aliphatic polycarbonate chains comprise a copolymer of fossil-based carbon dioxide and biobased propylene oxide.

(39) In certain embodiments, aliphatic polycarbonate chains comprise a terpolymer of carbon dioxide and biobased ethylene oxide along with one or more additional epoxides selected from the group consisting of propylene oxide, 1,2-butene oxide, 2,3-butene oxide, cyclohexene oxide, 3-vinyl cyclohexene oxide, 3-ethyl cyclohexene oxide, cyclopentene oxide, epichlorohydrin, limonene oxide, glicydyl esters, glycidyl ethers, styrene oxides, and epoxides of higher alpha olefins. In certain embodiments, such terpolymers contain a majority of repeat units derived from biobased ethylene oxide with lesser amounts of repeat units derived from one or more additional epoxides. In certain embodiments, terpolymers contain about 50% to about 99.5% biobased ethylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than about 60% biobased ethylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 75% biobased ethylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 80% biobased ethylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 85% biobased ethylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 90% biobased ethylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 95% biobased ethylene oxide-derived repeat units.

(40) In certain embodiments, the aliphatic polycarbonate chains comprise a copolymer of carbon dioxide and biobased propylene oxide along with one or more additional epoxides selected from the group consisting of ethylene oxide, 1,2-butene oxide, 2,3-butene oxide, cyclohexene oxide, 3-vinyl cyclohexene oxide, cyclopentene oxide, epichlorohydrin, limonene oxide, glicydyl esters, glycidyl ethers, styrene oxides, and epoxides of higher alpha olefins. In certain embodiments, such terpolymers contain a majority of repeat units derived from biobased propylene oxide with lesser amounts of repeat units derived from one or more additional epoxides. In certain embodiments, terpolymers contain about 50% to about 99.5% biobased propylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 60% biobased propylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 75% biobased propylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 80% biobased propylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 85% biobased propylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 90% biobased propylene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 95% biobased propylene oxide-derived repeat units.

(41) In certain embodiments, the aliphatic polycarbonate chains comprise a copolymer of carbon dioxide and biobased limonene oxide along with one or more additional epoxides selected from the group consisting of ethylene oxide, propylene oxide, 1,2-butene oxide, 2,3-butene oxide, cyclohexene oxide, 3-vinyl cyclohexene oxide, cyclopentene oxide, epichlorohydrin, glicydyl esters, glycidyl ethers, styrene oxides, and epoxides of higher alpha olefins. In certain embodiments, such terpolymers contain a majority of repeat units derived from biobased limonene oxide with lesser amounts of repeat units derived from one or more additional epoxides. In certain embodiments, terpolymers contain about 50% to about 99.5% biobased limonene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 60% biobased limonene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 75% biobased limonene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 80% biobased limonene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 85% biobased limonene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 90% biobased limonene oxide-derived repeat units. In certain embodiments, terpolymers contain greater than 95% biobased limonene oxide-derived repeat units.

(42) It is advantageous for many of the embodiments described herein that aliphatic polycarbonate polyols used herein have a high percentage of reactive end groups. Such reactive end-groups are typically hydroxyl groups, but other reactive functional groups may be present if the polyols are treated to modify the chemistry of the end groups, such modified materials may terminate in amino groups, thiol groups, alkene groups, carboxylate groups, isocyanate groups, silyl groups, epoxy groups and the like. For purposes of this invention, the term “aliphatic polycarbonate polyol” includes both traditional hydroxy-terminated materials as well as these end-group modified compositions.

(43) In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 90% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 95% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 96% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 97% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 98% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99.5% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99.7% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99.8% of the end groups are reactive groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99.9% of the end groups are reactive groups.

(44) In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 90% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 95% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 96% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 97% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 98% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99.5% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99.7% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99.8% of the end groups are —OH groups. In certain embodiments, aliphatic polycarbonate polyols utilized herein are characterized in that at least 99.9% of the end groups are —OH groups.

(45) In certain embodiments, aliphatic polycarbonate polyols utilized herein have an “OH number” (OH #) greater than about 20 as measured using methods well known in the art. In certain embodiments, aliphatic polycarbonate polyols utilized herein have an OH # greater than about 40. In certain embodiments, the aliphatic polycarbonate polyols utilized herein have an OH # greater than about 50, greater than about 75, greater than about 100, or greater than about 120.

(46) In certain embodiments, it is advantageous if the aliphatic polycarbonate polyols utilized herein have a substantial proportion of primary hydroxyl end groups. These are the norm for compositions comprising poly(ethylene carbonate), but for polyols derived from copolymerization of substituted epoxides with CO.sub.2, it is common for some or most of the chain ends to consist of secondary hydroxyl groups. In certain embodiments, such polyols are treated to increase the proportion of primary —OH end groups. This may be accomplished by reacting the secondary hydroxyl groups with reagents such as ethylene oxide, reactive lactones, and the like. In certain embodiments, the aliphatic polycarbonate polyols are treated with beta lactones, caprolactone and the like to introduce primary hydroxyl end groups. In certain embodiments, the aliphatic polycarbonate polyols are treated with ethylene oxide to introduce primary hydroxyl end groups. In certain embodiments, the aliphatic polycarbonate polyols are treated with biobased ethylene oxide to introduce primary hydroxyl end groups.

(47) In certain embodiments, in the aliphatic polymer compositions described above and herein, polycarbonate chains have a Mn in the range of 500 g/mol to about 250,000 g/mol. In some embodiments, Mn is measured by size-exclusion chromatography. In some embodiments, Mn is measured by gel permeation chromatography. In some embodiments, gel permeation chromatography comprises a polystyrene standard.

(48) In certain embodiments, polymer compositions described herein have a Mn greater than about 100,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn less than about 100,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn less than about 70,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn less than about 50,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn between about 500 g/mol and about 40,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn less than about 25,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn between about 500 g/mol and about 20,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn between about 500 g/mol and about 10,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn between about 500 g/mol and about 5,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn between about 1,000 g/mol and about 5,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn between about 5,000 g/mol and about 10,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn between about 500 g/mol and about 1,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn between about 1,000 g/mol and about 3,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 5,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 4,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 3,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 2,500 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 2,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 1,500 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 1,000 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 750 g/mol. In certain embodiments, polymer compositions described herein have a Mn of about 500 g/mol.

(49) In certain embodiments, polymer compositions of the present invention are characterized in that they have a narrow molecular weight distribution. This can be indicated by the polydispersity indices (PDI) of the polymer composition. In certain embodiments, polymer compositions described herein have a PDI less than 3. In certain embodiments, polymer compositions described herein have a PDI less than 2. In certain embodiments, polymer compositions described herein have a PDI less than 1.8. In certain embodiments, polymer compositions described herein have a PDI less than 1.5. In certain embodiments, polymer compositions described herein have a PDI less than 1.4. In certain embodiments, polymer compositions described herein have a PDI between about 1.0 and 1.2. In certain embodiments, polymer compositions described herein have a PDI between about 1.0 and 1.1.

(50) In certain embodiments, polymer compositions of the present invention do not have a narrow PDI. This can be the case if, for example, a polydisperse chain transfer agent is used to initiate an epoxide CO.sub.2 copolymerization, or if a plurality of polymer compositions with different molecular weights are blended. In certain embodiments, polymer compositions described herein have a PDI greater than 3. In certain embodiments, polymer compositions described herein have a PDI greater than 2. In certain embodiments, polymer compositions described herein have a PDI greater than 1.8. In certain embodiments, polymer compositions described herein have a PDI greater than 1.5. In certain embodiments, polymer compositions described herein have a PDI greater than 1.4. In certain embodiments, the head-to-tail content of the polymer is as determined by size exclusion chromatography.

(51) In certain embodiments, there an aliphatic polycarbonate is derived from mono-substituted epoxides (e.g., such as propylene oxide, 1,2-butylene oxide, epichlorohydrin, epoxidized alpha olefins, or a glycidol derivative), the aliphatic polycarbonate is characterized in that it is regioregular. Regioregularity may be expressed as the percentage of adjacent monomer units that are oriented in a head-to-tail arrangement within the polymer chain. In certain embodiments, aliphatic polycarbonate chains in the inventive polymer compositions have a head-to-tail content higher than about 80%. In certain embodiments, the head-to-tail content is higher than about 85%. In certain embodiments, the head-to-tail content is higher than about 90%. In certain embodiments, the head-to-tail content is greater than about 91%, greater than about 92/%, greater than about 93%, greater than about 94%, or greater than about 95%.

(52) In some embodiments, PDI is measured by size-exclusion chromatography. In some embodiments, PDI is measured by gel permeation chromatography. In some embodiments, gel permeation chromatography comprises a polystyrene standard.

(53) i. Substantially Alternating Aliphatic Polycarbonate Polyols

(54) In certain embodiments, compositions of the present invention comprise substantially alternating polycarbonates. In some embodiments, such substantially alternating polycarbonates are both biobased and fossil-carbon sequestering.

(55) In certain embodiments, polymer compositions of the present invention comprise substantially alternating aliphatic polycarbonate polymers containing a high percentage of carbonate linkages and a low content of ether linkages. In some embodiments, the percentage of carbonate linkages may be determined by .sup.1H or .sup.13C NMR spectroscopy. In some embodiments, the percentage of carbonate linkages may be determined by infra red (IR) or Raman spectroscopy.

(56) In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 85% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 90% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 91% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 92% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 93% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 94% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 95% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 96% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 97% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 98% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 99% or greater. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is 99.5% or greater. In certain embodiments, the percentages above exclude ether linkages present in polymerization initiators or chain transfer agents and refer only to the linkages formed during epoxide CO.sub.2 copolymerization.

(57) In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that they contain essentially no ether linkages either within the polymer chains derived from epoxide CO.sub.2 copolymerization or within any polymerization initiators, chain transfer agents or end groups that may be present in the polymer. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that they contain, on average, less than one ether linkage per polymer chain within the composition. In certain embodiments, aliphatic polycarbonate compositions of the present invention are characterized in that they contain essentially no ether linkages.

(58) In some embodiments, compositions of the present invention comprise aliphatic polycarbonate polyols having a structure P1:

(59) ##STR00009## wherein, R.sup.1, R.sup.2, R.sup.3, R.sup.4, α, and β are described above and herein: Y is, at each occurrence, independently —H, a reactive group (as described above and herein), or a site of attachment to any of the chain-extending moieties or isocyanates described in the classes and subclasses herein; n is at each occurrence, independently an integer from about 2 to about 50:

(60) ##STR00010##
is a covalent bond or a multivalent moiety; and x and y are each independently an integer from 0 to 6, where the sum of x and y is between 2 and 6.

(61) In certain embodiments, the multivalent moiety

(62) ##STR00011##
embedded within the aliphatic polycarbonate chain is derived from a polyfunctional chain transfer agent having two or more sites from which epoxide/CO.sub.2 copolymerization can occur. In certain embodiments, such copolymerizations are performed in the presence of polyfunctional chain transfer agents as exemplified in PCT Publication No. WO 2010/028362. In certain embodiments, such copolymerizations are performed as exemplified in U.S. Patent Publication No. U.S. 2011/0245424. In certain embodiments, such copolymerizations are performed as exemplified in Cyriac et al. Green Chem. 2011 (13), 3469-3475.

(63) In some embodiments, n is, at each occurrence independently an integer from about 2 to about 50. In some embodiments, n is, at each occurrence independently an integer from about 10 to about 50. In some embodiments, n is, at each occurrence independently an integer from about 20 to about 50. In some embodiments, n is, at each occurrence independently an integer from about 30 to about 50. In some embodiments, n is, at each occurrence independently an integer from about 40 to about 50. In some embodiments, n is, at each occurrence independently an integer from about 2 to about 25. In some embodiments, n is, at each occurrence independently an integer from about 2 to about 10.

(64) In certain embodiments, a polyfunctional chain transfer agent has a formula:

(65) ##STR00012## wherein each of

(66) ##STR00013##
x, and y is as described above and herein. In certain embodiments, such polyfunctional chain transfer agents are biobased.

(67) In certain embodiments, aliphatic polycarbonate chains in polymer compositions of the present invention comprise chains with a structure P2:

(68) ##STR00014##
wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4, Y,

(69) ##STR00015##
n, α, and β is as described above and herein.

(70) In certain embodiments where aliphatic polycarbonate chains have a structure P2,

(71) ##STR00016##
is derived from a dihydric alcohol. In such instances

(72) ##STR00017##
represents the carbon-containing backbone of the dihydric alcohol, while the two oxygen atoms adjacent to

(73) ##STR00018##
are derived from the —OH groups of the diol. For example, if the polyfunctional chain transfer agent were ethylene glycol, then

(74) ##STR00019##
would be —CH.sub.2CH.sub.2— and P2 would have the following structure:

(75) ##STR00020##

(76) In certain embodiments where

(77) ##STR00021##
is derived from a dihydric alcohol, the dihydric alcohol comprises a C.sub.2-40 diol. In certain embodiments, the dihydric alcohol is selected from the group consisting of: 1,2-ethanediol, 1,2-propanediol, 1,3-propanediol, 1,2-butanediol, 1,3-butanediol, 1,4-butanediol, 1,5-pentanediol, 2,2-dimethylpropane-1,3-diol, 2-butyl-2-ethylpropane-1,3-diol, 2-methyl-2,4-pentane diol, 2-ethyl-1,3-hexane diol, 2-methyl-1,3-propane diol, 1,5-hexanediol, 1,6-hexanediol, 1,8-octanediol, 1,10-decanediol, 1,12-dodecanediol, 2,2,4,4-tetramethylcyclobutane-1,3-diol, 1,3-cyclopentanediol, 1,2-cyclohexanediol, 1,3-cyclohexanediol, 1,4-cyclohexanediol, 1,2-cyclohexanedimethanol, 1,3-cyclohexanedimethanol, 1,4-cyclohexanedimethanol, 1,4-cyclohexanediethanol, isosorbide, glycerol monoesters, glycerol monoethers, trimethylolpropane monoesters, trimethylolpropane monoethers, pentaerythritol diesters, pentaerythritol diethers, and alkoxylated derivatives of any of these. In certain embodiments, any of the above dihydric alcohols are characterized in that they are derived from biomass.

(78) In certain embodiments where

(79) ##STR00022##
is derived from a dihydric alcohol, the dihydric alcohol is selected from the group consisting of: diethylene glycol, triethylene glycol, tetraethylene glycol, higher poly(ethylene glycol), such as those having number average molecular weights of from 220 to about 2000 g/mol, dipropylene glycol, tripropylene glycol, and higher poly(propylene glycol) such as those having number average molecular weights of from 234 to about 2000 g/mol. In certain embodiments, any of the above dihydric alcohols are characterized in that they are derived from biomass.

(80) In certain embodiments where

(81) ##STR00023##
is derived from a dihydric alcohol, the dihydric alcohol comprises an alkoxylated derivative of a molecule selected from the group consisting of: a diacid, a diol, or a hydroxy acid. In certain embodiments, the alkoxylated derivatives comprise ethoxylated or propoxylated molecules.

(82) In certain embodiments where

(83) ##STR00024##
is derived from a dihydric alcohol, the dihydric alcohol comprises a polymeric diol. In certain embodiments, a polymeric diol is selected from the group consisting of polyethers, polyesters, hydroxy-terminated polyolefins, polyether-copolyesters, polyether polycarbonates, polycarbonate-copolyesters, polyoxymethylene polymers, and alkoxylated analogs of any of these. In certain embodiments, the polymeric diol has an average molecular weight less than about 2000 g/mol. In certain embodiments, any of the above dihydric alcohols are characterized in that they are derived from biomass.

(84) In certain embodiments,

(85) ##STR00025##
is derived from a polyhydric alcohol with more than two hydroxy groups. In embodiments in which

(86) ##STR00026##
is derived from a polyhydric alcohol with more than two hydroxyl groups, these >2 functional polyhydric alcohols are a component of a mixture containing predominantly polyhydric alcohols with two hydroxyl groups. In certain embodiments, these >2 functional polyhydric alcohols are less than 20% of the total polyhydric alcohols mixture by weight. In certain embodiments, these >2 functional polyhydric alcohols are less than 10% of the total polyhydric alcohols mixture. In certain embodiments, these >2 functional polyhydric alcohols are less than 5% of the total polyhydric alcohols mixture. In certain embodiments, these >2 functional polyhydric alcohols are less than 2% of the total polyhydric alcohols mixture.

(87) In certain embodiments, the aliphatic polycarbonate chains in polymer compositions of the present invention comprise aliphatic polycarbonate chains where the moiety

(88) ##STR00027##
is derived from a triol. In certain embodiments, such aliphatic polycarbonate chains have the structure P3:

(89) ##STR00028##
wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4, Y,

(90) ##STR00029##
n, α, and β is as described above and herein.

(91) In certain embodiments where

(92) ##STR00030##
is derived from a triol, the triol is selected from the group consisting of: glycerol, 1,2,4-butanetriol, 2-(hydroxymethyl)-1,3-propanediol; hexane triols, trimethylol propane, trimethylol ethane, trimethylolhexane, 1,2,4-cyclohexanetrimethanol, pentaerythritol mono esters, pentaerythritol mono ethers, and alkoxylated analogs of any of these. In certain embodiments, such alkoxylated derivatives comprise ethoxylated or propoxylated molecules. In certain embodiments, any of the above triols are characterized in that they are derived from biomass.

(93) In certain embodiments,

(94) ##STR00031##
is derived from an alkoxylated derivative of a trifunctional carboxylic acid or trifunctional hydroxy acid. In certain embodiments, alkoxylated derivatives comprise ethoxylated or propoxylated molecules.

(95) In certain embodiments, where

(96) ##STR00032##
is derived from a polymeric triol, the polymeric triol is selected from the group consisting of polyethers, polyesters, hydroxy-terminated polyolefins, polyether-copolyesters, polyether polycarbonates, polyoxymethylene polymers, polycarbonate-copolyesters, and alkoxylated analogs of any of these. In certain embodiments, the alkoxylated polymeric triols comprise ethoxylated or propoxylated molecules. In certain embodiments, any of the above triols are characterized in that they are derived from biomass.

(97) In certain embodiments,

(98) ##STR00033##
is derived from a polyhydric alcohol with four hydroxy groups. In certain embodiments, aliphatic polycarbonate chains in polymer compositions of the present invention comprise aliphatic polycarbonate chains where the moiety

(99) ##STR00034##
is derived from a tetraol. In certain embodiments, such tetraols are characterized in that they are derived from biomass. In certain embodiments, aliphatic polycarbonate chains in polymer compositions of the present invention comprise chains with the structure P4:

(100) ##STR00035##
wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4, Y,

(101) ##STR00036##
n, α, and β is as described above and herein.

(102) In certain embodiments,

(103) ##STR00037##
is derived from a polyhydric alcohol with more than four hydroxy groups. In certain embodiments, such polyhydric alcohols are characterized in that they are derived from biomass. In certain embodiments,

(104) ##STR00038##
is derived from a polyhydric alcohol with six hydroxy groups. In certain embodiments, a polyhydric alcohol is dipentaerythritol or an alkoxylated analog or other derivative thereof. In certain embodiments, a polyhydric alcohol is sorbitol or an alkoxylated analog thereof. In certain embodiments, aliphatic polycarbonate chains in polymer compositions of the present invention comprise chains with the structure P5:

(105) ##STR00039##
wherein each of R.sup.1, R.sup.2. R.sup.3, R.sup.4, Y,

(106) ##STR00040##
n, α and β is as described above and herein.

(107) In certain embodiments, aliphatic polycarbonates of the present invention comprise a combination of bifunctional chains (e.g., polycarbonates of formula P2) in combination with higher functional chains (e.g., one or more polycarbonates of formulae P3 to P5).

(108) In certain embodiments,

(109) ##STR00041##
is derived from a hydroxy acid. In certain embodiments, such hydroxy acids are characterized in that they are derived from biomass. In certain embodiments, aliphatic polycarbonate chains in polymer compositions of the present invention comprise chains with the structure P6:

(110) ##STR00042##
wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4, Y,

(111) ##STR00043##
n, α, and β is as described above and herein. In such instances,

(112) ##STR00044##
represents the carbon-containing backbone of the hydroxy acid, while ester and carbonate linkages adjacent to

(113) ##STR00045##
are derived from the —CO.sub.2H group and the hydroxy group of the hydroxy acid. For example, if

(114) ##STR00046##
were derived from 3-hydroxypropanoic acid, then

(115) ##STR00047##
would be —CH.sub.2CH.sub.2— and P6 would have the following structure:

(116) ##STR00048##

(117) In certain embodiments,

(118) ##STR00049##
is derived from an optionally substituted C.sub.2-40 hydroxy acid. In certain embodiments,

(119) ##STR00050##
is derived from a polyester. In certain embodiments, such polyesters have a molecular weight less than about 2000 g/mol.

(120) In certain embodiments, a hydroxy acid is an alpha-hydroxy acid. In certain embodiments, a hydroxy acid is selected from the group consisting of: glycolic acid, DL-lactic acid, D-lactic acid. L-lactic, citric acid, and mandelic acid. In certain embodiments, any of the above hydroxy acids are characterized in that they are derived from biomass.

(121) In certain embodiments, a hydroxy acid is a beta-hydroxy acid. In certain embodiments, a hydroxy acid is selected from the group consisting of: 3-hydroxypropionic acid, DL 3-hydroxybutryic acid, D-3 hydroxybutryic acid. L-3-hydroxybutyric acid. DL-3-hydroxy valeric acid, D-3-hydroxy valeric acid, L-3-hydroxy valeric acid, salicylic acid, and derivatives of salicylic acid. In certain embodiments, any of the above hydroxy acids are characterized in that they are derived from biomass.

(122) In certain embodiments, a hydroxy acid is a α-ω hydroxy acid. In certain embodiments, a hydroxy acid is selected from the group consisting of: optionally substituted C.sub.3-20 aliphatic α-ω hydroxy acids and oligomeric esters. In certain embodiments, any of the above hydroxy acids are characterized in that they are derived from biomass.

(123) In certain embodiments, a hydroxy acid is selected from the group consisting of:

(124) ##STR00051## ##STR00052##
In certain embodiments, any of the above hydroxy acids are characterized in that they are derived from biomass.

(125) In certain embodiments,

(126) ##STR00053##
is derived from a polycarboxylic acid. In certain embodiments, such polycarboxylic acids are characterized in that they are derived from biomass. In certain embodiments, aliphatic polycarbonate chains in polymer compositions of the present invention comprise chains with the structure P7:

(127) ##STR00054##
wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4, Y,

(128) ##STR00055##
n, α, and β is as described above and herein, and y′ is an integer from 1 to 5 inclusive.

(129) In embodiments where the aliphatic polycarbonate chains have a structure P7,

(130) ##STR00056##
represents the carbon-containing backbone (or a bond in the case of oxalic acid) of a polycarboxylic acid, while ester groups adjacent to

(131) ##STR00057##
are derived from —CO.sub.2H groups of the polycarboxylic acid. For example, if

(132) ##STR00058##
were derived from succinic acid (HO.sub.2CCH.sub.2CH.sub.2CO.sub.2H), then

(133) ##STR00059##
would be —CH.sub.2CH.sub.2— and P7 would have the following structure:

(134) ##STR00060##
wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4, Y, n, α, and β is as described above and herein.

(135) In certain embodiments,

(136) ##STR00061##
is derived from a dicarboxylic acid. In certain embodiments, aliphatic polycarbonate chains in polymer compositions of the present invention comprise chains with the structure P8:

(137) ##STR00062##
wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4, Y,

(138) ##STR00063##
n, α, and β is as described above and herein.

(139) In certain embodiments,

(140) ##STR00064##
is selected from the group consisting of: phthalic acid, isophthalic acid, terephthalic acid, maleic acid, succinic acid, malonic acid, glutaric acid, adipic acid, pimelic acid, suberic acid, and azelaic acid.

(141) In certain embodiments,

(142) ##STR00065##
is derived from a diacid selected from the group consisting of:

(143) ##STR00066## ##STR00067##

(144) In certain embodiments,

(145) ##STR00068##
is derived from a phosphorous-containing molecule. In certain embodiments,

(146) ##STR00069##
has a formula —P(O)(OR).sub.k— where each R is independently an optionally substituted C.sub.1-20 aliphatic group or an optionally substituted aryl group and k is 0, 1, or 2.

(147) For example, if

(148) ##STR00070##
were derived from PhO—P(O)(OH).sub.2, then

(149) ##STR00071##
would be —P(O)OPh)- and P7 would have the following structure:

(150) ##STR00072##
wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4, Y, n, α, and β is as described above and herein.

(151) In certain embodiments,

(152) ##STR00073##
is derived from a phosphorous-containing molecule selected from the group consisting of:

(153) ##STR00074##

(154) In certain embodiments,

(155) ##STR00075##
has a formula —P(O)(R.sup.p).sub.p— where R.sup.p is an optionally substituted C.sub.1-20 aliphatic group or an optionally substituted aryl group and p′ is 0, 1, or 2. In certain embodiments,

(156) ##STR00076##
is derived from a phosphorous-containing molecule selected from the group consisting of:

(157) ##STR00077##
where R.sup.p is as described above and herein, and R.sup.e is, at each occurrence, independently selected from the group consisting of: halogen, —NO.sub.2, —CN, —SR.sup.f, —S(O)R.sup.f, —S(O).sub.2R.sup.f, —NR.sup.fC(O)R.sup.f, —OC(O)R.sup.f, —CO.sub.2R.sup.f, —NCO, —N.sub.3, —OR.sup.f, —OC(O)N(R.sup.f).sub.2, —N(R.sup.f).sub.2, —NR.sup.fC(O)R.sup.f, —NR.sup.fC(O)OR.sup.f; or an optionally substituted radical selected from the group consisting of C.sub.1-20 aliphatic, C.sub.1-20 heteroaliphatic, a 3- to 14-membered carbocycle, a 3- to 12-membered heterocycle, a 5- to 12-membered heteroaryl, and 6- to 10-membered aryl; where two or more adjacent R.sup.e groups can be taken together to form an optionally substituted saturated, partially unsaturated, or aromatic 5- to 12-membered ring containing 0 to 4 heteroatoms; where each occurrence of R.sup.f is independently —H, or an optionally substituted moiety selected from the group consisting of C.sub.1-6 aliphatic, C.sub.1-6 heteroaliphatic, 3- to 7-membered heterocyclic, 3- to 7-membered carbocyclic 6- to 10-membered aryl, and 5- to 10-membered heteroaryl; and p″ is an integer selected from 2-30.

(158) In certain embodiments,

(159) ##STR00078##
has a formula —PR— where R is an optionally substituted C.sub.1-20 aliphatic group or an optionally substituted aryl group.

(160) In certain embodiments, each

(161) ##STR00079##
in the structures herein is independently selected from the group consisting of:

(162) ##STR00080## ##STR00081##
wherein each R.sup.x is independently an optionally substituted moiety selected from the group consisting of C.sub.2-20 aliphatic, C.sub.2-20 heteroaliphatic, 3- to 14-membered carbocyclic, 6- to 10-membered aryl, 5- to 10-membered heteroaryl, and 3- to 12-membered heterocyclic; and z′ is an integer selected from 9-30.

(163) In certain embodiments, each

(164) ##STR00082##
in the structures herein is independently selected from the group consisting of:

(165) ##STR00083## wherein R.sup.x is as described above and herein.

(166) In certain embodiments, the moiety —Y in the structures herein is —H.

(167) In certain embodiments, —Y comprises an ester linkage to an optionally substituted C.sub.2-40 linker terminated with an —OH group. In certain embodiments, —Y is selected from the group consisting of:

(168) ##STR00084##

(169) In certain embodiments, —Y comprises an ester linkage to an optionally substituted C.sub.2-40 linker terminated with an —CO.sub.2H group. In certain embodiments, —Y is selected from the group consisting of:

(170) ##STR00085##

(171) In certain embodiments, the moiety —Y in the structures herein comprises a hydroxy-terminated polymer. In certain embodiments, —Y comprises a hydroxy-terminated polyether. In certain embodiments, —Y comprises

(172) ##STR00086##
where t′ is an integer from 1 to 20. In certain embodiments, —Y comprises

(173) ##STR00087##
where t′ is an integer from 1 to 20. In certain embodiments, —Y comprises

(174) ##STR00088##
where t′ is an integer from 1 to 20.

(175) In certain embodiments, —Y comprises a hydroxy-terminated polyester. In certain embodiments, —Y is selected from the group consisting of:

(176) ##STR00089##
where s is an integer from 2 to 20.

(177) In certain embodiments, aliphatic polycarbonate chains comprise:

(178) ##STR00090##

(179) wherein each of

(180) ##STR00091##
—Y, n, α, and β is as described above and herein.

(181) In certain embodiments, aliphatic polycarbonate chains comprise:

(182) ##STR00092##

(183) wherein each of —Y n, α, and β is as described above and herein.

(184) In certain embodiments, aliphatic polycarbonate chains comprise:

(185) ##STR00093##

(186) wherein each of —Y n, α, and β is as described above and herein.

(187) In certain embodiments, aliphatic polycarbonate chains comprise:

(188) ##STR00094##

(189) wherein each of —Y n, α, and β is as described above and herein.

(190) In certain embodiments, aliphatic polycarbonate chains comprise:

(191) ##STR00095##

(192) wherein each of —Y n, α, and β is as described above and herein.

(193) In certain embodiments, aliphatic polycarbonate chains comprise:

(194) ##STR00096##

(195) wherein each of

(196) ##STR00097##
—Y, n, α, and β is as described above and herein.

(197) In certain embodiments, aliphatic polycarbonate chains comprise:

(198) ##STR00098##

(199) wherein each of

(200) ##STR00099##
—Y, n, α, and β is as described above and herein.

(201) In certain embodiments, aliphatic polycarbonate chains comprise:

(202) ##STR00100##
wherein each of

(203) ##STR00101##
Y, n, α, and β is as described above and herein.

(204) In certain embodiments, aliphatic polycarbonate chains comprise:

(205) ##STR00102##

(206) wherein each of

(207) ##STR00103##
—Y, n, α, and β is as described above and herein.

(208) In certain embodiments, aliphatic polycarbonate chains comprise:

(209) ##STR00104##

(210) wherein each of —Y n, α, and β is as described above and herein.

(211) In certain embodiments, aliphatic polycarbonate chains comprise:

(212) ##STR00105##

(213) wherein each of

(214) ##STR00106##
—Y, n, α, and β is as described above and herein.

(215) In certain embodiments, aliphatic polycarbonate chains comprise:

(216) ##STR00107##

(217) wherein each of —Y n, α, and β is as described above and herein.

(218) In certain embodiments, aliphatic polycarbonate chains comprise:

(219) ##STR00108##

(220) wherein each of

(221) ##STR00109##
—Y, n, α, and β is as described above and herein.

(222) In certain embodiment, aliphatic polycarbonate chains comprise:

(223) ##STR00110##

(224) wherein each of —Y n, α, and β is as described above and herein.

(225) In certain embodiments, aliphatic polycarbonate chains comprise:

(226) ##STR00111##

(227) wherein each of

(228) ##STR00112##
—Y, R.sup.x, n, α, and β is as described above and herein.

(229) In certain embodiments, aliphatic polycarbonate chains comprise:

(230) ##STR00113##

(231) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(232) In certain embodiments, aliphatic polycarbonate chains comprise:

(233) ##STR00114##

(234) wherein each of

(235) ##STR00115##
R.sup.x, —Y n, α, and β is as described above and herein.

(236) In certain embodiments, aliphatic polycarbonate chains comprise:

(237) ##STR00116##

(238) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(239) In certain embodiments, aliphatic polycarbonate chains comprise:

(240) ##STR00117##

(241) wherein each of

(242) ##STR00118##
—Y, n, α, and β is as described above and herein.

(243) In certain embodiments, aliphatic polycarbonate chains comprise:

(244) ##STR00119##

(245) wherein each of —Y n, α, and β is as described above and herein.

(246) In certain embodiments, in polycarbonates of structures P2a, P2c, P2f, P2h, P2j, P2n, and P2r,

(247) ##STR00120##
is selected from the group consisting of: ethylene glycol; diethylene glycol, triethylene glycol, 1,3 propane diol; 1,4 butane diol, hexylene glycol, 1,6 hexane diol, neopentyl glycol, propylene glycol, dipropylene glycol, tripropylene glycol, and alkoxylated derivatives of any of these. In certain embodiments, any of the above diols are characterized in that they are derived from biomass.

(248) In certain embodiments, in polycarbonates of structures P2, P2a, P2b, P2b′, P2b″, P2b′″, P2c, P2c′, P2c″, P2c′″, P2d, P2f, P2g, P2h, P2i, P2j, P2k, P2n, P2o, P2r, and P2r-a, the embedded chain transfer agent is characterized in that it is derived from biomass. In certain embodiments, in polycarbonates of structures P2, P2a, P2b, P2b′, P2b″, P2b′″, P2c, P2c′, P2c″, P2c′″, P2d, P2f, P2g, P2h, P2i, P2j, P2k, P2n, P2o, P2r, and P2r-a, the embedded chain transfer agent is characterized in that it is not derived from biomass.

(249) In certain embodiments, in polycarbonates of structures P2, P2a, P2b, P2b′, P2b″, P2b′″, P2c, P2c′, P2c″, P2c′″, P2d, P2f, P2g, P2h, P2i, P2j, P2k, P2n, P2o, P2r, and P2r-a, —Y is —H.

(250) In certain embodiments, aliphatic polycarbonate chains comprise:

(251) ##STR00121##

(252) wherein each of —Y n, α, and β is as described above and herein.

(253) In certain embodiments, aliphatic polycarbonate chains comprise:

(254) ##STR00122##

(255) wherein each of —Y n, α, and β is as described above and herein.

(256) In certain embodiments, aliphatic polycarbonate chains comprise:

(257) ##STR00123##

(258) wherein each of —Y n, α, and β is as described above and herein.

(259) In certain embodiments, aliphatic polycarbonate chains comprise:

(260) ##STR00124##

(261) wherein each of —Y n, α, and β is as described above and herein.

(262) In certain embodiments, aliphatic polycarbonate chains comprise:

(263) ##STR00125##

(264) wherein each of —Y n, α, and β is as described above and herein.

(265) In certain embodiments, aliphatic polycarbonate chains comprise:

(266) ##STR00126##

(267) wherein each of —Y n, α, and β is as described above and herein.

(268) In certain embodiments, aliphatic polycarbonate chains comprise:

(269) ##STR00127##

(270) wherein each of —Y n, α, and β is as described above and herein.

(271) In certain embodiments, aliphatic polycarbonate chains comprise:

(272) ##STR00128##

(273) wherein each of —Y n, α, and β is as described above and herein.

(274) In certain embodiments, aliphatic polycarbonate chains comprise:

(275) ##STR00129##

(276) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(277) In certain embodiments, aliphatic polycarbonate chains comprise:

(278) ##STR00130##

(279) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(280) In certain embodiments, aliphatic polycarbonate chains comprise:

(281) ##STR00131##

(282) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(283) In certain embodiments, aliphatic polycarbonate chains comprise:

(284) ##STR00132##

(285) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(286) In certain embodiments, aliphatic polycarbonate chains comprise:

(287) ##STR00133##

(288) wherein each of —Y n, α, and β is as described above and herein.

(289) In certain embodiments, aliphatic polycarbonate chains comprise:

(290) ##STR00134##

(291) wherein each of —Y n, α, and β is as described above and herein.

(292) In certain embodiments, in polycarbonates of structures P3a, P3c, P3f, P3h, P3j, P3n, P3r, and P3r-a,

(293) ##STR00135##
is selected from the group consisting of: glycerol, 1,2,4-butanetriol, 2-(hydroxymethyl)-1,3-propanediol; hexane triols, trimethylol propane, trimethylol ethane, trimethylolhexane, 1,2,4-cyclohexanetrimethanol, pentaerythritol mono esters, pentaerythritol mono ethers, and alkoxylated analogs of any of these. In certain embodiments, such alkoxylated derivatives comprise ethoxylated or propoxylated molecules. In certain embodiments, any of the above triols are characterized in that they are derived from biomass. In certain embodiments, in polycarbonates of structures P3, P3a, P3b, P3c, P3d. P3f, P3g, P3h, P3i, P3j, P3k, P3n, P3o, P3r, and P3r-a, the embedded chain transfer agent is characterized in that it is derived from biomass. In certain embodiments, in polycarbonates of structures P3, P3a, P3b, P3c, P3d, P3f, P3g, P3h, P3i, P3j, P3k, P3n, P3o, P3r, and P3r-a, the embedded chain transfer agent is characterized in that it is not derived from biomass.

(294) In certain embodiments, in polycarbonates of structures P3, P3a, P3b, P3c, P3d, P3f, P3g, P3h, P3i, P3j, P3k P3n, P3o, P3r, and P3r-a, —Y is —H.

(295) In certain embodiments, aliphatic polycarbonate chains comprise:

(296) ##STR00136##

(297) wherein each of —Y n, α, and β is as described above and herein.

(298) In certain embodiments, aliphatic polycarbonate chains comprise:

(299) ##STR00137##

(300) wherein each of —Y n, α, and β is as described above and herein.

(301) In certain embodiments, aliphatic polycarbonate chains comprise:

(302) ##STR00138##

(303) wherein each of —Y n, α, and β is as described above and herein.

(304) In certain embodiments, aliphatic polycarbonate chains comprise:

(305) ##STR00139##

(306) wherein each of —Y n, α, and β is as described above and herein.

(307) In certain embodiments, aliphatic polycarbonate chains comprise:

(308) ##STR00140##

(309) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(310) In certain embodiments, aliphatic polycarbonate chains comprise:

(311) ##STR00141##

(312) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(313) In certain embodiments, aliphatic polycarbonate chains comprise:

(314) ##STR00142##

(315) wherein each of —Y n, α, and β is as described above and herein.

(316) In certain embodiments, in polycarbonates of structures P4a, P4c, P4f, P4h, P4j, P4n, and P4r, the embedded chain transfer agent is characterized in that it is derived from biomass. In certain embodiments, in polycarbonates of structures P4a, P4c, P4f, P4h, P4j, P4n, and P4r, the embedded chain transfer agent is characterized in that it is not derived from biomass.

(317) In certain embodiments, in polycarbonates of structures P4a, P4c, P4f, P4h, P4j, P4n, and P4r, —Y is —H.

(318) In certain embodiments, aliphatic polycarbonate chains comprise:

(319) ##STR00143##

(320) wherein each of —Y n, α, and β is as described above and herein.

(321) In certain embodiments, aliphatic polycarbonate chains comprise:

(322) ##STR00144##

(323) wherein each of —Y n, α, and β is as described above and herein.

(324) In certain embodiments, aliphatic polycarbonate chains comprise:

(325) ##STR00145##

(326) wherein each of —Y n, α, and β is as described above and herein.

(327) In certain embodiments, aliphatic polycarbonate chains comprise:

(328) ##STR00146##

(329) wherein each of —Y n, α, and β is as described above and herein.

(330) In certain embodiments, aliphatic polycarbonate chains comprise:

(331) ##STR00147##

(332) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(333) In certain embodiments, aliphatic polycarbonate chains comprise:

(334) ##STR00148##

(335) wherein each of —Y, R.sup.x, n, α, and β is as described above and herein.

(336) In certain embodiments, aliphatic polycarbonate chains comprise:

(337) ##STR00149##

(338) wherein each of —Y n, α, and β is as described above and herein.

(339) In certain embodiments, in polycarbonates of structures P5a, P5c, P5f, P5h, P5j, P5n, and P5r,

(340) ##STR00150##
is selected from the group consisting of: carbohydrates and their alkoxylated derivatives. In certain embodiments, any of the above triols are characterized in that they are derived from biomass.

(341) In certain embodiments, in polycarbonates of structures P5a, P5c, P5f, P5h, P5j, P5n, and P5r, the embedded chain transfer agent is characterized in that it is derived from biomass. In certain embodiments, in polycarbonates of structures P5a, P5c, P5f, P5h, P5j, P5n, and P5r, the embedded chain transfer agent is characterized in that it is not derived from biomass.

(342) In certain embodiments, in polycarbonates of structures P5a, P5c, P5f, P5h, P5j, P5n, and P5r, —Y is —H.

(343) For polycarbonates comprising repeat units derived from two or more epoxides, such as those represented by structures P2f, P2g, P2h, P2i, P2j, P2k, P2n, P2o, P2r, P2r-a, P3f, P3g, P3h, P3i, P3j, P3k, P3n, P3o, P3r, P3r-a, P4f, P4h, P4j, P4n, P4r, P5f, P5h, P5j, P5n, and P5r, depicted above, it is to be understood that the structures drawn may represent mixtures of positional isomers or regioisomers that are not explicitly depicted. For example, the polymer repeat unit adjacent to either end group of the polycarbonate chains can be derived from either one of the two epoxides comprising the copolymers. Thus, while the polymers may be drawn with a particular repeat unit attached to an end group, the terminal repeat units might be derived from either of the two epoxides and a given polymer composition might comprise a mixture of all of the possibilities in varying ratios. The ratio of these end-groups can be influenced by several factors including the ratio of the different epoxides used in the polymerization, the structure of the catalyst used, the reaction conditions used (i.e., temperature pressure, etc.) as well as by the timing of addition of reaction components. Similarly, while the drawings above may show a defined regiochemistry for repeat units derived from substituted epoxides, the polymer compositions will, in some cases, contain mixtures of regioisomers. The regioselectivity of a given polymerization can be influenced by numerous factors including the structure of the catalyst used and the reaction conditions employed. To clarify, this means that the composition represented by structure P2r above, may contain a mixture of several molecules as shown in the diagram below. This diagram shows the isomers graphically for polymer P2r, where the structures below the depiction of the chain show each regio- and positional isomer possible for the monomer unit adjacent to the chain transfer agent and the end groups on each side of the main polymer chain. Each end group on the polymer may be independently selected from the groups shown on the left or right while the central portion of the polymer including the chain transfer agent and its two adjacent monomer units may be independently selected from the groups shown. In certain embodiments, the polymer composition comprises a mixture of all possible combinations of these. In other embodiments, the polymer composition is enriched in one or more of these.

(344) ##STR00151##

(345) In certain embodiments, the aliphatic polycarbonate polyol is selected from the group consisting of Q1, Q2, Q3, Q4, Q5, Q6, and mixtures of any two or more of these.

(346) ##STR00152## where α, β, and n are as described above and herein; and; t is an integer from 1 to 12 inclusive, and R.sup.t is independently at each occurrence —H, or —CH.sub.3.

(347) In certain embodiments, the aliphatic polycarbonate polyol is selected from the group consisting of:

(348) Poly(ethylene carbonate) of formula Q1 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups:

(349) Poly(ethylene carbonate) of formula Q1 having an average molecular weight number of about 500 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups:

(350) Poly(ethylene carbonate) of formula Q1 having an average molecular weight number of about 1,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups:

(351) Poly(ethylene carbonate) of formula Q1 having an average molecular weight number of about 2,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups;

(352) Poly(ethylene carbonate) of formula Q1 having an average molecular weight number of about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups:

(353) Poly(propylene carbonate) of formula Q2 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups:

(354) Poly(propylene carbonate) of formula Q2 having an average molecular weight number of about 500) g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups:

(355) Poly(propylene carbonate) of formula Q2 having an average molecular weight number of about 1,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups:

(356) Poly(propylene carbonate) of formula Q2 having an average molecular weight number of about 2,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups;

(357) Poly(propylene carbonate) of formula Q2 having an average molecular weight number of about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups;

(358) Poly(ethylene-co-propylene carbonate) of formula Q3 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups;

(359) Poly(ethylene-co-propylene carbonate) of formula Q3 having an average molecular weight number of about 500 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups:

(360) Poly(ethylene-co-propylene carbonate) of formula Q3 having an average molecular weight number of about 1,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups;

(361) Poly(ethylene-co-propylene carbonate) of formula Q3 having an average molecular weight number of about 2,000 g/mol (e.g., n is on average between about 10 and about 11), a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups:
Poly(ethylene-co-propylene carbonate) of formula Q3 having an average molecular weight number of about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups;
Poly(ethylene carbonate) of formula Q4 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol (e.g., each n is between about 4 and about 16), a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups;
Poly(ethylene carbonate) of formula Q4 having an average molecular weight number of about 500) g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups:
Poly(ethylene carbonate) of formula Q4 having an average molecular weight number of about 1,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups:
Poly(ethylene carbonate) of formula Q4 having an average molecular weight number of about 2,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups;
Poly(ethylene carbonate) of formula Q4 having an average molecular weight number of about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups.
Poly(propylene carbonate) of formula Q5 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups;
Poly(propylene carbonate) of formula Q5 having an average molecular weight number of about 500 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups:
Poly(propylene carbonate) of formula Q5 having an average molecular weight number of about 1,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups:
Poly(propylene carbonate) of formula Q5 having an average molecular weight number of about 2,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups;
Poly(propylene carbonate) of formula Q5 having an average molecular weight number of about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups;
Poly(ethylene-co-propylene carbonate) of formula Q6 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups;
Poly(ethylene-co-propylene carbonate) of formula Q6 having an average molecular weight number of about 500 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups:
Poly(ethylene-co-propylene carbonate) of formula Q6 having an average molecular weight number of about 1,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups:
Poly(ethylene-co-propylene carbonate) of formula Q6 having an average molecular weight number of about 2,000 g/mol (, n is on average between about 10 and about 11), a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups;
Poly(ethylene-co-propylene carbonate) of formula Q6 having an average molecular weight number of about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups; and Mixtures of any two or more of these.

(362) In certain embodiments, the aliphatic polycarbonate polyol is selected from the group consisting of: a) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. b) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(363) ##STR00153##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and c) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 75 and 85%, and characterized in that the moiety

(364) ##STR00154##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. d) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 75%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. e) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 65%, and characterized in that the moiety

(365) ##STR00155##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and f) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(366) ##STR00156##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. g) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. h) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(367) ##STR00157##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and i) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 75 and 85%, and characterized in that the moiety

(368) ##STR00158##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. j) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 75%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. k) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 65%, and characterized in that the moiety

(369) ##STR00159##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and l) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(370) ##STR00160##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. m) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. n) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(371) ##STR00161##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and o) Poly(propylene carbonate) of formula P2a having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 75 and 85%, and characterized in that the moiety

(372) ##STR00162##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. p) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 75%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. q) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 65%, and characterized in that the moiety

(373) ##STR00163##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and r) Poly(ethylene carbonate) of formula P2c having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(374) ##STR00164##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10.

(375) In certain embodiments, for these polycarbonates (a), (b), (c), (d), (e), (f), (g), (h), (i), (j), (k), (l), (m), (n), (o), (p), (q), and (r), the moiety

(376) ##STR00165##
is selected from the group consisting of: ethylene glycol, diethylene glycol, triethylene glycol, 1,3 propane diol; 1,4 butane diol, hexylene glycol, 1,6 hexane diol, neopentyl glycol, propylene glycol, dipropylene glycol, tripopylene glycol, and alkoxylated derivatives of any of these.

(377) In certain embodiments, the aliphatic polycarbonate polyol is selected from the group consisting of: s) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. t) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(378) ##STR00166##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and u) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 75 and 85%, and characterized in that the moiety

(379) ##STR00167##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. v) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 75%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. w) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 65%, and characterized in that the moiety

(380) ##STR00168##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and x) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(381) ##STR00169##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. y) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. z) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(382) ##STR00170##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and aa) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 75 and 85%, and characterized in that the moiety

(383) ##STR00171##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. bb) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 75%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. cc) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 65%, and 65% and characterized in that the moiety

(384) ##STR00172##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and dd) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 90% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(385) ##STR00173##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. ee) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. ff) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(386) ##STR00174##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and gg) Poly(propylene carbonate) of formula P3a having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 75 and 85%, and characterized in that the moiety

(387) ##STR00175##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. hh) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 75%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. ii) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol ol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 65%, and characterized in that the moiety

(388) ##STR00176##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10; and jj) Poly(ethylene carbonate) of formula P3c having a number average molecular weight number of between about 1,000 g/mol and about 4,000 g/mol, a polydispersity index less than about 1.25, at least 95% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon value according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(389) ##STR00177##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10.

(390) In certain embodiments, for these polycarbonates (a), (b), (c), (d), (e), (f), (g), (h), (i), (j), (k), (l), (m), (n), (o), (p), (q), and (r), the moiety

(391) ##STR00178##
is selected from the group consisting of: glycerol, 1,2,4-butanetriol, 2-(hydroxymethyl)-1,3-propanediol; hexane triols, trimethylol propane, trimethylol ethane, trimethylolhexane, 1,2,4-cyclohexanetrimethanol, pentaerythritol mono esters, pentaerythritol mono ethers, and alkoxylated analogs of any of these. In certain embodiments, such alkoxylated derivatives comprise ethoxylated or propoxylated molecules.

(392) In certain embodiments, the aliphatic polycarbonate polyol is selected from the group consisting of: kk) Poly(ethylene carbonate) of formula Q1 having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 75%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. ll) Poly(ethylene carbonate) of formula Q1 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 65%, and characterized in that the moiety

(393) ##STR00179##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. mm) Poly(ethylene carbonate) of formula Q1 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(394) ##STR00180##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. nn) Poly(propylene carbonate) of formula Q2 having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. oo) Poly(propylene carbonate) of formula Q2 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(395) ##STR00181##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. pp) Poly(propylene carbonate) of formula Q2 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 75 and 85%, and characterized in that the moiety

(396) ##STR00182##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. qq) Poly(ethylene-co-propylene carbonate) of formula Q3 having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. rr) Poly(ethylene-co-propylene carbonate) of formula Q3 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 70%, and characterized in that the moiety

(397) ##STR00183##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. ss) Poly(ethylene-co-propylene carbonate) of formula Q3 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 70 and 85%, and characterized in that the moiety

(398) ##STR00184##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. tt) Poly(ethylene carbonate) of formula Q4 having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 75%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. uu) Poly(ethylene carbonate) of formula Q4 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 65%, and characterized in that the moiety

(399) ##STR00185##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. vv) Poly(ethylene carbonate) of formula Q4 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(400) ##STR00186##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. ww) Poly(propylene carbonate) of formula Q5 having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. xx) Poly(propylene carbonate) of formula Q5 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 65 and 75%, and characterized in that the moiety

(401) ##STR00187##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. yy) Poly(propylene carbonate) of formula Q5 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 75 and 85%, and characterized in that the moiety

(402) ##STR00188##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. zz) Poly(ethylene-co-propylene carbonate) of formula Q6 having a number average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 85%, and characterized in that the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. aaa) Poly(ethylene-co-propylene carbonate) of formula Q6 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 55 and 70%, and characterized in that the moiety

(403) ##STR00189##
is not derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10. bbb) Poly(ethylene-co-propylene carbonate) of formula Q6 having an average molecular weight number of between about 500 g/mol and about 3,000 g/mol, a polydispersity index less than about 1.25, at least 85% carbonate linkages, and at least 98% —OH end groups, an overall % biobased carbon according to ASTM D6866-16 (Method B) of between 70 and 85%, and characterized in that the moiety

(404) ##STR00190##
is derived from biomass, and the carbon atoms comprising the carbonate linkages in the polymer have a pMC of less than 10.

(405) In certain embodiments, the

(406) ##STR00191##
in the embedded chain transfer agent is a moiety derived from a polymeric diol or higher polyhydric alcohol. In certain embodiments, such polymeric alcohols are polyether or polyester polyols. In certain embodiments

(407) ##STR00192##
is a polyether polyol comprising ethylene glycol or propylene glycol repeating units (—OCH.sub.2CH.sub.2O—, or —OCH.sub.2CH(CH.sub.3)O—) or combinations of these. In certain embodiments,

(408) ##STR00193##
is a polyester polyol comprising the reaction product of a diol and a diacid, or a material derived from ring-opening polymerization of one or more lactones. In certain embodiments, any of the above polymeric diols or higher polyhydric alcohols are characterized in that they are derived from biomass.

(409) In certain embodiments where

(410) ##STR00194##
comprises a polyether diol, the aliphatic polycarbonate polyol has a structure Q7:

(411) ##STR00195## wherein, R.sup.q is at each occurrence in the polymer chain independently —H or —CH.sub.3; R.sup.a is —H, or —CH.sub.3; q and q′ are independently an integer from about 0 to about 40; and and n, α, and β are as described above and herein.

(412) In certain embodiments, an aliphatic polycarbonate polyol is selected from the group consisting of:

(413) ##STR00196##

(414) In certain embodiments where

(415) ##STR00197##
comprises a polyether diol characterized in that the polyether diol is derived from biomass, the aliphatic polycarbonate polyol has a structure Q7′:

(416) ##STR00198##
wherein R.sup.q, R.sup.a, q, q′, n, o, and are as described above and herein.

(417) In certain embodiments, an aliphatic polycarbonate polyol is selected from the group consisting of:

(418) ##STR00199##

(419) ##STR00200##

(420) In certain embodiments, where aliphatic polycarbonate polyols comprise molecules conforming to structure Q7 or Q7′, the moiety

(421) ##STR00201##
is derived from a commercially available polyether polyol such as those typically used in the formulation of polyurethane compositions.

(422) In certain embodiments where

(423) ##STR00202##
comprises a polyester diol, the aliphatic polycarbonate polyol has a structure Q8:

(424) ##STR00203## wherein, c at each occurrence in the polymer chain independently is an integer from 0 to 6; d at each occurrence in the polymer chain independently is an integer from 1 to 11; and each of R.sup.q, n, q, α, and β is as described above and herein.

(425) In certain embodiments, an aliphatic polycarbonate polyol is selected from the group consisting of:

(426) ##STR00204##
where α, β, q, and n are as described above and herein.

(427) In certain embodiments of formulae Q8, Q8a, Q8b, Q8c, Q8d, Q8e, or Q8f where the polycarbonate derived a polyester polyol, the polyester is characterized in that it is derived from biomass.

(428) In certain embodiments, where aliphatic polycarbonate polyols comprise molecules conforming to structure Q8, the moiety

(429) ##STR00205##
is derived from a commercially available polyester polyol such as those typically used in the formulation of polyurethane compositions.

(430) ii. Polyether Carbonates

(431) In certain embodiments, polymer compositions of the present invention comprise polyether carbonates (i.e., polymer chains containing carbonate linkages as described above, and ether linkages). In some embodiments, such polyether carbonates are both biobased and fossil-carbon sequestering.

(432) In certain embodiments, polymer compositions of the present invention comprise polyether polycarbonate chains comprising a structure:

(433) ##STR00206##
wherein each R.sup.1, R.sup.2, R.sup.3, R.sup.4, α, and β is described above and herein; and g and h are independently an integer from about 0 to about 500, wherein, on average in the composition, the value of h is greater than g.

(434) In some embodiments, the value of h is at least about twice the value of g. In some embodiments, the value of h is at least about three times, at least about four times, at least about five times, at least about ten times, at least about 20 times, at least about 50 times, or at least about 100 times greater than the value of g.

(435) In certain embodiments, polymer compositions of the present invention comprise polycarbonate polymers containing both carbonate linkages and ether linkages. In some embodiments, the percentage of carbonate linkages (or ether linkages) may be determined by .sup.1H or .sup.13C NMR spectroscopy.

(436) In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 5% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 10% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 15% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 20% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 25% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 30% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 35% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 40% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 45% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 5% and about 40%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 5% and about 30%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 5% and about 20%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 5% and about 10%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 20% and about 50%. In some embodiments, polyether carbonates of the present invention are characterized in that, on average in the composition, the percentage of carbonate linkages is between about 20% and about 40%.

(437) iii. Block Copolymers

(438) In certain embodiments, polymer compositions of the present invention comprise block copolymers. In some embodiments, such block copolymers are both biobased and fossil-carbon sequestering. In certain embodiments, such block copolymers comprise (in addition to the aliphatic polycarbonate, or polyether carbonate) blocks comprising polyethers, polyesters, polyolefins, polyamides (e.g., nylon), polyimides, or combinations of two or more of these.

(439) In some embodiments, provided block copolymers are of formula A-L-B, where A- is an aliphatic polycarbonate or polyether-carbonate chain as described above and herein, having from about 3 to about 500 repeating units, L is a linker moiety or a covalent bond, and —B is selected from the group consisting of polyethers, polyesters, polyolefins, polyamides, polyimides, and combinations of two or more of these, having from about 3 to about 500 repeating units.

(440) In some embodiments, A- is an aliphatic polycarbonate as described above and herein. In some embodiments, A- is a polyether carbonate as described above and herein.

(441) In certain embodiments, L is a covalent bond (i.e., A- is bonded directly to —B). In other embodiments, L is a polyfunctional moiety having appropriate functionality to form a covalent chemical bond with both the polycarbonate chain and the hydrophilic oligomer. In certain instances, L is a moiety formed by the reaction of one functional group on A- and one functional group on —B with a polyfunctional molecule capable of reaction with the functional groups on A- and —B thereby linking them. Examples of suitable polyfunctional moieties for L include, but are not limited to: agents that can form one or more linkages such as ester, amide, ether, amine, thioether, carbonate, or other similar linkages. Examples of polyfunctional molecules suitable for incorporation as L include, but are not limited to: phosgene, diacids, anhydrides, acrylates, diisocyanates, epoxides, diols, diamines, hydroxy mercaptans, mercapto acids, hydroxy acids, amino acids, and any precursors or reactive equivalents thereof.

(442) In certain embodiments, a linker L is a moiety formed directly by the reaction of complementary functional groups on termini of A- and —B. Examples of such moieties include, but are not limited to: L being an ester, (formed from an alcohol group on the terminus of A- and a carboxy group on the terminus of —B, or vice versa); L being an amide; (formed from an amine group on the terminus of A- and a carboxy group on the terminus of —B, or vice versa); L being an olefin (formed, for example, by olefin metathesis); L being a heterocycle, (for example a triazole formed by cycloaddition of an azide and an alkyne), and L being a cyclohexene ring formed by Diels Alder cycloaddition of a diene and a dienophile.

(443) In certain embodiments, a hydrophilic oligomer —B is a polyether chain. In some embodiments, —B is a polyolefin chain bearing hydrophilic functional groups. In certain embodiments, a hydrophilic oligomer —B is a polyamine chain. In certain embodiments, —B is selected from the group consisting of polyoxymethylene, poly(ethylene oxide), poly(propylene oxide), polyvinyl alcohol, poly(vinyl acetate), partially hydrolyzed poly(vinyl acetate), poly(acrylic acid), polyacrylamide, polyethyleneimine, poly(2-hydroxyethyl methacrylate), poly(N-vinylpyrrolidone), polypeptides, polysaccharides, polyepoxysuccinic acid, poly(methyl vinyl ether), poly(allylamine), poly(2-ethyl-2-oxazoline), and block, tapered or random copolymers of any two or more of the above. In some embodiments, —B is polyoxymethylene. In some embodiments, —B is poly(ethylene oxide). In some embodiments, —B is poly(propylene oxide).

(444) In some embodiments, A- has about 3 to about 500 repeating units. In some embodiments, A- has about 3 to about 25 repeating units. In some embodiments. A- has about 3 to about 15 repeating units. In some embodiments, A- has about 3 to about 10 repeating units. In some embodiments, A- has about 10 to about 20 repeating units. In some embodiments, A- has about 10 to about 50 repeating units. In some embodiments, A- has about 10 to about 100 repeating units. In some embodiments, A- has about 50 to about 500 repeating units. In some embodiments, A- has about 100 to about 500 repeating units. In some embodiments, A- has about 250 to about 500 repeating units. In some embodiments, A- has about 350 to about 500 repeating units. In some embodiments, A- has about 10 to about 250 repeating units. In some embodiments, A- has about 50 to about 100 repeating units.

(445) In some embodiments, B— has about 3 to about 500 repeating units. In some embodiments, B— has about 3 to about 25 repeating units. In some embodiments, B— has about 3 to about 15 repeating units. In some embodiments, B— has about 3 to about 10 repeating units. In some embodiments, B— has about 10 to about 20 repeating units. In some embodiments. A- has about 10 to about 50 repeating units. In some embodiments. B— has about 10 to about 100) repeating units. In some embodiments, B— has about 50 to about 500 repeating units. In some embodiments, B— has about 100 to about 500 repeating units. In some embodiments, B— has about 250 to about 500 repeating units. In some embodiments, B— has about 350 to about 500 repeating units. In some embodiments, B— has about 10 to about 250 repeating units. In some embodiments, B— has about 50 to about 100 repeating units.

(446) II. Methods

(447) In one aspect, the present invention provides methods of producing polymer compositions prepared using both the biobased carbon and and sequestered fossil CO.sub.2. In some embodiments, the invention encompasses methods of producing polymer compositions whose manufacture sequesters CO.sub.2 produced from a fossil carbon source while simultaneously utilizing biobased feedstocks as constituents of the polymer chain.

(448) In some embodiments, the present invention provides methods comprising the steps of: a) converting the biobased ethanol or biobased glycerol to a biobased epoxide; and b) copolymerizing carbon dioxide sequestered from a fossil carbon source with the biobased epoxide to produce a polymer composition as described above and herein.

(449) In some embodiments, the present invention provides methods comprising the steps of: a) fermenting carbohydrates derived from biomass to produce biobased ethanol; b) converting the biobased ethanol to a biobased epoxide; and c) copolymerizing carbon dioxide sequestered from a fossil carbon source with the biobased epoxide to produce a polymer composition as described above and herein.

(450) In some embodiments, the present invention provides methods comprising the steps of: a) treating vegetable oil to produce biobased glycerol; b) converting the biobased glycerol to a biobased epoxide; and c) copolymerizing carbon dioxide sequestered from a fossil carbon source with the biobased epoxide to produce a polymer composition as described above and herein.

(451) A. Methods of Manufacturing Biobased Ethanol and Biobased Glycerol

(452) i. Biobased Ethanol

(453) In certain embodiments, provided methods comprise a step of treating biomass to produce biobased ethanol (step (a)). Biobased ethanol is derived from biological feedstocks such as corn starch or cane sugar or glycerol obtained from biodiesel industry through a biological fermentation process.

(454) In some embodiments, a biological source includes first generation, second generation, and third generation sources. In some embodiments, a first generation biological source is selected from the group consisting of corn, wheat, sugar beet, sugar-cane, sorghum, and potatoes. In some embodiments, a second generation biological source is selected from the group consisting of corn stover, wheat straw, bagasse, wood chips, switchgrass, pulp, and paper waste. In some embodiments, a third generation biological source includes algae and cyanobactrial strains geneticially engineered to produce ethanol during autotrophic or heterotrophic growth.

(455) Methods of treating a biomass to produce biobased ethanol are well known. For example, in some embodiments, a sugar is provided by a biological source, and the sugar is converted to ethanol through fermentation. In some embodiments, the sugar provided by a biological source is sucrose. In some embodiments, a sugar provided by a biological source is a starch or lignocellulose, which may be hydrolyzed to hexose sugars suitable for microbial fermentation.

(456) In some embodiments, biobased ethanol has a % biobased carbon content measured according to ASTM D6866-16 (Method B) of 100%. In some embodiments, biobased ethanol has a pMC value measured according to ASTM D6866-16 (Method B) of about 95, 100, 102.5, 105, or 107.5.

(457) ii. Biobased Glycerol

(458) In certain embodiments, provided methods comprise a step of treating vegetable oil (triglycerides) to produce biobased glycerol (step (a)).

(459) In some embodiments, the step of producing biobased glycerol comprises transesterification of triglycerides to produce biodiesel and biobased glycerol, as according to Scheme 3.

(460) ##STR00207##

(461) In some embodiments, the step of producing biobased glycerol comprises the step of treating triglycerides with a base catalyst.

(462) B. Methods of Manufacturing Biobased Alkylene Oxides.

(463) In certain embodiments, provided methods comprise a step of converting the biobased ethanol to a biobased epoxide (step (b)), e.g., a biobased alkylene oxide. For example, bio-ethanol is provided from a biological source and converted to biobased ethylene oxide or Biobased Propylene Oxide.

(464) i. Production of Bio-Ethylene Oxide

(465) Biobased ethylene oxide is, for example, manufactured by Croda Inc. (Edison, N.J.). Methods of manufacturing ethylene oxide from bio-ethanol are disclosed in, for example, PCT Publication Nos. WO 2014/125191 and 2014/125192; the entire contents of each of which are incorporated herein by reference.

(466) For example, bio-ethanol is first converted (e.g., dehydrated) to form bio-ethylene, which in turn is converted (e.g., oxidized) to biobased ethylene oxide according to Scheme 4.

(467) ##STR00208##

(468) In some embodiments, bio-ethanol is converted to bio-ethylene. Methods of converting bio-ethanol to bio-ethylene are disclosed in, for example, Zhang et al. Ind. Eng. Chem. Res. 2013 (52), 9505-9514, the entirety of which is herein incorporated by reference. In some embodiments, bio-ethanol is dehydrated to afford bio-ethylene. In some embodiments, the step of dehydrating bio-ethanol to bio-ethylene comprises heating the reaction mixture. In some embodiments, the step of dehydrating bio-ethanol to bio-ethylene comprises a catalyst. In some embodiments, such a catalyst is selected from the group consisting of a phosphoric acid catalyst, an oxide catalyst (e.g., Alumina), a molecular sieve catalyst, and a heteropolyacid catalyst. In some embodiments, the step of dehydrating bio-ethanol to bio-ethylene comprises washing or purifying the reaction mixture.

(469) In some embodiments, bio-ethylene is converted to bio-ethylene oxide. Methods of converting ethylene to ethylene oxide are disclosed in, for example, U.S. Pat. No. 8,975,424, and PCT Publication Nos. WO 2015/102982, 2014/186480, and 2014/105924; the entire contents of each of which are incorporated herein by reference. In some embodiments, the step of converting bio-ethylene to bio-ethylene oxide comprises O.sub.2 gas. In some embodiments, the step of converting bio-ethylene to bio-ethylene oxide comprises a catalyst. In some embodiments, the step of converting bio-ethylene to bio-ethylene oxide comprises a silver catalyst that includes zinc. In some embodiments, the step of converting bio-ethylene to bio-ethylene oxide comprises a silver catalyst. In some embodiments, the step of converting bio-ethylene to bio-ethylene oxide produces CO.sub.2 as a byproduct. In some embodiments, the step of converting bio-ethylene to bio-ethylene oxide comprises removing CO.sub.2. In some embodiments, the step of converting bio-ethylene to bio-ethylene oxide comprises washing or purifying the reaction mixture. In some embodiments, the step of converting bio-ethylene to bio-ethylene oxide produces a glycol as a byproduct.

(470) ii. Production of Bio-Propylene Oxide

(471) In some embodiments, bio-ethanol or bio-glycerol is converted to bio-propylene oxide. In some embodiments, bio-ethanol or bio-glycerol is converted to bio-propylene, and bio-propylene is converted to bio-propylene oxide, according to Scheme 5.

(472) ##STR00209##

(473) In some embodiments, bio-ethanol is converted to bio-propylene. Methods of converting bio-ethanol to bio-propylene are disclosed in, for example, European Patent Publication No. EP 2090561A1; U.S. Pat. Nos. 6,441,262, 8,598,399, 9,061,954; US Patent Publications Nos. US 2011/0105815, 2011/0137096, 2016/0186070, and PCT Publication Nos. WO 2016/061262 or 2016/109370; the entire contents of each of which are incorporated herein by reference. In some embodiments, the step of converting bio-ethanol to bio-propylene comprises a catalyst. In some embodiments, the step of converting bio-ethanol to bio-propylene comprises a catalyst selected from the group consisting of crystalline silicate (e.g., crystalline silicate having a ratio of Si/Al of at least about 100), a molecular sieve catalyst (e.g., SAPO-5, SAPO-17, SAPO-18, SAPO-20, SAPO-34, SAPO-44, or SAPO56), a rhenium oxide-modified ZSM-5 zeolite catalyst, and a Co/Mn catalyst. In some embodiments, the step of converting bio-ethanol to bio-propylene comprises water. In some embodiments, the step of converting bio-ethanol to bio-propylene comprises heating the reaction mixture.

(474) In some embodiments, bio-glycerol is converted to bio-propylene. Methods of converting bio-glycerol to bio-propylene are disclosed in, for example. Sun et al. Applied Catalysis B: Environmental. 2015 (174-175), 13-30; Mota et al. Journal of Molecular Catalysis A: Chemical. 2016 (422) 158-164; or Wu et al. Catalysis Communications 2017 (92) 80-85; the entire contents of each of which are incorporated herein by reference. In some embodiments, the step of converting bio-glycerol to bio-propylene comprises a catalyst. In some embodiments, the step of converting bio-glycerol to bio-propylene comprises a catalyst selected from the group consisting of a Cu/Al.sub.2O.sub.3 catalyst (e.g., WO.sub.3-loaded Cu/Al.sub.2O.sub.3, MoO.sub.3-loaded Cu/Al.sub.2O.sub.3, V.sub.2O.sub.5-loaded Cu/Al.sub.2O.sub.3, or H.sub.3PO.sub.4-loaded Cu/Al.sub.2O.sub.3), an iron-molybdenum catalyst, a MoO.sub.3 modified Ni.sub.2P/Al.sub.2O.sub.3 catalyst, and a ZSM-5 catalyst. In some embodiments, the step of converting bio-glycerol to bio-propylene comprises H.sub.2. In some embodiments, the step of converting bio-glycerol to bio-propylene comprises heating the reaction mixture.

(475) In some embodiments, bio-propylene is converted to bio-propylene oxide according to methods disclosed in U.S. Pat. No. 9,174,200; Schultz et al. “Production of Propylene Oxide from Propylene Using Patented Silver Based Catalyst” (2016) Senior Design Reports (CBE). Paper 86. UPenn Scholarly Commons; or Schmidt et al. Chimica Oggi—Chemistry Today 2014 32(2), 31-35; the entire contents of each of which are incorporated herein by reference. In some embodiments, the step of converting bio-propylene to bio-propylene oxide comprises a catalyst. In some embodiments, the step of converting bio-propylene to bio-propylene oxide comprises a catalyst selected from the group consisting of a Ag—W oxide catalyst and a partly titanium substituted silica based zeolite (e.g., TS-1). In some embodiments, the step of converting bio-propylene to bio-propylene oxide comprises heating the reaction mixture. In some embodiments, the step of converting bio-propylene to bio-propylene oxide comprises O.sub.2. In some embodiments, the step of converting bio-propylene to bio-propylene oxide comprises hydrogen peroxide.

(476) C. Methods of Manufacturing Polycarbonates with Biobased and Fossil-Based Carbon

(477) In certain embodiments, provided methods comprise a step of copolymerizing carbon dioxide sequestered from a fossil carbon source with the biobased epoxide to produce a polymer composition as described above and herein (step (c)). Methods of performing epoxide-CO.sub.2 copolymerization are disclosed in PCT publication WO 2010/028362, the entirety of which is incorporated herein by reference.

(478) In certain embodiments, step (c) includes providing a polymerization system that copolymerizes carbon dioxide sequestered from a fossil carbon source with the biobased epoxide to produce a polymer composition as described above and herein. For example, in some embodiments, polymer compositions are derived from polymerization systems that copolymerize one or more epoxides with carbon dioxide in the presence of a chain transfer agents and a polymerization catalyst as shown in Scheme 6.

(479) ##STR00210##

(480) i. Chain Transfer Agents

(481) Suitable chain transfer agents include those described above with respect to

(482) ##STR00211##
embedded within the aliphatic polycarbonate chain. In certain embodiments, suitable chain transfer agents include polyfunctional chain transfer agents as exemplified in PCT Publication No. WO 2010/028362. In certain embodiments, copolymerizations are performed as exemplified in US Patent Publication No. US 2011/0245424. In certain embodiments, copolymerizations are performed as exemplified in Cyriac et al. Green Chem. 2011 (13), 3469-3475.

(483) Suitable chain transfer agents may have a broad array of chemical structures. In general, the only requirement is that each molecule of the chain transfer agent be capable of initiating two or more polycarbonate chains, this can occur by several mechanisms including: by ring-opening an epoxide monomer, by reacting with carbon dioxide molecules to yield a moiety capable of sustaining polymer chain growth, or by a combination of these. In some embodiments, a chain transfer agent may have two or more functional groups independently capable of reacting with carbon dioxide or an epoxide; examples of these include, but are not limited to molecules such as diacids, glycols, diols, triols, hydroxyacids, amino acids, amino alcohols, dithiols, mercapto alcohols, saccharides, catechols, polyethers, etc. In some embodiments, the chain transfer agent may include a multiply active functional group that is itself able to react multiple times to initiate more than one polymer chain. Examples of the latter include, but are not limited to functional groups having a single atom capable of reacting multiple times such as ammonia, primary amines and water, as well as functional groups having more than one nucleophilic atom such as amindines, guanidines, urea, boronic acids, etc.

(484) In some embodiments, a chain transfer agent is a polyhydric alcohol. In certain embodiments, a polyhydric alcohol is a diol, while in other embodiments the polyhydric alcohol is a triol, a tetraol or a higher polyol. In some embodiments, two hydroxyl groups are on adjacent carbons (i.e., the chain transfer agent is a glycol).

(485) In some embodiments, two hydroxyl groups are on non-adjacent carbons. In certain embodiments, two hydroxyl groups are on the opposite ends of a chain (i.e., the chain transfer agent is an α-ω diol). In certain embodiments, such α-ω diols include C.sub.3 to C.sub.20 aliphatic chains. In certain embodiments, such α-ω diols comprise a polyether. In certain embodiments, such α-ω diols comprise a hydroxy-terminated polyolefin. In certain embodiments, such α-ω diols comprise paraformaldehyde.

(486) In some embodiments, one —OH group of a diol is phenolic and the other is aliphatic. In other embodiments, each hydroxy group is phenolic. In certain embodiments, a chain transfer agent is an optionally substituted catechol, resorcinol or hydroquinone derivative.

(487) In some embodiments, polyalcohol chain transfer agents encompass naturally occurring materials such as sugar alcohols, carbohydrates, saccharides, polysaccharides, starch, starch derivatives, lignins, lignans, partially hydrolyzed triglycerides, and the like, as well as known derivatives of any of these materials. In certain embodiments, a chain transfer agent is starch. In certain embodiments, a chain transfer agent is isosorbide.

(488) In certain embodiments, a chain transfer agent is a polyamine. In some embodiments, a chain transfer agent is a diamine. In other embodiments, a chain transfer agent is a triamine, tetraamine or a higher amine oligomer.

(489) In some embodiments, a chain transfer agent is an amino alcohol. In some embodiments, a chain transfer agent is an amino acid. In some embodiments, a chain transfer agent is an amino thiol. In some embodiments, a chain transfer agent is an amino amide.

(490) In certain embodiments, a chain transfer agent is a diacid, a triacid or a higher polyacid. In some embodiments, a chain transfer agent is a diacid. In certain embodiments, a diacid is phthalic acid, isophthalic acid, terephthalic acid. In certain embodiments, a diacid is maleic acid, succinic acid, malonic acid, glutaric acid, adipic acid, pimelic acid, suberic acid, or azelaic acid. In some embodiments, a chain transfer agent is a triacid. In certain embodiments, a triacid is citric acid, isocitric acid, cis- or trans-aconitic acid, propane-1,2,3-tricarboxylic acid or trimesic acid.

(491) In some embodiments, a chain transfer agent is an amino acid. In certain embodiments, amino acid chain transfer agents include the naturally occurring amino acids. In certain embodiments, amino acid chain transfer acids include peptides. In some embodiments, the peptides contain between 2 and about 20 amino acid residues. In other embodiments, the chain transfer agent is a thiol acid.

(492) In some embodiments, the chain transfer agent is a hydroxy acid. In some embodiments, hydroxy acids are alpha-hydroxy acids. In certain embodiments an alpha hydroxy acid is selected from the group consisting of: glycolic acid, DL-lactic acid, D-lactic acid. L-lactic, citric acid and mandelic acid. In some embodiments, a hydroxy acid is a beta-hydroxy acid. In certain embodiments, a beta hydroxy acid is selected from the group consisting of: 3-hydroxypropionic acid, DL-3-hydroxybutryic acid, D-3 hydroxybutryic acid, L-3-hydroxybutyric acid, DL-3-hydroxy valeric acid, D-3-hydroxy valeric acid, L-3-hydroxy valeric acid, salicylic acid, and derivatives of salicylic acid. In some embodiments, a hydroxy acid is an α-ω hydroxy acid. In certain embodiments, α-ω hydroxy acids are selected from the group consisting of optionally substituted C.sub.3-20 aliphatic α-ω hydroxy acids. In certain embodiments, an α-ω hydroxy acid is a polyester oligomeric ester.

(493) In some embodiments, a chain transfer agent is provided as a carboxylate salt. In certain embodiments, a carboxylate salt is a group I or II metal salt. In some embodiments, a carboxylate salt is an ammonium salt. In certain embodiments, an ammonium cation is NH.sub.4. In some embodiments, an ammonium cation is a protonated primary, secondary, or tertiary amine. In some embodiments, a salt is a quaternary ammonium salt. In some embodiments, a quaternary ammonium cation of a salt is tetramethyl, tetrabutyl, or trahexylammonium ammonium. In certain embodiments, a carboxylate salt is a phosphonium carboxylate.

(494) In certain embodiments, a chain transfer agent is a polythiol. In some embodiments, a chain transfer agent is a dithiol. In some embodiments, a chain transfer agent is a trithiol, higher thiol oligomer.

(495) In some embodiments, a chain transfer agent is a thio alcohol. In some embodiments, a chain transfer agent is an amino thiol. In some embodiments, a chain transfer agent is a thiol carboxylic acid.

(496) In certain embodiments, a chain transfer agent comprises an active NH-containing functional group. In certain embodiments, a nitrogen atom of the NH-containing functional group is nucleophilic. In certain embodiments, an active NH-containing functional group is selected from the group consisting of C-linked amides, N-linked amides, O-linked carbamates N-linked carbamates, ureas, guanidines, amidines, hydrazones, and N- or C-linked thioamides.

(497) In certain embodiments, polymerization systems of the present invention include only one chain transfer agent, while in other embodiments, mixtures of two or more chain transfer agents are used.

(498) In certain embodiments, polymerization systems described above include a solvent in which a chain transfer agent dissolves. In certain embodiments, a chain transfer agent is poorly soluble in the epoxide, but is soluble in a mixture of epoxide and another solvent added to the reaction mixture. In certain embodiments, the solvent added to the polymerizations system is chosen from the group consisting of esters, nitriles, ketones, aromatic hydrocarbons, ethers, amines and combinations of two or more of these.

(499) In some embodiments, a polymerization initiator includes a multiply active functional group that is itself able to react multiple times to initiate more than one polymer chain. One subset of such multiply-active functional groups react multiple times at the same atom. Examples of such groups include, but are not limited to ammonia, primary amines, hydrogen sulfide and water, all of which remain nucleophilic after the first addition and are thereby able to react again initiating additional polymer chains. Another subset of multiply active functional groups can react at different atoms in the functional group to initiate multiple chains. Examples of such groups include, but are not limited to guanidines, ureas, boronic acids, hydroxyl amines, and amidines.

(500) In some embodiments, a chain transfer agent may contain a single multiply active functional group. In certain embodiments, a chain transfer agent may contain two or more multiply active functional groups.

(501) In some embodiments, a chain transfer agent used in any of the methods herein is derived from biomass.

(502) ii. Polymerization Catalysts

(503) In some embodiments, suitable polymerization catalysts include metal complexes, e.g., transition metal complexes. Thus, in some embodiments, such metal complexes are capable of catalyzing the copolymerization of carbon dioxide and epoxides. In certain embodiments, polymerization catalysts include those disclosed in R.-R. Ang et al., Journal of Cleaner Production. 102 (2015) 1-17; Zhang, et al., Chem. Rev. 2018 (118), 839-885; Liu et al., Current Opinion in Green and Sustainable Chemistry 2017 (3), 61-66; or Quin, et. al., Journal of CO2 Utilization 2015 (11), 3-9; U.S. Pat. Nos. 7,304,172 and 6,870,004; EP Patent No. EP 2258745B1; PCT Publication Nos. WO 2010/022388, 2008/136591, 2008/150033, 2009/137540, 2010/013948, 2010/147421, 2012/037282, 2013/022932, 2013/012895, 2013/096602, 2014/031811, 2016/012785, 2016/012786, and 2010/028362; and in Chinese Patent Publication Nos. CN 2007/10010706 and 2008/10229276; the entirety of each of which is hereby incorporated herein by reference.

(504) In some embodiments, polymerization catalysts include zinc complexes. In some embodiments, a zinc complex is a dialkylzinc complex (e.g., those described in U.S. Pat. Nos. 3,900,424 and 3,953,383; the entire contents of each of which are incorporated herein by reference). In some embodiments, a zinc complex is a diethylzinc complex. In some embodiments, a zinc complex is a zinc glutarate complex (e.g., those described in U.S. Pat. Nos. 4,783,445, 5,026,676, and 4,943,677; the entire contents of each of which are incorporated herein by reference). In some embodiments, a zinc glutarate complex is prepared from ZnO, Zn(OH).sub.2, or ZnEt.sub.2. In some embodiments, a zinc glutarate complex is prepared from glutaric acid, 2-ketoglutaric acid, 2,2-dimethylglutaric acid, 3-ketoglutaric acid, 3,3-dimethylglutaric acid, 3,3-tetramethylglutaric acid, 2-methylglutaric acid, methylglutaric acid, 3-methylglutaric acid, 3,3-tetramethylglutaric acid, or 3-phenylglutaric acid.

(505) In some embodiments, a zinc complex is an bis(phenoxy) zinc complex. For example, in some embodiments, a bis(phenoxy) zinc complex is a mononuclear (2,6-diphenylphenoxide).sub.2Zn(Et.sub.2O).sub.2 complex (e.g., as described in Darensbourg, et. al., Macromolecules 1995, 28 (22), 7577-7579; the entire contents of which are incorporated herein by reference), or fluorosubstituted complex such as a dimeric [Zn(O-2,6-F.sub.2C.sub.6H.sub.3).sub.2.THF].sub.2 (e.g., as described in Darensbourg, et. al., J. Am. Chem. Soc. 2000, 122 (50), 12487-12496; the entire contents of which are incorporated herein by reference).

(506) In some embodiments, a zinc complex is a β-diiminate zinc complex. In some embodiments, β-diiminate zinc complexes include those described in Allen, et al. J. Am. Chem. Soc. 2002, 124 (48), 14284-14285, and those described in Ellis et al., Chem. Sci. 2104 (5), 4004-4011; the entire contents of each of which are incorporated herein by reference.

(507) In some embodiments, polymerization catalysts include double metal cyanide (DMC) catalyst (e.g., in U.S. Pat. No. 4,500,704; the entire contents of which are incorporated herein by reference). A DMC catalyst may be prepared by the reaction between a metal salt (e.g., zinc chloride) and an alkali metal hexacyanometallate (e.g., potassium hexacyanocobaltate) in aqueous form.

(508) In some embodiments, polymerization catalysts include racemic dinuclear Co(III) complexes. In some embodiments, racemic dinuclear Co(III) complexes include those described in Liu, et al. Nat. Commun. 2015 (6), 8594; the entire contents of each of which are incorporated herein by reference.

(509) In some embodiments, polymerization catalysts include binary trivalent salen Ti complexes. In some embodiments, salen Ti complexes include those described in Wang et al. ACS Catal. 2015 (5), 393-396; and Wang, et al. Catal. Sci. Technol. 2014 (4), 3964-3972; the entire contents of each of which are incorporated herein by reference.

(510) In some embodiments, polymerization catalysts include Al porphyrin complexes. In some embodiments, Al porphyrin complexes include those described in Wu, et al. J. Polym. Sci. Pol. Chem. 2014 (52), 2346-2355; Sheng, et al. Rsc Adv. 2014 (4), 54043-54050; and Sheng, et al. Polym. Chem. 2015 (6), 4719-4724; the entire contents of each of which are incorporated herein by reference.

(511) In some embodiments, polymerization catalysts include heteronuclear Zn—Mg complexes. In some embodiments, heteronuclear Zn—Mg complexes include those described in Saini, et al. Chem. Commun. 2014 (50), 4164-4167; the entire contents of which are incorporated herein by reference.

(512) In some embodiments, polymerization catalysts include bimetallic nickel complexes. In some embodiments, bimetallic nickel complexes include those described in PCT Publication No. WO 2016/012786; the entire contents of which are incorporated herein by reference.

(513) In some embodiments, polymerization catalysts include dinuclear Zn catalysts. In some embodiments, dinuclear Zn catalysts include those described in Kissling, et al. Chem Eurn. J. 2015 (21), 8148-8157; the entire contents of which are incorporated herein by reference.

(514) In some embodiments, polymerization catalysts include metal complexes denoted L.sub.p-M-(L.sub.I).sub.m′, where L.sub.p is a permanent ligand set, M is a metal atom, and L.sub.I is a ligand that is a polymerization initiator, and m′ is an integer between 0 and 2 inclusive representing the number of initiating ligands present.

(515) In some embodiments, a metal atom, M, is selected from periodic table groups 3-13, inclusive. In certain embodiments, M is a transition metal selected from periodic table groups 5-12, inclusive. In some embodiments, M is a transition metal selected from periodic table groups 4-11, inclusive. In certain embodiments, M is a transition metal selected from periodic table groups 5-10, inclusive. In certain embodiments. M is a transition metal selected from periodic table groups 7-9, inclusive. In some embodiments, M is selected from the group consisting of Cr, Mn, V, Fe, Co, Mo, W, Ru, Al, and Ni. In some embodiments, M is a metal atom selected from the group consisting of: cobalt; chromium; aluminum; titanium; ruthenium, and manganese. In some embodiments, M is cobalt. In some embodiments, M is chromium. In some embodiments, M is aluminum.

(516) In certain embodiments, a metal complex is a zinc, cobalt, chromium, aluminum, titanium, ruthenium, or manganese complex. In certain embodiments, a metal complex is an aluminum complex. In other embodiments, a metal complex is a chromium complex. In yet other embodiments, a metal complex is a zinc complex. In certain other embodiments, a metal complex is a titanium complex. In still other embodiments, a metal complex is a ruthenium complex. In certain embodiments, a metal complex is a manganese complex. In certain embodiments, a metal complex is cobalt complex. In certain embodiments where a metal complex is a cobalt complex, the cobalt metal has an oxidation state of +3 (i.e., Co(III)). In other embodiments, the cobalt metal has an oxidation state of +2 (i.e., Co(II)).

(517) In certain embodiments, a permanent ligand set comprises a single multidentate ligand that remains associated with the metal center during catalysis. In some embodiments, the permanent ligand set includes two or more ligands that remain associated with the metal center during catalysis. In some embodiments, a metal complex comprises a metal atom coordinated to a single tetradentate ligand while in other embodiments, a metal complex comprises a chelate containing a plurality of individual permanent ligands. In certain embodiments, a metal complex contains two bidentate ligands. In some embodiments, a metal complex contains a tridentate ligand.

(518) In various embodiments, tetradentate ligands suitable for metal complexes of the present invention may include, but are not limited to: salen derivatives, derivatives of salen ligands, bis-2-hydroxybenzamido derivatives, derivatives of the Trost ligand, porphyrin derivatives, derivatives of tetrabenzoporphyrin ligands, derivatives of corrole ligands, phthalocyaninate derivatives, and dibenzotetramethyltetraaza[14]annulene (tmtaa) derivatives.

(519) In some embodiments, polymerization systems described above further include at least one co-catalyst. In some embodiments, a co-catalyst is selected from the group consisting of: amines, guanidines, amidines, phosphines, nitrogen-containing heterocycles, ammonium salts, phosphonium salts, arsonium salts, bisphosphine ammonium salts, and a combination of any two or more of the above.

(520) In embodiments where the co-catalyst is an ‘onium’ salt, there is necessarily an anion present to balance the charge of the salt. In certain embodiments, this is any anion. In certain embodiments, the anion is a nucleophile. In some embodiments, the anion is a nucleophile capable of ring-opening an epoxide. In some embodiments, the anion is selected from the group consisting of: azide, halides, alkyl sulfonates, carboxylates, alkoxides, and phenolates.

(521) In some embodiments, ionic co-catalyst include anions selected from the group consisting of: —OR.sup.w, —SR.sup.w, —OC(O)R.sup.w, —OC(O)OR.sup.w, —OC(O)N(R.sup.w).sub.2, —NR.sup.wC(O)R.sup.w, —CN, halo (e.g., —Br, —I, —Cl), —N.sub.3, and —OSO.sub.2R.sup.w wherein each R.sup.w is, independently, selected from hydrogen, optionally substituted aliphatic, optionally substituted heteroaliphatic, optionally substituted aryl and optionally substituted heteroaryl and where two R.sup.w groups can be taken together to form an optionally substituted ring optionally containing one or more additional heteroatoms.

(522) In some embodiments, polymerization catalysts include metal complexes where a metal atom coordinated to a multidentate ligand and at least one activating moiety tethered to a multidentate ligand. In certain embodiments, such metal complexes have the structure:

(523) ##STR00212## where

(524) ##STR00213##
represents a metal atom coordinated to a multidentate ligand; and (Z).sub.v represents one or more activating moieties, where “” is a covalent linker containing one or more atoms selected from the group consisting of C, O, N, S, and Si; Z is a activating functional group and m is an integer from 1 to 4 indicating the number of individual activating functional groups present in each activating moiety.

(525) In some embodiments, a metal complex

(526) ##STR00214##
comprises a metal atom coordinated to a single tetradentate ligand and in some embodiments, the metal complex comprises a chelate containing a plurality of individual ligands. In certain embodiments, a metal complex contains two bidentate ligands. In some embodiments, a metal complex contains a tridentate ligand.

(527) In some embodiments, each activating functional group is independently selected from the group consisting of neutral nitrogen-containing moieties, cationic moieties, phosphorous-containing moieties, and combinations of two or more of these.

(528) In various embodiments, tetradentate ligands suitable for metal complexes of the present invention may include, but are not limited to: salen derivatives, derivatives of salan ligands, bis-2-hydroxybenzamido derivatives, derivatives of the Trost ligand, porphyrin derivatives, derivatives of tetrabenzoporphyrin ligands, derivatives of corrole ligands, phthalocyaninate derivatives, and dibenzotetramethyltetraaza[14]annulene (tmtaa) derivatives.

(529) In certain embodiments, a tetradentate ligand is a salen ligand. In certain embodiments, a metal complex is a metallosalenate. In certain embodiments, a metal complex is a cobalt salen complex. In certain embodiments, a metal complex is a chromium salen complex. In some embodiments, a metal complex is an aluminum salen complex.

(530) In certain embodiments, at least one activating moiety is tethered to a carbon atom of a phenyl ring of the salicylaldehyde-derived portions of a salen ligand. In certain embodiments, at least one activating moiety is tethered to a carbon atom of a porphyrin ligand. In certain embodiments, at least one activating moiety is tethered to a pyrrole-carbon atom of a porphyrin ligand. In certain embodiments, at least one activating moiety is tethered to a carbon atom forming the bridge between the pyrrole rings of a porphyrin ligand.

(531) In certain embodiments, at least one activating moiety is tethered to one or more carbon atoms of only one phenyl ring of the salicylaldehyde-derived portions of a salen ligand.

(532) iii. Epoxides

(533) Suitable epoxides include those biobased epoxides described above and herein.

(534) In some embodiments, suitable epoxides include those having a structure:

(535) ##STR00215##

(536) R.sup.1, R.sup.2, R.sup.3, and R.sup.4 are as described above and herein.

(537) In certain embodiments, reaction mixtures include one or more epoxides selected from the group consisting of:

(538) ##STR00216##
wherein each R.sup.x′ is, independently, selected from optionally substituted aliphatic, optionally substituted heteroaliphatic, optionally substituted aryl and optionally substituted heteroaryl.

(539) In certain embodiments, reaction mixtures include ethylene oxide. In other embodiments, reaction mixtures include propylene oxide. In other embodiments, reaction mixtures include cyclohexene oxide. In other embodiments, reaction mixtures include epichlorohydrin. In certain embodiments, reaction mixtures include a glycidyl ether or glycidyl ester. In certain embodiments, reaction mixtures include phenyl glycidyl ether. In certain embodiments, reaction mixtures include 1-butyl glycidyl ether.

(540) In certain embodiments, reaction mixtures include ethylene oxide and propylene oxide. In certain embodiments, reaction mixtures include propylene oxide along with from about 0.1 to about 10% of a C.sub.4-C.sub.30 epoxide. In certain embodiments, reaction mixtures include propylene oxide along with from about 0.1 to about 10% of a glycidyl ether. In certain embodiments, reaction mixtures include propylene oxide along with from about 0.1 to about 10% of a glycidyl ester. In certain embodiments, reaction mixtures include ethylene oxide along with from about 0.1 to about 10% of a glycidyl ether. In certain embodiments, reaction mixtures include ethylene oxide along with from about 0.1 to about 10% of a glycidyl ester. In certain embodiments, reaction mixtures include ethylene oxide along with from about 0.1 to about 10% of a C.sub.4-C.sub.30 epoxide.

(541) In certain embodiments, reaction mixtures include epoxides derived from naturally occurring materials such as epoxidized resins or oils. Examples of such epoxides include, but are not limited to: Epoxidized Soybean Oil; Epoxidized Linseed Oil; Epoxidized Octyl Soyate; Epoxidized PGDO; Methyl Epoxy Soyate; Butyl Epoxy Soyate; Epoxidized Octyl Soyate; Methyl Epoxy Linseedate; Butyl Epoxy Linseedate; and Octyl Epoxy Linseedate. These and similar materials are available commercially from Arkema Inc. under the trade name Vikoflex®. Examples of such commerically available Vikoflex® materials include Vikoflex 7170 Epoxidized Soybean Oil. Vikoflex 7190 Epoxidized Linseed, Vikoflex 4050 Epoxidized Octyl Soyate, Vikoflex 5075 Epoxidized PGDO, Vikoflex 7010 Methyl Epoxy Soyate, Vikoflex 7040 Butyl Epoxy Soyate, Vikoflex 7080 Epoxidized Octyl Soyate, Vikoflex 9010 Methyl Epoxy Linseedate, Vikoflex 9040 Butyl Epoxy Linseedate. and Vikoflex 9080 Octyl Epoxy Linseedate. In certain embodiments, the polycarbonate polyols of the present invention incorporate epoxidized fatty acids.

(542) In certain embodiments of the present invention, reaction mixtures include epoxides derived from alpha olefins. Examples of such epoxides include, but are not limited to those derived from C.sub.10 alpha olefin, C.sub.12 alpha olefin, C.sub.14 alpha olefin, C.sub.16 alpha olefin, Cis alpha olefin, C.sub.20-C.sub.24 alpha olefin, C.sub.24-C.sub.28 alpha olefin and C.sub.30+ alpha olefins. These and similar materials are commercially available from Arkema Inc. under the trade name Vikolox®. Commerically available Vikolox®® materials include those depicted in Table 2, below. In certain embodiments, reaction mixtures including alpha olefins also include other simpler epoxide monomers including, but not limited to: ethylene oxide, propylene oxide, butylene oxide, hexene oxide, cyclopentene oxide and cyclohexene oxide.

(543) TABLE-US-00002 TABLE 2 Trade Name Formula Minimum Oxirane Vikolox 10 C.sub.10H.sub.20O  9.0% Vikolox 12 C.sub.12H.sub.24O  7.8% Vikolox 14 C.sub.14H.sub.28O  6.8% Vikolox 16 C.sub.16H.sub.32O  6.0% Vikolox 18 C.sub.18H.sub.36O  5.4% Vikolox 20-24 C.sub.20-24H.sub.40-48O  4.4% Vikolox 24-28 C.sub.24-28H.sub.48-56O 3.25% Vikolox 30+ C.sub.30+H.sub.60O 2.25%

(544) iv. Stoichiometry of Polymerization System

(545) Having described in detail each of the components of the polymerization system, we turn now to the relative ratios of those components. In certain embodiments, a metal complex and a chain transfer agent Y′-A-(Y′).sub.n′ are present in a defined ratio selected to maximize conversion of the epoxide monomers while achieving the desired molecular weight polycarbonate polyol, where -A- is a covalent bond or a multivalent moiety and each —Y group is independently a functional group capable of initiating chain growth of epoxide CO.sub.2 copolymers and each Y group may be the same or different, and n is an integer between 1 and 10 inclusive. In embodiments, where a co-catalyst is present, the ratios between a metal complex, a co-catalyst and a chain transfer agent are selected to maximize conversion of the epoxide monomers while achieving the desired molecular weight polycarbonate polyol.

(546) In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:10 to about 1:1000. In certain embodiments, the ratio is between about 1:50 and about 1:500. In certain embodiments, the ratio is between about 1:100 and about 1:500). In certain embodiments, the ratio is between about 1:100 and about 1:1000. In certain embodiments, the ratio is between about 1:500 and about 1:1000. In certain embodiments, the ratio is between about 1:50 and about 1:250. In certain embodiments, the ratio is between about 1:20 and about 1:100. In certain embodiments, the ratio is between about 1:100 and about 1:250. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio greater than 1:1000. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio less than 1:1000.

(547) In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio greater than 1:100. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio greater than 1:250. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio greater than 1:500. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio greater than 1:1250. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio greater than 1:1500. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio greater than 1:1750. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio greater than 1:2000.

(548) In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1000 to about 1:2000. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1000 to about 1:1750. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1000 to about 1:1500. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1000 to about 1:1300. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1100 to about 1:1300. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1500 to about 1:200). In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1750 to about 1:2000. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1250 to about 1:1500. In some embodiments, a metal complex and a chain transfer agent are present in a molar ratio ranging from about 1:1250 to about 1:1750.

(549) In some embodiments, a metal complex and a co-catalyst are present in a molar ratio ranging from about 0.1:1 to about 1:10. In certain embodiments, the ratio is from about 0.5:1 to about 5:1. In other embodiments, the ratio is from about 1:1 to about 4:1. In certain embodiments, the ratio between the metal complex and the co-catalyst is about 1:1. In other embodiments, the molar ratio between a metal complex and a co-catalyst is about 1:2.

(550) v. Reaction Conditions.

(551) In certain embodiments, step (c) further comprises one or more solvents. In certain other embodiments, step (c) is performed in neat epoxide without the addition of solvent.

(552) In certain methods, where a polymerization solvent is present, the solvent is an organic solvent. In certain embodiments, the solvent is a hydrocarbon. In certain embodiments, the solvent is an aromatic hydrocarbon. In certain embodiments, the solvent is an aliphatic hydrocarbon. In certain embodiments, the solvent is a halogenated hydrocarbon.

(553) In certain embodiments, the solvent is an ether. In certain embodiments, the solvent is an ester. In certain embodiments, the solvent is a ketone.

(554) In certain embodiments suitable solvents include, but are not limited to: Methylene Chloride, Chloroform, 1,2-Dichloroethane, Propylene Carbonate, Acetonitrile, Dimethylformamide, N-Methyl-2-pyrrolidone, Dimethyl Sulfoxide. Nitromethane, Caprolactone, 1,4-Dioxane, and 1,3-Dioxane.

(555) In certain other embodiments, suitable solvents include, but are not limited to: Methyl Acetate, Ethyl Acetate, Acetone, Methyl Ethyl Ketone, Propylene Oxide, Tetrahydrofuran. Monoglyme Triglyme, Propionitrile, 1-Nitropropane, Cyclohexanone.

(556) In certain embodiments, any of the above methods comprise aliphatic oxide present in amounts between about 0.5 M to about 20 M or the neat concentration of the aliphatic oxide. In certain embodiments, aliphatic oxide is present in amounts between about 0.5 M to about 2 M. In certain embodiments, aliphatic oxide is present in amounts between about 2 M to about 5 M. In certain embodiments, aliphatic oxide is present in amounts between about 5 M to about 20 M. In certain embodiments, aliphatic oxide is present in an amount of about 20 M. In certain embodiments, liquid aliphatic oxide comprises the reaction solvent.

(557) In certain embodiments, CO.sub.2 is present at a pressure of between about 30 psi to about 800 psi. In certain embodiments, CO.sub.2 is present at a pressure of between about 30 psi to about 500 psi. In certain embodiments, CO.sub.2 is present at a pressure of between about 30 psi to about 400 psi. In certain embodiments, CO.sub.2 is present at a pressure of between about 30 psi to about 300 psi. In certain embodiments, CO.sub.2 is present at a pressure of between about 30 psi to about 200 psi. In certain embodiments, CO.sub.2 is present at a pressure of between about 30 psi to about 100 psi. In certain embodiments, CO.sub.2 is present at a pressure of between about 30 psi to about 80 psi. In certain embodiments, CO.sub.2 is present at a pressure of about 30 psi. In certain embodiments, CO.sub.2 is present at a pressure of about 50 psi. In certain embodiments, CO.sub.2 is present at a pressure of about 100 psi. In certain embodiments, the CO.sub.2 is supercritical.

(558) In certain embodiments of the above methods, the reaction is conducted at a temperature of between about 0° C. to about 150° C. In certain embodiments, the reaction is conducted at a temperature of between about 23° C. to about 100° C. In certain embodiments, the reaction is conducted at a temperature of between about 23° C., and about 80° C. In certain embodiments, the reaction to be conducted at a temperature of between about 23° C. to about 50° C.

(559) In certain embodiments, a polymerization step of any of the above methods produces cyclic carbonate as a by-product in amounts of less than about 20%. In certain embodiments, cyclic carbonate is produced as a by-product in amounts of less than about 15%. In certain embodiments, cyclic carbonate is produced as a by-product in amounts of less than about 10%. In certain embodiments, cyclic carbonate is produced as a by-product in amounts of less than about 5%. In certain embodiments, cyclic carbonate is produced as a by-product in amounts of less than about 1%. In certain embodiments, the reaction does not produce any detectable by-products (e.g., as detectable by .sup.1H-NMR and/or liquid chromatography (LC)).

(560) In certain embodiments, a polymerization time is between about 30 minutes and about 48 hours. In some embodiments, the reaction is allowed to process for less than 24 hours. In some embodiments, the reaction is allowed to progress for less than 12 hours. In some embodiments, the reaction is allowed to proceed for between about 4 and about 12 hours.

(561) In certain embodiments, a polymerization reaction is allowed to proceed until the number average molecular weight of the polymers formed is between about 500 and about 400,000 g/mol. In certain embodiments, the number average molecular weight is allowed to reach a value between 500 and 40,000 g/mol. In other embodiments, the number average molecular weight is allowed to reach a value between 500 and 20,000 g/mol. In certain embodiments, the number average molecular weight is allowed to reach a value between 500 and 10,000 g/mol. In other embodiments, the number average molecular weight is allowed to reach a value between 500 and 5,000 g/mol. In other embodiments, the number average molecular weight is allowed to reach a value between 500 and 2,500 g/mol. In other embodiments, the number average molecular weight is allowed to reach a value between 1,000 and 5,000 g/mol.

(562) In certain embodiments, provided methods further include the step of sampling the reaction and determining the molecular weight of the polymer at a given time. In certain embodiments, this sampling and molecular weight determination are performed at two or more time intervals. In certain embodiments a plot of molecular weight gain over time is constructed and the method further includes the step of determining from this plot the time at which a desired molecular weight polymer will be present. In certain embodiments, the time at which the polymerization is ended is determined by this method.

(563) In certain embodiments, a polymerization reaction proceeds until between about 20% and about 100% of the provided epoxide is consumed. In certain embodiments, the conversion is between about 40% and about 90%. In certain embodiments, the conversion is at least 50%. In other embodiments, the conversion is at least 60%, at least 80% or at least 85%. In certain embodiments, at least 80% of the provided epoxide is converted to polymer.

(564) In certain embodiments, a method further includes the step of choosing the ratios at which the catalyst, the chain transfer agent and the epoxide substrate are provided. In certain embodiments, these ratios are selected to provide high epoxide conversion while providing polyol of the desired molecular weight in a selected length of time. In some embodiments, this selection of ratios includes the substeps of: i) selecting a desired length of time for which the reaction is to be run, ii) multiplying the selected length of time for which the polymerization reaction is to run by the turnover frequency of the catalyst under the reaction conditions iii) multiplying this result by the desired mol % conversion of epoxide, and iv) using the inverse of this result as the ratio of catalyst to epoxide used for the reaction. In some embodiments, the ratio of chain transfer agent to catalyst is determined by the additional following steps; v) taking the value from step (iii) above and multiplying this result by the molecular weight of the repeating unit of the polycarbonate; vi) selecting a desired molecular weight for the polyol and dividing the result from step (v) by this number; and vii) subtracting the number of chains produced per catalyst molecule from the result of step (vi) and taking the result as the ratio of chain transfer agent to catalyst used in step (1).

(565) To make the steps of the above-described method clear, the following example is provided: in a copolymerization of propylene oxide and CO.sub.2 using a catalyst that has a TOF of 1000 h.sup.−1 and which produces two polymer chains per catalyst molecule, a polymer with Mn of 2,000 g/mol is to be produced and it is desired that 80% of the provided epoxide is converted during a reaction time of 10 hours, one would perform the following steps to obtain the required ratios:

(566) First, taking 10 hours as the selected time interval and performing step (ii) of multiplying the selected interval of 10 hours, by the TOF of 1000 hr.sup.−1 gives 10,000 turnovers per catalyst molecule; next multiplying this number by the desired 80% conversion (step (iii)) and then inverting (step (iv)) provides a value of 1.25×10.sup.−4 corresponding to a catalyst to epoxide ratio of 1:8,000.

(567) Moving next to determination of the chain transfer agent loading, at step (iv) one multiplies the result of step (iii) by the molecular weight of the repeating unit of the polycarbonate (in this case C.sub.4H.sub.6O.sub.3=102 g/mol) and dividing by the desired Mn of 2,000 to give a value of 408. Subtracting the two chains per catalyst from this result in a chain transfer to catalyst ratio of 406:1. Therefore, for this example the molar ratio of catalyst to epoxide to chain transfer agent should be approximately 1:8,000:406.

(568) It will be appreciated that the method described above is simplified in certain respects. For example, the calculation described assumes that the reaction rate is linear throughout the duration of the polymerization. The calculation described also dismisses the contribution that the mass of the chain initiator adds to the molecular weight of the polymer chains. In certain embodiments, particularly those where a polymeric chain transfer agent such as a polyether is used, or where a very low molecular weight oligomer is produced, the contribution of the mass of the initiator to the Mn of the polymer may be significant. It will be understood by those skilled in the art that additional chain transfer agent can be added to account for this effect, and more specifically, that the calculations described above can be modified to account for this effect. Similarly, more detailed kinetic data could be used to account for changes in the reaction rate over time as the reaction proceeds. For instances where a mixture of epoxides is present, the molecular weight of the repeating unit may be approximated by using a weighted average of the molecular weights of the epoxides present in the mixture. This could be further refined by analyzing copolymer made under similar conditions to determine the mole percent incorporation of the different monomers (for example by using NMR spectroscopy) since all epoxides may not be incorporated into polymer with equal efficiency. These and other modifications will be readily apprehended by the skilled artisan and are specifically encompassed by the methods provided herein.

(569) In certain embodiments, it has been found that the turnover frequency of some catalysts decreases as the ratio of chain transfer agent to catalyst increases. This effect can be particularly noticeable at ratios higher than about 100:1. In these instances, the above-described methods may not produce the expected Mn and monomer conversion in a given time interval. In such cases it may be necessary to measure the TOF of the catalyst at various chain transfer agent ratios prior to performing the calculations described above. In general, such cases require the reaction interval be lengthened by an amount proportional to the falloff in catalyst activity at the catalyst to chain transfer agent ratio used, or in some embodiments the catalyst loading be increased by a compensatory amount.

(570) As noted above, water present in the reaction mixtures of the described methods can also act as a chain transfer agent. In certain embodiments, the calculations described above further include the method of measuring the water content of the reaction (preferably after the reaction vessel has been charged with epoxide, chain transfer agent and any solvent to be used, but prior to addition of the catalyst). The molar equivalents of water relative to catalyst are then calculated and the ratio of chain transfer agent to catalyst can be decreased accordingly. If this is not done and there is significant water present, the Mn will be lower than expected at a given % conversion.

(571) III. Methods of Determining Relative Amount of Biobased Carbon Present in Polycarbonates

(572) In one aspect, the present invention provides methods of determining the provenance of particular carbon atoms comprising the polymer compositions described above and herein.

(573) In some embodiments, the present invention provides methods comprising the steps of: a) treating a polymer composition described above and herein to liberate a cyclic carbonate of formula:

(574) ##STR00217## wherein R.sup.1, R.sup.2, R.sup.3, and R.sup.4 are as described above and herein; b) treating the cyclic carbonate to liberate carbon atoms labeled α as CO.sub.2, and carbon atoms labeled β as an epoxide of formula:

(575) ##STR00218## wherein R.sup.1, R.sup.2, R.sup.1, and R.sup.4 are as described above and herein; and c) measuring the radiocarbon content of the CO.sub.2 comprising carbon atoms labeled α, and the epoxide comprising carbon atoms labeled β.

(576) In some embodiments, the present invention provides methods comprising the steps of: a) treating a polymer composition described above and herein to liberate a cyclic carbonate of formula:

(577) ##STR00219## wherein R.sup.1, R.sup.2, R.sup.3, and R.sup.4 are as described above and herein; b) treating the cyclic carbonate to liberate carbon atoms labeled α as CO.sub.2, and carbon atoms labeled β as an epoxide of formula:

(578) ##STR00220## wherein R.sup.1, R.sup.2. R.sup.3, and R.sup.4 are as described above and herein; c) separating the CO.sub.2 from the epoxide; and d) measuring the radiocarbon content of the CO.sub.2 comprising carbon atoms labeled α, and the epoxide comprising carbon atoms labeled β.

(579) A. Treating a Polymer Composition to Liberate Cyclic Carbonate

(580) In some embodiments, a liberated cyclic carbonate of step (a) corresponds to linkages within polycarbonate chains within a polymer composition. For example, in some embodiments, treating poly(ethylene carbonate) chains liberates a cyclic carbonate having a structure

(581) ##STR00221##

(582) In some embodiments, treating poly(propylene carbonate) chains liberates a cyclic carbonate having a structure:

(583) ##STR00222##

(584) In some embodiments, the step of treating polycarbonate chains to liberate a cyclic carbonate comprises a base. In some embodiments, the step of treating polycarbonate chains to liberate a cyclic carbonate comprises a strong base.

(585) In some embodiments, a liberated cyclic carbonate corresponds to an epoxide used in the copolymerization of polycarbonate chains within a polymer composition.

(586) B. Treating Cyclic Carbonate to Liberate CO.sub.2 and an Epoxide

(587) In some embodiments, treating the cyclic carbonate to liberate carbon atoms labeled α as CO.sub.2, and carbon atoms labeled β as an epoxide. In some embodiments, a liberated epoxide of step (b) corresponds to the cyclic carbonate of step (a). For example, in some embodiments, treating a cyclic carbonate of formula:

(588) ##STR00223##
liberates carbon atoms labeled α as CO.sub.2, and carbon atoms labeled β as an epoxide of formula:

(589) ##STR00224##

(590) In some embodiments, treating a cyclic carbonate of formula:

(591) ##STR00225##
liberates carbon atoms labeled α as CO.sub.2, and carbon atoms labeled β as an epoxide of formula:

(592) ##STR00226##

(593) In some embodiments, reaction conditions for treating cyclic carbonate to liberate CO.sub.2 and an epoxide are disclosed in U.S. Pat. No. 4,069,234, the entirety of which is incorporated herein by reference. In some embodiments, the step of treating cyclic carbonate to liberate CO.sub.2 and an epoxide comprises heating to an elevated temperature. In some embodiments, the step of treating cyclic carbonate to liberate CO.sub.2 and an epoxide comprises heating to a temperature between about 25° C., and about 300° C. In some embodiments, the step of treating cyclic carbonate to liberate CO.sub.2 and an epoxide comprises heating to a temperature between about 100° C., and about 250° C. In some embodiments, the step of treating cyclic carbonate to liberate CO.sub.2 and an epoxide comprises holding the reaction at the elevated temperature for between about 0.5 hrs and about 24 hrs. In some embodiments, the step of treating cyclic carbonate to liberate CO.sub.2 and an epoxide comprises holding the reaction at the elevated temperature for between about 1.5 hrs and about 5 hrs.

(594) C. Separating the Epoxide and the CO.sub.2

(595) The epoxide and the CO.sub.2 can be separated according to means well known in the art. Suitable means of separation include condensing the epoxide from a gaseous mixture leaving the CO.sub.2 in the gas phase or chromatographic means such as gas chromatography or gas/liquid chromatography. The separation can also be performed as part of the analysis for example, by separation based on their mass/charge ratio in a mass spectrometer. In certain embodiments, the step of separating may comprise an integral part of the Radiocarbon Content measurement—as for example where gas chromatography or mass spectrometry are part of the measurement process.

(596) D. Measuring the Radiocarbon Content

(597) In some embodiments, radiocarbon content is measured by methods known in the art. In some embodiments, radiocarbon content is measured according to Method B disclosed in ASTM D6866-16.

(598) E. Additional Steps

(599) In some embodiments, methods described above and herein further comprise the step of using the measured radiocarbon content to confirm that the carbon atoms at the positions labeled α are derived from a fossil carbon source by having a pMC of less than about 1, less than about 0.1, or less than about 0.03.

(600) In some embodiments, methods described above and herein further comprise the step of measuring the radiocarbon content of any CTA that comprises part of the polycarbonate chains. In certain embodiments, the CTA is liberated from the polymer chain during the step of treating the polymer composition to liberate cyclic carbonate. During or after this step, the CTA (or one or more molecules arising from the CTA) can be isolated and the pMC and % biobased carbon of the CTA or its residues can be measured, e.g., according to ASTM D6866-16 (Method B). These data combined with the biocontent of the other polymer constituents permits determination of the overall % biobased carbon of the polymer composition.

(601) In some embodiments, methods described above and herein further comprise the step of using the measured radiocarbon content to confirm that the carbon atoms at the positions labeled β are derived from a biobased feedstock by having a pMC of at least about 95, at least about 99, or at least about 100.

EXAMPLES

Example 1

(602) This example demonstrates a method of the present invention with a chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where

(603) the chain transfer agent is 1,4-cyclohexanedimethanol;

(604) -L.sub.p is a salcy ligand

(605) ##STR00227##

(606) -M- is Co(III); and

(607) -L.sub.I is

(608) ##STR00228##

(609) ##STR00229##

(610) 24 mg of catalyst E1 (0.04 mmol), 0.45 g (3.1 mmol) 1,4-cyclohexanedimethanol and 20 mg (0.04 mmol) PPN.sup.+Cl.sup.− are held under vacuum in a Fisher-Potter bottle. The bottle is filled with nitrogen and 20 ml of biobased propylene oxide is added. The bottle is pressurized with 100 psi CO.sub.2 that is derived from the combustion of fossil fuel. After 41 h at 30° C. the bottle is opened and the polymer is isolated by pouring into methanol.

(611) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having the formula:

(612) ##STR00230##

Example 2

(613) This example demonstrates a method of the present invention with a chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where the chain transfer agent is propoxylated pentaerythritol;

(614) -L.sub.p is a salcy ligand

(615) ##STR00231##

(616) -M- is Co(III); and

(617) -L.sub.I is trifluoroacetate.

(618) ##STR00232##

(619) 51 mg of catalyst E2 (0.07 mmol), 0.5 g (1.4 mmol) of propoxylated pentaerythritol and 41 mg (0.08 mmol), PPN.sup.+Cl.sup.− are held under vacuum in a Fisher-Potter bottle. The bottle is filled with nitrogen and 20 ml of biobased propylene oxide is added. The bottle is pressurized with 100 psi CO.sub.2 that is derived from the combustion of fossil fuel. After 22 h at 30° C. the bottle is opened and the polymer is isolated by pouring into methanol.

(620) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(621) ##STR00233##

Example 3

(622) Example 3 was conducted using conditions similar to Example 2, except Poly(caprolactone) diol having an Mn of 530 g/mol is used as the chain transfer agent.

Example 4

(623) Example 4 was conducted using conditions similar to Example 2, except Poly(ethylene glycol) having an Mn of 400 g/mol is used as the chain transfer agent.

Example 5

(624) Example 5 was conducted using conditions similar to Example 2, except Poly(propylene glycol) having an Mn of 760 g/mol is used as the chain transfer agent.

Example 6

(625) Example 6 was conducted using conditions similar to Example 2, except 1,2-cyclohexane diol is used as the chain transfer agent.

Example 7

(626) This example demonstrates a method of the present invention with a chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where

(627) the chain transfer agent is 1,4 butane diol;

(628) -L.sub.p is a salcy ligand

(629) ##STR00234##

(630) -M- is Co(III); and

(631) -L.sub.I is trifluoroacetate.

(632) An oven dried glass vessel is charged with 11.5 mg of catalyst E2 (0.016 mmol) and 9.2 mg of PPN+Cl— (0.016 mmol). The vessel is purged with nitrogen and 1.4 butane diol (0.073 g, 0.8 mmol) is added as a solution in dry THF (0.5 mL). Biobased propylene oxide (4.5 mL, 64 mmol) is then added. The reaction vessel is pressurized with 300 psig dry carbon dioxide gas that is derived from the combustion of fossil fuel and stirred at 30° C. for 3 hours. The reaction is quenched with acid, diluted with 25 mL acetone and concentrated to afford crude polymer.

(633) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(634) ##STR00235##

Example 8

(635) This example demonstrates a method of the present invention with a chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where the chain transfer agent is 1,3 propane diol;

(636) -L.sub.p is a salcy ligand

(637) ##STR00236##

(638) -M- is Co(III); and

(639) -L.sub.I is trifluoroacetate.

(640) An oven dried glass vessel is charged with 11.5 mg of catalyst E2 (0.016 mmol) and 9.2 mg of PPN.sup.+Cl.sup.− (0.016 mmol). The vessel is purged with nitrogen and 1,4 propane diol (0.061 g, 0.8 mmol) is added as a solution in dry THF (0.5 mL). Biobased propylene oxide (4.5 mL, 64 mmol) is then added. The reaction vessel is pressurized with 300 psig dry carbon dioxide gas that is derived from the combustion of fossil fuel and stirred at 30° C. for 3× hours. The reaction is quenched with acid, diluted with 25 mL acetone and concentrated to afford crude polymer.

(641) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(642) ##STR00237##

Example 9

(643) This example demonstrates a method of the present invention with a chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where the chain transfer agent is 1,4 butene diol;

(644) -L.sub.p is a salcy ligand

(645) ##STR00238##

(646) -M- is Co(III); and

(647) -L.sub.I is trifluoroacetate.

(648) An oven dried glass vessel is charged with 11.5 mg of catalyst E2 (0.016 mmol) and 9.2 mg of PPN+Cl— (0.016 mmol). The vessel is purged with nitrogen and 1,4 butene diol (0.079 g, 0.8 mmol) is added as a solution in dry THF (0.5 mL). Biobased propylene oxide (4.5 mL, 64 mmol) is then added. The reaction vessel is pressurized with 300 psig dry carbon dioxide gas that is derived from the combustion of fossil fuel and stirred at 30° C. for 3 hours. The reaction is quenched with acid, diluted with 25 mL acetone and concentrated to yield 1.5 g of crude polymer.

(649) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(650) ##STR00239##

Example 10

(651) This example demonstrates a method of the present invention with a chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where the chain transfer agent is succinic acid;

(652) -L.sub.p is a salcy ligand

(653) ##STR00240##

(654) -M- is Co(III); and

(655) -L.sub.I is trifluoroacetate.

(656) An oven dried glass vessel is charged with 11.5 mg of catalyst E2 (0.016 mmol); 9.2 mg of PPN+Cl.sup.− (0.016 mmol); succinic acid (0.095 g, 0.8 mmol) and 0.5 mL THF. Biobased propylene oxide (4.5 mL, 64 mmol) is then added. The reaction vessel is pressurized with 300 psig dry carbon dioxide gas that is derived from the combustion of fossil fuel and stirred at 30° C. for 3 hours. The reaction is quenched with acid, diluted with 25 mL acetone and concentrated to afford the crude polymer.

(657) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(658) ##STR00241##

Example 11

(659) This example demonstrates a method of the present invention with a chain transfer agent Y-A-(Y).sub.n and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where

(660) the chain transfer agent is adipic acid;

(661) -L.sub.p is a salcy ligand

(662) ##STR00242##

(663) -M- is Co(III); and

(664) -L.sub.I is trifluoroacetate.

(665) An oven dried glass vessel is charged with 11.5 mg of catalyst E2 (0.016 mmol); 9.2 mg of PPN.sup.+Cl.sup.− (0.016 mmol); adipic acid (0.12 g, 0.8 mmol) and 0.5 mL THF. Biobased propylene oxide (4.5 mL, 64 mmol) is then added. The reaction vessel is pressurized with 300) psig dry carbon dioxide gas that is derived from the combustion of fossil fuel and stirred at 30° C. for 3 hours. The reaction is quenched with acid, diluted with 25 mL acetone and concentrated to afford the crude polymer.

(666) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(667) ##STR00243##

Example 12

(668) This example demonstrates a method of the present invention with a diacid chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where

(669) the chain transfer agent is maleic acid;

(670) -L.sub.p is a salcy ligand

(671) ##STR00244##

(672) -M- is Co(III); and

(673) -L.sub.I is trifluoroacetate.

(674) An oven dried glass vessel is charged with 11.5 mg of catalyst E2 (0.016 mmol); 9.2 mg of PPN.sup.+Cl.sup.− (0.016 mmol); maleic acid (0.095 g, 0.8 mmol) and 0.5 mL THF. Biobased propylene oxide (4.5 mL, 64 mmol) is then added. The reaction vessel is pressurized with 300 psig dry carbon dioxide gas that is derived from the combustion of fossil fuel and stirred at 30° C. for 3 hours. The reaction is quenched with acid, diluted with 25 mL acetone and concentrated to afford the crude polymer.

(675) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(676) ##STR00245##

Example 13

(677) This example demonstrates a method of the present invention with a biobased chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where

(678) the chain transfer agent is biobased isosorbide;

(679) -L.sub.p is a salcy ligand

(680) ##STR00246##

(681) -M- is Co(III); and

(682) -L.sub.I is trifluoroacetate.

(683) An oven dried glass vessel is charged with 11.5 mg of catalyst E2 (0.016 mmol) and 9.2 mg of PPN.sup.+Cl.sup.− (0.016 mmol). The vessel is purged with nitrogen and isosorbide (0.12 g, 0.8 mmol) is added as a solution in dry THF (0.5 mL). Biobased propylene oxide (4.5 mL, 64 mmol) is then added. The reaction vessel is pressurized with 300 psig dry carbon dioxide gas that is derived from the combustion of fossil fuel and stirred at 30° C. for 3 hours. The reaction is quenched with acid, diluted with 25 mL acetone and concentrated to afford the crude polymer.

(684) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(685) ##STR00247##

Example 14

(686) This example demonstrates a method of the present invention with a chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m utilizing a co-catalyst PPN+Cl—, where

(687) the chain transfer agent is paraformaldehyde with the avg. MW is 600 g/mol;

(688) -L.sub.p is a salcy ligand

(689) ##STR00248##

(690) -M- is Co(III); and

(691) -L.sub.I is trifluoroacetate.

(692) An oven dried glass vessel is charged with 11.5 mg of catalyst E2 (0.016 mmol); 9.2 mg of PPN.sup.+Cl.sup.− (0.016 mmol); paraformaldehyde (24 mg, 0.04 mmol); and dry THF (0.5 mL). Biobased propylene oxide (4.5 mL, 64 mmol) is then added. The reaction vessel is pressurized with 300 psig dry carbon dioxide gas that is derived from the combustion of fossil fuel and stirred at 30° C. for 3 hours. The reaction is quenched with acid, diluted with 25 mL acetone and concentrated to afford the crude polymer.

(693) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(694) ##STR00249##

Example 15

(695) This example demonstrates a method of the present invention with a chain transfer agent and a catalyst L.sub.p-M-(L.sub.I).sub.m, where,

(696) the chain transfer agent is dipropylene glycol:

(697) -L.sub.p is

(698) ##STR00250##
where each X is trifluoroacetate:

(699) -M- is Co(III); and

(700) -L.sub.I is trifluoroacetate.

(701) In a glovebox, catalyst (5.4 mg, 1.0 equiv) is charged to an oven-dried 20 mL glass liner. The liner is inserted into a stainless steel high pressure reactor. The system is purged with N.sub.2 five times and purged with CO.sub.2 twice. While under the positive flow of CO.sub.2 that is derived from the combustion of fossil fuel, a solution of dipropylene glycol (75 μL) in biobased propylene oxide (5 mL, 25,000 equiv) is charged to the reaction vessel. The reaction is heated to 50° C., then pressurized with carbon dioxide (300 psi) and stirred.

(702) After 6 h the reaction is vented and quenched with acidic methanol (0.2 mL). The reaction is cooled to room temperature, and the resulting polymer is diluted with acetone (5 mL) and transferred to a foil pan. The unreacted propylene oxide and acetone is removed by evaporation.

(703) The polycarbonate polyol composition thus obtained consists predominantly of polymer chains having a formula:

(704) ##STR00251##

EQUIVALENTS

(705) All material cited in this application, including, but not limited to, patents and patent applications, regardless of the format of such literature and similar materials, are expressly incorporated herein by reference in their entirety. In the event that one or more of the incorporated literature and similar materials differs from or contradicts this application, including but not limited to defined terms, term usage, described techniques, or the like, this application controls.