Method of recycling a polyester
10259768 · 2019-04-16
Assignee
Inventors
- Rafael Auras (Okemos, MI, US)
- Fabiola Maria Iñiguez-Franco (East Lansing, MI, US)
- Maria Rubino (East Lansing, MI, US)
- Daniel Holmes (DeWitt, MI, US)
- Susan E. Selke (East Lansing, MI, US)
- Xiaoyi Fang (Hudson, OH, US)
Cpc classification
Y02W30/62
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
C08J2367/04
CHEMISTRY; METALLURGY
International classification
Abstract
A method of recycling a polyester includes the steps of providing the polyester, preparing a solution containing water and an alcohol, submerging the polyester in the solution, and hydrolytically depolymerizing the polyester while the polyester is submerged in the solution.
Claims
1. A method of recycling a polyester, with said method comprising the steps of: preparing a solution containing water and an alcohol; submerging a poly(lactic acid) in the solution; and hydrolytically depolymerizing the poly(lactic acid) while the poly(lactic acid) is submerged in the solution.
2. The method according to claim 1 wherein the step of preparing the solution is further defined as preparing the solution containing from 20 to 70 percent by volume of the alcohol and the balance being the water, based on a total of 100 percent by volume of the solution.
3. The method according to claim 1 wherein the step of preparing the solution is further defined as preparing the solution containing from 40 to 50 percent by volume of the alcohol and the balance being water, based on a total of 100 percent by volume of the solution.
4. The method according to claim 1 wherein the step of preparing the solution is further defined as preparing the solution containing 50 percent by volume of the alcohol and 50 percent by volume of water.
5. The method according to claim 1 wherein the step of preparing a solution is further defined as preparing a solution of water and an alcohol selected from ethanol, methanol, 1-butanol, and 1-propanol.
6. The method according to claim 1 wherein the alcohol is further defined as ethanol and the step of preparing the solution is further defined as preparing the solution containing the ethanol and the water.
7. The method according to claim 6 wherein the step of preparing the solution is further defined as preparing the solution containing from 40 to 50 percent by volume of ethanol and the balance being water, based on a total of 100 percent by volume of the solution.
8. The method according to claim 1 wherein the alcohol is further defined as 1-butanol and the step of preparing the solution is further defined as preparing the solution containing from 20 to 30 percent by volume of 1-butanol and the balance being water, based on a total of 100 percent by volume of the solution.
9. The method according to claim 1 wherein the step of preparing a solution is further defined as preparing a solution of water and an alcohol with the solution having a pH of from 10 to 14.
10. The method according to claim 1 wherein the step of hydrolytically depolymerizing the poly(lactic acid) is further defined as hydrolytically depolymerizing the poly(lactic acid) while submerged in the solution at a temperature of from 40 to 90 C.
11. The method according to claim 1 wherein the water is further defined as heavy water and the step of preparing the solution is further defined as preparing the solution containing the heavy water and the alcohol.
12. The method according to claim 1 wherein the method further comprises the step of forming the poly(lactic acid) into a film having a thickness of from 18 to 38 micrometers.
13. The method according to claim 12 further comprising the step of cutting the film into a plurality of pieces prior to the step of submerging the poly(lactic acid) in the solution.
14. The method according to claim 12 wherein the step of preparing the solution is performed independent of the step of forming the film.
15. The method according to claim 1 wherein the step of submerging the poly(lactic acid) includes submerging the poly(lactic acid) in the solution for a time period of from 6 to 3000 hours.
16. The method according to claim 1 wherein the poly(lactic acid) has at least 100,000 monomer units.
17. The method according to claim 1 wherein the poly(lactic acid) has a number average molecular weight of from 1.2110.sup.3 to 1.2110.sup.6 Daltons.
18. A method of recycling a polyester, with said method comprising the steps of: preparing a solution containing water and an alcohol; submerging a polyglycolic acid in the solution; and hydrolytically depolymerizing the polyglycolic acid while the polyglycolic acid is submerged in the solution.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) The advantages of the present disclosure will be readily appreciated, as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings.
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DETAILED DESCRIPTION
(44) The present disclosure describes a method of recycling a polyester. In the embodiments described in detail below, the method may be described as a chemical recycling method of the polyester utilizing a depolymerization step to reduce the polyester into its monomer form. The monomer formed by the method may then be used as a raw material for the production of a new polyester having the same and/or similar properties as the virgin polyester. The method advantageously reduces or even eliminates the formation of contaminants and/or environmentally harmful byproducts by utilizing one or more green solvents, such as an alcohol selected from ethanol, methanol, 1-butanol, and/or 1-propanol, and/or combinations thereof. Additionally, the method may be performed at a low or moderate temperature, such as at a temperature of from about 40 to 80 C., which reduces or even eliminates racemization and/or decomposition of the monomer. This allows for formation of the new polyester having chemical and/or physical properties that are the same/substantially the same and/or similar as the virgin polyester.
(45) Embodiments of the method of recycling the polyester will now be described. The method comprises the step of providing the polyester. The polyester may be any polymer containing an ester group on the primary polymer chain. The polyester may also be any known polyester that swells when contacted with an alcohol. Non-limiting examples of polyesters include thermoplastic polyesters, thermoset polyesters, and polyester resins. In an embodiment, the polyester is further defined as poly(lactic acid) (PLA), and the step of providing the polyester is further defined as providing the poly(lactic acid). In alternative embodiments, the polyester could be further defined as polyglycolic acid (PGA), polycaprolactone (PCL), polyhydroxyalkanoate (PHA), polyethylene terephthalate (PET), polybutylene terephthalate (PBT), and/or the like, and/or combinations thereof.
(46) PLA is a biodegradable thermoplastic aliphatic polyester derived or formed from corn starch or sugar cane utilizing lactic acid (LA) as a precursor. PLA may be used in many different products, including medical products (such as sutures, stents, and drug delivery systems), agricultural products, packaging products (such as film and a rigid thermoforms for containers for food and non-food products), etc. The PLA for the embodiments of the method may be provided by obtaining the PLA from used and/or discarded products, such as used and/or discarded medical, agricultural, and/or packaging products mentioned above. Alternatively, the PLA can be provided by purchasing the PLA from any suitable manufacturer.
(47) In an embodiment, the PLA may be provided in any form, shape, and/or configuration, and the PLA may have suitable any molecular weight and/or molecular size (in terms of monomer units). In a non-limiting example, the PLA has at least 100,000 LA or monomer units. In another non-limiting example, the PLA has from about 100,000 to 150,000 LA or monomer units. In yet another non-limiting example, the PLA has about 130,000 LA or monomer units. It is to be appreciated that the foregoing ranges are not limiting, and the PLA may have a number of monomer units that is larger or smaller than the ranges identified above. Additionally, and in another embodiment, the PLA has a number average molecular weight (M.sub.n) of from about 1.2110.sup.3 to 1.2110.sup.6 Da. In yet another embodiment, the PLA has a weight average molecular weight (M.sub.w) of from about 2.510.sup.4 to 2.510.sup.6 Da. The number average molecular weight of the PLA is also non-limiting, and may be larger or smaller than the range identified above.
(48) In an embodiment, the method further includes the step of forming the polyester into a polyester film having a thickness of from about 18 to 38 micrometers. The polyester film may be further defined as a thin film of polyester. The polyester may be formed into the film utilizing any suitable processing technique known in the art including, but not limited to, casting, spraying, extruding, thermoforming, molding, and/or the like.
(49) Once the polyester film has been formed, the method includes the step of reducing the polyester film into a plurality pieces. The step of reducing the polyester film into the plurality of pieces is performed prior to submerging the polyester in a water-alcohol solution, which is described in further detail below. As described in further detail below, reducing the polyester film into the plurality of pieces improves the water-alcohol solution-to-polymer during the depolymerization step. In an embodiment, the step of reducing the polyester film is further defined as cutting the polyester film into a plurality of pieces utilizing any suitable cutting technique. Alternative ways of reducing the polyester film include breaking, trimming, grinding, smashing, etc. the polyester film into the plurality of pieces.
(50) The method further includes the step of preparing a solution containing water and an alcohol. This step of preparing the solution is performed independent of the step of forming the polyester film. In an embodiment, the step of preparing the solution is further defined as combining the water and the alcohol. Combining may be performed by adding the alcohol to the water or by adding the water to the alcohol in a container, vessel, or the like, and mixing the water and alcohol together to form the solution. Mixing may be accomplished utilizing any suitable mixing technique for any suitable time period or duration to form the water-alcohol solution.
(51) In an embodiment, the step of preparing the solution is further defined as preparing the solution containing from about 20 to 70 percent by volume of the alcohol and the balance being water, based on a total of 100 percent by volume of the solution. Without being bound by any particular theory, it has been found hydrolytic degradation of the PLA during the subsequent depolymerization step is faster utilizing a water-alcohol solution with the alcohol present in the amount of from 20 to 70 percent by volume. This is attributed to faster water penetration into the polymer matrix of the PLA starting with chain cleavage or breakage after immediate swelling of the PLA matrix due to the presence of the alcohol molecules. In another embodiment, the step of preparing the solution is further defined as preparing the solution containing from about 40 to 70 percent by volume of the alcohol and the balance being water, based on a total of 100 percent by volume of the solution. In another embodiment, the step of preparing the solution is further defined as preparing the solution containing from about 40 to 50 percent by volume of the alcohol and the balance being water, based on a total of 100 percent by volume of the solution. In another embodiment, the step of preparing the solution is further defined as preparing the solution containing from about 45 to 55 percent by volume of the alcohol and the balance being water, based on a total of 100 percent by volume of the solution. In still another embodiment, the step of preparing the solution is further defined as preparing the solution containing about 50 percent by volume of the alcohol and about 50 percent by volume of the water, based on a total of 100 percent by volume of the solution. Without being bound by any particular theory, it has been found that faster hydrolytic degradation occurs when the PLA is in contact with a solution containing about 50 percent by volume. This is due to a competitive balance between the swelling effect of the alcohol expanding the PLA network, which allows for maximum sorption of the water into the PLA matrix and cleavage of the main chain of the polymer due to hydrolysis. It should be appreciated that the amount of alcohol present in the solution can be any percent by volume falling within the 20 to 70 percent range, with the balance being water.
(52) The alcohol for the solution is not particularly limited. In an embodiment, the alcohol for the solution is selected from ethanol, methanol, 1-butanol, and 1-propanol, and the step of preparing the solution is further defined as preparing a solution of water and an alcohol selected from ethanol, methanol, 1-butanol, and 1-propanol. It should be appreciated that the alcohol may be a combination of two or more of the above-listed alcohols.
(53) In another embodiment, the alcohol is further defined as ethanol and the step of preparing the solution is further defined as preparing the solution containing the ethanol and the water. With the alcohol further defined as ethanol, the step of preparing the solution is further defined as preparing the solution containing from about 40 to 50 percent by volume of ethanol and the balance being water, based on a total of 100 percent by volume of the solution. In yet another embodiment, the alcohol is further defined as 1-butanol and the step of preparing the solution is further defined as preparing the solution containing the 1-butanol and the water. With the alcohol further defined as 1-butanol, the step of preparing the solution is further defined as preparing the solution containing from about 20 to 30 percent by volume of 1-butanol and the balance being water, based on a total of 100 percent by volume of the solution.
(54) In addition, the step of preparing the solution is further defined as preparing a solution of water and an alcohol with the solution having a pH of from 10 to 14. In another embodiment, the step of preparing the solution is further defined as preparing a solution of water and an alcohol with the solution having a pH of about 11. In an alternative embodiment, the pH of the solution could be within the acidic range; however, the inventors of the present disclosure have found that hydrolysis of the subsequent hydrolytic depolymerization step increases when the pH of the solution falls within the basic range, particularly at a pH of about 11.
(55) As previously mentioned, the solution contains water. In one embodiment, the water wholly contains hydrogen oxide (H.sub.2O) molecules. In another embodiment, the water is further defined as heavy water and the step of preparing the solution is further defined as preparing the solution containing the heavy water and the alcohol. Heavy water may be described as water in which the hydrogen in the water molecules is partly or wholly replaced by the hydrogen isotope deuterium. Heavy water may also be described as an enriched water mixture containing deuterium oxide (D.sub.2O), as well as hydrogen-deuterium oxide (DHO) and hydrogen oxide (H.sub.2O) molecules.
(56) Once the solution is prepared, the method further comprises the step of submerging the polyester in the solution. The method further includes the step of hydrolytically depolymerizing the polyester while the polyester is submerged in the solution. In an embodiment, a ratio of polyester to water-ethanol solution is from about 1 g of polyester/10 mL of solution to 4 g of polyester/10 mL of solution. Accordingly, the step of hydrolytically depolymerizing the polyester is performed simultaneously with the step of submerging the polyester in the solution. Typically, hydrolytic depolymerization begins as soon as the polyester is submerged in the solution and continues until the polyester is at least partially depolymerized. In an embodiment, the polyester is completely depolymerized during the hydrolytic depolymerizing step. In an embodiment, the step of submerging the polyester includes submerging the polyester in the solution for a time period of from 6 to 3000 hours. In another embodiment, the step of submerging the polyester includes submerging the polyester in the solution for a time period of from 20 to 150 days. In another embodiment, the step of submerging the polyester includes submerging the polyester in the solution for a period of 6 to 41 hours to achieve 95% of depolymerization of the polyester.
(57) As used herein, the term hydrolytic depolymerization describes the depolymerization of the polyester by hydrolysis reaction(s). In essence, the polymer chain(s) of the polyester is/are broken down due to the cleavage of the ester bonds with the water reducing the polyester down into its monomer form. For example, poly(lactic acid) may be hydrolytically depolymerized to reduce the poly(lactic acid) down into lactic acid (the monomer form of poly(lactic acid)). This is accomplished by breaking down the ester linkage between the polymer units/chains. The hydrolytic depolymerizing step may also be performed utilizing a suitable catalyst such as, but not limit to, at least one of a metal compounds, a cationic compound, and an organic compound. Additionally, the step of hydrolytically depolymerizing the polyester is performed at a moderate temperature. For instance, the step of hydrolytically depolymerizing the polyester is further defined as hydrolytically depolymerizing the polyester while submerged in the solution at a temperature of from about 40 to 80 C. As used herein, a temperature falling within the range of from about 40 to 80 C. is considered to be a moderate temperature. In another embodiment, the depolymerizing step is performed at a temperature of about 40, 50, 60, 70, or 80 C., or any value or range of values there-between. In another embodiment, the depolymerizing step takes place at standard pressure, such as at 1 atm. It should be appreciated that depolymerization can also be performed at higher pressures.
(58) Hydrolytic depolymerization of PLA is illustrated by the chemical reactions shown in
(59) In an embodiment, the method further comprises the step of analyzing the depolymerized polyester after the step of separating the depolymerized polyester from the solution. Analysis may be formed on the depolymerized polyester, which is or primarily includes the monomer, to determine the suitability of the monomer (such as its purity, etc.) for subsequent processing of the monomer for forming a new polyester having the same/substantially the same chemical and/or physical properties as the virgin polyester. Various known techniques may be used to perform desired analysis/analyses on the monomer.
(60) To further illustrate embodiments of the present disclosure, the following Examples are given herein. It is to be understood that the Examples are provided for illustrative purposes and are not to be construed as limiting the scope of the present disclosure.
EXAMPLES
(61) In various embodiments, PLA films were immersed in pure water, 50% and 95% ethanol solutions for up to 180 days. The change in molecular weight, sorption of water, sorption of ethanol, and lactic acid released were monitored. Glass transition temperature and percent crystallinity as a function of ethanol content were also measured. PLA experienced faster hydrolytic degradation in contact with 50% ethanol than with 95% ethanol or pure water. NMR methodologies were developed to measure sorption of deuterated water and ethanol in PLA. More water was sorbed in 50% ethanol, explaining the higher hydrolysis. During exposure, PLA experienced solvent induced crystallization (SIC). Higher percent crystallinity was found in films exposed to 50% ethanol with the formation of -form crystals. The hydrolysis of PLA was correlated with the release of lactic acid during exposure. Mathematical models are proposed to explain the concurrent SIC and hydrolytic degradation of PLA.
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(63) Chemicals and reagents used include the following: PLA resin and/or pellets (3.8-4.2% D-LA) with a weight and number average molecular weight (M.sub.w, M.sub.n) of 2.350.0710.sup.5 Da and 1.210.0810.sup.5 Da, respectively. In addition, chemicals and reagents include: CAPS (3-(cyclohexylamino)-1-propanesulfonic acid), HEPES (N-(2-Hydroxyethyl)piperazine-N-(2-ethanesulfonic acid)), sodium citrate, ethanol (HPLC grade), acetonitrile (HPLC grade), methanol (HPLC grade), 1-butanol (HPLC grade), 1-propanol (HPLC grade), formic acid, tetrahydrofuran (THF), water (HPLC grade), L(+) LA, malonic acid, deuterium oxide (D, 99.9%) (D.sub.2O) chloroform-D (D, 99.8%) (CDCl.sub.3), and N, N-Dimethylformamide (DMF).
(64) The following process carried out the production of PLA film. PLA pellets were dried at 60 C. for 24 h under vacuum (85 kPa) and processed in a Randcastle cast film microextruder with a screw of 1.5875 cm diameter, 24/1 L/D ratio extruder, and 34 cc volume. The extrusion temperatures were 193, 212, 215, 215 and 210 C. for zone 1, 2, and 3 transfer tube and die, respectively, with a rotation speed of from 49-60 rpm. The film thickness was 27.99.9 m.
(65) The storage experiments were conducted as follows. Ten disks 2.0 cm in diameter separated by glass beads on a stainless-steel wire were placed in cells containing pure water, 50% ethanol, or 95% ethanol by volume, previously conditioned at 40 C. The total disk surface area to fluid volume was 1.79 cm.sup.2/mL. Degradation and release experiments were conducted at 40 C. using a migration cell.
(66) Preliminary experiments on hydrolytic degradation of PLA were performed in different water alcohol solutions: 50% ethanol, 50% methanol, 50% 1-propanol and 20% 1-butanol by volume at 70 C. All the solutions were preconditioned before testing. After determining 50% ethanol as the main solvent to be used in the study of the Ea of PLA hydrolytic degradation, migration cells containing 50% ethanol by volume were stored at 40, 60, 70 and 80 C. All cells were first conditioned at the set temperature. Cells that contained water were also conditioned and stored at 60, 70, 80 and 90 C. Experiments designed to control the pH of the 50% ethanol solution during the hydrolytic degradation of PLA were performed at 80 C. with pH values of 4, 7 and 11, using sodium citrate (0.1M), HEPES (0.3M) and CAPS (0.1M) as buffer solutions, respectively. Samples of film were retrieved periodically to assess number average molecular weight (M.sub.n), weight average molecular weight (Mw) and polydispersity index (PDI). M.sub.n was assessed where 10 mg of film were dissolved in THF (2 mg/mL) and tested using size exclusion chromatography (SEC). The measurements were conducted in triplicate.
(67) To study the hydrolytic degradation and SIC of PLA by water-ethanol solutions, the change in molecular weight of PLA was analyzed during exposure to determine the rate of hydrolysis caused by the cleavage of the ester bonds. The sorption of water in PLA was studied since hydrolysis depends on the presence of water molecules in the polymer matrix. However, the ethanol molecules in the solvent solutions influenced the water sorption in PLA due to the swelling effect. Swelling studies were carried out and the initial first order reaction equation for M.sub.n reduction was modified to account the effect of PLA swelling in the rate constant. Crystallinity studies of PLA were performed over the exposure time to assess the concurrent SIC by ethanol molecules along with the hydrolysis of amorphous regions in the polymer matrix by water molecules. Finally, LA release was assessed as the result of the concurrent SIC and hydrolysis of the polymer chains and a model was proposed to predict the LA release when PLA is exposed to water-ethanol solutions.
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(69) It has been evaluated that the effect of organic solvents like ethanol in contact with PLA swell the polymer matrix and increase chain mobility. The creation of free volume due to swelling allows more water molecules to diffuse in and get sorbed in the PLA matrix. This accelerates the hydrolysis rate. The diffusion and sorption of water and ethanol during hydrolytic degradation can help to describe the mechanism of solvent assisted hydrolysis.
(70) The determination of water and ethanol sorption is as follows. Diffusion of H.sub.2O in PLA has been reported, D values of 3.5310.sup.15 m.sup.2/s at 80% relative humidity (RH) and 1.510.sup.11 m.sup.2/s at 90% RH in vapor systems, and 2.9210.sup.12 m.sup.2/s in immersion conditions were reported for PLA at 40 C. In various experiment, to simultaneously measure the rate of diffusion and sorption of water in PLA in ethanol solutions created technical challenges since the H.sub.2O peaks overlap with PLA resonances in the .sup.1H NMR spectrum.
(71) Furthermore, excluding all extraneous sources of water from NMR measurements to ensure accurate measurements is extremely difficult. In contrast, D.sub.2O does not suffer the same issues and allows for the accurate measurement of sorption.
(72) Therefore, D.sub.2O water was used to simulate the diffusion of H.sub.2O in PLA, but recognize that D.sub.2O will cause a different hydrolysis rate in PLA than H.sub.2O as is shown in
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(75) Ethanol sorption appears to follow Fick's law of diffusion. The analytical solution with constant concentration assumed on both disk faces is:
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where M.sub.t is the amount of ethanol sorbed at time t (g-EtOH/g-PLA), M.sub., is the amount of ethanol at equilibrium (g-EtOH/g-PLA), t is time(s), 1 is thickness of the expanded disk (m) and D is the diffusion coefficient (m.sup.2/s). The nonlinear regression (nlin-fit) function in MATLAB 2011b (MathWorks, Natick, Mass.) was used to fit Eq. (1). This provides an estimate of M.sub. and D.
(77) Experiments were performed using the .sup.1H NMR technique to study the relationship between ethanol concentration and polymer expansion when PLA films were exposed to different concentrations of ethanol over 24 h.
(78) The initial first order reaction M.sub.n=Mn.sub.0 exp (kt), can be modified to account for the effect of PLA swelling. A model based on the assumption that the expansion of the polymer is due to an increase in void space, not expansion of the chains, predicts that the rate constant is:
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where V.sub.o is the initial void space in the PLA matrix. V.sub.d is the volume of the disk, p is a constant, and p is the ethanol fraction (p=0, 0.5, 0.95). This model incorporates the effect of expansion due to ethanol in the rate constant. When p=0 (pure water), k=V.sub.o/V.sub.d; and when p=1 (no water), k=0. Fitting M.sub.n=M.sub.no exp(kt) to the experimental data in
(80) Setting the derivative of k with respect to p in Eq. (2) equal to zero gives the maximum rate of decay in M.sub.n. This occurs when the volume fraction of ethanol reaches p0.45 (
(81) Hydrolytic degradation of PLA occurs in the amorphous regions since they have a larger void volume than the crystalline regions and water can penetrate amorphous regions more readily. Since hydrolysis reduces the amorphous regions, the degree of crystallinity increases, even though the crystalline regions remain unchanged. On the other hand, exposure of PLA to ethanol causes softening in the polymer, resulting in the movement and realignment of polymer chains, which induces crystallinity. Therefore, it is a combination of structural changes in PLA including swelling and induced crystallinity when exposed to different combined solvents that affects hydrolysis.
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(83) For assessing the crystallinity of PLA during hydrolytic degradation, DSC and XRD techniques were used. DSC was applied to calculate the percent crystallinity and identify changes in T.sub.m, T.sub.C, and T.sub.g using DSC thermograms. The identification of the type of crystals formed during PLA hydrolysis was performed by the XRD technique.
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(85) The increase in crystallinity can be explained by the depression of T.sub.g due to the process of SIC. If T.sub.g falls below the test temperature (40 C.), the polymer chains have sufficient mobility and tend to rearrange into a crystalline structure, which is a more stable configuration. It has been found that the transport of acetone in poly(ethylene terephthalate) (PET) induces crystallization in three stages. The first stage is the transport of the solvent by diffusion, which is controlled by the concentration gradient. The second stage involves swelling by the solvent and the third stage is secondary crystallization, in the case of PLA, the second stage present in PET is observed in
(86) In order to quantify the crystallization kinetics, the Avrami theory was applied according to:
X.sub.c=1exp(Kt.sup.n)(Eq. 3)
where X.sub.c is the relative crystallinity of the polymer, t is time, K is the crystallization rate constant, and n is the Avrami exponent. As observed in
(87) The XRD profiles of PLA films during hydrolytic degradation are shown in
(88) In contrast, some sharp peaks began to appear after 3 days exposure to 50% and 95% ethanol (
(89) Crystallinity results can be correlated with DSC thermograms of PLA before and after being hydrolyzed by water-ethanol solutions for various times (
(90) Another explanation could be the production of locally ordered structures during hydrolysis, promoting the occurrence of cold crystallization at lower temperatures. The double melting peaks could be attributed to the formation of two different crystalline structures formed during the DSC heating process. Some crystals that could be formed during crystallization from melt are the and -forms that have approximately the same energy and therefore the possibility to coexist. The high T.sub.m corresponds to melting of the more stable structure, which is the -crystal, while the low T.sub.m is ascribed to the less perfect crystal that is the -form. The early peak could also be attributed to the devitrification of the rigid amorphous fraction (RAF).
(91) For PLA exposed to ethanol solutions (
(92) However, after 60 days of immersion, a small endothermal peak started to appear and became stronger over time. This phenomenon could be explained by hydrolysis process, which is reflected in the change of the molecular weight distribution (MWD) of PLA (
(93) During hydrolysis of the amorphous regions of PLA, low molecular weight water-soluble oligomers and monomers are released.
(94) The highest release of LA in 50% ethanol concurs with the fastest reduction in M.sub.n (
(95) A model that predicts LA release is proposed based on the process of chain scission into progressively lower molecular weights, followed by diffusion of LA-mers through the PLA matrix, followed by crossing the interface into the fluid, and finally dissolving into LA in the various water-ethanol solutions. The resulting concentration of LA in the solution is described by:
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where C.sub.f is the concentration of LA in the solution, Q and R are constants, A is the disk surface area, V.sub.f is fluid volume, t is time, and k is the rate constant in Eq. (2). Fitting Eq. (4) to the experimental data gave Q=0.9 g/cm.sup.2 and R=2.232. The predicted LA release from PLA hydrolysis immersed in water, 50% and 95% ethanol are the curves in
(97) During LA release consider that the migration rate of molecules within the polymer matrix depends on several factors, including the size of the migrants, density and the T.sub.g of the polymer.
(98) Therefore, changes in T.sub.g will affect the release of LA previously discussed since T.sub.g will determine the flexibility of polymer chains and the free volume within the matrix. When PLA was exposed to water (T.sub.g=53 C.) (
(99) The migrants from PLA are LA and LA-mers, which are degradation products from the hydrolysis of polymer chains. This disclosure carries out the quantification of alkali decomposition products based on the conversion of lactide and LA-mers to LA. A theoretical prediction for the rate of diffusion of oligomers up to 5 units was made based on the free volume theory as a function of the T.sub.g of the polymer during hydrolysis experiments (
(100) Predicted values showed that the smaller the molecular weight of the oligomer, the faster the diffusion through PLA. Therefore, the LA quantified during release experiments can be identified as mostly LA released from the PLA matrix and not from the alkali hydrolysis of LA-mers released from PLA in the solution. It has been shown that the long-term migration of LA-mers in water at 40 C. show that until three months exposure to water, no LA-mers were detected. However, by six months, 3.46 g/cm.sup.2 of LA-mers up to 13 units were quantified. In the experiment, the initial presence of LA-mers in the PLA films were not detected by MALDI-TOF. Therefore, at the early stages the LA quantified during the experiments can be attributed to the hydrolytic degradation of PLA in contact with the water-ethanol solutions and released as mostly LA into solution.
(101) The exposure of PLA disks to different water-ethanol solutions led to the hydrolytic degradation of the polymer with concurrent SIC. Hydrolysis was accelerated by the immersion of PLA in 50% ethanol, which showed a faster reduction in Mn than in 95% ethanol and pure water. Hydrolysis is related to the amount of water molecules available to start chain scission, so NMR techniques were applied to study water sorption in PLA. Higher sorption of D.sub.2O was found when PLA was exposed to 50% ethanol, explaining the faster hydrolysis.
(102) A new model was proposed to explain the rate of hydrolysis, accounting for the effect of PLA swelling due to ethanol sorption. The rate of degradation for 50% ethanol was 0.0230 gmol.sup.1 d.sup.1. This was the maximum rate of decay in Mn meaning that 50% concentration provides the optimal competitive balance between swelling and hydrolysis. During PLA hydrolysis the % X.sub.C increased, indicating that SIC occurred in PLA when exposed to 50% and 95% ethanol.
(103) In the crystallization process of PLA, three different regions were identified. Regions I and II were due to SIC by ethanol. The Avrami equation was found to describe the crystallization process well. Region III was due to hydrolysis of the amorphous regions. XRD studies showed the formation of -crystal during SIC. LA release was studied as an indication of hydrolysis of PLA. PLA immersed in 50% ethanol showed the highest release of LA, which is in accordance with the fastest decay in M.sub.n by hydrolysis. A model was proposed to predict LA release during hydrolysis when PLA is exposed to different ethanol-water solutions.
(104) In addition, samples were retrieved at defined times during 6 months to assess M.sub.w, M.sub.n, water and ethanol sorption, thermal and physical properties, and LA release. The molecular weight of PLA was determined by the following process. At various times throughout the experiments, M.sub.w and M.sub.n, were determined by weighing approximately 10 mg of film retrieved from the test cells and dissolved in THF (2 mg/mL).
(105) A gel permeation chromatograph (GPC) (Waters 1515, Waters, Milford, Mass., USA) equipped with a refractive index detector (Waters 2414) and a series of three columns of HR Styragel (HR4, HR3 and HR2) were used (each 7.8 mm300 mm, Waters Styragel). An elution of THF at a flow rate of 1 mL/min was applied with a flow rate ramping time of 5 min and a total run time of 45 min. The temperature of the detector and column was 35 C. and the injection volume was 100 L. A calibration curve was made from polystyrene standards-Shodex SM-105 (Waters, Milford, Mass.), which contained a molecular weight range of 1.3710.sup.3 to 2.4810.sup.6 Da. The Mark-Houwink constants for the correction were K=0.0164 mL/g and =0.704 for PLA solutions in THF at 35 C. The measurements were conducted in triplicate.
(106) The deconvolution of the molecular weight distribution (MWD) was carried out in Fityk using nonlinear least-squares curve fitting for a LogNormal function.
(107) The process for water and ethanol sorption is as follows. Water and ethanol sorbed by PLA film were measured at 40 C. using migration cells. The water (H.sub.2O) in the solvents (water, 50% ethanol, 95% ethanol) was replaced with D.sub.2O to avoid contamination from environmental water and interference with measurements.
(108) Ethanol sorbed was determined using the .sup.1H NMR (proton nuclear magnetic resonance) technique and water sorbed using D-NMR (Deuterium NMR). Samples of film were taken periodically. For ethanol sorption, the samples were rinsed with D.sub.2O and for water sorption with H.sub.2O to remove the solvent from the surface. For ethanol sorption, samples were dissolved in CDCl.sub.3 with DMF as the internal standard, and for water sorption, samples were dissolved in THF with CDCl.sub.3 as the internal standard. For ethanol and D.sub.2O sorption measurements, samples were analyzed using a Varian Inova 600 MHz superconducting NMR-Spectrometer equipped with a Nalorac 5 mm PFG switchable probe operating at 599.892 MHz and 92.069 MHz for .sup.1H and .sup.2H, respectively. Experiments were conducted in triplicate.
(109) PLA samples, after hydrolysis in 50% ethanol at 80 C., were analyzed by 13 CNMR (carbon nuclear magnetic resonance) on a 500 MHz Varian DirectDrive 2 Spectrometer equipped with 5 mm PFG One NMR probe. The gHMBC (gradient heteronuclear multiple bond correlation) experiment was run on a Bruker Avance 900 MHz NMR spectrometer equipped with a 5 mm TCI triple-resonance cryoprobe operating at 898.76 and 226.02 MHz for 1H and 13 C, respectively. Samples were dissolved in CDCl3 and run at ambient temperature. 7,292 transients were collected for the carbon NMR with a 1.0 s recycle delay; data were zero-filled to 262144, and 0.5 Hz exponential multiplication was used. gHMBC data were collected with a 1.5 recycle delay, 96 scans per increment and 350 increments. Linear prediction and zero-filling were applied to the carbon dimension, and unshifted sine-bell squared windows were used in both dimensions.
(110) A differential scanning calorimeter was used to determine the T.sub.g, T.sub.m, crystallization temperature (T.sub.c) and % X.sub.C of the PLA samples. The samples where cooled from 25 to 5 C. and then run at a temperature range of 5210 C., with a heating rate of 10 C./min using liquid nitrogen with a flow rate of 70 mL/min. The first heat scans of the samples are reported. The data obtained were analyzed using the Thermal Analysis Universal 2000 version 4.5A software. Percentage crystallinity was calculated using the heat of fusion of the 100% crystalline for PLA sample of 93.7 J/g.
(111) The X-ray diffraction study (XRD) analyses were performed using a Bruker AXS D8 Advance X-ray diffractometer (Bruker Co., Billerica, Mass., USA) equipped with a Global Mirror filtered Cu K radiation source set at 40 kV and 100 mA. Samples were scanned in the 2 range from 2 to 400 at a rate of 0.24/min and an increment of 0.01.
(112) In dynamic mechanical analysis (DMA), to determine the T.sub.g of PLA, the loss factor (tan delta) was measured as a function of temperature when PLA samples were immersed between 4 and 7 days in the various ethanol-water solutions during testing. A TA RSA-G2 Solids Analyzer Immersion System (TA Instruments, New Castle, Del., USA) equipped with a tension geometry at a frequency of 1 Hz was used. The samples were cooled down from 25 to 10, 10, 10, 30, and 60 C. for 0, 25, 50, 75 and 95% ethanol volume and then heated to 60 C. at a heating constant rate of 5 C./min using liquid nitrogen. The data obtained was analyzed using the TA Instruments TRIOS software.
(113) Release of LA into the three different solvent systems (water, 50% ethanol and 95% ethanol) was determined using the migration cell at 40 C. Four replicates were performed for each of the solvent systems. LA quantification was carried out since lactide and oligomers are degradation products of PLA that are able to migrate and easily decompose to LA. Samples containing 0.5 mL of simulant were taken periodically and exposed to alkali hydrolysis. For ethanol solutions, the ethanol was evaporated using a Savant SCI 10 Speed Vac Concentrator System (Savant Instruments, Holbrook. N.Y. USA) and then reconstituted with 0.5 mL of water. Samples were then saponified with 50 L of 0.2 M sodium hydroxide, followed by heating for 15 min in a water bath at 60 C. After cooling at room temperature, 50 L of 0.2 M hydrochloric acid was added. LA was analyzed with an LC/MS/MS system with a triple quadrupole/linear ion trap (AB/Sciex QTRAP 3200. Framingham. Mass., USA). Separation was carried out on an Ascentis Express CI8, 2.7 m, 1002.1 mm reverse phase column (Sigma-Aldrich, St. Louis. Mo. USA.) with a flow rate of 0.2 mL/min. Solvents were A: 1% formic acid and B: methanol. Solvent programming was isocratic for 3 min with 1% B. then a linear gradient to 95% B up to 2 min. followed by the isocratic mode for 2 min. A linear gradient was then carried out in 0.01 min-1% B and held for 3 min in the isocratic mode. The oven temperature was 40 C.
(114) Mass spectrometric analyses were performed in the negative-ion mode following the Ambient Pressure Chemical Ionization (APC1) method; the curtain gas was set to 20, gas-1 20 and gas-2 20, with a temperature of 650 C. The calibration curve was made from 0.25 to 15 g/mL by treating the LA standard solutions in the same way as the samples and using malonic acid as the internal standard.
(115) In one embodiment, the hydrolysis in different alcohol solutions was explored. The hydrolytic degradation of PLA in contact with water-ethanol solutions was evaluated. PLA showed faster hydrolytic degradation when it was in contact with 50% ethanol at 40 C. This is due to the competitive balance between the swelling effect of ethanol expanding the PLA network allowing the maximum sorption of water into the PLA matrix and the cleavage of the main chain of the polymer due to hydrolysis. To further explore the swelling effect of alcohol solutions, different alcohol solutions all at mostly 50% volume with water were used to evaluate the competitive balance between swelling and water sorption.
(116) Since no differences were found among the alcohols except with methanol, which exhibited slower hydrolysis, 50% ethanol was used to assess the effect of temperature on the hydrolytic degradation of PLA and to calculate the Ea. Ethanol was also selected since it can be produced from renewable resources such as sugar cane or cornstarch, reducing the negative impact of using solvents derived from fossil resources for the recycling of PLA. Additionally, the boiling point of 50% ethanol solution is higher than 50% 1-propanol (92 and 88 C., respectively) and around the same as 20% 1-butanol (93 C.). Thus, the hydrolysis and recycling can be performed at higher temperatures without reaching the boiling point, which would create process complications. Lastly, ethanol is a more economical choice than that of 1-propanol and 1-butanol.
(117) In another embodiment the hydrolytic degradation of PLA in 50% ethanol was determined. To study the effect of temperature on the hydrolytic degradation of PLA in 50% ethanol, PLA was exposed at different temperatures above the glass transition temperature (Tg) of the polymer immersed in 50% ethanol (Tg=36 C. [15]): 40, 60, 70 and 80 C.
(118) The crystallinity of PLA film immersed in 50% ethanol at 40 C. was analyzed during hydrolysis. The degree of crystallinity of the film increased from around 3%-25% after 168 h of immersion, and then between 360 h and 2880 h the crystallinity further increased to 50%. At the point that the MWD started to show more than one peak below 60 kDa, the crystallinity of the film was 40% corresponding to the region in which the crystallinity increases due to the hydrolysis of the amorphous regions of the PLA. This behavior could reflect complex kinetics where the ester bonds of PLA oligomer chain may have different susceptibility to cleavage. That means selective scission occurs where the degradation is not homogeneous and the accumulation of different low molecular weight fractions is more evident at prolonged hydrolysis time. In terms of chemical recycling of PLA, the crystalline residues could prolong the reaction period required for obtaining a high yield of LA.
(119) In another embodiment, a deconvolution study of the MWD was performed to understand the reaction kinetics to study the effect of temperature on the hydrolytic degradation of PLA in 50% ethanol. Different deconvolution functions have been used such as Gaussian and Lorentzian functions. However, it has been shown that these functions are not appropriate since the curves for solid-state reactions are asymmetrical, whereas LogNormal can properly fit asymmetric functions. The LogNormal function was used to perform the deconvolution of the peaks followed by the kinetics analysis of the separated peaks to calculate the rate constants. The deconvolution of the peaks was carried out when skewness of the distribution was observed and when more than one peak was detected in the MWD. This occurred when Mn was below 60 kDa where the MWD distribution deviated from monomodal at all temperatures.
(120) The hydrolytic degradation of PLA leads to random cleavage of the ester bonds where longer chains of the polymer are more susceptible to hydrolysis than the shorter chains. The hydrolysis products of PLA contain fragments of water-soluble products like oligomers and LA fragments. To understand the hydrolysis of PLA, the proposed M.sub.n from the deconvoluted portions of the original MWD were plotted as a function of time (
(121) To further understand PLA degradation, recombination reactions, which may result in crosslinking were considered. Recombination reactions of PLA have been seen when the polymer has been exposed to thermal degradation or degradation by composting. They can also happen when cyclic oligomers recombine with linear molecules by ring opening reactions favoring the formation of longer chains. In another embodiment, cross linking was discarded as a side reaction after NMR experiments were carried out. In particular, gHMBC and 13CNMR were run on PLA exposed to 50% ethanol at 80 C. to probe for any new carbon resonances that may have formed that correspond to cross-linking (e.g., carbon resonances around 100 ppm due to orthoesters). Aside from peaks attributable to PLA, oligomers and lactide, there was no evidence of crosslinking.
(122) After the process of separating the individual data of the M.sub.n obtained by peak deconvolution, the kinetic analysis of selected M.sub.n is the most prevalent reaction was carried out for each temperature.
(123) In various embodiments, the effect of temperature on the hydrolytic degradation of PLA in 50% ethanol was determined. To evaluate the effect of temperature on the hydrolytic degradation of PLA for chemical recycling, the activation energy as stated by the Arrhenius equation must be estimated. Commonly, the effect of temperature on the hydrolysis of PLA is estimated by linearizing the Arrhenius equation Eq. (38) set forth below by plotting the natural logarithm ln(k) from the equation as a function of the reciprocal temperature to avoid fitting a non-linear equation. However, when the Arrhenius equation is used for parameter estimation, high correlation is found when Ea and k.sub.o are simultaneously estimated, resulting in high relative error.
(124) During hydrolytic degradation of PLA, the number of carboxylic acid chain ends increases, making the hydrolysis a self-catalyzed reaction due to the accumulation of the acidic polymer fragments in the specimens. So, the pH decreases over time, for example from pH=8.7 to pH=4.6 at 40 C. after 2800 h. Besides temperature, the hydrolysis mechanism of PLA may depend on the pH of the media due to the different susceptibility of the ester groups in lactic acid oligomers. It is important to study the influence of the pH on the hydrolysis rate constant of PLA. A parameter estimation approach was used to estimate the parameters of Eqs. (35) and (36).
(125) When PLA was immersed in 50% ethanol at 80 C. and different pH the MWD shifted towards lower molecular weight as hydrolysis proceeded. As in the hydrolysis of PLA in 50% ethanol without controlling the pH of the solution, the MWD at the latest stages of the degradation did not show a monomodal distribution. Therefore, for the analysis of the kinetics the same deconvolution procedure of the MWD was performed as in
(126) After the analysis of the hydrolytic degradation of PLA in 50% ethanol at different pH at 80 C., where the rate increased exponentially with pH, thereby supporting the proposed equation, the estimation of using Eq. (38) was carried out to be able to estimate Ea from Eq. (37). For the estimation of , it was necessary to find the optimum pH.sub.ref to have low correlation between parameters. Since there is no information on the pH.sub.ref, the pH average was initially used (pH.sub.ref=7.33). A final pH.sub.ref=7.697 was determined. The optimum pH.sub.ref was used for the final estimation of the parameters presented in
(127) To estimate the Ea as a function of pH using Eq. (37), it was necessary to find the optimum T.sub.ref to have low relative errors in the final estimation. The methodology to estimate the T.sub.ref is shown in the supporting information giving a T.sub.ref of 56.538 C. with a correlation coefficient of 4.108010.sup.5 between Ea and k.sub.ref and a relative error of 1.63 and 3.31%, respectively.
(128) In one embodiment, the hydrolytic degradation of PLA depends on the pH of the media. However, it is important to study whether the pH correction previously applied would affect the Ea of hydrolysis. Eq. (36) was applied to estimate Ea without considering the change of pH during hydrolysis. For the non-linear regression estimation, the optimum T.sub.ref 57.688 C. with the lowest correlation was used for the final estimation of the parameters as presented in the supporting information giving a correlation coefficient of 1.297610.sup.5 between Ea and k.sub.ref and a relative error of 1.79 and 3.52%, respectively. The activation energy of the hydrolytic degradation of PLA in 50% ethanol without considering the change of pH during hydrolysis was 9.34110.sup.4 J/mol (
(129) In another embodiment, the hydrolytic degradation of PLA in water was determined. The understanding of how 50% ethanol solution contributes to the hydrolytic degradation of PLA for chemical recycling purposes and the effect of temperature on the hydrolysis of PLA was studied in water without ethanol. PLA films were immersed in water at different temperatures above the Tg: 60, 70, 80 and 90 C.
(130) In one embodiment, shown in
(131) In one embodiment, the effect of the temperature on the hydrolytic degradation of PLA in contact with water was determined. The activation energy was estimated using the reparameterization of the Arrhenius equation (Eq. (36) below) without considering the change of pH during hydrolysis since the pH did not have an effect on the Ea of PLA when it was hydrolyzed by a 50% ethanol solution. So, it was assumed that it would not have an effect on the Ea in water. The procedure for the estimation was the same as in 50% ethanol. For the final estimation of the parameters, the optimal T.sub.ref of 75.931 C. was used since it gave a correlation coefficient of 1.551610.sup.5 between Ea and k.sub.ref and a relative error of 2.48 and 2.20%, respectively, which are acceptable and very low. The final estimation of the Ea of the hydrolytic degradation of PLA in water was 10.14310.sup.4 J/mol (
(132) Even though the values of the Ea for the hydrolytic degradation of PLA in water and in 50% ethanol were different these values are within the range of values (from 4 to 1010.sup.4 J/mol) when PLA was exposed to different environments. These environments include 100% relative humidity (40-80 C.), steam high pressure (100-130 C.), water high pressure (180-350 C.; 140-180 C.), pH 7 buffer solution (37-70 C.; 50-75 C.), basic media of pH 10 (50-70 C.) and acidic media of pH 2 (40-120 C.). In another embodiment, some of the studies were performed using a range of temperatures below and above the Tg that could affect the final estimation. However, the Tg was not reported in solution, but of the initial PLA samples.
(133) In yet another embodiment, the present invention provides an alternative method for chemical recycling of PLA. For that, it is important to consider the LA-oligomers yield during the hydrolysis reactions. Ea values have been reported within the range of this study in aqueous phase but at higher temperatures (120-250 C.), obtaining high yields (95%) of LA when hydrolysis was close to the Tm. When PLA is hydrolyzed in the solid state, crystalline residues, as discussed for
(134) Future studies should be conducted to estimate the yield of LA-oligomers when PLA is hydrolyzed in 50% ethanol to re-polymerize PLA. It is important to study the crystallization behavior of PLA at high temperatures when PLA is immersed in 50% ethanol and how it will affect the yield of LA oligomers for the chemical recycling of PLA and establish the separation process and purification of LA from the water-ethanol solution. It is expected that small increases in temperature can be translated into greater gain of LA-oligomers for recycling PLA.
(135) The hydrolytic degradation of PLA by water-ethanol solutions for chemical recycling was studied. The hydrolysis of PLA at moderate temperatures above the Tg was carried out in 50% ethanol solution and in water to study the effect of temperature. The analysis of the MWD indicated that the hydrolysis in 50% ethanol and water was preferentially carried out by bulk erosion showing a multi-modal distribution at the latter stages of the hydrolysis. The deconvolution of MWD indicated that multiple reaction pathways followed first order kinetics. The Ea for the hydrolysis of PLA in water was around 9% higher than in 50% ethanol at moderate temperatures: 10.14310.sup.4 and 9.34110.sup.4 J/mol, respectively. These values were estimated after the reparameterization of the Arrhenius equation to obtain near zero correlation between parameters and therefore producing a better estimation. Also, the Ea for the hydrolytic degradation of PLA in 50% ethanol was estimated taking in consideration the change of pH, however; no differences were found in the estimations. In one embodiment, an alternative method of using 50% ethanol to hydrolyze PLA at moderate temperatures for PLA chemical recycling was performed.
(136) NMR Analysis
(137) The .sup.1H-NMR spectrum of PLA film with ethanol is shown in
(138) Water identification using the NMR technique led to some modifications in the media for quantification purposes. .sup.1H-NMR spectra cannot provide direct evidence of the real amount of water sorbed in the experiments due to the inevitable contamination by environmental water, which would interfere with the actual concentration of water sorbed by the PLA film. If the sample is contaminated with water from the surroundings, it will show up around 1.56 ppm when PLA is dissolved in CDCl.sub.3, where the chemical shift changes depending on the solvent used to dissolve the polymer under study.
(139) Another issue is that the peaks of the water overlap with those of the CH.sub.3 group of PLA at 1.56 ppm using CDCl.sub.3 as the solvent according to
(140)
EtOH+D.sub.2OEtOD+HOD
(141) Typically, a single peak for the mixture is exhibited due to rapid exchange between D.sub.2O and ethanol. This is not the case for these measurements because of the low concentration of the D.sub.2O/EtOH mixture in the NMR tube, with the lowest concentration detected in sorption experiments of 0.08 L/mL and 0.24 L/mL (8.8810.sup.5 and 1.8910.sup.4 g/mL) for D.sub.2O and EtOH, respectively. It is worth mentioning that with sorption experiments using 100% D.sub.2O, two peaks were seen in the spectrum. In this situation, it could be assumed that there was a proton transfer from the end groups of PLA in the presence of D.sub.2O. EXSY NMR (Exchange Spectroscopy) was carried out to verify that both peaks belong to the D.sub.2O in the system. Indeed, cross-peaks were observed between the resonances. Hence, for quantitative purposes, the two peaks were taken into consideration for water sorption in PLA since they represent the water content in the solvent systems under study.
(142) Model for Change in Molecular Weight, Including Polymer Expansion
(143) Let N be the number of polymer chains in the disk at time t and M.sub.t be the number-average molecular weight (M.sub.n). In time t+t, scission during hydrolytic degradation will cause n cuts in the polymer chains, leaving Nn chains uncut and 2 new chains. Since the total mass before and after scission is the same, the molecular weight at time t+t is:
(144)
If t is small, n will be small compared to N. The equation above then reduces to
(145)
so that
(146)
where V.sub.d is the volume of the polymer disk. The quantity N/V.sub.d is related to the initial density of the PLA. The quantity n/V.sub.d is determined by the concentration c of the water in the disk and by the contact time t between the PLA and water. Then
(147)
where c is the concentration of water and is a rate constant. In the limit as t approaches zero,
(148)
where M.sub.0 is the initial M.sub.n. If c is constant due to fast diffusion,
M=M.sub.oe.sup.ct(Eq. 11)
(149) If diffusion of water and ethanol into the disk can be considered fast compared to the rate of scission, the mass of water occupying the voids inside the disk is:
(150)
where p is the volume fraction of water in the ethanol-water mix surrounding the disk, V.sub.0 is the total volume of voids initially in the disk, and V is the increase in this volume due to expansion by ethanol.
(151) If the expansion of the disk found earlier (0.06p) is assumed to apply to only the voids, not the chains, then
(152)
Model for LA Release
(153) From the model for change in molecular weight
(154)
fitting this model to the number molecular weight vs time data for all environments (water, 50% ethanol, 95% ethanol) gave
(155)
With this information, a prediction for the release of LA can be proposed. The mechanism of LA release begins with chain scission inside the disk. This results in chains with very different molecular weights diffusing through the PLA matrix at the same time, crossing the interface some time later into the fluid, and further dissolving into LA monomers, mostly before leaving the PLA matrix. The increment of mass of PLA entering the fluid surrounding the disk in infinitesimal time dt appears to follow the relationship:
(156)
where dm is the infinitesimal mass, M is the molecular weight at time t, which is M=M.sub.0 exp(kt), and R is a constant that accounts for all the above effects. When t is small, M is large and dm is small. When t is large, M is small and dm is large.
(157) Since mass leaves the disk by diffusion, dm can be proportional to the disk surface area A. It then enters the surrounding fluid volume V.sub.f, and increases the LA concentration. The above relationship therefore becomes:
(158)
where C.sub.f is the concentration of PLA in the fluid and B is another constant. Integrating and applying the boundary condition m=0 at t=0:
(159)
where Q is a constant. The A/V.sub.f ratio used in the experiments reported was 1.79 cm.sup.2/mL.
Theoretical Diffusion Coefficients of LA-Oligomers
(160) To predict the diffusion coefficients of LA and LA-mers, the free volume model/theory proposed by Ventras and Ventras was applied. The diffusion coefficient (D.sub.1) can be determined using the following equation, which depends on temperature, concentration, and the free-volume characteristics of the system:
(161)
where {circumflex over (V)}.sub.FH/y is the term where the free-volume characteristics of the system are included, with {circumflex over (V)}.sub.FH being the average hole free volume per gram of mixture and y the average overlap factor for the mixture introduced, since the same free-volume is available to more than one jumping unit. To calculate the trace diffusion coefficient of LA, the mass fraction of LA in PLA film, .sub.1, is assumed to approach 0. Accordingly, the weight fraction of PLA in PLA film, .sub.2, is close to 1. is the ratio of critical molar volume of LA jumping unit to critical molar volume of PLA jumping unit, and {circumflex over (V)}.sub.1*, and {circumflex over (V)}.sub.2* are the specific hole free volume of LA and PLA required for a jump, respectively. {circumflex over (V)}.sub.FH/y was calculated using the following equation:
(162)
where
(163)
and K.sub.21T.sub.g1 are LA free volume parameters, T is temperature in K, Y.sub.2 is the overlap factor for the free volume of pure PLA, and {circumflex over (V)}.sub.FH2 is the specific hole free volume of the equilibrium liquid polymer at any temperature. {circumflex over (V)}.sub.FH2 was calculated depending on the glass transition temperature of PLA (T.sub.g2):
{circumflex over (V)}.sub.FH2={circumflex over (V)}.sub.2.sup.0(T.sub.g2)[f.sub.H2.sup.G+.sub.2(TT.sub.g2)]TT.sub.g2(Eq. 21)
{circumflex over (V)}.sub.FH2={circumflex over (V)}.sub.2.sup.0(T.sub.g2)[f.sub.H2.sup.G+(.sub.2.sub.c2)(TT.sub.g2)]T<T.sub.g2(Eq. 22)
where {circumflex over (V)}.sub.2.sup.0(T.sub.g2) is the specific volume of the polymer at T.sub.g2, f.sub.H2.sup.G is the fractional hole free volume of PLA at T.sub.g2, .sub.2 is the thermal expansion coefficient for the equilibrium liquid polymer, and .sub.c2 is the thermal expansion coefficient for the sum of the specific occupied volume and the specific interstitial free volume for the equilibrium liquid polymer. The following equations were used to calculate free volume parameters:
(164)
where
(165)
and K.sub.22 are PLA free volume parameters, (C.sub.1.sup.g).sub.2 and (C.sub.2.sup.g).sub.2 are the Williams-Landel-Ferry (WLF) constants, {circumflex over (V)}.sub.1.sup.0(0) and {circumflex over (V)}.sub.2.sup.0(0) are the specific volume of equilibrium liquid of LA and PLA at 0 K, respectively. Viscosity-temperature and density-temperature data for pure LA was used to determine
(166)
where n.sub.1 is viscosity, {circumflex over (V)}.sub.c is the LA molar volume at the critical temperature, M.sub.1 is the molecular weight of LA and {circumflex over (V)}.sub.1.sup.0 is the specific volume of the pure LA at T. The diffusion coefficient of oligomers up to five units of LA was predicted using the scaling law:
(167)
where M.sub.0 is the molecular weight of LA, M is the molecular weight of the oligomers, is a scaling exponent deviation to the Rouse theory, which depends on the geometry of the solute, polymer type and the temperature difference, T and T.sub.g.
Initial Amount of Lactic Acid Oligomers
(168) Matrix-assisted laser desorption-ionization time-of-flight mass spectrometry (MALDI-TOF MS; Axima-CFR Plus, Shimadzu Europa, Duisburg, Germany) was used to analyze the presence of lactic acid oligomers in PLA film before hydrolysis through contact with water, 50% and 95% ethanol. a-cyano-4-hydroxycinnamic acid (10 mg/mL in 50/50 acetonitrile/water with 1 mg/mL diammonium hydrogen citrate) and dithranol (10 mg/mL in tetrahydrofuran) were used as MALDI matrix agents. Sample solutions of PLA in THF were prepared at concentrations of 0.1 and 0.01 mg/mL to be analyzed. The negative ion mode was used and the detector m/z range was 200-1500 Da.
(169) The hydrolytic degradation of PLA film at different temperatures was studied using a migration cells as recommended by ASTM D475411. Shortly, the cells comprised disks of PLA film inserted in a stainless-steel wire and separated by glass beads having a total disk surface area fluid volume of 1.79 cm.sup.2.Math.mL.sup.1. Migration cells were stored in a chamber at different temperatures: 40, 60, 70, and 80 C., containing 50% ethanol solution previously conditioned. Experiments at 100 C. were performed using pressure vessels with an internal thread with polytetrafluoroethylene (PTFE) bushings as pressure seals, and the temperature was controlled in an oil bath. Experiments controlling the pH of 50% ethanol solution during the hydrolytic degradation of PLA were performed at 80 and 100 C. with a pH of 11 using a 3-(cyclohecylamino)-1-propanesulfonic acid as a buffer. Samples of film were retrieved periodically to assess number average molecular weight (M.sub.n). M.sub.n was assessed as previously described where 10 mg of film were dissolved in tetrahydrofuran (2 mg. mL.sup.1) and tested using gel permeation chromatography (GPC) technique. The measurements were conducted in triplicate.
(170) Parameter Estimation: Order of Reaction
(171) To calculate the order of the reaction for the hydrolytic degradation of PLA, the general rate law was used:
(172)
where k is the rate constant of hydrolysis (h.sup.1) and is the order of reaction. The parameters k and were estimated separately using the lowest root mean square error (RMSE).
(173) After data analysis and to calculate the hydrolysis rate constant, the first order reaction equation was used:
M.sub.n=M.sub.n.sub.
where M.sub.n.sub.
Parameter Estimation: Activation Energy
Step 1: Re-Parameterization of the Arrhenius Equation
(174) The effect of temperature on the hydrolytic degradation of PLA can be described using the Arrhenius equation:
(175)
(176) where k.sub.o(h.sup.1) is the pre-exponential factor, R is the universal gas constant (8.314 J/mol.Math.K), and T is temperature (K). A reparameterization of the Arrhenius equation is proposed in this study to estimate Ea and to avoid a high correlation between parameters k.sub.o and Ea as previously explained. This can be done by introducing the reference temperature (T.sub.ref) that corresponds to the rate constant of hydrolysis (k.sub.ref):
(177)
(178) The hydrolytic degradation of PLA can be described by the change of M.sub.n as a function of time (Eq. (37)). Then, to describe the effect of temperature on the hydrolysis of PLA, the following model is proposed by inserting Eq. (35) in Eq. (33), resulting in:
(179)
(180) The hydrolytic degradation can also be pH dependent; therefore, the dependence of pH was introduced in Eq. (36) as an empirical form of secondary model that has been applied similarly for water activity studies:
(181)
where is a constant which reflects the pH dependence of the hydrolytic degradation and pH.sub.ref is the reference pH.
(182) To estimate , experiments involving hydrolysis of PLA at one temperature and different pH's were performed 80 C. at pH 4, 7, and 11. The following equation was used to estimate and pH.sub.ref:
M.sub.n=M.sub.n.sub.
Step 2: Scaled Sensitivity Coefficient (X)
(183) When parameter estimation is performed, two or more parameters may be involved. Therefore, it is essential to determine if those parameters can be estimated accurately, easily and simultaneously. The sensitivity coefficient (SC) indicates the magnitude of change of the response due to perturbation in parameters, and is an important tool to determine the correlation among parameters. The SC is obtained by taking the first derivative of the dependent variable () with respect to the parameter of interest (i.e. X.sub.E.sub.
(184)
(185) E.sub.a indicates the sensitivity of the rate to temperature. When temperature is constant, it is not possible to estimate E.sub.a, or to plot its SSC. Therefore, a new concept was developed to show the temperature-dependent SSC when there are multiple isothermal experiments. So, a (T.sub.sim) approach was proposed to plot X of E.sub.a by inserting a linear increasing dynamic temperature function in the model:
(186)
where T.sub.L is the lowest temperature (K), T.sub.H is the highest temperature (K), t is time and t.sub.max is the maximum time duration.
(187) For the SSC of Eqs. (10) and (11) the same concept as T.sub.sim was applied since pH is changing during the hydrolysis reaction. So, a pH.sub.sim approach was proposed by inserting the following function in the models to plot X when pH is changing over time:
(188)
where pH.sub.L is the lowest pH and pH.sub.H is the highest pH.
Step 3: Estimation of the Optimum pH.sub.ref and T.sub.ref
(189) The goal is to obtain near zero correlation among parameters for better estimation since by reducing the correlation, the relative errors will be reduced. To reach the goal it was important to find the optimum pH.sub.ref and T.sub.ref as explained in the supporting information provided online.
(190) To estimate Ea in Eq. (37), assuming it is constant over all temperatures and over all pH, it was necessary to estimate from Eq. (38) for later use as a fixed value in Eq. (37). In order to estimate , the optimum pH.sub.ref was obtained from Eq. (38) by plotting the correlation between k.sub.ref and versus a possible range of pH.sub.ref. The optimum pH.sub.ref was used to estimate the parameters k.sub.ref, M.sub.no and . Once was estimated, the value was applied as a constant in Eq. (37) and pH.sub.ref used was the optimum pH.sub.ref previously estimated.
(191) The optimum T.sub.ref was obtained from a plot of the correlation between k.sub.ref and Ea as a function of the possible range of T.sub.ref using Eq. (37) and Eq. (36). For the final estimation the optimum T.sub.ref value was used to estimate the parameters k.sub.ref, M.sub.no and Ea.
(192) The nonlinear regression (nlinfit) function in MATLAB 2016a (MathWorks, Natick, Mass., USA) was used to estimate all the parameters. Mean comparisons of the studied parameters among treatments were done using the Tukey HSD test (p<0.05) with JMP 9.0 (Cary, N.C., USA) statistical software.
(193)
(194) Therefore, the results of increasing the reaction temperature at 100 C., pH 11 to accelerate hydrolysis reaction.
(195) All combinations of the aforementioned embodiments throughout the entire disclosure are hereby expressly contemplated in one or more non-limiting embodiments even if such a disclosure is not described verbatim in a single paragraph or section above. In other words, an expressly contemplated embodiment may include any one or more elements described above selected and combined from any portion of the disclosure. In various non-limiting embodiments, all values and ranges of values between and including the aforementioned values are hereby expressly contemplated.
(196) One or more of the values described above may vary by 5%, 10%, 15%, 20%, 25%, etc. Unexpected results may be obtained from each member of a Markush group independent from all other members. Each member may be relied upon individually and or in combination and provides adequate support for specific embodiments within the scope of the appended claims. The subject matter of all combinations of independent and dependent claims, both singly and multiply dependent, is herein expressly contemplated. The disclosure is illustrative including words of description rather than of limitation. Many modifications and variations of the present disclosure are possible in light of the above teachings, and the disclosure may be practiced otherwise than as specifically described herein.
(197) It is also to be understood that any ranges and subranges relied upon in describing various embodiments of the present disclosure independently and collectively fall within the scope of the appended claims, and are understood to describe and contemplate all ranges including whole and/or fractional values therein, even if such values are not expressly written herein. One of skill in the art readily recognizes that the enumerated ranges and subranges sufficiently describe and enable various embodiments of the present disclosure, and such ranges and subranges may be further delineated into relevant halves, thirds, quarters, fifths, and so on. As just one example, a range of from 0.1 to 0.9 may be further delineated into a lower third, i.e. from 0.1 to 0.3, a middle third, i.e. from 0.4 to 0.6, and an upper third, i.e. from 0.7 to 0.9, which individually and collectively are within the scope of the appended claims, and may be relied upon individually and/or collectively and provide adequate support for specific embodiments within the scope of the appended claims. In addition, with respect to the language which defines or modifies a range, such as at least, greater than, less than, no more than, and the like, it is to be understood that such language includes subranges and/or an upper or lower limit. As another example, a range of at least 10 inherently includes a subrange of from at least 10 to 35, a subrange of from at least 10 to 25, a subrange of from 25 to 35, and so on, and each subrange may be relied upon individually and/or collectively and provides adequate support for specific embodiments within the scope of the appended claims. Finally, an individual number within a disclosed range may be relied upon and provides adequate support for specific embodiments within the scope of the appended claims. For example, a range of from 1 to 9 includes various individual integers, such as 3, as well as individual numbers including a decimal point (or fraction), such as 4.1, which may be relied upon and provide adequate support for specific embodiments within the scope of the appended claims.