PRE-FORMS FOR MAKING BIODEGRADABLE CONTAINERS AND RESIN THEREFOR
20220089863 · 2022-03-24
Assignee
Inventors
Cpc classification
B29K2067/00
PERFORMING OPERATIONS; TRANSPORTING
B29C49/0005
PERFORMING OPERATIONS; TRANSPORTING
B29L2031/712
PERFORMING OPERATIONS; TRANSPORTING
Y02W90/10
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
C08K5/0083
CHEMISTRY; METALLURGY
C08L63/00
CHEMISTRY; METALLURGY
B29K2067/04
PERFORMING OPERATIONS; TRANSPORTING
B29K2995/006
PERFORMING OPERATIONS; TRANSPORTING
C08L2205/02
CHEMISTRY; METALLURGY
C08L63/00
CHEMISTRY; METALLURGY
C08L67/04
CHEMISTRY; METALLURGY
B29B11/14
PERFORMING OPERATIONS; TRANSPORTING
B29C49/071
PERFORMING OPERATIONS; TRANSPORTING
C08L67/04
CHEMISTRY; METALLURGY
International classification
Abstract
A preform for a biodegradable container wherein the preform includes from about 40 to about 99 weight percent of a polymer derived from random monomeric repeating units having a structure of
##STR00001##
wherein R.sup.1 is selected from the group consisting of CH.sub.3 and a C.sub.3 to C.sub.19 alkyl group, wherein the polymer comprises from about 20 to about 99 wt. % of the preform and wherein the monomeric units wherein R.sup.1═CH.sub.3 comprise 75 to 99 mol percent of the polymer and wherein the preform has a body having a uniform wall thickness throughout the body of the preform. A resin adapted for forming the preform is also disclosed.
Claims
1. A resin adapted for forming a preform for a biodegradable container wherein the resin comprises from about 0.1 to about 10 weight percent of at least one nucleating agent; from about 0.05 to about 3 weight percent of at least one melt strength enhancer; and from about 40 to about 99 weight percent of a polymer derived from random monomeric repeating units having a structure of ##STR00005## wherein R.sup.1 is selected from the group consisting of CH.sub.3 and a C.sub.3 to C.sub.19 alkyl group, wherein the monomeric units wherein R.sup.1═CH.sub.3 comprise 75 to 99 mol percent of the polymer and wherein the preform has a body having a uniform wall thickness throughout the body of the preform.
2. The resin of claim 1, wherein the resin comprises from about 40 to about 99 weight percent of poly(hydroxyalkanoate) copolymer and from about 1 to about 60 wt. % additional additives.
3. The resin of claim 2 wherein the poly(hydroxyalkanoate) copolymer comprises poly-3-hydroxybutyrate-co-3-hydroxyhexanoate (P3HB-co-P3HHx).
4. The resin of claim 1, wherein the uniform wall thickness of the preform is selected from a thickness ranging from about 1.5 mm to about 5 mm.
5. The resin of claim 1, wherein the preform has a length ranging from about 75 mm to about 120 mm.
6. The resin of claim 1, wherein the preform, after being reheated has a final mass to height ratio ranging from about 0.4 to about 0.5 grams/mm.
7. The resin of claim 1, wherein the preform has a finish selected from the group consisting of PCO 1810, PCO 1881, 30/25, 29/25, 26 mm finishes, and the like.
8. The resin of claim 1, wherein the resin further comprises from about 1 weight percent to about 60 weight percent of polymers selected from the group consisting of poly(lactic acid), poly(caprolactone), poly(ethylene sebicate), poly(butylene succinate), and poly(butylene succinate-co-adipate), and copolymers and blends thereof.
9. The resin of claim 1, wherein the resin further comprises from about 0.1 weight percent to about 5 weight percent of a reheat agent selected from the group consisting of carbon black, infrared absorbing pigments, and mixtures thereof.
10. The resin of claim 1, wherein the resin further comprises from about 0.1 weight percent to about 10 weight percent of a filler selected from the group consisting of calcium carbonate, talc, starch, zinc oxide, neutral alumina, and mixtures thereof.
11. The resin of claim 1, wherein the resin further comprises up to about 15 weight percent of a plasticizer selected from the group consisting of sebacates; citrates; fatty esters of adipic acid, succinic acid, and glucaric acid; lactates; alkyl diesters; alkyl methyl esters; dibenzoates; propylene carbonate; caprolactone diols having a number average molecular weight from about 200 to about 10,000 g/mol; poly(ethylene) glycols having a number average molecular weight of about 400 to about 10,000 g/mol; esters of vegetable oils; long chain alkyl acids; adipates; glycerols; isosorbide derivatives or mixtures thereof; poly(hydroxyalkanoate) copolymers comprising at least 18 mole percent monomer residues of hydroxyalkanoates other than hydroxybutyrate; and mixtures thereof.
12. The resin of claim 1, wherein the preform is made by an injection molding or compression molding process.
13. The resin of claim 1, wherein the resin comprises from about 0.1 weight percent to about 10 weight percent of at least one nucleating agent selected from the group consisting of erythritols, pentaerythritol, dipentaerythritols, artificial sweeteners, stearates, sorbitols, mannitols, inositols, polyester waxes, nanoclays, polyhydroxybutyrate, boron nitride, and mixtures thereof.
14. The resin of claim 1, wherein the resin comprises from about 0.05 weight percent to about 3 weight percent at least one melt strength enhancer selected from the group consisting of a multifunctional epoxide; an epoxy-functional, styrene-acrylic polymer; an organic peroxide; an oxazoline; a carbodiimide; and mixtures thereof.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
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DETAILED DESCRIPTION
[0038] The present invention answers the need for preforms made from biodegradable materials that are capable of being easily processed into plastic containers. The biodegradable materials and containers made therefrom answer a need for disposable containers having increased biodegradability and/or compostability.
[0039] As used herein, “ASTM” means American Society for Testing and Materials.
[0040] As used herein, “alkyl” means a saturated carbon-containing chain which may be straight or branched; and substituted (mono- or poly-) or unsubstituted.
[0041] As used herein, “alkenyl” means a carbon-containing chain which may be monounsaturated (i.e., one double bond in the chain) or polyunsaturated (i.e., two or more double bonds in the chain); straight or branched; and substituted (mono- or poly-) or unsubstituted.
[0042] As used herein, “PHA” means a poly(hydroxyalkanoate) as described herein having random monomeric repeating units of the formula
##STR00003##
wherein R.sup.1 is selected from the group consisting of CH.sub.3 and a C.sub.3 to C.sub.19 alkyl group. The monomeric units wherein R.sup.1 is CH.sub.3 is about 75 to about 99 mol percent of the polymer.
[0043] As used herein, “P3HB” means the poly-(3-hydroxybutyrate).
[0044] As used herein, “P3HHx” means the poly(3-hydroxyhexanoate)
[0045] As used herein, “biodegradable” means the ability of a compound to ultimately be degraded completely into CO.sub.2 and water or biomass by microorganisms and/or natural environmental factors, according to ASTM D5511 (anaerobic and aerobic environments), ASTM 5988 (soil environments), ASTM D5271 (freshwater environments), or ASTM D6691 (marine environments). Biodegradability can also be determined using ASTM D6868 and European EN 13432.
[0046] As used herein, “compostable” means a material that meets the following three requirements: (1) the material is capable of being processed in a composting facility for solid waste; (2) if so processed, the material will end up in the final compost; and (3) if the compost is used in the soil, the material will ultimately biodegrade in the soil according to ASTM D6400 for industrial and home compostability.
[0047] As used herein, “glass transition temperature” or “T.sub.g” is the point at which amorphous regions of a polymer are converted from a brittle, glasslike state to a rubbery, flexible form.
[0048] All copolymer composition ratios recited herein refer to mole ratios, unless specifically indicated otherwise.
[0049] Unless otherwise noted, all molecular weights referenced herein are weight average molecular weights, as determined in accordance with ASTM D5296.
[0050] For the purposes of this disclosure, the preforms described herein are made from poly(hydroxyalkanoate) materials wherein at least about 50 mol %, but less than 100%, of the monomeric repeating units have CH.sub.3 as R.sup.1, more preferably at least about 60 mol %; more preferably at least about 70 mol %; more preferably at least about 75 to 98 mol %. In some embodiments, a minor portion of the monomeric repeating units have R.sup.1 selected from alkyl groups containing from 3 to 19 carbon atoms. Accordingly, the copolymer may contain from about 0 to about 30 mol %, preferably from about 1 to about 25 mol %, and more particularly from about 2 to about 10 mol % of monomeric repeating units containing a C.sub.3 to C.sub.19 alkyl group as R.sup.1.
[0051] In some embodiments, a preferred PHA copolymer for use with the present disclosure is poly-3-hydroxybutyrate-co-3-hydroxyhexanoate (P3HB-co-P3HHx). In certain embodiments, this PHA copolymer preferably comprises from about 94 to about 98 mole percent repeat units of 3-hydroxybutyrate and from about 2 to about 6 mole percent repeat units of 3-hydroxyhexanoate.
Synthesis of Biodegradable PHAs
[0052] Biological synthesis of the biodegradable PHA materials used to make the preforms described herein may be carried out by fermentation with the proper organism (natural or genetically engineered) with the proper feedstock (single or multicomponent). Biological synthesis may also be carried out with bacterial species genetically engineered to express the copolymers of interest (see U.S. Pat. No. 5,650,555, incorporated herein by reference).
Melt Temperature
[0053] Preferably, the biodegradable PHAs of the present invention have a melt temperature (T.sub.m) of from about 30° C. to about 170° C., more preferably from about 90° C. to about 165° C., more preferably still from about 130° C. to about 160° C.
Molded Articles
[0054] According to the disclosure, a polymeric container is formed from a resin comprising a polymer or copolymer materials (e.g., PHA) which are injected, compressed, or blown by means of a gas into shape defined by a female mold. In particular the molded articles may be plastic bottles that hold carbonated and non-carbonated liquids, as well as dry materials including, but not limited to powders, pellets, capsules, and the like.
[0055] Injection molding of thermoplastics is a multi-step process by which a PHA resin material is heated until it is molten, then forced into a closed mold where it is shaped, and finally solidified by cooling. The resulting PHA preform resembles a tube with open and closed ends, wherein the open end may be threaded.
[0056] Reheat injection stretch blow molding is typically used for producing bottles and other hollow objects (see EPSE-3). In this process, a PHA preform is heated and then placed into a closed, hollow mold. The preform is then expanded by air and a stretch rod, forcing the PHA against the walls of the mold. Subsequent cooling air then solidifies the molded article in the mold. The mold is then opened and the article is removed from the mold.
[0057] Blow molding is preferred over injection molding for containers, as it is easier to make extremely thin walls in a blow molding process. Thin walls mean less PHA in the final product, and production cycle times are often shorter, resulting in lower costs through material conservation and higher throughput. Extrusion blow molding may also be used to produce thin-walled containers.
PHA Preforms
[0058] The design and structure of the PHA preform has a significant effect on the reheat behavior of the preform, the temperature profile of the preform and the blowability of the preform upon reheating. In order to determine how the thickness and length of the preform affects the performance of the preform, three preforms 10, 12, and 14 of different lengths as shown in
TABLE-US-00001 TABLE 1 Temperature Zone Preform 10 Preform 12 Preform 14 Zone 1 90 85 75 Zone 2 40 35 30 Zone 3 50 50 50 Zone 4 80 80 80 Zone 5 100 100 100 Zone 6 100 100 100 Zone 7 0 0 100 Zone 8 0 0 0 Zone 9 0 0 0 Zone 10 0 0 0 Overall 95 77 68
[0059] As shown by the following figures, oven settings that provided enough heat to induce pliability sufficient for free blow preforms resulted in deformation of the preforms. The thinner, longer preforms 12 and 14 required less heat as evidenced by the overall oven settings. The preform 14 also required zone 7 to be used in order to adequately heat the end cap due to the length of the preform.
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[0061] The following Table 2 and
TABLE-US-00002 TABLE 2 Preform 10 Zone 1 Zone 2 Zone 3 Zone 4 10B 151 154 159 97 10C 158 158 158 98 10D 149 161 160 99 10E 157 152 157 97 10F 157 157 157 97 Average 154.4 156.4 158.2 97.6
[0062] As seen in the foregoing table, the temperature inside the preform was consistent throughout the length of the preform, which gives consistent pliability and helps avoid areas prone to blow-outs.
[0063] The following Table 3 and
TABLE-US-00003 TABLE 3 Preform 12 Zone 1 Zone 2 Zone 3 Zone 4 12B 167 166 157 81 12C 164 162 158 82 12D 161 161 157 80 12E 163 163 158 81 12F 168 159 155 80 Average 164.6 162.2 157.0 80.8
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[0065] The following Table 4 and
TABLE-US-00004 TABLE 4 Preform 14 Zone 1 Zone 2 Zone 3 Zone 4 14B 163 155 144 77 14C 167 151 151 81 14D 155 142 143 78 14E 152 162 1149 80 14F 79 51 140 79 Average 159.3 152.5 146.8 79.0
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[0067] Based on the foregoing examples, it was observed that the preform design is important for controlling deformation of the preform during reheating. The shortest preform 10 deformed less than the taller preforms 12 and 14, but was still pliable and had less deformation upon reheating. The longer preforms 12 and 14 had more issues with uniformity and repeatability during reheating. The shorter preform 10 with thicker walls made bigger free-blown articles and was less prone to blow outs during reheating compared to the taller preforms 12 and 14. Preform 10 also had more uniformity of material distribution during reheating than preforms 12 and 14. During reheating, preform 10 had a colder inside temperature but also a smaller temperature differential throughout the length of the preform than preforms 12 and 14. Preforms 12 and 14 had much greater temperature differentials throughout the length of the preforms during reheating.
PHA Preform Formulations
[0068] PHA preforms made according to the disclosure are formed from a resin which may contain from about 40 to 99 weight percent of poly(hydroxyalkanoate) copolymer and from about 1 to about 60 wt. % polymer modifiers. In some embodiments, the poly(hydroxyalkanoate) copolymer is poly-3-hydroxybutyrate-co-3-hydroxyhexanoate (P3HB-co-P3HHx). In other embodiments, the PHA composition includes from about 1.0 to about 15.0 weight percent of at least one poly(hydroxyalkanoate) comprising from about 25 to about 50 mole percent of a poly(hydroxyalkanoate) selected from the group consisting of poly(hydroxyhexanoate), poly(hydroxyoctanoate), poly(hydroxydecanoate), and mixtures thereof.
[0069] In some embodiments, the PHA resin formulation may include from about 0.5 weight percent to about 15 weight percent of at least one plasticizer selected from the group consisting of sebacates, citrates, fatty esters of adipic, succinic, and glucaric acids, lactates, alkyl diesters, citrates, alkyl methyl esters, dibenzoates, propylene carbonate, caprolactone diols having a number average molecular weight from 200-10,000 g/mol, polyethylene glycols having a number average molecular weight of 400-10,000 g/mol, esters of vegetable oils, long chain alkyl acids, adipates, glycerol, isosorbide derivatives or mixtures thereof.
[0070] In other embodiments, the PHA resin formulation preferably also includes from about 0.1 weight percent to about 10 weight percent, or from about 0.1 to about 20 weight percent, of at least one nucleating agent selected from sulfur, erythritols, pentaerythritol, dipentaerythritols, inositols, stearates, sorbitols, mannitols, polyester waxes, compounds having a 2:1; 2:1 crystal structure chemicals, boron nitride, and mixtures thereof.
[0071] In some embodiments, the PHA resin formulation preferably includes from about 0 to about 1 percent by weight, such as from about 1 to about 0.5 percent by weight of a melt strength enhancer/rheology modifier. This melt strength enhancer may for instance be selected from the group consisting of a multifunctional epoxide; an epoxy-functional, styrene-acrylic polymer; an organic peroxide such as di-t-butyl peroxide; an oxazoline; a carbodiimide; and mixtures thereof.
[0072] Without being bound by theory, this additive is believed to act as a cross-linking agent to increase the melt strength of the PHA formulation. Alternatively, in some instances, the amount of the melt strength enhancer is from about 0.05 to about 3 weight percent. More preferred melt strength enhancers include organic peroxides, epoxides, and carbodiimides, preferably in an amount from about 0.05 to about 0.2 weight percent of the PHA formulation.
[0073] In some embodiments, the PHA resin formulation may include one or more performance enhancing polymers selected from poly(lactic acid), poly(caprolactone), poly(ethylene sebicate), poly(butylene succinate), and poly(butylene succinate-co-adipate), and copolymers and blends thereof. The performance enhancing polymers may be present in the formulation in a range of from about 1 to about 60 percent by weight. In some embodiments, from about 0.1 to about 15 weight percent of polylactic acid fibers are included in the polymer formulation for structural support of containers made from the polymer formulation.
[0074] In some embodiments, the polymer formulation includes from about 0.1 to about 5 weight percent of a reheat agent such as carbon black or another infrared absorbing material. In other embodiments, the polymer includes from about 0.1 to about 20 weight percent (preferably from about 0.1 to about 10 weight percent) of a filler selected from calcium carbonate, talc, starch, zinc oxide, neutral alumina, and mixtures thereof.
[0075] In some embodiments, the polymer formulation includes a slip agent. The most common slip agents are long-chain, fatty acid amides, such as erucamide and oleamide. One or more slip agents, for example calcium stearate or fatty acid amides is/are typically included in the polymer formulation. When included in the formulation, the amount of slip agent may range from about 0.1 to about 3 percent by weight of a total weight of the polymer formulation.
[0076] Exemplary formulations that may be used to make preforms for biodegradable containers according to the disclosure are shown in the following table.
TABLE-US-00005 TABLE 5 PHA PHA PHA polymer polymer polymer wt. % wt. % wt. % 3 mol % 6 mol % 9 mol % Weight % Weight % Weight % Hexanoate Hexanoate Hexanoate Polylactic Weight % Organic Weight % Weight % Polylactic Formula in polymer in polymer in polymer acid Pentaerythritol peroxide JONCRYL Inositol acid fibers 1 59.34 — — 39.56 1 0.1 — — — 2 69.23 — — 29.67 1 0.1 — — — 3 79.12 — — 19.78 1 0.1 — — — 4 99 — — — 1 — — — — 5 94 — — 5 1 — — — — 6 98.9 — — — 1 0.1 — — — 7 65.87 32.93 — — 1 0.2 — — — 8 98.8 — — — 1 — 0.2 — — 9 24.7 74.1 — — 1 — 0.2 — — 10 49.4 49.4 — — 1 — 0.2 — — 11 74.1 24.7 — — 1 — 0.2 — — 12 93.8 — — — 1 — 0.2 — 5 13 49.4 — 49.4 — 1 — 0.2 — — 14 74.1 — 24.7 — 1 — 0.2 — — 15 98.2 — — — 1 — 0.8 — — 16 97.8 — — — — — 0.2 2 —
[0077] With the formulations provided, PHA containers made from the preform formulations should degrade rapidly, but the degradation kinetics will depend on the design of the container, with thicker walled materials taking longer to fully degrade. It is preferred that the containers undergo degradation according to TUV Austria Program OK 12, have a shelf-life of at least 24 months, and have a moisture vapor transmission rate of about 20 g/m.sup.2/day or less as determined under ASTM E96. The containers may have a volume ranging from about 25 mL to about 40 L or more.
[0078] The present disclosure is also further illustrated by the following embodiments:
[0079] Embodiment 1. A preform for a biodegradable container wherein the preform comprises: from about 0.1 to about 10 weight percent of at least one nucleating agent; from about 0.05 to about 3 weight percent of at least one melt strength enhancer; and from about 40 to about 99 weight percent of a polymer derived from random monomeric repeating units having a structure of
##STR00004##
[0080] wherein R.sup.1 is selected from the group consisting of CH.sub.3 and a C.sub.3 to C.sub.19 alkyl group, wherein the monomeric units wherein R.sup.1═CH.sub.3 comprise 75 to 99 mol percent of the polymer and wherein the preform has a body having a uniform wall thickness throughout the body of the preform.
[0081] Embodiment 2. The preform of Embodiment 1, wherein the preform comprises from about 40 to about 99 weight percent of poly(hydroxyalkanoate) copolymer and from about 1 to about 60 wt. % additional additives.
[0082] Embodiment 3. The preform of Embodiment 2 wherein the poly(hydroxyalkanoate) copolymer comprises poly-3-hydroxybutyrate-co-3-hydroxyhexanoate (P3HB-co-P3HHx).
[0083] Embodiment 4. The preform of Embodiment 1, wherein the uniform wall thickness of the preform is selected from a thickness ranging from about 1.5 mm to about 5 mm.
[0084] Embodiment 5. The preform of Embodiment 1, wherein the preform has a length ranging from about 75 mm to about 120 mm.
[0085] Embodiment 6. The preform of Embodiment 1, wherein the preform, after being reheated has a final mass to height ratio ranging from about 0.4 to about 0.5 grams/mm.
[0086] Embodiment 7. The preform of Embodiment 1, wherein the preform has a finish selected from the group consisting of PCO 1810, PCO 1881, 30/25, 29/25, 26 mm finishes, and the like.
[0087] Embodiment 8. The preform of Embodiment 1, wherein the preform further comprises from about 1 weight percent to about 60 weight percent of polymers selected from the group consisting of poly(lactic acid), poly(caprolactone), poly(ethylene sebicate), poly(butylene succinate), and poly(butylene succinate-co-adipate), and copolymers and blends thereof.
[0088] Embodiment 9. The preform of Embodiment 1, wherein the preform further comprises from about 0.1 weight percent to about 5 weight percent of a reheat agent selected from the group consisting of carbon black, infrared absorbing pigments, and mixtures thereof.
[0089] Embodiment 10. The preform of Embodiment 1, wherein the preform further comprises from about 0.1 weight percent to about 10 weight percent of a filler selected from the group consisting of calcium carbonate, talc, starch, zinc oxide, neutral alumina, and mixtures thereof.
[0090] Embodiment 11. The preform of Embodiment 1, wherein the preform further comprises up to about 15 weight percent of a plasticizer selected from the group consisting of sebacates; citrates; fatty esters of adipic acid, succinic acid, and glucaric acid; lactates; alkyl diesters; alkyl methyl esters; dibenzoates; propylene carbonate; caprolactone diols having a number average molecular weight from about 200 to about 10,000 g/mol; poly(ethylene) glycols having a number average molecular weight of about 400 to about 10,000 g/mol; esters of vegetable oils; long chain alkyl acids; adipates; glycerols; isosorbide derivatives or mixtures thereof; poly(hydroxyalkanoate) copolymers comprising at least 18 mole percent monomer residues of hydroxyalkanoates other than hydroxybutyrate; and mixtures thereof.
[0091] Embodiment 12. The preform of Embodiment 1, wherein the preform is made by an injection molding or compression molding process.
[0092] Embodiment 13. A method for making a biodegradable container from the biodegradable preform of Embodiment 1 comprising forming the container in a process selected from the group consisting of reheat injection stretch blow molding, injection blow molding, and injection stretch blow molding.
[0093] Embodiment 14. The method of Embodiment 13, wherein the biodegradable preform is molded into a biodegradable container having a volume ranging from about 25 mL to about 40 L.
[0094] Embodiment 15. The preform of Embodiment 1, wherein the preform comprises from about 0.1 weight percent to about 10 weight percent of at least one nucleating agent selected from the group consisting of erythritols, pentaerythritol, dipentaerythritols, artificial sweeteners, stearates, sorbitols, mannitols, inositols, polyester waxes, nanoclays, polyhydroxybutyrate, boron nitride, and mixtures thereof.
[0095] Embodiment 16. The preform of Embodiment 1, wherein the preform comprises comprises from about 0.05 weight percent to about 3 weight percent at least one melt strength enhancer selected from the group consisting of a multifunctional epoxide; an epoxy-functional, styrene-acrylic polymer; an organic peroxide; an oxazoline; a carbodiimide; and mixtures thereof.
[0096] The foregoing description of preferred embodiments for this disclosure has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise form disclosed. Obvious modifications or variations are possible in light of the above teachings. The embodiments are chosen and described in an effort to provide the best illustrations of the principles of the disclosure and its practical application, and to thereby enable one of ordinary skill in the art to utilize the disclosure in various embodiments and with various modifications as are suited to the particular use contemplated. All such modifications and variations are within the scope of the disclosure as determined by the appended claims when interpreted in accordance with the breadth to which they are fairly, legally, and equitably entitled.