146 292 THS 100‘? LIBRARY Michigan State University This is to certify that the thesis entitled A STUDY OF MASS TRANSFER OF MOISTURE IN BIODEGRADABLE SHEETS AND RESINS presented by MAHESH KHURANA has been accepted towards fulfillment of the requirements for the MS. degree in Packaging “W Major Wure 87 v14 —- 09 Date MSU is an Affirmative Action/Equal Opportunity Employer ..-.-.—.--------—---.-------—.‘.--.-.-.-o--u--.--n-.-.-.-.-.— PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5108 K:IProj/Aoc&PrelelRC/DateDue.indd A STUDY OF MASS TRANSFER OF MOISTURE IN BIODEGRADABLE SHEETS AND RESIN S By Mahesh Khurana A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Packaging 2009 ABSTRACT A STUDY OF MASS TRANSFER OF MOISTURE IN BIODEGRADABLE SHEETS AND RESINS By Mahesh Khurana Through this research the moisture sorption of two biopolymers, Biomax® and Sorona®, was investigated. DuPont Biomax® is a hydro-biodegradable modified polyester. Sorona®, Poly(trimethylene terephthalate), is a thermoplastic polyester produced by condensation of terephthalic acid and 1,3-propanediol (derived form renewable sources). The moisture sorption profile of both polymers was assessed at 23 and 40°C using gravimetric technique. The moisture sorption isotherms of both polymers showed a positive temperature dependence, i.e. more moisture was sorbed at higher temperature. The solubility, diffusion and permeability coefficients of both polymers were also determined. The impact of processing was evaluated by comparing the sorption of moisture on resin and sheet of both polymers. The moisture sorption in resins was significantly lower than in sheets at either temperature, which is due the morphological changes during the extrusion. The effect of moisture on physical and mechanical properties of both polymers was evaluated. Moisture sorption in Sorona® has little or no impact on the tensile strength, Tg and crystallinity. In Biomax®, the water acts as a plasticizer as shown by a drop in glass transition temperature from 40 to 30°C. Also, the mechanical properties of ® Biomax were drastically reduced after the moisture sorption. 5a my fiamily and [cicada iii ACKNOWLEDGEMENTS I am really thankful to Dr. Maria Rubino, my major advisor for her unlimited and invaluable support, guidance, and mentoring through out the course of my Master’s degree. She was always there for the support and guidance, whenever I needed. I would also, like to thank my other committee members, Dr. Rafael Auras and Dr. Laurent Matuana, for their support and suggestions which helped me a lot in my research. I also thank the Center for Food & Pharmaceutical Packaging Research (CFPPR) for the financial support to this project. Next I would like to thank my family, especially my brother, without their support I wouldn’t have been able to come to US for my Masters. Also the family and fi'iends back in India who prays for my well being. I am also thankful to the faculty and staff of The School of Packaging and a special thank to the friends at school and also outside the school for their help. I would really like to add here my personal appreciation to Dr. A.F. Venero and Marcelo Man'cheno from VTI Corporation for their suggestions and support. Last but not least, I would like to thank GOD for everything. Thank you all Mahesh Khurana iv Table of Contents List of Tables .................................................................................................................... vii List of Figures ................................................................................................................. viii Chapter 1: Introduction ................................................................................................. 1 1. Background ................................................................................................................... 1 2. Scope of the Study ........................................................................................................ 4 3. References ..................................................................................................................... 5 Chapter 2: Background and Methodology ................................................................... 7 1. Introduction ................................................................................................................... 7 2. Biodegradable Polymers ............................................................................................... 7 2.1. Classification of Biodegradable Polymers ............................................................. 7 2.1.1. Renewable Source-based Polymers ............................................................ 8 2.1.2. Petroleum-based Biodegradable Polymers ................................................. 8 2.1.3. Polymers from Mixed Petroleum and Renewable Sources ........................ 9 2.2. DuPont Biomax® ................................................................................................... 9 2.3. DuPont Sorona® ................................................................................................... 11 3. Mass Transfer Phenomenon ........................................................................................ 12 3.1. Sorption ................................................................................................................ 13 3.2. Diffusion .............................................................................................................. 14 3.3. Permeability.......... ............................................................................................... 15 3.4. F ickian and Non-Fickian Kinetics ....................................................................... 16 3.5. Parameters Affecting Permeability ...................................................................... 17 4. Methods for Studying the Sorption in Polymeric Materials ....................................... 19 4.1. Gravimetric Method ............................................................................................. 20 5. Symmetrical Gravimetric Analyzer (SGA-lOO) ......................................................... 22 6. Noise Quantification ................................................................................................... 24 7. Consistency Test ......................................................................................................... 26 8. References ................................................................................................................... 27 Chapter 3: A Study of Mass Transfer of Moisture in Biodegradable Sheets and Resins .................................................................................................. 32 1. Introduction ................................................................................................................. 32 2. Theoretical Background .............................................................................................. 35 2.1. Sorption by Polymer Film ................................................................................... 35 2.2. Consistency Test .................................................................................................. 36 3. Experimental ............................................................................................................... 37 3.1. Materials .............................................................................................................. 37 3.2. Differential Scanning Calorimeter ....................................................................... 38 3.3. Instrument SGA-lOO ............................................................................................ 39 3.4. Noise Quantification ............................................................................................ 4O 3.5. Sorption Experiment ............................................................................................ 4O 4. Results and Discussion .............................................................................................. 41 4.1. Physical Properties .............................................................................................. 41 4.2. Instrument Noise and Drift ................................................................................. 41 4.3. Equilibrium Criterion Determination .................................................................. 45 4.4. Moisture Uptake in Sheets .................................................................................. 45 4.5. Consistency Test and Correction ........................................................................ 48 4.6. Sheet Moisture Sorption Results ......................................................................... 51 4.7. Effect of Temperature on Permeability, Diffusion, and Solubility ..................... 56 4.8. Resin Moisture Sorption Results ......................................................................... 57 5. Conclusions ................................................................................................................ 58 6. References .................................................................................................................. 59 Chapter 4: The Effect of Moisture Sorption on the Physical and Mechanical Properties of Biomax® and Sorona® ....................................................... 62 1. Introduction ................................................................................................................ 62 2. Methodology .............................................................................................................. 63 2.1. Polymer Processing ............................................................................................. 63 2.2. Conditioning of the Samples ............................................................................... 64 2.3. Physical Properties .............................................................................................. 64 2.3.1. Differential Scanning Calorimeter (DSC) ................................................ 64 2.3.2. X-Ray Diffraction (XRD) ......................................................................... 65 2.3.3. Dynamic Mechanical Analyzer (DMA) ................................................... 65 2.4. Mechanical Properties ......................................................................................... 66 2.5. FT-InfraRed ......................................................................................................... 66 3. Results and Discussion ............................................................................................... 67 3.1. Physical Properties .............................................................................................. 67 3.2. Mechanical Properties ......................................................................................... 70 3.3. FT-IR Results ...................................................................................................... 72 4. Conclusions ................................................................................................................ 73 5. References .................................................................................................................. 74 Chapter 5: Conclusions ................................................................................................ 76 1. Conclusions ................................................................................................................ 76 2. Future Work Recommendations ................................................................................. 78 vi List of Tables Chapter 2: Table 2.1: Physical and mechanical properties of Biomax® 4026 .................................... 10 Table 2.2: Physical and mechanical properties of Sorona®, PTT ..................................... 11 Chapter 3: Table 3.1: Processing condition for Biomax® and Sorona® ............................................. 38 Table 3.2: Regression analysis of the equipment’s noise and drift ................................... 44 Table 3.3: Average Solubility, Diffusion and Permeability coefficients for Biomax® and Sorona® sheets at 23°C and 40°C ............................................................. 55 Table 3.4: Enthalpy of sorption and activation energy of Biomax® and Sorona® sheets (average of 3 runs 1 SE.) ................................................................................ 56 Table 3.5: Moisture uptake in Biomax® and Sorona® resin after 1400 minutes .............. 57 Chapter 4: Table 4.1: Physical properties of dried and sorbed Biomax® and Sorona® samples ........ 68 vii List of Figures Chapter 2: Figure 2.1: Schematic of Symmetrical Gravimetric Analyzer (SGA-100) ....................... 23 Chapter 3: Figure 3.1: Schematic of Symmetrical Gravimetric Analyzer (SGA-lOO) ....................... 39 Figure 3.2: Percent weight change vs. time and linear regression line for a 50 mg standard weight at 40°C, 90% RH ................................................................. 42 Figure 3.3: Residual output vs. time for 50 mg standard weight at 40°C, 90% RH ......... 43 Figure 3.4: Average percent weight gain (3 runs) vs. time (min) for Biomax® sheets at 23°C and 40°C ............................................................................................ 46 Figure 3.5: Average percent weight gain (3 runs) vs. time (min) for Sorona® sheets at 23°C and 40°C ............................................................................................ 48 Figure 3.6: Experimental Mt/Moo (before correction) and theoretical Mt/MOo vs. square root of time (secondm) for a Biomax® sheet at 23°C and 30% RH ............... 47 Figure 3.7: Average of K values of different relative humidities for Biomax® and Sorona® sheets before and afier correction at 23°C and 40°C ....................... 49 Figure 3.8: Experimental Mt/M00 after correctiong and theoretical Mt/M00 vs. square root of time (secondl/ ) for a Biomax sheet at 23°C and 30% RH .............. 50 Figure 3.9: Moisture sorption isotherms of Biomax® and Sorona® sheets at 23°C and 40°C ......................................................................................................... 52 Chapter 4: Figure 4.1: DMA results for Biomax® dried and sorbed samples .................................... 68 Figure 4.2: Refractogram from XRD analysis for Biomax® dried sample ....................... 69 ® Figure 4.3: Stress-strain curves for Biomax® and Sorona samples ................................ 71 ® Figure 4.4: Mechanical properties of dried and sorbed Biomax® and Sorona samples. 71 Figure 4.5: IR Spectrum of Biomax® sheet before and after moisture sorption ............... 72 viii Chapter 1 Introduction 1. Background The US packaging industry uses around one-third of the total plastics produced in the country.1 Plastic is the largest segment of the packaging industry, accounting for approximately 50% of the total materials used in industry.2 Most of the plastics used currently are derived from the petroleum sources and do not degrade easily after disposal. In 2006, only 10% of the total packaging plastic was recycled; the remainder landed in landfills, accounting for 6% of the total Municipal Solid Waste (MSW).3 Dwindling petroleum sources and landfill sites have prompted the development of alternative and environmentally friendly polymers. In the past few years, many new alternative polymers have been developed that are either derived from non-petroleum sources or are biodegradable. A few examples of such polymers are Poly(lactic acid) (PLA), Poly(s- caprolactone)(PCL), and Polyhydroxylalkanoates (PHA).4 The global production of biodegradable polymers in 2006 has increased 20-folds since 1995,5 but it is still just a small fraction of the total polymer production. The major obstacle to commercialization of these ‘novel’ polymers in the packaging industry is their cost and the limited knowledge about their performance properties. Especially the barrier properties of such polymers to different gases and vapours dictate the use of polymer in food and pharmaceutical industry. Polymeric packaging materials are permeable to small molecules like water vapour, organic vapours, and gases. Because these permeants are often responsible for product deterioration, their permeation through the polymer determines the shelf life of the product. Water is one of the permeants responsible for the deterioration of most food and pharmaceutical products. Therefore, a thorough understanding of water vapour permeation through the new alternative biodegradable polymers is of great commercial importance. Permeation process in polymers is characterized by the sorption of compounds by the polymer, their diffusion through the polymer, and finally desorption of the permeant from the polymer to product or environment. Sorption is the uptake of the permeant, water vapour, gases, or liquid, by the polymer membrane. Sorption of the permeant molecule depends on the affinity between permeant and polymer.6 After sorption, the permeant diffuses through the polymer’s free volume from the high concentration to low concentration (or chemical potential) side and polymer characteristics also play an important role. Thus permeability of gases through common packaging polymers can be defined as: P = D * S (1) where P is the permeability coefficient, D is the Fickian diffusion coefficient and S is the solubility coefficient. Extensive research had been conducted for the evaluation of mass transfer properties of polymers using various methods. While isostatic and quasi-isostatic methods are generally used to evaluate the permeation of the permeant through the polymer membrane;7'” gravimetric methods, using a spring balance, an electrobalance, or a quartz crystal microbalance, evaluate the permeant sorbed in the polymer.”'16 The gravimetric sorption method has the advantage that it can record real time mass (moisture) uptake in a controlled environment at both the steady state as well as during the transient state. The moisture content at steady state at different water activities can be used to generate the moisture sorption isotherm, defined as the relation between the moisture and polymer membrane at a constant temperature and pressure. The moisture content at the steady state is used to determine the solubility coefficient (S) by the following relation: Moo 5 = (2) v.p where M00 is mass at steady state, v is the volume of the polymer and p is the permeant force in unit of concentration or pressure. The transient state and the steady state data can be used in determination of diffusion coefficient (D).17 As discussed earlier, several alternative polymers have recently been developed. Biomax® and Sorona® are two such alternative polymers developed by DuPont. Biomax® l8, 19 is an aliphatic-aromatic hydro-biodegradable polyester. It is a co-polymer of polyethylene terephthalate (PET), produced by adding up to three different monomers to ® can be used for oriented make this polymer degradable through hydrolysis.19 Biomax films, blown films, molded plastic articles, or coating in disposable products such as bowls, plates, cups, and sandwich wraps.20 To the best of the author’s knowledge no research has been conducted to study the moisture uptake of Biomax®. Sorona®, Poly(trimethylene terephthalate) (PTT), derived from renewable corn sugar, is a thermoplastic polyester produced by condensation of 1,3-propanediol and terephthalic acid.” PTT was developed several years ago but was not commercialized due to high costof production. However recent developments have reduced the cost significantly. Sorona® has several unique characteristics such as high elasticity and recovery as compared to PET or nylon and better chemical properties as compared to PET,22 hence it is gaining a lot of attention in packaging and textile industry. Research had been conducted to tailor the physical and mechanical properties of Sorona® through blending it with other polymer or nano-composites,2]‘ 23 but fewer researchers have studied the moisture uptake of Sorona®. 2. Scope of the Study The main goal of this study was to generate a moisture sorption profile for Biomax® and Sorona® sheets and resins using a gravimetric method and to generate the moisture sorption isotherms of both polymers sheets at 23 and 40°C. The effect of processing, from resin to polymer, on the moisture sorption was evaluated. Lastly, the effect of moisture sorption on physical and mechanical properties of both polymers was investigated. 3. References: l. 10. ' 11. 12. 13. Szabo, F. Int Polym Sci Technol 2001, 28, 11, T/1-9. Tapuriah, V. The Future of Plastics in Packaging; Frost & Sullivan: 6 May, 2003. Municipal Solid Waste Generation, Recycling, and Disposal in the United States: Facts and Figures for 2006; United States Environmental Protection Agency: Washington, DC, 2007. Gross, R. A.; Kalra, B. Science 2002, 297, 5582, 803—807. The Future of Global Markets for Biodegradable Packaging; Pira International Ltd: 2006. Hernandez, R. J.; Selke, S. E. M.; Culter, J. D., In Plastics Packaging: Properties, Processing, Applications and Regulations. First ed.; Hanser Gardner Publications, Inc.: 2000. Gavara, R.; Catala, R.; Hemandez-Munoz, P.; Hernandez, R. J. Packag Technol and Sci 1996, 9, 215-224. Duncan, B.; Urquhart, J .; Roberts, S. Review of Measurement and Modelling of Permeation and Diffusion in Polymers; National Physical Laboratory: 2005. Yasuda, H.; Rosengren, K. J Appl Polym Sci 1970, 14, 11, 2839-2877. Apostolopoulos, D.; Winters, N. Packag Technol and Sci 1991, 4, 131-138. Barr, C. D.; Giacin, J. R.; Hernandez, R. J. Packag Technol and Sci 2000, 13, 4, 157-167. Hernandez, R. J .; Gavara, R. J Polym Sci, Part B: Polym Phys 1994, 32, 2367- 2374. Hernandez, R. J.; Giacin, J. R.; Grulke, E. A. J Membr Sci 1992, 65, 1-2, 187- 199. 14. 15. 16. ' 17. 18. 19. 20. 21. 22. 23. Wong, 8.; Zhang, Z.; Handa, Y. P. J Polym Sci, Part B: Polym Phys 1998, 36, 2025-2032. Wong, C. H.; Bhethanabotla, V. R. Fluid Phase Equilib 1997, 139(371). Oliverira, N. S.; Oliverira, J .; Gomes, T.; F erreira, A.; Dorgan, J .; Marrucho, I. M. Fluid Phase Equilib 2004, 222-223, 317-324. Crank, J., In The Mathematics of Diffusion. Second ed.; Oxford University: 1975. Nagarajan, V.; Singh, M.; Kane, H.; Khalili, M.; Bramucci, M. J Polym Environ 2006, 14, 3, 281-287. DuPont Launches Biodegradable Polyester - Biomax®, Press Release. http://www.(mont.com.tw/020604-e.htm (April, 2008) Leaversuch, R., Biodegradable Polyesters: Packaging Goes Green. Plastics Technology 2002. Liu, W.; Mohanty, A. K.; Drzal, L. T .; Misra, M.; Kurian, J. V.; Miller, R. W.; Strickland, N. Ind Eng Chem Res 2005, 44, 4, 857-862. Kurian, J. V. J Polym Environ 2005, 13, 2, 159-167. Khonakdar, H. A.; Jafari, S. H.; Asadinezhad, A. Iran Polym J 2008, 17, 1, 19-38. Chapter 2 Background and Methodology 1. Introduction The first part of this chapter presents an overview of biodegradable polymers and their classification based on raw materials. The second part focuses on the mass transfer phenomenon, followed by sorption and diffusion kinetics. The last part includes the details of the gravimetric equipment used for this study and noise quantification. 2. Biodegradable Polymers Biodegradable polymers can be define as polymers whose chemical structure changes significantly under specific environment condition as the action of natural occurring micro-organisms. Bio-based polymers can be defined as polymers produced from renewable agricultural or biomass feedstock. Biodegradable or bio-based polymers can make the base for environment friendly and eco-efficient products that can compete and capture current market dominated by petroleum-based polymers. 2. 1 Classification of Biodegradable Polymers Different approaches have been used to formulate biodegradable polymers. Depending on the sources of raw materials, biodegradable polymers can be divided in three categories:" 2 a) Renewable source-based biodegradable polymers b) Petroleum- based biodegradable polymers 0) Polymers from mixed petroleum and renewable sources 2. 1.] Renewable Source-based Polymers Poly(lactic acid) (PLA) obtained from a renewable agricultural source (corn) is synthesized by condensation polymerization of lactic acid or ring opening polymerization of lactide.”4 PLA is currently used in packaging as thermoformed containers for fresh produce and short shelf life products.3’ 5 Poly hydroxyalkanoates (PHA) is a class of biodegradable polymers produced from renewable resources by microbial fermentation. PHA alone is very brittle and difficult to process, therefore various copolymers have been biosynthesized.6 2.1.2 Petroleum-based Biodegradable Polymers Petroleum-based biodegradable polymers can be divided into two main categories: aliphatic biodegradable polyesters and aromatic-aliphatic co-polyesters. Aliphatic Polyesters: Poly(e-caprolactone) (PCL), is a biodegradable thermoplastic obtained by ring opening polymerization of e-caprolactone (obtained form crude oil) using a catalyst.7 PCL has good barrier properties and is easy to process, but due to the high cost it is generally blended or copolymerized.5’ 8 Poly(butylene succinate) (PBS) is a petroleum-based polymer made by condensation polymerization of 1,4- butanediol with aliphatic dicarboxilic acids. Aliphatic-Aromatic Co-polyesters: These are generally based on terephthalic acid. Poly(butylenes adipate-co-terephthalate) (PBAT) is a thermoplastic co-polyester produced by condensation of 1-4-butanediol, terephthalic acid and adipic acid. PBAT has barrier and mechanical properties similar to LDPE and has been approved for food contact applications.9 Easter Bio® from Eastman Chemicals and Biomax® from DuPont, a hydro-biodegradable polyester, also belong to petroleum-based polymer category.lo Other petroleum based polymers are Polyesteramides (PEA), made by copolycondensation of polyamide and adipic acid.” Poly(vinyl alcohol) (PVOH) is manufactured by hydrolysis of poly(vinyl acetate) in alcohol and has been reported to be biodegradable. I 2 2. 1.3 Polymers from Mixed Petroleum and Renewable Sources Poly(trimethylene therephathalate) (PTT), tradenarne Sorona® from Dupont, is a 3-carbon glycol terephthalate (3GT) synthesized by condensation of 1,3-propanediol and terephthalic acid.” Propanediol can be produced from renewable sources (corn). PTT has mechanical and barrier properties similar to PET.l4 Other polymers in this class are Polyurethanes (PU) manufactured from polyols (vegetable oil based) and isocyanate.7 Various biodegradable blends have been studied, such as starch based blends, PLA based blends or PHA based blends. In this study we focused on two of the alternative polymers——Biomax® and Sorona®. 2.2 DuPont"! Biomax® Biomax® (4026) is a hydro-biodegradable modified polyester, developed by E.I. DuPontTM de Nemours & Co. (Wilmington, DE). The material is based on polyethylene terephthalate (PET) and is synthesized by the polymerization of terephthalic acid, ethylene glycol, glutaric acid, and sulfonic acid saltm’ '5 Properties of Biomax® are shown in Table 2.1. Table 2.1 : Physical and mechanical properties 0fBi0max® 4026* Properties Density, g/cm3 1.35 Glass Transition Temperature (Tg), °C 30 Melting Temperature (Tm), °C 195 Decomposition Temperature, °C 340 Flexural Modulus, GPa 3 Tensile Strength at Break, MPa 30 * Published on Matweb16 Biomax® has been awarded a ‘COMPOSTABLE’ logo by The Biodegradable Products Institute (BPI),l7 because it meets ASTM D 6400-99 “Standard Specification of Compostable Plastics”.'8 The polymer can be incorporated with up to three aliphatic monomers according to the end-use. These monomers create weak spots, thus making Biomax® degradable through hydrolysis. The moisture cleaves the polymer’s larger molecules into smaller molecules, which are then consumed by natural micro-organisms. Although Biomax® is intended mainly for composting, it can also be recycled, incinerated, or landfill.19 Biomax® has been blended with soy proteins and polycaprolactone (PCL), and with cotton (Bionature by Kurabo, Japan).2°’ 2' It is easy to process and can be processed in standard PET equipment with minor changes. It can be used as blown film, oriented film, or molded articles. Its major applications can be single-use products, such as waste bags, blister packs, geotextiles, seed mats and coating for disposable eating utensils (Cups, bowls or plates)”: 22 10 2.3 DuPontm Sorona® . Sorona® is the trade name for Poly(trimethylene terephthalate) (PTT) manufactured by E.I. DuPontTM de Nemours & Co. (Wilmington, DE). PTT is a condensation polymer of 1,3-propanediol (PDO) and terephthalic acid (TPA). DuPont has developed a technique to produce PDO from renewable resources (corn) or via biological processes.[3 Sorona®, a three carbon glycol terephthalate (3GT), can also be produced using only petroleum resources. Both type of polymers, petroleum-based and bio-based, are expected to have similar properties as they have the same chemical structure. Table 2.2: Physical and mechanical properties of Sorona®, PTT” ’4 Properties Density, g/cm3 1.33 Glass Transition Temperature (Tg), °C 45-55 Melting Temperature (Tm), °C 228 Flexural Modulus, GPa 3.76 Tensile Strength, MPa 67.6 Sorona®, 3GT is member of the thermoplastic aromatic polyester family, which includes polyethylene terephthalate (PET)-2GT and polybutylenes terephthalate (PBT)- 4GT.'3‘ 23 Sorona® glass transition temperature is in the range of 45-55°C, which is lower than that of PET (80°C), but higher than that of PET (25°C).l4 Sorona® has a semi- crystalline molecular structure with a zigzag shape that gives it excellent stretch recovery and tensile and compressive properties. Sorona® has comparable strength, stiffness, and heat resistance as of PET. As expected from linear aromatic polyesters, Sorona® has a good barrier to moisture, is dimensionally stable, and has good weather and chemical 11 resistance. Sorona® can also be used as engineering therrnoplastics because of its good thermal and mechanical properties.”’ 24 Sorona® can be cast into films at a setting comparable to polypropylene. Sorona® has been blended with other polymers to offset its relatively high cost and tailor to specific perfonnance-cost profile.14 Sorona® has also been used as Polymer/Clay nanocomposites (PCNs), produced by dispersing nanoscale composites in a polymer matrix. PCN possesses the excellent combination of barrier and mechanical properties, which may eliminate the need for multilayer polymers for packaging application (reviewed by Khonakdar, et al.).14 3. Mass Transfer Phenomenon Historically, the main purpose of a package was containment (cellophane used for bread in 1930’s), but today packaging plays more active role in protecting the product, providing utility and communication. One of the major roles of packaging is to provide shelf life to the product. Currently, plastic is the leader in packaging industry because of its benefits like light weight, appearance, aesthetics, economy, and many others. Plastics allow permeability of small molecules to through them. Polymer allows moisture, aroma, and gases to pass through them, which can modify or deteriorate the product contained by the package. Although this mass transfer can also be used to improve shelf life of some products, for example modified-atmosphere packaging (MAP).25 Mass transfer or permeation processes in polymers is characterized by the sorption of compounds by the polymer, their diffusion through the polymer, and finally their desorption from the polymer to product or environment. 12 3.1 Sorption Sorption is the uptake of the permeant, such as moisture, flavor, aroma or colorant by the polymeric packaging material. Sorption of the permeant molecule depends on the affinity between permeant and polymer. When a polymer comes in contact of a liquid or vapour phase, sorbates in both phases are exchanged until their potentials become equal. The equilibrium of every sorbate can be established by a partition coefficient. At low concentration levels, as in case in packaging, the mixing of permeant with polymers behaves as ideal solution. The relationship between sorbate concentration and partial pressure follows Henry’s law of linear sorption isotherm?" Ci 2 S . Pi (1) where C ,- is concentration of the permeant S (Solubility Coefficient) is Henry’s Law proportionality constant and p,- is the equilibrium vapor pressure of the permeant. Henry’s law holds only at low concentration or when there is no interaction between the polymer and permeant, as in case of Oz and N2 at low pressures or moisture 26. 27 sorption in hydrophobic polymer. The solubility coefficient (S) is an equilibrium partition coefficient for distribution of the penetrant between polymer phase and vapor phase and is given as: C _ p S_ Cv (2) where Cp is the concentration of penetrant in the polymer and CV is the concentration of penetrant in the vapor phase at the steady state. 13 3.2 Diffusion Diffusion can be defined as the movement of substance within itself or another substance. Diffusion, for polymeric packaging materials, can be defined as the process through which the matter (permeant) transport from high concentration side to low concentration side as a result of random molecular motions. Diffusion coefficient (D) is the quantitative measurement of the rate at which a penetrant diffuses. D is defined as the rate of transfer of the penetrant across unit area of a section, divided by the space gradient of concentration. This definition holds good only for the one dimensional diffusion and when diffusion is normal to the section. The basic equations describing above definition are Fick’s first law:28 F=— 99 6x (3) where F is the rate of transfer, D is the diffusion coefficient, C is the concentration of penetrant, x is space coordinate . The negative sign in Eq. 3 indicates that the permeant molecules flow from high concentration side to low concentration side. For unsteady or transient state, the rate of flow of permeant can be described by Fick’s second law which can be written as 2 a z Di; 6: ax (4) where t is the time. To obtain the flux (F) or D from above equations, initial and boundary conditions associated with the experimental method are needed. The solution of 14 Eq. 4 is given analytically and a power-series of solution is derived. Crank28 presented simplified equations related to the first approximation of the power series. Thus the values of D obtain through these equations are only approximate values. Mass sorbed on the polymer film as a function of time provides the necessary information to calculate the diffusion coefficient of the permeant in the polymer. 3.3 Permeability Permeability can be defined as the transfer of gases, vapors, liquid through a homogeneous packaging material. It is the mass transfer of the permeants from higher concentration side to the lower concentration side through the polymer. Mass transfer of permeant through cracks, perforation or other defect is not considered as permeability. Permeability is the overall process of sorption of permeant in the polymer, its diffusion through the polymer and finally desorption on other side. Permeability of simple gases through common packaging polymer at steady state is given by following relation: P = D . s (5) where P is the permeability coefficient, D is the F ickian diffusion coefficient and S is the solubility coefficient. The above equation holds at low concentrations of the permeant and when there is no interaction between permeant and polymeric material. The permeability diffusion and solubility coefficients of a material are dependent on the temperature and sometimes the environment relative humidity (RH). The dependence of P, D and S can be described by a Van’t Hoff-Arrhenius equation: S(T)=Soexp(—AHS /RT) (6) D(T)=Doexp(-ED/RT) (7) P(T)=PoeXP(-Ep/RT) (8) 15 where AHS = enthalpy of sorption ED = activation energy of diffusion Ep = activation energy of permeation R = Gas constant and, T = Temperature Enthalpy of sorption (AHS) can also be considered as sum of two terms AHS = AHC + AH," (9) where AHC is the enthalpy of condensation of pure gaseous penetrant to the liquid phase and AH," is the partial molar enthalpy of mixing the condensed penetrant with polymer segments. As the solubility depends on the heat of sorption and unlike activation energy of diffusion, it can take positive or negative values. 3.4 F ickian and Non-Fickian Kinetics The diffusion behavior of polymer films can be classified in three classes on the basis of relative rates of diffiision and polymer relaxation:29 a) Case I or Fickian diffusion in which diffusion is a function of concentration, diffusion is much less than relaxation. b) Case 11 diffusion, where the diffusion is very rapid as compared to relaxation. c) Non-Fickian or anomalous diffusion, where the rate of polymer relaxation is almost same as rate of diffusion. According to Fick’s law, distribution of diffusant during sorption is governed by the one-dimensional differential equation for diffusion, given by Eq. 3. Assumption for Eq. 3 is that when the ambient pressure changes from a initial to a final value, concentration at the film surface also changes to final value instantaneously. A sorption 16 curve is a plot of the amount of vapor absorbed or desorbed as a function of square root of time. Sorption curve which follows the above-mentioned assumption of D and surface concentration is known as Fickian or normal type sorption. The fickian sorption kinetics was also explained on the basis of sorption and desorption curves by Crank.28 If diffusion is only dependent on the concentration, then in the initial stage the curves are linear; for absorption this is true up to 60% or more of Moo. / . '2 axrs and Above the linear portion the sorption curves become concave towards t steadily approaches the final steady state value. Diffusion in some systems is found to be dependent on other factors such as time, polymer relaxation, etc. Generally, this is the case in glassy polymer systems and is called anomalous or non-Fickian diffusion. In such cases the diffusion rate is on the order of the polymer relaxation time scale. A simple deduction of diffusion coefficients from experiment showing this behavior is difficult and often explained by Flory Huggins30 and clustering effect“ wherein the first mechanism accounts for increase in diffusion coefficient, the other explains decrease in diffusion coefficient. 3.5 Parameters Affecting Permeability There are many factors that affect the permeability, sorption and diffusion, of packaging materials towards moisture, gases, and organic vapors; these factors can be environmental (temperature, relative humidity), polymer (chemical structure and morphology), permeant (molecular size, concentration). Permeability or sorption in polymers has been found to be different in the regions below and above T8 of polymer. As also explained above in case of glassy polymer, below T8, diffusion is generally found to anomalous or non-Fickian. Glassy polymers are 17 not in a state of true thermodynamic equilibrium and have very long relaxation times. These long relaxation times let the polymer to homogenize with the penetrant environment. Generally, to define the sorption and diffusion in this state a dual mode sorption model theory is used.32 Normally the diffusion at temperature above T8 is rather simple and follows Fickian kinetics. At temperature above T8, the polymer is in rubbery state and its molecular chains are free to move. The micro-Brownian motion of polymers molecules at temperature above Tg enable the polymer to reach the equilibrium rapidly and diffusion is not time dependent. Diffusion in semi-crystalline polymers and polymers with‘rigid chain conformations is usually found to non-Fickian even above the Tg. The barrier properties of a polymer also depend on its chemical structure and morphology. The barrier properties of polymer will increase with the increase in the crystallinity and orientation. It has been proved that the permeation of molecules take place only through the amorphous region of the polymer, thus increasing the crystalline region will increase the barrier properties.33 Orientation of polymer brings the chains closer and the molecular mobility in oriented region decreases, thus decreasing the permeability. Generally with the increase in temperature the segmental motion of polymer chains increases and thus increasing the free volume of the polymer and the diffusion of penetrant through the polymer. Also with the increase in temperature the permeant molecules have the required energy to diffiise through a polymer. The effect of temperature is best defined by the Arrhenius-type relationships given by Eq. 6-8. Generally barrier properties of the polymer decreases with increase in temperature. But few polymers have been reported which do not follow this trend. Polystyrene and 18 Polylactide have been reported to have negative activation energy.3 Temperature also affects the partition coefficient, thus affecting solubility. With the increase in temperature the solubility decreases. There are few exception to this rule also, e. g., the partition coefficient of SARAN and ethyl acetate, n-hexanal and d-limonene were found to decrease at 0.2 vapor activity.34 The diffusion of a penetrant through any polymer will be governed by the molecular size and vapor pressure of the penetrant. As the energy required by a smaller and lighter molecule to move is low, therefore they can easily diffuse through polymers.26 Diffusion of permeant through polymer is also affected by the vapor pressure of the permeant, which defines the mobility of permeant at particular temperature. The sorption of a molecule in a polymer will be affected by the affinity of the penetrant and polymer. 4. Methods for Studying the Sorption in Polymeric Materials The first study of gas permeation through a polymer was conducted by Thomas Graham in 1829.35 Since then extensive research had been conducted for the evaluation of mass transfer properties of polymers using various methods. While isostatic and quasi- isostatic methods are generally used to evaluate the permeation of the permeant through the polymer membrane?“10 gravimetric methods, using a spring balance, or an electrobalance, or a quartz crystal microbalance, evaluate the permeant sorbed in the polymer.4045 For this research the moisture sorption in two polymers was evaluated using a gravimetric method. 19 4.1 Gravimetric Method Gravimetric technique is considered as a type of isostatic technique. In this technique the polymer sample is exposed to the permeant and weight change is recorded as the function of time. The gravimetric sorption method has the advantage that it can record real time mass (moisture) uptake in a controlled environment at both the steady state (M00) as well as during the transient state (Mt). Thus it is possible to obtain both sorption isotherms (from steady state uptake) and the diffusion coefficient (fiom transient state sorption). The gravimetric sorption method has been adopted by many researchers to measure the sorption of moisture or organic vapors in polymer. Different types of balance for this technique have been reported, such as Cahn 40, 41, 43, 46, 47 . - 4 ,4 .4 suspensmn electrobalance, quartz crystal microbalance, 5 8 9 Rubotherm magnetic suspension balance,50 or spring balance.5 "53 The appropriate solution of the diffusion equation (Fick’s laws) for a gravimetric technique, given by Crank,28 can be written as: M __8_ °° — D(2n +1)27r2t Moo — ”2 n=0( (2n+1)2 exp [2 (11) where l is thickness of the sheet, M, is the amount of penetrant sorbed by polymer sheet sample at time t, ‘ M00 is steady state sorption after theoretical infinite time Assumptions for Fick’s equations and Eq. (11) are: temperature and pressure remains constant, polymer sheet has a constant thickness, during the experiment, moisture uptake follows fickian behavior (D is independent of concentration), vapor 20 concentration on both sides of the sheet is constant, and sheet is initially free of penetrant 26’ 28. The Eq. 11 can be solved for Mthoo =0.5 with approximate error of 0.001 %: 2 D = 0.049 [— (12) t 1 / 2 where t1/2, half time, is the time when Mt/Mw =0.5 and can be determined experimentally by plotting Mt/M00 vs. square root of time. The solubility coefficient (S) is defined as the equilibrium partition coefficient for the distribution of permeant between the polymer phase (Cp) and vapor phase (CV) and is expressed as the mass of permeant sorbed at steady state by a unit volume of polymer per unit of driving force (partial pressure). 5 = Ea = £49. CV v.P (13) where M00 is the mass of the vapor absorbed by the polymer at equilibrium, v is the volume of the polymer, p is the permeant force in units of concentration or pressure. S is calculated from the sorption experiments by dividing the steady state sorption (kg of sorbate / kg of polymer) by density of polymer and vapor pressure. Once the solubility and diffusion coefficient are determined, the permeability coefficient can be calculated using Eq. 1. 21 For this study a symmetrical gravimetric analyzer (SGA-lOO) from VTI Corp was utilized. 5. Symmetrical Gravimetric Analyzer (S GA-I 00) A Symmetrical Gravimetric Analyzer (SGA-100, from VTI Corp., Hialeah, FL) equipped with a Cahn Electrobalance Model D-200 (Cahn Instruments Co., Cerritos, CA) was used to measure moisture sorption in the polymer sheets and resins. The SGA-lOO 40’ 54 and is capable of generating uses a continuous flow method for the sorption studies, relative humidity from 2 to 98% with variability of i1.0% RH. The operational temperature range of the equipment is from 5° to 60°C with variability of i0.1°C. The main components of the SGA-lOO are shown in Fig. 2.1. The equipment is divided into three different sections each of which is maintained at different, constant temperature. 22 Electrobalance Chamber Thermal Zone 1 Sample Water Chamber Bath Thermal Zone 2 Vaporizer . . . L? / Dew Point Analyzer 1 l Vapor Mass Flow ,_ ; Generation Controllers M 1. Chamber L : . t ' Thermal Zone3 Figure 2.1 : Schematic of Symmetrical Gravimetric Analyzer (SGA-I 00) The lower section is the vapor generation chamber, which includes a vaporizer, a chilled mirror Dew Point Analyzer (DPA) and the mass flow controllers. The temperature of this section is maintained at 15°C above the experiment temperature, to prevent vapor condensation in the tubing. The water vapor activity is monitored by a chilled mirror dew point analyzer (DPA), which measures the dew point of the vapors before it enter into the sample chamber and send a signal to the software. Software then send the signals to the mass flow controllers, which generates the target relative humidity by mixing wet and dry 23 streams of nitrogen gas. In case of the organic vapors, the vapor activity is monitor by measuring the sample chamber temperature and the vaporizer temperature and the Wagner Equation is used to adjust specific vapor activity.50’ 55 The middle section contains double walled aluminum block which includes the sample and reference chamber. Both chambers are insulated and of identical size (10.8 x 3.8 x 3.8 cm). The aluminum block is maintained at constant temperature by a circulating water bath. Film samples can be suspended from the arm of the microbalance, while resin or powder samples can be placed in a glass pan suspended form the arm of the microbalance. Both sample and reference chambers have a platinum thermometer to measure the chamber temperature as well as the incoming vapor stream temperature. The uppermost chamber encloses the CAI-TN electrobalance, with maximum capacity of 100 mg and resolution of 0.1 pg. This section is also thermally insulated and is maintained at 40°C. The electrobalance-charnber is purged with a dry nitrogen stream to prevent moisture or organic vapors from condensation. The weight change of the sample is recorded by the Flow System Software (developed by VTI Corporation) on a computer connected to the system. The software is also use to define the different experiment parameter like temperature, relative humidity, etc. 6. Noise Quantification Every analytical or instrumental measurement is made up of two component— signal and noise. Noise can be defined as the unwanted, extraneous signals.” 57 Noise can originate from small fluctuations of various sources like in the power provided to the instrument or from external source such as other instruments nearby or building vibration. Noise is random in nature; it can be positive or negative therefore it is treated 24 statistically. Ideally when no analyte is present there should be no signal, but in practice recorded signal include some random signals. There are several types of noise — white noise, drift or flicker noise, and line noise. White noise can be due to the thermal motion of charge carrier (thermal noise) or when electron crosses a junction (shot noise). Drift or flicker noise has a magnitude that is inversely proportional to the frequency of the signal being measured. It is still not understood what causes the drift. Drift becomes significant at low frequencies. Line or environmental noise can be due to the power lines, conductors in the instrument or building vibrations.” 57 Therefore, to get reliable and robust results from an analytical instrument, its noise should be quantified. The amplitude of noise and the drift of gravimetric equipment were quantified using standard stainless steel weights. Ideally, the stainless steel should not absorb any moisture, the weight change observed is the noise associated with the instrument. A least square method for regression was used to evaluate the amplitude of noise and drift. The assumptions for the hypothesis testing of regression analysis are: (i) the relationship between x and y is linear, (ii) the errors are independent and (iii) normally distributed and (iv) variances of the errors are constant across the observations. The linear model for experimental observation can be written as:58 yi=fl0+fl1xi+gi i=112!”°n (14) where x and y represent the time and weight change respectively and ,6} is the slope of the regression line. The drift is given by the slope of the regression line and the amplitude of noise of the equipment was calculated as 35, where s is the square root of means squared error (MSE). Based on the empirical rule, y,- i 38 contains 99.7% of the distribution. 25 7. Consistency Test To determine the experimental data fit to the model described by Eq. 11 certain assumptions are made:28 0 The polymer is free of any vapor at the start of the sorption experiment. 0 The vapor concentration at each side of the polymer sheets at time=0 is the same as the vapor concentration at equilibrium. e The vapor concentration remains constant through out the experiment. 0 The thickness of the polymer sheet is constant. However, any significance variation or departure from any of these assumptions or conditions will affect the calculated value of the diffusion and permeability coefficients. Thus a consistency test was established by Hernandez et a1. 59 For the consistency test, Eq. 11 was solved by keeping Mthco equal to 0.25, 0.50, and 0.75 to obtain t1/4, tl/z, and t3/4, respectively. The basis of the test was that the ratio between t1/4, t1 ,2, and t3/4 remains fixed, irrespective of the penetrant-polymer system:59 I Kl zflzozso K2 =M=0.103 K, =tfl=a413 tl/2 t3/4 t3/4 9 , To determine the validity of the data obtained, experimental K1, K2 and K3 were compared to the theoretical values. 26 8. References: 1. 10. 11. 12. 13. 14. . Biodegradable Polymers in North America & Europe; MarTech, New York: July 1998. Mohanty, A. K.; Misra, M.; Hinrichsen, G. Macromol Mater Eng 2000, 276/277, 1-24. Auras, R.; Harte, B.; Selke, S. Macromol Biosci 2004, 4, 835-864. Auras, R.; Harte, B.; Selke, S. J Appl Polym Sci 2004, 92, 1790-1803. Gross, R. A.; Kalra, B. Science 2002, 297, 5582, 803-807. Pool, R. Science 1989, 245, 1187. Okada, M. Prog Polym Sci 2002, 27, 87-133. Bastioli, C. Polym Degrad Stab 1998, 59, 263-272. Yarnarnoto, M.; Witt, U.; Skupin, G.; Beimbom, D.; Muller, R., In Biopolymers, Polyesters 111: Applications and Commercial Products. Wiley-VCH: Weinheirn, 2002. Nagarajan, V.; Singh, M.; Kane, H.; Khalili, M.; Bramucci, M. J Polym Environ 2006, 14, 3, 281-287. Grigat, E.; Koch, R.; Timmermann, R. Polym Degrad Stab 1998, 59, 1-3, 223- 226. Chiellini, E.; Corti, A.; Solaro, R. Polym Degrad Stab 1999, 64, 2, 305-312. Kurian, J. V. J Polym Environ 2005, 13, 2, 159-167. Khonakdar, H. A.; Jafari, S. H.; Asadinezhad, A. Iran Polym J 2008, 17, 1, 19-38. 27 15. 16. 17. 18. 19. ° 20. 21. 22. 23. 24. 25. 26. 27. Akiko, M.; Mureo, K.; Makoto, M. Biodegradable Oriented Aromatic Polyester Film and Method of Manufacture. W00110928, 2001. Matweb DuPont Biomax® 4026. http://www.matweb.com/search/datasheet.aspx?matid=33539&n=1 (April, 2008) “Compostable Logo” of the Biodegradable Products Institute gains momentum with approval DuPontTM Biomax® resin. htmzl/wwwbpiworld.m/Files/PressRelease/PRY U WigUndf (April, 2007) Standard Specification for Compostable Plastics. In ASTM D6400-O4, ASTM Book of Standards, 2000; Vol. 08.03. DuPont Launches Biodegradable Polyester - Biomax®, Press Release. http://www.dupont.com.tw/020604-e.htm (April, 2008) Mungara, P.; Chang, T.; Zhu, J.; Jane, J. J Polym Environ 2002, 10, 1/2, 31-37. Editor of textileinfo, I. C. L. A forecast on the textile processing industry in 21C. http://textileinfo.com/en/tech/2lc/02.html (April, 2008) Mohanty, A. K.; Misra, M.; Drzal, L. T. J Polym Environ 2002, 1-2, 10, 19-26. Liu, W.; Mohanty, A. K.; Drzal, L. T.; Misra, M.; Kurian, J. V.; Miller, R. W.; Strickland, N. Ind Eng Chem Res 2005, 44, 4, 857-862. Drown, E. K.; Mohanty, A. K.; Parulekar, Y.; Hasija, D.; Harte, B. R.; Misra, M.; Kurian, J. V. Composi Sci Technol 2007, 67, 3168-3175. Farber, J. M. J Food Prot 1991, 54, 1, 58-70. Hernandez, R. J .; Selke, S. E. M.; Culter, J. D., In Plastics Packaging: Properties, Processing, Applications and Regulations. First ed.; Hanser Gardner Publications, Inc.: 2000. Gerlowski, L. E. In Water Transport Through Polymer, American Chemical Society, Dallas, Texas, 1989; Koros, W. J ., Ed. American Chemical Society: Dallas, Texas, 1989; pp 177-191. 28 28. 29. 30. ° 31. 32. 33. 34. 35. 36. ‘ 37. 38. 39. 40. 41. Crank, J ., In The Mathematics of Diffusion. Second ed.; Oxford University: 1975. Alfrey, A.; Gumee, E. F .; Lloyd, W. G. Journal of Polymer Science 1966, C12, 249. Flory, P. J ., In Principle of Polymer Chemistry. Cornell University Press: Ithaca, NY, 1953. Freeman, 3.; Yampolskii, Y.; Pinnau, I., In Materials Science of Membranes for Gas and Vapor Separation. Wiley & Sons, Ltd.: 2006. Barrer, R. M.; Barrie, J. A.; Slatter, J. Journal of Polymer Science 1958, 27, 177- 197. Meares, P. J Appl Polym Sci 1965, 9, 917-932. Baner, A. L.; Kalyankar, V.; Shound, L. H. J Food Sci 1991, 56, 4, 4. Stannett, V. J Membr Sci 1978, 3, 97-115. Gavara, R.; Catala, R.; Hemandez-Munoz, P.; Hernandez, R. J. Packag Technol and Sci 1996, 9, 215-224. Duncan, B.; Urquhart, J .; Roberts, S. Review of Measurement and Modelling of Permeation and Diffusion in Polymers; National Physical Laboratory: 2005. Yasuda, H.; Rosengren, K. J Appl Polym Sci 1970, 14, 11, 2839-2877. Apostolopoulos, D.; Winters, N. Packag Technol and Sci 1991, 4, 131-138. Barr, C. D.; Giacin, J. R.; Hernandez, R. J. Packag Technol and Sci 2000, 13, 4, 157-167. Hernandez, R. J .; Gavara, R. J Polym Sci, Part B: Polym Phys 1994, 32, 2367- 2374. 29 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. Hernandez, R. J .; Giacin, J. R.; Grulke, E. A. J Membr Sci 1992, 65, 1-2, 187- 199. Wong, B.; Zhang, Z.; Handa, Y. P. J Polym Sci, Part B: Polym Phys 1998, 36, 2025-2032. Wong, C. H.; Bhethanabotla, V. R. Fluid Phase Equilib 1997, 139, 371-389. Oliverira, N. S.; Oliverira, J .; Gomes, T.; Ferreira, A.; Dorgan, J.; Marrucho, I. M. Fluid Phase Equilib 2004, 222-223, 317-324. Karniya, Y.; Hirose, T.; Mizoguchi, K.; Naito, Y. J Polym Sci, Part B: Polym Phys 1986, 24, 1525-1539. Hernandez, R. J .; Giacin, J. R.; Lawrence, B. A. J Plast Fihn Sheet 1986, 2, 187- 211. Moylan, C. R.; Best, M. E.; Ree, M. J Polym Sci, Part B: Polym Phys 1991, 29, 87-92. Smith, A. L.; Mulligan, S. R.; Shirazi, H. M. J Polym Sci, Part B: Polym Phys 2004, 3906. Qin, Y. Impact of Polymer Processing on Sorption of Benzaldehyde Vapor in Rubbery Polypropylene. MS. Thesis, Michigan State University, East Lansing, MI, 2006. C. C. McDowell, D. T. C., and B. D. Freeman. Rev Sci Instrum 1998, 69, 6, 2510-2513. Dhoot, S. N.; Freeman, B. D.; Stewart, M. E.; Hill, A. J. J Polym Sci, Part B: Polym Phys 2001, 39, 1160-1172. Palamara, J. E.; Mulcahy, K. A.; Jones, A. T.; Danner, J. R.; Duda, J. R. Ind Eng Chem Res 2005, 44, 26, 9943-9950. Nielsent, T. J .; Giacin, J. R. Packag Technol and Sci 1994, 7, 247-258. 30 55. 56. 57. ' 58. 59. Golding, P. D.; Machin, W. D. J Chem Soc 1992, 88, 14, 1985-1991. Skoog, D. A.; Holler, F. J .; Crouch, S. R., In Principles of Instrumental Analysis. Sixth ed.; Thomson Brooks/Cole: 2007. Robinson, J. W.; Frame, E. M. 8.; Frame 11, G. M., In Undergraduate Instrumental Analysis. Sixth ed.; Marcel Dekker: 2005. Lyman, O. R.; Longnecker, M., In An Introduction to Statistical Methods and Data Analysis. 5th ed.; Duxbury Press, A Division of Wadsworth, Inc.: 2000. Hemandez-Munoz, P.; Gavara, R.; Hernandez, R. J. J Membr Sci 1998, 3993, 1- 10. 31 Chapter 3 A Study of Mass Transfer of Moisture in Biodegradable Sheets and Resins 1. Introduction Dwindling petroleum sources and landfill sites have prompted the development of alternative and environmentally fi'iendly polymers for different applications. In the past few years, many new alternative polymers have been developed that are either derived from non-petroleum sources or are biodegradable. A few examples of such polymers are Poly(lactide) (PLA), Poly(s-caprolactone) (PCL), and Polyhydroxylalkanoates (PHA).l The global production of biodegradable polymers in 2006 has increased 20-folds since 1995,2 but this represent just a small fi'action of the total polymer production. The major obstacle to commercialization of these ‘novel’ polymers in the packaging industry is their cost and the limited knowledge about their performance properties. The US packaging industry uses around one-third of the total plastics produced in the country.3 Plastic is the largest segment of the packaging industry, accounting for approximately 50% of the total materials used in industry.4 The barrier properties of polymer to different gases and vapors dictate the application of polymer as a package to be used in the food and pharmaceutical industries. Therefore, it is important to measure the barrier properties of these alternative polymers for their application in packaging industry. Unlike glass or metal packaging, plastic packaging materials are permeable to small molecules like water, volatiles and gases. Extensive research had been conducted for the evaluation of mass transfer properties of polymers using various methods. While 32 isostatic and quasi-isostatic methods are generally used to evaluate the permeation of the permeant through the polymer membrane?”9 gravimetric methods, using a spring balance, an electrobalance, or a quartz crystal microbalance, evaluate the permeant sorbed in the polymer.""'4 The gravimetric sorption method has the advantage that it can record real time mass (moisture) uptake in a controlled environment at both the steady state (M00) as well as during the transient state (Mt). The M, and M.,o values can be use to determine the solubility (S) and diffusion (D) coefficients experimentally and hence calculate the permeability (P) coefficient using the following relation: P=D*S (D The above equation holds at low concentrations of the permeant and when there is no interaction between permeant and polymeric material. In the above equation D follows d Fickian kinetics (is independent of concentration) and S follows Henry’s law. In this research moisture sorption of two environment friendly polymers, Biomax® and Sorona®, was studied using the gravimetric method. Biomax® (4026) is a hydro-biodegradable modified polyester, developed by DuPont. The material is based on polyethylene terephthalate (PET) and is synthesized by the polymerization of terephthalic acid, ethylene glycol, glutaric acid, and sulfonic acid salt.15‘ 1" Biomax® has been awarded a ‘COMPOSTABLE’ logo by The Biodegradable Products Institute (BPI).17 Biomax® can be used for oriented films, blown films, moulded plastic articles, or coating in disposable products such as bowls, plates, cups, and sandwich wraps.18 Because it is modified polyester, it can be easily processed using standard PET equipment. Biomax® has been blended with soy proteins and polycaprolactone (PCL), and with cotton (Bionature by Kurabo, J apan).'9' 2° 33 Sorona®, Poly(trimethylene terephthalate) (PTT) is a thermoplastic polyester produced by condensation of 1,3-propanediol and terephthalic acid.21 The propanediol (PDO) monomer can be derived from corn (a renewable resource). PTT was developed several years ago but was not commercialized due to the high cost of production of PDQ. However, recent developments have reduced the cost significantly. Sorona® belongs to the thermoplastic aromatic polyester family and due to three carbon glycol in its backbone it has better mechanical properties as compared to the other two members of this family (PET and PBT). Sorona® has high elasticity and recovery as compared to PET or nylon and better chemical properties than PET;22 hence it is gaining much attention in the packaging industry. Research had been conducted to tailor the physical and mechanical properties of Sorona® through blending it with other polymer or nano- composites,” 23 but few researchers have studied the moisture uptake of Sorona®. This study aims to generate a moisture sorption profile of Biomax® and Sorona® sheets and resins using a gravimetric method. The solubility and diffusion coefficients of both polymer sheets were determined through the sorption data. 34 2. Theoretical Background 2.1 Sorption by Polymer Film In a gravimetric method for moisture sorption, weight gain of polymer sample is recorded under specific relative humidity and temperature till the steady state is reached. The weight gain data is used to obtain the moisture sorption isotherm and the diffusion coefficient. Sorption during the transient state can be used to estimate the diffusion coefficient (D) using the following equation 24 M 8 ° D—2n+127r2t 1_(___22 ( ) = 2 Moo 71' n=0 (Mi-1 l (2) where l is thickness of the sheet, M, is the amount of penetrant sorbed by the polymer sheet sample at time t, and M00 is the steady state sorption after theoretical infinite time. The‘fit of the experimental data model described by Eq. 2 is based on the following assumptions” 25 o The polymer sheet has a constant thickness 0 Temperature and pressure remain constant during the experiment 0 Moisture uptake follows Fickian behavior (D is independent of concentration) 0 Vapor concentration on both sides of the sheet is constant and the change in concentration from initial concentration to final is instantaneous o The sheet is initially free of penetrant The Eq. 2 can be solved for Mt/Moo =0.5 with approximate error of 0.001 %: [2 tl/Z where t1/2, half time, is the time when MI/M00 =0.5 determined experimentally. 35 The solubility coefficient (S) is defined as the equilibrium partition coefficient for the distribution of permeant between the polymer phase (Cp) and vapor phase (CV) and is expressed as the mass of permeant sorbed at steady state by a unit volume of polymer per unit of driving force (partial pressure). S=B=Mw C v.P (4) v where M00 is the mass of the vapor absorbed by the polymer at equilibrium, v is the volume of the polymer, p is the permeant force in units of concentration or pressure. The common unit of S is kg/m3Pa and is calculated by dividing the steady state sorption (kg sorbate / kg polymer) by polymer density and vapor pressure. Once the solubility and diffusion coefficient are determined, the permeability coefficient can be calculated using Eq. 1. 2.2 Consistency Test The assumptions in determining D through Eq. 2 are listed above. However, any significance variation or departure from any of these assumptions or conditions will affect the calculated value of the diffusion and permeability coefficients form experimental data. Thus to determine the fit of experimental data to the Eq 2, a 126, was utilized. consistency test for gravimetric method, established by Hernandez et 3 Eq. (2) was solved for Mt/M,o equal to 0.25, 0.50, and 0.75 to obtain t1/4, III/2, and t3/4 respectively. The basis of the test was that the ratio between t1 /4, t1 /2, and t3/4 remains fixed, irrespective of the penetrant-polymer system 26: t K1=tfl =0.250 K2 = 5'11- =0.103 K3 =fl =0.413 t1/2 t3/4 t3/4 (5) 9 9. 36 3. Experimental 3.1 Materials i Biomax® (4026) and Sorona® resin pellets were obtained from E.I. DuPontTM de Nemours & Co. (Wilmington, DE). Biomax® pellets were odourless and opaque white in appearance with density of 1344.3 kg/m3 (1.34 g/cc). Sorona® pallets were odourless and translucent in appearance with density of 1334.7 kg/m3 (1.33 g/cc). Both polymer types were processed using a DSM twin screw Micro-Extruder and Injection Molder (TS/I-02, DSM, Netherlands), to obtain small discs of approximately 25.4 mm diameter and 2 mm thick. A compression molding press (Carvar Hydraulic Press, Wabash, IN) was used to process the discs into sheets form, for the sorption experiments. The sheets samples were cooled quickly in the compression press by rushing cold water through the platens. The processing conditions for both polymers are given in Table 3.1. The thickness of both polymer sheets was maintained at 4 to 6 mils. 37 Table 3.1: Processing condition for Biomax® and Sorona® Biomax® Sorona® Micro-Extruder and Injection Molder Barrel Temperature, °C 200 250 Melt Temperature, °C 190 240 Screw Speed, rpm 100 150 Process Cycle Time, min 2 3 Transfer Cylinder Temperature, °C 190 240 Mold Temperature, °C 60 85 Pressure, psi 100 120 Compression Press Platen Temperature, °C 200 250 Compression Pressure, psi 10,000 12,000 Cooling Time, min 5 7 3.2 Differential Scanning Calorimeter (DSC) A differential scanning calorimeter (TA Instruments, New Castle, DE) was used to determine the percent crystallinity of both polymers’ sheets and resins using one heating cycle followed by one cooling cycle. Biomax® samples were heated from 10°C to 210°C at a rate of 10°C/min and then cooled down to 10°C at a rate of 5°C/min. Sorona® samples were heated from 10°C to 265°C at a rate of 10°C/min and then cooled to 10°C at a rate of 5°C/min. The data were analyzed with Universal Analysis software (TA Instruments). 38 3.3 Instrument SGA-I00 A Symmetrical Gravimetric Analyzer - SGA-lOO (VTI Corp., Hialeah, FL) equipped with a Cahn Electrobalance Model D-200 (Cahn Instruments Co., Cerritos, CA) was ‘used to measure the sorption of moisture in the polymer sheets and resins. It is capable of generating relative humidity from 2 to 98% with variability of dz] .0% RH. The instrument is divided into three thermally isolated sections: a vapor generation chamber, sample chamber, and electrobalance chamber. The aluminum sample chamber (10.8 x 3.8 x 3.80m) can be maintained at a constant temperature with variability of 101°C. The relative humidity inside the sample chamber is obtained by mixing wet and dry streams of nitrogen using mass flow controllers. The electrobalance has a maximum capacity of 100 mg with resolution of 0.1 pg. The main components of the SGA-lOO are shown in Fig. 3.1. ‘ Electrobalance Chamber Thermal Zone 1 , Sample Water. -. . Chamber Bath i ’ ' ‘ i w: Thermal Zone2 t Vaporiz ' Dew Point er ‘ ;———-/ Analyzer L— Vapor Mass .. . Generation Flow M Chamber Controllers Thermal Zone3 Figure 3.1: Schematic of Symmetrical Gravimetric Analyzer (SGA-I 00) 39 3.4 Noise Quantification Every measurements carried out by an analytical instrument is made up of two components - signal and noise. Noise can be defined as the unwanted, extraneous signals which can make the actual signals indiscemible.27’ 28 A protocol was implemented to quantify the noise level associated with the SGA-100 by measuring the amplitude of the noise and the drift. To quantify the noise level, three standard stainless steel weights of 20, 50, and 100mg were exposed to 5%, 50%, and 90% at three different temperatures. Weight change of the standard stainless steel weight was recorded every 10 minutes for 72 hours. 3. 5 Sorption Experiment The sheet and resin samples were stored in a desiccator to remove the moisture from the samples at 23°C. To minimize the variation in thickness within the sample, small pieces of the sheets (around 1 cm2 and 30 mg) were used. The samples were suspended on the arm of the electrobalance. After conditioning at 60°C and 0% RH for 1h, the sheet samples were exposed to a specific relative humidity (10, 30, 50, 70 and 90%) at a constant temperature (23 and 40°C). The weight gain (moisture uptake) was recorded, from i=0 to the time at which no more weight gain was observed (steady state), at 2 min interval thus providing a detailed information about the transient state. In this sorption study, the steady state was determined by a specific equilibrium criterion. The resin samples of both polymers were exposed (after conditioning) to specific relative humidity of 50 and 90 % RH at two different temperatures (23° and 40°C). All the sorption experiments of sheets and resins of both polymers were done in triplicate and standard error was calculated. 40 4. Results and Discussion 4.1 Physical Properties The thickness of the processed Biomax® sheets was measured as 0.14 i 0.03 mm (5.5 at 1 mil) and for Sorona® as 0.11:!:0.03 mm (4.53:1 mil). The density of Biomax® and Sorona® sheets was measured at 23°C as 1344.3 kg/m3 (1.34 g/cc) and 1334.7 kg/m3 (1.33 g/cc), respectively ( in accordance with ASTM D792-00). The percent crystallinity of polymer sheet and resin was calculated using the following formula: AH =100x ’" 1‘ AH (6) where AB,“ is enthalpy of fusion and AH0 is the heat of melting of purely crystalline ® resin was found out to be around 18.3 % polymer. The percent crystallinity of Biomax and after processing the percent crystallinity of Biomax® sheets dropped to 9.5 %. The percent crystallinity of Sorona® polymer was found to be 42 % for resin and 26 % for sheets. The drop in percent crystallinity after processing is due to the quenching of the polymer samples during sheet making in the compression press. 4.2 Instrument Noise and Drift: To evaluate the amplitude of noise and drift of the equipment, a least squares method for regression was adopted.28 The assumptions for the hypothesis testing of regression analysis are: (i) the relationship between x and y is linear, (ii) the errors are independent and (iii) normally distributed and (iv) variances of the errors are constant across the observations. The linear model for experimental observation can be written 9 3822 yi:fl0+fl1xi+8i i=1!2’°”n (7) 41 where x and y represent the time and weight change respectively and ,8] is the slope of the regression line. The percent weight change vs. time graph of 50 mg standard weights at 40°C and 90% RH is shown in Fig. 3.2. The drift of the equipment is given by the slope of this regression line. The noise residual output vs. time plot for the same experiment is shown in Fig. 3.3. 0.025 I 0.020 . in 0.015 1 J I" 2 1 .1 o u ' 3" 0.010 E g y =2*10'O6x + 0.0102 0.005 1 0.000 +— 1 . - —r—— 0 1000 2000 3000 4000 Elap Time (min) Figure 3.2: Percent weight change vs. time and linear regression line for a 50 mg standard weight at 40°C, 90% RH 42 0.005 1 Amplitude 0.003 m A of Noise .21. 0.001 ' cc :1 __ _ E 8 -0.001 -: 05 1 -0.003 j -0.005 i Elap Time (min) Figure 3.3: Residual output vs. time for 50 mg standard weight at 40°C, 90% RH The results from linear regression statistical analysis are given in Table 3.2. The significant F values of all the experiments (not shown in table) were found to be very close to 0, thus null hypothesis H0 (,81 = 0) was rejected, concluding that the weight change (y) and time (x) are not independent (01 = 0.05). A small drift ranging from 10'06 to 10'07 was observed in the equipment at different experimental conditions. Both positive and negative drift was observed during the experiments. The drift of the equipment was not found to be dependent on either weight or experimental conditions. The amplitude of the noise was calculated as the difference between the experimental values and the predicted value (std. metal weight’s actual weight). The amplitude of noise of the equipment can be given as 33, where s is the square root of means squared error (MSE) from the residual analysis. Based on the empirical rule, yi i 35 contains 99.7% of the distribution. The amplitude of noise under different conditions is given in Table 3.2. The noise level was found to be very low as compared to the signal. 43 Although the noise amplitude increased with weight, the Signal to Noise ratio (S/N) was improved. The noise was independent of humidity and temperature, except for 20 mg weight, where an increase in noise was observed with increase in temperature. Table 3.2: Regression analysis of the equipment ’s noise and drift Standard Amplitude of Weight Condition Regression Line MSE (sz) noise (3s) % S/N 20 mg 10°C 90% y = 1*10'06x + 0.0183 1.10*10'°6 0.003145 6359.30 23°C 90% y = -4*10*’°x + 0.0269 1.56*10'°° 0.003744 5341.88 40°C 90% y = -6*10*’6x + 0.0185 2.10110:06 0.004351 4596.64 50 mg 10°C 5% y = -4*10’06x — 0.0062 5.02810“6 0.006723 7437.16 10°C 50% y = -2*10*’7x - 0.0083 2.371104)6 0.004615 10834.24 10°C 90% y = -5*10'06x + 0.0107 3.85*10'°° 0.005890 8488.96 23°C 5% y = -3*10*’6x + 0.0091 4.67:“10"6 0.006481 7714.86 23°C 50% y = -3*10'06x + 0.0064 3.62110“6 0.005710 8756.57 23°C 90% y = -6*10*’6x - 0.0093 6.84*10'°° 0.007847 6371.86 40°C 5% y = -4*10*’7x - 0.0026 3.61*10'°° 0.005697 8776.55 40°C 50% y = -1*10*’°x + 0.0007 5.3111006 0.006916 7229.61 40°C 90% y = 2*10'°°x + 0.0102 3.56*10’°° 0.005661 8832.36 100 mg 23°C 90% y = -7*10*’6x - 0.0063 1.58*10*’5 0.011923 8387.15 44 4.3 Equilibrium Criterion Determination The fundamental driving force that promotes the diffusion of a molecule through a polymer is the difference between the chemical potential of the fluid and the polymer phase. When the chemical potential of permeant in the fluid and polymer phase becomes equal, an equilibrium or steady state is reached.25 In the gravimetric method, the steady state is said to be reached when the weight gain of the sample is zero or negligible. In this study, the steady state is controlled and determined by an equilibrium criterion, provided in the flow system software of the SGA-100. The equilibrium criterion for both polymer types was set as ‘weight change of 0.005% in 30 min’. It means if the weight change of the polymer is less than 0.005 % for continuous 30 minutes, the steady state or equilibrium is considered to be reached. 4.4 Moisture uptake in Sheets The moisture sorption in both polymer sheets followed F ickian kinetics. The average percent moisture uptake for the triplicate runs vs. time (min) for Biomax® sheets at 23°C and 40°C for different water activities is shown in Fig. 3.4. The time taken to reach the steady state increased with relative humidity. The time to reach the steady state at 40°C was less than that at 23°C, due to higher saturated vapor pressure at higher temperatures. 45 2.5 ++++++++ ++++++++++H~H++++++H+H+1+I 20 ++++ + $43 23°C .5 3 an 1.5 ++ fl -= f .2.” 4* g 10 f xxxxxxxxxxxxxxxxxxmmmxxml - + + °\° r 05 _: ““.‘mammmx ... III-II-I I-III- I O 0 QOOOOOOOOOOOOOOO. z 0 200 400 600 800 1000 Time (min) 2.5 #+WW+++++++++ + +-H—H—H+H++HHH- I ++ 2.0 $++ 40°C + .5 f 2.” 1.5 ,_ + 0 + 3 1.0 ~ +fm e\° +x 3"“. A an“: 0.5 4K; ‘ f'lll III I I I- a: 00 ‘ Q .0 0 «one. = 0 50 100 150 200 250 300 Time (min) Figure 3.4: Average percent weight gain (3 runs) vs. time (min) for Biomax® sheets at 23 °C and 40°C, S. E. bars are shown only for the lost data point. 0 10% RH I 30%RH A 50%RH X 70% RH + 90%RH 46 The average percent moisture uptake vs. time for Sorona® sheets at 23°C and 40°C at different relative humidities is shown in Fig. 3.5. Moisture uptake increased with the increased water activity and temperature. The moisture uptake in Sorona sheets (0.03- 0.5%) was much lower than in Biomax sheets (0.1-2.5%) due to lower affinity to water of Sorona than Biomax® to water. 0.60 0.50 ' 23°C W 5 0.40 ”new DD ++++ a ++++ '50 030 +£ppmxxxxWI '5 3 3 I 1 f 0 100 200 300 400 500 600 700 800 900 1000 Time (min) 0.60 +++++++++-H--H++++ = 0.50 +++++++++++ ++ + ++ 5 0.40 ff 40°C in 41- xxxxxxxoxxxxmxmntm: '50 0 30 1%?” '3 3 0.20 if ‘ u ...aaaanusaaaaaum - A ‘ A ...IIIIIIIIIIIIIIIII I 0.10 .- .«mum I 0.00 I ‘ . ‘ 0 50 100 150 200 250 300 350 400 450 Time (min) Figure 3.5: Average percent weight gain (3 runs) vs. time (min) for Sorona® sheets at 23 °C and 4 0°C, S. E. bars are shown only for the last data point. 910%RH I 30%RH A 50%RH X 70% RH + 90%RH 47 4.5 Consistency Test and Correction To determine the fit of the experimental data to the model defined by Eq. 2, theoretical Mt/Moo values were calculated using Eq. 2. The experimental Mt/M,o and theoretical Mt/M00 vs. square root of time (secondm) are shown in Fig. 3.6. 1.20 j 1.00 0.80 4: l— Theoretical l Mt/Moo O 8 040 . Emmmmm :tT—EEEEQQQH 0.20 > 000 _.e_ .————_ .__fi___._"__.x._,z_____fi__ 0.00 50.00 100.00 150.00 200.00 Time (sec)“2 Figure 3. 6: Experimental M/Moo (before correction) and theoretical M,/M,,o vs. square root of time (second/0) for a Biomax® sheet at 23 °C and 3 0% RH The initial part of the curve was concave and a large difference was observed between experimental and theoretical values. A similar difference was found for all the sorption experiments for both polymers. Ki parameters, for consistency test, of each sorption experiment were calculated for both polymers sorption runs (Fig. 3.7). As seen, 48 K3 Values K2 Values 6 . C Temperature Ci After correction 49 Temperature theoretical K,- value. for both polymers experimental the K1 and K2 values differed from the theoretical values by more than 100%. ' K1 Values Biomax® 00000000 mm m m va ow %_ .. w. W m: C o m mm smsxss w W9 W.; 5T w . m. w c .. mm. 8 .. w Temperature Figure 3. 7: Average of K,- values of different relative humidities for Biomax® and Sorona® sheets before and after correction at 23 °C and 4 0°C, dotted line represents the Before correction This deviation of experimental data from the theoretical model could be related to the time taken by the vapors inside the sample chamber to reach the target experimental vapor activity, as one of the assumptions for Eq. 2 is that the sorbate concentration around polymer sample changes stepwise from the initial zero concentration to the target experimental concentration. However, this is hardly possible in actual experiments. Therefore, to compensate for the time taken by vapors to reach the target constant relative humidity a correction in experimental data was proposed. The linear part of the experimental Mt/M,O curve was extrapolated to the x-axis (Fig. 3.6). The time obtained on x-axis by extrapolation was then considered as the zero time for the sorption experiments. After the correction, the experimental Mt/M,o and theoretical Mt/Mm (from Eq. 2) values were obtained. A very good fit was observed between the time-corrected experimental and the theoretical values for the same Biomax® sheet (Fig. 3.8). 1.20 5 1.00 . | 0.80 «.- 8 E 0.60 - 2 I Corrected 0.40 ~ Experimental —Th oretical 0.20 - e 0.004 ~w—«--—~-’- . ———— O 50 100 150 200 Time (sec)m Figure 3. 8: Experimental M/M,o (after correction) and theoretical M/M.no vs. square root of time (secondw) for a Biomax® sheet at 23 °C and 3 0% RH 50 The K, parameters were also calculated using the new corrected tm, tm, and t3/4. As seen in Fig. 3.7, the difference between the experimental and theoretical K, values was reduced to 0-10%, hence verifying the validity of corrected experimental data. A similar correction was applied to all sorption experiments of both types of polymer sheets. The corrected data were used to calculate the solubility and diffusion coefficients. 4. 6 Sheet Moisture Sorption Results The moisture sorption of the polymer sheet at the steady state was used to generate the moisture sorption isotherms for Biomax®(a) and Sorona®(b) sheets at 23°C and 40°C (Fig. 3.9). The polyester Sorona® sheets had low moisture sorption (0.5% at 40°C, 90%RH) as compared to Biomax® (2.5% at 40°C, 90%RH), which is a hydro- biodegradable polymer. Moisture sorption in both polymers was dependent on the RH. For Sorona® sheet the moisture sorption increased significantly with increase in temperature, except at 10% RH. For Biomax® moisture sorption was found to be slightly dependent on temperature only in the middle range of the relative humidities. a) Biomax® Isotherm 2.5 7 +23°C +4 0 2.0 7 O C .E. l (6 SE 1.5 - .1: .29 Q) 3 1.0 c,\" 0.5 r 0.0 ——__"T_-—"— '1— ".T' H ‘*—' '1 0 20 40 60 80 100 % Relative Humidity 51 b) Sorona® Isotherm .9 ON 1 + 23°C + 40°C .9 LII 1 .9 4:. % Weight Gain o DJ 0.2 0.1 0.0 “T '_—"_“—“ 1 i 1 1 0 20 40 60 80 100 % Relative Humidity Figure 3. 9: Moisture sorption isotherm of Biomax®(a) and Sorona®(b) sheets at 23 °C and 40°C, error bars are SE. for 3 runs Most food and biomaterials are characterized by negative heat of sorption, which means equilibrium moisture sorption isotherm corresponding to lower temperature is situated above to that corresponding to higher temperature.30 But both Biomax® and Sorona® did not followed this pattern, the moisture sorption at 40°C was more as compared to 23°C. Though not common but similar isotherms with such a positive temperature dependence have been reported previously.3 "33 For Biomax® sheets this behavior may be due to two reasons: (1) it is a hydro-biodegradable polymer and 40°C is above the glass transition temperature; thus, increasing the movements within the chain and allowing more moisture to be sorbed; and (2) the moisture sorption is driven by the hydrolysis of the ester linkages, as also seen in the case of PLA films.32 52 A sum of square technique was applied to the determine the best estimated diffusion from the experimental data.9 The best estimated diffusion coefficient can be defined as diffusion coefficient for which the difference between the experimental and the theoretical curve (Eq. 2) is least. A representative plot of the sum of squares values as function of diffusion coefficient values (calculated around ill/2) was used, from which the best estimated diffusion coefficient was determined from minimum sum of square value (plot not shown). Table 3.3 presents the best estimated diffusion, solubility, and permeability coefficients of Biomax® and Sorona® sheets at 23°C and 40°C. As the temperature increases the mobility of the chain and free volume increases, so more permeant can pass through the sheet easily. Hence, diffusion coefficient of both polymer sheets increased with increase in temperature. For Biomax® sheet, the diffusion coefficient drops at 90% RH which can be related to the condensation of vapors on the sheet at high water activity. The solubility coefficient of both polymers increased with relative humidity. A statistical analysis, Least Square Means Difference (LSMD),29 was conducted to determine whether the solubility and diffusion coefficients of both polymers differed as a function of relative humidity. The solubility coefficient of Biomax® was found to be slightly dependent on the RH and temperature. The S increased significantly with increased in RH from 10% to 50% and from 50% to 90%. The diffusion coefficient of Biomax® slightly increased with increase in RH except at 90% RH at both temperatures, where a drop in D was observed which could be related to the condensation of vapors on the sheet at high humidity. The changes in diffusion coefficient of Sorona® sheets were not statistically significant (LSMD results) because of the unequal residual variance at different RH. The solubility 53 coefficient of Sorona® sheets at 23°C increased significantly with increase in RH from 10% to 50% and 50% to 90% and at 40°C a significant increased was observed from 10% to 70% and higher RH. 54 vd H 5d a vd H EN 0 mod H so; 5d H dmd e md H Ah.— 0 cod H wNN om ed H 91. m wd H mud on 5d H mdd ad H 3...4 m ed H mm a 3d H mm; on d._ H $5 a m._ H 346 a 8d H dad v; H 36 m md H mod n mod H x: cm N; H on...” a n; H Pd 9 cod H and md H mod n Nd H mm; a 3d H em; cm _d H Sam m N; H ovd a :d H dmd md H add a vd H NN.N a mod H cm; 3 ae— : 2.25 Z: J _ 2.2 f. 25...; 1: am 5. o