1! t, 5)}.3: s 1 a ' ‘ .2; . .fig . 5.2 .. .r .72: Ly . 3 . 1 00"... .1 at. Slut? ‘1 I .13. 5 101.... .- .. x I. a... . Z 3.»! A. “.muofin‘ . 6.9.2... .. . . iii! .3- n. ‘l.|l.. .I. 011.7 OIL? . . . . . {.3 . . RE 95.... 9%....” , 9.3.3:: . _ , , _... x... . .l. . £99999. tilllllll“ \llllllll L, B R A. W H \l W 3 ”JAMM 6537 Michigan st... University | This is to certify that the thesis entitled Barrier Characteristics of Metallocene Polyolefins to Organic Vapors presented by David A. Singleton has been accepted towards fulfillment of the requirements for Masters degree in Packaging JM Major professor Date [1/19/49 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution PLACE IN REFURN Box to remove this checkout from your record. TO AVOID FINE return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 1m mu BARRIER CHARACTERISTICS OF METALLOCENE POLYOLEFINS TO ORGANIC VAPORS By David A. Singleton A THESIS Submitted to Michigan State University In partial fulfillment of the requirements For the degree of MASTER OF SCIENCE School of Packaging 1998 ABSTRACT BARRIER CHARACTERISTICS OF ME'TALLOCENE POLYOLEFINS TO ORGANIC VAPORS by David A. Singleton A Waters ISO-C ALC Gel Permeation Chromatograph was employed to characterize Affinity 1140 (metallocene) and Attane 4201 (ULDPE) films by their Molecular Weight Distributions. It was also used to obtain the weight average molecular weight, the number average molecular and the dispersion index of the selected films. Data to calculate the diffusion and solubility coefficients was obtained using the CAHN D200 Digital Recording Balance with ethyl acetate and limonene as the organic vapors. This study focused on the effects of the sorbates at 23°C and 32°C; the values gained were evaluated to determine if there were significant differences between the sorption processes of the samples. For each experimental sorption plot produced by the Digital Balance, a second plot was calculated by the Fickian model to establish the Pickian behavior of the selected polymers. A few of the metallocene and slightly more of the ULDPE tests resulted in what appeared to be dual sorption but the majority of the plots had good agreement, which proved the Fickian nature. To my wife Genise T., as Christ loved the church so is my love for you To my parents Euan and Eloise, for their love and support To my sisters Mychele and Stephani For their love and friendship To my family For their endless encouragement AKNOWLEDGEMENTS The author acknowledges God the Father who through my Lord and Savior Jesus Christ allowed the completion this work; he has given me life changing experiences by opening doors that would have been closed to me. I give sincere thanks to the Lord for his mercy and his grace while granting this great opportunity to complete the research. The author also wishes to thank Dr. Ruben Hernandez, major professor, for the privilege of working with him throughout the research and for his guidance, help, and patience. Dr. Jack Gaicin and Dr. Randy Beaudry, members of the committee, for their guidance and instruction. Dr. Rafael Gavara for his invaluable tutoring and comments on the research during his time here in the United States. Special thanks to Dr. James Jay for enlightenment, the study in Africa and economic assistance received during my time spent at MSU. Pastor Nick S. Edwards, his wife and the entire New Testament C.O.G.I.C. family for their influence, drive and endless encouragement. iv TABLE OF CONTENTS LIST OF FIGURES LIS'T OF TABLES INTRODUCTION LITERATURE REVIEW Characteristics of Polyolefins General Characteristics of Polyethylenes Linear Low-Density Polyethylene Ultra Low-Density Polyethylene Characteristics of Metallocene polyethylene Properties of Metallocene polyolefins Summary Gel Permeation Chromatography Mass Transfer in Polymeric films Sorption Measurements MATERIALS 5: METHODS Packaging Materials Polyolefins Sorbates Methods Film sample preparation Sorption Measurements Gas Chromatographic Analysis Calibration Curves Calculating the Diffusion Coefficient Molecular Weight Distribution Statistical Analysis ix 10 10 1‘1 13 14 16 24 24 24 24 26 28 30 33 RESULTS AND DISCU$ION Film Thickness Molecular Weight Distribution Diffusion and Solubility Coefficients Statistical Analysis SUMMARY AND CONCLUSIONS APPENDD( A APPENDIX B APPENDD( C BIBLIOGRAPHY 88618283 LIST OF FIGURES 1. Permeability model for gas or vapor transfer through a package wall 2. Schematic of the Cahn Digital Recording Electro-Balance 3. Calibration curve for Ethyl Acetate by gas chromatograph 4. Molecular Weight Distribution for the selected polymer films. 5. Sorption of Ethyl Acetate by Affinity film at 23°C 6. Sorption of Limonene by Affinity film at 32°C 7. Sorption of Limonene by Atlane film at 23°C 8. Sorption of Ethyl Acetate by Attane film at 32°C 9. Minimization of the Sum of Squares study 10. Example of Bimodal sorption of Ethyl Acetate by ULDPE at 32°C 11. A—1. 12. A-2. 13. A-3. 14. A4. 15. A-S. 16. A-6. 17. A-7. 18. A-8. 19. A-9. Sorption of Ethyl Acetate by ULDPE at 32°C, test 1 Sorption of Ethyl Acetate by ULDPE at 32°C, test 3 Sorption of Ethyl Acetate by ULDPE at 32°C, test 4 Sorption of Ethyl Acetate by ULDPE at 23°C, test 5 Sorption of Ethyl Acetate by ULDPE at 23°C, test 6 Sorption of Ethyl Acetate by Metallocene at 23°C, test 1 Sorption of Ethyl Acetate by Metallocene at 23°C, test 2 Sorption of Ethyl Acetate by Metallocene at 32°C, test 3 Sorption of Ethyl Acetate by Metallocene at 32°C, test 4 21 27 32 43 45 47 49 55 56 57 58 59 60 61 62 20. A-10. Sorption of Ethyl Acetate by Metallocene at 32°C, test 5 21. A - 11. Sorption of Limonene by ULDPE at 23°C, test 1 22. A - 12. Sorption of Limonene by ULDPE at 23°C, test 2 23.A-13. 24. A - 14. 25. A-15. 26. A - 16. 27. A - 17. 28. A - 18. 29. A - 19. 30. A - 20. 31. A - 21. Sorption of Limonene by ULDPE at 23°C, test 3 Sorption of Limonene by ULDPE at 32°C, test 4 Sorption of Limonene by ULDPE at 32°C, test 5 Sorption of Limonene by ULDPE at 32°C, test 6 Sorption of Limonene by Metallocene film at 22°C, test 2 Sorption of Limonene by Metallocene film at 22°C, test 3 Sorption of Limonene by Metallocene film at 32°C, test 4 Sorption of Limonene by Metallocene film at 32°C, test 5 Sorption of Limonene by Metallocene film at 32°C, test 6 63 65 66 67 69 71 72 73 74 LIST OF TABLES 1. New-generation resins: where they fit in the market. 2. Commercial Classification of Polyethylene Resins 3. Calibration data for Ethyl Acetate in Xylene with a .07 p 1 injection volume 4. Thickness values of the selected samples 5. Statistics for the Molecular Weight Distribution of the selected polymers 6. Summary of D x 10“ mZ/s 7. Summary of S x 105, Pa'1 8. Differences and averages of the Dual Sorption process, Ethyl Acetate sorbate 9. Differences and averages of the Dual Sorption process, Limonene sorbate 32. A-1. 33. A-2. 34. A-3. 35. A-4. 36. A-5. 37. A-6. 38. A-7. 39. A-8. 40. A-9. Sorption of Ethyl Acetate by ULDPE at 32°C, test 1 Sorption of Ethyl Acetate by ULDPE at 32°C, test 3 Sorption of Ethyl Acetate by ULDPE at 32°C, test 4 Sorption of Ethyl Acetate by ULDPE at 23°C, test 5 Sorption of Ethyl Acetate by ULDPE at 23°C, test 6 Sorption of Ethyl Acetate by Metallocene at 23°C, test 1 Sorption of Ethyl Acetate by Metallocene at 23°C, test 2 Sorption of Ethyl Acetate by Metallocene at 32°C, test 3 Sorption of Ethyl Acetate by Metallocene at 32°C, test 4 31 37 41 42 51 52 55 56 57 59 60 61 62 41. A-10. Sorption of Ethyl Acetate by Metallocene at 32°C, test 5 42. A - 11. Sorption of Limonene by ULDPE at 23°C, test 1 43. A - 12. Sorption of Limonene by ULDPE at 23°C, test 2 44. A - 13. Sorption of Limonene by ULDPE at 23°C, test 3 45. A - 14. Sorption of Limonene by ULDPE at 32°C, test 4 46. A - 15. Sorption of Limonene by ULDPE at 32°C, test 5 47. A - 16. Sorption of Limonene by ULDPE at 32°C, test 6 48. A - 17. Sorption of Limonene by Metallocene film at 22°C, test 2 49. A - 18. Sorption of Limonene by Metallocene film at 22°C, test 3 50. A - 19. Sorption of Limonene by Metallocene film at 32°C, test 4 51. A - 20. Sorption of Limonene by Metallocene film at 32°C, test 5 52. A - 21. Sorption of Limonene by Metallocene film at 32°C, test 6 31. 8-1. Data pts for the sorption of Ethyl Acetate by Metallocene film, test 1 32. B-2. Data pts for the sorption of Ethyl Acetate by Metallocene film, test 2 33. B—3. Data pts for the sorption of Ethyl Acetate by Metallocene film, test 3 34. B-4. Data pts for the sorption of Ethyl Acetate by Metallocene film, test 4 35. B—5. Data pts for the sorption of Ethyl Acetate by Metallocene film, test 5 36. B-6. Data pts for the sorption of Limonene by Metallocene film, test 2 63 65 66 67 68 69 70 71 72 73 74 76 37. B-7. Data pts for the sorption of Limonene by Metallocene film, test 3 38. B-8. Data pts for the sorption of limonene by Metallocene film, test 4 39. B9. Data pts for the sorption of Limonene by Metallocene film, test 5 40. B-‘IO. Data pts for the sorption of Limonene by Metallocene film, test 6 41. B-11. 42. B-12. 43. B-13. 44. B-14. 45. B—15. 46. B-16. 47. B-17. 48. B-18. 49. B-20. 50. B-21. 51. B-21. 52C-1. 53. C - 2. 54.03. Data pts for the sorption of Ethyl Acetate by ULDPE, test 1 Data pts for the sorption of Ethyl Acetate by ULDPE, test 2 Data pts for the sorption of Ethyl Acetate by ULDPE, test 3 Data pts for the sorption of Ethyl Acetate by ULDPE, test 4 Data pts for the sorption of Ethyl Acetate by ULDPE, test 5 Data pts for the sorption of Limonene by ULDPE, test 1 Data pts. for the sorption of Limonene by ULDPE, test 2 Data pts for the sorption of Limonene by ULDPE, test 3 Data pts for the sorption of Limonene by ULDPE, test 4 Data pts for the sorption of limonene by ULDPE, test 5 Data pts for the sorption of Limonene by ULDPE, test 6 Data used in Minitab to perform the Analysis of Variance General Linear Model Analysis of Variance for Sorption General Linear Model Analysis of Variance for Diffusion 81 82 83 86 87 89 91 95 97 97 INTRODUCTION Metallocene catalyzed polyolefins are a relatively recent development and initially producers are boasting of their remarkable physical properties. Polymerization of olefins using metallocenes was originally introduced in the 1950’s but was not commercially feasible at that time. The way was paved in the 1980’s when co-catalysts were discovered. Actual commercialization began in the early 1990’s with Dow Chemical and Exxon as the production leaders (Innes, Intertech Conferences, 1996). There are numerous reports concerning the physical characteristics and economic forecasts of metallocene polyolefins, but not much is known about the barrier characteristics to organic substances. This information is important since industry needs it to better understand and apply metallocenes. Therefore the focus of this research was: 1. To characterize selected metallocene polyolefins according to their molecular weight distribution. 2. To determine the solubility and diffusion coefficients of selected sorbates in metallocenes and LLPDE. 3. To evaluate the diffusion coefficient of selected sorbate in metallocene polyolefins. LITERATURE REVIEW The continual increase in consumer demand for packaged foods of higher quality, freshness and convenience has producers scurrying to develop new ways to ensure consumer loyalty. These innovations require improved but cost effective means of distribution. To meet this need, after 1970 the food industry began intensely to replace metal and glass with polymers to contain and transport their products. Polyethylene and polypropylene (polyolefins), polystyrene, polyethylene terephthalate and poly-vinyl chloride have been the polymers of choice to handle the conversion. Plastic packages enhance attractiveness, add value, and are of lighter weight and less expensive than glass or metal packaging. However, in contrast with them, polymers have limited barrier capabilities. That is, that polymers allow the diffusion and sorption of low molecular weight molecules. When designing a plastic package for food applications correct selection of packaging material is crucial. Incorrect polymer choices can contribute to the excessive loss of quality in packaged food by decreasing shelf life in food by flavor scalping volatile flavor components or increase unnecessarily in cost. Plastics allow oxygen and water from the external environment to enter package, which may promote deterioration of the product. They also permit the escape of flavor and aroma components of the product from the product / package system to the external environment. Therefore, when designing a product / package system, the barrier properties of these polymeric materials are of utmost importance. There is a large body of information available to determine how polyolefins allow water, oxygen and carbon dioxide to permeate through them; this is vital to food and pharmaceutical / medical packagers. In addition to these, researchers have shown an interest in the barrier properties of plastics to organic compounds. This has lead to the development of test methods to study the permeability of various organic compounds and also gain a better understanding of permeation and sorption phenomena (Gillette, 1988; Hernandez, 1986; Zobel, 1988) Metallocene catalyzed polyolefins are reported as having enhanced characteristics without the process of blending polymers. Major polymer producers, such as Dow Chemical and Exxon, are now generating homogeneous resins with improved overall performance than that of conventional heterogeneous polyolefins. This is accomplished by the use of metallocene catalysts in place of the standard catalysts. Using this technology, reactions can be controlled to produce polymers for specific applications. The polymers created by this process will compete in the packaging films and medical packaging markets, which are currently dominated by low density PE, linear low density PE, and ethylene vinyl acetate (EVA). Metallocene polymers will also battle for use in the increasingly important market of minimally processed fruit. By the year 2000, fresh-cut (ready-to-use) produce is expected to occupy 25% of the shelf space in the United States (Leaversuch, 1995). Producers of metallocene polyethylene have pointed out that their resins show 3 higher oxygen and moisture transmission rates which are essential elements for today’s modified atmosphere packaging. Many other areas of industry are seeking to benefit from this new generation of polymer. Table 1 lists the metallocene resin, application and the polymer likely to be replaced. The production of metallocene films is based on a new generation of catalysts called single site catalysts. The new catalytic process affects how monomers are bonded. Catalysts are added to the reactor to control polymer chain formation. Along with heat and pressure, they cause molecules to string together and yield a polymer. The type of polymer depends on how the molecules combine. Ziegler-Natta catalysts, the catalyst for producing the common polyethylene, have multiple reaction sites that produce polymers with broad ranges of molecular sizes. Ziegler-Natta processes normally produce polyethylenes with wide molecular weight and composition distributions. When single site catalysts are used, they allow remarkable control over molecular architecture. This control produces molecules having almost identical structures and compositions yielding polymers that have unique properties. Single site catalysts have many reaction sites, but unlike Ziegler-Natta catalysts, the molecules string together in the exact same way, thus they are considered ”single”. The resulting polymers are much more predictable in performance, due to their uniformity, and are very flexible in their design potential (Demetrakakes, March 1995, Schwank, August 1993). Saga 65o 3:889 .mfia was—ca ES “82.83380 82 E022 83.5.. .152: 895m gunfivasgm 829$»... amaeasmmmz Bod/fine: 98 33:8 E9?— <> so 55 En: <>m 1028; 59568 23 s 8% 5633a mm: wagon; 88 stag €92 5:: $5.: 9529: €65 mag—imam: 65238289953 «85383 getahmi wfiwS—omm poop. conch .mcouaoamms 38%. >62 €53 Bod .933 1333.93 3.2995536 mimosaaaafifim 5.32 as... Bod: 8 \w «Eamon—mom comma—ma? Samson Snow €93 dEOU tonom ”ooBomv $qu «5 E a .65 98:3 ”mafia comwbawéfiz .H ~33. Metallocene catalysts combine mineral-based chemistry and carbon-based chemistry. Carbon-based compounds (lignands) are attached to metal atoms such as Titanium, hafnium and Zirconium. The process is expensive because it is extremely difficult and at the present time can only done by hand in small amounts (V ernyl, 1995). Characteristics of Polyolefins Polyolefins are a group of therrnoplastics obtained from the polymerization of olefins. An olefin is a member of the alkene series. The term polyolefin is used specifically when referring to ethylene polymers, the alkyl derivatives of ethylene (the a-olefins) and the dienes (Manson 1992,). Polyolefins are used in applications ranging from packaging films to electrical insulation and from containers to pipes. Since the 1950’s, polyolefins have been recognized as versatile materials due to its diverse balance in properties, resistance to chemicals, ease of processibility and total value. These credits are what make polyolefins the most widely used form of plastic there is today. Polyolefins are polymers that are considered commodities and are manufactured from petroleum refining and natural gas. The polymerization processes are clean and leave virtually no waste byproducts or residue making them an environmentally friendly material. Many products of polyolefins (Geotextiles) are used today by civil engineers to improve our environment in construction that .- _——_. J'fl' stabilizes the soil by preventing erosion. After production, pre-consumer scrap is being repelletized and put to use as plastic lumber or footwear. The automotive industry uses polyolefins molded into engine parts and interiors which makes cars less corrosive and lighter resulting in increased longevity and greater fuel efficiency. They are also used to clean up oil, fuel and other hazardous chemical spills. (American Polyolefin Association, 1996) General characteristics of polyethylenes Since polyethylene is a family of resins, there are many different types of polyethylenes based on its molecular weight and molecular architecture. Types range from ultra low-density polyethylenes to ultra high-density polyethylenes that are characterized by their density (Table 2). Their pr0perty differences depend mostly on the degree of branching in the polymer chain, which determines crystallinity (density). The degree of crystallinity in a polymer can be determined from the relationship between its crystalline and amorphous regions. It is the ratio of the two regions and may be expressed in terms of mass or volume. The density gradient technique is a common way of finding a polymers density. The density / crystallinity relationship can be expressed as: a, = (1) a", = ca, (2) where av is the volume crystallinity and am is the mass crystallinity; p, pc, pa are the density of the sample, of the 100% crystalline and 100% amorphous, respectively. Multiplying av or am by 100 give the percent crystallinity (Hernandez, 1997). In general, polyethylene resins can be branched or linear. Branched polyethylenes have short and long branched chains but linear polyethylenes have only short branches. Since crystallinity levels distinguish the groups, branched ethylenes are on the low end and linear on the high end. Branched polymer molecules are not able to pack together tightly and therefore have lower densities. Changes to the polymer’s crystallinity directly affect many important polymer properties. Generally, as crystallinity increases so will the polymer’ 5 density, opacity, heat sealing temperatures and strength However, permeability, impact and tear strength, clarity, and heat sealing ranges will decrease. Density can be controlled during fabrication by the amount and type of comonomer, the reaction conditions and the catalyst used. The amount of comonomer used determines the amount of short chain branching. The choice of comonomer determines the length of the branches. Hexene-1, butene-1 and 4- methyl-pentene-1 are alpha-olefins used, however octene-1 is the most common choice. Hexene and octene yield tougher polymers than butene because they yield longer side chains. The octene-1 comonomer is most used because it produces better physical properties (Taylor, 1994). Table 2. Commercial Classification of Polyethylene Resins, (Source: V. Firdaus and P. Tong, The Wiley Encyclopedia of Packaging Technology, 1997) Pob'ethylme Densiy, g/ml High-density polyethylene (HDPE) 0.940 - 0.970 Medium—density polyethylene (MDPE) 0.926 - 0.939 Low-density polyethylene (LDPE) 0.915 - 0.940 Linear low-density polyethylene (LLDPE) 0.915 - 0.926 Very low-density polyethylene (VLDPE) and 0.88 - 0.915 Ultra low-density polyethylene (ULDPE) The increase in the comonomer content decreases the polymer’ 5 density because, the stereo irregularity in the polymer backbone increase. As crystallinity or density decreases, so do the polymer’s melting point, modulus, and hardness. Stress crack resistance, creep resistance, elongation and melt viscosity all increase as molecular weight increases. Linear Low-Density Polyethylene Linear low-density polyethylene (LLDPE) is similar to conventional low— density polyethylene but differs from it by having short chain branching and a narrower molecular weight distribution. LLDPE became popular in the 1980's and due to its mechanical properties, its use has increased into markets that were once dominated by LDPE. When compared to conventional LDPE, LLDPE boasts improvements in tensile strength, tear resistance and impact strength making it perfect for film applications. In addition, its greater crystallinity makes it stiffer than LDPE giving it 10 - 15°C higher melting temperatures. It has been considered for use as piping, sheet extruding and molding applications due its low temperature impact, stress crack and warping resistance (Hernandez,1997; Taylor, 1994). Ultra Low-Density Polyethylene Very low-density polyethylene is a linear polyethylene and has a density range of 0.890 to 0.910 g / cc. Ultra low-density polyethylene also lies within this 10 range. According to Dow Chemical Company, ULDPE has a density range of 0.880 to 0.890g/ cc. ULDPE offers great flexibility, which was not previously available with LLDPE. It is also tough with a broad operating temperature range that is comparable to linear low-density polyethylene. ULDPE is a relatively new copolymer that has penetrated almost all of the traditional ethylene markets, although most of its success has been in film and sheet applications. Ethylene Vinyl-Acetate (EVA) is the principal victim of the ULDPE assault because it offers better physical properties and comparable optical characteristics. Characteristics of Metallocene polyethylene As indicated, the molecular weight and molecular weight distributions are extremely important and useful parameters of a polymer. For a given resin, a low molecular weight promotes lower temperature processing while high molecular weights are better for finished part properties. The molecular weight distribution of a polymer reveals how its low, medium and high molecular weight components are combined. With these figures, the processor is able to predict the ease of a polymers fabrication. Low molecular weight portions act somewhat like plasticizers; by lowering the melt viscosity and melting temperature, this makes fabrication easier. Increasing high molecular weight components increases the melt viscosity while enhancing the polymer’ 5 mechanical properties (Mason, 1992). Composition and molecular weight distributions become narrower 11 (717 .. 54— n E 2 ) when single site catalysts are employed. This means that there are similar numbers of side comonomer branches at the same place on both sides of the polymer chain (Steininger, 1996). With conventional polymers, processibility is sacrificed, as these distributions become narrower. They have lower shear sensitivity resulting in decreased output rates, which slows productivity and increases the difficulty of producing packages. Narrow distributions in conventional polymers also create surface imperfections due to their higher tendency to melt fracture. To overcome the disadvantages Dow Chemical has produced polyolefin metallocenes by replacing the long chained branching with a linear, short chain branched polymer structure. The technology was called ”INSITE" or constrained geometry catalyst technology (CGCT) and actually improves the melt processibility and polymer flowability without sacrificing other desirable properties. Reported improvements in polymer properties include lower heat seal initiation temperatures, improved clarity, greater toughness and improved resistance to environmental stress cracking. Improved flexibility at low temperatures and better control of melting point has also been indicted. lrnprovements in heat sealability are due to the elimination of high molecular weight/ high density components. For the packager, this means wider sealing windows and reductions in product deterioration usually caused by inconsistent seals). The properties of metallocenes enable them suitable for increased line speeds. This is very important with today’s form fill and seal machines. However, with all of these advances little 12 on the barrier properties to organic vapors has been reported (Steininger, 1996, Simon, 1994). Properties of Metallocene Polyolefins Summary 0 Sealability - This improvement is caused by the absence of the high molecular weight / high-density component. The result is lower peak melting points than those of existing polyolefins. o Optics - improved haze and gloss are also the result of dismissing the high molecular weight/ high density component. 0 Cleanness — Polymers with broad molecular weight distribution tend to be cloudy and oily when melted. The low molecular weight component is eliminated when a metallocene catalyst is utilized. Consequently these polymers have extremely low extractables and are some of the cleanest polymers available. 0 Toughness -- Control of the molecular weight distribution allows the careful addition of comonomers. Increasing the comonomer content enhances the mechanical properties. Values of the dart impact and puncture resistance of the metallocene-catalyzed films are much higher than in conventional polyethylenes (Simon, April 1994). 13 Gel Permeation Chromatography The molecular weight (MW) of a polymer chain is calculated by multiplying the molecular weight of the monomer unit by the degree of polymerization plus the weights of the end-group. Since there is no way to polymerize polymer chains with the same length the molecular weight of a polymer sample is expressed as two averages, the number-average molecular weight (T4... ) and the weight average molecular weight (It? to ). The number-average molecular weight is based on the total number of molecules in the sample being considered and is given by: T] Z w” (3) where w, is the mass of the sample, this is divided by N ,. , the number of molecules (or moles) in the sample. The weight average molecular weight is the average molecular weight based on the total molecular weight in the polymer sample. It is calculated as: I)?» = ZwiM, (4) where M, is the molecular weight and W is the total mass of the sample. It?" and H w along with the dispersion index (Q= ill—n : Tl— .) describe a polymer’ 5 molecular 14 weight distribution. (Throne, 1986) Many important characteristics (tensile strength, melt viscosity, impact strength) are affected by small changes to the MWD and many polymer choices are guided by this parameter. If a converter needs a polymer for heat sealing one with a broad MWD may be selected. They are characterized by good melt strength over a wide temperature range and viscosities that are shear sensitive over wide processing ranges however, low tack is possible. Polymers having a narrow MWD are most likely used for oriented films and / or applications requiring high melt strength. Consequently, for quality purposes processors need an effective means of monitoring their polymer choices. Gel permeation chromatography (GPC) is a common, although expensive method of measuring MWD. The procedure is automatic and usually takes approximately 30 - 45 minutes to reveal not only the MWD but also most polymer additives and some impurities. The GPC process separates the polymer sample molecules by their effective molecular size in a selected solvent. Since the molecular size is directly correlated to the molecular weight, the results of the analysis can be interpreted in terms of MWD. The polymer sample to be analyzed is dissolved in a steadily flowing stream of solvent, the mobile phase, then passed through a column containing a highly porous gel, the immobile phase. This gel has a variety of pore sizes to provide the optimum size range for each separation. The molecular separation process is as follows; the larger molecules permeate the porcus gel quicker than the smaller molecules that permeate into the gel more 15 readily. The time it takes for a specific fraction of substance to pass through a column or ”elute” is called the ”retention” time, since the column retains the smaller molecules longer, they have the greater retention time. The molecules therefore pass through the detector in descending order of molecular size. The detector measures the concentrations and plots the MWD on a strip recorder. Mass Transfer in Polymeric films The mass transfer of gases and vapors is very important to the packaging industry because it affects the quality and shelf life of the packaged product. The phenomenon of mass transfer is the diffusion of a molecule through a flat media driven by difference in concentration across the media. The diffusing molecule tends to reach equilibrium by dissolving into a polymeric material on the high concentration side, and passing through the media to the low concentration side. The tendency of the system to reach thermodynamic equilibrium in concentration of the permeant and the polymeric material allows diffusion to occur. The chemical composition and chain mobility of the polymer effect the motion of the penetrant. According to Van Amerongen (1950) the diffusing molecules actually passes though a polymer structure the free volume in the polymer chains, which are caused by thermal vibrations. This process is said to be an active diffusion process. The diffusion process is low in highly crystalline polymers because the path of diffusion is through the amorphous regions of the polymer, the tight packing of the 16 polymer chains leave fewer voids for molecules to pass through. In partially crystalline polymers (polyolefins) increasing the crystallinity will decrease the molecule’s ability to permeate. (Throne, 1986) From these considerations it is clear that there is no polymer that provides a complete barrier to the transport of gas or vapor molecules (Brown, 1991). Interaction between product and package is certain when utilizing polymeric materials because they are not inert substances and are able to dissolve gases, vapors and other low molecular weight substances. In the packaging industry, several mass transfer processes are important: migration, sorption and permeability. Migration is the movement of molecules present in the packaging material (called migrants) into the product, while sorption (scalping) describes the uptake of product molecules into the polymeric packaging material. These may include flavors, aromas and colorant components. This process is greatly influenced by the chemical composition, size, shape and polarity of the penetrant (Hernandez, 1997). Sorption is enhanced when the chemical structure of the package is similar to that of the sorbate (Van Krevelen, 1990). Permeability is the steady state transfer or ”permeation” of molecules from the external environment through the wall of the package along with the transfer of product molecules to the external environment (Figure 1). The following equation gives the rate of the diffusion across a sheet of polymer film 17 F=i (5) where q is the quantity of permeant travelling across the sheet in time t, and A is the area of the sheet exposed to the penetrant. Adolf Fick is credited for developing the fundamental laws of diffusion. They describe the mechanisms of the migration process that is present in packaging systems (Crank, J. 1975). Fick’s first law describes the rate of transfer of the diffusing molecule per unit area and is expressed as: “—095 (6) where cis the concentration of the permeant in the polymer, xis the direction of the diffusion, and Dis the diffusion coefficient. The negative indicates that diffusion occurs in the direction of decreasing concentration In steady state flow, this rate is directly proportional to the concentration gradient, 3% . When a polymer sheet, with thickness 13 , sees penetrant contact on both sides but with different concentrations, the flow rate of the penetrant across the sheet is given by 17:02.23. 18 Diffusion as a function of time is given by Fick’s second law: 0c 62C 5;")? (8) where tis time. If the diffusant concentration is relatively low, this is usually true for packaging situations, the diffusion coefficient is believed to be independent of polymer relaxation and penetrant concentrations. When Dvaries with time the diffusion is said to be non-Fickian. The concentration of a penetrant in a polymer can be found by using Henry's law of solubility: C=kp (9) where kis Henry’s constant (commonly expressed as S, the solubility coefficient). According to Hernandez (1994) and Gavara and Hernandez (1994) when the diffusion coefficient is independent of permeant concentration, the permeability of the permeant into a packaging material can be calculated by rewriting Henry’s law of solubility as: P = DS (10) where Pis the permeability coefficient, Dis the diffusion coefficient and Sis the solubility coefficient. This is the simplest and most common relation of P, Band 5 19 Figure 1 gives a visual perspective on the relationship between these coefficients. When aromas or flavors are involved, as compared to the use simpler gases, the process of diffusion increases in complexity. The diffusion coefficient may vary depending on the concentration of permeant (Bagley and Long, 1958, Crank, 1975, Berens, 1977). 20 Phase 1 Package wall Phase 2 ( + __' F P2 ———‘ C2 C1 P1 K‘ a ————4 r“; ____. gQ / T {R Sorption Diffusion Desorption (F ick’s law) Figure 1. Permeability model for gas or vapor transfer through a package wall. (Source: Dr. R. I. Hernandez, The Wiley Encyclopedia of Packaging Technology, 1997) Sorption Measurements The sorption coefficient together with the diffusion coefficient is one of the important parameters used when selecting a polymer for barrier purposes. The gravimetric technique is a widely accepted method of obtaining S values. Using a polymer sample of known weight, the solubility of the sample can be obtained by monitoring the weight of the vapor sorbed by the sample. While testing, one can record the continual measure of weight change by the polymer sample as a function of time. This can be done after equilibrium vapor pressure is reached (Baner, 1987). According to Hernandez et al. (1986) both the solubility and the diffusion coefficients can be determined by using the sorption measurements. The equation used to obtain the diffusion of sorbate through a polymer film is describe by Crank (1975), using only the first two terms of the series, as: 8 (—D7r2t) 1 (—9D7r2t) —'=1- — ex —————+—ex —— 11 M (7:2)[ p (2 9 p 32 ( ) where M. is the amount of sorbate sorbed or desorbed by the polymer sample at time (t), M... is the equilibrium sorption level at steady state, t is time to attain M. and E is the thickness of the polymer sample. A first approximation of the diffusion coefficient can be calculated by the following equation: (12) where f is the thickness of the film sample and ms is the time required to reach the sorption level equal to half the equilibrium value, M... The solubility coefficient can be calculated by the following equation 5 = . (13) where Cw is the weight gain by the polymer sample from the time zero to equilibrium, Fw is the weight of the film before exposure to the permeant and p is the partial pressure of the sorbate. MATERIALS AND METHODS Materials Polyolefin films 0 Attane 4201, Ultra Low Density Polyethylene Resin (Dow Plastics, Midland, MI) 0 Affinity PF 1140, Metallocene polymer (Dow Plastics, Midland, MI) Sorbates Ethyl Acetate and Limonene were used as the sorbate molecules. O-xylene was used as the solvent to make the standard calibration curve for ethyl acetate and acetonitrile was use to make the standard calibration curve for limonene. o Ethyl Acetate (CHaCOOC2Hs) EM Science (Gibbstown, NJ) Molecular weight 88.11 Boiling point 77°C Density 0.902 - Limonene (CioHra) Aldrich Chemical Company (Milwaukee, WI) Molecular weight 136.24 Boiling point 175.5-176°C Density 0.8402 - O-xylene (Cal-14(CHa)2) J. T. Baker Incorporated (Phillipsburg, NI) 24 Molecular weight 106.17 Boiling point 143 -145°C Density 0.8811 0 Acetonitrile (CHsCN) EM Science (Gibbstown, NJ) I-IPLC grade Molecular weight 41.05 Boiling point 81 .6°C Density 0.78745 0 Nitrogen Gas 99.98% pure, dry nitrogen was used as the carrier gas. Methods Film sample preparation Rectangular samples of Affinity PF 1104 and Attane 4201 film were cut and placed in a vacuum oven for 48 hours to remove excess moisture. Each sample weighed between 85 and 105 milligrams. A small triangle was cut from the sample to enable it to be suspended inside the digital balance. After a second weighing, the samples were placed onto the nichrome wire, which is connected directly to the balance. This allows them to hang freely in the hang down tube. Nitrogen was flowed through the balance to remove any remaining moisture. This was done until the graph of the digital balance was flat; at that point, the sample was considered completely dry. Then the test to measure the sorption of the organic compound began. The thickness of the film was measured using a Testing Machines Inc. micrometer model 549 (Amityville, NY.) This had to be done before testing to insure correct thickness was taken. Measuring after completion of a test can yield incorrect data due to the polymer swelling as sorption occurs. Sorption Measurements The weight gained by polyolefin sample films due to the sorption of the organic compounds can be carried out by the gravimetric technique (Hernandez et al, 1996, Nielsen and Giacin, 1994). This technique has several advantages, which are: (i) relative ease in handling the polymer sample; (ii) recording of the weight gain by the sample film as a function of time; (iii) accurate measurement of sorbate uptake; (iv) data for determining the sorption (S) and diffusion coefficients (D). The CAI-IN D-200 Digital Recording Balance (CAHN Instruments, Cerritos, CA) was utilized to handle this task. Figure 2 presents a schematic of the Digital Recording Balance. The hang down tube of the digital balance was encased in a Therrnotron Controlled Temperature / Humidity Chamber SMSSH (Thermotron Industries, 26 853m wfipuooom 3&5 o5 wo owgoaom .N 3:me £95m Bfibom 839m M; 5 .8389? _obcoo gmgfioh Eogofi 27 Holland, MI). The tests were run at temperatures of 23°C and 32°C. Nitrogen gas was bubbled through the selected liquid organic to convert it to vapor. The average concentration c, of organic vapor in the hang down tube of the digital balance during this exercise was calculated as follows: (14) where C1-- is the calibration factor, AR is the average area response, Vi is the volume injected into the gas chromatograph. At the completion of one test, the balance w prepared for another test by flushing the system with nitrogen gas. Gas Chromatographic Analysis A 50-11] sample was taken from the sampling port of the hang down tube with a Hamilton 500 ul 1750 gastight ® syringe. The sample was injected directly into a Hewlett- Packard (Model 5890A, Avondale, PA) gas chromatograph equipped with flame ionization detection was utilized for the analysis of the permeant concentration. The chromatograph was interfaced with a Hewlett-Packard model 3392A integrator for quantification. The settings of the gas chromatography are as follows: Column: Supelco SPB-5 Fused silica capillary column 30 m length and 0.32 mm ID. carrier gas: Helium at 1.5 ml/ min Purge on: 1 min. Zero: as same as signal after ignition Attenuation: 0 Temperature cycle for ethyl acetate: Range 2 Detector temp. 250° Injection temp. 220°C Initial temp. 40°C Initial time 4 min Temp. Rate 5°C/ min Final temp. 220°C Final time 10 min Temperature cycle for limonene: Range 2 Detector temp. 250° Injection temp. 220°C Initial temp. 75°C Initial time 1 min Temp. Rate 5°C/ min Final temp. 220°C Final time 10 min Inlegmtor settings: Zero 0,1447 Attenuation 2 Chart speed 1.0 Area rejection 1000 Threshold 0 Peak width 0.04 Retention time: Ethyl acetate 4.64 minutes Limonene 5.93 minutes Standard calibration curves of detector area response versus mass injected were prepared from standard solutions of known concentration; this was done for each permeant. Calibration Curves To build the calibration curve for ethyl acetate, five 4-ml vials (Supelco, Bellefonte, PA) were prepared containing varying concentrations of ethyl acetate in o-xylene. First the tare weight of each vial was taken then two drops of ethyl acetate (Pasteur pipet, VWR Scientific, West Chester, PA) was added to vial 1. The same vial was weighed again then filled with o-xylene and weighed a final time. Vial 1 contained the largest concentration of ethyl acetate; the remaining vials were prepared using it as stock. Drops from vial 1 were placed into vial 2, weighed, and then the vial was filled with o—xylene and weighed again. Vials 3 - 5 were prepared in similar fashion. The concentration, g / cm3, of ethyl acetate in via] 1 was calculated by: (15) where War is the weight of the drops of ethyl acetate, px is the specific gravity of xylene, Wx is the weight of the xylene drops. Three samples of 7 )4] were taken from each vial and injected into the gas chromatograph model 5890A (Hewlett Packard, Boise, ID) using a 100 pl Microliter® liquid syringe (Hamilton Co., Reno, NV) (see table 3). The average area responses of these injections were plotted against the mass of ethyl acetate present in each vial to build the calibration curve. (Figure 3) Table 3. Calibration data for Ethyl Acetate in Xylene with a 7 p 1 injection volume MASS INJECI‘ED AVERAGE AREA RESPONSE (GRAMS) 6.5259E-06 81,632,500 1.367OE-06 15,942,134 2.0500E-07 451,066 4.7318E-08 206,932 1.0884E-08 40,301 31 9.0E+07 .///‘/ <3: 6.0E+07 - //” 8. 1 8 a: g 3.01~:+07 4- y - 1.246E+13x f R2 - 0.9988 /. / / 0.0E+00 o/ . 1 . . 1 , 0.0E+00 2.05.06 4.0E—06 6.0E-06 Mass, grams Figure 3. Calibration curve for Ethyl Acetate by gas chromatograph 32 Calculating the Diffusion Coefficient The sorption data (time and experimental wt. gain) obtained by testing each sample in the digital balance was transferred to an Excel worksheet. The worksheet was designed to handle most of the calculations needed to find the experimental diffusion coefficient and display the associated equilibrium sorption plot. In addition to the sorption data, the vapor pressure of the penetrant, thickness of film and the concentration of penetrant in the hang down tube were the inputs for the worksheet’ 5 analysis. When the sorption data was placed into the worksheet, it immediately listed the maximum wt. gain. To find t1/2, the maximum gain was simply divided by 2; the time needed to reach that weight was considered t1/2. Once this value was entered into the appropriate cell, the experimental diffusion coefficient was calculated using equation (12). To determine if the diffusion process had Fickian behavior, another column was added beside the columns of raw data. This was to demonstrate the results of a curve produced by using data generated by equation (ll). If this calculated data curve had good agreement with the experimental data curve, then the diffusion behavior of the polymer sample would be considered Fickian. A numerical procedure was applied to determine the best estimate of the diffusion coefficient value. This was accomplished by the minimization of the sum of squares technique. The same data used to calculate the diffusion coefficient was placed in an expanded worksheet that plotted the diffusion coefficient values against 33 sum of squares. If the calculated D value matched the lowest D value on the D vs. SS curve then it was considered the best estimation of D. Molecular Weight Distribution The molecular weight distribution was determined using gel permeation chromatography. A Waters 150-C ALC-GPC (Waters Assoc. Inc., Milford, MA) equipped with a series of four u-Styragel® column (pore size 10‘, 10", 105 and 106 A) was the GPC apparatus used. The test conditions were: Solvent 1,2,4, trichlorobenzene Flow rate 0.5 ml/ min Injection volume 0.1 ml Temp. 135°C Statistical Analysis The statistical analysis was performed using Minitabeor Windows Release 10.5 Xtra (Minitab Inc., State College, PA). A General Linear Model analysis of variance was done for sorption and diffusion with the alpha set at 0.05 to yield results with a 95% confidence level. The aim was to determine if any statistically significant difference existed between the sorption and diffusion coefficients of Metallocene and ULDPE films at the same temperature. If the analysis produced p—values greater than 0.05 the conclusion was that no significant difference existed at 95% confidence. The best estimates of the sorption and diffusion coefficients were used in the Minitab worksheet as the responses and film, sorbate and temperature interactions made up the model. Table C - 1 in Appendix C shows the setup of the Minitab worksheet. RESULTS AND DISCUSSION Film thickness Table 4 shows the results of the efforts to gain the thickness of the selected film samples. The table illustrates the closeness of the thickness of the polymers and lends us one view of their similarity. Table 4. Thickness measurements of the selected polyethylene samples. ATI'ANE AFFINITY 1.90 2.00 1.89 2.05 1.90 1.90 1.90 1.87 1.90 1.90 1.91 1.92 1.90 1.80 1.90 1.90 1.99 1.80 1.90 1.85 1.99 1.82 1.90 1.83 Avg- 1.92 1.89 St. Dev. 0.0334 0.074 gr, 1.764 3.91 Molecular Weight Distribution The GPC study to determine each polymer sample’s Molecular Weight Distribution yielded the expected results. Table 5 shows the number average molecular weight, the weight average molecular weight and the dispersion index. It is clearly seen that the Attane polymer had a significantly higher A7... and a much lower A7. . The dispersion index was the final confirmation of the difference in molecular weight distributions showing that the Affinity (metallocene) polymer had a MWD that was much narrower than the Attane (ULDPE) polymer. Figure 4 presents the comparison of the distributions with the Attane represented by the bold solid curve and the Affinity by the thin solid curve. Table 5. Statistics for the Molecular Weight Distribution of the selected polymers ATTANE AFFINITY Mw 79,170 60,190 Mn 17,800 25,080 DI 4.4 2.4 37 ESE .85on goo—om 05 ecu cousnwamfi 2&6?» .3162on .v gamma £5 25 mm 3 3 1R 8 mu 3 2 4 _ - - _ _ _ . - Ammo: 2.8.; ANZMUOAQPNEV 3:": ram? 5.. ma Diffusion and Solubility Coefficients The diffusion and solubility coefficients of Ethyl Acetate and Limonene in the polymer samples were obtained at 23°C and 32°C. As expected, the diffusion coefficient increased when the temperature was increased. Also as expected the solubility coefficient value decreased with an increase in temperature. The metallocene polymer reached equilibrium faster (higher diffusion coefficients) at both temperatures when ethyl acetate was the sorbate. The opposite was observed when limonene was the sorbate. It appeared that ULDPE sorbed more ethyl acetate than the metallocene polymer, when limonene was sorbed temperature altered that trend. At 23°C the metalallocene film sorbed more limonene but at 32°C ULDPE sorbed more. Summaries of the results are presented in Tables 6 and 7. Plots of Mt/ M .0 were done for each test, examples of these are shown in Figures 5 - 8. Superimposed onto the experimental data curve is the calculated data curve produced by using equation 11, the Fickian model. As seen in Figures 5 - 8 the calculated curves are in good agreement with the experimental curves, therefore we can state that the polymer’ 5 diffusion process showed a Fickian behavior. We can also consider that equation 12 will provide a good first estimation of diffusion coefficient. After the first estimation of D using equation 12, a search to improve the accuracy of the diffusion coefficient was performed by minimizing of the sum of 39 squares between the experimental and the calculated values. Figure 9 gives an example of the plots produced by this analysis. As stated earlier, the D value on the curve that minimizes the sum of squares is considered the best estimate of the diffusion coefficient. Statistical Analysis The results of the ANOVA are presented in tables C - 2 and C - 3 in Appendix C. In fire ANOVA for diffusion analysis, the p-values for temperature was 0.035, lower than 0.05 indicating that differences in behavior of the diffusion coefficient exist as you change the temperature, this was expected. In the same test the p-value for the interactions of film x sorbate was 0.055 pointing out that there may be differences. Tables C - 2 and C - 3 also show that the p-values for film with respect to sorption (0.278) and diffusion (0.979) were greater than 0.05, this indicates that no statistically significant difference existed. Table 6. Summary of D x 10“ m2 s1 METALLOCENE ULDPE 23°C 32°C 23°C 32°C ETHYL ACETATE 7.5 7.7 6.7 7.0 LIMONENE 1.5 1.7 1.8 1.9 41 Table 7. Summary of S x 105, cm3 (STP) cm'3 Pa-1 (STP = standard temperature and pressure = 273.15K; 1.013 x 105 Pa) METALLOCENE ULDPE 23°C 32°C 23°C 32°C ETHYL * ACETATE 11.9 9.2 5.7 12.2 LIMONENE 183 102 175 118 * It is suspected that the sorbate concentration in the gas phase was lower than the calculated value, and therefore the reported value 5.7 is suspected to be an anomalous low value. N 1 weight gain, mgs 0 25000 50000 seconds 0 Experimental Gain Theoretical Gain Figure 5. Sorption of Ethyl Acetate by Metallocene film at 23°C 1: Experimental Gain is the weight gained by the polymer sample as recorded by the Digital Recording Electrobalance 1 Theoretical Gain is the weight gained by the polymer sample as calcuted by the Fickian Model (equation 11) 43 weight gain, mgs 0 111111111 llLLlJlLllLLLIAAAALAJ T l 0 50000 100000 150000 seconds A Experimental Gain Theoretical Gain Figure 6. Sorption of Limonene by Metallocene film at 32°C weight gain, mgs lb 1 N 1 seconds A Experimental Gain Theoretical Gain Figure 7. Sorption of Limonene by ULDPE film @23°C 45 weight gain, mgs 0 ‘K A A A l L A A l A A L i A A A l V I I 7 fl 0 20000 40000 60000 80000 seconds Theoretical Gain] 0 Experimental Gain ....... Theoretical Gain2 Figure 8. Sorption of Ethyl Acetate by ULDPE film at 32°C $5 1.8 1.6 J’ 1.4 J 1.2 1. 0.8 1 0.6 ~ 0.4 1 0.2 -I Figure 9. Minimization of the Sum of Squares study Trrrt YTTI 111 I YTYYTVI'Y'YIVYYY IVY IT! 4441#A411%AAA AAAAAr l O l T 55-14 15-13 155-13 215-13 Diffusion Coefficient 47 2.5E—13 3E-13 Some of the sorption curves appeared to show a phenomenon called bimodal diffusion, as described by Hernandez and Gavara (1992). This process differs from what we commonly deem a normal sorption curve. When we would usually consider the sorption process to have reached steady state, the curve begins to increase again until reaching a second equilibrium (see Figure 10). Bimodal diffusion is described as two simultaneous but independent diffusion processes, one fast and the other slow. The difference goes unnoticed until the fast diffusion process begins to reach steady state at that time the slow diffusion process becomes a factor. The cause of the phenomena has not been determined, in these studies the changes in temperature, sorbate concentration or film sample didn’t appear to be the main factor as to when the anomalous sorption would occur. It did however occur most often during the tests run with ethyl acetate as the sorbate and ULDPE as the film sample. All of the tests run with that combination resulted in an apparent ”bimodal” sorption curve. The bimodal treatment as indicated in Hernandez and Gavara (1992) was not applied because there was not a confirmed fact; instead, ”upper” and ”lower” sorption curves were calculated from which two D values were obtained (Figure 10)to give a sense of how the diffusion may change. One curve followed the plot with the slower diffusion rate (the higher curve); the other curve followed what we typically consider a normal sorph'on plot. Tables 8 and 9 present these D values along with the differences and averages. weight gain, mgs o i} r 1 r l r 1 AL I 1 1 A l l I j 0 20000 40000 60000 seconds Theoretical Gain] 0 Experimental Gain ------- Theoretical gain2 Figure 10. Example of Bimodal sorption of Ethyl Acetate by ULDPE at 32°C 49 The dual sorption phenomena may simply be a polymer relaxation that manifests itself after long sorption periods. The differences between the upper and lower sorption curves were much greater in the ULDPE film, and occurred more when the temperature was increased to 32°C. This could be a demonstration of the contrasts in polymer properties that exists between the two films. It could also be an indication that the ULDPE film relaxes more than the Metallocene film as temperature increases. 50 Table 8. Differences and averages of the Dual Sorption process, Ethyl Acetate sorbate Metallocene ULDPE 23 °C 32°C 23°C 32°C 51W" 7.6 7.6 7.0 7.0 9.3 9.9 8.0 process F‘s”) 7.5 7.2 6.0 6.8 7.3 7.1 5.9 process Difference 0.1 0.4 1.0 0.2 2.0 2.8 2.1 Avg. 7.55 7.4 6.5 6.9 8.3 8.5 6.95 51 Table 9. Differences and averages of the Dual Sorption process, limonene sorbate Metallocene ULDPE 23°C L 32°C 23°C 1 32°C 5’0"” 1.6 2.5 0.0 2.5 2.4 process FWD 1.5 2.1 0.0 2.0 2.1 process Difference 0.1 0.4 0.0 0.5 0.3 Avg. 1.55 2.3 0.0 2.25 2.25 52 SUMMARY AND CONCLUSIONS Sorption studies by the gravimetric procedure were done at 22°C and 32°C focusing on the determination of the diffusion and solubility coefficients. The tests were done utilizing the CAHN D-200 Digital Recording Balance and analyzed with the gas chromatograph. From the results presented in the previous section, the following conclusions were made: 1. The calculated sorption plots according to the Fickian model matched well with the experimental sorption plots of both polymers thus their diffusion processes had Fickian behavior. 2. Although the Affinity PF 1140 (metallocene) film has different physical properties (narrower molecular weight distribution, increased crystallinity, density, etc.), it behaved similarly to Attane (ULDPE) with respect to the sorption coefficient of ethyl acetate and limonene. Statistical analysis proves with a 95% level of confidence that no significant differences existed between the film samples. Therefore, we did not confirm claims by metallocene producers that the metallocene films sorb much less than LDPE or ULDPE. 53 APPENDIX A 2 ,. 2 - 9 vii V W ' o 0 0.0.9 9 9....9.2.?.3.3...f ................... U) 60 S a 1 . b0 2 3° 0; 3 0 \ i ‘ i i A ‘ ‘ i L 1 ‘ 1D 0 20000 40000 60000 80000 seconds 0 Experimental Gain Theorectical Gainl ------- Theoretical Gain2 Figure. A-1. Sorption of Ethyl Acetate by ULDPE at 32°C, test 1 Table. A-1. Sorption of Ethyl Acetate by ULDPE at 32°C, test 1 Wto 0.1065 mg 106.5 Max Gain 1.9699 mg 1.85 half of Max 0.98 mg 0.93 thickness 4.86E—05 meters 4.86E-05 time1/2 1585 seconds 1500 D1/2 7.31E-14 mz/s 7.7E-14 Dmm 7.30E-14 m2/ s 9.30E-14 c 4.24 mg/ L 4.24 p 122 pascals 122 S 1.51E-04 Pa-1 1.42E-04 o°°AA °°°°l U) 50 a r -§ 1 4 b0 3:” 3° 0) 3 0 g e 1 1 . . e e e 1 0 20000 40000 60000 seconds Theoretical Gainl 0 Experimental Gain ------- Theoretical gainZ Figure. A-2. Sorption of Ethyl Acetate by ULDPE at 32°C, test 3 Table. A-2. Sorption of Ethyl Acetate by ULDPE at 32°C, test 3 wto 0.10346 mg 103.46 Max Gain 1.8744 mg 1.7256 half of Max 0.9372 mg 0.8628 thickness 4.86E-05 meters 4.86E-05 time1/2 1523 seconds 1375 D1 /2 7.6E-14 m2/ 8 8.4E-14 Dear-“hm 7.1E-14 m2/ 5 9.9E-14 C 4.84 mg/ L 4.84 p 139 pascals 139 S 1.30E-04 Pa“1 1 .20E-04 55 weight, mgs 0 o o o 0 o o o 0 0 ,,6..6.-9..9 ............................................ 9,.0 i. I i ITL 0%4414461 11.11 0 20000 40000 60000 seconds Experimental Gain Theoretical Gainl ------- Theoretical Gain2 Figure. A-3. Sorption of Ethyl Acetate by ULDPE at 32°C, test 4 Table. A-3. Sorption of Ethyl Acetate by ULDPE at 32°C, test 4 wto 0.0971 mg 97.1 Max Gain 1.9573 mg 1.7476 half of Max 0.97865 mg 0.87 thickness 4.86E-05 meters 4.86E-05 time1/2 192 seconds 1646 D1 /2 6.0E-14 m2/ 8 7.0E-14 Dcalculated 5.90E-14 m2/ S 8.0E-14 c 8.35 mg/ L 8.35 p 240 pascals 240 S 8.38E-05 Pa.1 7.49E-05 56 4*] )_.| _.+__ _ _..-. __.r._. .. weight gain, mgs O L I 4 I; A ‘ 0 20000 0 Experimental Gain A A i 60000 80000 40000 seconds Theoretical Gain1 ------- Theoretical Gain3 Figure. A-4. Sorption of Ethyl Acetate by ULDPE at 23°C, test 5 Table. A-4. Sorption of Ethyl Acetate by ULDPE at 23°C, test 5 Wto Max Gain half of Max thickness time1/2 D1/2 Dcalculated c P S 0.09223 1.2986 0.6493 4.86E-05 1722 6.7E-14 6.00E-14 9.70 279 5.05E-05 mg 92.2291 mg 1.2541 mg 0.63 meters 4.86E-05 seconds 1680 m2/ s 6.9E-14 m2/ s 7.0E-14 mg / L 9.70 pascals 279 Pa-1 4.87E-05 57 I I I I weight gain, mgs I i I I I I I O L 1 1 1 I A A 1 ' A 4' A I L 1 4 A T i T T 0 20000 40000 60000 80000 seconds Theoretical Gain1 0 Experimental Gain ....... Theoretical GainZ Figure. A-5. Sorption of Ethyl Acetate by ULDPE at 23°C, test 6 Table. A-5. Sorption of Ethyl Acetate by ULDPE at 23°C, test 6 wto 0.10014 mg 100.14 Max Gain 1.5335 mg 1.49 half of Max 0.76675 mg 0.745 thickness 4.86E-05 meters 4.86E-05 time1/2 1714 seconds 1645 D1/2 6.8E-14 m2/ 8 7.0E-14 Damaged 6.80E-14 m2/ 8 7.0E-14 c 8.05 mg/ L 8.05 p 232 pascals 232 S 6.61E-05 Pa-1 6.42E-05 58 OJ N T—‘T‘F'fi—‘T— ‘T—""'Y_"'_‘+—‘ " ‘r—_ ‘*"""”‘—'— _ ‘ weight gain, mgs 41 T 0 25000 seconds I 0 Experimental Gain — Theoretical Gain I Figure. A-6. Sorption of Ethyl Acetate by Metallocene at 23°C, test 1 Table. A—6. Sorption of Ethyl Acetate (by Metallocene at 23°C, test 1 wto 0.1011 mg Max Gain 2.5537 mg half of Max 1.28 mg thickness 4.79E-05 meters time /2 1486 seconds D1 /2 7.6E-14 m2/ s Dmted 8.0E-14 1112/ S c 7.93 mg / L p 228 pascals S 1.11E-04 Pa-1 59 .._.. oooooo°°°°°°v: ::°6 0‘ 2 i I "J I °° I E I .5 I «1 90 I 3 I on 1 ' 3 '8 I 3 I I I I l I o 1 r 1 A 9 1 j. A I 0 25000 50000 seconds 0 Experimental Gain —Theoretical Gain Figure. A-7. Sorption of Ethyl Acetate by Metallocene at 23°C, test 2 Table. A-7. Sorption of Ethyl Acetate by Metallocene at 23°C, test 2 wto Max Gain half of Max thickness time1/2 [)1/2 Dcalculated c P S 0.100 2.4573 1.22865 4.79E-05 1489 7.56E-14 7.50E-14 13.63 392 6.26E-05 mg mg mg meters seconds m2/ s m2/ 5 mg / L pascals Pa-1 60 weight gain, mgs L L l A 40000 80000 1 20000 c: otb L r t L I 1 I. seconds Theoretical Gain1 0 Experimental Gain ------- Theoretical Gain2 Figure. A-8. Sorption of Ethyl Acetate by Metallocene at 32°C, test 3 Table. A-8. Sorption of Ethyl Acetate by Metallocene at 32°C, test 3 wt0 0.08822 mg 88.215 Max Gain 2.2146 mg 2.0549 half of Max 1.1073 mg 1.02745 thickness 4.79E-05 meters 4.79E-05 time1/2 1594 seconds 1479 D1/2 7.06E-14 mZ/s 7.61E-14 Dcakumed 7.20E-14 mZ/ s 7.80E-14 c 8.63 mg/ L 8.63 p 248 pascals 248 S 10.11E-5 Pa-1 9.38E-5 61 9.0.9 ------------------------------------------ I i I i m I b0 I E I 3 I .2" a) 3 033A....11..L.A.A, 21211 0 40000 80000 120000 seconds 0 Experimental Gain Theoretical Gain1 ------- Theoretical Gain2 Figure. A-9. Sorption of Ethyl Acetate by Metallocene at 32°C, test 4 Table. A-9. Sorption of Ethyl Acetate by Metallocene at 32°C, test 4 wto 0.0995 mg Max Gain 1.9225 mg half of Max 0.96125 mg thickness 4.79E—05 meters time1 / 2 1680 seconds D1 /2 6713-14 m2/ 5 Dcalculated 7.5E-14 1112/ S c 4.16 mg /L p 120 pascals S 16.2E-5 Pa-1 99.5 1.7565 0.87825 47913-05 1534.5 7.3E-14 7.6E-14 4.16 120 14.8E-5 62 weight gain, mgs 0 20000 40000 60000 seconds Figure. A-10. Sorption of Ethyl Acetate by Metallocene at 32°C, test 5 Table. A-10. Sorption of Ethyl Acetate by Metallocene at 32°C, test 5 wto 0.092291 mg Max Gain 1.6808 mg half of Max 0.8404 mg thickness 4.79E-05 meters time1/2 1481 seconds D1 /2 7.6E-14 m2/ 8 DWM 7.5E-14 m2/ 5 c 8.35 mg/ L p 240 pascals S 7.58E-05 Pa-1 63 01 L .2. i A I a, 4 i I E . \ I i . 3 I i. I 1 :a I I no I I .8 2 ‘ a I I I 1 I I 0 ‘AI 1 - 1_1 1 1 1 I 1 - 1_+ 1 1 1 A 1 A 1‘ - 1# A_A 1 1 1 1 1 I 0 40000 80000 1 20000 1 60000 seconds A Experimental Gain —Theoretical Gain Figure. A - 11. Sorption of Limonene by ULDPE at 23°C, test 1 Table. A - 11. Sorption of Limonene by ULDPE at 23°C, test 1 wto 0.1075261 mg Max Gain 5.2787 mg half of Max 2.63935 mg thickness 4.86E-05 meters time1/2 7308.492 seconds D1 /2 1.59E-14 m2/ S Dcalculated 1.601344 m2/ 8 c 0.66 mg / L p 18.88 pascals S 2.60E-03 Pa-1 7*‘1‘ r—“ If co 4 T , w I 1 I 5 I I 6 I I 9° I I 3:3 I l .29 I m 2 I 3 I O 4 mm_1 ;%1 1 1 1 1 1 m1 . 1 . 1 . 1 1 1 1 1 fir 1 1 1 I 0 50000 100000 150000 seconds A Experimental Gain ——Theoretical Gain Figure. A - 12. Sorption of Limonene by ULDPE at 23°C, test 2 Table. A - 12. Sorption of Limonene by ULDPE at 23°C, test 2 wto 0.103436 mg Max Gain 4.6718 mg half of Max 2.3359 mg thickness 4.86E-05 meters time1/2 6214.5 seconds D1 /2 1.87E-14 m2/ S Dcalculated 2.00E-14 m2/ S C 1.41596 mg / L p 40.75416 pascals S 1.11E-03 Pa-1 65 “‘I—T ‘Y 1' v w 4 .p. -_ Y‘fifi‘h'fl’“ f-WhT—Y‘TV _ ‘i— Y‘ weight gain, mgs N 7 T 0 20000 40000 60000 80000 100000 120000 140000 160000 seconds A Experimental Gain ——'Iheoretical Gain Figure. A - 13. Sorption of Limonene by ULDPE at 23°C, test 3 Table. A - 13. Sorption of Limonene by ULDPE at 23°C, test 3 wto 0.10159 mg Max Gain 4.9183 mg half of Max 2.45915 mg thickness 4.86E-05 meters time1/2 5960.97 seconds D1 /2 1.94E-14 m2/ S Dcalculated 2.20E-14 m2/ S c 1.09 mg / L p 31.32 pascals S 1.55E-03 Pa-1 66 Y‘ 47".“ SI a: I I if“ I .g 3% I °° I 4.0 '50 I 132 I 3 I I I 1~ I I 0 50000 100000 150000 seconds A Experimental Gain —Theoretical Gain1 Figure. A - 14. Sorption of Limonene by ULDPE at 32°C, test 4 Table. A - 14. Sorption of Limonene by ULDPE at 32°C, test 4 wto 0.102111 mg Max Gain 5.4158 mg half of Max 2.7079 mg thickness 4.86E-05 meters time1/2 5599.82 seconds D1 /2 2.07E-14 m2/ S Dmted 2.00E-14 m2/ s c 1.59 mg/ L p 45.80 pascals S 1.16E-03 Pa-1 67 \l 0‘ U1 N 09 uh .'—r‘ i—V—r-w—‘I'fi—w—f—‘I—rfifl Tfi—f—+‘”T“Y_ 1‘71 weight gain, mgs 0 1L1114141111111111IA11111141fi1A 0 20000 40000 60000 80000 100000 120000 140000 seconds A Experimental Gain Theoretical Gain1 ------- Theoretical Gain2 Figure. A - 15. Sorption of Limonene by ULDPE at 32°C, test 5 Table. A - 15. Sorption of Limonene by ULDPE at 32°C, test 5 Wto 0.092658 mg 92.658 Max Gain 6.059 mg 5.8598 half of Max 3.0295 mg 2.9299 thickness 4.86E-05 meters 4.86E—05 time1/2 6801 seconds 6604 D1 /2 1.70E-14 m2/ 5 1.8E-14 Dmhed 2.00E-14 m2/ 5 2.5E-14 c 1.98 mg / L 1.98 p 57 pascals 57 S 1.15E-03 Pa-1 1.11E-03 68 weight gain, mgs 0 1 4 A 1 A 1 1 1 1 A ‘ A A 4 - .1 A A 1 A A g1 11 MA 1 1 I Y f 0 40000 80000 120000 seconds A Experimental Gain Theoretical Gain1 ------- Theoretical Gain2 Figure. A - 16. Sorption of Limonene by ULDPE at 32°C, test 6 Table. A - 16. Sorption of Limonene by ULDPE at 32°C, test 6 wto 0.101573 mg 101.5728 Max Gain 6.1249 mg 5.9728 half of Max 3.06245 mg 2.9864 thickness 4.86E-05 meters 4.86E-05 time1/2 5794.15 seconds 5595.32 D1/2 2.00E-14 m2/ s 2.07E-14 Dmted 2.10E-14 m2/ 8 2.40E-14 1.68 mg / L 1.68 48.40 pascals 48.40 1.25E-03 Pa-1 1.22E—03 (D'Ufi 69 .A-A-A-A-A-A-A-O.O.9.9.H—‘A_ _ __ _ ,, I I I I I i I 1 . J l 1 7 I .1 3’0 5 I E .s: 4 (6 5° 3 i=1; '8 2 3 1 0 . 0 50000 A Experimental Gain ------- Theoretical Gain2 100000 150000 seconds Theoretical Gain1 Figure. A - 17. Sorption of Limonene by metallocene film at 22°C, test 2 Table. A - 17. Sorption of Limonene by metallocene film at 22°C, test 2 Wto 0.09623 Max Gain 6.5548 half of Max 3.2774 thickness 4.792E-05 time 1/2 8634 D exp 1.5E-14 Dcalulated 1.5E-14 c 1.25 p 36 S 1.90E-03 0.09623 mg 6.3302 mg 3.1651 meters 4.79214E—05 s 8239 m2/ 8 1 .4E-14 m2/ 5 1 .6E-14 mg / L 1.25 pascals 36 Pa-1 1 .83E-03 70 weight gain, mgs o b A L A l i l i l 41 A T 0 50000 100000 150000 200000 250000 seconds A Experimental Gain —Theoretical Gain Figure. A - 18. Sorption of Limonene by metallocene film at 22°C, test 3 Table. A - 18. Sorption of Limonene by metallocene film at 22°C, test 3 wto 0.09154 mg Max Gain 6.52340 mg half of Max 3.26170 mg thickness 4.79E-05 meters time1/2 7262 seconds D1 /2 1.55E-14 m2/ 5 Dcalculated 1.7E-14 m2/ 5 c 1.26 mg / L p 36 pascals S 1.96E-03 Pa-1 1h weight gain, mgs 0) seconds I 0 50000 100000 150000 A Experimental Gain —Theoretical Gain Figure. A - 19. Sorption of Limonene by metallocene film at 32°C, test 4 Table. A - 19. Sorption of Limonene by metallocene film at 32°C, test 4 wto 0.08931 Max Gain 7.2289 half of Max 3.61445 thickness 4.79E-05 time1/2 7067 D1/2 1.59E-14 Dcmgd 1.90E-14 c 2.14 p 62 S 1.31E-03 mg mg mg meters seconds m"2/ s m"2/ s mg / L pascals Pa-1 72 weight gain, mgs 0 A 1 1 m +- L 1 I u v 0 50000 100000 seconds A Experimental —Theoretical Gain Figure. A - 20. Sorption of Limonene by metallocene film at 32°C, test 5 Table. A - 20. Sorption of Limonene by metallocene film at 32°C, test 5 wto 0.09076 0.007256 Max Gain 7.2558 mg half of Max 3.6279 mg thickness 4.79E-05 meters time1/2 6768 seconds D1/2 1.66E-14 m"2/ s Dcalculated ZOE-14 m"2/ S c 12.11 mg / L p 349 pascals S .2E-3 Pa-1 U1 0‘ .5. weight gain, mgs 03 ~ +—Y—r-+-r-*r~—+*T—‘r'r ifiT~+—r~ I I I I I I J 2 . 1 0 EA! 4 g I 44 ‘ 4 r i—T 0 50000 100000 150000 seconds A Experimental —Theoretical Gain1 ————— Theoretical Gain2 Figure. A - 21. Sorption of Limonene by metallocene film at 32°C, test 6 Table. A - 21. Sorption of Limonene by metallocene film at 32°C, test 6 wto 0.08965 mg 89.646 Max Gain 6.7478 mg 6.5 halfof Max 3.3739 mg 3.25 thickness 4.78E-05 mg 4.775E-05 time1/2 6153 meters 5834 D1/2 1.82E-14 1112/ s 1.9E-14 Dcalculated 2.1E-14 mz/s 2.5E-14 c 1.68 mg/ L 1.68 p 48 pascals 48 S 1.55E-03 Pa-l 1.50E-03 74 APPENDD( B Table B-1 . Dam pts for the sorption of Ethyl Acetate by Metallocene film, test 1 Time Experimental Gain Theoretical Gain 0 0 0.100670724 120 0.0943 0.377707955 3120 1.8872 1.8739152 5520 21914 2265276987 8520 2.2765 2.454933182 11520 2.3128 251987855 14520 23338 2542118271 17520 2.355 2549733983 20520 23724 2552341888 23520 23848 2553234932 26520 23991 2553540743 29520 24114 2553645465 32520 24247 2553681325 35520 24344 2553693605 38520 2.4447 255369781 41520 24523 255369925 44520 2463 2553699743 47520 2481 2553699912 50520 25 255369997 53520 25231 255369999 56520 25411 2553699996 59520 25527 2553699999 62520 25537 25537 65520 25478 25537 68520 25417 25537 B - 2 Data pts for the sorption of Ethyl Acetate by Metallocene film, test 7 Time Expaimenlal Gain Theoretical Gain 0 120 2400 4800 7200 9600 12000 14400 168(1) 19200 21600 24000 264(1) 31200 33720 36120 40920 43320 45720 48120 52920 57720 0 0.0832 1.6619 2.1338 22529 2.3021 23242 23471 23593 2.3708 23763 23905 2.4045 24062 24134 24275 24324 2445 24535 24573 2.4491 24478 24388 24223 24034 2.3968 0.09687049 0.366302137 1.622554769 2107895857 2311032588 2396069593 2431667751 2446569838 2452808144 2455419621 2456512836 2456970478 2457162056 2457242254 2457275826 2457290312 2457295944 2457298302 2457299289 2457299702 2457299875 2457299948 2457299978 2457299991 2457299998 2457299999 76 B - 3. Data pts for the sorption of Ethyl Acetate by Metallocene film, test 3 Time Experimental Gain Theoretical Gain] Theoretical GainZ 0 120 4920 9720 14520 19320 24120 28920 33720 38520 43320 48120 52920 57480 62520 67320 72120 76920 81720 86520 91320 96120 100920 105720 110520 0 0.0172 1.8647 20238 20424 20549 20695 20778 20941 21123 21284 21298 21247 21376 21633 2.1874 22025 22095 22146 22077 21993 21869 2188 21846 21701 0.087302888 0.308650532 1.837392064 213234344 2196662561 2210688437 2213747017 2214413993 2214559438 2214591155 2214598071 2214599579 2214599908 2214599978 2214599996 2214599999 22146 2.2146 22146 22146 22146 22146 22146 22146 22146 0.083959943 0.32297882 1.857320268 2084856636 2122386949 2128577276 2129598321 2129766735 2129794513 2129799095 2129799851 2129799975 2129799996 2129799999 21298 21298 21298 21298 21298 2.1298 21298 21298 21298 21298 21298 1r B - 4. Data pts for the sorption of Ethyl Acetate by Metallocene film, test 4 Time Experimental Gain 777eozetz'ca1 Gain] Heatetical Gain2 0 120 4680 9480 14280 19080 23880 28680 33480 38280 43080 47880 52680 57480 62280 67080 71880 76680 81720 86280 91080 95880 100680 105480 110280 0 0.0625 1.5772 1.7283 1.7565 1.7769 1.7983 1.8158 1.8261 1.8344 1.8413 1.8472 1.8539 1.8624 1.8722 1.8804 1.8876 1.8949 1.9047 1.9124 1.9172 1.9177 1.9206 1.9225 1.9224 0.075787863 0.259833075 1.536463026 1.830325896 1.900491541 1.917245029 1.921245268 1.922200407 1.92428466 1.92248292 1.922495922 1922499026 1922499767 1922499944 1922499987 1922499997 1922499999 1.9225 1.9225 1.9225 1.9225 1.9225 1.9225 1.9225 1.9225 0.069243892 0.294288284 1.589268444 1.737926357 1.754437111 1.756270884 1.756474553 1.756497174 1.756499686 1.756499965 1.756499996 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 1.7565 B - 5. Data pts. for the sorption of Ethyl Acetate by Metallocene film, test 5 Time Expaimental Gain Heomfical Gain 0 120 41880 47880 53880 56760 0 0.0069 1.3417 1.6324 1.6808 1.6794 1.6772 1.6777 1.6801 1.6806 1.6783 1.6792 1.68 1.6796 1.6791 1.6791 1.6777 1.6767 1.6747 1.6702 1.6655 0.066259683 0.235990329 1.161704017 1.475453677 1 .60264323 1.651052786 1.669477926 1.676490711 1679159843 1.680175741 1.680562401 1.680709568 1.680765581 1.6807869 1.680795014 1.680798102 1.680799278 1.680799725 1.680799895 1.68079996 1.680799984 B - 6. Data pts for the sorption of Limonene by Metallocene film, test 2 Time Experimental Gain Theozetical Gain1 Theomtical GainZ 120 2880 5880 11880 17880 23880 29880 35880 41880 47880 53880 59880 71880 77880 89880 95880 101880 107880 113880 119880 125880 137880 0.0001 1.1204 2.4262 4.0223 4.9193 5.4355 5.754 5.968 6.1108 6.2037 6.2609 6.2969 6.3205 6.3299 6.3283 6.31 6.3336 6.362 6.4027 6.4442 6.4725 6.5003 6.5251 6.552 0.435732538 1989140942 2844657708 4.015434805 4.807441406 5.35210324 5.726979555 5985007862 6.1626097 68 6.284853878 6.368994993 6.426909662 6466772564 6.49421036 6.513095906 6526094903 6535042166 6541200603 654543948 6548357116 6.550365337 6551747604 6552699023 6553804636 0.436502426 2018223141 2885667907 4.058784516 4826269826 5.334280728 5.670687521 5893460987 6.040984901 6.138677441 6.2033709 6.246211875 6.274581809 6.293368803 6.305809831 6314048466 6319504213 632311709 6325509591 6327093941 6.328143121 6328837904 6.329298 6329804447 B - 7. Data pts for the sorption of Limonene by Metallocene film, test 3 Time Experimental Gain Ibeozetical Gain 125 110318 120336 130354 140371 150389 160406 170424 180442 190459 200477 210494 220512 240547 0.000621 0.030996 0.685301 1.930706 4.075775 5.545209 6.046552 6.247765 6.338631 6.387013 6.416213 6.436004 6.443096 6.446504 6.458208 6.470909 6.479404 6.489013 6.492m4 6.493104 6.494904 6.4982 6.502804 6.5073 6.510904 6.515904 6.5213 6.523404 0.494477375 1236296751 2284979752 3231825424 4.258023698 5543968899 6.099893339 6340261372 6.444212569 6.489158518 6508596149 651700104 6520635109 6.522206723 652288625 6523180124 6523307195 6523362138 6523385899 6.523396172 6523400615 6523402536 6525403367 6523403726 6523403882 6523403949 6523403978 652340399 81 B - 8. Data pts for the sorption of Limonene by Metallocene film, test 4 Time Expeziniental Gain Theoretical Gain 0 120 6480 12960 19440 25920 32400 38880 45360 51840 58320 64800 71280 77760 84240 90720 97200 103680 110160 116640 123120 129600 136080 142560 149040 0 0.0177 3.3812 5.2386 6.1145 6.5507 6.8186 6.9831 7.0802 7.1328 7.151 7.1667 7.1763 7.1835 7.1887 7.1918 7.1989 7.2094 7.2181 7.2206 7264 7.2252 7.2289 7.2192 7.2217 0284974192 0.54456822 3862339704 5301587483 6124142394 6595630949 6865897512 7.020819712 7.109624216 7 .160528735 7 .189708223 7206434489 721602232 7221518256 7.224668637 7226474498 7227509654 7228103026 7228443158 7228638129 722874989 7228813954 7228850677 7228871727 7228883793 82 B - 9. Data pts for the sorption of Limonene by Metallocene film, test 5 Time Expen'mental Gain Theozetical Gain 0 120 6120 12120 18120 24120 30120 36120 42120 48120 54120 60120 66120 72120 78120 84120 90120 96120 102120 108120 114120 120120 126120 132120 138120 0 0.011 3.3858 5.232 6.1017 6.5418 6.7867 6.9322 7.0215 7.0757 7.1034 7.1227 7.1309 7.133 7.1438 7.1613 7.1714 7.1937 7.2075 7.2225 7.2363 7.2468 7.2494 7.2558 7.2506 0286034631 0555322644 384085646 5259217888 6.08687901 6571429392 685512001 7.021212989 7.118455818 7.175388794 7208721471 7228236828 7239662528 7246351958 7250268434 7252561422 7.253903902 7254689887 725515006 7255419478 7255577215 7255669566 7255723634 725575529 7255773824 B - 10. Data pts for the sorption of Limonene by Metallocene film, test 6 Time EApen'mental Gain Theoretical Gain] Theozetical GainZ 0 120 6600 12600 18600 114600 1206(X) 126600 132600 138600 0 0.0021 3.566 5.0908 5.7996 6.1407 6.322 6.4241 6.4801 6.5089 6.5159 6.5132 6.5367 6.5636 6.6048 6.6583 6.7003 6.7354 6.742 6.7418 6.7478 6.744 6.7222 6.7226 6.7138 0266008501 0520246582 3.738106016 5.003908834 5.736440724 6.161261495 6.407636542 655052194 6.633388437 6.681446926 6709318483 6725482615 6736193196 674012833 6743446719 6745275311 6746335805 6746950839 6747307528 6747514391 6747634361 6747703937 6747744288 674776769 6747781262 025623985 0540183337 3915007339 5.149101351 5.793772455 6130795129 6306985384 6399094934 6447248387 647242227 6485582788 6492462904 6496539081 6497885943 6498923107 6499437017 6499705681 6499846135 6499919562 6499957948 6499978016 6499988507 6499993992 6499996859 6499998358 B - 11. Data pts for the sorption of Ethyl Acetate by ULDPE, test 1 Time Experimental Gain Theoretical Gain1 Theoretical Gain2 0 120 2880 5880 8880 11880 14880 17880 20880 23880 26880 32880 0 0.0245 1.424 1.7514 1.8149 1.8443 1.8525 1.8628 1.8748 1.8759 1.8809 1.8936 1.8998 1.9051 1.9116 1.9086 1.9268 1.9468 1.9605 1.9662 1.9678 1.9699 1.9618 1.9583 1.9548 0077656443 0287283142 1382052273 1.762541696 1896753397 1944097197 1960797941 1966689207 1968767378 1969500462 1969759061 1969882462 1969893813 1969897818 196989923 1969899728 1969899966 1969899988 1969899996 1969899999 1969899999 1.9699 1.9699 1.9699 1.9699 0072929803 0307797258 1.44106917 1.744473157 1822768128 1842972642 1848186546 1849532027 1849879236 1849968836 1849991958 1849999464 1849999862 1849999964 1849999991 1849999998 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 85 B - 12. Data pts for the sorption of Ethyl Acetate by ULDPE, test 2 Time Experimental Gain Theoretical Gain1 Theoretical CainZ 0 120 2880 5880 8880 11880 14880 17880 20880 23880 26880 29880 32880 35880 38880 41880 44880 47880 50880 53880 56880 59880 62880 65880 68880 0 0.0521 1.3459 1.6482 1.7042 1.7256 1.738 1.7395 1.7558 1.7694 1.7736 1.79 1.8022 1.8084 1.8338 1.8478 1.865 1.8715 1.8744 1.8722 1.8701 1.8603 1.8539 1.8508 1.8569 0073891688 0273044678 1313780335 1.676178499 1.804311(B8 1849617307 186563711 1871301537 1873304417 1874012614 1874263025 1874351567 1874382875 1874393945 1874397859 1874399243 1874399732 1874399905 1874399967 1874399988 1874399996 1874399999 1874399999 1.8744 1.8744 0068025767 0293350636 1365277088 1.637970685 1.704288801 1720417177 1.724339552 1.725293463 1.725525451 1.72558187 1725595591 1725598928 1.725599739 1725599937 1725599985 1725599996 1725599999 1.7256 1.7256 1.7256 1.7256 1.7256 1.7256 1.7256 1.7256 B - 13. Data pts for the sorption of Ethyl Acetate by ULDPE, test 3 Time Experimental Gain Theoretical Gain1 Theoretical GainZ 0 120 2880 5880 8880 11880 14880 41880 47880 53880 59880 62880 0 0.0094 1.2798 1.6193 1.6972 1.7257 1.7476 1.7586 1.7801 1.7864 1.8012 1.8132 1.8247 1.8357 1.8402 1.8517 1.8551 1.861 1.8675 1.8888 1.9028 1.9239 1.9383 1.9526 1.9573 0077159732 0279076108 1346915518 1731892441 1874055334 1926557133 1945946433 1953107044 1955751511 1956728132 1957088805 1957222004 1957271196 1957289362 1957296071 1957298549 1957299464 1957299802 1957299927 1957299973 195729999 1957299996 1957299999 1957299999 1.9573 006889304 0269626273 1284493631 1.603246817 1702603553 1733574121 1743227982 1746237195 1747175199 1747467585 1747558725 1747587134 174759599 174759875 174759961 1747599879 1747599962 1747599988 1747599996 1747599999 1.7476 1.7476 1.7476 1.7476 1.7476 87 B - 14. Data pts for the sorption of Ethyl Acetate by ULDPE, test 4 Time Experimmtal Gain Theoretical Gain] Theoretical GainZ 0 120 3480 7080 10680 14280 17880 21480 25080 28680 32280 35880 39480 43080 46680 50280 53880 57480 61080 68280 71880 82680 0 0.0143 0.9551 1.1446 1.1869 1.2064 1.2212 1.2307 1.2401 1.2476 1.2541 1.2595 1.2647 1.2695 1.2731 1.2761 1.2781 1.2788 12778 1.2789 12819 1.2849 1.2887 1.293 12986 005119278 0.176910053 0931711771 1.175419712 1257242043 1284714007 1293937758 1297(B4646 129807443 1298423539 1298540753 1298580108 1298593321 1298597758 1298599247 1298599747 1298599915 1298599972 129859999 1298599997 1298599999 1.2986 12986 1.2986 1.2986 0049438522 0.195712848 0998952851 1.193104083 1239518186 125061404 1253266639 1253900775 1254052373 1254088614 1254097278 1254099349 1254099844 1254099963 1254099991 1254099998 1254099999 1.2541 12541 12541 1.2541 12541 12541 12541 1.2541 B - 15. Data pts for the sorption of Ethyl Acetate by ULDPE, test 5 Time Experimental Gain Theoretical Gain1 Theoretical GainZ 123 3480 7080 10680 14280 17880 21480 25080 28680 32280 35880 39480 43080 46680 50280 53880 57480 61080 68280 71880 79080 82680 86280 0 1.1842 1.4248 1.4633 1.4725 1.479 1.4861 1.4929 1.4983 1.5026 15081 1.5138 1.5173 1.5191 1.5189 1.5198 1.5209 1.5221 1.5236 1.5249 1.527 1.5292 1.5313 1.5335 1.5328 0242064389 1220663198 1.458503 1515520786 1529189799 1532466705 1533252286 1533440615 1533485763 1.533496587 1533499182 1533499804 1533499953 1533499989 1533499997 1533499999 1.5335 1.5335 1.5335 1.5335 1.5335 1.5335 1.5335 1.5335 1.5335 0243902273 1.2159372(B 1.43097227 1.477286579 1.487261777 1.48941024 1.489872977 1.489972642 1.489994108 1.489998731 1.489999727 1.489999941 1.489999987 1.489999997 1.489999999 1.49 1.49 1.49 1.49 1.49 1.49 1.49 1.49 1.49 1.49 89 B - 16. Data pts for the sorption of Limonene by ULDPE, test 1 Time Experimental Gain Theoretical Gain 0 120 7320 14520 21720 28920 36120 43320 50280 57720 64920 72120 86520 93720 100920 108120 115320 122520 129720 136920 144120 151320 158520 165720 0 (10005 126692 519503 444996 447579 44907 510124 511022 511609 511883 555123 512104 512141 512145 512115 5121 512195 512348 512466 512563 512676 512753 512785 512787 (1208094353 (1359923428 12643817036 51651960383 44272220833 44655953158 44893382523 51040289219 51128806488 51187427435 51222226144 51243757448 51257079695 51265322684 515N1£ZZX¥3 Sifififififikiii 51275531231 51276739361 51277486877 51277949394 51278235571 5127841264 51278522199 51278589988 51278631931 B - 17. Data pts. for the sorption of limonene by ULDPE, test 2 Time ExperimmtalGain Theoretical Gain 0 480 7680 14880 101280 108480 115680 122880 130080 134880 142080 149280 159720 169200 0 0.0072 2.7247 3.7846 4.1866 4.3657 4.4627 4.5214 4.5594 4.5824 4.5994 4.6108 4.6196 4.625 4.6273 4.6258 4.6199 4.6251 4.6369 4.6501 4.6554 4.6589 4.6544 4.6612 4.6718 0.184169435 0718233417 2864115351 3769437604 422122504 4.446814976 4559458512 4615704667 4.643789988 4.657813796 4.664816287 4.668312831 4670058756 4.670930547 4.671365857 4.67158322 4.671691756 4.67174595 4.671773011 4.671786524 4.671791518 4.671795765 4671797885 4671799227 467179969 4: B - 18. Data pts for the sorption of Limonene by ULDPE, test 3 Time Erpm’mental Gain Theoretical Gain 0 600 6600 12600 18600 114600 120600 126600 132600 135480 0 0.0083 2.6697 3.8829 4.3936 4.6355 4.7536 4.8009 4.8214 4.8233 4.8173 4.8137 4.8095 4.8072 4.8146 4.8326 4.8538 4.874 4.8933 4.9078 4.9148 4.9175 4.9183 4.9161 4.914 0.193886839 0824531932 2737383679 3.66121529 4193093138 4499926827 4676939716 477905879 4837971479 4871958322 4891565397 4902876757 4909402301 4913166901 4915338705 4.916591623 4917314434 4917731425 4917971988 4918110769 4918190832 4918237021 4918263667 491827904 4918283904 B - 019. Data pts for the sorption of Limonene by ULDPE, test 4 Time Erpen’menlal Gain Theoretical Gain1 Theoretical GainZ 0 120 7320 14520 21720 28920 36120 43320 115320 122520 129720 136920 144120 151320 158640 165720 0 0.0188 3.2023 4.3697 4.8264 5.0643 5.1849 5.2464 5.2839 5.3052 5.3236 5.3312 5.338 5.3522 5.3554 5.3749 5.4019 5.4158 5.4111 5.3946 5.3861 5.3806 5.3638 5.352 5.325 0.213499043 0.419778501 3.173086672 4259673183 4819511907 5.108255548 5257179373 5333989052 5373604786 5394(B7191 5.404575507 5.410010801 5.412814134 5.414259995 541500572 5.415390338 5.415588711 5.415691024 5.415743794 5.415771011 5415785049 5.415792289 5.415796023 5.415797971 5.415798942 0212608117 0.418026776 3.15984546 4241897672 4799400202 5086938924 5235241293 5311730447 5351180866 5371528006 5382022347 5387434959 5390226594 5391666422 5392409(B4 5392792048 5392989593 5393091479 5393144029 5393171132 5393185111 5393192321 5393196039 539319798 5393198946 B - 20. Data pts for the sorption of Limonene by ULDPE, test 5 Time Expaimmtal Gain Theoretical Gain] Theoretical Gain2 0 120 6120 12120 18120 24120 30120 36120 43080 49080 55080 61080 67320 91080 97080 103200 109200 114000 121200 127200 133080 139200 0 0.0294 26889 4.6001 5.2805 5.5577 5.7162 5.8094 5.8598 5.8875 5.9065 5.9234 5.9326 5.9535 5.9593 5.9815 5.9555 5.9743 5.9968 6.038 6.0367 6.0509 6.0568 6.059 6.058 0238854962 0.494327393 3.45002755 4659067393 5307303749 5.655373477 5842271002 5942626432 600243059 6028624812 6042689912 6050242228 605441303 605647496 6057644169 6058271981 6058609087 6058790098 6058888685 6058940229 6058963655 6058982767 6058990747 6058994969 6058997332 0231002196 0.496119153 3.473750537 4647152607 5.24331553 5546306233 5700404327 5778755388 5822819619 5840997353 5.85039808 5854939127 5857394465 5858543364 5859161064 5859475134 5859634822 5859716015 5859757872 585977858 5859787531 5859794462 5859797184 5859798549 5859799272 B - 21. Data pts. for the sorption of Limonene by ULDPE, test 6 Time Expaimental Gain Theoretical Gain] Theoretical Gain2 0 120 6120 12120 18120 24120 30120 36120 42120 48120 54120 60120 66120 72120 78120 84120 90120 96120 102120 108120 114120 120120 126120 132120 138120 0 0.0133 3.188 4.6383 5.2542 5.5588 5.7313 5.8299 5.8913 5.9314 5.9501 5.9728 5.9775 5.9821 5.983 6.0117 6.0487 6.0861 6.1031 6.1249 6.1246 6.1148 6.1113 6.0949 6.092 0241452839 0.484081907 3365267397 4577759222 5256674593 5.637664054 585146998 5971454885 6038788741 6076575562 6097780999 6109681195 6116359419 6120107145 6122210317 613390587 6124052939 6124424641 6.124633235 6124750295 6124815988 6124852854 6124873542 6124885152 6124891668 0.35456827 0.488003567 3.406416812 4598561112 536430736 557823641 5.761370061 5859507305 5912093202 5940270847 5955369567 5963460071 5.967795289 5970118274 597136303 597233001 597387408 5972578917 5972681535 5972736521 5972765986 5972781774 597279034 5972794767 5972797196 95 APPENDIX C C - 1. Data used in Minitab to perform the Analysis of Variance Sorbate Temp Film Sorption Diffusion 1 23 1 7.5 7.6 1 23 1 14.8 7.5 1 32 1 9.38 7.61 1 32 1 6.3 7.5 1 32 1 11.1 8.0 1 23 2 4.87 6.9 1 23 2 6.42 7.0 1 32 2 14.2 7.7 1 32 2 12 8.4 1 32 2 7.5 7.0 2 23 1 190 1.4 2 23 1 196 1.55 2 32 1 131 1.59 2 32 1 200 1.66 2 32 1 155 1.9 2 23 2 260 1.59 2 23 2 110 1.87 2 23 2 155 1.94 2 32 2 116 2.07 2 32 2 110 1.8 2 32 2 122 2.07 Sorbates 1 & 2 are Ethyl Acetate and Limonene respectively Film 1 8: 2 are Affinity (Metallocene) & Attane (ULDPE) respectively Temp is measured in °C Sorption is at value x 105 and Diffusion is at value x 10'14 XXXX 96 C - 2. General Linear Model Analysis of Variance for Sorption Source DF Seq SS Adj SS Adj MS F p film 1 1449 1426 1426 1.28 0.278 Temp 1 2525 2370 2370 2.13 0.168 Sorbate 1 116649 117138 117138 105.33 0.000 Film x Temp 1 189 129 129 0.12 0.739 Film x Sorbate 1 1256 1167 1167 1.05 0.324 Temp x Sorbate 1 2873 2853 2853 2.48 0.140 Film x Temp x Sorbate 1 405 405 405 0.36 0.557 Error 13 14457 14457 1112 Total 20 139804 C - 3. General Linear Model Analysis of Variance for Diffusion Source DF Seq SS Adj SS Adj MS F p fihn 1 0.009 0.000 0.000 0.000 0.979 Temp 1 0.481 0.554 0.554 5.50 0.035 Sorbate 1 173.409 166.061 166.061 1648.72 0.000 Film x Temp 1 0.056 0.090 0.090 0.90 0.361 Film x Sorbate 1 0.400 0.448 0.448 4.45 0.055 Temp x Sorbate 1 0.084 0.073 0.073 0.73 0.409 Film x Temp x Sorbate 1 0.137 0.137 0.137 1.36 0.265 Error 13 1.309 1.309 0.101 Total 20 175.886 97 BIBLIOGRAPHY Anonymous, Polyolefins, American Polyolefin Association, [Onljne] Available http: / /www.apa-polyolefin.com (1996) Bagley E. and Long F., I. Am. Chem. Soc. 77, 2172 (1958). Baner A. L., The measurement and analysis of the diffusion of toluene in polymeric films. Masters Thesis. Michigan State University, East Lansing, MI. (1987). Berens, A., Polymer, 18, 697 (1977). Brown R. Permeability, Handbook of Plastics Test Methods, 2“d Ed. George Goodwin Ltd. Essex, England. 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