THE MEASUREAENT AND ANALYSIS OF. THE DIFFUSION 0E TOLIEIE IN POLYMERIC FILMS - v ‘ Thesis for Th6 DegrééEjtofM S f ' MICHIGAN STATE UNIVERSITY. f ‘- - ~ ‘~ ALBERT LAWRENCE BANER'TIT: '3 ‘ 198T IUIIIIIIIIIIIII‘IIHIIIII ’IIIIIIIIIIIIIII 23 01395 3108 n ’ m «5% PLACE II RETURN BOX To roman this Momma your wood. TO AVOID FINES Mum on or We dul- duo. THE MEASUREMENT AND ANALYSIS OF THE DIFFUSION 0F TOLUENE IN POLYMERIC FILMS by Albert Lawrence Baner III A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1987 Abstract The Measurement and Analysis of the Diffusion of Toluene In Polymeric Films by Albert Lawrence Baner The measurement and analysis of the diffusion of organic vapors in polymeric films is complex and the interpretation of the results is not very well understood. A quasi- isostatic system for measuring the permeation of organic vapors has been developed and a detailed description of the apparatus and analysis is given. The system is used to study the vapor concentration dependent diffusion and permeation of organic vapors in oriented polypropylene and Saran (polyvinylidene chloride) polymeric films. The results from the quasi-isostatic permeation measurements are compared to results obtained from gravimetric electrobalance sorption studies. It was found that the permeation, diffusion and sorption processes for toluene vapors in these films are highly dependent on the concentration of vapor in contact with the film. This is partly due to the increased segmental mobility of the polymer chains due to the sorption of the toluene permeant by the polymer. The diffusion coefficients were evaluated ii Albert Lawrence Baner using the half time and lag time methods from the sorption and permeation studies respectively. The lag time and half time diffusion coefficients are transient state diffusion coefficients and significantly differed from the calculated steady state diffusion coefficient. The steady state diffusion coefficients were evaluated from the steady state permeability coefficient from permeability experiments and by the solubility coefficient from equilibrium sorption experiments. The difference between the transient diffusion coefficients and the steady state diffusion coefficients is explained in terms of the free volume theory for diffusion. iii Dedicated to my grandfather, Albert Lawrence Baner. iv Acknowledgements For Financial Support During The Development of This Thesis: Plastics Institute of America Mobil Chemical Co. Films Division For Professional Guidance and Assistance: Dr. T. W. Downes Dr. J. R. Giacin Mr. R. Hernandez For Support and Understanding: My Parents Table Of Contents List of Figures List of Tables Nomenclature Introduction Literature Review The Importance of Studying the Permeation Behavior of Organic Vapors Through Polymeric Packaging Materials The Level of Organic Volatiles In the External and Internal Package Environments The Permeation Mechanism For the Transfer Of Organic Vapors Through Polymers Permeability Theory For Organic Vapor Permeation In A Sheet Sorption and Desorption Theory of Organic Vapors In A Sheet Characteristics of Organic Vapor Mass Transport Through Polymers Above Their Class Transition Temperatures Permeation Measurement Sorption Measurement Solubility Characteristics Diffusion Characteristics Free Volume Theory Permeability Characteristics vi ix xi 15 21 24 24 26 30 33 36 39 ‘——E‘ ‘3” ~.- - Lyon'zvflao- I? a‘ ‘i" in a z i: I Mate Anal S Ch Organic Vapor Permeation Measurement Techniques Organic Vapor Sorption Measurement Techniques Interpretation of Data From Quasi-Isostatic Permeation Measurement Materials Analytical Method Treatment of Film Samples Permeation Studies Permeation Cell Design Vapor Permeation Quantitation Permeation Data Analysis Permeation Test Method Sorption Studies Solubility Test Method Solubility Quantitation and Data Analysis Results and Discussion Characteristics of Steady State Permeation of Toluene Through Test Films Permeation Rate Permeability Coefficient Lag Time Diffusion Coefficient vii 42 50 52 S6 S7 57 S7 57 59 6O 65 71 71 75 77 7T 79 82 84 Ex C01 App‘ ‘ . ' Blblj I Sorption Studies Penetrant/Polymer Interaction and Consideration of Free Volume Effects Experimental Error Analysis Permeation Measurements Sorption Error Analysis Conclusion Notes on Permeation Cell Design and Usage Concentration Dependent Diffusion In Organic Vapor Polymer Systems Conclusions on the Usefulness of the Method Conclusions On The Theoretical Importance Appendices Saturation Vapor Concentration Versus Temperature Test For the Validity of Assuming Toluene Vapor Behaves As an Ideal Gas Gas Chromatograph Calibration Procedure Limits of Detectability of Permeation Method Experimental Data Bibliography viii 9O 97 114 114 130 133 133 137 139 142 144 146 148 151 152 155 ‘ x6.- _v\-' 1 ll 12 List of Figures Figure Title 1 Schematic of Permeation Test Apparatus 2 Permeation Cell System 3 Schematic Diagram of Sorption/Desorption Apparatus 4 Log Permeability Rate versus Toluene Vapor Activity 5 Log Permeability Coefficient versus Toluene Vapor Activity 6 Log Lag Time Diffusion Coefficient versus Toluene Vapor Activity 7 Lag Time and Half Time Diffusion Coefficients versus Toluene Vapor Activity 8 Toluene Vapor Solubility versus Vapor Activity In Oriented Polypropylene 9 Toluene Vapor Solubility versus Vapor Activity In Polyvinylidene Chloride 10 Comparison of Lag Time and Steady State Diffusion Coefficient versus Toluene Vapor Activity 11 Comparison of Lag Time and Steady State Diffusion Coefficients versus Equilibrium Solubility of Toluene 12 Transmission Profile Curve Error Analysis 13 Toluene Saturation Vapor Concentration versus Temperature ix Page 66 67 72 80 83 87 92 95 96 102 108 118 145 List of Tables Table Title 1 Odor Threshold Values for Compounds In Air 2 3 Permeation Measurement Results Polynomial Equations Log Permeability Coefficient versus Vapor Activity Linear Regression Equations Log Diffusion COefficient versus Vapor Activity Toluene Solubility as a Function of Vapor Activity Estimate of Permeation Measurement Uncertainty Variation or Experimental Permeation Rates Relative Error of Permeation Measurement Uncertainties Variation of Experimental Lag Times Page 78 85 88 91 115 120 121 125 Nomenclature Symbol a vapor activity - vapor pressure of permeant/saturated vapor pressure of permeant (p/po) vapor activity on the high concnetration side of permeation test film A area of film sample (cmz) A Frequency factor free volume theory Eqn.(32). b characteristic parameter of Langmuir equation, Eqn. (27) B measure pf minimum hole size for jump process in free volume theory Eqn. (35). c. or c 1 1 concentration of permeant in the face of the polymer in contact with the permeant (gm/cm3) c concentration of permeant in the face of the film in contact with 2 the zero or low permeant vapor concentration Cs Equilibrium solubility of a contacting vapor concentration in a polymer c sorbed concentration of vapor corresponding to a complete monolayer sorption Eqn. (27) D differential diffusion coefficient (cmz/sec) D integral diffusion coefficient (cm2/sec) D preexponential diffusion coefficient or limiting diffusion coefficient Eqn. (29) (cm2/sec) xi Dlag integral diffusion coefficient from lag time data Eqn. (17) (cm2/sec) Dss Steady state diffusion coefficient (cm2/sec) Ds Diffusion coefficient from sorption curve Eqn. (23) (cmZ/sec) Dd Diffision coefficient from desorption curve Eqn (23) Dt1/2 Half time diffusion coefficient Eqn. (22) D(c) diffusion coefficient as a function of concentration E activation energy of permeation Eqn. (38) (kcal/mol) E activation energy of diffusion Eqn. (29) (kcal/mol) f fractional free volume Eqn. (33) f fractional free volume at zero vapor concentration Eqn. (35) Hs heat of sorption Eqn. (25) (kcal/mol) ierfc inverse error function k limiting slope of plot of ln(M§-Mt) versus t, Eqn. (24) K constant relating vapor pressure dependence of permeability coefficient Eqn. (41). kg killigram L thickness of the film sample before swelling (cm or mil) mg milligram mmHg millimeters mercury M amount of diffusant taken up by sheet in time t Eqn. (19) M Equibrium sorption at infinite Eqn. (19) mil 0.001 inches n,m indices xii n number of monolayers present for sorption Eqn (28) OPP orientated polypropylene OPP/PVDC OPP coated on one side with PVDC PVDC polyvinylidene chloride or saran PPm P P parts per million permeant concentration in nitrogen (lg/ml, w/v) Permeability rate at steady state (g/mz'hour) Permeability Coefficient (g'structure/Mz'day'ppm) or (g'structure/mz'day'a) limiting permeability coefficient, The permeability coefficient at zero permeant partial pressure po saturation vapor pressure permeant partial pressure at the ingoing side of the film permeant partial pressure at outgoing side of film quantity of permeant in low concentration permeation cell chamber amount of permeant which passes through membrane in time t heat of vaporization for pure liquid penetrant Eqn (28) heat of absorption Eqn (28) correlation coefficient ideal gas law constant Relative humidity . standard deviation Solubility coefficient (g/cm3 ppm) integral solubility coefficient (g/cm3 ppm) prexponential solubility coefficient Eqn (25) xiii or the solubility coefficient at zero permeant concentration Eqn (26) time time required for sorption to reach 1/2 Mé Eqn (22) absolute temperature (OK) Polymer glass transition temperature volume of permeation cell chamber (cm3) crystalline mass fraction in semicrystalline polymer Eqn (36) proportionality factor for diffusion coefficient vapor activity dependency Eqn (31) or statistical probability of a type I error effectiveness f actor of penetrant molecule for increasing the free volume of polymer Eqn (33) constant in modified BET equation Eqn (28) summation operator relaxation effects in diffusion Eqn. (60) proportionality factor for diffusion coefficient concentration dependency Eqn (30) modified proportionality factor for steady state diffusion coefficient concentration dependency Eqn (49) microgram proportionality factor for solubility coefficient vapor concentration dependency Eqn (26) fickian effects in diffusion Eqn (60) xiv 9 TT 00 lag time (time) Eqn (17) pi - 3.14159 infinity KY tT CC QU V8 vaj abc to per pol uti sui app stu pra Vap Sui ana Introduction The study of the diffusion of organic vapors through polymeric packaging films is needed to characterize the film's ability to exclude deleterious vapors from interacting with the product and to prevent loss of product volatiles which may decrease product quality and shelf life. It is known that the diffusion of organic vapors in polymers is dependent on the concentration of the vapors in the polymer, which is related to the permeant concentration above the polymer (Meares, 1965a). This behavior makes it important to monitor and specify the permeant concentration at which a permeability rate or diffusion coefficient is measured. Most methods used for measuring organic vapor permeation in polymers have at least one of the following limitations: (1) they utilize complex and difficult to use apparatus, (2) they are not suitable for testing thin films and soft polymers, (3) they can only be applied to a limited permeant concentration and/or (4) they cannot study the effects of copermeants (Talwar, 1974). The purpose of this study is to develop and evaluate a practical method for comparing the relative diffusion rates of organic vapors in common packaging films. This required the development of a suitable measurement technique as well as a method for data analysis. To be of maximum value as a test method for determining the permeation and diffusion of organic vapors in packaging films the method must have the following attributes: (l) the apparatus must be inexpensive and easy to use, (2) it must be capable of evaluating films at different thicknesses, barrier properties, and structure, (3) it can test the complete organic vapor pressure range from zero to saturation vapor pressure, (4) the effects and interactions of copermeants and relative humidity can be studied, and (5) tests can be made at different temperatures.' A quasi-isostatic test procedure is selected as the method which can be adapted to allow evaluation of the above listed criteria. In addition to a good vapor permeation measurement technique for vapor permeation through films, the analysis and interpretation of the data is equally important for prOper application to packaging problems. One of the difficulties in studying the permeation and diffusion of organic vapors in polymers is the vapor concentration dependency of diffusion. Studies were conducted on the concentration dependent diffusion of toluene in films containing oriented polypropylene and polyvinylidene chloride polymers. Interpretation of experimental results from permeation and sorption studies for these organic vapor-polymer systems is discussed. Evaluation is made of the applicability of the lag time tl' we re ’50-; um“; ex; res diffusion coefficient to these systems where the diffusion coefficient is concentration dependent and Henry's law solubility is not obeyed. The permeability coefficient from permeation measurements and the solubility coefficient, which is obtained by sorption measurements, were used to calculate the diffusion coefficient using the relationship, P-D'S. Diffusion coefficients derived from this expression were compared to the lag time diffusion coefficient and the results interpreted using the free volume theory. t} sc se ma P0] Whe deSi °rga1 Produ Literature Review The Importance of Studying The Permeation Behaviour Of Organic Vapor Through Polymeric Packaging Materials The loss or gain of organic vapors by a product in a package occurs by two mechanisms: the mass transfer or permeation of the vapor in or out of the package and sorption or desorption of organic volatiles by the packaging material. In absolute barrier systems like well closed metal or glass containers the loss or gain of organic volatiles from the package system is insignificant. The phenomena of sorption and permeation are especially applicable to the semipermeable package systems constructed from polymeric materials. This study will address one aspect of the phenomenon; the measurement of the mass transfer of organic volatiles through polymeric packaging films by permeation. When selecting a package system for a product it is important to know the product's characteristics and what effect the gain or loss of organic vapor can be expected to have on product quality. It is desirable to identify which vapors are the most important] determinates of product quality and to quantify the level of organic vapor gain or loss which will affect product quality. For example, the loss or gain of a specific volatile component from a product may change its functional properties. In the case of a food products the food's aroma serves as a sensitive and primary indicator of quality (Niebergall, 1978). The equilibrium vapor pressures and types of organic volatiles in the product and the concentrations and types of vapors in the environment the package will be exposed to need to be identified. This information is important because the permeant vapor pressure and the type and/or mixture of vapors that come in contact with the package will determine the magnitude of sorption and permeation in and out of the polymer package. The Level of Organic Volatiles in The External and Internal Package Envirements In foods and other products the absence or presence of volatiles in the package or product may create changes in the sensory properties of flavor and smell. Loss of volatiles from the product may reduce the flavor below a threshold concentration of the volatile in the food so that consumers cannot detect the product's characteristic flavor. A product can also be deemed unacceptable when contaminating volatiles entering the headspace of the package from the external environment exceed the threshold levels for detection of those volatiles. Product aroma vapors exhibit readily observable odors at total vapor concentrations in air of 0.1 to 1 ppm (g/ml) (Weurman, 1974). The main components (by weight) of such vapors will be present in amounts from 0.001 to 0.1 ppm while trace components will be found in the 10'5 ppm range and lower (Weurman, 1974). Table 1 lists threshold values for some common volatile compounds (Weurman, 1974). From this table it is apparent that trace components are capable of contributing to the overall quality of the product. The quantity of a volatile that can be lost or gained before it is under the threshold level of the volatile is determined by the headspace volume of the package, the content of the package and interaction with these volatiles by the product and package. Predicting the levels of the volatiles in the internal or external environment of the package is quite difficult. For the external environment volatiles the OSHA maximum exposure concentration limits for humans are indicative of the levels of organic volatiles that may be found in a work environment. The OSHA limits for toluene, methyl ethyl ketone, and ethyl acetate are 0.2 ppm gag/ml) averaged over 8 hours, 0.59 ppm, and 1.4 ppm respectively (Weast, 1983). Although these levels seem low it is likely that volatile concentrations may exceed these levels in poorly ventilated areas such as storage rooms and in trucks or when the package is stored in close proximity to a strong source of volatiles. The volatile concentration in the headspace of the package is dependent Table l Odor Threshold Values For Compounds In Air Taken from flmmgn Eggpgmsg To Environmental Qdors, C. Weurman, Academic Press, 1974. Compound source: Teranishi Leithe Laffort Acetone 1.1 2.0x10-3 Benzene 0.96 Butyric Acid 2.4x10-h 2.0x10-7 Ethanol 0.10 0.00012 0.01 Isopropanol 0.09 0.01 Menthol 0.01 Methyl acetate 6.0x10-4 Methyl butyrate 1.0x10'5 Phenol 2.0x1o'3 Vanillin 5.0x10-7 OSHA Exposure Limits Taken from table D-132 flgmdbgod 9f Chemisgzy and Physics, R.C. Weast ed., CRC Press, (1982). Ethyl acetate 1.4 ppm Isopropanol 0.98 ppm Methyl Ethyl Ketone 0.59 ppm Toluene 0.2 ppm averaged over 8 hours Values given in ppm gag/m1). on the equilibrium vapor pressure of the volatiles with the product and the rate of loss or gain through the package walls. Vapor pressure of pure aroma volatiles are reported to lie in the range of 10 to 10.3 mmHg (Haring, 1974). These volatiles are usually present as minor components of the packaged product. The total content of aromatic materials in food products (with the exception of spices) is usually in the range from 1 to 100 mg. per kg. (Niebergall, 1978). For solutions of materials the ideal case is assumed to hold true so that the partial vapor pressure of an odorant in the headspace above a mixture will be directly proportional to the odorant concentration as predicted by Raoult's law or by Henry's law, p-kc (Haring, 1974). For Raoult's law, k is the saturated vapor pressure of the pure odorant at the test termperature. For Henry's law, k is a constant which is specific for dilute solutions. In some cases positive deviations can occur in Raoult's law if the solute and solvent belong to chemically different types (Haring, 1974). The prediction of volatiles in solid products is much more difficult because the odorants are no longer in one homogeneous liquid phase and sorption/desorption of the vapor by different parts of the product is likely to occur. The Permeation Mechanism For The Transfer of Organic Vapors Through Polymers The rate of permeation of a substance through a material is usually described by the permeability coefficient (P), expressed as the quantity of permeant that passes through a material of a unit thickness, per unit time, per unit surface area for a given concentration or pressure gradient of the permeant (e.g. grams- mils/mz- day-»mmHg). The permeability coefficient (P) can be determined from direct measurement of the rate of transfer of a substance through a material or from the relationship P =fl3-S, where D and S are separately determined (Crank and Park, 1968). D is the diffusion coefficient which describes the rate of movement of a diffusing permeant through the polymer, usually expressed as lengthz/unit time (e.g.cmZ/sec). S is the solubility coefficient of the permeant in the polymer, expressed as the amount of permeant sorbed in the polymer matrix per gram or volume of polymer per unit pressure gradient (e.g. g/g'mmHg). Mass transport through polymeric materials occurs by a diffusion process rather than by a flow process such as Knudsen or Poiseuille flow that occurs through porous materials (Lebovitz, 1966). The diffusion processs is influenced by the characteristics of the polymer per and diffusant molecule, vapors the concentration of the diffusant in the polymer. permeation is to occur, the following processes in succession: molecule into the surface of the polymer film; penetrant molecule through the of the permeant molecule from the other surface of the (Lebovitz, 1966). Meares process in the following way : "Where constitute a single uniformly throughout the polymer gradient The polymer sheet separates two partial pressures so substance dissolves pressure the temperature, permeant molecule polymer matrix; (1965a) phase, of the chemical potential of that more in 10 and in the case of organic Thus, if has to undergo the (i) dissolution of the penetrant (ii) diffusion of the and (iii) desorption film describes the permeation the diffusate and polymer are miscible and diffusion takes place determined by the the diffusate. gases with unequal of the diffusing the polymer at the high This sets side than the low pressure side. up a concentration gradient across the polymer film and diffusion takes place down this gradient. There is a continuous net dissolution of the diffusant into the polymer at the high pressure side and a net evaporation of the diffusant at the low pressure side side maintaining the gradient. Usually after a transient state buildup a steady state of flow is g, E’EI’.J 11 attained with a constant transmission rate, provided ' a constant pressure difference is maintained across the film. It is speculated that some flow may also take place through an interconnecting capillary or crack system as a result of a pressure gradient or nature of the polymer structure. A partially crystalline polymer consists of almost impermeable crystalline regions and relatively amorphous regions. Boundaries between these regions may act like a network of cracks and pores." The diffusion process is able to take place because polymer molecules have a random kinetic agitation or heat motion. The polymer chain segments have vibrational, rotational and translational motions that continually create temporary "holes" in the polymer matrix. The creation of these "holes" allows penetrant molecules to move through the polymer matrix under the influence of the concentration gradient. The amplitude and motion of the polymer molecules is directly related to the temperature, chemical composition and morphology of the polymer. The glass transition temperature (Tg) marks the transition from a "glassy" polymer state to a "leathery" polymer physical state. This increased flexibility of the polymer is caused by the unfreezing (on heating) of micro brownian motion of polymer chain segments 20—50 carbon atoms in length (Boyer, 1977). 12 This increase in polymer chain segmental mobility above the glass transition temperature corresponds with an increase in permeability and diffusion. Small diffusant molecules like the permanent gases: oxygen, nitrogen and carbon dioxide, have almost no effect on the polymer molecules while sorbed into the polymer matrix. Their kinetic agitations are rapid compared to those of the polymer chains. The rate of diffusion of these molecules is therefore controlled by their agitation which is related to the amount of energy present in the system, as measured by the temperature. If a concentration gradient is present across a film the frequency of the jumps of the diffusate past the polymer chains gives a net flux of the diffusate molecules through the film (Meares, 1965a). Organic vapors which are comparable in size or larger than the polymer chain segments diffuse by a more complicated mechanism which is dependent on the motions of both the polymer and diffusant molecule. The molar volumes of organic penetrants are larger than the molar volumes of the permanent gases. Organic molecules may also have greater solubility in the polymer. These effects result in significant swelling of the polymer by sorbed organic molecules.- Organic molecules sorbed by the polymer act as a plasticizer, lowering the glass transition temperature and increasing the polymer's segmental motions at all temperatures, which results in further plasticization and swelling :11 (Hear molec diffk P01, tem ten: dis Qui 13 (Meares,l965b). Diffusion depends on the frequency of penetrant molecular jumping and polymer chain segmental mobility, therefore the diffusion and permeability will increase with the sorbed vapor content. The sorbed vapor content of a polymer is primarily related to the chemical similarities between the polymer and diffusate and the vapor pressure of the diffusate that the polymer is exposed to (Fujita, 1968). The diffusion of organic vapors in polymers is dependent largely 'on the segmental mobility of the polymer chains at a given temperature. For a given polymer, in the absence of any plasticizing agents, the cohesive energy density, which is a quantitative measure of the attractive forces holding the polymer chains together in the polymer matrix, determines the polymer's melt and glass transition temperatures. Polymers which are soft and rubbery at room temperature (250 C) are referred to as elastomers. The distribution of their molecular segments and kinetic motions are quite similar at the molecular level to those of molecules in a normal liquid (Meares, 1965a; Rogers, 1965). Because the behavior of normal liquids has been well studied the mechanisms of sorption, diffusion and permeation of organic vapors are best understood for elastomers and polymers well above their glass transition temperatures (e.g. polyethylene, polypropylene). Diffusion and permeation _in polymers at temperatures below the polymer's Tg has anomalous I I '8 A. ”'11 "a 5L1'sv'o": I! . and mo (Herna permea polyme temper l4 and more complex behavior that is not well understood at this time (Hernandez, 1984). The remaining discussion will be limited to the permeation, diffusion and sorption characteristics of organic vapors in polymers at temperatures well above the polymer's glass transition temperature. ' a ‘ -.~.~m “Aunt-D's.“ and A mt in( a p, 0the £11: of ‘ SUI: 15 Permeability Theory For Organic Vapor Permeation In A Sheet The general theory of permation can be expressed by a series of mathematical expressions which are summarized here from Rogers (1964). A more complete treatment of the mathematical expressions can be found in Crank (1973). The rate of permeation or the transmission rate (P) (or flux, J) is defined as the amount of penetrant passing, during unit time, through a surface of unit area normal to the direction of flow: P-Q/At (1) Where Q is the total amount of permeant which has passed through area (A) during time (t). Given a unit area of film L (cm) thick exposed to a penetrant at pressure p1 on one side and a lower pressure p2 on the other side the concentration of the penetrant in the first layer of film (x - 0) is c1 and in the last layer (x - L) is c When the rate 2. of permeation through a plane at a distance x from the high pressure surface is P, the rate through a plane at a distance x + dx will be P + (3P/3x)dx. Therefore the amount retained per unit volume of polymer is equal to the rate of change of concentration with time: - OP/ax - Dc/Bt (2) In the steady state of flow Dc/bt is zero, P is constant and the rate of permeation is directly proportional to the concentration gradient as expressed by Fick's first law of diffusion: Where I COUS tar to give The equ layer 0 in the coeffic 0f Vapo: linear ; 50 that 16 P - -D ac/Qx (3) Where D is the differential diffusion coefficient. Assuming D to be constant, this can be integrated between the two concentrations c and 1 x-L j{C1 PJNx-O dx - - D c2 dc P - D (cl-c2) / L (4) C2: to give: The equilibrium concentration c1 and c2 of penetrant in the surface layer of the polymer can be related to the partial pressures p1 and p2 in the gaseous phase by Henry's law, c - S'p. Here S is the solubility coefficient of the penetrant in the polymer and c is the concentration of vapor (g/g) in the polymer. When Henry's law is obeyed there is a linear relationship between concentration and pressure and S is constant so that: P - D S (pl-p2) / L or P - D-S - P°L / (pl-p2) (5) Where P is the permeability coefficient which is the quantity of permeant permeated through a film of thickness L per unit membrane area, per unit permeant driving force. Unlike permeant-polymer systems involving permanent gases such as oxygen, D and S are not constant for all permeant pressures for organic permeant-polymer systems. When D varies as a function of the concentration of permeant for organic permeant-polymer systems, D - f(c). From Equations (3) and (4) the l7 expression of Fick’s second law takes into account the change in the diffusion coefficient with concentration at different locations within the polymer: 3c/3t - 3/3x (D(c) 3c/3x) (6) A mean value of D can be calculated for a range of permeant concentrations (c), to give the mean or integral value of the diffusion coefficient ,D, over the concentration range C1 to c c1 °1 C1 D -Icz D(c) dc /‘[c2 dc - [c2 D(c) / (cl-c2) (7) Determination of D over several consecutive ranges of concentration 2 Rogers (1964): enables one to estimate the dependence of D on concentration. Equation (7) simplifies to Equation (8) when c2-0 (ie most permeation experiments) and D is determined for a number of values: C1 '1') - 1 / clfo D(c) dc (8) When experimental conditions are such that c2 is always zero and.D is determined for a number of values of c1, D can be expressed as some explicit function of c. Then D as a function of c can be found by simple differentiation. In any case D can be plotted versus c and the slope as a function of c leads to an estimate of the desired concentration dependence of D(c) (Rogers, 1965a). In the steady state of flow through a planar membrane the permeability ET... 5 fl 2.le L 18 rate P is constant by definition: P - - D (dc/dx) - a constant (9) Therefore regardless of the fact that D(c) may be a function of concentration and dc/dx is therefore nonlinear, the product of these two quantities is a constant in the steady state of flow. By integration between c1 and c2, the two surface concentrations of the membrane of thickness (L) one obtains: c 1 P - (1 / L>ch2 D(c) dc - D (cl-c2) / L (10) Where D is the integral diffusion coefficient defined by equation (7). When c1>>ci10 equation (10) reduces to: P L -‘{: D(c) dc or D(c) - d(L P)/dc (11) and an estimate of the dependence of D(c) on c can be obtained either analytically or graphically from the dependence of (L P) on c (Rogers, 1964). Another estimate of D follows from the definition of the permeability coefficient as the product of the diffusion and solubility coefficients. When the diffusion process is concentration dependent: P - i (pl-p2) / L (12) where P is the value of the permeability coefficient for the pressure gradient (pl-p2), corresponding to the equilibrium surface concentrations c and c which define the integral diffusion coeffient. l 2 Thus from Rogers (1964): 19 C 1 P - [l/(c1-c2)J02 D dC]° [(cl'c2)/(p1-P2)]‘ [(p17p2)/L] (13) rd. UI UH / § (14). cl 'UI so that For the usual experimental conditions where c2 and p2 are approximently equal to zero, the quantity S - (cl-c2)/(p1-p2)reduces to the solubility coefficient, S - cl/pl. The above permeability theory derivation only considers the case where D and P are functions of concentration and S is constant. However in many organic permeant-polymer systems the solubility coefficient (S) is a function of the concentration of permeant in the polymer and does not always follow Henry's law, partricularly at high permeant concentrations. When a permeant diffuses through a membrane in which it is soluble there is an interval of time from when the permeant first enters the membrane until the steady state of permeation is established. During this time both the rate of flow and the concentration at any point in the membrane vary with time. If the diffusion coefficient is constant, the membrane is initially free of permeant and the permeant is continually removed from one side of the membrane (c2- 0), the amount of permeant (Qt)which passes through the membrane in time (t) is given by (Crank, 1975): 20 a: (Qt/LC1 - Dt/L2 - 1/6 - 2/Tr20é(-1)n/n2exp(-Dn2‘r[2t/L2) (15) As t goes to ”the steady state of permeation is approached and the exponential terms become negligibly small so that the transmission profile curve of Qt versus t tends to the line Qt - Dcl/L (t-L2/6D) (16) This line has the intercept,9 , on the t-axis given by: EB - L2/6D (17) From the lag time the diffusion coefficient can be deduced from Equation 17 and finally the solubility can be obtained from Equation 14 (Daynes, 1920 and Barrer, 1941). Frisch (l957,l958,l959) and Pollack and Frisch (1959) have developed expressions which allows the calculation of the diffusion coefficient from time lag data for systems in which the functional dependence of D on any or all of the variables: concentration, spatial coordinates and time, are known or can be assumed. Frisch (1957) gives expressions for the time lag in linear diffusion through a membrane with a concentration dependent diffusion coefficient. Frisch's method yields numerical values for parameters of the diffusion coefficient ‘concentration dependence expression (i.e. D - Doexp(5c)). This method can be quite complex as the concentration (c) as a function of x is necessary and can be very complicated (Crank and Park, 1968). 21 Pollack and Frisch (1959) have shown for a large class of functional diffusion concentration dependencies (D(c) on c the following inequality holds: 1/6 sen/L2 S 1/2 (13) Thus an estimate of the integral diffusion coefficient can be made using the time-lag expression derived for a constant D, Equation 17 is at worst too small by a factor of three (Rogers, 1964). 21 a Sorption And Desorption Theory of Organic Vapors In A Sheet When the concentration of permeant within the surfaces of a membrane of thickness (L) is maintained constant over time, the amount of diffusant, Mt, taken up by the sheet in a time t is given by (Crank and Park, 1968): w Mt/M‘ - 4(Dt/L2)1/2[1/Tr1/2 + ZZ(-1)nierfc(nL/2(Dt)1/2] (19) "’0 The uptake of permeant by the membrane is considered to be a process controlled by a constant diffusion coefficient D, and M,,is the equilibrium sorption at infinite time. The value of D can be deduced from a graph of Mt/M¢,versus (t/L2)l/2 when the slope of the initial approximately linear portion of the graph up to 50% of the M¢,is a staight line (Crank and Park, 1968). If D is a function of concentration and increases as the concentration of the permeant increases, the graph is linear over a larger increase in Mt' Another form of the sorption-desorption equation is (Crank and Park, 1968): 22 an lit/Mn - [1-8/ ZISII/(Zmfl)l-eXP[(-D(2m+1)2‘rr2t)/L2] (20) «5-0 From Equation 20 the value of t/L2 for which Mt/M‘r 1/2 which is written as (t/L2)1/2 is approximated by (Crank and Park, 1968): (t/L2)l/2 = 01/1313) 1n[u2/16 - 1/9 (TI2/16)9] (21) The diffusion cofficient, assumed to be constant, determined from Equation 21 is sometimes referred to as the half-time diffusion coefficient is given by - (0.04919 L2)/t (22) Dtl/Z 1/2 Co e t a i e ende t D usion Coe f cient: For systems where there is a concentration dependent diffusion coefficient (e.g. polymer-organic vapor systems) the initial gradient from each sorption curve yields a mean of integral diffusion coefficient values (D) using Equation 22 (Crank and Park, 1968). Calculations have shown that this integral diffusion coefficient obtained from one experiment is a reasonable approximation to Equation 8 (Crank and Park, 1968). The limits of integration here become the concentration c1 at the surface of the sheet and c2 in the center of the sheet. By measuring the integral diffusion coefficient at several versus c can be drawn and permeant concentrations a graph of Dc 1 1 23 numerical or graphical differentiation with respect to cl gives a first approximation to the relationship between D and c. The average of the values of the integral diffusion coefficients calculated from sorption and desorption data is Dave - 1/2 (D5 + Dd) (23) a better approximation to D than either Ds or D separately (Rogers, d 1964). In many polymer systems the diffusion coefficient depends fl approxinitely either linearly or exponentially on concentration. For these cases Crank (1956) has produced correction curves 01 showing the difference between (l/cflj’o D(c) dc and D/Do' When Mt/Mg’is greater than 0.4 or so the solution of Equation 20 then becomes (Rogers, 1964): ln(l- Mt/M_) - ln(k/n2) - Dwgt/LZ (24) The value of D can then be calculated from the limiting slope (k) at large values of t of a plot of 1n(M~ - Mt) versus t or t/L2 (Rogers, 1964). Characteristics of Organic Vapor Mass Transport Through Polymers Above Their Glass Transition Temperature Most investigations involving the diffusion of organic vapors in polymers above their Tg have been theoretical sorption-desorption types of studies, where the effects of the type of polymer, penetrant, temperature and penetrant concentration on the diffusion coefficient have been measured (Fujita, 1968). The published permeation data for organic vapors in polymers is very limited and is divided between results from studies with glassy polymers and studies with polymers above their glass transition temperatures. The glass transition temperature, (Tg), of a polymer marks the change in polymer properties from glassy type structure properties to an amorphous type structure.) WSEW-.ESTPSEEE‘AEEQBS{93.5.95111131'1‘1‘18 the Onset 0f P°1Ymer chain segmental mobility for a polymer (Rodriguez, 1970). Recently there has been a number of papers published involving studies on the organic vapor permeation characteristics of various commercial homopolymer and laminate structures and applying the results to packaging problems with foods (Hilton and Nee, 1978, Becker et. al., 1983, Gilbert et. al., 1983, Murray, 1984, DeLassus, 1986). The conditions of a typical permeation measurement utilizes: (i) .9) cons one appr cor: (iii come the mano cond isos orga for 1986 accu Cone amOu time Perm Vapo a th ast 1968 Farm to b. 25 constant surface concentration of permeant at the film surfaces where one surface of the film is maintained at a penetrant concentration of approximently zero and the other is at the equilibrium concentration corresponding to a permeant pressure P1; (ii) constant temperature; and (iii) the diffusion coefficient is assumed to be a function of concentration only. Traditionally the literature on studies involving the diffusion of gases and vapors through polymer membranes utilized a manometric technique for quantitation under the above mentioned test conditions (Stannett et.a1., 1972). Recently both isostatic and quasi- isostatic test methods have been described for studying the diffusion of organic vapors through barrier films using gas chromatographic analysis for quantitation (Stannett et al., 1972, Zobel, 1982, Baner et. al., 1986, Hernandez et. a1. 1986). In the quasi-isostatic method, the accumulation of diffusate in the low partial pressure (low concentration) side of the film is measured as a function of time. The amount of vapor, q, which has passed through a unit area of film during time, t, is plotted as a function of time giving a characteristic permeation curve or transmission profile (see Figure 16). Typically, vapors permeating through a polymer at a temperature above its Tg, gives a the plot of (q) versus (t) that is convex towards the time axis and asymptotically approaches a straight line as the time increases (Fujita, 1968). When the asymptotic portion of the curve gives a rate of permeation dq/dt, which is independent of time, the permeation is said to be in steady state. The slope of this straight line gives the perm C 011C the The sol and equ 501 C06 EEC bec hoi in' PT 1!) eq DI 26 permeation rate (P) for the given experimental conditions. The concentration of diffusate in the film no longer changes with time when the steady state is reached. M me t' The surface concentration of a diffusant in contact with its vapor or solution can be interpreted in terms of the diffusion coefficient (Crank and Park, 1968). The surface concentration is usually obtained from the equilibrium determination of the uptake of vapor by the solid polymer. Sorption kinetic measurement can also be used to calculate the diffusion coefficient. Determination of the diffusion coefficient by the sorption technigue has many advantages over the permeation lag time method because such problems as leakage, membrane distortion, and problems from holes in the membrane are eliminated (Crank and Park, 1968). However interpretation of the diffusion coefficient when time effects are present is still a problem for the sorption method as well. In a sorption experiment a uniform film of a given polymer initially equilibrated with vapor of a given diffusate substance at a certain pressure or concentration is suddenly exposed to a different pressure or concentration of the same vapor. The gain or loss in weight of the film is measured as a function of time (t), while a constant pressure or concentration is maintained. In most experiments the initial pressure or 27 concentration in contact with the film is zero (Fujita, 1968). Data from a sorption experiment is generally reported in the form of a sorption curve. The sorption curve is produced by plotting the amount of vapor M(t) (in grams) absorbed in or desorbed from a unit gram or cubic centimeter of dry polymer against the square root of time (t) (Fujita, 1968). For theoretical analysis a plot M(t)/M¢,against the ratio (t)1/2L is made, where L is the thickness of the dry film and M“, is the equilibrium sorbed concentration of vapor in the polymer. This plot is refemerdto as the reduced sorption curve (Fujita, 1968). The distribution of diffusant and its change with time in a given film during absorption and desorption are governed by the one-dimensional differential equation due to Pick with the space coordinate in the direction of film thickness (Fujita, 1968). Solutions of Fick's equation applied to sorption experiments where at t-O the concentration of diffusate is uniform in the film is subject to the following assumptions: 1) D is a function of c only; 2) when the ambient pressure of the permeant is changed from an initial value to a final pressure the concentrations in the film instantaneously increase to an equilibrium value with the contacting pressure (Fujita, 1968). Sorption curves having characteristics expected from the above assumptions are called Fickian or normal type. Studies of the diffusion of small molecules in polymers at temperatures well above the polymer's glass transition temps are i behax Fuji! line; over and l COOCI film: Each abov¢ fUnCT Y'I'I'Ten ConCE 28 temperature have shown that the kinetics of sorption of organic vapor are invariably Fickian (Fujita, 1968). Deviations from Fickian sorption behavior have been observed when the temperature of the sorption measurements are at or below the polymer's glass transition temperature (Fuj ita, 1968) . The following is a summary of important Fickian sorption features from Fujita (1968): (a) Both absorption and desorption curves are linear in the initial stage. For absorption, the linear region extends over 60% or more of M”. For D(c) increasing with c the absorption curve is linear almost up to the final sorption equilibrium. (b) Above the linear portions both absorption and desorption curves are concave to the abscissa axis. (c) For the same initial and final concentrations a series of absorption curves or desorption curves for films of different thicknesses are superposable to a single curve if each curve is replotted in the form of a reduced curve. (d) The reduced absorption curve always lies above the corresponding reduced desorption curve if D is an increasing function of c . Both reduced curves coincide over the entire range of t when D is constant. The divergence of the two curves increases the more concentration dependent D is on c. (e) For absorptions the initial slope of the rec p“ FUJ inc al’E At the so: mea Per .P COTl EXC‘ by! E.Be 29 reduced curve becomes larger as the concentration increment increases provided that D increases with c in the concentration range studied. Fujita (1968) further notes that criteria (a), (b) and (c) are independent of the form of D as a function of c thus when these criteria are satisfied the system is said to exhibit Fickian sorption. At the molecular level the essential conditions for Fickian sorption is the high mobility of polymer segmental units. This explains why the sorption kinetics of organic vapors by polymers become Fickian when the measurement is carried out at temperatures well above the glass transition temperature (Fujita, 1968). Permeability is related to diffusion and solubility by the relationship P - D-S. The complex permeability process is best understood by considering the effects of various factors on solubility and diffusion. This portion of the text on the characteristics of the permeation and diffusion of organic vapors through polymer membranes follows from the excellent review in the chapter on Permeability and Chemical Resistance by C.E. Rogers from the book Emgineerimg Desigm for Plasgics edited by E.Baer (1964). 30 W The solubility of a mobile component in a solid can be described as the distribution of the component between two or more phases. The uptake of penetrant by a solid is called sorption and can be considered to have adsorption or absorption as the basic mechanism (Rogers, 1964). There is no way of distinguishing between either physical adsorption and chemisorption or between absorption and adsorption, so that the overall process is best considered a composite of these various modes (Rogers, 1964). The dependence of the solubility coefficient on temperature generally follows an Arrhenius type relationship: S - Soexp(- Hs/RT) (25) Where Hs is the apparent heat of solution (Rogers,1964). The process of sorption by a polymer may be considered to involve two stages: first condensation of vapor onto the polymer surface followed by solution of the condensed vapor (Rogers, 1964). The heat of solution can be expressed as the sum of the molar heat of condensation ( He) and the partial molar heat of mixing ( H1). The heat of mixing is always positive and the heat of condensation can be positive or negative depending on whether the molecule is a gas or vapor. For permanent gases, H3 is slightly positive so that S increases slightly with 31 temperature. However for the more condensable vapors (like organic compounds) Hs is negative due to the relatively large heat of condensation, thus the solubility decreases with increasing temperature (Rogers, 1964). A sorption isotherm is a curve that relates the equilibrium concentration of the penetrant in the polymer (c), to the concentration of penetrant (p) surrounding the solid, at any constant temperature. There are four basic types of isotherms observed in polymer systems. These isotherms depend on the degree of penetrant-polymer interaction (Rogers, 1964). Type I follows Henry's law where the concentration is linearly dependent upon pressure. Type II is characteristic in systems where only a unimolecular layer of sorbed substance forms on the substrate showing a concave curve towards the pressure axis. Type III sorption is characteristic of multilayer adsorption where the attractive forces between penetrant and solid are greater than those of the penetrant molecules themselves, giving a sigmoid shaped curve. Type IV sorption forms a convex curve towards the pressure axis. Type IV sorption results when forces between the penetrant and substrate are relatively small so that the sorption process occurs essentially randomly. The solubility coefficient at a given permeant partial pressure can be calculated from these sorption isotherms by dividing the sorbed concentration (c) by the corresponding ingoing pressure (p). An empirical equation describing the type IV isotherm for the sorption of po] Iu’he par (R0 wheT 32 of nonpolar organic molecules in polyethylene and other nonpolar polymers is: S - So exp 87c) (26) Where So is the extrapolated value of S at c-O and.0'is a characteristic parameter for the penetrant-polymer system at a given temperature (Rogers et.a1., 1960). The Langmuir equation for sorption leads to a type II isotherm. The solubility coefficient can be written as: S - c/p -b cm/ (1 + bp) (27) where cm is the maximum possible sorption and b is a parameter characteristic of the system (Rogers, 1964). The modified BET equation can be used to describe type II, III, and IV isotherms (Rogers,1964). s - c/p -_E:9mil;(.u_lj_cezeofl_t_n_(moflfll (Po-p)-[1 + < -1>
- (a (P/Po)n+l] (28)
where: p0 is the permeant saturated vapor pressure
cm is the sorbed concentration of vapor
corresponding to a complete monolayer sorption
e - exp(Q1-QL / R T) where Q1 is the heat of
adsorption for the first layer, QL is the
heat of vaporization for the pure liquid
penetrant.
n - number of layers on which sorption can take
place
1964:
on t1
the 5
to SE
Chemi
The t
tempe
by an
Vhere
(Rege
the e
energ:
pre~e:
freque
33
The magnitude of the solubility for a penetrant in a polymer increases
with : (i) the chemical similarity of the penetrant-polymer; (ii) the
more condensable or lower the boiling point of the vapor; (iii) the
larger the molar volume of the condensed penetrant; and (iv) the lower
the percent crosslinking and the crystallinity of the polymer (Rogers,
1964). The sorption of penetrant by the polymer has a profound effect
on the solid's properties. In addition to the plasticizing action of
the sorbed penetrant there may be changes in the polymer structure due
to swelling and distortion incurred during sorption as well as actual
chemical attack on the polymer (Rogers, 1964).
s C t r tics
The temperature dependence of diffusion coefficients over small
temperature ranges at a constant vapor concentration can be represented
by an Arrhenious type relationship:
D - Doexp (-Ed/ R T) (29)
Where Ed is the apparant activation energy for the diffusion process
(Rogers, 1964). The activation energy of diffusion is associated with
the energy required for ‘hole' formation in the polymer matrix plus the
energy required to move the molecule through the polymer structure. The
pre-exponential factor, (Do), can be thought of as being related to the
frequency and magnitude of the holes or ‘looseness' within the polymer
3h
microenvironment in the absence of penetrant. The activation energy of
the polymer increases at temperatures above the polymer's glass
transition temperature (Rogers, 1964).
The magnitude of the concentration dependence of diffusion in any given
polymer is dependent on the temperature, molecular size, chemical
similarity between penetrant and polymer and the penetrant concentration
in the polymer. The solubility coefficient is often essentially
constant at low vapor activities for the more volatile vapors while the
diffusion coefficient exhibits significant concentration dependence.
The concentration dependence of the diffusion coefficient can be
represented by the equation:
D - Do exp (Kc) (30)
Where 5 is a characteristic constant, Do is a pre-exponential factor
representing the diffusion coefficient at zero concentration or the
limiting diffusion coefficient and c is the concentration of permeant in
the polymer (Rogers, 1964).
The diffusion coefficient may deviate significantly from a linear or
exponential dependence on c when the measurements are made over wide
temperature ranges and vapor concentration, or activity, especially with
more easily condensable vapors (Rogers, 1964). Such behavior has been
observed for allyl chloride in polyvinylacetate; for n-alkyl acetates in
polymethylacrylate; and for hydrocarbons in polyethylene (Meares, 1958a
35
b; Fujita, 1960; Rogers, 1960). The concentration dependence in these
systems can be represented by a simple exponential function of vapor
activity:
D - Do exp (aka (31)
1)
Where1 (36)
Where the quantity (1-Xm) is the amorphous mass fraction of the the
semicrystalline polymer. Crystallites in the polymer serve to decrease
the segmental mobility of polymer chains in the amorphous phase of the
polymer (Ng et. al., 1985).
ran‘
Uhe
pro
coe
act
5V5
dii
1th
‘JaF
HEr
(RC
red
39
Pegmgability Characteristics
The temperature dependence of the permeability coefficient over small
ranges of temperature can be described by an Arrhenius type relation:
P - 5; exp (-Ep/ R T) (37)
Where Ep is the apparant activation energy for the overall permeation
process and the prexponential factor Po, is the permeability
coefficient at zero degrees Kelvin (Rogers, 1964). The apparant
activation energy Ep follows from the definition P - D S where:
Ep - Ed + H8 (38)
and
P - D -S (39)
The concentration dependence of the permeability coefficient for
systems that follow the solubility behaviour in Equation (26) and
diffusion behaviour described by Equation (31) can be written as a
combination of the two equations:
P - Po exp (da + 3c) (40)
1
When the sorbed vapor concentration increases rapidly with increasing
vapor pressure, a plot of log P versus vapor activity becomes nonlinear
(Rogers et a1, 1960). When the solubility of the vapor approximates
Henry's law, log P varies linearly with vapor pressure or activity
(Rogers, 1964). At sufficiently low vapor activities Equation (40)
reduces to a linear dependence of P on vapor pressure:
1 - $0 + K°p (41)
whe
In
wit
thT
St?
th
ke
hO
where K is a constant and p is the vapor pressure (Cutler et.aL, 1951).
In most polymer-penetrant systems the permeability generally increases
with the chemical similarity between components. The permeation rate
through the nonpolar polymer membrane polyethylene, is lowest for
strongly polar penetrant molecules and greatest with hydrocarbons in
the following order: alcohols, acids, nitro-derivatives, aldehydes and
ketones, esters, ethers, hydrocarbons and halogenated hydrocarbons
(Rogers, 1964). The molecular weight of the polymer has been found to
have little effect on the rate of permeation (Rogers, 1964). The
limiting diffusion coefficient (Do) decreases and the limiting
solubility coefficient (80) increases exponentially with an increase
in the overall molecular volume and cross sectional area of the
penetrant. As a consequence of this compensating behavior, Po is much
less dependent on the penetrant size and shape than either S0 or D0 is
individually (Rogers, 1964).
An empirical relationship has been developed for the permeability
factor of polyethylene (PE) to a number of organic liquids that can be
useful in prediction of the permeability of PE to different organic
vapors (Salame, 1961, 1981). This relationship is based on the number
of carbon atoms in the penetrant molecule as well as on the other
functional groups or atoms present in the molecule and the molecular
structure of the penetrant.
hl
The permeation rate can be expected to decrease as the symmetry and
cohesive energy density of the polymer increases (Rogers, 1964). This
occurs mainly due to a decrease in the diffusion coefficient.
Furthermore, the permeability decreases with an increased degree of
cross linking and crystallinity in the polymer (Rogers, 1964). The
diffusion coefficient is also largely responsible for this decrease in
permeability. The solubility is affected relatively little, except at
high degrees of crosslinking and crystallinity. There does not appear
to be any simple relationship between the initial polymer density (as
related to crystallinity content and morphology) and the value of P and
D for vapors that markedly swell a polymer (Rogers, 1964). Variations
in polymer density and morphology in the absence of vapor, are due to
structural differences such as chain branching and to the thermo-
mechanical history of the sample (i.e. orientation and crystallization
conditions) (Rogers, 1964). The presence of solvent undoubtedly
disrupts the initial local configuration of crystalline and amorphous
regions so that the effective density and local molecular
configurations vary in a nonlinear fashion both with time and as a
function of distance in the sample (Rogers, 1964).
Orga
to r
graT
iso:
org
5am
cyl
ove
anc
men
Va:
re;
dis
the
Ch;
d1!
Pa:
h2
Organic Vapor Permeation Measurement Techniques
There are three common techniques which have been used by researchers
to measure the permeation of organic vapors through polymer films. A
gravimetric technique, an absolute pressure type method and an
isostatic or quasi-isostatic type method.
The gravimetric technique measures the weight gain or loss of an
organic permeant permeating through a known surface area of a film
sample. One of the more common approaches, the cup test, uses a shallow
cylindrical dish containing liquid_penetrant with the membrane sealed
over the top. The assembled cup is placed in a controlled temperature
and atmosphere environment and the weight loss of permeant through the
membrane is measured (Lebovits, 1966; Martinovich and Boeke, 1957). A
variation of this method involves filling a polymer pouch with silica
gel absorbant, exposing it to an organic vapor atmosphere and measuring
the uptake of vapor by the increase in weight over time (Laine and
Osburn, 1977). The steady state permeation rate in these methods is
reached when there is a constant weight gain or loss by the pouch or
dish. The problems associated with these gravimetric methods include
the limited vapor pressure range that can be used which prevents
characterizing the concentration dependence of the permeability and
diffusion coefficients and the lack of sensitivity of the method,
particularly with the low permeation rates found with high barrier
iii
the
prc
V0
so
0t
de
PI
MC
et
Inc
d1
h3
films. Other problems associated with the gravimetric method include
the inability to evaluate the effects of co-permeants and sealing
problems with the dish or when forming a pouch (Talwar, 1974).
The two remaining methods can be described as partition cell methods,
where the permeant being tested is isolated on one side of the film and
then detected on the other side as a function of time.
The absolute pressure method uses volumetric or manometric measuring
techniques to directly measure the permeating gas or vapor. For
pressure measurements this is done using a pressure gauge such a a
MacLeod gauge or a calibrated capillary tube containing mercury for
volumetric measurements. The sample is clamped into a permeation cell
so that the only path for the vapor to move from one chamber to the
other is through the film sample. The steady state permeation rate is
determined from the conditions when there is a constant increase in
pressure or volume with time in the low pressure side of the cell.
Most organic vapor permeation measurements made before 1970 are
(be www1.1473
variations of a high vacuum/time-lag technique that was developed by
Barrer and Skirrow (1948), and Rouse (1947) for measuring the
permeation of gases such as 0 and CO2 (Stannet et.aL, 1972). Rogers
2
et al (1956), Meyers et a1 (1957) and Meares (1958a) have made
modifications and refined this method for measuring the permeation and
diffusion of organic vapors through polymer films. A pressure-volume
metho<
well I
AmerOT
The AT
procer
Sheeti
‘Dow (
polyme
organi
(ROger
The ma
aPplic
Permea
theore
Vapor.
80me p
useful
c°mple
long p.
Fm~'the
the fi.
USed W:
hh
method was developed for measuring vapor permeabilities that correlates
well with results obtained from the manometric measuring technique (Van
Amerongen, 1946).
The American Society for Test Methods, ASTM, has developed a standard
procedure D-l434-82 (Gas Transmission Rate of Plastic Film and
Sheeting) which uses the pressure differential method and the so called
‘Dow Gas Transmission Cell' for determining gas transmission rates of
polymer films. This method is not considered suitable for measuring
organic vapor permeation without some modifications to the test cell
(Rogers, 1964).
The manometric/volumetric high vacuum methods have found widespread
applicability and usage and are accepted techniques for measuring the
permeation of gases and vapors through polymer membranes. Most
theoretical studies of permeation and diffusion of specific organic
vapor-polymer systems have used this method (Rogers, 1964). There are
some problems with this method however, that detract from its overall
usefulness. The high vacuum/lag time apparatuses used are quite
complex and must have perfect seals in order to maintain a vacuum over
long periods of time (particularly when testing high barrier films).
Furthermore because there is an absolute pressure differential across
the film, thin or easily deformable pressure sensitive films cannot be
used without some kind of film support, especially at high pressure
diff
bec:
vapc
of j
vap
Mos
dif
qua
isc
the
t8!
fil
pe
In
ar
CC
1&5
differentials. A more fundamental problem with the method also exists
because the detection system cannot differentiate between co-permeating
vapors. The method is therefore restricted to measuring the permeation
of pure vapor only and the effects of copermeants, in particular water
vapor, cannot be evaluated.
Most of the problems associated with the gravimetric and pressure
differential methods can be avoided by the use of an isostatic and
quasi-isostatic permeation method. With the isostatic and quasi-
isostatic methods there is no absolute pressure differential between
the two sides of the film. The partial pressure differential of the
test vapor, provides the driving force with the total pressure on both
sides of the film being equal to one atmosphere. This system allows
films of any type and thickness to be evaluated over a range of
permeant partial pressure values.
In an isostatic system the film sample is clamped in a permeation cell
and the desired permeant concentration, in a carrier gas, is flowed
continually over one side of the film. An inert carrier gas stream
(the same as the permeant carrier gas) is flowed simultaneously over
the low concentration side of the film carrying the permeant vapor to a
detector. The steady state permeation rate is equal to the steady
state concentration of permeant in the sweep gas times the sweep gas
flow rate.
116
An early isostatic test method was developed that used chemical
sorption of the permeating gases for quantification (Davis, 1946).
Chemical sorption methods suffer from lack of sensitivity and better
permeant detection methods are now available. Thermal conductivity
detectors have been used to measure the increase of permeant in the
sweep gas (Ziegel et al.1969; Pastenak et a1, 1970). Small thermistors
were also used to detect the presence of permeant in the sweep gas
(Yasuda and Rosengren, 1970; Giacin and Gyeszly, 1981). One of the
major problems with these uses of thermal conductivity detectors and
thermistors is their inability to distinguish between contaminating
vapor or co-permeants in the sweep gas. To a lesser degree, there are
problems of calibrating these detectors for the specific permeant vapor
and concentrations found and the effect of sweep gas flow rate on
calibration. The use of a flame ionization detector (FID) has the
advantage that the detector is relatively unaffected by the presence of
the carrier gas and water vapor (Zobel, 1982). However the FID alone
cannot distinguish between co-permeating organic vapors. A gas
chromatograph sampling system coupled with an FID was used to separate
and detect a complex mixture of organic permeants (Caskey, 1967, Pye
el. al., 1976, Hernandez,l984).
One of the problems with the isostatic method is that the detectors
exhibit a limit of sensitivity which must be exceeded to allow the
117
detection of the minute amounts of vapor that may pass through a high
barrier film sample. An FID can only detect about 10-4 to 10-2}13 of a
compound. This may cause problems when testing high barrier film
samples where permeation rates are exceedingly low. This problem may
be overcome by using a cold trap in the sweep gas stream to condense
out and accumulate the organic vapors over a given time interval
(Niebergall et al, 1978). The accumulated sample is then injected into
a gas chromatograph with an FID for separation and detection.
The quasi-isostatic measurement technique is a variation of the
isostatic method, where instead of having a sweep gas flowing through
the low concentration side of the permeation cell the low concentration
chamber is initially filled with the inert sweep gas and then sealed.
The accumulation of permeant in the low concentration chamber is then
measured as a function of time. The Lyssy quasi-isostatic permeability
apparatus model L63 uses thermistors in the static cell chamber
(Lockhart, 1969). Problems with using the thermistors as detectors
include the calibration of the thermistor and the lack of specificity
of the thermistor to co-permeants and contaminating vapors. A
technique was developed whereby gas samples from the static cell
chamber were removed periodically and injected directly into a gas
chromatograph with an FID for quantitation (Gilbert and Pegaz, 1969,
Baner et. al., 1986). This method overcomes the problem of mixed
vapors and the effect of relative humidity on the detector.
118
A third variation of the isostatic type of vapor permeability is the
static type system. Here a volatile liquid permeant is placed in a
reservoir below a film sample to provide the concentration gradient
driving force through the film. The permeating vapor then accumulates
above the film in the upper chamber of the permation cell . This
chamber is sampled using a gas tight syringe and injected into a
gas chromatograph with FID for quantition (Gilbert and Pegaz, 1969;
Hilton and Nee, 1978; Murray and Dorschner, 1983). One of the problems
with using this method is that it is limited to testing only at the
saturation vapor pressure of the permeant, so that the concentration
dependence of the permeation and diffusion process cannot be studied.
Other problems cited include the establishment of a concentration
gradient in the vapor phase next to the membrane surface, as in the
case of rapidly permeating film-firmeant systems, which may lead to
anomalous results (Meyers et al, 1957).
Other methods for determining the permeability rates of organic vapors
in polymer films have been developed but have not seen widespread use
and acceptance. Stannett et al, (1972) discusses several of these
other measurement systems.
The measurement systems of Niebergall et a1, (1978), Gilbert and Pegaz,
(1969); and Caskey, (1967) all contain the necessary elements for an
b9
accurate and versatile method for determining the permeability of
organic vapors through polymer packaging films. A successful system to
use for routine and theoretical evaluation of polymer film barrier
properties for packaging applications and research needs to be able to
evaluate the permeability of the test film as a function of the
following parameters:
(1) thickness
(2) type of film
(3) barrier properties
(4) permeant concentration
(5) co-permeants including relative humidity
(6) simple and inexpensive design
(7) reproducibility
With these requirements in mind a quasi-isostatic system based the
Gilbert and Pegaz (1969) design was developed.
50
Organic Vapor Sorption Measurement Techniques
The most common and simplest methods of sorption measurement are
gravimetric techniques that measure the weight gain of the polymer,
when the polymer sheet is exposed to a constant vapor pressure or
concentration (Crank, 1968). Early techniques involved placing a
specimen in an organic vapor atmosphere and than removing it at
intervals to measure its weight gain (Park, 1950). This method
produced errors due to the interuption of the sorption process and
errors due to the presence of an air barrier surrounding the polymer
through which the permeant must diffuse to reach the polymer (Crank and
Park, 1968). One of the more common gravimetric techniques suspends
the polymer sample from a calibrated quartz spring and the weight gain
is measured by observing the deflection of the spring over time.
Examples of this method have been demonstrated by Prager and Long
(1951), Kishimoto and Enda (1964), and Jacques and Hopfenberg (1974).
More recently what is described by Crank and Park (1968) as a magnetic-
weighing method or by others as an electrobalance method (Cahn
Instrument Co., Paramount CA.) has been used to measure the sorption of
organic vapors by polymers by Berens (1977, 1979), Berens and
Hopfenberg (1978, 1981), Choy et. a1. (1984) and Ng et a1. (1985). The
quartz spring and elctrobalance avoid the error of interupting the
51
sorption process for measurement and the error due to ‘air barrier' can
be overcome by applying a vacuum to the systems (Crank and Park, 1968).
Crank and Park (1968) describe several other methods for making
sorption measurements. Other methods include a "vibroscope" method
where the resonant frequency of a filament varies as the square root of
the mass per unit length. Volumetric absorption and pressure decrease
measuring apparatuses have also been developed to measure the uptake of
permeant by the polymer as well as a light absorption measurement
technique (Crank and Park, 1968).
qua
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PET
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52
Mgasugememts
The data obtained from the quasi-isostatic permeation method gives the
quantity of vapor permeated through a film of surface area (A) of
thickness (L) as a function of time. The quantity of vapor which had
permeated through the test film in a given time, Q(t), is plotted
versus the time elapsed from the introduction of vapor into the high
concentration chamber of the permeation cell, to give the
characteristic transmission profile or permeation curve (see Fi4gure 112).
The permeability coefficient P, the integral diffusion coefficient‘D,
and the solubility coefficient S can be determined from the ‘time lag'
method developed by Daynes (1920) and Barrer (1939), using appropriate
solutions of the diffusion equation. The permeability constant is
determined by multiplying the slope of the linear portion of the
permeation curve, which is the steady state permeation rate, by the
membrane thickness and dividing by the area of the membrane and the
permeant pressure differential. As a rule, the determination of the
thickness of the membrane is the least accurate part of the permeation
test, particularly in the case of organic vapor where the effect of
film swelling by the vapors is ignored. Typical units for the
permeability constant of vapors are grams-cm/mz-day-mmHg or in the
U.S. cc-mil/lOOinz-day-atm. When a penetrant diffuses through a
membrane in which it is soluble there is an interval from the time the
per
est
lir.
lag
aft
It
con
193
dif
fun
con
(Fr
be 1
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53
penetrant first enters the membrane until the steady state of flow is
established. The intercept on the time axis of the extrapolated
linear steady state portion of the permeation curve is called the time
lag, 9. Under ordinary conditions the steady state of flow is reached
after a period of two to three times the time lag (Amerongen, 1946).
It has been shown that the time lag is directly related to the
constant integral diffusion coefficient D by the relationshipG-L2/6D (Barrer
1939). Expressions have been developed which allow the calculation of
diffusion coefficients from the time lag data for systems in which the
functional dependence of D on any or all of the variables:
concentration, spatial coordinate and time is known or can be assumed
(Frisch, 1957, 1958). Even if the exact functional dependence of D on
c is not known an estimate of the integral diffusion coefficient D can,
be made using time lag data. With some minor restrictions the
following inequality holds for a very large class of functional
dependencies of D on c (Pollak and Frisch, 1959):
1/6 9 D/L2ei 1/2 (28)
Thus an estimate of the integral diffusion coefficient made using the
time lag expression for a constant D, D2:L2/60, is at worst too small
by a factor of three (Frisch, 1957). For most purposes this order of
accuracy is quite sufficient since the experimental error in obtaining
raw data may be of greater significance than this theoretical variance
(Frisch, 1959). The integral diffusion coefficient calculated by the
til
the
ex;
196
Fro
501
int.
whe:
0th
can 1:
the c
the f
the f
aVeraé
54
time lag method has been shown to agree within experimental error with
the steady state of flow D calculated from sorption-desorption type
experiments for organic vapors within polyethylene (Rogers et al,
1960).
From equations (12) and (13) the concentration dependency of the
solubility coefficient can be determined from calculation of the
integral solubility coefficient at different vapors concentrations
where P - D S (pl-p2)/L, so that S - P / D using P and D data
obtained from the time lag method.
Thus a single permeation experiment allows calculation of the P, D and
S for a given temperature, vapor concentration and film-permeant
combination. In order to determine the concentration dependence of P,
D and S for a given system it is necessary to make permeation
measurements at several ingoing vapor concentrations and then plot the
integral P, D and S versus the concentration of vapor in the polymer.
An estimate of the average permeant concentration in the polymer (c)
can be obtained from the relationship S - (cl-c2)/(p1-p2). Here c is
1
the concentration of vapor in the film at the high pressure side of
the film, p1, and c2 (which isaIO) is the concentration of vapor in
the film at low vapor pressure side of the film, p2 (where pé%0).
Then using S and the known partial pressure of permeant (p1) the
average permeant concentration in the polymer c, can be calculated
55
(Rogers, 1964).
Determination of c is however usually made by equilibrium sorption
studies. It has been shown that instead of plotting log D versus c,
log D can be plotted versus the activity al- pl/po to predict the
vapor activity dependence of the diffusion coefficient (Rogers, 1964).
The behavior of P or S as a function of the vapor activity on the high
concentration side of the film has not been described in the
literature.
The extrapolation of the graph of log D or log D versus concentration
or vapor activity to zero concentration or activity gives the limiting
diffusion coefficient, Do' A method was developed by Meares (1965b)
which analyzes the transient permeation state from the transmission
profile curve to determine the limiting coefficient Do for an organic
vapor penetrant-polymer system. This method is often referred to as
the small times approximation of D.
(3) S
Perhea
HMS.
(1) Orientated Polypropylene (OPP)
Mobil Chemical Co. Films Division, Macedon, N.Y. 14502 Mobil
Bicor 306 16 1.0 mil homopolymer orientated 5.5 times
machine direction, 8 times in the cross machine direction. This
is representative of a nonpolar polyolefin type film commonly
used for its intermediate barrier properties and structural
characteristics.
(2) Polyvinylidene chloride (SARAN)
Dow Chemical U.S.A., Midland, MI 48640 . Dow #7323662,
Film # X0 1621 10. 1.1 mil uniform material Crystallinity
41% made by a blown bubble process. Saran is a polar type
material used for its superior barrier properties. This Saran
is considered a high barrier type PVDC copolymer.
(3) Saran coated orientated polypropylene (OPP/PVDC)
Mobil Chemical Co. Films Division, Macedon, N.Y. 14502 Mobil
250 ASW acrylic coating/homopolymer/white opaque polypropylene/
homopoymer skin/saran coating 1.7 - 2.0 mil total thickness,
saran coating 0.2-0.3 mil. Titanium dioxide filler in opaque
layer. This is an example of a commonly used laminate of the
polypropylene and PVDC films.
2.9M; .
Toluene. Analytical Reagent 99.98% pure
b-range 110.70 to 110.750C Mallinckrodt, Inc. Paris, KY
56
Tr
Al
wi
sa
ma
SC
hu
P .
Hit
Clo;
Analytical Method
Treatment of Film Samples
All film samples were tested at a room temperature range of 21 to 27°C
with a total pressure of one atmosphere on each side of the film
sample. The films were tested as they were received from the
manufacturer with the exception of damaged samples with nicks and
scratches which were discarded. All films were tested at 0% relative
humidity (RH) and were stored in a desiccator over CaSO desiccant for
4
2 weeks at 27°C prior to testing.
W
Permeation Cell Design:
Prior to each new test with the permeation cell, the cell parts,
fittings, and o-rings were baked out in a laboratory oven at 70°C
overnight to remove any residual sorbed permeant from the previous
test. After removal from the oven the hot cells were allowed to cool
to ambient temperature before beginning a new test. The septa were
replaced and fresh vacuum grease applied to the o-rings. The new film
samples were placed in the cell and the bolts tightened to a 0.010" gap
between the sections while the valves were left open to release any
trapped air. The upper and lower cell chambers were flushed with pure
nitrogen at a rate of 500 cc/min for 5 minutes and then the valves
closed. Before introducing the permeant into the center ring,
57
he
CC
Cl“
8)
m
58
headspace samples were taken to check for residual vapor. The permeant
concentration was also monitored at the sample port after the mixing
chamber to be sure it maintained a constant concentration level. An
exhaust line was connected to one side of the center ring and a test
run begun by connecting a permeant line from the dispensing manifold to
the center cell chamber. The moment the permeant is first introduced
is recorded as time zero. The initial permeant flow rate is set at 70
ml/min. With this flow rate the permeant concentration reaches 95% of
its ingoing concentration in 3-5 minutes depending on the permeant
concentration used from Equation 42 (Hernandez, 1984):
time - (center ring volume/gas flow rate)~ln[(co-ci)/(ct-ci)] (42)
This high of a permeant flow rate ensures that a constant permeant
concentration is rapidly attained and is maintained in the high
concentration cell chamber of the permeation cell throughout the
duration of the experiment including the early stages when the sample is
rapidly absorbing permeant. Where c is the incoming vapor
i
concentration; co is the initial vapor concentration in the center ring;
and ct is the vapor concentration at some time t. When the desired
ingoing permeant concentration is reached in the high concentration cell
chamber, the permeant flow rate is reduced to 30 ml/min and is
maintained. The permeant flow rate is measured downstream from the
permeation cell with a soap bubble flow meter. The permeant
concentration is monitored at the center ring and mixing chamber
sampling port throughout the run.
V:
H-
H
59
Vapor Permeant Quantitation
The flux or permeability rate through the film samples was determined
by periodically removing samples (0.5 cc) from the cell's headspace
with a gas tight syringe and immediately injecting the sample into a
Hewlett Packard 5830A gas chromatograph (GC) equipped with dual flame
ionization detectors. The GC was interfaced to a Hewlett Packard
18850A automatic integrator. The column was a 1/8" o.d. X 6’ stainless
steel column packed with 5% SP2100 on 100/120 mesh supelcoport (Supelco
Inc., Bellefonte, Pa.). The chromatographic analysis conditions were:
injection port temperature 200°C, column temperature 175°C, flame
ionization detector temperature 350°C, and a Helium carrier gas flow
rate of 30 cc/min. This analysis gave a retention time of 1.33
toluene. The automatic integrator parameters used were slope
sensitivity of 0.01 and an area unit reject of 100.
One half milliliter gas samples were taken with a 0.5 cc Hamilton
#1750RN gas tight syringe (Hamilton Co., Reno, Nev.) for all sampling.
For each headspace sample, a .5 cc volume of nitrogen gas was introduced
into the low concentration cell chamber, the syringe pumped several
times to facilitate mixing and then a 0.5 cc sample removed for
analysis. This procedure replaced the sample volume removed by each
sample and avoided excessive puncturing of the septa . Each sample from
the headspace removes approximentely 1% of the total quantity of
6O
permeated vapor in the cell's headspace and replaces it with nitrogen.
Permeation Data Analysis
The total quantity of permeant in the cell headspace is calculated for
each sample by dividing the response in area units (au) obtained from
the 60's integrator by the sample volume (0.5 ml) and multiplying it by
the detector calibration factor (grams permeant/ GC area unit response)
and the volume of the permeation cell's headspace (50 ml).
Q - (GC au /O.5 m1)-(calibration factor g/au)~ 50 ml
This gives the total number of grams of permeant in the headspace at a
given time, t. The procedure for calibrating the gas chromatograph can
be found in Appendix C.
As the data is collected it is plotted on a graph with total permeant
accumulated in the headspace versus the elapsed time. The curve
produced is the transmission profile curve. The steady state
permeation region is the portion of the curve where there is a steady
increase in permeant concentration with time resulting in a straight
line on the transmission profile curve. Several measurements must be
made in the steady state region to confirm its linearity. Headspace
measurements are discontinued when adequate data has been collected. It
is proposed that the run be carried out to a minimum of two to three
times the lag time (Siegel and Coughlin, 1970). Eventually with this
type of system, the permeation rate decreases as the permeant partial
61
pressure driving force across the film decreases due to accumulation of
permeant in the cell's headspace. To impose a constant driving force,
the permeability run is usually terminated when the permeant
concentration in the lower concentration cell chamber is equal to 2 to
3% of the high cell concentration. However, it was found that
measurments in the lower concentration cell chamber could be taken up
to concentrations of 10% of the driving force in the high concentration
cell chamber before there was a measurable decrease in the permeation
rate. For some film-permeant concentration systems tested, particularly
those with large diffusion and permeation coefficients, no measurable
change in the permeation rate was observed up to 50% of the vapor
pressure differential accumulated in the headspace.
According to theory, the slope of the steady state region of the
transmission rate profiles gives the permeation rate of the film for
the specific conditions of the test. The most accurate method for
determining the permeation rate from a series of data points is to
plot the transmission profile curve and determine graphically where the
curve appears linear and apply linear regression analysis for these
data points. The linear regression line gives the best straight line
fit for a given set of data points. The slope of the linear regression
line is the flux or permeation rate (e.g. grams/hour).
The permeability coefficient (P) for a specific film-permeant test
thi
thi
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of
an
Al
pe
pe
Ec
62
combination is calculated by multiplying the permeation rate
(grams/hour) by 24 hours/day and dividing it by the film surface area
(50 cm2) and the permeant concentration (ppm, w/v). For homopolymer
films the permeability coefficent can also include units for the films
thickness in the numerator by multiplying (g/dayocm51ppm) by the
thickness of the film (mils or cm). The permeability coefficient for
laminate films is expressed as grams-structure/day-cmzoppm(w/v).
Laminate structures have different layer thicknesses and combinations
of layers which exhibit different behavior towards the test permeant
and have potential variation with permeant concentration dependency.
All layers of a laminate contribute to the permeability coefficient,
making it a unique measurement specific for that film structure. The
permeability coefficent is sometimes referred to as the integral
permeability coefficient, due to its theoretical derivation from
Equations (12), (13) and (14).
The lag time «9) can be determined from the x axis intercept of the
linear regression line calculated for the steady state permeation
region of the transmission profile curve. The integral diffusion
coefficient (D) can be calculated from the equation D - L2/6e. This
diffusion coefficient is referred to as Dlag’ the lag time diffusion
coefficient. Each reported lag time diffusion coefficient is defined
for a specific film-penetrant combination and set of test conditions.
Dlag is well defined theoretically for a homopolymer film which has a
uni:
COR!
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lam:
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com]
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63
uniform structure throughout the film. Homopolymer films are
considered to have the same Do throughout the film due to a relatively
uniform structure. In the case of laminate films each film layer has
its own characteristic Do and permeant concentration dependent
diffusion coefficient. Estimating the diffusion coefficient for a
laminate is further complicated because there is a permeant
concentration gradient present in the film. The Dlag determined is a
composite of these respective diffusion rates and is specific for that
combination of film layers and thicknesses under specific test
conditions. The Dlag for laminate film structures is referred to as an
effective lag time diffusion coefficient, specific to that particular
5 truc ture .
An integral or average solubility coefficient (S) can be determined
from the permeability coefficient (P) and the lag time diffusion
coefficient (Dlag) using equation (13). To get the solubility
coefficient in the units (gram/cmD-ppm) the units of the permeability
must be converted to (grams-cm/ seCocm2 ppm). Like the P and Dlag’ the
solubility coefficient for organic vapors is not well defined because
the permeant concentration gradient in the polymer matrix is not
exactly known. This is particularly true for laminate structures.
Therefore the solubility coefficient should be considered an effective
solubility coefficient. The solubility coefficient calculated this way
assumes that the solubility of the vapor in the polymer follows a
Her
1152'
6h
Henry's law relationship and that the diffusion coefficient calculated
using the time lag method (Dlag) represents the true steady state
diffusion coefficient. Determination of the solubility coefficient is
best determined directly by sorption measurements.
I011
65
The test method used was based on the quasi-isostatic permeation
measurement technique. The principles of this method have been
described in the literature review.
Figure 1 shows a schematic of the test apparatus, while an expanded
view of the permeability cell is presented in Figure 2. The
permeability cells used were constructed from aluminum or stainless
steel by the Michigan State University Engineering Department machine
shop. The cell was based on the design of Gilbert and Pegaz (1969).
The cell consists of three main components; a top and a bottom section
each containing a 50ml cavity, and a center ring with a hole the same
diameter as the cavities. The cavities in the top and bottom section
of the cell form the headspace volumes into which the permeating vapors
accumulate. This cell design allows two film samples to be evaluated
simultaneously. The top and bottom sections of the cell are equipped
with inlet and outlet valves that allow flushing of the cell with
nitrogen prior to a test run. This gives an initial headspace
composition of 100% nitrogen in the cell chamber. The center ring
section of the cell has two Swagelok quick connects (Crawford Fitting
Co., Solon, Ohio) which allow the cell to be easily connected and
BREHIVRCFT
Fig,
66
P -‘ -u- - -‘
B - Water Bath
81 - Glass Mixing Device
82 - Glass Vapor Generator
R - Regulator
V - Needle Valve
' B - Rotameter
C - Cells (Double Chamber)
F - To Waste and Gas Flow Bubble Meter
1’ - Three Way Valve
Figure 1. Schematic of Permeation Test Apparatus
Le
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67
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68
disconnected from the permeant dispensing manifold and to an exhaust
line that discharges into a fume hood. The center ring allows the
permeant vapor mixture to pass simultaneously over two film samples.
Two 4"x4" film samples are held in place and sealed between the two
sections of the cell by VitonR o-rings. VitonR is a flourocarbon
elastomer compound which is resistant to attack and swelling by most
organic vapors. The surface area of the film exposed to the permeant
is approximentely 50cm2, determined from the center diameter of the 0-
rings. The cell sections and film samples are clamped together by
tightening two bolts until there is a 0.010" gap, determined by a
feeler gauge, between the cell sections. Assembling the cells in this
manner ensures reproducing the same headspace volume, for each test.
As shown each section of the cell contains a sampling port with a
septum that allows sampling the headspace and center ring permeant
concentrations with a gas tight syringe. The sorption of vapor by the
septa is minimized by using teflon coated silicone septa and placing
the inert teflon side towards the inside of the cell.
A constant permeant vapor concentration in nitrogen carrier gas is
generated by bubbling nitrogen through a 100 ml graduated cylinder
containing 70 m1 of the liquid permeant. The nitrogen is dispersed in
the liquid by a fritted glass fitting with an average pore size of 60pm
(Fischer Scientific Inc., Pittsburg, Pa.) to ensure saturation of the
n1
vi
OL‘
CC
0]
Si
69
nitrogen with the organic vapor. The top of the cylinder is stoppered
with a 100% silicone rubber stopper with two holes for the inlet and
outlet of 1/8" o.d. copper tubing. The cylinder is submersed in a 32°C
constant temperature water bath which maintains the temperature of the
organic liquid above the test temperature (27°C) to ensure that the
saturation vapor pressure of the organic permeant in the nitrogen is
reached. A 250 ml erlenmeyer flask stoppered with a 100% silicone
stopper is placed downstream from the graduated cylinder and acts as a
trap for entrained toluene liquid droplets.
The nitrogen stream containing the organic vapor at its saturation
vapor pressure can be used as the permeant concentration driving force
or it can be mixed with pure nitrogen gas to provide lower penetrant
driving force concentrations. The nitrogen flow rates are controlled
by Nupro ‘3' series valves (Crawford Fitting Co., Solon, Ohio) with
vernier handles and monitored by Gilmont #1 shielded flow meters
(Gilmont Instruments Inc., Great Neck, N.Y.). The nitrogen tank
regulator is set at 5 psi.
The permeant concentration supplied to the center ring can also be
measured at a sampling port before the mixing chamber (see Figure 2).
After the mixing chamber the permeant mixture flows to a dispensing
manifold. Up to four permeation cells can be connected to the
dispensing manifold by Swagelok quick connects.
70
The lines carrying the permeant vapor are made from 1/8" o.d. copper
refrigeration tubing, with the exception of the dispensing manifold
which is constructed from 3/8" o.d. copper tubing. All fittings and
tubing connectons used were brass Swagelok fittings.
With this apparatus design and set up, permeation tests are limited to
ambient temperature testing (i.e. 250C). To test at temperatures
other than ambient temperature the cell could be placed in a
temperature controlled box or chamber (e.g. an oven or refrigerator).
71
Solubility Studies
Solubility Test Method
The solubility test method used is based on a continuous gravimetric
sorption technique using an electrobalance.
Figure 3 shows a schematic diagram of the sorption/desorption test
apparatus. The central component of the apparatus is a Cahn
Electrobalance model RG (Cahn Instruments, Inc., Cerritos, CA.). The
balance may be described as an electric current-to-torque transducer.
Initially the polymer sample is suspended on the sample wire on one
side of the balance beam arm and counter weights are added to the
opposite arm to balance the beam. As the sample absorbs/desorbs vapor
its weight increase/decrease produces a torque about the central axis
of the balance which is measured by the amount of current needed by the
torque converter to keep the beam level. The change in current is
transmitted by the balance control unit to a strip chart recorder
which also records the time function. The balance output is calibrated
in grams of weight sorbed by the polymer. This calibration can be
performed by using a calibration weight set purchased from Cahn
Instruments. Further description of the balance hardware and operation
can be obtained from Cahn Instruments (Berens, 1977, Cahn Instruments,
72
B-Water bath, generation of permeant
Vapor phase diluted in Nitrogen
Ct-Computer terminal
Cu-Control unit
F-Gas flow bubble meter '
Ho-Hood
N-Needle valve
8- Printer
T-Nitrogen tank
R - Rotarneter
Re-Regulator
S-Sarnple port
51-Sarnpling film
Sc-Strip chart
Si-Electn'cal input/output signal
Tv-Three way valve
Wm-Cahn electncal balance
Figure 3. Schematic Diagram of Sorption/Desorption
Apparatus.
73
Cerritos, 0a.).
The electrobalance and sample tube were kept in a constant temperature
environment of 21 tiO.5°C. For a sample mass of 10 mg, the sensitivity
of the balance is approximately Slig. The test system in Figure 3
allows for the continuous collection of sorption data of an organic
vapor by a polymer film from time zero to steady state conditions. By
performing several experiments at varying vapor concentrations the
solubility as a function of penetrant concentration can be determined.
The electrobalance is placed in a vacuum jar that has three hang down
tubes attached. As shown in Figure 3, the polymer film sample to be
tested is suspended directly on one of the arms of the electrobalance
and a constant concentration of dry penetrant vapor in nitrogen is
flowed continually through the sample hang-down tube. Using this
method the polymer sample is totally surrounded by the penetrant vapor
at a total pressure of one atmosphere. A constant concentration of
vapor was produced by employing a vapor generator system similar to
that detailed for the permeation measurement system. The flow rate of
the vapor was kept constant at 10 ml/min and was monitored continuously
by a rotometer. All fittings and tubing were brass and copper
respectively. The fittings and tubing were washed with methylene
chloride and methanol and baked out in a hot oven prior to assembling.
The vapor exits the vacuum jar via the middle hang-down tube where it
7h
then flows to a fume hood.
The concentration of vapor in contact with the polymer sample was
monitored throughout the measurement by removing a gas sample via the
sample port in the sample hang-down tube. The gas sample was taken
using a gas tight syringe and injecting the sample into a gas
chromatograph for quantition ( see permeation test method for syringe
and gas chromatograph specifications and conditions). In order to
begin sorption experiments at the precise permeant vapor concentration
of the test the following was developed to introduce the sample into
the sample hang-down tube at time zero. The penetrant vapor was flowed
through the empty electrobalance apparatus until the concentration of
vapor in the electrobalance equilibrated. Then the sample hang-down
tube was carefully removed and the preweighed polymer sample was
suspended on the sample wire and the hang-down tube placed back on the
vacuum jar. The polymer sample of approximately 10 mg was preweighed
on a Analytical balance to an accuracy of 1x10.4 grams. The time when
the hang-down tube was replaced was marked on the strip chart recorder
as time zero. Problems with electrostatic attraction between the
polymer sample and hang-down tube were sometimes experienced. An anti-
static spray was obtained Cahn Intruments and applied to the surfaces
of the hang-down tube to dissipate electrostatic build up prior to
introducing the sample.
75
The gain in weight of the sample due to penetrant (i.e. toluene vapor)
sorption was monitored continually until the system attains steady
state or equilibrates. The sample was assumed to reach equilibrium
when no further sample weight gain was observed over 24 hours. This
procedure was repeated at several penetrant concentration levels. For
each concentration level, a new film sample was utilized. All
measurements were carried out at 0% relative humidity, using toluene
vapor of greater then 99% purity.
Solubility Quantitation and Data Analysis:
The output from the strip chart recorder during a sorption measurement
is converted to polymer weight gain over time by calibration. The
equilibrium solubility (Cs) in grams of vapor sorbed per gram of dry
polymer is obtained by dividing the equilibrium weight gain (M‘Q by the
polymer at t —an, by the dry weight of the polymer. The equilibrium
weight gain of the polymer represents the maximum amount of vapor the
polymer will sorb at a given vapor concentration.
A simple approximation of the integral diffusion coefficient was made
using Equation:
- 0.04919 L2 / c (22)
Dt1/2 1/2
Where ttl/2 is the time required for the sorption curve M(t) versus t
to reach one-half the value of M,pand L is the thickness of the dry
76
polymer. The use of this expression to determine D is an approximation
for penetrant/polymer systems where the diffusion coefficient is
concentration independent, Henry's law solubility is followed and the
system follows Fickian sorption (Fujita, 1968).
The equilibrium solubility (Cs) for a given vapor concentration
corresponds to the concentration of vapor in the outer surface of a
polymer film from a permeation experiment. From the equilibrium
solubility (Cs) the solubility coefficient, representing an upper bound
for the solubility coefficient in a permeation experiment, is obtained.
In a permeation experiment there is a concentration gradient of
permeant in the film ranging from Cs at the penetrant interface to
essentially zero at the opposite side of the film. The solubility
coefficient is calculated by dividing Cs by the permeant concentration.
‘II
14.5.7. 'HJ
I“
Results and Discussion
Characteristics of Steady State Permeation of Toluene Through Test Films
The Quasi-isostatic permeation measurement method was employed to
determine the permeation rates and permeability coefficients for the
film-permeant systems investigated at the given test condition of
permeant vapor activities. This method also yields the integral
diffusion coefficient (D) by the lag time method (Barrer, 1939). The
results of the permeation measurements are summarized in Table 2. In
this discussion the permeant vapor activity (a) will be used as a
measure of the penetrant concentration in describing the concentration
dependence of the diffusion process. The permeant activity is defined
as the ratio of the measured test permeant partial pressure over the
equilibrium permeant saturation partial pressure at the temperature of
the test. A plot showing the variation of toluene equilibrium vapor
concentration with temperature can be found in Appendix A, along with
sample calculations and the equilibrium vapor pressure references.
Because the experiments were run at different temperatures,vapor
activity was used in an attempt to correct the effect of temperature on
the permeant driving force concentration and to allow a more accurate
comparison between data acquired at different temperatures. Vapor
activity (a) ranges from 0 to 1.0, where a value of (a) - 1.0 indicates
the vapor pressure is equivalent to the equilibrium vapor pressure of
the penetrant.
77
diHDHIJITI-a
78
Table 2
2armaa£12n_nsassrsa2nt_ns§nlts
a o b c d e f g
a F ppm P P 9 ”leg
Toluene - Oriented Polypropylene (OPP) 1.0 mil :
0.11 78.2 1611 0.24 0.524 2.9 1.03
0.26 81.0 4123 1.46 1.34 1.81 1.65
0.31 81.0 48*3 2.38 1.85 1.43 2.09
0.52 80.9 81:4 22.5 10.4 1.08 2.76
0.59 81.1 93*3 50.0 20.3 0.66 4.56
0.68 78.7 10015 109.0 38.6 0.52 6.13
0.71 81.1 112*5 724.0 244. 0.36 8.23
Toluene - High Barrier Saran (PVDC) 1.1 mil :
0.56 74.2 73*3 0.0016 0.00068 237.6 0.015
0.63 80.1 9613 0.119 0.045 40.5 0.089
0.77 82.5 12525 36.6 11.48 5.62 0.64
0.85 83.2 14135 39.0 11.06 4.97 0.73
Toluene - OPP/PVDC (OPP side towards permeant)
.27
.36
.52
.60
.62
.84
000000
2.0 mil total thickness:
78.4 4012 0.004 0.0035 105.2 0.14
79.0 54t2 0.035 0.023 35.5 0.34
79.7 7992 0.95 0.436 12.2 0.98
80.0 9223 43.1 17.2 2.66 4.5
80.0 94t2 33.6 13.1 2.22 5.4
81.9 13513 214.0 61.2 0.66 18.0
Toluene - OPP/PVDC (PVDC side towards permeant)
2.0 mil total thickness:
78.9 4032 0.0034 0.0030 88.3 0.14
80.0 9435 48.6 19.6 1.9 6.4
79.3 97*3 106.6 38.2 1.7 9.0
85.5 15015 334.0 94.6 0.44 27.0
All
results are averages of four replicate samples
(a) g - vapor activity - (p/po)
(b) F - temperature of test
(c) ppm - permeant concentrat gn in gitrogen gMg/ml)
(d) P - permeability rate x10 (g/m ' hr)
(e) P - permeability coefficient (g'structure/m 'day'a)
(f) 6- lag time (hour) 1
(g) Dlag - lag time diffusion coefficient x10+ 0 (cm2/sec)
79
Permeation Rate
For better illustration of the relationship between vapor activity and
permeation rate (P), the values of Table 2 are presented graphically in
Figure 4, where the permeation rate (P) is plotted as a function of
toluene vapor activity. The permeation rate (P) of these penetrant-
polymer systems varied exponentially with the permeant vapor activity.
Linear regression analysis of the plot of the log of the permeation rate
versus vapor activity gave correlation coefficients (r) ranging from
0.94 to 0.99 for the respective film-permeant combinations. For the
oriented polypropylene structure, the relationship between the
permeation rate (P) (g/m%»hr) and toluene vapor activity (a) is given
by:
P - 5.9x10'4 exp(ll.9-a) (43)
For the Saran structure the relationship between (P) and (a) is given
by:
P - 2.5x10'14 exp(38.2-a) (44)
For the Saran coated oriented polypropylene the relationship between (P)
and (a) is given by:
P - 2.8x10'7 exp(20.8’a) (45)
P - 2.8x10'7 exp(21.1-a) (46)
Equation 45 was tested with the OPP layer next to the toluene vapor and
Equation 46 was tested with the Saran layer next to the toluene
permeant.
Log Permeability Rate (9 / mzhr)
i-‘
O
I-‘
O
10
I
.5
I
U1
80
ll 1 L 1 l J 1 1. l l
0 .l .2 .3 .4 .5 .6 .7 .8 .9 1.0
Toluene Vapor Activity (p/po)
Figure 4. Log Permeability Rate versus Toluene Vapor
Activity.
0 OPP; IPVDC; AOPP/PVDC (OPP next to toluene vapor);
‘OPP/PVDC (PVDC next to Toluene vapor).
81
There was no statistical difference shown between the linear regression
line slopes for the OPP/PVDC laminate film structure, regardless of
which surface (i.e. OPP or PVDC) is placed next to the toluene permeant
at the 0‘- 0.05 level of significance. There is almost six orders of
magnitude difference between the pre-exponential factor for the
permeation rate regression lines for toluene through OPP/PVDC laminate
and the PVDC homopolymer. However the slopes of the regression lines of
log P vs (a) for the OPP/PVDC and PVDC are not statistically different
at the 0‘ - 0.05 level of significance. The similarity between the
behavior of the toluene permeation concentration dependency between
these two films suggests that the PVDC layer in the laminate controls
the toluene permeation behavior in this film. The difference in the
magnitude of the permeation rates can be explained in part by the
difference in the thickness of the PVDC layers. The specific molecular
structure and processing history of the two PVDC's may also vary and
contribute to the differences in observed barrier properties. The
thickness of the PVDC in the laminate coating of 0.2 to 0.3 mils and is
applied as a latex coating, as compared to 1.1 mils for the high barrier
PVDC (Mobil, 1986). The PVDC in the laminate is a latex coating and is
not expected to be as good a barrier material as the high barrier PVDC
in the homopolymer due to the differences in structure as well as
residual surfactants in the latex from processing (Brown, 1986).
82
Permeability Coefficient
The permeability coefficient (P), is the permeation rate normalized to
the permeant concentration or vapor activity. The permeability
coefficient varied exponentially with toluene vapor activity, but was
not linear like the permeation rate, as shown Figure 5 where the
permeabililty coefficients (g~structure/m2-day-vapor activity) for OPP,
PVDC and PVDC coated OPP are plotted as a function of vapor activity
(a). The log P vs (a) curves had different convexities and
concentration dependencies depending on the film structure and permeant.
The OPP-toluene, film-permeant combination, displayed a somewhat convex
shaped curve to the activity axis, while the film structures containing
the PVDC material were concave to the activity axis. Polypropylene,
although it had a higher overall permeabililty coefficient than the PVDC
and PVDC containing films, was less concentration dependent. For
example, between the experimental vapor activity range of 0.3 to 0.7,
the permeability coefficient (P) for toluene through OPP increased by
one and one-half orders of magnitude. For toluene permeation, through
PVDC-coated polypropylene, the permeability coefficient increased by
almost 4 orders of magnitude over the same range. At a toluene vapor
activity of 0.8, the predicted permeability coefficients for toluene
permeation through the OPP and PVDC-coated polypropylene are equivalent.
In his chapter Rogers (1964) described the variation of the permeability
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coefficient with organic permeant vapor activity as an exponential
function of vapor activity where the log of P becomes progressively non-
linear at higher vapor activities. In cases where the solubility of
the vapor in the polymer approximates Henry's law, log P varies linearly
with vapor activity (Rogers, 1964). At very low vapor activities, the
permeability coefficient can be reduced to a linear dependence on vapor
pressure (Cutler et al, 1951). A curve similar to that obtained for the
OPP-Toluene system, was observed for benzene in polyethylene by Rogers
et. al. (1960). Log P vs (a) curves similar to the concave curves
obtained for the PVDC-Toluene, film-permeant combination, were measured
by Zobel, (1982) for a PVDC/OPP/PVDC film and benzyl acetate as the
permeant. Based on these observations and comparisons to other published
data, there is some support for modeling these log P vs (a) curves using
polynomials. Equations for the four log P vs (a) curves found in Figure.
5 were fitted using a cubic polynomial curve fitting program. The
polynomial equations and least squares regression coefficients for the
fit of the line to the points are given in Table 3.
Diffusion Coefficient
The lag time diffusion coefficient (Dlag) is derived from Fick’s second
law of diffusion assuming a constant diffusion coefficient and solving
using the boundary conditions of the permeation experiment (page S93of
results) for the concentration in the polymer. Then using the mass
‘1
. . e 5:5235. i»
a
85
Table 3
Polynomial Equations
log10 Permeability Coefficient (P) versus Vapor Activity
OPP - Toluene 3 2
log P - l.316557(a) - 0.6758886(a) + 3.100905(a) - 0.6156436
experimental vapor activity range: 0.1 - 0.7
least squares polynomial fit (r): 0.9559
PVDC - Toluene 3 2
log P - l30.3141(a) - 306.1882(a) + 253.6787(a) - 72.15646
experimental vapor activity range: 0.55 - 0.85
least squares polynomial fit (r): 0.9438
OPP/PVDC - Toluene (OPP3next to vapor)2
log P - l.60863(a) - 5.775069(a) + 12.29352(a) - 5.412251
experimental vapor activity range: 0.27 - 0.84
least squares polynomial fit (r): 0.9454
OPP/PVDC ; Toluene (PVDC3next to vapor}
log P - l3.27l79(a) - 34.3645(a) + 32.64957(a) - 9.089249
experimental vapor activity range: 0.27 - 0.85
least squares polynomial fit (r): 0.9964
P - permeability coefficient (g-structure/mzoday.vapor activity)
a - vapor activity (p/po)
86
balance to describe the flow of permeant through the film the result
obtained from solving Fick's second law is applied. At steady state
conditions Equation 17 then describes the lag time for the flow of
permeant to reach steady state.
9 - L2/6D1ag
Equation 17 assumes that the diffusion coefficient in the expression is
independent of concentration, spatial coordinates in the polymer and
time. For the laminate structure the diffusion coefficient is more
appropriately referred to as an effective diffusion coefficient composed
of the different diffusion processes from each of the polymer layers.
A plot of the log of the diffusion coefficient versus toluene vapor
activity for the respective test films is presented in Figure 6. As
shown, the lag time diffusion coefficient follows a linear exponential
dependence on the vapor activity for the test film structures. Linear
regression analysis of the log of the lag time diffusion coefficient
(Dlag) versus vapor activity produced correlation coefficients ranging
from 0.94 to 0.98. The regression lines and data for the lag time
diffusion coefficients are given in Table 4. The inverse log of the y
intercept of the linear regression equation gives the theoretical
limiting diffusion coefficient which is the diffusion coefficient at
zero vapor concentration where there would be no sorbed permeant in the
polymer and thus no penetrant polymer interaction (Rogers, 1965). It
is necessary to extrapolate the curves outside of the experimental vapor
activity region to find the limiting diffusion coefficient.
2
Log Lag Time Diffusion Coefficient (cm /sec)
10'
10
10
10
10
-10
-11 A
-12
87
* a
I
I
I
/
l
/
I
Y
1 l Lg l J
0 .l .2 .3 .4 1.0
Toluene Vapor Activity (p/po)
Figure 6. Log Lag Time Diffusion Coefficient versus
Toluene Vapor Activity
0 OPP; 'PVDC; A OPP/PVDC (OPP next to vapor),-
AOPP/PVDC (PVDC next to vapor)
88
Table 4
Linear Regression Equations loglo D188 vs Vapor Activity
OPP - Toluene
log Dla - 1.39(a) - 10.15
experimgntal vapor activity range: 0.1 - 0.7
correlation coefficient (r): 0.98
PVDC - Toluene
log D - 5.93(a) - 14.96
experigéntal vapor activity range: 0.55 - 0.85
correlation coefficient (r): 0.94
OPP/PVDC - Toluene (OPP towards vapor)
log Dla - 3.90(a) - 11.87
experimgntal vapor activity range: 0.27 s 0.84
correlation coefficient (r): 0.979
OPP/PVDC - Toluene (PVDC towards vapor)
log D - 4.l2(a) - 11.87
experigéntal vapor activity range: 0.27 - 0.85
correlation coefficient (r): 0.985
D1 - lag time diffusion coefficient (cmz/sec)
a
a - vapor activity - (p/po)
89
The slopes of the regression lines for the diffusion of toluene through
the OPP/PVDC film with either the OPP or the PVDC layer next to the
toluene permeant are not significantly different from one another at the