Molecular migration of low sorbing organic liquids into polymeric geomembranes

Laboratory test results of sorption/desorption for tetrahydrofuran, tetralin, 1,4-dioxan, methyl acetate, ethyl acetate and butyl acetate into high density polyethylene, linear low density polyethylene, very low density polyethylene and polypropylene geomembranes at 25, 50 and 70 °C are presented. Partition coefficients are calculated from the measured increase in the mass of geomembranes immersed in the liquid of interest, from the initial value until the mass becomes constant. From the initial linear portions of the sorption curves, the diffusion coefficients of liquids into the geomembranes are calculated using the Fick equation. From a temperature dependence of sorption, diffusion and permeation coefficients, the Arrhenius parameters are calculated for each of these processes. Results of the preliminary findings reported here might be useful in the applications of geomembranes in containment facilities. © 1999 Society of Chemical Industry     

Migration of substituted aromatic solvents into polyurethane/polystyrene semi‐interpenetrating polymer network

The molecular transport of substituted aromatic solvents through polyurethane/polystyrene (PU/PS, 50/50) semi interpenetrating polymer network has been investigated at 20, 40, and 60°C. Sorption–desorption–resorption–redesorption (S‐D‐RS‐RD) experiments were performed to determine the true value of transport coefficients. Sorption results are obtained by a gravimetric method and diffusion coefficients have been calculated using Fick's equation for the linear data points of time dependent sorption/resorption curves. It was observed that most of the systems follow the Fickian mode of transport. The first order kinetic equation was used to estimate the kinetic rate constant of sorption. Activation parameters for different transport processes were evaluated and the results were used to discuss the polymer–solvent interactions. The concentration profiles at different depths along the thickness of membranes and at different time intervals were computed using Fick's equation under appropriate boundary conditions. The rate of evaporation of liquids has been calculated for desorption and redesorption processes, and these results depend on the volatility of aromatic solvents. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 378–390, 2007     

Molecular transport of esters,aldehydes, aromatic liquids,and a ketone into fluoroelastomer membrane at 30, 40, and 50°C

Molecular transport of esters, aldehydes, substituted aromatic liquids, and a ketone through a fluoroelastomer (FC‐2120) membrane sample was studied at 30, 40, and 50°C. Sorption results were obtained by using a gravimetric method and concentration‐independent diffusion coefficients were calculated using Fick's diffusion equation. Permeability coefficients were calculated from sorption and diffusion data. Concentration profiles of the liquid penetrants were calculated by solving the Fick's equation under appropriate initial and boundary conditions and these plots are displayed to show the variations in liquid concentrations with reference to the nature of liquids chosen, membrane thickness, as well as the time of polymer immersion in the liquids. Arrhenius activation parameters were also estimated from a temperature dependence of diffusion and sorption coefficients. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 840–847, 2003     

Sorption/desorption and diffusion kinetics of ketones and nitriles into fluoropolymer membranes

Analysis of sorption/desorption and diffusion kinetics of ketones and nitriles at 25, 44, and 60°C into three Du Pont's VITON fluoropolymer membranes loaded with different amounts of carbon black has been undertaken by use of a sorption/desorption technique. The transport results are affected by the percent loading of carbon blacks. Diffusion coefficients have been calculated from Fick's equation. These results show a decrease with increasing amount of carbon black. Experimental results have been analyzed by considering swelling of the membranes. Sorption/desorption results have been analyzed from a calculation of the concentration profiles, which are obtained from the analytical solution of Fick's equation. These results have been compared with a numerical solution based on the finite difference method. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 635–647, 1997     

Sorption,diffusion, and swelling characteristics of sodium alginate and its blend membranes with poly(vinyl alcohol) in water–acetic acid mixtures

Sorption, diffusion, and swelling characteristics of sodium alginate and its blend membranes with poly(vinyl alcohol) were investigated for water–acetic acid mixtures by using a gravimetric method at 30, 40, and 50°C. The membranes were characterized by X‐ray diffraction and Fourier transform infrared techniques. Concentration‐independent diffusion coefficients were obtained by applying Fick's relationship before completion of equilibrium sorption. Permeation coefficients were calculated from sorption and diffusion coefficients. Concentration profiles of liquids were computed considering the sheet geometry for the membrane by solving Fick's equation under suitable boundary conditions. Arrhenius activation parameters were computed for the transport processes. Experimental results and calculated quantities were discussed to understand membrane–solvent interactions. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 1139–1150, 2004     

A study on molecular transport of organic esters and aromatics into viton fluoropolymers

Molecular transport of organic liquids into Viton fluoropolymers has been investigated by a sorption—desorption gravimetric method. Diffusion coefficients have been calculated from Fick's equation. The sorption—desorption results have been used to calculate the concentration profiles by solving Fick's diffusion equation under suitable boundary conditions. A numerical method based on the finite difference technique was also used to calculate the concentration profiles of liquids as a function of sorption time and thickness of the Viton fluoropolymers. The dependence of sorption, desorption, diffusion, and permeation properties of the liquids on temperature showed a significant effect. The Arrhenius activation parameters have been estimated for diffusion, permeation, and sorption processes. The experimental and calculated results are discussed to study the type and nature of interactions between Viton fluoropolymers and the solvent molecules. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 717–723, 1997     

Molecular transport of n‐alkanes through diol chain‐extended polyurethane membranes

Molecular transport of n‐alkanes was investigated by calculating sorption, diffusion, and permeation of liquids through the diol chain‐extended polyurethane (PU) membranes in the temperature interval 25–60°C. Sorption experiments were performed gravimetrically. Diffusion coefficients were calculated from Fick's equation. These results showed a dependency on the nature and size of interacting n‐alkane molecules as well as morphology of the chain‐extended PUs. Transport kinetics followed an anomalous trend. Using the temperature‐dependent transport parameters, activation energies were calculated for diffusion and permeation processes using an Arrhenius equation. The van't Hoff relationship was used to obtain enthalpy and entropy of sorption. Concentration profiles of liquids through PU membranes were computed using Fick's equation, solved under appropriate initial and boundary conditions. A correlation was attempted between transport properties of liquids and physicomechanical properties of PU membranes. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 874–882, 2005     

Experimental and simulation studies on molecular transport of substituted monocyclic aromatic liquids into fluoropolymer sheet membranes: Liquid structure–diffusion, –sorption,and –permeation relationships

The present study reports an investigation on the molecular transport of 10 monocyclic aromatic liquids (benzene, chlorobenzene, 1,2‐dichlorobenzene, bromobenzene, toluene, p‐xylene, trimethylbenzene, ethylbenzene, methoxybenzene, and ethoxybenzene) at 40 and 50°C through sheet polymeric membranes (FLS‐2650) using a sorption gravimetric technique. Diffusion and permeation coefficients of these liquids were calculated from the sorption data using Fick's diffusion equation. Sorption results were analyzed typically in the case of benzene and chlorobenzene to compute the concentration profiles at different depths along the thickness direction of the sheet membranes and at different time intervals by solving the Fick's equation under appropriate boundary conditions, based on the numerical simulation method developed in “C” language using a finite‐difference method. Transport results were analyzed to establish the relationships between the penetrating liquid structures with diffusion, permeation, and sorption data. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 991–996, 2004     

Sorption,diffusion, and permeation of esters,aldehydes, ketones,and aromatic liquids into tetrafluoroethylene/propylene at 30, 40, and 50°c

The coefficients of sorption, diffusion, and permeation for five organic esters, three aldehydes, one cyclic ketone, and three substituted aromatic liquids have been calculated for tetrafluoroethylene/propylene copolymer membranes at 30, 40, and 50°C with the sorption–gravimetric technique. With the sorption data, the concentration‐independent diffusion coefficients have been calculated from Fick's diffusion equation. Analytical solutions of Fick's equation under suitable boundary conditions have been obtained so that the liquid concentration profiles in the polymeric membranes at different times and different depths of liquid penetration could be computed. Because of the linearly increasing trend of the diffusion coefficients with temperature, efforts have been made to estimate Arrhenius parameters. Experimental values and the computed quantities have been used to determine the membrane–solvent interactions and to propose suitable applications for the membranes under investigation in various situations. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3201–3209, 2003     

Sorption and migration of aliphatic organic esters into VITON® fluoroelastomer membranes

Sorption and migration of six aliphatic esters into four VITON^® fluoroelastomers were studied by a gravimetric sorption method in the temperature interval of 30–60°C. Fick's equation was used to obtain diffusion coefficients. The dependence of fluorine contents and the polymer morphology on the sorption and diffusion characteristics of esters was investigated. The permeability coefficients were obtained from the sorption and diffusion data. Fick's equation was solved to compute the concentration profiles of liquids at various locations within the membrane materials using initial and boundary conditions. These profiles were compared with those obtained from the numerical method based on finite difference technique. Activation parameters for diffusion and sorption were calculated using the Arrhenius relationship. These results were discussed in terms of molecular size and shapes of the esters. For higher esters, namely, n- and iso-amyl acetates, a concentration dependency of the diffusion coefficient was investigated. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1223–1235, 1997     

Sorption and Diffusion of Organic Liquids into Fluoroelastomer Membranes

Abstract

Sorption and diffusion of organic liquids into fluoropolymer (FC-2179) membranes have been investigated from 30 to 60°C using a gravimetric method. Diffusion coefficients, percent mass uptake, and apparent activation energies for the transport processes have been estimated. Diffusion coefficients of the liquids into the membrane have been computed from Fick's relation. A Flory–Huggins-type interaction parameter was obtained from the solubility parameter concept. Furthermore, the activation parameter values and heat of sorption data have been studied in terms of heat of mixing. The values of diffusion coefficients did not show any considerable dependence on solvent concentration. However, solvent transport as analyzed from an empirical equation was found to be of the anomalous type. Molecular transport also showed a dependence on the chemical nature of the liquids. The concentration profiles of liquids have been calculated at different penetration depths of the membrane at different time intervals by solving Fick's differential equation under suitable initial and boundary conditions. A numerical method based on the finite difference technique was also used to predict the concentration profiles of liquids, and these are compared with the profiles computed from an analytical solution of Fick's equation.     

Sorption/diffusion of aqueous mixtures of 1,4‐dioxane/tetrahydrofuran through blend membranes of poly(vinyl alcohol) and sodium alginate: Their compatibility and pervaporation separation studies

Blend membranes of poly(vinyl alcohol) (PVA) and sodium alginate (NaAlg) were prepared by solution casting and crosslinked with glutaraldehyde (GA). Polymer blend compatibility was studied in water by measuring solution viscosity at 30°C. From the viscosity data, interaction parameters were determined to find the blend compatibility. Thickness of the membranes ranged between 35 and 40 μm. Circular disc‐shaped samples were cut from the thin membranes to perform gravimetric sorption experiments in water + 1,4‐dioxane and water + tetrahydrofuran mixtures at 30°C. Diffusion coefficients were calculated using Fick's equation. Concentration profiles of liquids were computed by solving Fick's equation under suitable boundary conditions. Diffusion coefficients show a dependence on the composition of the blends as well as composition of binary mixtures. A correlation was attempted between concentration profiles and diffusion coefficients of the transporting liquids. Degree of swelling and sorption coefficients were calculated from the gravimetric sorption data. Sorption kinetics was studied using an empirical equation to understand the nature of sorption–diffusion anomalies. Membrane selectivity for water + 1,4‐dioxane and water + tetrahydrofuran mixtures were calculated from the pervaporation experiments. A correlation between sorption and membrane selectivity was attempted. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 178–188, 2005     

Sorption,desorption, resorption,redesorption, and diffusion of haloalkanes into polymeric blend of ethylene–propylene random copolymer and isotactic polypropylene

Molecular transport of haloalkanes into sheets of a polymeric blend of an ethylene–propylene random copolymer and isotactic polypropylene has been studied by a sorption gravimetric technique in the temperature interval of 25–70°C. For all liquids, equilibrium sorption, desorption, resorption, redesorption, and degree of penetrant overshoot have been influenced by the nature of the liquid and the temperature. Diffusion coefficients were calculated from the sorption–desorption kinetic curves using Fick's mathematical relations. The values of diffusion coefficients followed the Arrhenius-type behavior. The temperature-dependent sorption data were analyzed using the van't Hoff relation. The activation parameters for diffusion and heat of sorption data were discussed in terms of the molecular interactions between liquids and the polymer chain segments. The experimental and calculated results are discussed on the basis of the chemical nature of liquids. © 1995 John Wiley & Sons, Inc.     

Effect of carbon black loading on fluoroelastomer–solvent interactions

An analysis of the molecular transport of organic liquids into fluoroelastomer membranes containing varying amounts of carbon black has been undertaken by the sorption–desorption gravimetric method. The variation in carbon black loading and temperature showed a significant effect on their transport characteristics. Diffusion coefficients were calculated from Fick's equation. Experimental sorption–desorption results were analyzed in terms of concentration profiles obtained from a solution of Fick's equation as well as by a numerical method based on the finite difference technique. Arrhenius activation parameters were estimated from the temperature-dependent diffusion and permeation data. The results of this study are discussed in terms of polymer–solvent interactions. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 68:815–825, 1998     

Sorption equilibria and diffusion of toluene,methanol, and cyclohexane in/through elastomers

Molecular transport of toluene, methanol, and cyclohexane and their mixtures in Chemraz 505 elastomer has been investigated using gravimetric techniques for short and long time exposure in these solvents. The sorption–desorption results have been used to calculate the diffusion coefficients by solving Fick's equation under appropriate boundary conditions. The dependence of sorption, desorption, diffusion, and permeation on temperature and composition changes was also studied. The results are discussed in terms of possible interactions between Chemraz 505 polymer and the solvent molecules. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43449.     

Free‐volume microprobe study of iodine diffusion in polymers

The effect of iodine sorption on the free‐volume of three polymers, namely, acrylonitrile–butadiene–styrene, poly(ethylene terephthalate) and polycarbonate have been investigated by the positron annihilation lifetime technique. Diffusion coefficients have been evaluated from the sorption curves using Crank's solution for Fick's second law of diffusion. The positron results are explained in terms of iodine filling the free‐volume holes, swelling and conformational changes. It has also been found that the diffusion process in acrylonitrile–butadiene–styrene and poly(ethylene terephthalate) deviates from Fick's law of diffusion whereas in polycarbonate, the diffusion process obeys Fick's law. Further, for polymers in which diffusion deviates from Fick's law, the sorption process has been separated into diffusion‐controlled (Fickian) and relaxation‐controlled (non‐Fickian) parts using the dual‐mode sorption model. Interestingly, the present results show that the polymers which deviate from Fickian diffusion also deviate from Fujita's free‐volume theory of diffusion and vice versa. The positron results also indicate that sorbed iodine in the polymer acts as an inhibitor of ortho‐positronium. © 2001 Society of Chemical Industry     

Sorption kinetics and diffusion of alkanes into tetrafluoroethylene/propylene copolymer membranes

Sorption kinetics and diffusion of hexane, heptane, octane, nonane, decane, cyclohexane, and 2,2,4-trimethylpentane through tetrafluoroethylene/propylene copolymer membranes were studied using the gravimetric sorption method at 30, 45, and 60°C. Coefficients of diffusion were calculated from Fick's equation. From these data, the permeability coefficients were obtained. Analytical solutions of Fick's relations were used to estimate the liquid concentration profiles into the polymeric membranes at different times. The profiles of liquid concentrations were also simulated for the polymer–solvent systems using the numerical simulation method. Activation parameters for diffusion and sorption were evaluated and these results are discussed in terms of the molecular sizes and geometries of liquids (i.e., shape) as well as temperature. The diffusion coefficients follow a systematic decrease with increasing size of the penetrant molecules. The activation energies i.e., E_D values, increase with increasing size of n-alkanes. © 1996 John Wiley & Sons, Inc.     

Water sorption of poly(methyl methacrylate): 2. Effects of crosslinks

Glassy crosslinked networks were made by copolymerization of methyl methacrylate both with ethylene glycol dimethacrylate and with triethylene glycol dimethacrylate, using a redox initiator. Residual monomer was largely or wholly removed by extraction with water, by heating at 100°C, or by γ-irradiation. Water sorption conformed approximately to Fick's laws but with a retarded swelling component which increased with crosslink density. Approximate values were obtained for apparent diffusion coefficients both in sorption and desorption. The pattern of results was similar for both dimethacrylate systems. Values of diffusion coefficients were little influenced by crosslink density up to a dimethacrylate feed of 50 wt%. The saturation value for water uptake increased with increasing feed of dimethacrylate to more than twice the value for the linear polymer, i.e. poly(methyl methacrylate).     

Sorption and diffusion of hydrocarbon vapors in glassy polymers

Sorption isotherms in the region of low relative pressures have been determined at several temperatures for methane, propane, and chlorodifluoromethane in polystyrene and for propane in bisphenol-A polycarbonate and poly(vinylacetate). The results are well represented by the isotherm equation of Dual Sorption Theory as applied to glassy polymers. The temperature dependence of the isotherm parameters is examined and discussed; the Langmuir component to sorption decreases as the glass transition temperature is approached and measurements with poly(vinylacetate) confirm that this component is absent above the transition. Average diffusion coefficients were obtained from sorption (desorption) rate curves at constant pressure for propane in polystyrene and polycarbonate and a procedure developed for their analysis to yield the diffusion coefficients of the two sorbed species of penetrant. For the polycarbonate there is evidence of mobility in that fraction of the penetrant: population exhibiting Langmuir-type sorption.     

A study of sorption/desorption and diffusion of substituted aromatic probe molecules into semi interpenetrating polymer network of polyurethane/polymethyl methacrylate

The sorption-desorption-resorption-redesorption experiments have been conducted to evaluate the transport behaviour of polyethylene glycol (PEG) based polyurethane/polymethyl methacrylate (PU/PMMA, 50/50) semi interpenetrating polymer network (SIPN) with aromatic probe molecules. Molecular migration depends on the nature of the organic solvent, membrane-solvent interaction, temperature, solubility parameter, molecular volume and free volume available within the polymer matrix. The transport parameters like sorption (S), diffusion (D) and permeation (P) coefficients have been calculated for IPN-aromatic probe molecule systems. Sorption and diffusion results measured at different temperatures viz. 20, 40 and 60 °C are found to follow Fickian mechanism. The liquid concentration profiles in the membranes during sorption and resorption processes have been simulated by solving Fick's diffusion equations and by using numerical method. Equilibrium swelling results have been used to measure the molecular mass between cross links, degree of cross linking and cross link density using Flory-Rehner theory. It is found that the mass uptake values decreased with increase in cross link density during polymer-solvent interactions. The estimated Arrhenius activation energy for diffusion (E_D) and permeation (E_P) are indicative of nature of liquid and their interaction with membrane. Thermodynamic parameters like change in entropy (ΔS) and enthalpy (ΔH) have been calculated using van't Hoffs equation. The rate of evaporation of liquids have been calculated for desorption and redesorption runs, and these results depend on volatility of solvents.