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,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     

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     

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.     

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/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     

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,diffusion, and swelling characteristics of geomembranes in the presence of halo‐organic liquids

Sorption/desorption results of halogen‐containing liquids into high‐density polyethylene, linear low‐density polyethylene, very low‐density polyethylene, and polypropylene geomembranes are presented at 25, 50, and 70°C. Sorption results are obtained by a gravimetric method, and diffusion coefficients have been calculated by using Fick's equation from the initial linear portions of the sorption/desorption curves. Swelling of the geomembranes was studied from a measurement of the increase in volume, thickness, and diameter. From a temperature dependence of sorption and diffusion coefficients, the Arrhenius parameters have been calculated. Liquid concentration profiles have been computed using Fick's equation for the appropriate initial and boundary conditions. The results of this study may have relevance in selecting the suitable geomembrane for a specific application in hazardous waste chemical ponds and other similar situations.     

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 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     

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     

Studies on molecular transport of n‐alkanes through poly(tetrafluoroethylene‐co‐propylene) elastomeric membrane

Molecular transport of a series of n‐alkanes through commercial TFE elastomer (FA 150L) has been studied in the temperature range 30–50 °C using sorption‐gravimetric method. The Fickian diffusion equation was used to calculate the diffusion coefficients, which were dependent on the size of the alkanes and temperature. The diffusion coefficients at 30°C varied from 4.53 × 10^?8 cm²/s (n‐heptane) to 0.18 × 10^?8 cm²/s (n‐hexadecane). The liquid concentration profiles have also been computed using analytical solution of Fick's equation with the appropriate initial and boundary conditions and these were presented as a function of penetration depth of molecular migration and time of immersion. These results have been discussed in terms of molecular size of alkanes as well as temperature. In all the liquid penetrants, the transport phenomenon was found to follow the anomalous behavior. From the temperature dependence of diffusion and permeation coefficients, the Arrhenius activation parameters have been estimated. These parameters do not exhibit any systematic variation with the size of the penetrants. The resulting low diffusion coefficients, contribute to the superior barrier performance of the membrane, is due, in part, to the high glass transition temperature of Aflas? TFE elastomer. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2228–2235, 2006     

Molecular transport of n‐alkanes into PU/PBMA interpenetrating polymer network systems

The methylene diisocyanate (MDI) and toluene diisocyanate (TDI) based polyurethane/polybutyl methacrylate (PU/PBMA‐50/50) interpenetrating polymer network (IPN) membranes have been prepared. The molecular migration of n‐alkane penetrants such as hexane, heptane, octane, nonane, and decane through PU/PBMA (50/50) membranes has been studied at 25, 40, and 60°C using a weight gain method. From the sorption results, diffusion (D) and permeation (P) coefficients of n‐alkane penetrants have been calculated. Molecular migration depends on membrane‐solvent interactions, size of the penetrants, temperature, and availability of free volume within the membrane matrix. Attempts have been made to estimate the parameters of an empirical equation and these data suggest that molecular transport follows Fickian mode. From a study of temperature dependence of transport parameters, activation energy for diffusion (E_D) and permeation (E_P) have been estimated from the Arrhenius relation. Furthermore, sorption results have been interpreted in terms of enthalpy (ΔH) and entropy (ΔS) of sorption. The liquid concentration profiles have been computed using Fick's equation with appropriate initial and boundary conditions. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 739–746, 2003     

Synthesis and characterization of polyacrylamide‐grafted sodium alginate copolymeric membranes and their use in pervaporation separation of water and tetrahydrofuran mixtures

Polyacrylamide‐grafted sodium alginate (PAAm‐g‐Na‐Alg) copolymeric membranes have been prepared, characterized, and used in the pervaporation separation of 10–80 mass % water‐containing tetrahydrofuran mixtures. Totally three membranes were prepared: (1) neat Na‐Alg with 10 mass % of polyethylene glycol (PEG) and 5 mass % of polyvinyl alcohol (PVA), (2) 46 % grafted PAAm‐g‐Na‐Alg membrane containing 10 mass % of PEG and 5 mass % of PVA, and (3) 93 % grafted PAAm‐g‐Na‐Alg membrane containing 10 mass % of PEG and 5 mass % of PVA. Using the transport data, important parameters like permeation flux, selectivity, pervaporation separation index, swelling index, and diffusion coefficient have been calculated at 30°C. Diffusion coefficients were also calculated from sorption gravimetric data of water–tetrahydrofuran mixtures using Fick's equation. Arrhenius activation parameters for the transport processes were calculated for 10 mass % of water in the feed mixture using flux and diffusion data obtained at 30, 35, and 40°C. The separation selectivity of the membranes ranged between 216 and 591. The highest permeation flux of 0.677 kg/m² h was observed for 93% grafted membrane at 80 mass % of water in the feed mixture. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 272–281, 2002     

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 and diffusion of n-alkanes into bromobutyl rubber membranes

Sorption and diffusion of n-alkanes into bromobutyl rubber membranes were investigated in the temperature interval 25–60°C by a sorption gravimetric method. The Fickian diffusion equation was used to calculate the diffusion coefficients, which were dependent on the size of the alkanes, their interactions with the chain segments of the polymer and temperature. The diffusion coefficients varied from 0.34×10^?7 cm²/s (n-hexadecane) to 9.94×10^?7 cm²/s (n-hexane). The activation energy for diffusion varied from 14kJ/mol (n-hexane) heptane to 2.0kJ/mol for n-hexadecane. The sorption/swelling results are discussed in terms of first and second order kinetic equations. The molar mass between chain-entanglement-crosslinks was estimated from swelling data. The experimental and calculated results showed a systematic dependence on the increasing size of the alkanes. None of the solvents showed any degradative effects on the polymer.     

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     

Syntheses and characterization of blend membranes of sodium alginate and poly(vinyl alcohol) for the pervaporation separation of water + isopropanol mixtures

The blend membranes of sodium alginate and poly(vinyl alcohol) have been prepared by physical mixing in different ratios (75, 50, and 25%) of sodium alginate with poly(vinyl alcohol). The membranes were crosslinked with glutaraldehyde and used in the pervaporation separation of water + isopropanol mixtures at 30°C. The crosslinking reaction was confirmed by Fourier transform infrared spectra. Permeation flux increased with an increase in mass % of water in the feed mixture as well as with an increase in the amount of poly(vinyl alcohol) in the blend, but separation selectivity decreased. Diffusion coefficients of water + isopropanol mixtures have been calculated using the Fick's equation from the sorption data. Arrhenius activation parameters were calculated for 10 mass % of water in the feed mixture using the values of flux and diffusion coefficients obtained at 30, 40, and 50°C. The diffusion and pervaporation results have been explained on the basis of solution‐diffusion principles. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 3642–3651, 2002     

Water Diffusivity and Drying Kinetics of Air Drying of Figs

The aim of this study is to evaluate experimentally the effective diffusion coefficient and the drying kinetics of whole unpeeled figs (Ficus carica L. var. tsapela) in terms of drying conditions. Estimation of the effective diffusion coefficient was carried out employing Fick's law for unsteady diffusion, which was solved analytically and numerically. In both methods, shrinkage effect was considered. The results from the two methods were compared and presented together with the limited results from the literature. The estimated effective diffusion coefficient values by both methods were fitted to a modified Arrhenius equation. Finally, a model predicting drying kinetics was developed. The model's coefficients were associated to the experimental conditions.