A model to predict the solubility and permeability of gaseous penetrant in the glassy polymeric membrane at high pressure

In this work, the transport properties of gaseous penetrant through several dense glassy polymeric membranes are studied. The nonequilibrium lattice fluid (NELF) in conjunction with the modified Fick's law and dual mode sorption model was used to simulate the gas transport in glassy polymeric membranes. The approach is based on the sorption, diffusion, in which solubility is calculated based on the NELF model, and diffusion coefficient is obtained from the product thermodynamic coefficient and molecular mobility. The governing equation is solved by the finite element method using COMSOL multi-physics software. The developed model for gas permeability of glassy polymeric membrane can be applied in a wide range of pressure and temperature. The comparison of the calculated permeability and solubility of gasses with the experimental data represented the ability of the developed model. Increasing feed gas temperature increases the gas permeability, while this variation leads to lower gas solubility in the glassy polymeric membranes. The effect of feed temperature and pressure on permeability and solubility is investigated, and the experimental data from literature are described by the developed model. A good prediction of the experimental data can be observed over the considered condition.     

Effects of chain stiffness and penetrant size on penetrant diffusion in simple polymers: deduced relations from simulation and PRISM theory

Molecular dynamics simulations in the NVT ensemble were performed for a repulsive system of bead-spring polymer chains with angle constraints. The diffusion coefficients of spherical penetrants were measured for different size penetrants as the angle constraints were varied. The scaling of the diffusion coefficient with penetrant size varies as a function of chain stiffness from liquid-like behavior to polymeric behavior. Free volume distributions were calculated from both simulation and PRISM theory. It is found that free volume distributions and mean void size are constant with chain stiffness although the diffusion coefficient changes by a factor of two. This suggests that while free volume is necessary for diffusion to occur, binary collisions and chain relaxation also play a role in determining penetrant diffusion. The relative contributions of these factors to the diffusion coefficient may change as a function of chain stiffness.     

Diffusion and Sorption of Organic Liquids Through Polymer Membranes. IX. Bromobutyl Rubber,Chlorosulfonated Polyethylene,and Epichlorohydrin Versus Substituted Monocyclic Aromatic Liquids

Sorption and diffusion of four monocyclic aromatic liquids—namely, chlorobenzene, o-dichlorobenzene, bromobenzene, and nitrobenzene into bromobutyl rubber, chlorosulfonated polyethylene, and epichlorohydrin—have been investigated in the temperature interval of 25–60°C by using a gravimetric technique. The transport results have been analyzed by using the Fickian model of diffusion. The dependence of transport coefficients on the size and shape of the penetrant molecules has been discussed. Transport coefficients have not shown any systematic variation with the penetrant size, but the results are greatly influenced by the polymer-solvent interactions. The Arrhenius activation parameters have been estimated from a temperature dependence of sorption, diffusion, and permeation coefficients. The first-order kinetic rate constants have been obtained from the time-dependent sorption data. Enthalpy and entropy of sorption for the polymer-solvent systems have been studied. The molar mass between network crosslinks was calculated from the Flory-Rehner theory. Computed parameters and experimental results are used to discuss the transport mechanism in terms of the type and nature of the polymer membranes and solvent molecules. None of the polymer membranes studied have shown any degradative reactions and significant swelling in the presence of the chosen solvents. The present results would have applications in areas such as those including the studies on barrier properties, separation science, and chemical pond lining, etc.     

A Model for the Diffusion of Moisture in Adhesive Joints. Part I: Equations Governing Diffusion

A methodology is proposed to relate the diffusion coefficient of small penetrant molecules in polymers to temperature, strain, and penetrant concentration. The approach used is based on well-known free volume theories. It is assumed that the transport kinetics is governed by the constant redistribution of the free volume, caused by the segmental motions of the polymeric chains. An expression for the diffusion coefficient is inferred from the temperature, strain, and penetrant concentration dependence of the free volume. The stress dependence of solubility is predicted from the Hildebrand theory. It is shown that the resulting constitutive equations exhibit many features desirable for joint durability studies. Finally, a non-Fickian driving force arising from differential swelling is included in the governing equations.     

High gas permeability in open-structure membranes

For most polymeric membranes, the gas permeability coefficient (P) is often interpreted as the product of diffusivity (D) and solubility (S) of a penetrant gas in the polymer (P=D S). The basic assumption is that molecular diffusion is primarily responsible for mass transport in the membrane permeation process. However, for some open structure membranes, such as poly(1-trimethylsilyl-1-propyne) [PTMSP] or poly(dimethylsiloxane) [PDMS], the high permeabilities of some gases yield much higher diffusivities when calculated from the above relationship (P=D S) than when calculated by using the direct kinetic measurement of diffusivity. It is hypothesized that this discrepancy is due to the convective transport of gas molecules through such open structured polymers. In most cases, the convective contribution to mass transport through membranes is negligible. However, for polymer membranes with high free volume, such as PTMSP, whose free volume fraction is 20 to 25%, the convective term may dominate the permeation flux. In this study, a non-equilibrium thermodynamic formalism is employed to properly treat the diffusion term and convective term that constitute the Nernst-Planck equation. The current analysis indicates that the total permeation flux, which consists of a diffusion term and a convective term, agrees well with the experimental data for several permeation systems: pure components propane and n-butane/PTMSP, pure gas hydrogen/PTMSP, and mixed gas hydrogen/PTMSP. Also, the permeation systems of a nonporous rubbery membrane, PDMS, and eight organophosphorus compounds were included in the study. It is recommended that the proposed model be validated by using other polymers with high free volumes and high permeabilities of gases and vapors, such as poly(1-trimethylgermyl-1-propyne) [PTMGeP] and poly(4-methyl-2-pentyne) [PMP]. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

Numerical simulation of anomalous penetrant diffusion in polymers

This work introduces a new numerical algorithm that can be used to analyze complex problems of penetrant transport. Penetrant transport in polymers often deviates from the predictions of Fick's law because of the coupling between penetrant diffusion and the polymer mechanical behavior. This phenomenon is particularly important in glassy polymers. This leads to a model consisting of two coupled differential equations for penetrant diffusion and polymer stress relaxation, respectively. If the polymer relaxation is the rate-limiting step, both the concentration and stress profiles are very steep. A new algorithm based on a finite difference method is proposed to solve the model equations. It features the development of a tridiagonal iterative method to solve the nonlinear finite difference equations obtained from the finite difference approximation of the differential equations. This method was found to be efficient and accurate. Numerical simulation of penetrant diffusion in glassy polymers was performed, showing that the integral sorption Deborah number is a major parameter affecting the transition from Fickian to anomalous diffusion behavior. © 1993 John Wiley & Sons, Inc.     

POSSIBILITY OF CONCENTRATION POLARIZATION OCCURRING INSIDE THE MEMBRANE DURING STEADY STATE PERVAPORATION

Mathematical equations are derived for describing the pervaporation transport of pure penetrant through polymeric membranes by assuming the chemical potential gradient as the driving force for the flow of penetrant. An imaginary phase (liquid or vapor) is assumed to be present and is in thermodynamic equilibrium with the membrane phase for deriving these equations. The mathematical equations obtained are similar to those derived by Okada and Matsuura (1991) using the pore-flow model. The possibility of concentration polarization occurring inside the membrane is predicted based on the analysis of binary mixture pervaporation. Experimental profiles of binary penetrant concentration in the membrane are established and these profiles substantiate the prediction of concentration polarization occurring inside the membrane. Pervaporation and sorption data from liquid and vapor phase at 25° C are reported for the acetic acid-water-polyamide system.     

Effects of sorption modes on the transport and physical properties of nylon 6

The presence of low molecular weight molecules in a polymeric matrix often has a marked effect on material properties. Knowledge of specific penetrant distributions and component interactions is important for an elucidation of structure-property relationships, plasticization phenomena, and any modification of structure induced by the presence of penetrants. The sorption-mode characteristics of water, methanol, and ethanol in Nylon 6 films have been investigated by the application of the differential sorption method. The sorption and diffusion behavior were interpreted in terms of clustering theory with suitable account being made for penetrant molecular size and hydrogen-bonding capability. The examination of transport and mechanical properties of these films indicates a pronounced dependence of those properties on the concentration of penetrants. The effect of penetrant cluster formation at characteristic concentrations of sorbed penetrant is to decrease the concentration dependence of both diffusion and mechanical relaxation processes in the case of alcohols. The onset of water clustering apparently only affects the mechanical relaxation process. The samples were further characterized by DSC, X-ray diffraction and density measurements to detect any significant changes in the structure of Nylon 6 induced by the penetrant conditioning.     

THE EFFECT OF TEMPERATURE TREATMENT ON PENETRANT TRANSPORT IN COAL

The macromolecular structure of coals thermally treated at 35^°C, 100^°C and 150^°C was investigated by dynamic penetrant transport in thin coal sections. The effects of temperature, carbon content in coal, and penetrant type on the transport mechanism were investigated. Dynamic swelling studies showed that penetrant transport into coal is a function of the average molecular weight between crosslinks, M_c. The penetrant transport mechanism at low activity is Fickian diffusion. The transport mechanism deviates from Fickian diffusion to anomalous transport, when the carbon content in coal and penetrant activity increase. Variations of the diffusion coefficients and relaxation constants were determined using a diffusion/relaxation coupled model.     

The formation of nodular structures in the top layer of ultrafiltration membranes

The formation of nodular structures in the top layer of ultrafiltration membranes is considered. A critical review of mechanisms described in the literature is given. Flat-sheet poly(ether sulfone) membranes and hollow-fiber poly(ether sulfone)/polyvinylpyrrolidone membranes were made by coagulation of a polymer solution in a nonsolvent medium under different circumstances. From these experiments, a number of empirical rules are found to describe the resulting morphology of the top layer. A new mechanism for the formation of a nodular structure is proposed. It is based on the small diffusion coefficient of the polymer molecules compared to the diffusion coefficient of solvent and nonsolvent combined with a high degree of entanglement of the polymer network. For unstable compositions, phase separation will proceed by growth in amplitude of concentration fluctuations. The rapid diffusional exchange of solvent for nonsolvent in the top layer leads to vitrification of the maxima of the concentration fluctuations that form the nodules. Complete disentanglement of the polymer chains between the nodules is not reached, which explains the small pores and the low porosity of ultrafiltration membranes. © 1994 John Wiley & Sons, Inc.     

A “free volume” model of permeation of gas and liquid mixtures through polymeric membranes

A recent “free volume” model of gas permeation (3) has been extended to the transport of gas mixtures through nonporous polymeric membranes. The present model assumes that the rates of transport of the components of a mixture depend on the free volume of the gas-polymer system, and that the effect of these components on the free volume is additive. The latter assumption limits the model to relatively dilute systems, with total penetrant concentrations of perhaps less than 0·2 volume-fraction. The prediction of permeation fluxes and permeability coefficients requires the knowledge of specified free-volume parameters which can be determined from measurements of diffusion coefficients and viscosities of the pure penetrant-polymer systems. When the systems are sufficiently dilute to obey Henry's law, the permeability coefficients for the components of a gas mixture can be predicted using only permeability measurements with the pure components. The extended free-volume model can be applied also to the permeation of liquid mixtures. The theoretical predictions are compared with the results of several experimental studies, and the potential usefulness and limitations of the model are discussed.     

Effects of heat treatment on the properties of heterogeneous cation permeable membranes from blends of poly(ether sulfone)/sulfonated poly(phenylene sulfide) and phenolphthalein poly(ether ether ketone)/sulfonated poly(phenylene sulfide)

The effects of heat treatment on the properties of membranes prepared from blends of poly(ether sulfone)/sulfonated poly(phenylene sulfide) (SPPS) and phenolphthalein poly(ether ether ketone)/SPPS were studied in detail. The membranes' fundamental properties, including water content, transport number, diffusion coefficient of electrolytes, flux, and so on, changed with both treated temperature and time, whereas the ion‐exchange capacity and electrical resistance remained approximately unchanged. The trends may have been due to the possible structural change resulted from the shrinking of the polymers forming the membranes. Furthermore, the membranes also retained a good physical appearance at temperatures below 220°C. Therefore, a series of heterogeneous membranes with desired conductivities and selectivities as well as proper water contents, which could satisfy different industrial purposes, such as electrodialysis, diffusional dialysis, and proton exchange, were achieved by simple heat treatment for a proper time and at a proper temperature. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 494–499, 2005     

溶剂在高分子膜中传递现象研究的进展

溶剂在高分子膜中吸收和解吸的传递机理非常复杂,对其传递过程的研究有助于膜分离过程的开发、膜材料的选择。本文对溶剂在高分子膜中传递现象研究的进展作简要介绍。     

Modelling of the pervaporative flux through hydrophilic membranes

This work presents a simplified model of wide applicability for the determination of the pervaporation flux through hydrophilic membranes, provided that the adsorption isotherm of the permeating species onto the pervaporation membrane has a linear shape. The model predicts the pervaporation flux as a function of the activity of the penetrant in the liquid phase and the operation temperature. Experimental results obtained working with two polymeric membranes (CMC‐CF‐23 and Pervap 2256) applied to the dehydration of tetrahydrofuran (THF) and to the separation of methanol from alcohol–ether mixtures, respectively, have been satisfactorily correlated and the characterising parameters have been obtained. Furthermore, the model has been also tested against results obtained with two ceramic membranes, Pervap SMS and zeolite NaA, applied to the dehydration of ketonic mixtures and of tetrahydrofuran respectively. Copyright © 2005 Society of Chemical Industry     

Performance control of asymmetric poly(phthalazinone ether sulfone ketone) ultrafiltration membrane using gelation

We studied the influence of the gelation conditions on the formation kinetics of the polyphthalazine ether sulfone ketone (PPESK) membrane via wet phase inversion process experimentally and theoretically. Membrane formation and its morphology were first observed with an online optical microscope - CCD camera system. The resulting membranes prepared under various gelation conditions were then characterized by the gelation parameter, optical microscope, and SEM. Lastly, the relationship between the final membrane structure/permeation properties and the gelation parameter was discussed extensively. The results showed that both the gelation rate and the membrane flux increased dramatically as the gelation temperature increased. Moreover, the membrane structures became loose, and the porosity of membrane increased. Different non-solvent could change the solubility parameter between the polymer and the non-solvent, and thus the gelation rate greatly. With the increasing number of carbons in non-solvent, the gelation rate became slow, and the membrane gradually changed from a finger structure into a sponge structure. Adding NMP into the non-solvent changed the difference in the chemical potential and the solubility parameter between the polymer solution and the non-solvent, which in turn changed the gelation rate of polymer solution greatly. With the increasing concentration of NMP in non-solvent, the gelation rate became very slow and sponge structures formed with the non-solvent system of 80% NMP. A novel conclusion could be made that we could control the flux and reject of membrane just by changing the mean diffusion coefficient of skin, D, and the diffusion coefficient of skin, D1, in the process of membrane formation. This work was presented at 13 ^th YABEC symposium held at Seoul, Korea, October 20–22, 2007.     

A theory for the diffusion of large molecules in amorphous polymers above Tg

A general theory of diffusion of large molecules in rubbery amorphous polymers is of interest for the scientific understanding and with regard to material design and process optimization. A broadly applicable model would be useful in developing controlled transport of plasticizers and other additives through polymeric substances. A diffusion model is presented which has been developed for large molecular penetrants above the T_g of the amorphous polymer allowing for required increase in redistribution of the free volume of the polymer structure, as well as the penetrant size and shape. Applicability of the model is demonstrated by comparing theoretically developed diffusion curves for DNOP and DNDP in PVC vs. their weight fractions at 82°C and 91°C. These theoretically derived plots are compared with experimental D vs. w₁ curves for these systems generated at lower temperature.     

SOLUTE DIFFUSION IN SWOLLEN MEMBRANES III. NON-EQUILIBRIUM THERMODYNAMIC ASPECTS OF SOLUTE DIFFUSION IN POLYMER NETWORK MEMBRANES

The Kedem-Katchalsky phenomenological coefficients L_p, L_D and L_pD of albumin transport through PVA membranes were calculated through knowledge of the corresponding multicomponent diffusion coefficients. Non-equilibrium thermodynamic considerations for non-ideal systems of hydrophilic solutes in water were used to describe the transport of albumin through swollen non-porous (gel) polymeric membranes. Experimental results and the effect of polymer structure are also discussed.     

氯甲基化/季铵化新型聚芳醚砜酮超滤膜的研制

本文对含二氮杂萘结构聚芳醚砜酮进行改性制得氯甲基化聚芳醚砜酮。选用N-甲基一2-吡咯烷酮作制膜溶剂，依据正交设计方法制得了一系列氯甲基化聚芳醚砜酮超滤膜。考察了聚合物浓度、添加剂种类和添加量以及制膜蒸发时间等对膜性能的影响。将氯甲基化聚芳醚砜酮超滤膜浸入三甲胺溶液进行季铵化反应，得季铵化聚芳醚砜酮超滤膜。并考察了膜的抗污染性。     

Sequential vapor sorption of additional penetrants in preswollen polymers

Uptake and removal of a second penetrant in polymer samples preexposed to another vapor dictate many industrially important processes. Both the kinetics and equilibrium sorption can be strongly affected by the presence of the first permeant in the polymeric matrices. A novel experimental setup was constructed to study penetrant uptake in sequence. Sorption of the second vapor took place while the partial vapor pressure of the first vapor was maintained, so that diffusion into the preswollen polymer approximated transport in a pseudobinary system. Polybutylene was chosen in this work to illustrate the capability of this versatile experimental system. Both the rate of diffusion and equilibrium sorption of the second vapor were found to depend on the prevailing composition of the preswollen polymer for all penetrant pairs studied.