Solute diffusion through swollen polymer membranes

Experiments were designed to study the role of the solvent in the transport of a solute through a solvent-swollen polymer membrane. A single solute (an organic dye), a single polymer (cross-linked natural rubber), and 24 different organic solvents were used for this purpose. The solute diffusion coefficient D was calculated from the measured permeability P and distribution coefficient K, and was compared to the diffusion coefficient of the solute in the pure solvent. The main parameters of the solvent were shown to be its viscosity and the degree it swells the polymer. At high swelling, the results are in agreement with a model that pictures the resistance to solute diffusion as hydrodynamic interaction with the solvent while the polymer acts as an obstruction that increases the tortuosity of the diffusion path. At very low swelling, the diffusion coefficient approaches an asymptotic limit which is independent of solvent viscosity. However, even with as low as 10% solvent, some effects of viscosity are still seen. These results are discussed in terms of a quantitative theory for the obstruction effect proposed by Meares and compared to other literature data.     

Crosslinked poly(vinyl alcohol) hydrogels as swollen elastic networks

Transparent crosslinked PVA hydrogels were prepared by electron beam irradiation of aqueous solutions under nitrogen. These weak hydrogels, upon swelling at 30°C in water, showed low elastic moduli (up to 50 psi), low ultimate tensile strength (up to 4 psi), and low extensibility to break (not higher than 85%). Values of the molecular weight between crosslinks M_c were calculated from swelling and from tensile experiments. In fact, two values of M_c were calculated for each swelling experiment, (a) allowing for observed variation in the polymer–solvent interaction parameter χ₁ with concentration, and (b) fixing χ₁ = 0.494 according to literature data. The correlation of the M_c obtained from tensile data with the M_c obtained from swelling data, by (a) or (b), was approximately linear and gave the same per cent agreement.     

Polar and steric effects in reverse osmosis

The effects of polar parameter Σσ^* and steric parameter ΣE_s on reverse osmosis separations of alcohols, aldehydes, ketones, and ethers (noncyclic) in aqueous solutions involving single solute systems and porous cellulose acetate membranes are discussed. The least-squares and multiple-regression analyses of solute transport parameter data show that the separation of aldehydes, just as that of alcohols, is predominantly a function of Σσ^*, and that of ethers is predominantly a function of ΣE_s, whereas that of ketones is best represented as a function of both Σσ^* and ΣE_s. The results also indicate that even where water is preferentially sorbed at the membrane solution interface, solute separation in reverse osmosis is affected by the nonpolar character of the solute molecule. A general expression for solute transport parameter in reverse osmosis is presented for further study.     

Phase transition in swollen gels

Summary The swelling and mechanical behaviour of networks of copolymers of acrylamide, methylenebisacrylamide and of the quaternary salt-N,N,N-trimethyl-N-methacrylamido-2-ethylammonium chloride (mole fraction of salt x _s =0-0.17) in water-acetone mixtures was investigated. In the range x _s >0.01 the phase transition was observed; with increasing concentration x _s both the extent of transition and the critical concentration of acetone in the mixture, at which the collapse takes place, increase. It was found that, compared with the ester group, the attachment of the positive charge to the main chain through the amide bond increases the extent of transition and decreases the critical acetone concentration. The jumpwise change in the gel volume accompanying the collapse is accompanied by a similar change in the shear modulus of the gel.Dedicated to Dr. Karel Duek on the occasion of his 60th birthday for his important contribution to polymer science     

Fatigue mechanism of fiber-reinforced polypropylene swollen by oil

Fatigue mechanism was investigated for the fiber-reinforced polypropylene (FRPP) swollen by a small amount of oil. The curves of applied cyclic stress (S) vs. logarithm of cycles to failure (N) shifted into smaller values of S and N, respectively, by adding oil into the polymer and with increasing a test temperature. The endurance limiting stress (σ_e) for the swollen FRPP, defined as the stress at a long lifetime, became much the same as the one for the swollen unfilled polypropylene, though the former was considerably larger than the latter for the breaking strength measured in standard bending test. The activation energy and the activated volume, which have been determined by the Eyring's model from the S–N curves at higher stress levels, suggest that the introduction of a small amount of oil into the polymer lowers a motional unit associated with a fatigue process from 30 to several repeat units. The major decrease in σ_e by swelling can be explained in terms of the crack–nucleation theory. It is indicated that this decrease yields from the change in the stress–concentration factor.     

Elastic properties of swollen real polymer networks

Summary In this paper a new set of stress-strain relations (uniaxial, equi-biaxial, unequibiaxial extensions and pure shear) for swollen networks were presented. Which are derived from the molecular theory of rubber elasticity with constraints of junctions and trapped entanglements and with crosslinks, trapped entanglements and carbon black-polymer interactions. They successed in relating the elastic equation of state to the volume fraction of polymer in swollen networks by three molecular parameters C₁, C₂ and C₃. The relation of stress-strain for uniaxial extension was verified by experiments. It is shown that this relation can successfully predict the dependence of V2 on the C₁, C₂ and C₃, and the contribution of modulus for swollen networks from the trapped entanglement which it shows that role of entanglements can only approach to a limited value, never to zero.     

Crosslinking structure of keratin. V. Number and type of crosslinks in microstructures of untreated and potassium cyanide treated human hair

The pattern of the crosslinks in the microstructures of hair was investigated by analyzing the reaction of hair with aqueous KCN by means of chemical and physical methods. It was found that the disulfide (SS) bonds in hair were selectively converted to monosulfide (S) crosslinks by the treatment with 0.08M aqueous KCN solution. The KCN-treated hairs swollen with an 11M LiBr solution containing N-ethylmaleimide showed rubberlike elasticity in a solution composed of equal volumes of 8M LiBr and diethylene glycol monobutyl ether. Stress-strain relations of the swollen hairs were analyzed by applying a rubber elasticity theory. It was demonstrated that: the conversion reactions of SS to S links occur between the low-sulfur (LS) proteins at the initial step of the reaction; SS bond scission between the high-sulfur (HS) proteins commences at a faster rate through the conversion reactions of intermolecular SS bonds to intramolecular S bonds; and the SS bonds within the matrix proteins are less reactive than the intermolecular bonds in the LS proteins. The number and the type of crosslinks in microstructures of the intact hair were also determined. The percentage ratios of the different crosslinks in LS proteins were 27.0% intermolecular SS, 39.0% intermolecular X, and 34.0% intramolecular SS + X links, where X are the crosslinks other than SS links; the values in the HS proteins were 11.9% intermolecular SS and 88.1% intramolecular SS links. The percentages of the number of crosslinks in LS and HS proteins were 13.8 and 86.2% of the total number of crosslinks of hair, 627 μmol/g, respectively. © 1996 John Wiley & Sons, Inc.     

Phase transition in swollen gels 30. Temperature-induced phase transition in positively charged poly(N-isopropylacrylamide) hydrogels in water and aqueous NaCl solutions

Summary The swelling and mechanical behaviour of ionized networks of N-isopropylacrylamide with an ionic comonomer, (2-acrylamidoethyl)trimethylammonium chloride (mole fractions x _S= 0−0.1), in the presence of a crosslinker, N,N'-methylenebisacrylamide, was investigated in water as a function of temperature and in aqueous NaCl solutions (c _NaCl= 10⁻⁵− 1 M) at 23 °C. On heating, a continuous decrease in the swelling degree in water, Q _w, was observed; increasing x _S shifts the volume transition temperature, T _tr, (from the swollen to collapsed state) to higher temperatures. The expected decrease in the swelling degree, Q, with increasing NaCl concentration in aqueous NaCl solutions was observed and two shrinking regions in ionic gels were found. The decrease in Q _w with increasing temperature and the decrease in Q with increasing c _NaCl are accompanied by an increase in equilibrium shear modulus of gels, so that the mechanical behaviour of gels is predominantly determined by the swelling degree. The experimental swelling behaviour could be, in the first approximation, described by the theory of polyelectrolyte networks in which repulsion of charges on the chain and finite chain extensibility were considered. Received: 7 June 2001 / Accepted: 21 September 2001     

Rheology of a cellulose graft copolymer. Comparison with other closely packed gel thickeners

Hydrolyzed cellulose–polyacrylonitrile graft copolymer is a polyelectrolyte gel suspension with a high viscosity in water. It is a closely packed swollen gel particle suspension in the appropriate concentration range and has similar rheological properties to other thickeners of this type. Viscosities η in either water or salt solution are reduced to a single master curve by use of the reduced viscosity function η/cQ, where c is weight fraction of polymer and Q is swelling volume in excess solvent of the same ionic strength. The effective molecular weight between crosslinks, M_c, determined from shear modulus, corresponds to M_c values for other closely packed gel thickners of similar η/cQ. Among all examples of this class of thickener, the plateau values of η/cQ, which occur at cQ > 2, are approximately inversely proportional to M_c.     

Flow of water through highly swollen membranes

The difference between the hydraulic permeability K under a pressure gradient and the diffusive permeability P under a concentration gradient can be explained by the incipient viscous flow at high degree of swelling. This flow is opposed by the friction resistance of the macromolecules of the highly swollen membrane. It comes to an end at a critical swelling H_c when the number of permeant molecules is not more sufficient for a complete solvation of the macromolecules of the membrane. Below this swelling, K equals PV₁/RT, where V₁ is the molar volume of the permeant, and above it the difference K ? PV₁/RT is proportional to H/(1 ? H) ? H_c/(1 ? H_c). The proportionality factor depends on the friction coefficient of the macromolecular segments and on the average lateral chain clustering. The data on poly(glycerol methacrylate) suggest that on the average the aggregates contain two chains.     

Phase transition in swollen gels

Summary The swelling and mechanical behaviour of networks of copolymers of acrylamide, methylenebisacrylamide and sodium 2-(2-carboxybenzoyloxy)ethylmethacrylate (mole fraction of salt x _s =0–0.2) in water-acetone mixtures was investigated. In the range x _s 0.01 phase transition (collapse) was observed, with both the extent of the collapse and the critical acetone concentration in the mixture at collapse, a _c , increasing with increasing concentration of the salt. A comparison between these results and those obtained for networks with a quaternary ammonium salt led to a conclusion that an exchange of the positive charge of the ammonium salt (NCl) for the negative charge of the sodium salt (COONa) in the side chain decreases the critical content of salt necessary for the collapse, X _s ^c , from 0.03 to 0.01, and the collapse takes place at lower concentrations of acetone. The collapse may also take place in a mixed solvent waterethanol; the dependence of network swelling on the concentration of ethanol is roughly the same as that on the concentration of acetone.     

The state of water in swollen ionomers containing sulfonic acid salts

The proton magnetic resonance relaxation times and heat capacity of water in perfluoroethylene sulfonic acid (Nafion), chlorosulfonated polyethylene (SPE), and sulfonated polysulfone (SPS) were measured as a function of temperature. Only the relaxation data for water present in Nafion conformed to the BPP model. The data indicate that the presence of fine pores, ～12 Å in diameter, causes water–surface interactions to play a significant role. For materials with the same pore size, a difference in spin-lattice relaxation time T₁ may be correlated to the Flory–Huggins parameter χ calculated for the interaction of water with the neutral portion of the polymer backbone. Only a part of the water present in Nafion and SPE undergoes freezing, while no transition was observed for water in SPS for temperatures down to ?60°C. For Nafion and SPE, the heat of fusion ΔH_f calculated from combined FID data and the DSC study was ?20 cal/g.     

Deformation behavior of poly(dimethyl siloxane) networks. I. Applicability of various theories to modulus prediction

The shear moduli of end-linked poly(dimethyl siloxane) networks were measured as a function of mol wt between chemical crosslinks (M_c) and the dilution-at-cure (C_x). The results were interpreted in terms of theories that take into account contributions from trapped entanglements. It was found that the network deformation follows the predictions of the theory of “phantom” networks, with an added contribution from trapped entanglements. At high mol wts of the precursor polymer, network imperfections play a role, as seen in the frequency dependence of the shear modulus. This results in deviation from predicted behavior. © 1993 John Wiley & Sons, Inc.     

Crosslinking structure of keratin. I. Determination of the number of crosslinks in hair and wool keratins from mechanical properties of the swollen fiber

Hair and wool keratin fibers which had been treated with an 11 M LiBr solution containing N-ethyl maleimide showed typical rubberlike elasticity in a solution composed of equal volume of 8 M LiBr and diethylene glycol mono-n-butyl ether. Stress–strain curves and equilibrium force–temperature relations were measured for swollen hair and wool fibers. The non-Gaussian effects on deformation and the energy component in retractive forces were analyzed. On the basis of rubber elasticity theory, a method for estimation of the number of mechanically effective crosslinks in keratin fibers was proposed. A linear relationship between the crosslink density and the disulfide content was obtained from the data for a variety of keratin fibers (i.e., two different human hairs, horse hair, and 17 different wools). From the results of thermodynamical and non-Gaussian treatments for swollen keratin, it was suggested that the swollen fiber consists of a two-phase structure: a mechanically stable phase of higher crosslinked domains and rubbery phase with lower crosslink density. It was further found that considerable amounts of nondisulfide covalent crosslinks are present in wool and hair keratins.     

Morphology and fracture properties of modified bisphenol A and novolac type vinyl ester resins

The morphology–toughness relationship of vinyl ester resins was studied as a function of their modification. Bisphenol A based and novolac‐based vinyl ester resins were modified by a star‐shaped polyether polymer with vinyl and hydroxyl functionalities and/or by a polyisocyanate. The polyisocyanate‐containing systems were termed vinyl ester/urethane hybrids. The morphology of the crosslinked resins was studied with dynamic mechanical thermal analysis and atomic force microscopy with ion‐eroded specimens and discussed. The toughness of the crosslinked resins was assessed by the linear elastic fracture mechanics with compact tension specimens. The fracture toughness and energy changed fairly linearly as functions of M_c and M_c^0.5, respectively, where M_c is the mean molecular mass between crosslinks. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4012–4022, 2006     

Kinetics of release of particulate solutes incorporated in cellulosic polymer matrices as a function of solute solubility and polymer swellability. I. Sparingly soluble solutes

A comparative study has been made of the kinetics of release into water of simple hydrophilic, but sparingly soluble, solutes (exemplified by CaSO₄ or SrSO₄) incorporated in varying amounts in cellulosic polymer matrices of low or high water swellability. Hydrophobic cellulose acetate films (cast from an acetone dope containing a dispersion of the appropriate salt particles occupying a fractional volume ϵ_N = 0.1–0.4 in the loaded hydrated matrix) were found to be particularly useful for this purpose because they could be easily hydrolyzed to cellulose, thus producing hydrophilic polymer matrices containing identical amounts and distributions of solute particles. The kinetic behavior observed exhibited the same main features as previously noted in drug release studies. Thus, a √t kinetic law was obeyed in all cases (apart from a relatively short initial period), while the diffusion coefficient calculated by application of the Higuchi model tended to rise with increasing solute load. This tendency was very strong in the case of the hydrophobic weakly swollen matrix and much weaker in the case of the hydrophilic one. On the reasonable assumption that the diffusion of solute in the salt-depleted matrix (which controls the release rate) occurs via aqueous pathways, the tortuosity τ of these pathways was calculated and found to attain extremely high values in the case of lightly loaded (ϵ_N = 0.1) matrices. These high τ values were drastically reduced upon either (1) increase of the salt load or (2) hydrolysis to cellulose. This behavior is shown to result from the fact that at ϵ_N = 0.1, the salt particles were fully coated with cellulose acetate so that water taken up to fill the space vacated by released salt is in the form of globules dispersed in a weakly hydrated polymer matrix and, hence, is ineffective in providing continuous aqueous pathways. In (1), these globules are increasingly bridged by gaps left in the original loaded matrix, as a result of incomplete coating of the solute particles with polymer. In (2), bridging is similarly effected by the formation of aqueous pathways through the polymer when its degree of hydration is sufficiently increased. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67: 277–287, 1998     

Modeling of the variations of permeate flux,concentration polarization,and solute rejection in nanofiltration system

A numerical model is presented and experimentally validated for predicting the local concentration polarization and the related separation performance of nanofiltration (NF) system. The model combines computational fluid dynamics for describing the transport phenomena in NF channel, with Spiegler-Kedem-Katchalsky model for considering the permeation properties through NF membrane. Particular attention is given to the modeling of spatially varied solute rejection and solute transport through membrane, representing essential distinctions from the modeling of reverse osmosis (RO) membrane. Also, an experimental-numerical framework is proposed to determine model parameters related to solute transport, including reflection coefficient and solute permeability as functions of feed solute concentration. The usefulness of this model is highlighted by predicting concentration polarization under different conditions related to operations, membrane systems (NF vs. RO), and solute types (NaCl vs. MgSO₄). Also, the contributions by convection and diffusion to solute transport are clarified, benefiting by the modeling of solute transport. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1076–1087, 2019     

Mechanical properties of crosslinked polyurethanes

Stress–strain and stress–relaxation behavior of polyurethane elastomers based on poly(ethylene adipate), poly(ethylene maleate), polyethylene glycol, and 4,4′-diphenylmethane diisocyanate (MDI) have been studied. The elastomers were crosslinked by an excess of MDI and by dicumyl peroxide (DiCup); the latter was supposed to form additional crosslinks on the unsaturated bonds. The determined values of Young's modulus, Mooney-Rivlin elastic parameters C₁ and C₂, relaxation moduli E(10 sec) and E(100 sec), as well as relaxation speed were used to estimate the effect of MDI- and DiCup-formed crosslinks on the mechanical behavior of polyurethanes. It was found that while the elastomers crosslinked by MDI only apparently displayed viscoelastic properties, the polyurethanes additionally crosslinked by DiCup exhibited more elastic behavior. The results obtained were explained on the basis of changes in the amount of secondary bonding due to the additional network junctions formed by DiCup at nonpolar groups.     

Interactions between dyes and polyelectrolytes: Effect of polymer–polymer interactions

The competition between methyl orange dye and various polymers [gelatin, poly(vinyl alcohol), polyacrylamide, etc.] for the binding sites on quaternized poly(1-vinylimidazole) in aqueous solutions was studied. The method used was based on a well-known effect of dissolved polyelectrolytes on the rate of diffusion of solutes through semipermeable membranes. The final results are expressed as the ratio of C₁^″(bound)/C₁^′(bound), where C₁^″(bound) is the amount of the solute adsorbed to a mixture of two polymers and C₁(bound) is the amount of solute bound to a single polymer. In the case of quaternized poly(1-vinylimidazole) it was found that as much as 15% of the solute bound to the polymer can be replaced by another, “nonadsorbing” polymer.