Plasticized microporous poly(vinylidene fluoride) separators for lithium‐ion batteries. I. Swelling behavior of dense membranes with respect to a liquid electrolyte—Characterization of the swelling equilibrium

Some poly(vinylidene fluoride) (PVdF) microporous separators for lithium‐ion batteries, used in liquid organic electrolytes based on a mixture of carbonate solvents and lithium salt LiPF₆, were characterized by the study of the swelling phenomena on dense PVdF membranes. We were interested in the evolution of the swelling ratios with respect to different parameters, such as the temperature, swelling solution composition, and salt concentration. To understand PVdF behavior in microporous membranes and, therefore, to have a means of predicting its behavior with different solvent mixtures, we correlated the swelling ratios in pure solvents and in solvent mixtures to the solvent–polymer interaction parameters and solvent–solvent interaction parameters. We attempted a parametric identification of swelling curves with a very simple Flory–Huggins model with relative success. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 532–543, 2004     

Scaling and structural properties of a polymer in a simple solvent: A study based on integral equations

We present a statistical mechanical theory for polymer–solvent systems based on integral equations derived from the polymer Kirkwood hierarchy. Integral equations for pair monomer–monomer, monomer–solvent, and solvent–solvent correlation functions yield polymer–solvent distribution, chain conformation in three dimensions, and scaling properties associated with polymer swell and collapse in athermal, good, and poor solvents. Variation of polymer properties with solvent density and solvent quality is evaluated for chains having up to 100 bonds. In good solvents, the scaling exponent v has a constant value of about 0.61 at different solvent densities computed. For the athermal solvent case, the gyration radius and scaling exponent decrease with solvent density. In a poor solvent, the chain size scales as N^v with the value of the exponent being about 0.3, compared with the mean field value of ⅓. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3025–3033, 1998     

Unusual swelling behavior of films of polyvinyl- and polyvinylidene/fluorides in various solvents

The swelling of PVF and PVDF films in various solvents was investigated. It was found that in the swollen state both polymers show little tendency to retain the solvent that leaks out under a mild pressure and evaporates quickly when the specimen is exposed to air. The equilibrium swelling ratios were measured in numerous solvents. From the results it is concluded that the solubility parameters are δ_PVDF = 12.0–12.3, δ_PVF = 12.0–12.1. The unusual swelling behavior is explained by strong polymer–polymer interactions via dipoles which tend to replace polymer–solvent interactions once the sample is withdrawn from the solvent.     

Kinetics of solvent absorption and permeation through a highly swellable elastomeric network

To model a polymer gel or an elastomer undergoing a large change in volume under the action of a solvent diffusing in or out of it, a theoretical approach based on an elastohydrodynamic point of view is proposed. Drawing a parallel between the polymer network/solvent system of interest and a liquid flowing through a porous medium, the friction between the polymer and the solvent is described phenomenologically. An equation that couples the large elastic deformations undergone by the polymer network and the diffusion process is derived and then solved numerically in various cases. Special emphasis is placed on the influence of the shear elasticity during the diffusion process. During the swelling process, a nonzero shear modulus induces a nonisotropic swelling at the surface that is responsible for the “sigmoidal” shape of the mass uptake of solvent with the square root of time, as well as for the presence of a “front” in the concentration profile when the solvent advances inside the network. In a permeation process, the solvent flux deviates from its linear behavior as soon as a nonnegligible deformation of the membrane is present. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 166–182, 2003     

Investigation of polymer–solvent interactions in poly(styrene sulfonate) thin films

The swelling behavior of acid form poly(styrene sulfonate) (PSS‐H) thin films were investigated using in situ spectroscopic ellipsometry (SE) to probe the polymer–solvent interactions of ion‐containing polymers under interfacial confinement. The interaction parameter (χ), related to the polymer and solvent solubility parameters in the Flory–Huggins theory, describes the polymer‐solvent compatibility. In situ SE was used to measure the degree of polymer swelling in various solvent vapor environments, to determine χ for the solvent‐PSS‐H system. The calculated solubility parameter of 40–44 MPa^1/2 for PSS‐H was determined through measured χ values in water, methanol, and formamide environments at a solvent vapor activity of 0.95. Flory–Huggins theory was applied to describe the thickness‐dependent swelling of PSS‐H and to quantify the water‐PSS‐H interactions. Confinement had a significant influence on polymer swelling at low water vapor activities expressed as an increased χ between the water and polymer with decreasing film thickness. As the volume fraction of water approached ～0.3, the measured χ value was ～0.65, indicating the water interacted with the polymer in a similar manner, regardless of thicknesses. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1365–1372     

Thermodynamics of deformation and swelling of crosslinked polymers under small deformations

A system of equations and physical relationships that show the quasi-static processes of deformation and swelling of crosslinked polymers in solvents under small deformations of the polymer matrix is proposed. The system is obtained via linearization of the respective equations of the nonlinear theory. This makes it possible to reveal the relationship between the constants of the linear theory and the parameters that characterize the elastic and thermodynamic properties of a solvent-swollen crosslinked polymer under finite deformations. Different types of problems that describe the stress-strain state of inhomogeneously swollen crosslinked polymers, as well as the thermodynamics of their deformation and swelling in a solvent medium, are discussed in terms of the linear theory.     

A molecular thermodynamic model for the swelling of thermo-sensitive hydrogels

A new molecular thermodynamic model for describing the swelling behavior of thermo-sensitive hydrogels was developed. The model consists of two terms. One is the contribution of the mixing of hydrogel network and water, which is dependent on the local polymer concentration and the interaction between polymer segment and solvent. A closed packed lattice model for polymer solution developed by Yang et al. was adopted for this term. The other is the elastic contribution derived from the network elasticity, which is dependent on the cross-linking degree of gel network. The elastic Gibbs energy model based on the Gaussian chain model developed by Flory was adopted. The model equation has two parameters. One is an energy parameter ? reflecting the interaction between water and gel network, the other is a size parameter V^* that represents the cross-linking degree of the hydrogel. When the energy parameter ? is expressed as a quadratic of inverse temperature, this model can describe the swelling equilibrium behavior of neutral thermo-sensitive hydrogels quite well. The influences of model parameters were discussed in details. The experimental swelling curves of two kinds of polyacrylamide-based gels were correlated and good agreement was obtained.     

Solution properties of cellulose triacetate. II. Solubility and viscosity studies

The solubility of cellulose triacetate in a range of solvents was measured, and the results for tetrachloroethane, chloroform, and acetic acid were compared with those from initial phase separation in solvent–nonsolvent mixtures and viscosity–concentration studies. The correlation found between solubilities, precipitation values, and values of the Huggins viscosity constant is discussed with reference to the type of polymer–solvent interaction proposed previously to explain fractionation behavior. A qualitative comparison of solubility–swelling behaviour was also made for a very low molecular weight cellulose triacetate sample in a wide range of solvents. Results are compared with those for higher molecular weight samples and discussed with regard to the cohesiveenergy densities of solvent and polymer. Some attempt has been made to predict suitable solvents for cellulose triacetate, based on consideration of their molecular structures.     

Network structure and swelling behavior of poly(acrylamide/crotonic acid) hydrogels in aqueous salt solutions

Hydrogels with various ionic group contents were prepared from acrylamide and crotonic acid (CrA) monomers with 0–12.9 mol % CrA in aqueous solutions by radiation‐induced polymerization and gelation with γ rays from a ⁶⁰Co source. The volume swelling ratio of the poly(acrylamide/crotonic acid) hydrogels was investigated as a function of the pH and ionic strength of the swelling medium and the type of counterion in the swelling medium. The volume swelling ratio increased with an increase in pH and a decrease in the ionic strength. The volume swelling ratio of these hydrogels was evaluated with an equation, based on the Flory–Huggins thermodynamic theory, the James–Guth phantom network theory, and the Donnan theory of swelling of weakly charged ionic gels, that was modified here for the determination of the molecular weight between crosslinks (M_c) and the polymer–solvent interaction parameter (χ). The modified equation described very well the swelling behavior of the charged polymeric network. The same equation also provided the simultaneous measurement of these parameters for the systems investigated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1656–1664, 2003     

Swelling behavior of the filling-type membrane

A model that can express the swelling of the filling-type membrane was developed by modifying a model that was developed for a crystalline polymer. The filling-type membrane is composed of two different polymers. One is porous substrate and another is a polymer that filled pores of the substrate. The filling technique can effectively suppress polymer swelling due to the substrate matrix. The model needs two parameters: one is a unit ratio of tie segments in the substrate to the filling polymer, f, which can express a mechanical strength of the substrate, and another is the Flory interaction parameter, χ, between the filling polymer and a solvent that expresses a mixing energy. A porous high-density polyethylene film was used as a porous substrate, and plasma-graft filling polymerization technique could make the filling-type membrane. Methylacrylate was used as a grafting monomer that filled the pores of substrate. A swelling behavior of the filling-type membrane and pure poly(methylacrylate) were measured by the vapor sorption method at different solvent activities. The model was in good agreement with experimental results for the filling-type membrane. Using the model, swelling of the filling-type polymer was compared with a crosslinked polymer, which can be expressed by Flory and Rehner model. The comparison showed that the filling technique is a good way to suppress polymer swelling, and a high crosslinking density is needed to obtain the same level of swelling suppression effect the filling type membrane showed. © 1997 John Wiley & Sons, Inc.     

Physico-chemical analysis of semi-crystalline PEEK in aliphatic and aromatic solvents

Polyether ether ketone (PEEK) is a semi-crystalline thermoplastic polymer having excellent mechanical and thermal properties. Exposure of this polymer to aliphatic and aromatic solvents can lead to degradation or swelling of the polymeric material. The present work described the plasticization and stability analysis of semi-crystalline PEEK under different aromatic and aliphatic solvent environment. A variety of solvents (acetone, benzene, benzyl alcohol, chloroform, methanol, and toluene), based on their Hildebrand’s Solubility Parameter, were chosen for investigation. The physico-chemical characteristics of virgin and treated polymeric samples were investigated using Gas Chromatography–Mass Spectrometry (GC–MS), Thermogravimetric Analysis (TGA), Differential Scanning Calorimetry (DSC), and Fourier Transform Infrared Spectroscopy (FTIR) techniques. The results indicated that the solvent exposure did not significantly affect the thermal behavior and chemical structure of the polymer. However, it seems that certain components of the polymer were leached into the solvent phase as revealed by the GC–MS analysis. The present study identified PEEK as a potentially suitable polymer for the applications where high resistance to aliphatic and aromatic solvents is needed.     

Phase equilibria in polymer/solvent systems VII swelling pressure and swelling equilibrium between gaseous or liquid phases and a gel in a multicomponent system

Differential equations for swelling pressure and swelling equilibria in two-phase systems consisting of many components have been derived. The result includes simple equilibria of gaseous or liquid solvent and a gel which are known from the literature.     

Phase equilibria in solvent mixture–ion exchange resin catalyst systems

Phase equilibria for solvent mixtures and strong acidic ion exchange resins in H⁺ form are investigated. Experimental data on ternary non-reactive solvent–solvent–polymer systems as well as reactive multicomponent systems are presented for moderately and highly cross-linked poly(styrene-co-divinylbenzene) (PS-DVB) resins. Esterification of acetic acid with ethanol is used as a model reaction. The data are correlated with a combination of thermodynamic models derived for polymer solutions and gels. Independently determined data is used whenever possible with a goal of reducing cross-correlations between the model parameters. The limitations of the thermodynamic modeling approach for solvent–ion exchange resin systems are discussed. It is shown that, due to glass transition of the polymer matrix, the underlying assumptions are not entirely valid in low dielectric constant media and at high cross-link densities.     

Stress–strain behavior of swollen polymeric networks

The network parameters of swollen, solution-crosslinked polymer filaments can be collected from deswelling measurements in solutions of nonpermeating polymer or, as shown in this paper, from the stress–strain relation when in equilibrium with the surrounding solvent. The degree of swelling, at which the partial molar free energy of elasticity equals zero, is found to vary with solvent power in agreement with earlier findings on other systems. Comparison with results of studies on rubber networks crosslinked in the absence of diluent show that previously observed discrepancies between theory and experiment can be attributed to the deficiency of the single term involving the one-third power of the volume fraction of polymer in the swollen network to describe the contribution of the partial elastic free energy.     

Closed-packed lattice model for polymer solution systems considering the chain length dependence effect: Correlating LLE,VLE, and gel swelling behaviors using identical interaction energy parameters

We propose a new Helmholtz energy of mixing equation following the original Flory–Huggins (F–H) closed-packed lattice model. Also, to overcome F–H mean-field approximation, we introduce new universal constants to consider chain length dependence of polymer in solvent and consider specific interactions to describe strongly interacting polymer systems. Our proposed model successfully describes liquid–liquid equilibria (LLE) for binary polymer–solvent systems using identical interaction parameters which do not depend on the polymer molecular weight. We also describe vapor–liquid equilibria (VLE) for polymer/solvent systems and swelling equilibria of thermosensitive hydrogel systems using the same energy parameters obtained from LLE calculations.     

Computer‐Aided Estimation of Diffusion Coefficients in Non‐Solvent/Polymer Systems

A novel method for estimating the mutual and self‐diffusion coefficients of a non‐solvent/polymer system is proposed in this work. The idea is to study the evaporation process from non‐solvent/solvent/polymer systems as a one‐dimensional numerical experiment and to use polymer solution weight versus time data to fit the unknown parameters of the diffusion‐coefficient correlations based on free‐volume theory. For this purpose, the evaporation process is modeled as a coupled heat‐ and mass‐transfer problem with a moving boundary, and the Galerkin finite‐element method is used to solve simultaneously the non‐linear governing equations. This method is successfully applied to the estimation of water–cellulose acetate diffusion coefficients and is valid over the whole range of temperatures and concentrations for practical applications in membrane technology. Additionally, there is a detailed discussion on if water affects the morphology of the final cellulosic membrane by studying the concentration profiles of the constituents of the casting solution.     

Acrylic polymer/silica organic–inorganic hybrid emulsions for coating materials: Role of the silane coupling agent

Acrylic polymer/silica organic–inorganic hybrid emulsions were synthesized by a simple method, that is, a conventional emulsion polymerization and subsequent sol–gel process, to provide water‐based coating materials. The acrylic polymer emulsions contained a silane coupling agent monomer, such as methacryloxypropyltriethoxysilane, to form highly solvent‐resistant hybrid films. On the other hand, the hybrid films from the surface‐modified polymer emulsions, in which the silane coupling agent was located only on the surface of the polymer particles and the particle core was not crosslinked, did not exhibit high solvent resistance. A honeycomblike array structure, which was derived from the polymer particles (diameter ≈ 50 nm) and the silica domain, on the hybrid film surfaces was observed by atomic force microscopy. The crosslinked core part and silane coupling agent containing the shell part of the polymer particles played important roles in attaining high solvent resistance. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4736–4742, 2006     

Permeation of a solvent mixture through an elastomeric membrane—The case of pervaporation

This article presents a model for the permeation of solvent mixtures through an elastomer in the particular case of pervaporation. An analytical expression for each solvent permeation rate is derived, in the limited case of a membrane that undergoes small swelling, without making any assumptions on the solvent diffusion coefficients and their dependence on solvent concentrations. Applying this analytical expression to different situations, we fitted most of the curves previously published on pervaporation experiments. In particular, we correlated the synergy developed by a mixture of two solvents in the permeation process with the sign of their Flory–Huggins interaction parameter χ_AB. This explains why, in most cases (χ_AB > 0), a molecule permeating easily through a membrane is mixed with a molecule permeating much less easily; the latter can see its permeation flux increase by a factor 10 or 100 because the swelling of the polymer induced by the more permeable molecule “opens the meshes of the network” allowing the less permeable molecule to pass through more easily. Within our analysis, the efficiency of the pervaporation process, expressed through the separation factor, is derived very simply as a function of the interaction coefficients and the viscosities of solvents and exhibits an exponential dependence on the volume fraction of either component as seen in most experiments. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 183–193, 2003     

Group contribution method for the swelling behavior of thermo‐responsive hydrogels

A group contribution method is introduced to describe the swelling behavior of thermo‐sensitive hydrogel systems. The accuracy of group contribution calculations is strongly dependent on the choice of thermodynamic model. Therefore, we revise the modified double lattice (MDL) model and develop a new expression for the interaction energy parameter using the association theory of Sanchez to take into account complex polymer/solvent mixing. The net Helmholtz energy for a hydrogel is established by combining the revised MDL model and modified Flory–Rehner elastic model. Group parameters are generated by fitting to experimental swelling data from both homopolymer and copolymer gel systems. The effect of salt on the volume phase transition is modeled by introducing an additional salt‐specific parameter to investigate various stimuli‐response swelling behavior. Calculated swelling equilibria using the new group contribution method shows excellent agreement with experimental data and various stimuli‐response volume phase transitions. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 455–463     

Volume Phase Transition of Polymer Networks in Polymeric Solvents

A strong concentration dependence of the solvent–polymer interaction parameter χ is known to be a requirement for the first‐order volume phase transition in uncharged polymer networks in solvents. Another possibility for the observation of phase transition in nonpolar networks is to increase the number of lattice sizes occupied by a solvent molecule. This possibility has been indicated earlier and is worked out in detail in this paper. Using the theory of swelling equilibrium, we examine the polymer network systems immersed in a polymer melt. The critical conditions for the phase transition in both uncharged and ionic networks are described.