Theoretical analysis of sorption of a binary solvent in a polymer phase. II. Occurrence of maxima and minima in the curve of total sorption

It has been shown that sorption equilibrium in the system polymer–mixed solvent and the total sorption as one of its manifestations can be derived from osmotic equilibrium. The equilibrium relation for the dependence of the osmotic pressure II (as the potential for total sorption) on the composition of the ternary polymer-containing phase also includes the preferential sorption ε. This complication leads to difficulties in the analysis of the dependence of II on composition: for this reason, analysis has been limited to the case of a very dilute polymer phase. If preferential sorption is neglected, the occurrence of an extremum on the curve representing the dependence of the total sorption on the composition of the mixed solvent is affected by the Flory-Huggins parameters as in the occurrence of an inversion in preferential sorption, with the exception that in the former case the difference in the molar volumes of the solvent components contributes a term smaller by a factor of two. In the general case, however, the contribution of preferential sorption to the osmotic pressure (which has always a negative sign) also plays its role. Consequently, while total sorption, at a low preferential sorption and at a large positive value of the solvent–solvent interaction parameter χ₁₂, can exhibit a maximum, a larger preferential sorption can overcompensate the effect of the parameter χ₁₂, so that a minimum appears. The coexistence of a minimum with a maximum on the same curve is possible in some cases with positive χ₁₂. The latter theoretical predictions have not yet been confirmed experimentally. At a negative χ₁₂ the extremum is always a minimum.     

The effect of polymer side chains on vapor sorption in polyacrylate and polymethacrylate solutions

The segment fraction Ψ₁ activity coefficients, a₁/Ψ₁, of solvents have been determined by the piezoelectric sorption method for 0.1 ≤ Ψ₁ ≤ 0.5 in binary solutions of chlorinated methanes [carbon tetrachloride (CCl₄), chloroform (CHCl₃), and dichloromethane (CH₂Cl₂)] with aromatic hydrocarbons (benzene and toluene) in poly(methyl methacrylate), poly(methyl acrylate), poly(ethyl methacrylate), and poly(n-butyl acrylate) at 23.5°C. The present results for toluene in PMMA agree with previously published values obtained by gas-liquid chromatography. For CCl₄ and the aromatic hydrocarbons, the polymer–solvent interaction parameter χ is positive and constant, while for the polar solvents (CHCl₃ and CH₂Cl₂), χ is negative and increases with increasing Ψ₁. The effect of the polymer side chains on vapor sorption in nonpolar and polar solvent systems is discussed in terms of the χ parameter.     

Polymer brush in mixed solvent. The role of flory interaction parameter χAB of the solvent components

The properties of polymer brush in binary solvent are considered on the base of the mean-field theory. The role of the interaction parameter χ_AB of the two components on the brush parameters was specially considered. The mixture of two precipitants was shown to be a good solvent for the polymer brush provided that their interaction parameter χ_AB is sufficiently great.     

Vapor sorption isotherms for benzene and n-hepatane with poly(styrene-co-butadiene)

Vapor sorption measurements of Flory–Huggins interaction parameters χ for three poly(styrene-co-butadiene) + solvent systems at 25°C are reported. For Philprene 1502 + benzene: χ = 0.379–0.297 v2₂; for Philprene 1502 + n-heptane: χ = 0.595 + 0.030 v₂ for Solprene 1204 + benzene: χ = 0.516–0.026 v₂. The volume for fractions of polymer v₂ range from ca. 0.4 to 0.9.     

A Flory–Huggins thermodynamic approach for predicting sorption equilibrium in ternary polymer systems

The Flory–Huggins theory as modified by Pouchlý has been applied to calculate preferential (λ) and total (Y) sorption coefficients for a ternary polymer system. The ternary interaction function (?₁?₂?₃G_T(u₁, ?₃)) is described as the product of three independent binary functions. This expression allows prediction of λ and Y from binary interaction parameters χ, χ, g, g, and g₁₂(?₁₀). Three ternary polymer systems are used to check the validity of the expression. Moreover for polymer systems in which the parameters g and/or g are unknown, a procedure to evaluate them has been developed and verified on systems for which sufficient experimental information is available.     

Sorption properties of polypropylene

The sorption properties of atactic polypropylene (APP) and isotactic polypropylene (IPP) were studied by equilibrium sorption of various organic solvents. The variation of the Flory-Huggins interaction parameter χ for the APP-CCl₄ system at 25°C was expressed as a function of the volume fraction v₂ of polymer by the relation: x = 0.113 exp {1.879 v₂}. The average molecular weight M _c of the polymer chains between successive crystallites for IPP subjected to different thermal treatments was calculated to be 250 to 350 by the equation of Flory and Rehner. From the variation of M _c with solvent concentration, we estimated the number fraction of polymer chains actually contributing to elastic deformation. The clustering function for solvent in the polymer calculated by the method of Zimm and Lundberg decreased linearly from a positive value to ?1 with increasing solvent concentration. Clustering of solvent molecules was found to occur more easily in APP than in IPP.     

A procedure for predicting sorption equilibrium in ternary polymer systems from Flory–Huggins binary interaction parameters and the inversion point of preferential solvation

A procedure has been developed, based on the Flory–Huggins theory as generalized by Pouchlý, which permits the calculation of preferential (λ) and total (Y) sorption coefficients from previous information on the binary interaction parameters, χ, χ, and g₁₂(?₁₀) and on the mixture composition at which the sign of λ inverts. The expressions obtained were applied to 10 cosolvent polymer systems for which experimental values of λ and Y are known. Practically in all the studied systems, the theoretical predictions are in fair accordance with the experimental data.     

A thermodynamic analysis on the coincidence of extrema conditions in the sorption equilibrium for ternary polymer systems

Flory-Huggins theory of polymer solutions has been used to express the condition of extrema values in the total sorption, as well as the inversion point in the preferential adsorption parameters for termary polymer systems. Two approaches have been followed, the first considers the binary and ternary interaction parameters independent of polymer concentration and solvent composition. In the second one, this dependence has been introduced. Our attention is focused on the volume fraction of solvent mixture dependence of the above parameters, in order to confirm or not the coincidence between the extrema values and the inversion point. Several cosolvent and cononsolvent ternary polymer systems, have been used to test the validity of the equations obtained. Also, it has been verified, from an experimental point of view, that in cosolvent ternary polymer systems there is coincidence in both compositions while in cononsolvent ternary polymer systems, such coincidence does not appear.     

Melting temperatures of poly(2,6-dimethyl-1,4-phenylene oxide) in methylene chloride solutions: Thermodynamic analysis

Melting temperatures were observed visually for poly-(2,6-dimethyl-1,4-phenylene oxide) in methylene chloride at nine concentrations (polymer weight fractions ranging from 0.0042 to 0.2362). The data were analyzed upon the assumptions that ΔH_u and ΔS_u, the molar heat and entropy of fusion per polymer unit, are constant over the temperature range studied, and that a Flory-Huggins chemical potential expression with a concentration-independent pair interaction parameter, χ₁ = (0.5 + ψ₁) + ψ₁Φ/T, satisfactorily describes the polymer unit activity in the binary solutions. Computation gave ΔH_u = 1404 cal/mole of units (therefore Δh = 11.7 cal/g), ψ₁ = ?0.569₁, and Φ = 342.₄°K. The effect of using various combinations of data points upon the values of these three parameters, as determined by least-squares linear regression treatment of the melting temperature expression, is indicated.     

Adsorption preferentielle dans le systeme: Polystyrene-acetone-cyclohexane

The co-solvent system polystyrene-cyclohexane-acetone has been studied by the light-scattering technique. The selective adsorption parameter exhibits a dependence on solvent composition with the inversion point at u₂ = 0.470. The co-solvent behaviour is discussed in relation to the binary liquid interaction parameters χ_ij the ternary interaction parameter being negligible for this system.     

Preferential sorption and permeation of binary liquid mixtures in poly (vinyl chloride) membrane by pervaporation

Preferential sorptions and pervaporation selectivities in poly (vinyl chloride) (PVC) membrane for various binary liquid mixtures were investigated. Methanol/n-propanol, benzene/n-hexane, and ethanol/water mixtures were selected as the binary liquid mixture. In the methanol/n-propanol mixture, methanol was preferentially sorbed in the PVC membrane and predominantly permeated. In the benzene/n-hexane mixture, benzene was incorporated and permeated preferentially. In the ethanol/water mixture, ethanol was preferentially sorbed in the PVC membrane and water was preferentially permeated. The preferential sorptions were analyzed according to Mulder's model derived from Flory-Huggins thermodynamics. The pervaporation selectivity in these systems were discussed using a sorption selectivity and diffusion selectivity. © 1995 John Wiley & Sons, Inc.     

Effect of carbon dioxide sorption on the phase behavior of weakly interacting polymer mixtures: Solvent‐induced segregation in deuterated polybutadiene/polyisoprene blends

The effect of carbon dioxide (CO₂) sorption on the lower critical solution temperatures of deuterated polybutadiene/polyisoprene blends was determined with in situ small‐angle neutron scattering. CO₂ was a poor solvent for both polymers and exhibited very weak selectivity between the blend components. The sorption of modest concentrations of CO₂, at pressures up to 160 bar, induced phase segregation at temperatures well below the binary‐phase‐separation temperature and caused an increased asymmetry in the lower critical solution temperature curve. The origin of solvent‐induced phase segregation in this weakly interacting polymer blend system was attributed predominantly to an exacerbation of the existing disparity in the compressibility of the components upon CO₂ sorption. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3114–3126, 2003     

Solvent quality as reflected in concentration‐ and temperature‐dependent Flory–Huggins interaction parameters

Flory–Huggins interaction parameters (χ) between poly(dimethylsiloxane) (weight‐average molecular weight = 152 kg/mol) and various solvents (methyl ethyl ketone, toluene and n‐octane) were determined as a function of composition and temperature with vapor‐pressure measurements. These data, complemented by independent information for dilute and very concentrated solutions, serve as the basis for a discussion of solvent quality via different theoretical relations. Regardless of polymer concentration, the χ values fall from methyl ethyl ketone via toluene to n‐octane, the ketone being the worst solvent and the hydrocarbon being the best solvent. The variation of χ with composition and temperature is complex. Within the range of moderate polymer concentrations, the influences of composition decrease with increasing solvent quality. Additional effects become noticeable at the ends of the composition scale. The enthalpy parts (χ_H) and entropy parts (χ_S) of the Flory–Huggins interaction parameter, obtained from χ(T), vary considerably with composition and change their sign in some cases; these constituents of the Flory–Huggins interaction parameter do not permit a direct assessment of solvent quality. A clear‐cut picture is, however, regained with a comparison of the interdependence of χ_S and χ_H. The elimination of explicit concentration influences re‐establishes the order in the solvent quality setup via χ. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 651–662, 2001     

Interaction of segmented polyurethanes and polyurethane-ureas with water

Sorption of water vapor by oligomeric homopolymers and triblock copolymers of ethylene oxide and propylene oxide, and by polyurethanes and polyurethane - ureas derived from them is discussed. While the sorption isotherms (plots of ψ₁ vs a₁, where ψ is he volume fraction of sorbed water and a₁ is activity) for most polymers investigated here are smooth and convex towards the abscissa, those found with polyurethane-ureas containing long hard blocks have a “toe” at low activities. The plots of a₁/ψ₁ vs a₁ are shown to facilitate the analysis of data and the interpretation in terms of the D'Arcy-Watt theory. Smooth isotherms are fitted by a simple equation with two parameters. The first is related to the limiting value, χ₀, (at ψ₁ → 0) of the χ parameter characterizing the polymer-water interaction. The dependences of χ₀ on the polymer composition (content of hard segments or oxyethylene units) can provide information on the interaction between hard and soft segments. The second parameter is used in the computation of parameters characterizing the clustering tendency of water molecules. This tendency depends mainly on the content of oxypropylene units but is also raised by urethane or urea groups, though not so much as by oxypropylene groups.     

Crystallization and melting of poly(2,6-dimethyl-1,4-phenylene oxide) in ternary mixtures with toluene and polystyrene

The crystallization and melting temperatures of an unfractionated poly(2,6-dimethyl 1,4-phenylene oxide) (PPO) sample, PM2, were determined at 0.25°C/min cooling and heating rates in five binary toluene—PM2 and fifteen ternary toluene—polystyrene—PM2 solutions. The total polymer weight fraction range studied was 0.12–0.40 and the PM2 weight fraction range was 0.026–0.40. The heat of fusion H_f of the PM2 was computed to be 10.1 cal/g from the melting point depressions. A toluene—PM2 pair interaction parameter χ13 = 0.890 – 223.5/T was found. Although a reliable polystyrene–PM2 interaction parameter could not be computed, the data are consistent with χ23 = 0. Setting χ23 = 0 we calculate the toluene—polystyrene interaction parameter to be χ12 = 0.495 – 15.46/T. This χ12 is in remarkable agreement with values reported in osmotic pressure studies.     

Flow microcalorimetry and competitive liquid sorption II. Liquid sorption and wetting on macroreticular hydrophilic/hydrophobic networks

Three different types of polymer networks (polymer resins) were investigated by flow microcalorimetry and selective liquid sorption from 1-propanol(1)-water(2) mixtures. Type 1 network structure is formed by non-polar, non-swelling, macroporous resins (Amberlite XAD-2, Amberlite XAD-4). The composite isotherms for alcohol sorption were S-shaped. 1-Propanol is preferentially sorbed up to x₁≈0.5. Macroreticular non-ionic resins, Amberlite XAD-7 and XAD-8, represent the second type of polymer structure. These particles have a considerable extent of swelling in the binary liquid mixture and 1-propanol was preferentially sorbed by the polymer. The composite isotherms were U-shaped and exhibit maxima and minima. The third type of network structure is attached to macroreticular polar, hydrophilic ion-exchange resins (Chelite-S, Amberlyste A-21). Depending on the composition range of the binary liquid mixture, the resins may swell to a different extent and water is preferentially embeded in the porous polymer network. The swelling of the polymer networks was monitored by the gravimetric technique in separate experiments. The sorption capacity determined from the liquid uptake of the resins was related to the sorption capacity derived from the reduced surface excess. The enthalpy effect accompanying the sorption process was determined by flow and immersion microcalorimetry. The enthalpy of displacement isotherms reveals differences in polarity and swelling ability of the polymer network fairly well. Structural changes in the adsorption layers and formation of alcohol-water clusters on the surfaces play an important role.     

Mutual selective exclusion of unlike polymers in dilute solution and its measurement by light scattering

The interaction of unlike polymer molecules (components 2 and 4) in a ternary solution can be regarded as selective exclusion or desorption of one polymer by another. A relation is derived between the coefficient of selective sorption and the interaction parameters A₂₄ and A₂₄₄ which are analogs of the second and third virial coefficients. The ratio between the apparent light-scattering molecular weight and the true value for a polymer solute in a ternary system with one component of a binary solvent polymeric is more involved than in a ternary system in which both solvent components are of low molecular weight. Under certain conditions, the introduction of polymer component 2 into a dilute solution of polymer component 4 may lead to a decrease in the total intensity of scattered light.     

Quantitative approach for the prediction of preferential sorption in the case of pervaporation of a physico-chemically similar binary mixture

Selective transport by pervaporation of physico-chemically similar and polar components through a polar membrane is complicated due to competitive sorption and diffusion phenomena. In the present study the mechanism of preferential sorption has been predicted for such a system, methanol-ethylene glycol-cellophane. The mechanism has been explained in terms of intercrystalline swelling of the polymer matrix in presence of increasing methanol concentration in the feed. The reduction in preferential sorption at increasing wt% of methanol in the feed may be due to the increasing accessibility of the membrane towards ethylene glycol. This phenomenon has been quantitatively explained by considering a non-linear dependence on concentration of the binary liquid-polymer interaction parameter. Theoretical sorption data have been derived from the Flory-Huggins thermodynamics by using the swelling equilibrium condition. The coupling and plasticization phenomena in sorption are explained in terms of liquid-polymer interaction parameters. The theoretical results show good agreement with previously published experimental data.     

Structure of a typical amine-cured epoxy resin

A technique for estimating M_c, the molecular weight between crosslinks, of amine-cured epoxy resins is described. The technique is based upon the stoichiometry of the curing reaction and the amount of primary amino and epoxy groups remaining in the polymer at a given time. The M_c values so calculated are shown to be consistent with M_c results obtained from separate measurements of swelling and the polymer–solvent interaction parameter χ₁ for the range of polymer concentration in which both measurements could be obtained. A means of estimating the relative reaction rates of the primary and secondary amino groups with the epoxy groups is given. Under proper curing conditions the amine–epoxy reaction goes very nearly to completion. The presence or absence of an exotherm has no noticeable effect on the course of the reaction between bisphenol A-epichlorohydrin (Epon 828) and methylene dianiline.     

Thermodynamics of water sorption in acrylic homonetworks and IPNs

The equilibrium thermodynamic properties of poly(hydroxyethyl acrylate) and poly(ethyl acrylate)-i-poly(hydroxyethyl acrylate) hydrogels are investigated starting from the water sorption isotherms of the systems. Partial enthalpy and entropy of the sorbed water in the gel differ markedly from the values of pure water at the lowest water contents, and tend to those of liquid water as saturation is approached. The residual mixing free energy is calculated, as a means of assessing the intensity of the water-polymer interaction. Its small positive magnitude shows that water-polymer hydrogen bonds are labile compared to water-water and polymer-polymer hydrogen bonds, and thus the stability of the gel state is still mainly due to the combinatorial entropic contribution to the mixing free energy. An equation correctly describing the sorption isotherms, when combined with the thermodynamic equations, can deliver the true water-polymer interaction parameter and its dependence on the polymer volume fraction in the gel.