Measurement of activity coefficients in polymer solutions by the reversedflow technique

Summary The reversed-flow, gas-chromatographic method for measuring activities and activity coefficients in binary liquid mixtures is now extended to the determination of activity coefficients of the solvent in polymer-solvent systems over the whole range of polymer concentration, as well as for the calculation of Flory-Huggins interaction parameters. The parameters found by the present method are compared with those determined by other techniques or calculated theoretically.     

Crystal-liquid crystal binary phase diagrams

We propose a new theoretical scheme for the binary phase diagrams of crystal-liquid crystal mixtures by a combination of a phase field model of solidification, the Flory-Huggins theory for liquid-liquid mixing and Maier-Saupe-McMillan (FH-MSM) model for nematic and smectic liquid crystal orderings. The phase field theory describes the crystal phase transition of anisotropic organic crystal and/or side chain liquid crystalline polymer crystals while the FH-MSM model explains isotropic, nematic and smectic-A phase transitions. Self-consistent calculations reveal several possible phase diagram topologies of the binary crystal-liquid crystal mixtures. The calculated phase diagrams were found to accord well to the reported experimental results.     

Enthalpy of mixing for polymer solutions based on Gibbs excess function limit of hard spheres mixtures

Enthalpy of mixing of polymer with solvent has been evaluated by the new polymer/solvent theory proposed by the authors in a previous article. The new theory was based on the excess Gibbs function limit of hard sphere mixtures with infinite size difference. The calculated enthalpy of mixing for polymer/solvent mixtures by the new theory, agreed with experimental data with good accuracy and indicated that the theory is capable to produce the enthalpy of mixing in the whole concentration range of polymer compared with Flory–Huggins theory. Also the calculations provided information on the studied polymer chains and the molecular interaction effects which were consistent with the properties of polymers and solvents used in the mixtures.     

Influence of the chain composition on the thermodynamic properties of binary and ternary polymer solutions

Thermodynamic properties of binary and ternary polymer solutions (one or two uncharged polymers in one solvent) were studied. Poly(vinyl pyrrolidone) (PVP), fully hydrolyzed poly(vinyl alcohol) (PVA) homopolymers, and water-soluble poly(vinyl alcohol-co-vinyl acetal, -vinyl propional, and -vinyl butiral) copolymers with various acetal content and chain structure, respectively, were used in the experiments. The hydrophilic/hydrophobic character of the PVA-based macromolecules and their compatibility with the PVP homopolymer were systematically regulated by changing the chemical structure of the copolymers (acetal content and/or length of side chains). The water activities in binary and ternary solutions of the chemically different polymers were determined by a gel-deswelling method developed here for ternary solutions. On the basis of the Flory-Huggins theory, the relevant solvent-segment and segment-segment pair interaction parameters (chi) have been calculated. The chi12 segment-solvent interaction parameters proved to be sensitive indicators for changes in the chemical structure of the copolymers. With increase of either the acetal content or the length of side chains in the copolymer, chi12 approached the value characteristic of a theta condition. No significant differences could be revealed in the segment-segment interaction parameters obtained for the PVP-copolymer mixtures with various acetal derivatives, when the chi12 and chi13 interaction parameters determined in binary solutions were used in the calculations for chi23. Determination of the parameters chi1,23 as suggested by Panayiotou, however, showed that increasing the acetal content or the length of the hydrophobic side chains in the copolymer resulted in a reduction in the interaction between the PVA "acetals" and PVP molecules.     

Phase equilibria in polymer–liquid–liquid systems

The phase equilibria in polymer–liquid 1–liquid 2 ternary systems have been calculated on the basis of the Flory-Huggins theory of polymer solutions. A new approximation method based on the “cluster” concept has been introduced for mixed solvents comprising a solvent and a nonsolvent. This concept has been verified with polystyrene–solvent–methanol systems.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

Approach to generalization of concentration dependence of zero-shear viscosity in polymer solutions

The possibility of constructing zero-shear viscosity master curves valid for the entire range of concentration for a large number of polymer solutions in different solvents independent of molecular weight and the nature of the solvent is considered. The results obtained show that the parameters characterizing the individual macromolecular chain., viz., the dimensions of the polymer coil and the rheological effectiveness of segmental interactions, are significant in determining the viscosity of polymer solutions from very dilute to highly concentrated ones. The relation between the parameter of rheological interaction and characteristics of polymer solutions such as the flexibility of the polymer chain and the Flory-Huggins parameter is discussed. This permits one to separate the influence of the energy and entropy factors on the concentration dependence of zero-shear viscosity.     

基于链端体积分数的聚合物溶液理论

提出“链端体积分数”的概念以克服Flory-Huggins(FH)理论中的平均场假设.将聚合物多链体系看成一条“间隔连续链”,使一些热力学量写成路径积分的形式.在聚合物/溶剂体系中,保留了FH理论的无热熵假设,把总熵分为两部分,建立了一个新的聚合物溶液理论.计算了聚苯乙烯/环己烷体系的FH相互作用参数和相分离曲线,并与实验数据和FH理论作了比较,结果表明,我们的理论结果比FH的理论结果有了很大的改进.     

Solubility Parameter of Gatifloxacin and Its Correlation with Antibacterial Activity

The solubility parameter of gatifloxacin was calculated theoretically by Fedors’ method and also determined experimentally using the standard solubility method. The molar volume of gatifloxacin was determined experimentally by the flotation method. Three solvents, ethyl acetate, propylene glycol and water were used to prepare nine binary mixtures having different solubility parameter values varying from 8.9 to 23.4 H. The δ ₂ solubility parameter of gatifloxacin was found to be 12.4 H. The cumulative transport of gatifloxacin from the binary solvent mixtures (ethyl acetate–propylene glycol and propylene glycol–water) exhibited an inverse parabolic relationship to the solubility parameter of the solvent mixtures. Transport studies revealed that the extent of gatifloxacin rejection from solvent mixtures was dependent on its solubility parameter and system composition. In the selected organisms (bacteria), a minimum zone of inhibition was observed in a solvent mixture having the solubility parameter nearest to the solubility parameter of gatifloxacin. Two models were employed for the evaluation of the antibacterial activity of gatifloxacin in binary mixtures.     

Mean‐field‐theory for polymers in mixed solvents. Thermodynamic and structural properties

Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approaches criticality. Both the single and the many chain problems are examined. When the mixed solvent is near criticality without solute, addition of a small amount of polymers shifts the criticality towards either enhanced compatibility or induced phase separation depending upon the value of the parameter describing the interaction asymmetry of the solvents with respect to the polymer. The polymer‐solvent effective interaction parameter increases strongly when the solvent mixture approaches criticality. Accordingly, the apparent excluded volume parameter decreases and may vanish or even become negative. Consequently, the polymer undergoes phase transition from a swollen state to an unperturbed state or even takes a collapsed configuration. The effective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of ternary mixtures of polymers in mixed solvents are investigated within the Edwards Hamiltonian model. It is shown that the effective potential on a test chain in strong solutions could be written as an infinite series expansion of terms describing interactions via one chain, two chains etc. This summation can be performed following a similar scheme as in the Ornstein‐Zernike series expansion.     

Determination of thermodynamic properties of isotactic poly(1-butene) at infinite dilution using density and inverse gas chromatography

The partial molar volumes, V1(M), and the molar volume of isotactic crystalline low-molecular-weight poly(1-butene), iPBu-1, V1, have been calculated from the measured density of {iPBu-1 + solvent (n-hexane, n-heptane, n-nonane, n-decane, p-xylene, cyclohexane and chloroform)} systems. Some of the thermodynamic quantities were also obtained for the iPBu-1 with eight hydrocarbons (n-octane, n-decane, n-undecane, n-dodecane, n-tridecane, o-xylene, m-xylene, p-xylene) by the method of inverse gas chromatography at various temperatures. The weight fraction activity coefficients of the solvent at infinite dilution, omega2(infinity) and the Flory-Huggins thermodynamic interaction parameters, chi21(infinity), between polymer and solvents were determined. The partial molar free energy, deltaG2(infinity), the partial molar heat of mixing, deltaH2(infinity), at infinite dilution and the polymer solubility parameter, delta1, were calculated. Additionally, the (solid + liquid) binary mixtures equilibria, SLE, of iPBu-1 with three hydrocarbons (n-octane, n-decane and m-xylene) were studied by a dynamic method. By performing these experiments over a large concentration range, the T-x phase diagrams of the polymer-solvent systems were constructed. The excess Gibbs energy models were used to describe the nonideal behaviour of the liquid phase. The omega2(infinity) were determined from the solubility measurements and were predicted by using the UNIFAC FV model.     

The effect of molecular weight heterogeneity on the second virial coefficient of linear polymers in good solvents

The effect of molecular weight heterogeneity on the second virial coefficient A₂ in good solvents is studied for binary mixtures of monodisperse poly(α-methylstyrenes). It is concluded that A₂ for polymer mixtures passes through a maximum with variation of the mixing ration. From comparison with the data, it is concluded that no available theory quantitatively explains both the molecular weight dependence of A₂ of monodisperse polymer and the variation of A₂ of mixtures with the mixing ratio. The interpenetration function for two polymer coils with different molecular weights is discussed on the assumption that the thermodynamic interaction between two polymer coils in good solvents can be approximated by a hard-sphere model.     

Phase behavior of polymer mixtures with nonadditive hard-sphere potential

The phase behavior of a binary mixture of homopolymers in which macromolecules are composed of tangent hard spheres was studied. The interaction of unlike units is characterized by the contact distance (1/2)(σ_A + σ_B)(1 + Δ), where σ _i is the diameter of the ith sphere (unit) and Δ is the nonadditivity parameter. The effect of nonadditivity was taken into account by means of the perturbation theory relative to the additive system (Δ = 0) considered earlier (Polymer Science, 47, 2146 (2005)) in terms of the Percus-Yevick approximation. The theoretical consideration presented is completely analytical. It was found that a polymer mixture experiences phase separation with an increase in pressure; the two-phase region extends with an increase in both the size ratio between the units α = σ_A/σ_B and the length of the chain per se. Closed phase diagrams were first predicted for athermal mixtures; such diagrams appear at Δ < 0 and certain values of α. It was shown that the thermodynamics of an incompressible mixture of hard-chain molecules at α = 1 follows the Flory-Huggins theory with the temperature-independent interaction parameter. Phase separation in polymer solutions with the nonadditive hard-sphere potential was also analyzed.     

Dilute solution properties of anionic polystyrene in ternary mixture toluene-2-butanone-2-methyl-1-propanol

Several polystyrene samples with relatively narrow molecular weight distributions have been prepared by anionic polymerization. Dilute solution properties of these samples in binary and ternary liquid mixtures were investigated by light scattering and viscometry, using toluene and 2-butanone as solvents and 2-methyl-1-propanol as non-solvent. At 25° experiments were performed to find a set of compositions of the mixed solvent where the second virial coefficient of the osmotic pressure expansion equals zero for the polymer solution, and a set of compositions of the mixed solvent where the intrinsic viscosity of the polymer solution equals the value for polystyrene a theta solvent, such as cyclohexane at 34.5°. The results suggest that these sets of compositions are not identical. The specific effects of sorption and preferential sorption which give rise to the difference between the sets of compoisitions are qualitatively discussed in terms of the Flory-Huggins theory.     

Sorption phenomena of organic solvents in polymers: Part I

In this work we use the vapor-sorption equilibrium data to show the degree of solvent upturn in each solvent-polymer system. For this purpose, 23 isothermal data sets for four polymer + solvent binaries, one block copolymer + solvent binary and for the corresponding polymer pairs have been used in the temperature range of 25-70 °C. Solvents studied are benzene, carbon tetrachloride, chloroform and pentane. Homopolymers studied are polyisobutylene, poly(ε-caprolactone), poly(ethylene oxide), n-heptadecane, polystyrene, poly(vinyl chloride), poly(vinyl methyl ether), and n-tetracosane.According to these data sets, solvent weight fraction in the polymer is plotted against solvent-vapor activity that is calculated assuming an ideal gas phase of pure solvent vapor neglecting the vapor pressure of the polymer. We use the Flory-Huggins theory to obtain dimensionless interaction parameter, χ. Also the Zimm-Lundberg clustering theory and non-ideality thermodynamic factor, Γ are used to interpret the equilibrium data.     

Effect of polymer size and chain length on depletion interactions between two colloids

A density functional theory based on the weighted density has been developed to investigate the depletion interactions between two colloids immersed in a bath of the binary polymer mixtures, where the colloids are modeled as hard spheres and the polymers as freely jointed tangent hard-sphere chain mixtures. The theoretical calculations for the depletion forces between two colloids induced by the polymer are in good agreement with the computer simulations. The effects of polymer packing fraction, degree of polymerization, polymer/polymer size ratio, colloid/polymer size ratio on the depletion interactions, and colloid-colloid second virial coefficient B2 due to polymer-mediated interactions have been studied. With increasing the polymer packing fraction, the depletion interaction becomes more long ranged and the attractive interaction near the colloid becomes deeper. The effect of degree polymerization shows that the long chain gives a more stable dispersion for colloids rather than the short chain. The strong effective colloid-colloid attraction appears for the large colloid/polymer and polymer/polymer size ratio. The location of maximum repulsion Rmax is found to appear Rmax approximately sigmac+Rg2 for the low polymer packing fraction and this is shifted to smaller separation Rmax approximately sigmac+sigmap2 with increasing the polymer packing fraction, where sigmap2 and Rg2 are the small-particle diameter and the radius of gyration of the polymer with the small-particle diameter, respectively.     

Application of the perturbed chain SAFT equation of state to complex polymer systems using simplified mixing rules

A simplified perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is applied to polymer systems that include a variety of non-associating (esters, cyclic hydrocarbons), polar (ketones) as well as associating (amines, alcohols) solvents. The solvent pure-component parameters that are not available in the literature are estimated by correlating vapor-pressure and liquid-density data. The performance of the simplified PC-SAFT is compared to the original PC-SAFT equation of state for polymer systems of varying complexity. It is shown that the applied simplification is not at the expense of the accuracy of equation of state, while the computational time and complexity are significantly reduced, especially for associating systems. With no binary interaction parameter, simplified PC-SAFT is successfully able to predict vapor–liquid equilibria of polymers with non-associating solvents. In the case of associating solvents, a small binary interaction parameter k_ij is usually needed for the satisfactory correlation of the experimental data.     

Investigation of thermodynamic properties of poly(methyl methacrylate-co-n-butylacrylate-co-cyclopentyl styryl-polyhedral oligomeric silsesquioxane) by inverse gas chromatography

The thermodynamic properties of poly(methyl methacrylate-co-butyl acrylate-co-cyclo -pentylstyryl polyhedral oligomeric silsesquioxane) (poly(MMA-co-BA-co-styryl-POSS)) were investigated by means of inverse gas chromatography (IGC) using 20 different kinds of solvents as the probes. Some thermodynamic parameters, such as molar heats of sorption, weight fraction activity coefficient, Flory-Huggins interaction parameter, partial molar heats of mixing and solubility parameter were obtained to judge the interactions between POSS-contained polymers and solvents and the solubility of the polymers in these solvents. It was found that acetates, aromatic hydrocarbons and hydrocarbon halides were good solvents, n-hexane, ethanol, n-propanol, n-butanol and n-pentanol were moderate solvents, while n-heptane, n-octane, n-nonane, n-decane and methanol were poor solvents for all POSS-contained polymers within the experimental temperature range. Incorporation of POSS in polymer increased the solubility of polymers in solvents, and the more the POSS in polymer was, the better the solubility was and stronger the hydrogen bonding interaction was, but the POSS content in polymers seemed to have no obvious influence on the solubility parameter of polymers.     

Solubility calculation of pharmaceutical compounds – A priori parameter estimation using quantum-chemistry

Pure-component electrostatic properties for pharmaceutical compounds and intermediates (xanthene, ibuprofen, aspirin, p-hydroxyphenylacetic acid, p-toluic acid and o-anisic acid) were obtained by quantum-chemical methods. Afterwards, these properties were used for the a priori determination of the pure-component parameters for the Perturbed-Chain Polar Statistical-Associating Fluid Theory (PCP-SAFT). These parameters were applied to perform solubility calculations for binary solute–solvent mixtures. In these calculations the only parameter fitted was the binary parameter. The results show a good agreement of the modeled solubility and experimental data for the considered solutes in non-polar and polar solvents. Finally, the application of different combination rules to also predict the binary interaction parameter in the mixture was investigated.     

Solvent size effect on the depletion layer of a polymer solution near an interface

By varying polymer concentration phi0p and Flory-Huggins parameter chi, the effect of solvent size on the depletion interaction between polymer coils and a hard wall was investigated by the real-space version of self-consistent field theory (SCFT). The depletion profiles and depletion thickness indicated that the depletion effect is strong in less good solvent with large molecular volume. Through the analysis of the respective free energies of polymer coils and solvent molecules, we found that the increment in the translation entropy of the solvent is the key to strengthening the depletion interaction. On the basis of the SCFT results, we define a solvent with volume about one to six times that of the polymer segment as a "middle-sized solvent". The density oscillations previously studied by Van der Gucht et al. and Maassen et al. were also observed in our simulation, and the addition of middle-sized solvent will magnify the amplitude of the oscillations. The solvent-size-dependent depletion interaction may be an explanation for the reduced entanglement and promoted crystallization behavior of polymer coils prepared from the solution with middle-sized solvent.