A new theory for polymer/solvent mixtures based on hard-sphere limit

Based on hard-sphere limit of binary mixtures with different molecular size of components a theory has been developed for calculating activities of solvents in polymer/solvent mixtures. The theory considers various chain configurations for polymer molecules, varying from extended chain to the coiled chain. According to this theory the activity of solvent can be calculated from molecular weights (MWs) and densities as the only input data. The only adjustable parameter in the calculations, is the hard-sphere diameter of polymer, which provides useful criteria for the judgement on the chain configuration of polymer.The activity calculations have been performed for seven binary mixtures of polymer/solvent and compared with experimental data at various temperatures and for a varying range of MWs of polymers.The solvents in the mixtures were both of polar and nonpolar natures. The activity calculations for the same systems were performed by the well-known Flory-Huggins theory. Comparing the results of calculations with those of Flory-Huggins theory indicates that, the proposed theory is able to predict the activities of the solvent with good accuracy.The radius of gyration, excluded volume and interaction parameter for polymer chain have been calculated using the parameter obtained in the new theory. The calculated interaction parameter in the new theory, is interpreted in terms of attraction, repulsion and interchange energy of polymer and solvent in the mixture.     

Evaluation of the flory-huggins interaction parameter for poly(styrene-co-acrylo-nitrile) and poly(methyl-methacrylate) blend from enthalpy of mixing measurements

A direct determination of enthalpy of mixing (ΔH _mix) is of interest in predicting miscibility in polymer—polymer systems. Such measurements present, however, working difficulties, so a reliable indirect approach has been attempted. The enthalpy of mixing ΔH _m is obtained by application of Hess law to heat of solution measurement for blends and their components in a common solvent. For SAN/PMMA blend, corresponding to the weight ratio 50∶50, the experiments were performed by the Hess law approach at 29.4 and 49.3°C on dilute polymer solutions, for various concentrations, getting very good correlation data. This leads to a negative value of the interaction parameterFH _χ(1,2) and by ΔG _mix diagram it is possible to make a comparison for each temperature in accordance with the LCST behaviour of these mixtures.     

Incompatibility in polymer solutions: Light scattering of two polymers in a single solvent

The fluctuation theory of light scattering for moderately concentrated polymer solutions is extended in a phenomenological fashion to include angle-dependent terms up to sin² (θ/2). The treatment is based on an uncoupling of the center of mass and segment contributions to the free enthalpy. In particular, equations are derived for three-component mixtures containing two polymer and one solvent component. These are applied near the region of incompatibility. The results are compared with Debye's theory of critical opalescence. It is found that the Debye l parameter should be of the order of magnitude of the radii of gyration of the polymer molecules. This is confirmed by some experiments.     

Thermodynamical study on pressure-induced compatibility in UCST polymer-containing mixtures

The pressure effect on polymer-containing systems has been intensely studied in the past decades, and there has been increased interest in the effects of pressure on the miscibility of polymers[1—6]. One reason is the realization that such pressure effects could be important in many situations where such blends are used, e.g. when mixing a blend in an extruder or in forming arti-cles from a blend by injection molding. Another is the thermodynamics of typical polymer blends that are understood…     

Solubility and Solution Thermodynamics of Some Sulfonamides in 1-Propanol + Water Mixtures

The solubilities of sulfadiazine (SD), sulfamerazine (SMR) and sulfamethazine (SMT) in some 1-propanol + water co-solvent mixtures were measured at five temperatures from 293.15 to 313.15 K over the polarity range provided by the aqueous solvent mixtures. The mole fraction solubility of all these sulfonamides was maximal in the 0.80 mass fraction of 1-propanol solvent mixture (δ _solv = 28.3 MPa^1/2) and minimal in water (δ = 47.8 MPa^1/2) at all temperatures studied. The apparent thermodynamic functions Gibbs energy, enthalpy, and entropy of solution were obtained from these solubility data by using the van’t Hoff and Gibbs equations. Apparent thermodynamic quantities of mixing were also calculated by using the ideal solubilities reported in the literature. Nonlinear enthalpy–entropy relationships were observed for these drugs in the plots of enthalpy versus Gibbs energy of mixing. The plot of ?_mix H° versus ?_mix G° shows different trends according to the slopes obtained when the mixture compositions change. Accordingly, the mechanism for the solution process of SD and SMT in water-rich mixtures is enthalpy driven, whereas it is entropy driven for SMR. In a different way, in 1-propanol-rich mixtures the mechanism is enthalpy driven for SD and SMR and entropy driven for SMT. Ultimately, in almost all of the intermediate compositions, the mechanism is enthalpy driven. Nevertheless, the molecular events involved in the solution processes remain unclear.     

Free energy of an inhomogeneous polymer–polymer–solvent system. II

A complete expression for the enthalpy of mixing of inhomogeneous polymer–polymer–solvent systems applicable for small as well as large concentration fluctuations has been developed. This is used to express the free energy of inhomogeneous polymer–polymer–solvent systems in an extended form of the Landau-Ginzburg functional. The gradient energy parameters obtained here are consistent with the published results. The free energy functional has been applied to develop a generalized continuity equation for spinodal decomposition in polymer–polymer systems. A linearized version of this continuity equation has been used to study the effect of the gradient terms on the dominant wavelength during spinodal decomposition.     

Lattice treatment of thermodynamic properties of ring and linear polymer mixtures

Expressions for the entropy and free energy of mixing a solvent with a mixture of linear and cyclic polymer molecules are derived. The entropy of mixing is deduced from the number of ways of arranging on a honeycomb lattice a mixture of totally flexible molecules made up of N_R rings and N_C chains. An equation is obtained through the combination of two independent expressions for the number of ways of arranging rings and chains. The free energy of mixing is deduced from the entropy and the enthalpy of mixing, using two distinct interaction parameters for ring and for chain molecules. The chemical potentials for solvent, ring polymer, and linear polymer are derived from the free energy of mixing. These quantities are found to be functions of the mole fraction of rings in the polymer mixture. © 1993 John Wiley & Sons, Inc.     

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.     

Opposite trends in thermodynamic compatibility between copolyamide and chitosan in their binary blend

Gibbs energy, enthalpy, and entropy of mixing in binary blends of chitosan with ter‐copolyamide 6/66/610 at ambient conditions have been determined over the entire concentration range using thermodynamic cycle based on dissolution of individual polymers and their blends of different composition in a common solvent – formic acid. Experimental procedure included stepwise equilibrium vapor sorption of glacial formic acid on the cast films and isothermal microcalorimetry of dissolution of these films in liquid glacial formic acid at 25 °C. Formic acid appeared to be a very good solvent for individual polymers and their blends. Flory‐Huggins interaction parameter determined from sorption isotherms was negative and varied from ?2.56 to ?1.79 depending upon blend composition. The enthalpies of dissolution of individual polymers and their blends were strongly exothermic and varied from ?200 to ?40 Joule/g. Independent thermodynamic cycles for Gibbs free energy and enthalpy remarkably revealed similar trends in concentration dependence of different thermodynamic functions of mixing between chitosan and copolyamide. At high chitosan content, the binary blend is characterized by large and negative values of Gibbs free energy, enthalpy, and entropy of mixing that provide high polymer compatibility. On the contrary, at high copolyamide content the blends are incompatible and are characterized by positive values of enthalpy, entropy, and Gibbs free energy of mixing. Such complicated thermodynamic behavior is the result of the superposition of strong molecular interactions (H‐bonds) between polymers in the blend and isothermal fusion of copolyamide crystallites. Thermodynamic analysis correlates well with the data obtained by polarized microscopy. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2603–2613, 2007     

Theoretical estimation of thermodynamic properties of the system PS/PPO on the basis of modified combining rule of Sanchez-Lacombe lattice fluid model

The three scaling parameters described in Sanchez-Lacombe lattice fluid theory (SLLFT), T^*, P^* and ρ^* of pure polystyrene (PS), pure poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and their mixtures are obtained by fitting corresponding experimental pressure-volume-temperature data with equation-of-state of SLLFT. A modified combining rule in SLLFT used to match the volume per mer, υ^* of the PS/PPO mixtures was advanced and the enthalpy of mixing and Flory-Huggins (FH) interaction parameter were calculated using the new rule. It is found that the difference between the new rule and the old one presented by Sanchez and Lacombe is quite small in the calculation of the enthalpy of mixing and FH interaction parameter and the effect of volume-combining rule on the calculation of thermodynamic properties is much smaller than that of energy-combining rule. But the relative value of interaction parameter changes much due to the new volume-based combining rule. This effect can affect the position of phase diagram very much, which is reported elsewhere [Macromolecules 34 (2001) 6291]     

Enthalpy characteristics of sodium phenylalaninate solvation in mixtures of water with ethanol at 298 K

The heat effects of mixing for aqueous solutions of sodium phenylalaninate (NaPheAla) with mixtures of water and ethanol are measured by calorimetry at 298.15 K. The standard enthalpies of transfer of a stoichiometric mixture of ions, and of an organic ion of α-PheAla^? from water to water-alcohol mixtures are calculated. The enthalpy coefficients of binary and ternary ion-alcohol interactions are calculated using the McMillan-Mayer theory. The obtained enthalpy characteristics are compared with previously studied systems containing synthetic β- and natural α-alanine.     

Thermodynamics of ionization of 2,4-dinitrophenol in water-dimethylsulfoxide solvents

The ionization constants of 2,4-dinitrophenol were measured in water-dimethylsulphoxide solvent mixtures at five temperatures ranging from 20 to 40°C. The enthalpy and entropy contributions to the ionization process are discussed. The results indicate that in water-rich solvent mixtures the ionization process is controlled by the entropy factor while in the dimethylsulphoxide-rich solvent mixtures it is controlled by the enthalpy factor.     

New statistical mechanical model for calculating Kirkwood factors in self-associating liquid systems and its application to alkanol+cyclohexane mixtures

A new statistical mechanical model for calculating Kirkwood factors in self-associating molecular liquids and their mixtures with nonassociating components has been developed in a consistent way which is based on an extended version of the Flory-Huggins model taking into account chemical association equilibria. The majority of molecular parameters involved into the theory has been fixed by independent quantum mechanical ab initio calculations of associated molecular clusters. The model is also able to predict other thermodynamic mixture properties such as the enthalpy of mixing and also the infrared absorbance of monomer alcohol species as function of concentration. Experimental results of nine alcohol+cyclohexane mixtures taken from the literature have been used to test the new model. The Kirkwood correlation factor gK, the molar enthalpy of mixing HmE, and the monomer IR absorbance can be described simultaneously in excellent agreement with experimental data covering the whole range of mole fraction including temperature dependence of gK, HmE, and the IR absorbance. Two parameters have been adjusted freely for each system. A third parameter for the nonspecific intermolecular dispersion interactions has been adjusted within a limited range of possible values given by physical arguments. The model opens a new way of a more reliable understanding of structures and equilibrium properties of hydrogen bonded systems in the condensed liquid state.     

Kinetics and dynamics of dissolution/mixing of a high-viscosity liquid phase in a low-viscosity solvent phase

We studied mixing in the initially separated binary mixture of polystyrene/5CB liquid crystal and ternary mixtures of water/surfactant C12E5/polymer PEG system. In both systems the domains of one phase were characterized by a much higher viscosity than the solvent matrix. We demonstrated experimentally that during mixing these domains decrease their size linearly with time without a visible change of the optical contrast (i.e., without a rapid change of their compositions). Computer simulations and a theoretical model explain quantitatively our experimental observations.     

内压与液体混合物的超额焓

本文在前文提出的通用液体混合模型的基础上, 对其中某些近似假设和混合规则进行了合理的修正, 从而得到了一个液体混合物的超额焓与组分内压间的关系式。对于正常液体混合物, 式中有两个可调的修正系数, 对于醇-烃混合物, 则有三个可调参数。对十六个二元液体混合物的计算结果表明, 关系式不仅能准确地描述一般液体混合物的超额焓随浓度的变化规律, 而且亦适用于具有S型H^E-x曲线的复杂液体混合物。     

Relaxation and Miscibility of the Blends of a Poly (Ether Imide) (Ultem™) and a Phenol-A-Based Copolyester (Ardel™) by Inverse Gas Chromatography

Inverse gas chromatography (IGC) was used to analyze the secondary transition temperatures and the miscibility of binary mixtures of poly (ether imide) (Ultem™) and a copolyester of bisphenol-A with terephthalic and isophthalic acids (50/50) (Ardel™) in three compositions (25/50, 50/50 and 75/25). Retention diagrams of the mixtures of Ultem™ and Ardel™ for n-nonane, n-decane, n-butyl acetate and isoamyl acetate were obtained at temperatures between 60 and 285 °C. Second-order transition temperatures of the mixtures were determined according to the slope change in retention diagrams of the solvents. The glass transition temperatures of the mixtures suggested the miscibility of the polymers. Polymer–polymer interaction parameters of binary mixtures of the polymers were determined at temperatures between 260 and 285 °C by Flory–Huggins theory. The polymer–polymer interaction parameters were dependent on the solvent used. The small values of polymer–polymer interaction parameters close to zero suggest some weak interactions between the polymers in the mixture. It was concluded that it was possible to obtain more meaningful information related to the interactions of polymers in a mixture from IGC measurements, if binary polymer–solvent interaction parameters of the used solvent probes were around 0.5.

     

Heats of Mixing of Mixed Solvent Solutions of Alkali Metal Salts of Substituted Benzenesulfonic Acids

The enthalpy change on mixing solutions of methyl-substituted benzenesulfonic acids and their salts, with salts having a common cation or anion, at constant ionic strength in mixtures of 1,4-dioxane with water, were measured at 25°C. The heat effects of mixing solutions having a common anion increase almost linearly with the reciprocal value of the dielectric constant of the solvent. The heat effects of mixing solutions having a common cation, which are all negative in water-rich solutions, become endothermic after a certain value of the dielectric constant is passed. The results are discussed in terms of the solute-solvent structural properties. This revised version was published online in July 2006 with corrections to the Cover Date.     

聚合物-溶剂相互作用参数研究

根据液体混合的通用Gibbs自由能模型,导得了一个能满意地描述高分子溶液中聚合物-溶剂相互作用参数随浓度和温度变化的方程。它由焓贡献和熵贡献两部分组成,在形式上与Koningsveld-Kleintijen关系式相同,但它的熵贡献是浓度的复杂函数,而不象Koningsveld建议的是一个随意的常数。该方程能够很好地解释高分子溶液的某些特性。