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]     

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.     

Modeling of thermodynamic behavior of PVT properties and cloud point temperatures of polymer blends and polymer blend + carbon dioxide systems using non-cubic equations of state

In recent years, many factors influencing phase behavior of polymer blends have been studied because of their widely technological importance, as a simple method of formulating new materials with tailored properties which make them suitable for a variety of applications. This work has three main goals which were reached by using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS), which in previous works have shown their ability to handle long chain and associating interactions. First, both equations of state were tested with the correlation of the specific volumes of pure blends (PBD/PS, PPO/PS, PVME/PS, PEO/PES) and the prediction of the specific volumes for blends; second, the modeling of blend miscibilities in the liquid–liquid equilibria (LLE) of PBD/PS, PPG/PEGE, PVME/PS, PEO/PES, and PnPMA/PS blends; third, the modeling of the phase behavior of PS/PVME blends at various compositions in the presence of CO₂. PC-SAFT and SL pure-component parameters were regressed by fitting pure-component data of real substances (liquid pressure–volume–temperature, PVT, data for polymers and vapor pressure and saturated liquid molar volume for CO₂) and the fluid phase behavior of blend systems were simulated fitting one binary interaction parameter (k_ij) by regression of experimental data using the modified likelihood maximum method. Results were compared with experimental data obtained from literature and an excellent agreement was obtained with both EoS, which were also capable of predicting the fluid phase behavior corresponding to the critical solution temperatures (LCST: lower critical solution temperature, UCST: upper critical solution temperature) of blends.     

A simple statistical mechanical theory for the mutual solubility of fluid mixtures of water and organic solvents under high pressure

A simple statistical mechanical theory is presented to explain phase diagrams of fluid mixtures with both a lower critical solution temperature and an upper critical solution temperature under pressure. By postulating a temperature dependence for the interaction free energy parameter of the constituent molecules and a pressure dependence for the excess volume, phase diagrams with both lower critical solution temperature, and upper critical solution temperature and their pressure dependence can be reproduced by quadratic surfaces in temperature-concentration-pressure space. The topological aspects of the observed phase diagrams in this space have been related to our theoretical model, and the thermodynamical meaning of the topologies has been interpreted based on our model. Experimental data for the mutual solubility of water and 2-butanol under pressure and that of water and 3-methylpyridine with added salts have been analyzed quantitatively and theoretical parameters are determined.     

Characterization of the interaction energies for polystyrene blends with various methacrylate polymers

The binary interaction energies between styrene and various methacrylates were determined from newly examined phase boundaries with lattice–fluid theory. Because the blends of polystyrene (PS) and poly(cyclohexylmethacrylate) (PCHMA) were only miscible at high molecular weights when the blends were prepared by solution casting from tetrahydrofuran, we examined the miscibility of other blends by changing the molecular weights of PS or methacrylate polymers. On the basis of the phase‐separation temperature caused by the lower critical solution temperature, the miscibility of PS with the various methacrylates appeared to be in the order PCHMA > poly(n‐propyl‐methacrylate) (PnPMA) > poly(ethyl methacrylate) (PEMA) > poly(n‐butyl‐methacrylate) (PnBMA) > poly(iso‐butyl‐methacrylate) > poly(methyl methacrylate) (PMMA) > poly(tert‐butyl methacrylate), and the branching of butylmethacrylate appeared to decrease the miscibility with PS. The interaction energies between PS with various methacrylates obtained from phase boundaries with lattice–fluid theory reached minimum value corresponding to the styrene/n‐propylmethacrylate interaction. They were in the order PnPMA < PEMA < PCHMA < PnBMA < PMMA. The difference in the order of miscibility and interaction energies might be attributed to the terms related to the compressibility. The phase‐separation temperatures calculated with the interaction energies obtained here indicated that the PS/PEMA and PS/PnPMA blends at high molecular weights were miscible, whereas the PS/PnBMA blends were immiscible at high molecular weights. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2666–2677, 2000     

Study of the binary mixtures of {monoglyme + (hexane,cyclohexane, octane,dodecane)} by ECM-average and PFP models

Excess molar volumes and excess permittivity of binary mixtures involving monoglyme and alkanes, such as n-hexane, cyclohexane, n-octane and n-dodecane, were calculated from density and relative permittivity measurements for the entire composition range at several temperatures (288.15, 298.15 and 308.15) K and atmospheric pressure. The excess permittivity was calculated on the basis of a recent definition considering the ideal volume fraction. Empirical equations for describing the experimental data in terms of temperature and concentration are given. The experimental values of permittivity have been compared with those estimated by well-known models from literature. The results have indicated that better predictions are obtained when the volume change on mixing is incorporated in these calculations. The contribution of interactions to the excess permittivity was analysed by means of the ECM-average model. The Prigogine–Flory–Patterson (PFP) theory of the thermodynamics of solutions was used to shed light on the contribution of interactions to the excess molar volume. The work concludes with an interpretation of the information given by the theoretical models and the behaviour of both excess magnitudes.     

Modeling mercury porosimetry using statistical mechanics

We consider mercury porosimetry from the perspective of the statistical thermodynamics of penetration of a nonwetting liquid into a porous material under an external pressure. We apply density functional theory to a lattice gas model of the system and use this to compute intrusion/extrusion curves. We focus on the specific example of a Vycor glass and show that essential features of mercury porosimetry experiments can be modeled in this way. The lattice model exhibits a symmetry that provides a direct relationship between intrusion/extrusion curves for a nonwetting fluid and adsorption/desorption isotherms for a wetting fluid. This relationship clarifies the status of methods that are used for transforming mercury intrusion/extrusion curves into gas adsorption/desorption isotherms. We also use Monte Carlo simulations to investigate the nature of the intrusion and extrusion processes.     

ASPECTS OF THERMODYNAMICS OF POLYMER MIXTURES

In this brief review article some aspects of the thermodynamics of polymer mixtures are discussed, mainly based on the author's research. The studies of poly (methyl methacrylate)/chlorinated polyethylene (CPE), poly (butyl acrylate)/CPE and CPE/CPE (different chlorine content) mixture verify the "dissimilarity" and "similarity" principles for predicting miscibility of polymer mixtures. The sign of heat of mixing of oligomeric analogues is not sufficient in predicting the miscibility. The Flory equation of state theory has been applied to simulate the phase boundaries of polymer mixtures. The empirical entropy parameter Q_(12) plays an important role in the calculation, this reduces the usefulness of the theory. With energy parameter X_(12)≠0 and Q_(12)≠0 the spinodals so calculated are reasonable compared to experiments. A hole model was suggested for the statistics of polymer mixtures. The new hole theory combines the features of both the Flory equation of state theory and the Sanchez lattice fluid theory and can be reduced to them under some conditions.     

An improvement in the flory corresponding-states theory of polymer solutions

The original Flory corresponding-states theory of polymer solutions requires an entropic correction parameter Q₁₂, the sign and value of which seem to be arbitrary, and the physical meaning of which is obscure. Moreover, calculated excess volumes of mixing for many polymer solutions are often in significant disagreement with experimental data. In order to eliminate these problems, we have modified the kinetic part of the partition function, introduced an effective mass for the mixture segment, and adopted the nonlinearity of the number of degrees of freedom with respect to the composition for the mixture segment. In addition, the effect of nonrandom configurations of the segments in the mixture has been included. In the improved equations, derived in this work, the Flory interaction parameter χ can be considered to comprise three parts: (a) a kinetic part due to the contribution of the average number of degrees of freedom and the effective mass of the mixture; (b) a free volume part; and (c) an interaction part including the contributions due to the contact interaction and the nonrandom configuration of the segments in the mixture, caused by the interaction. The improved theory is in good agreement with literature data on polystyrene solutions and poly (dimethyl siloxane) solutions.     

Nematic–isotropic phase behaviors of polydisperse polymer/liquid‐crystal systems: Chain‐length‐dependent interaction parameter

Phase behaviors of polydisperse polystyrene (PS)/nematic liquid‐crystal systems [P‐ethoxy ‐ benzylidene ‐ p ‐ n‐butylaniline (EBBA)] are investigated with a thermo‐optical analysis technique. We also develop a thermodynamic framework to describe the phase behaviors of polydisperse PS/EBBA systems. The proposed model is based on a modified double‐lattice model to describe isotropic mixing and Maier–Saupe theory for anisotropic ordering. To correlate the polymer chain length and energy parameters in a nematic–isotropic biphasic region and to apply the primary interaction parameter in an isotropic–isotropic phase‐transition behaviors of polydisperse PS/EBBA systems. The proposed model shows remarkable agreement with experimental data for the model systems in comparison with an existing model. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1031–1039, 2006     

Statistical thermodynamics evaluation of polymer–polymer miscibility

The Simha and Somcynsky (S–S) statistical thermodynamics theory was used to compute the solubility parameters as a function of temperature and pressure [δ = δ(T, P)], for a series of polymer melts. The characteristic scaling parameters required for this task, P*, T*, and V*, were extracted from the pressure–temperature–volume (PVT) data. To determine the potential polymer–polymer miscibility, the dependence of δ versus T (at ambient pressure) was computed for 17 polymers. Close proximity of the δ versus T curves for four miscible polymer pairs: PPE/PS, PS/PVME, and PC/PMMA signaled the usefulness of this approach. It is noteworthy, that the tabulated solubility parameters (derived from the solution data under ambient conditions) propounded the immiscibility of the PVC/PVAc pair. The computed values of δ also suggested miscibility for polymer pairs of unknown miscibility, namely PPE/PVC, PPE/PVAc, and PET/PSF. In recognizing the limitations of the solubility parameter approach (the omission of several thermodynamic contributions), these preliminary results are auspicious because they indicate a new route for estimating the miscibility of any polymeric material at a given temperature and pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2909–2915, 2004     

Contact angles, pore condensation, and hysteresis: insights from a simple molecular model

We discuss the thermodynamics of adsorption of fluids in pores when the solid-fluid interactions lead to partial wetting of the pore walls, a situation encountered, for example, in water adsorption in porous carbons. Our discussion is based on calculations for a lattice gas model of a fluid in a slit pore treated via mean field density functional theory (MFDFT). We calculate contact angles for pore walls as a function of solid-fluid interaction parameter, alpha, in the model, using Young's equation and the interfacial tensions calculated in MFDFT. We consider adsorption and desorption in both infinite pores and in finite length pores in contact with the bulk. In the latter case, contact with the bulk can promote evaporation or condensation, thereby dramatically reducing the width of hysteresis loops. We show how the observed behavior changes with alpha. By using a value of alpha that yields a contact angle of about 85 degrees and maintaining the bulk fluid in a supersaturated vapor state on adsorption, we find an adsorption/desorption isotherm qualitatively similar to those for graphitized carbon black where pore condensation occurs at supersaturated bulk vapor states in the spaces between the primary particles of the adsorbent.     

缔合溶液热力学性质与谱学性质的关联

缔合溶液具有与理想溶液显著不同的热力学和谱学性质,对于热力学和谱学的研究,有助于我们理解缔合溶液的特殊行为.谱学技术中核磁共振(NMR)、红外(IR)和拉曼(Raman)光谱是研究分子间相互作用和溶液结构等微观性质的有效方法,谱学已成为分子热力学研究体系"四面体结构"中的第四个顶点.本文对缔合溶液中热力学(汽液平衡和焓)和谱学(NMR,IR和Raman)联系的最新研究进展进行了综述,着重介绍相关的模型,如化学缔合模型、局部组成(LC)、格子流体氢键(LFHB)理论以及统计缔合流体理论(SAFT).     

Surface tension of polystyrene blends: Theory and experiment

Surface tension of linear–linear and star/linear polystyrene blends were measured using a modified Wilhelmy method. Our results show that for both polystyrene blend systems, the surface tension‐composition profile is convex, indicating a strong surface excess of the component with lower surface energy. Star/linear blends display more convex surface tension profiles than their linear–linear counterparts, indicative of stronger surface segregation of the branched‐component relative to linear chains. As a first step toward understanding the physical origin of enhanced‐surface segregation of star polymers, self‐consistent field (SCF) lattice simulations (both incompressible and compressible models) and Cahn‐Hilliard theory were used to predict surface tension‐composition profiles. Results from the lattice simulations indicate that the highly convex surface tension profiles observed in the star/linear blend systems are only possible if an architecture‐dependent, Flory interaction parameter (χ = 0.004) is assumed. This conclusion is inconsistent with results from bulk differential scanning calorimetry (DSC) measurements, which indicate sharp glass transitions in both the star/linear and linear/linear homopolymer blends and a simple linear relationship between the bulk glass transition temperature and blend composition. To implement the Cahn‐Hilliard theory, pressure‐volume‐temperature (PVT) data for each of the pure components in the blends were first measured and the data used as input for the theory. Consistent with the experimental data, Cahn‐Hilliard theory predicts a larger surface excess of star molecules in linear hosts over a wide composition range. Significantly, this result is obtained assuming a nearly neutral interaction parameter between the linear and star components, indicating that the surface enrichment of the stars is not a consequence of complex phase behavior in the bulk. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1666–1685, 2009     

Rationalizing the meaning of coefficients in Flory-Huggins approach to polymer-solvent interactions

The Flory-Huggins interaction parameter for a polymer solution can be represented as the product of two functions, which separately take into account the effects of the polymer volume fraction and temperature. The latter factor contains three constants, usually viewed as best-fit coefficients. They are expressed in terms of two thermodynamic quantities, namely, the excess partial molar heat capacity of the solution and a reference temperature, thus allowing to guess their physical meaning. The formulae so obtained were tested with satisfactory results for two solutions of polystyrene in acetone and for two polymer blends (PC/PMMA and PS/PVME.) Furthermore, an attempt was made to calculate the above-mentioned reference temperature from data referring to the phases in solution.     

Structural, elastic constant, and vibrational properties of wurtzite gallium nitride: a first-principles approach

Perdew-Wang proposed generalized gradient approximation (GGA) is used in conjunction with ultrasoft pseudopotential to investigate the structural, elastic constant, and vibrational properties of wurtzite GaN. The equilibrium lattice parameters, axial ratio, internal parameter, bulk modulus, and its pressure derivative are calculated. The effect of pressure on equilibrium lattice parameters, axial ratio, internal parameter (u), relative volume, and bond lengths parallel and perpendicular to the c-axis are discussed. At 52 GPa, the relative volume change is observed to be 17.8%, with an abrupt change in bond length. The calculated elastic constants are used to calculate the shear wave speeds in the [100] and [001] planes. The finite displacement method is employed to calculate phonon frequencies and the phonon density of states. The first- and second-order pressure derivative and volume dependent Gruneisen parameter (γ(j)) of zone-center phonon frequencies are discussed. These phonon calculations calculated at theoretical lattice constants agree well with existing literature.     

Microscopic theory of orientational order, structure and thermodynamics in strained polymer liquids and networks

A microscopic integral equation theory of the segmental orientational order parameter, structural correlations and thermodynamics of strained polymer solutions, melts and networks has been developed. The nonclassical problem of the consequences of intermolecular excluded volume repulsions and chain connectivity is addressed. The theory makes several novel predictions, including effective power law dependences of the orientational order parameter on monomer concentration and chain degree of polymerization, and strain hardening of the bulk modulus. The predictions of a nearly classical strain dependence, and supralinear scaling with segment concentration, of the strain-induced nematic order parameter is in agreement with nuclear magnetic resonance experiments. The absolute magnitudes of the a priori calculated orientational order parameter agree with simulations and experiments to within a factor of 2. The possible complicating influence of "trapped entanglements" in crosslinked networks is discussed. Extensions of the theory are possible to treat the mechanical response of flexible polymer liquids and rubbers, and the structure, thermodynamics, and mechanical properties of strained liquid crystal forming polymers.     

Group contribution multifluid lattice theory for simultaneous predictions of thermodynamic properties of pure fluids and mixtures

A unified group contribution (GC) lattice equation of state (EOS) was formulated based on the multifluid approximation of the nonrandom lattice fluid theory. The GC-EOS requires segment size and interaction energy parameter from functional group characteristics. The unique feature of the approach is that a single set of group parameters are used for both pure fluids and mixtures. The approach was found to be quantitatively applicable for predicting thermodynamic properties of real pure fluids and mixtures. Its potential utility was demonstrated for vapor pressures, vapor–liquid coexistence densities of pure fluids and phase equilibrium properties of mixtures including polymeric solutions.