Theoretical calculation of Flory-Huggins and scattering interaction parameters by means of the lattice fluid theory for PVME/PSD blends

By fitting the spinodals of poly(vinyl methyl ether)/deuterated polystyrene (PVME/PSD) systems, the adjustable parameters epsilon (12)* and delta epsilon* in the Sanchez-Balasz lattice fluid (SBLF) theory could be determined for different molecular weights. According to these parameters, Flory-Huggins and scattering interaction parameters were calculated for PVME/PSD with different molecular weights by means of the SELF theory. From our calculation, Flory-Huggins and scattering interaction parameters are both Linearly dependent on the reciprocal of the temperature, and almost linearly on the concentration of PSD. Compared with the scattering interaction parameters, the Flory-Huggins interaction parameters decreased more slowly with an increase in the concentration for all three series of blends.

Thermodynamics of blends of poly(ethylene oxide) with poly(methyl methacrylate) and poly(vinyl acetate): prediction of miscibility based on Flory solution theory modified by Hamada

Flory solution theory modified by Hamada et al. (Macromolecules, 1980, 13, 729) was used to predict the miscibility of blends of poly(ethylene oxide) with poly(methyl methacrylate) (PEO-aPMMA) and with poly(vinyl acetate) (PEO-PVAc). Interaction parameters of a PEO-aPMMA blend with the weight ratio of PEO/aPMMA = 50/50 at the temperature range of 393-433 K and PEO-PVAc blends with different compositions and temperatures were calculated from the determined equation-of-state parameters based on Flory solution theory modified by Hamada ed al. Results show that interaction parameters of the PEO-aPMMA blend are negative and can be comparable with values obtained from neutron-scattering measurements by Ito et al. (Macromolecules, 1987, 20, 2213). Also, interaction parameters and excess volumes of PEO-PVAc blends are negative and increase with enhancing the content of PEO and the temperature. (C) 1998 Elsevier Science Ltd. All rights reserved.

Pressure effects on the thermodynamics of trans-decahydronaphthalene/polystyrene polymer solutions: Application of the Sanchez-Lacombe lattice fluid theory

The cloud-point temperatures (T-cl's) of trans-decahydronaphthalene(TD)/polystyrene (PS, (M) over bar (w) = 270 000) solutions were determined by light scattering measurements over a range of temperatures (1-16degreesC), pressures (100-900 bar), and compositions (4.2-21.6 vol.-% polymer). The system phase separates upon cooling and T-cl was found to increase with rising pressure for constant composition. In the absence of special effects, this finding indicates positive excess volume for the mixing. Special attention was paid to the demixing temperatures as a function of pressure for different polymer solutions and the plots in the T-phi plane (where phi signifies volume fractions). The cloud-point curves of polymer solutions under different pressures were observed for different compositions, which demonstrated that pressure has a greater effect on the TD/PS solutions when far from the critical point as opposed to near the critical point. The Sanchez-Lacombe lattice fluid theory (SLLFT) was used to calculate the spinodals, the binodals, the Flory-Huggins (FH) interaction parameter, the enthalpy of mixing, and the volume changes of mixing. The calculated results show that modified PS scaling parameters can describe the thermodynamics of the TD/PS system well. Moreover the SLLFT describes the experimental results well.

Thermodynamics of PMMA/SAN blends: Application of the Sanchez-Lacombe lattice fluid theory

Polymer blends of poly(methyl methacrylate) (PMMA) and poly(styrene-co-acrylonitrile) (SAN) with an acrylonitrile content of about 30 wt % were prepared by means of solution-casting and characterized by virtue of pressure-volume-temperature (PVT) dilatometry. The Sanchez-Lacombe (SL) lattice fluid theory was used to calculate the spinodals, the binodals, the Flory-Huggins (FH) interaction parameter, the enthalpy of the mixing, the volume change of the mixing, and the combinatorial and vacancy entropies of the mixing for the PMMA/SAN system. A new volume-combining rule was used to evaluate the close-packed volume per mer, upsilon*, of the PMMA/SAN blends. The calculated results showed that the new and the original volume-combining rules had a slight influence on the FH interaction parameter, the enthalpy of the mixing, and the combinatorial entropy of the mixing. Moreover, the spinodals and the binodals calculated with the SL theory by means of the new volume-combining rule could coincide with the measured data for the PMMA/SAN system with a lower critical solution temperature, whereas those obtained by means of the original one could not.

Phase-separation behavior of the system PES/phenoxy: An application of the Sanchez-Lacombe lattice fluid theory

Cloud-point curves reported for the system polyethersulfone (PES)/phenoxy were calculated by means of the Sanchez-Lacombe (SL) lattice fluid theory. The one adjustable parameter epsilon(12)*/k (quantifying the interaction energy between mers of the different components) can be evaluated by comparison of the theoretical and experimental phase diagrams. The Flory-Huggins (FH) interaction parameters are computed based on the evaluated epsilon(12)*/k and are approximately a linear function of volume fraction and of inverse temperature. The calculated enthalpies of mixing of PES/phenoxy blends for different compositions are consistent with the experimental values obtained previously by Singh and Walsh [1].

Application of the Sanchez-Lacombe lattice fluid theory to the system pvme/ps and model calculations

Cloud point curves reported in the literature for five representatives of the system poly(vinyl methyl ether)/polystyrene were evaluated theoretically by means of the Sanchez-Lacombe lattice fluid theory. The measured phase separation behavior can be described within experimental error using only one adjustable parameter (quantifying the interaction between the unlike mers). The Flory-Huggins interaction parameters calculated from this theoretical description depend in good approximation linearly on composition (volume fractions) and on the inverse temperature. An evaluation of these data yields a maximum heat effect which is almost one order of magnitude less (ca. -0.25 J/cm(3)) than obtained via Hess's cycle (dissolution of the components and of the blend) from calorimetric measurements. Model calculations on the basis of the present theory demonstrate that the critical points shift to a different extent upon a certain relative change in the molar mass of the blend components. The sensitivity of the calculated phase diagrams against changes in the scaling parameter decreases in the following order: interaction energies between unlike mers, differences in the scaling temperatures, pressures and densities.

Defect evolution and hydrodynamic effects in lamellar ordering process of two-dimensional quenched block copolymers

The effects of hydrodynamic interactions on the lamellar ordering process for two-dimensional quenched block copolymers in the presence of extended defects and the topological defect evolutions in lamellar ordering process are numerically investigated by means of a model based on lattice Boltzmann method and self-consistent field theory. By observing the evolution of the average size of domains, it is found that the domain growth is faster with stronger hydrodynamic effects. The morphological patterns formed also appear different. To study the defect evolution, a defect density is defined and is used to explore the defect evolutions in lamellar ordering process. Our simulation results show that the hydrodynamics effects can reduce the density of defects. With our model, the relations between the Flory-Huggins interaction parameter chi, the length of the polymer chains N, and the defect evolutions are studied.

Pressure effects on thermodynamics of phase behavior in polystyrene/methylcyclohexane solutions

The calculations presented in this paper are based on the Sanchez-Lacombe (SL) lattice fluid theory. The interaction energy parameter, g*(12)/k, required in this approach was obtained by fitting the cloud points of polystyrene (PS) /methyleyclohexane (MCH) polymer solutions under pressure. The SL lattice fluid theory was used to calculate the spinodals, the binodals, and the Flory-Huggins (FH) interaction parameter of the solutions. The calculated results show that the SL lattice fluid theory can describe the dependences of thermodynamics of PS/MCH solutions on temperature and pressure very well. However, the calculated enthalpy and the excess volume changes indicate that the Clausius-Clapeyron equation cannot be suitable to describe pressure effect on PS/MCH solutions. Further analysis on the thermodynamics of this system under pressure shows that the role of entropy is more important than the excess volume in the present case.

Temperature and pressure dependence of phase separation of trans-decahydronaphthalene/polystyrene solution

The cloud-point temperatures (T-c1's) of ti-ans-decahydronaphthalene (TD)/polystyrene (PS, M-w = 270 kg/mol) solutions were determined by fight scattering measurements over a range of temperatures (1-16 degreesC), pressures (100-900 bar), and compositions (4.2-21.6 vol% polymer). The system phase separates upon cooling and the T-c1 was found to increase with the rising pressure for the constant composition. In the absence of special effects this finding indicates positive excess volumes. The special attention was paid to the demixing temperatures as a function of the pressure for the different polymer solutions and the plots in the T-volume fraction plane and P-volume fraction plane. The cloud-point curves of polymer solutions under changing pressures were observed for different compositions, demonstrates that the TD/PS system exhibits UCST (phase separation upon cooling) behavior. With this data the phase diagrams under pressure were calculated applying the Sanchez-Lacombe (SL) lattice fluid theory. Furthermore, the cause of phase separation, i.e., the influence of Flory-Huggins (FH) interaction parameter under pressure was investigated.

Effect of chain-length dependence of interaction parameter on spinodals for polydisperse polymer blends

The chain-length dependence of the Flory-Huggins (FH) interaction parameter is introduced into the FH lattice theory for polydisperse polymer-blend systems. The spinodals are calculated for the model polymer blends with different chain lengths and distributions. It is found that all the related variables r(n), r(w), r(z), and chain-length distribution, have effects on the spinodals for polydisperse polymer blends.

Thermodynamics of phase behavior in PEO/P(EO-b-DMS) homopolymer and block co-oligomer mixtures under pressure

The cloud-point temperatures (T-cl's) of poly(ethylene oxide) (PEO) and poly(ethylene oxide)-block-polydimethylsiloxane (P(EO-b-DMS)) homopolymer and block-oligomer mixtures were determined by turbidity measurements over a range of temperatures (105 to 130degrees), pressures (1 to 800 bar), and compositions (10-40 wt.-% PEO). The system phase separates upon cooling and T-cl was found to decrease with an increase in pressure for a constant composition. In the absence of special effects, this finding indicates negative excess volumes. Special attention was paid to the demixing temperatures as a function of the pressure for the different polymer mixtures and the plots in the T-phi plane (where phi signifies volume fractions). The cloud-point curves of the polymer mixture under pressures were observed for different compositions. The Sanchez-Lacombe (SL) lattice fluid theory was used to calculate the spinodals, the binodals, the Flory-Huggins (FH) interaction parameter, the enthalphy of mixing, and the volume changes of mixing. The calculated results show that modified P(EO-b-DMS) scaling parameters with the new combining rules can describe the thermodynamics of the PEO/P(EO-b-DMS) system well with the SL theory.

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 rho* 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, v* 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]

Effects of pressure and molecular weight on the miscibility of polystyrene and cyclohexane

With the aid of Sanchez-Lacombe lattice fluid theory (SLLFT), the phase diagrams were calculated for the system cyclohexane (CH)/polystyrene (PS) with different molecular weights at different pressures. The experimental data is in reasonable agreement with SLLFT calculations. The total Gibbs interaction energy, g*(12) for different molecular weights PS at different pressures was expressed, by means of a universal relationship, as g(12)* =f(12)* + (P - P-0) nu*(12) demixing curves were then calculated at fixed (near critical) compositions of CH and PS systems for different molecular weights. The pressures of optimum miscibility obtained from the Gibbs interaction energy are close to those measured by Wolf and coworkers. Furthermore, a reasonable explanation was given for the earlier observation of Saeki et al., i.e., the phase separation temperatures of the present system increase with the increase of pressure for the low molecular weight of the polymer whereas they decrease for the higher molecular weight polymers. The effects of molecular weight, pressure, temperature and composition on the Flory Huggins interaction parameter can be described by a general equation resulting from fitting the interaction parameters by means of Sanchez-Lacombe lattice fluid theory.

无定形1，2－聚丁二烯的分子链结构和分子链的相互作用

聚合物的结构决定了它的分子链的运动，分子链的运动又可表征聚合物的结构，而且聚合物的宏观性质又受到它的微观运动的影响。因此有目的地开发各种聚合物材料，充分利用其独特的性质，都离不开研究它的微观运动。这就是结构－性能－运动的关系。1，2－聚丁二烯作为一种弹性体，近十几年研究得较多，主要局限在它的链节结构（1，2－链节）与其物理机械性能的关系方面，其目的是为了弥补顺丁橡胶的不足。对于1，2－链节与其分子链的微观运动则研究得较少。然而这方面的研究对于1，2－聚丁二烯弹性体的开发和应用无疑是有益的。研究1，2－聚丁二烯的链节结构与其分子链的相互作用，首先需要选择适当的表征分子链的各种相互作用的参数。聚合物分子链的长程运动，可分为分子链内旋转运动和分子链间相互作用。其中分子链间相互作用通常用聚合物的内聚能密度表示，分子链内旋转运动决定分子链的柔顺性，而它们二者共同影响聚合物的玻璃化温度。因此实验中首先测定1，2－聚丁二烯的玻璃化温度和内聚能密度，从研究1，2－链节与1，2－聚丁二烯分子链的忌的相互作用和分子链间的相互作用着手。实验需要的1，2－聚丁二烯样品部分是用丁基锂制备的，也有别人提供的钼体系和铁体系的样品。样品的1，2－链节含量从8％至90％。主要用线膨胀法（还有DSC法及扭摆法）测定了1，2－聚丁二烯的玻璃化温度。不仅发现了1，2－聚丁二烯的玻璃化温度随1，2－链节增多而提高，而且得到了它们在玻璃化转变时的体积膨胀系数。这个系数对于后面研究分子链柔顺性是有用的。聚合物的内聚能密度是其溶解度参数的平方。实验选用特性粘数法测定1，2－聚丁二烯的溶解度参数，其中关键在于选择适当的溶剂。这方面失败的教训是由于所用的溶剂在化学结构和极性上与聚合物的相差甚大。由于这种限制，测定1，2－聚丁二烯的溶解度参数时，难以找到化学结构和极性合适且溶解度参数又相当的纯溶剂。因此按照溶解度参数理论，配制了不同溶解度参数的环已焓一甲苯混合溶剂，代替部分纯溶剂。测定结果表明，1，2－链节含量为16％的样品，其溶解度参数为8.6（[卡／立方厘米]~(1/2)），其余含量较高的样品，都是8.5（[卡/立方厘米]~(1/2)）。用混合溶剂测定聚合物的溶解度参数还是第一资，其可靠性取决于混合溶剂的溶解度参数的准确性。根据溶解度参数理论，我们提出克分子体积相近，且无特殊的相互作用的二元混合溶剂的溶解度参数，等于它们各自的溶解度参数按体积分数的加合。环已烷和甲苯的克分子体积分别为108.7和106.8立方厘米，它们的溶解度参数的极性分量S_极 → 0，再假定混合时没有吸热效应，它们二者按体积分数加合的溶解度参数可以定量使用。用时还从三个方面进行了验证，(1)用克分子体积相差较大(分别为147.4和89.4立方厘米)的正庚焓－苯混合溶剂作为反证；(2)根据特性粘数理论，用Matsuo方程；(3)由三元(溶剂1－溶剂2－聚合物)体系的Flory-Huggins相互作用参数等，它们都证实了上面提出的混合溶剂测定1,2－聚丁二烯溶解度参数的条件。根据前面的实验结果发现，1，2－链节与1，2－聚丁二烯的玻璃化温度有关，与其内聚能密度基本无关。建么1，2－链节必定与其分子链柔顺性有关。为了更准确地说明1，2－链节对1，2－聚丁二烯分子链柔顺性的影响，需要选择表征分子链柔顺性的参数。聚合物的分子链中相互作用的直观表现是它的分子链柔顺性，而分子链的柔顺性起因于它的链状分子和分子链的内旋转运动。因此我们选用分子链内旋转的参数（内旋转势垒和内旋转异构化能）表征1，2－聚丁二烯分子链的柔顺性。目前文献报道的计算分子链内旋转异构化能的方法，大多数是根据Gibbs-DiMarzio的玻璃化转变理论。这些方法一般都比较复杂。我们提出从聚合物发生玻璃化转变时的温度和体积膨胀系数，计算分子链内旋转异构化能的简便方法。这个方法的基本出发点是认为聚合物发生玻璃化转变时的自由体积，对不同结构的聚合物并非常数，其原因在于玻璃化转变时的聚合物体积膨胀系数部分地来自于分子链构象变化的贡献。分子链内旋转引起构象变化时，分子链的内旋转异构化能也相应地变化。因此玻璃化转变时，分子链的构象变化既对聚合物的体积膨胀系数有影响，又与分子链内旋转异构化能有联系，那么此时的聚合物的体积膨胀系数，与单个分子链的内旋转异构化能必然有某种联系。若用Δα·Tg（Δα是随态和玻璃态的体积膨胀系数）表示玻璃化温度Tg下，单个分子链处于能量状态∈的几率，Ng表示相同温度下，分子链中处于相同能量状态中的柔顺链分数，按照统计力学原理得到∈=-K·TgLn((Δα·Tg)/(1-Δα·Tg))。(1)

Studies on coarsening of microdomains in binary polymer mixtures by Lattice Boltzmann methods

An improved free energy approach Lattice Boltzmann model(LBM) is proposed by introducing a forcing term instead of the pressure tensor. This model can reach the proper thermodynamic equilibrium after enough simulation time. On the basis of this model, the phase separation in binary polymer mixtures is studied by applying a Flory-Huggins-type free energy. The numerical results show good agreement with the analytic coexistence curve. This model can also be used to study the coarsening of microdomains in binary polymer mixtures at the early and intermediate stages.