Liquid-liquid phase equilibria in polymer solutions and polymer mixtures

The pressure dependence of liquid-liquid equilibria in weakly interacting binary macromolecular systems (homopolymer solutions and blends) will be discussed. The common origin of the separate high-temperature/low-temperature and high-pressure/low-pressure branches of demixing curves will be demonstrated by extending the study into the region of metastable liquid states including the undercooled, overheated and stretched states (i.e. states at negative pressures). The seemingly different response of the UCST-branch of solutions and blends when pressurized (pressure induced mixing for most polymer solutions, pressure induced demixing for most blends) will be explained in terms of the location of a hypercritical point found either at positive (most solutions) or negative pressure (most blends). Further, it is shown that the pressure dependence of demixing of homopolymer solutions and blends may be described using a ‘master-curve’ which, however, is sometimes partly masked by degradation or by vapour-liquid and/or solid-liquid phase transitions. Experimental results demonstrating the extension of liquid-liquid phase boundary curves into the metastable regions will be presented, and the existence of solubility islands in the vicinity of the hypercritical points discussed.     

Phase Behavior of Polymer Blends

The present report deals with some results on phase behavior, miscibility and phase separation for several polymer blends casting from solutions. These blends are grouped as the amorphous polymer blends, blends containing a crystalline polymer or two crystalline polymers. The blends of PMMA/PVAc were miscible and underwent phase separation at elevated temperature, exhibited LCST behavior. The benzoylated PPO has both UCST and LCST nature. For the systems composed of crystalline polymer poly(ethylene oxide) and amorphous polyurethane, of two crystalline polymers poly(-caprolactone) and poly[3,3,-bis-(chloromethyl) oxetane], appear a single T_g, indicating these blends are miscible. The interaction parameter B's were determined to be –14 J cm^–3, –15 J cm^–3 respectively. Phase separation of phenolphthalein poly(ether ether sulfone)/PEO blends were discussed in terms of thermal properties, such as their melting and crystallization behavior.This revised version was published online in November 2005 with corrections to the Cover Date.     

Pressure dependence of the demixing behaviour in polymer blends: I. Experimental procedure

The most common way to influence the liquid-liquid phase behaviour in partially miscible (co-)polymer blends is changing the blending temperature. Since most extruders can handle pressures, up to 300 bar, pressure may also be used to influence the miscibility of polymers during blending. We have developed equipment and an experimental procedure to study the pressure dependence of the liquid-liquid demixing behaviour of high-viscous polymer blends under equilibrium conditions. Small amounts (1–4 grams) of specially made polymers are blended in the ‘DSM MINI EXTRUDER’. After a chosen mixing time, a small portion of the blend is injected into a small capillary tube and kept at the blending temperature. The phase behaviour of the blends as a function of temperature and pressure is studied via laser light scattering (at a scattering angle of 90°) in a specially made 400 bar/250°C window autoclave, where the capillary cell is placed in a high temperature grade silicon oil.     

Ginzburg number and phase behavior of binary polymer blends in pressure fields

In some polymer blends the temperature and pressure dependence of thermal composition fluctuations have been measured with small angle neutron scattering. The Ginzburg number Gi, the Flory‐Huggins parameter Γ, and the phase boundaries were determined for pressure fields up to 150 MPa. In polymer blends the compressibility leads to a strongly increased Gi which could be appreciably larger than in low molecular liquids and which decreases with increasing pressure fields. Usually, the phase boundaries of UCST as well as of LCST blends shift with pressure to higher temperatures. One blend having PDMS as one component, however, shows an abnormal decrease of the phase boundaries with increasing pressure. The Clausius‐Clapeyron equation correctly predict from the experimentally determined Γ and Gi the observed pressure dependence of the phase boundaries.     

Liquid-liquid equilibria of polymer solutions: Applicability of extended Redlich-Kister expansion

We developed a simple and improved expression for the Helmholtz energy of mixing which uses a Taylor series of an exponential function based on extending the Redlich-Kister expansion. This model incorporates the chain-length dependence of polymers and specific interactions such as hydrogen bonds. The proposed model can accurately predict most phase diagrams of various binary polymer solutions including upper critical solution temperature (UCST), lower critical solution temperature (LSCT), both UCST and LCST, and closed miscibility loops. Our model fits experimental data of the complex phase behavior of polymer solutions well.     

几种典型固体聚合物体系的~（13）C自旋－晶格弛豫特性

用固体高分辨ＮＭＲ系统地研究了几种典型的均聚物，共聚物，聚合物共混物以及用接枝共聚物增容的不相容聚合物共混体系的１３Ｃ自旋－晶格弛豫特性。研究结果表明：１３Ｃ自旋－晶格弛豫时间（Ｔ１（Ｃ））是表征固体聚合物体系的很有用参数，它能提供有关本体聚合物微观形态结构的信息，并可望建立聚合物的微观结构与宏观性能的关系，它不仅能准确无误地反映共混体系中可能存在的各种相互作用，而且能定性地给出相互作用的大小和准确地指明相互作用产生的位置，因而为揭示共混体系的相容机理提供了最直接的证据，另外Ｔ１（Ｃ）还能给出增容剂对不相容共混体系的增容作用和增容机制的直接实验证据     

Liquid-liquid equilibria and theta temperatures in homopolymer-solvent solutions from a perturbed hard-sphere-chain equation of state

The perturbed hard-sphere-chain (PHSC) equation of state is used to calculate liquid-liquid equilibria of binary nonpolar solvent/homopolymer systems exhibiting both an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST). Systems studied include polyisobutylene, polyethylene, and polystyrene solutions. Equation-of-state parameters of homopolymers are obtained by regressing the pressure-volume-temperature data of polymer melts. In polymer solutions, however, theory overestimates the equation-of-state effect which causes the LCST at elevated temperature. To correct the overestimated equation-of-state effect, an empirical adjustable parameter is introduced into the perturbation term of the PHSC equation of state. An entropy parameter is also introduced into the Helmholtz energy of the mixture to correlate quantitatively the dependence of critical temperatures on polymer molecular weight. For systems exhibiting a LCST, two adjustable parameters are required to obtain quantitative agreement of theoretical critical temperatures with experiment as a function of polymer molecular weight. For systems exhibiting both an UCST and a LCST, three adjustable parameters may be necessary. The need for so many empirical binary parameters is probably due to the oversimplified perturbation term which is based on the mean-field assumption. © 1996 John Wiley & Sons, Inc.     

Application of the sCPA equation of state for polymer solutions

Specific interactions, for example hydrogen bonding, dominate in numerous industrially important polymeric systems, both polymer solutions and blends. Typical cases are water-soluble polymers including biopolymers of special interest to biotechnology (e.g. the system polyethyleneglycol/dextran/water). Furthermore, most polymer blends are non-compatible and the requirement for compatible polymer pairs is often the presence of hydrogen-bonding interactions (e.g. polyvinylchloride/chlorinated polyethylene). In this work we give at first a short, comparative evaluation of existing thermodynamic models suitable for polymeric systems that take into account, explicitly, specific interactions like HB. The range of application of the models in terms of phase equilibria and their specific characteristics (accuracy of calculation, degree of complexity) are discussed. Finally, vapor–liquid equilibria (VLE) calculations for a number of polymer+solvent systems (including five different polymers) with a novel and very promising model are presented. This model is in the form of an equation of state that is (in its general formulation) non-cubic with respect to volume and has separate terms for physical and chemical interactions. The model has recently been proposed and has already been successfully applied to non-polymeric hydrogen-bonding systems (alcohol/water/hydrocarbons). This is the first time that it is extended to polymer solutions.     

Effects of chain configuration on UCST behavior in blends of poly(L‐lactic acid) with tactic poly(methyl methacrylate)s

Chain configuration influences phase behavior of blends of poly(methyl methacrylate) (PMMA) of different tactic configurations (syndiotacticity, isotacticity, or atacticity) with poly(L ‐lactic acid) (PLLA). Blends system of sPMMA/PLLA is immiscible with an asymmetry‐shaped UCST at ～250 °C. The phase behavior of the sPMMA/PLLA blend is similar to the aPMMA/PLLA blend that has been already proven in the previous work to exhibit similar UCST temperatures (230–250 °C) and asymmetry shapes in the UCST diagrams. On the other hand, the iPMMA/PLLA blend remains immiscible up to thermal degradation without showing any transition to UCST upon heating. The blend system with UCST, that is, sPMMA/PLLA, can be frozen in a state of miscibility by quenching to rapidly solidify from the homogeneous liquid at UCST, where the T_g‐composition relationship for the sPMMA/PLLA blend fits well with the Gordon‐Taylor T_g model with k = 0.15 and the blend's T leads to χ₁₂ = ?0.26 for the UCST‐quenched sPMMA/PLLA blend. Both parameters (k and χ) as characterized for the frozen miscible blend suggest a relatively weak interaction between the two constituents (sPMMA and PLLA) in the blends. The interaction strength is likely not strong enough to maintain a thermodynamic miscibility when the blend is at ambient temperature or any lower temperatures below UCST. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2355–2369, 2008     

Phase equilibria of poly(ethylene-co-vinyl acetate) copolymers in subcritical and supercritical ethylene and ethylene---vinyl acetate mixtures

Experimental high-pressure phase equilibrium data (cloud point and coexistence data) are reported for solutions of commercial poly(ethylene---co-vinyl acetate) samples in supercritical ethylene and ethylene---vinyl acetate (VA) mixtures. These data are correlated with an equation of state rooted in statistical associating fluid theory (SAFT). SAFT captures the effects of polymer MW, incorporated VA%, and free VA on the cloud point pressure, and on the size of the fluid-liquid miscibility gap, over a broad range of temperatures (50–250°C) and polymer concentrations. Free VA is found to behave as a cosolvent (lowering the cloud point pressure), except at low temperatures (< 100°C) and with low VA-containing copolymers, in which case free VA, if present in large excess (> 70 wt.%), behaves as a polar antisolvent due to favorable self-interactions among the free VA molecules. SAFT predicts a shift in the phase transition type, from upper-critical-solution-temperature (UCST), to upper-lower-critical-solution-temperature (U-LCST) with increasing free VA in the monomer mixture.     

Effect of Pressure on the Miscibility of Polyethylene/Poly(ethylene‐alt‐propylene) Blends

Summary: Effect of density, and hence pressure, on the miscibility of a 50:50 mol/mol PE/PEP blend was studied using a coarse‐grained MC simulation approach on a high‐coordination lattice, with the conformations of the coarse‐grained chains constrained by the RIS model. Interchain pair correlation functions are used to assess the miscibility of the mixtures. Miscibility increases with increasing temperature over the range −50–150 °C. It is rather insensitive to pressure at high temperatures, but at −50 °C, the blend miscibility increases with decreasing pressure. The findings are consistent with the fact that the blend is an UCST blend and that the simulation temperatures used, except −50 °C, were considerably higher than the UCST of the blend. The pressure dependence of the blend miscibility observed near −50 °C is also in agreement with the experimental observation that the blend exhibits a negative volume change of mixing. The present work demonstrates that the coarse‐grained MC approach, when it is used with periodic boundary cells of different sizes filled with the same number of chains, is capable of capturing the pressure dependence of UCST blends. In addition, such a simulation also provides us with insights about the molecular origin of the observed pressure dependence of miscibility. In the present case, the segregation of PE and PEP chains at low temperatures and high pressure simply originates from the fact that fully extended segments of PE chains tend to cluster so that their intermolecular interactions can be maximized. As the temperature increases, there is a decrease in the probability of a trans state at a C C bond in PE, and therefore the attraction between the PE chains is reduced at higher temperatures, promoting miscibility and the UCST behavior.

Density (pressure) dependence of the 2^nd shell pair correlation function values for a 50/50 PE/PEP blend at −50 °C.     

Miscibility maps for polymer blends: Effects of temperature,pressure, and molecular weight

We study a Gibbs free energy model for describing the thermodynamics of compressible polymer blends in the case of nonpolar polymers. This model is a mean field model equivalent to the cell model of Prigogine et al. and close also to the model by Flory‐Orvoll and Vrij. The model is expressed as a function of the interaction energies between monomer pairs (a, b, and c), the degrees of polymerization (X_A and X_B), a close packing parameter ρ₀, the temperature, and the pressure. We derive an analytical expression regarding blend miscibility. All the already observed phase behaviors are recovered: the occurrence of two kinds of upper critical solution transition (UCST): case‐I and case‐II UCST for which the pressure has a destabilizing or stabilizing effect, respectively, and lower critical solution transition; cases where the pressure have a non‐monotonous effect on the UCST temperature; cases where the spinodal lines close up under high pressures; and the so‐called hour‐glass transition. The model allows for making explicit the effect of the different physical parameters on phase behavior. We calculate complete miscibility maps regarding the occurrence of the various possible kinds of transitions in the 2D space b/a and X_A, for different values of , applied pressure P, and chain length ratios. This approach may come as a complement to already existing, more quantitative and elaborated approaches. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 419–443     

高分子链的去拥挤转变及低温流动

简述了拥挤理论的基本原理,运用拥挤理论来说明高分子链间弱相互作用对高分子链所处的状态的影响,特别是对高分子玻璃化转变的影响.在实验中,采用固体核磁共振方法探测高分子的链间邻近度,并比较了不同链间邻近度的高分子样品在玻璃化转变温度以下的压力诱导流行行为,发现即使测试温度比高分子玻璃化转变温度低132℃,高分子链在压力下依...     

COMPATIBILITY AND PHASE BEHAVIOR OF PS/SBR BLEND Ⅰ. EFFECT OF MOLECULAR WEIGHT OF PS

The results of this study reveals not only the sensitivity of the compatibility of PS with SBR to the molecular weight (MW) of PS and temperature, but also some other interesting characteristics, i. e., unusual morphology change during the process of mixing with increase in temperature of specimen preparation observed under optical microscope and double-peak UCST curves for three blends with PS of low MW from DSC data. Acording to the amount of inward shift of the component T_g's and the broadening of the transition regions, it may be said that this polymer pair is compatible only when the MW of PS is low, and even then there still exists micro-heterogeneity.     

(p,V,T) Behaviour and miscibility of (polysulfone+THF+carbon dioxide) at high pressures

The (p,V,T) behaviour and the miscibility of polysulfone in binary fluid mixtures of tetrahydrofuran (THF) and carbon dioxide (CO₂) have been investigated in the temperature range from (300 to 425) K at pressures up to 70 MPa. Densities of polysulfone solutions (mass fraction=0 to 0.496) in a solvent mixture of THF and CO₂ with a mass fraction of CO₂ of 0.1 were determined as a function of pressure from the homogeneous one-phase region through the phase separation point into the two-phase region at selected temperatures. The densities at the demixing pressures at these temperatures were also determined. No significant changes in density were found across the phase boundary, indicating that coexisting phases must have similar densities, which is often the case with (liquid+liquid) phase separation in high-pressure systems. The variations of density or specific volume with polymer concentration have also been investigated at selected temperatures and pressures. The data show unique features which are helpful in understanding the phase behaviour of this system which shows multiple miscibility windows. The isothermal compressibility of the polymer solutions as determined from the density data does not show any significant dependence on polymer concentrations. The compressibilities display the expected decrease with pressure and increase with temperature.     

Phase diagram for microphase separation transition in poor solvent polymer solutions

In the present paper, we consider the possibility of microphase separation transition in poor solvent polymer solutions. It is shown that this phenomenon can take place if the following two conditions are fulfilled: i) there is a large entropic contribution to the entropy of polymer/solvent mixing, i.e., solvent acts like a plastisizer; ii) this entropic contribution is nonlocal. Both conditions are met below the glass transition temperature for the pure polymer near the so-called Berghmans point when the glass transition curve intersects the liquid-liquid phase separation curve for polymer solutions. The phase diagram for the microphase separation transition is calculated within the framework of weak segregation approximation first proposed by Leibler for block-copolymer systems. The regions of stability of different microdomain structures (lamellar, triangular, body-centered-cubic) are obtained. It is shown that under certain conditions the phase diagram can have two critical points related to the macro- and microphase separation respectively.This paper is dedicated to Prof. E. W. Fischer on the occasion of his 65th Birthday.This work was done in the course of the Humboldt Research Award stay of A.R. Khokhlov at the Max-Planck-Institute for Polymer Research in Mainz. During this stay A.R.K. greatly benefited from numerous discussions with Professor E.W. Fischer who introduced him to the fascinating field of glass transition in polymer systems and formulated several new directions for future research.     

羧化聚苯醚和聚苯乙烯共混物的形态研究

研究了同时具有最高临界互溶温度和最低临界互溶温度的羧化聚苯醚／聚苯乙烯共混体系随退火温度的变化而发生的相形态结构的变化．研究了此共混体系的相分离机理．并发现了此特殊共混体系低温和高温区的相分离机理是不同的．从分子的结构和分子间特殊相互作用上探讨了此共混体系产生特殊相行为的原因．     

Artificial multiple criticality and phase equilibria: an investigation of the PC-SAFT approach

The perturbed-chain statistical associating fluid theory (PC-SAFT) is studied for a wide range of temperature, T, pressure, p, and (effective) chain length, m, to establish the generic phase diagram of polymers according to this theory. In addition to the expected gas-liquid coexistence, two additional phase separations are found, termed "gas-gas" equilibrium (at very low densities) and "liquid-liquid" equilibrium (at densities where the system is expected to be solid already). These phase separations imply that in one-component polymer systems three critical points occur, as well as equilibria of three fluid phases at triple points. However, Monte Carlo simulations of the corresponding system yield no trace of the gas-gas and liquid-liquid equilibria, and we conclude that the latter are just artefacts of the PC-SAFT approach. Using PC-SAFT to correlate data for polybutadiene melts, we suggest that discrepancies in modelling the polymer density at ambient temperature and high pressure can be related to the presumably artificial liquid-liquid phase separation at lower temperatures. Thus, particular care is needed in engineering applications of the PC-SAFT theory that aims at predicting properties of macromolecular materials.     

混合高聚物分相过程标度、分形与Monte Carlo模拟

基于光散射、Monte Carlo模拟标度理论和分形(Fractal)概念研究和分析了高分子混合体系不稳相分离过程结构函数的标度行为和成因, 结果表明相分离的形态是一种分形结构, 其分形维数不随时间变化. 结构函数的标度行为起源于相态的分形结构. 相态的分形结构是不稳相分离特征之一.