Application of the ISM EoS for polymer solutions and blends

A method for predicting an analytical equation of state for polymer mixtures and blends from surface tension and liquid state density at normal (ordinary) temperature (γ_n, ρ_n), as scaling constants, is presented. B₂(T) follows a promising corresponding-states principle. Calculation of (T) and b(T), the two other temperature-dependent constants of the equation of state, are made possible by scaling. As a result, γ_n and ρ_n are sufficient for determination of thermophysical properties of polymer mixtures and blends.

We applied the procedure to predict liquid density of poly(ethylene glycol) (PEG-200) + 1-octanol solutions and poly(propylene glycol) (PPG) + poly(ethylene glycol) (PEG-200) blends at compressed state with temperature range from 298.15 to 338.15 K and pressures up to 40 MPa. In this work, the ISM EoS is extended to polymer mixtures and blends as well as pure case without proposing any mixing rule.     

Volumetric profile of polymer melts from the ISM equation of state

Knowledge of the volumetric or pressure–volume–temperature (PVT) profile of molten polymers is important for both engineering and polymer physics. Ihm–Song–Mason (ISM) equation of state (EOS) has been employed to predict the volumetric properties of 12 molten polymers. The significance of the present paper is three temperature-dependent parameters of the ISM EOS to be determined using corresponding states correlations based on the molecular scaling constants, dispersive energy parameters between segments/monomers (ε) and segment diameter (σ) rather than bulk properties, e.g. the liquid density and temperature both at normal boiling point. The ability of the ISM EOS has been evaluated by comparing the results with 1390 literature datapoints for the specific volumes over the temperature range from 293 to 603.5 K and pressure range from 0.1 to 200 MPa. The average absolute deviation (AAD) of the calculated specific volumes from literature data was found to be 0.52%. The isothermal compressibility coefficients, κ_T values of molten polymers have also been predicted using the ISM EOS. From 684 datapoints examined, the AAD of estimated κ_T was equal to 7.55%. Our calculations on the volumetric and thermodynamic properties of studied polymers reproduce the literature data with reasonably good accuracy.     

Calculation of Density for Mixtures of Carbon Dioxide with Nitrogen and Methane from the ISM Equation of State

In this paper the analytical equation of state (EoS) proposed by Ihm‐Song‐Mason was applied to calculate molar volume of mixtures of carbon dioxide with nitrogen and methane. The pair interaction potential has been used to evaluate the second virial coefficients and the ISM EoS parameters (i.e. α and b). The calculated values of the aforesaid quantities were applied to predict the molar volumes for mixtures of carbon dioxide with nitrogen and methane. Agreement with experiment was excellent for both mixtures.     

Application of GC-PPC-SAFT EoS to amine mixtures with a predictive approach

The GC-PPC-SAFT equation of state (EoS) is a combination of a group contribution method [S. Tamouza et al., Fluid Phase Equilib. 222-223 (2004) 67-76; S. Tamouza et al., Fluid Phase Equilib. 228-229 (2005) 409-419] and the PC-SAFT EoS [J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244-1260] which was adapted to the polar molecules [D. Nguyen-Huynh et al., Fluid Phase Equilib. 264 (2008) 62-75]. It is here applied to the vapour pressure and liquid molar volume of primary, secondary and tertiary amines and their mixtures with n-alkanes, primary and secondary alcohols, using previously published group parameters. The mixing enthalpy is also evaluated for the binary systems. Binary interaction parameters k_ij are computed using a group-contribution pseudo-ionization energy, as proposed by Nguyen-Huynh [D. Nguyen-Huynh et al., Ind. Eng. Chem. Res. 47 (2008) 8847-8858]. A unique corrective parameter for the cross-association energy between amines and alcohols is used.The agreement with experimental data in correlation and prediction were found rather encouraging. The mean absolute average deviation (AAD) on bubble pressure is about 3.5% for pure amines. The mean AAD on the vapour-liquid equilibria (VLE) are respectively 2.2% and 5.5% for the amine mixtures with n-alkanes and alcohols. The AADs on saturated liquid volume are about 0.7% for the pure compounds and 0.9% for the mixtures. Prediction results are qualitatively and quantitatively accurate and they are comparable to those obtained with GC-PPC-SAFT on previously investigated systems.     

Calculating thermodynamic properties from perturbation theory: II. An analytic representation for the square-well chain fluid

An analytic representation of thermodynamic properties of the freely jointed square-well chain fluid is developed based on the thermodynamic perturbation theory of Barker–Henderson, Zhang and Weitheim. By using a real function expression for the radial distribution function and incorporating structural information for square-well monomer of TPT1 model, an analytic expression for the Helmholtz energy of square-well chain fluid is expanded from Zhang’s analytic expressions for thermodynamic properties of square-well monomer. The expression leads to good predictions of the compressibility factor, residual internal energy and constant-volume heat capacity for 4-mer, 8-mer and 16-mer square-well fluids when compared with the Monte Carlo (MC) simulation results. The incorporating structural information for square-well dimer of TPT-D model is also calculated. To obtain the constant-volume heat capacity needed, NVT MC simulations were performed.     

On-line analysis of polymer melt processes

Molten polymer process streams are difficult to analyze either in- or on-line because of sampling problems due to the high temperature and viscosity of the molten state. Real-time monitoring of chemical compositions in these processes can significantly improve safety and product quality and minimize process costs and waste. The information content of the mid-infrared spectrum combined with the recent development of rugged process Fourier transform (FT) IR spectrometers is stimulating the application of process FT-IR to industrial polymer melt processes. Sampling considerations for polymer melts are reviewed. Also, the use of FT-IR spectrometry for on-line measurements of the polymer composition for polymer blends and copolymers in the melt, and the question of how this information could be used to monitor and control the quality of the product given by the process are discussed.     

高聚物双流体配位模型状态方程的简化

对高聚物以流体配位模型状态方程进行了简化，忽略了其中的Ｑ项，以简化的状态方程对４２个纯高聚物（聚丙烯、聚苯乙烯、聚异丁烯和聚丁烯－１），２种纯溶剂（苯，环己烷）和２个高聚物／溶剂混合系（聚异丁烯／苯和聚异丁烯／环己烷）进行关联，结果表明，简化的状态方程与原方程同样具有很好的关联精度和温度适用性。     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

Common Intersection Points of Bulk Modulus for Liquefied Natural Gas (LNG) Mixtures

During recent developments on the theories and experimental techniques of compressed liquids and liquid mixtures, it has been revealed that there exist some regularities. Among these, the regularity found by Huang and O'Connell is that the isotherms of reduced bulk modulus of compressed liquids as a function of molar volume intersect at a common point. This intersection is a useful tool for evaluating the reliability of an equation of state (EOS) for producing equilibrium properties of matter. This paper also deals with an extension of the above regularity to some liquefied natural gas (LNG) mixtures including: N₂+CH₄, N₂+C₂H₆, CH₄+C₂H₆, CH₄+C₃H₈, and CH₄+C₄H₁₀ at different temperatures. The present work gives a theoretical analysis for the common bulk modulus point in terms of a statistical‐mechanical equation of state for mixtures. In addition, we have calculated excess molar volume of N₂+CH₄ mixture in terms of temperature and compared it with experimental values.     

Phase behaviour of globular protein and flexible polymer in an aqueous medium

A simple model for the phase behaviour of a globular protein and a flexible polymer in an aqueous medium is described, in which both the compact feature of the protein and the flexble feature of the polymer have been included. The phase diagrams calculated by using the model suggest that for a given protein, the behaviour depends strongly on the polymer molecular weight. Fluid-fluid-solid three-phase and fluid-fluid two-phase equilibria can be found only when the polymer molecular weight is sufficiently high; otherwise, the only two-phase region in the phase diagram is a fluid-solid two-phase region.     

Adsorption of TX100 and TX165 at the aqueous solution–air interface: free enthalpy of adsorption and equation of state

Surface tension measurements of aqueous solutions of TX100 and TX165 were made at different temperatures. The thermodynamic parameters of the adsorption calculated from the surface tension measurements, using several methods, have given slightly different values. The equation of state for the TX100 and TX165 monolayers at the solution–air interface was analysed. There is excellent agreement between the modified Volmer equation of state and the experimental π–A isotherms. Received: 13 July 1999/Accepted in revised form: 20 October 1999     

高聚物高压下的状态方程

本文从高分子体系内分子链间相互作用能出发,得到了一个描述高聚物高压下的等温状态方程 从实验中发现n、m为普适常数,n=6.14,m=1,16.在不存在转变的情况下,该方程对处于玻璃态、结晶态及液态高聚物体系均适用.     

双流体高聚物配位溶液理论——纯物质的状态方程及其应用

以Ｆｌｏｒｙ局部组合型囚胞理论为雏形，引进空穴数，建立了更符合流体特性的双流体高聚物配位统计模型，以配位分数和局部位分数替代原局部组成中面积接触分数和局部面积接触分数概念，用拟化学近似处理局部配位分数，导出纯物质的状态方程，并应用于聚丙烯（ＰＰ）、聚丁烯－１（ＰＢＴ）、聚苯乙烯（ＰＳ）三个体系的关联，取得了良好的关联精度，根据ＰＰ和ＰＢＴ的链节结构与空穴数的关系，预言了高聚物的链节结构和空穴数与聚     

Measurement of thermal diffusivity in polymer melts using forced Rayleigh light scattering

Thermal diffusivity measurements on three polymer melts were made using the Forced Rayleigh Light Scattering technique. The polymers, which were tested at room temperature where they are in the molten state, included a polydimethylsiloxane and two polyisobutylenes. The optical setup and procedures developed in this study to conduct thermal Forced Rayleigh Light Scattering experiments are shown to be capable of producing thermal diffusivity data with a high degree of accuracy and precision. From measurements on a reference fluid (ethanol), experimental error was estimated to be no greater than 2%, and could be reduced to less than 1% by appropriate design of a series of experiments. Discrepancies of 4 and 14% in thermal diffusivity data on the polymer samples between measured values and those found in the literature were observed. It is suggested that these deviations are attributable to either sample variations or to errors in the techniques used in previous investigations. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1069–1078, 1999     

A new cubic equation of state for prediction of VLE of polymer solutions

A new cubic equation of state (CEOS) is proposed based on temperature–pressure superposition principle. A generic CEOS form, with the Peng–Robinson parameters, is used and a temperature-dependent attractive term a(T)$a(T)$ is developed, allowing an easy calculation of thermodynamic properties and vapor–liquid equilibrium. The new equation is applied to pure polymer and polymer solutions and its results are compared with those of two others equations of state. For polymer solutions, two mixing rules without binary interaction parameters were used. The vapor–liquid equilibrium (VLE) predictions showed good agreement with experimental data as well as pressure–volume–temperature (PVT) behavior of polymer liquids, attesting the appropriate form of the new equation proposed.     

About the numerical pitfalls characteristic for SAFT EOS models

This study demonstrates that SAFT EOS models might exhibit the practically unrealistic and even non-physical predictions due to the two factors, namely the temperature dependencies of a segment packing fraction and the very high-polynomial orders by volume. The first factor is responsible for predicting the negative values of the heat capacities at very high pressures and the intersections of isotherms at high densities. The very high-polynomial orders of several SAFT EOS models result in prediction of the additional stable unrealistic critical points and the pertinent fictive phase equilibria. It is demonstrated that the unrealistic phase splits might present the globally stable states established by the models, while the VLE matching the experimental data might be in fact metastable. In addition, the excessive complexity of certain SAFT models might result in wrong prediction of auxiliary thermodynamic properties of the experimentally available fluid phases. The undesired predictions discussed in the present study arise queries regarding the robustness and the over-all physical validity of the models under consideration in their present forms. This study discusses the ways of removing the numerical pitfalls.     

Confinement effects on the morphology of photopatterned porous polymer monoliths for capillary and microchip electrophoresis of proteins

We find that the morphology of porous polymer monoliths photopatterned within capillaries and microchannels is substantially influenced by the dimensions of confinement. Porous polymer monoliths were prepared by UV-initiated free-radical polymerization using either the hydrophilic or hydrophobic monomers 2-hydroxyethyl methacrylate or butyl methacrylate, cross-linker ethylene dimethacrylate and different porogenic solvents to produce bulk pore diameters between 3.2 and 0.4 microm. The extent of deformation from the bulk porous structure under confinement strongly depends on the ratio of characteristic length of the confined space to the monolith pore size. The effects are similar in cylindrical capillaries and D-shaped microfluidic channels. Bulk-like porosity is observed for a confinement dimension to pore size ratio >10, and significant deviation is observed for a ratio <5. At the extreme limit of deformation a smooth polymer layer 300 nm thick is formed on the surface of the capillary or microchannel. Surface tension or wetting also plays a role, with greater wetting enhancing deformation of the bulk structure. The films created by extreme deformation provide a rapid and effective strategy to create robust wall coatings, with the ability to photograft various surface chemistries onto the coating. This approach is demonstrated through cationic films used for electroosmotic flow control and neutral hydrophilic coatings for electrophoresis of proteins.     

Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids I. Single component n-alkane systems

The aim of this work is to develop spherically symmetric effective potentials allowing bulk thermodynamic properties and surface tension of molecular fluids to be predicted semiempirically by the use of statistical mechanical methods. Application is made to the straight chain alkane fluids from methane to decane. An effective Lennard-Jones potential is generated with temperature-dependent parameters fitted to the critical temperature and pressure and to Pitzer's acentric factor. Insertion of this potential into the generalised van der Waals (GvdW) density functional theory yields bulk properties in good agreement with experiments. The surface tension is overestimated for the longer alkane chains. In order to account for the surface tension, an independently adjustable attractive range of interaction is required and obtained through the use of square-well potentials chosen so as to leave the bulk thermodynamics unaltered while the attractive range is fitted to the surface tension at a single temperature. The GvdW theory, which includes binding energy, entropic and profile shape contributions, then generates surface tension estimates that are of good accuracy over the full range of available experimental data. It appears that, given a sufficiently flexible form, effective potentials combined with simple statistical mechanical theory can reproduce both bulk and non-uniform fluid data of great variety in an insighful and practically useful way.     

Persistence of regions with high segment density in polyethylene melts

Proton nuclear magnetic resonance (NMR) spin-spin relaxation measurements were made on three commercial-grade polyethylenes in the melt state, free of solvent. All samples exhibit a three-component relaxation behavior, with components being assigned to amorphous low-molecular weight material (non-network fraction), amorphous entangled network fraction, and an ordered or high-segmental-density fraction, in order of decreasing relaxation times. Sample thermal history is shown to have a considerable effect on the overall relaxation behavior, and therefore on the relative amounts of each of the three components in the melt. An adequate thermal treatment of samples produces an equilibrium melt with invariant composition of the three fractions. The effects of thermal history on the relative amount of high-segment-density regions in the melt parallels its effect on the fraction of crystalline material in the solid polymer. These results are evidence for the persistence of ordered regions in polyethylene at temperatures well above the crystalline melting point of the polymer. We further comment on the nature of the two slower relaxing components and present examples of how the components manifest themselves in other polymer characterization techniques. © 1992 John Wiley & Sons, Inc.