聚合物液体的状态方程

本文分析介绍了三个最广泛使用的聚合物液体状态方程，Ｆｌｏｒｙ、ＳＬ和ＳＳ方程及作者开发的三个新方程ＳＨＴ、ＳＨＴＦ和ＯＣＭ的理论基础和假设，并用１５个聚合物液体、１７个大分子量烃液体和６个常用有机溶剂的Ｐ－Ｖ－Ｔ数据作了比较。结果表明，ＯＣＭ方程精度最好，其他方程精度按ＳＳ、ＳＨＴ、ＳＨＴＦ、Ｆｌｏｒｙ、ＳＬ依次变差。结论是开放胞腔更接近液体的真实结构，空穴的引入可以改进胞腔理论的计算精度，Ｌ－Ｊ位能可以较好地反映液体中分子间的作用力。     

Effect of polydispersity on the cloud-point curves of polymer mixtures

A method is presented for the calculation of cloud-point curves of polymer–polymer mixtures when the polymers involved are polydisperse. The method is based on the Flory–Huggins free energy of mixing with a concentration-independent χ parameter. Numerical results are given for cases in which the molecular weight distributions are represented by the Schulz–Flory type. When the two polymers have similar average molecular weights and polydispersities, the cloud-point curves become flatter as the polydispersity increases. When the two polymers have similar average molecular weights but differ in polydispersity, the cloud-point curves become more skewed as the difference in the polydispersity increases. The results point out that, if the polydispersity effect is not properly accounted for, the value of χ deduced from experimental cloud points is liable to be in error, especially with regard to its temperature coefficient and its concentration dependence.     

Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations

A volume-translated Peng-Robinson (VTPR) equation of state (EOS) is developed in this study. Besides the two parameters in the original Peng-Robinson equation of state, a volume correction term is employed in the VTPR EOS. In this equation, the temperature dependence of the EOS energy parameter was regressed by an improved expression which yields better correlation of pure-fluid vapor pressures. The volume correction parameter is also correlated as a function of the reduced temperature. The VTPR EOS includes two optimally fitted parameters for each pure fluid. These parameters are reported for over 100 nonpolar and polar components. The VTPR EOS shows satisfactory results in calculating the vapor pressures and both the saturated vapor and liquid molar volumes. In comparison with other commonly used cubic EOS, the VTPR EOS presents better results, especially for the saturated liquid molar volumes of polar systems. VLE calculations on fluid mixtures were also studied in this work. Traditional van der Waals one-fluid mixing rules and other mixing models using excess free energy equations were employed in the new EOS. The VTPR EOS is comparable to other EOS in VLE calculations with various mixing rules, but yields better predictions on the molar volumes of liquid mixtures.     

Excess volumes and excess enthalpies of cyclohexanone with alkanes,benzene, toluene and tetrachloromethane at 298.15 K

Excess volumes and excess enthalpies have been measured for binary liquid mixtures of cyclohexanone with n-hexane, n-heptane, 2,2,4-trimethylpentane, benzene toluene and tetrachloromethane at 298.15 K. The results have been discussed in terms of the difference in molecular shape and specific interactions between unlike molecules. The Prigogine—Patterson—Flory equation of state theory has been used to evaluate the free volume and interactional contributions of the excess properties, and to predict excess volumes and excess enthalpies. The calculated values of V^E and H^E are in qualitative agreement with the experimental data in all the systems.     

Correlation of the mutual diffusion coefficients of binary liquid mixtures

A correlative UNIDIF model for the mutual diffusion coefficients of binary liquid mixtures is developed using statistical thermodynamics and the absolute reaction rate theory. In this model, a mole fraction average of the logarithm of the pure-component limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIQUAC equation which comprises two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from data regression, for each binary mixture. Mutual diffusion coefficients of nonpolar+nonpolar, nonpolar+polar and polar+polar fluid mixtures are correlated in this study. Optimal binary interaction parameters are presented. Correlation results using the UNIDIF model for mutual diffusion coefficient are satisfactory and are superior to those from other methods.     

Paul J. Flory

Paul J. Flory was a pioneer in the development of a quantitative understanding of polymer science and a leader in placing it among the major scientific disciplines. Through his energy, skill and genius, and by the judicious interplay of experiment and theory, he demonstrated that polymers are not the complicated, intractable systems they were thought to be earlier, but are treatable in a rigorous and straight-forward manner. From his first scientific paper on polymers in 1936 to his last contributions, published posthumously, in 1986, Paul Flory was involved in shaping a consistent view of polymer science. A unique ability, to perceive the dominant cause in a complex effect and to formulate the action of this most important element of a situation in a simple and straightforward model, made his contributions so helpful and relevant that still today his models are often chosen over later, more refined, more accurate ones – Flory's models and concepts are of penetrating insight and a simplicity that allows all polymer scientists to understand and use them. Flory was involved in a very broad range of topics: among other topics, he laid the foundation of the understanding of polymerization reactions, illuminated the thermodynamics and hydrodynamics of polymer solutions and through this the nature of the polymer-solvent interactions and the θ-state, formulated important models of rubber elasticity, and investigated with excellent success polymeric crystals and liquid crystals. A contribution of great importance was the development of the rotational isomeric state method to the treatment of macromolecules of arbitrary size and structure and for many properties. His achievement was recognized by numerous awards, honorary degrees, and the Nobel Prize in 1974. Paul J. Flory, born on June 19, 1910, died on September 8, 1985.     

改进的聚合物溶液理论

在高分子溶液理论中引入Gibbs分布 ,用统计物理学方法重新推导出了聚合物溶液的热力学公式 .将高分子溶液的自由能和熵分三部分进行了计算 ,无热平动部分 ,无热构象部分和构象有热部分 .无热平动自由能和无热构象自由能分别等于Flory Huggins混合自由能公式的前两项 ,构象有热部分引入了Gibbs分布 ,考虑了链段 溶剂分子相互作用对高分子构象的影响 .在分子间的相互作用足够小时 ,又回到了FH公式     

Enthalpy of mixing for polymer solutions based on Gibbs excess function limit of hard spheres mixtures

Enthalpy of mixing of polymer with solvent has been evaluated by the new polymer/solvent theory proposed by the authors in a previous article. The new theory was based on the excess Gibbs function limit of hard sphere mixtures with infinite size difference. The calculated enthalpy of mixing for polymer/solvent mixtures by the new theory, agreed with experimental data with good accuracy and indicated that the theory is capable to produce the enthalpy of mixing in the whole concentration range of polymer compared with Flory–Huggins theory. Also the calculations provided information on the studied polymer chains and the molecular interaction effects which were consistent with the properties of polymers and solvents used in the mixtures.     

A quantitative model for the specific volume of polymer–diluent mixtures in the glassy state

A mathematical model to describe the specific volume of glassy mixtures of a polymer and a low molecular weight diluent or additive is presented. The model is based on understandable physical assumptions and relies on parameters that can be determined experimentally or estimated from methods available in the literature. The predictions of the model show good agreement with the experimental data for mixtures of four polymers with diluents that in the pure state are liquid, glassy, or crystalline. The observed negative departure from volume additivity, as defined by simple additivity of the specific volume of the pure glassy polymer and the pure amorphous diluent, is the result of the relaxation of the excess volume of the glassy mixture relative to the equilibrium state caused by mixing two components with different glass transition temperatures. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1037–1050, 1998     

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.

     

Flory状态方程理论与聚合物混合物的热力学

由Flory状态方程理论的化学位公式推导了二元混合物的亚稳单相极限线,同时导出了状态方程参数的温度、压力依赖性,计算表明Flory理论是可以像McMaster修正理论一样描述聚合物的相溶性行为的。 指出前人的工作由于假定相互作用能和熵参数均为0,分子量和状态方程参数对相界的影响被誇大了,相分离也只发生在很窄的浓度范围内。如果考虑了实际体系中相互作用能和熵参数均不为0,上述因素对相界的影响以及相界的形状将趋于合理。     

A novel equation of state for the prediction of thermodynamic properties of fluids

This work proposes a new equation of state (EOS) based on molecular theory for the prediction of thermodynamic properties of real fluids. The new EOS uses a novel repulsive term, which gives the correct hard sphere close packed limit and yields accurate values for hard sphere and hard chain virial coefficients. The pressure obtained from this repulsive term is corrected by a combination of van der Waals and Dieterici potentials. No empirical temperature functionality of the parameters has been introduced at this stage. The novel EOS predicts the experimental volumetric data of different compounds and their mixtures better than the successful EOS of Peng and Robinson. The prediction of vapor pressures is only slightly less accurate than the results obtained with the Peng-Robinson equation that is designed for these purposes. The theoretically based parameters of the new EOS make its predictions more reliable than those obtained from purely empirical forms.     

Prediction of thermodynamic behavior of binary mixtures by applying the crossover approach to Soave–Redlich–Kwong equation of state

Thermodynamic analysis of binary mixtures near the critical region is essential for many chemical process designs. In this research, based on isomorphism principle and incorporating general crossover approach the original Soave–Redlich–Kwong (SRK) equation of state (EOS) was developed for the binary mixtures. We have introduced an additional term in the crossover function in order to take into account the difference between the classical critical parameters and the real critical parameters. The applicability of this crossover EOS was verified against methane–ethane mixture to describe their thermodynamic properties over a wide range of thermodynamic states, because of their wide applications. It is shown that based on this approach we can received too much more accuracy for predicting thermodynamic properties in comparison with classical form of SRK EOS.     

Closed-packed lattice model for polymer solution systems considering the chain length dependence effect: Correlating LLE,VLE, and gel swelling behaviors using identical interaction energy parameters

We propose a new Helmholtz energy of mixing equation following the original Flory–Huggins (F–H) closed-packed lattice model. Also, to overcome F–H mean-field approximation, we introduce new universal constants to consider chain length dependence of polymer in solvent and consider specific interactions to describe strongly interacting polymer systems. Our proposed model successfully describes liquid–liquid equilibria (LLE) for binary polymer–solvent systems using identical interaction parameters which do not depend on the polymer molecular weight. We also describe vapor–liquid equilibria (VLE) for polymer/solvent systems and swelling equilibria of thermosensitive hydrogel systems using the same energy parameters obtained from LLE calculations.     

Excess volume of mixing and equation of state theories

Equation-of state theories of Flory and of Sanchez and Lacombe describe both enthalpy and volume of mixing of binary systems using single component properties and only one binary parameter X₁₂. We have evaluated this parameter from literature enthalpy data for numerous mixtures of two aromatic hydrocarbons, of alkanes with aromatic compounds, and of alkanes with carbonyl compounds. We have used this X₁₂ for calculation of excess volumes and compared the results with our previously measured experimental data. The agreement was fair for mixtures of two nonpolar components. Nevertheless, mixtures containing either cyclohexane or benzene displayed anomalies that could be traced to special packing of molecules in these compounds when pure. For mixtures of carbonyl compounds with alkanes, the theories predicted the qualitative trends correctly, but the quantitative agreement was rather poor. These results tend to support a model in which the enthalpy(cohesive energy) is inversely proportional to volume (as in the theories considered) only for dispersive interaction. When polar-polar interactions are involved, the dependence of excess volume on the excess enthalpy is much weaker.     

Improper matching of solvation energy components in G-based mixing rules

The physical significance of terms in two excess Gibbs free energy (G^ex)-based mixing rules, the modified Huron–Vidal (MHV1) and Wong–Sandler (WS) mixing rule, are examined through the use of solvation free energy. It is found that these mixing rules are in fact matching the charging contributions of solvation in an equation of state (EOS) to the complete solvation free energy in a liquid activity coefficient model (LM). The cavity contributions in the EOS are canceled as a result of the constant liquid molar volume to molecular volume ratio. The underlying idea of G^ex-based mixing rules that the EOS should behave like a LM at some limiting condition breaks down due to such an improper matching of solvation free energy components.     

Excess volume and surface tension of some flavoured binary alcohols at temperatures 298.15, 308.15 and 318.15 K

ABSTRACT

From the measured work of Ching-Ta and Chein-Hsiun Tu, we have presented the theoretical results of Surface tension and excess volume for three binary systems: namely 2-Propanol+Benzyl alcohol(1), 2-Propanol+2-Phenylethnol(2) and Benzyl alcohol+2-Phenylethanol(3) at temperatures 298.15, 308.15 and 318.15 K and atmospheric pressure over the concentration range 0.05–0.95. Theoretical results were computed from Flory model, Ramaswamy and Anbananthan (RA) model and model devised by Glinski, and studied the mixing properties and interactions of these liquids. Deviations in the surface tension (?σ) were evaluated and fitted to the Redlich–Kister polynomial equation to derive the binary coefficients and standard errors. Moreover, McAllister multi-body interaction model based on Eyring’s theory of absolute reaction rates has also been applied. For liquid mixtures, the free energy of activation is additive, based on the proportions of the different components of the mixture and interactions of like and unlike molecules. The behaviour of the liquids was studied and correlated with the molecular interactions from these liquid state models. Conclusively, these non-associated and associated models were compared and tested for different systems showing that the McAllister multi-body interaction model yields good results as compared to associated models, while Flory model shows more deviations.     

Intermolecular interactions in polymer blends: 1D and 2D NMR studies

Most mixtures of high molecular weight polymers are not miscible in the absence of specific intermolecular interactions. We have used two dimensional NMR in solutions and in the solid state to probe these interactions and to gain a molecular level understanding of the forces that control polymer blend formation. The results show that weak, but specific intermolecular interactions often control the phase structure of polymer blends.     

Density, Viscosity, Velocity and Refractive Index of Binary Mixtures of Poly(Ethylene Glycol) 200 with Ethanolamine, m-Cresol and Aniline at 298.15 K

Densities, absolute viscosities, ultrasonic velocities and refractive indices of binary mixtures of poly(ethylene glycol) 200 with ethanolamine, m-cresol and aniline have been measured at 298.15 K, under atmospheric pressure, over the entire composition range. The experimental data have been used to calculate acoustic impedance, specific heat ratio and relative association for these binary mixtures. Excess molar volume, deviation in viscosity, deviation in refractive index, deviation in isentropic compressibility, excess acoustical impedance and excess Gibbs energy of activation for viscous flow have been plotted to determine the nature and extent of interaction present in the solutions. The results have been fitted to Redlich-Kister polynomial equation. The results have been explained in terms of specific intermolecular and intramolecular interactions present in the mixtures and are found to support each other. The isothermal compressibility for the binary mixtures was predicted by an equation based on Flory??s statistical theory and three rigid sphere equations.