Bong Ho Chang

Chain length dependence of liquid—liquid equilibria of binary polymer solutions

Abstract The proposed model in our previous study 1 improves the mathematical approximation defect and gives a new expression for the configurational energy of mixing using the fractional form rather than the algebraic form with second-order approximation for the configurational energy of non-random mixing 2 . In this study, we introduce new universal constants to take into account the chain length dependence of a polymer in a solvent. Our proposed model shows a slight discrepancy when compared with experimental data and gives a better understanding of phase equilibria dependence on the chain length of the polymer.

VAPOR-LIQUID EQUILIBRIA AND LIQUID-LIQUID EQUILIBRIA CALCULATIONS OF BINARY POLYMER SOLUTIONS

Abstract We investigate vapor–liquid equilibria (VLE) for polymer/solvent systems using the same model binary parameters obtained from liquid–liquid equilibria (LLE) calculations. For the systems affected by free-volume differences between molecules, the VLE calculation results are corrected by Elbro et al.s conceptual expression. In addition, we present the semi-quantitative description of contribution to VLE by oriented interaction. Our proposed model is directly applicable to VLE of binary polymer solution systems for various temperature ranges as well as for LLE calculations.

Liquid–liquid equilibria of binary polymer solutions with specific interactions

Abstract In our previous study, we proposed a new expression for the configurational energy of mixing taking into account non-random mixing effect and chain-length dependence of the polymer. But our model can not predict lower critical solution temperature (LCST) behaviours of liquid–liquid equilibria for binary polymer solutions. In this study, we extend our previous model to describe LCST behaviours of binary polymer solutions by employing a secondary lattice concept as a perturbation term to account for oriented interactions (or specific interactions).

Salting-out in the aqueous single-protein solution: the effect of shape factor

A molecular-thermodynamic model is developed to describe salt-induced protein precipitation. The protein-protein interaction goes through the potential of mean force. An equation of state is derived based on the generalized van der Waals partition function. The attractive term including the potential of mean force is perturbed by the statistical mechanical perturbation theory. The precipitation behaviors are studied by calculating the partition coefficient with various conditions such as the ionic strength and the shape of protein. Our results show that the protein shape plays a significant role in the protein precipitation behavior.

Molecular thermodynamics approach for liquid–liquid equilibria of the symmetric polymer blend systems

Abstract We extended and simplified the modified double-lattice model for polymer solution systems to binary polymer blend systems. The model has three model parameters, C β and C γ in a primary lattice and C a in a secondary lattice. Those are not adjustable parameters but universal constants. In comparison with Mullers Monte-Carlo simulation data for symmetric polymer blend ( r 1 =32 and r 2 =32), C γ is determined and C β is negligible for symmetric polymer blend systems. Also, C a is obtained from comparing with Panagiotopolous’ Monte-Carlo simulation data. In addition, oriented interactions between polymer segments are considered based on the secondary lattice concept. The proposed model describes very well phase behaviors of ordinary and oriented polymer blend systems.

Molecular thermodynamics of binary polymer solutions using modified double lattice model: Chain length dependence of primary lattice

In a previous study we modified a double lattice model by introducing a new interaction parameter, which improved the mathematical approximation defect, and gave a new expression for the Helmholtz energy of mixing. In the model the universal constants Cβ and Cγ in the primary lattice were determined by comparing them with literature Monte Carlo simulation data, which is the only case for r1 = 1 and r2 = 100 (case I). In this study we introduce new universal constants, Cβ and Cγ, as a function of the chain length of a polymer in a solvent (case II) by comparing them with other literature simulation data for various polymer chain lengths. The proposed model is compared with polymer–solvent systems. In an upper critical solution temperature phase behavior the theoretical results of case II were improved over those of case I. However, in a lower critical solution temperature phase behavior those of case I were not very sensitive to Cβ and Cγ.

Molecular thermodynamics approach for binary polymer solutions on the non-random mixing effect

Abstract The lattice model gives a starting point for a theoretical description of the thermodynamic properties of polymer solution systems. Classical models, such as the Flory—Huggins model and the quasi-chemical model, present too narrow or parabolic coexistence curves when compared with experimental data. It is well known that failures of the lattice model are due to mathematical approximations for the effects of non-random mixing in order to gain an analytical solution. Moreover, the existing configurational energy of mixing, in which the residual terms are truncated, results in significant errors in the prediction of the coexistence curve calculations for polymer solution systems. The proposed model in this study improves the mathematical approximation defect and gives a new expression for the configurational energy of mixing. To correlate the energy of mixing term, including the effect of non-random mixing on the configurational thermodynamic properties of a binary mixture with simulation data, we use Monte-Carlo simulation data. Monte-Carlo simulation gives essentially exact results for the lattice model. The configurational Helmholtz energy is obtained upon combining the Gibbs—Helmholtz equation with Guggenheims athermal entropy of mixing as a boundary condition. The coexistence curves generated by the proposed model are compared with experimental data.

Liquid-liquid equilibria of polymer solutions : a closed miscibility loop phase behavior

In the phase behavior of binary polymer/solvent mixtures, a lower critical solution temperature (LCST) and hour-glass shaped and closed miscibility loop phase behavior are encountered. The closed miscibility loop phase behavior may be mainly due to highly oriented interactions such as hydrogen bonding. The purpose of this study is to describe closed miscibility loop phase behavior in the liquid-liquid equilibria of polymer solutions. To consider highly oriented interactions (or specific interactions), we employed a secondary lattice concept as a perturbation term.

Solvent activities of ordinary and associated binary polymer solutions: group-contribution method

Abstract A specified group-contribution method is proposed to estimate vapor–liquid equilibria (VLE) of ordinary and associated binary polymer solutions. van der Waals (vdW) energy parameters for dispersion and polar forces for ordinary systems without hydrogen bonding (h-b; Case I) are determined. In addition, the h-b energy parameters for associated systems are employed. Two cases are, respectively, taken into account for associated systems: solvent activities by the h-b interactions are nearly independent of the temperature (Case II); and solvent activities by the h-b interactions strongly depend on the system temperature (Case III). The temperature-dependent h-b parameter is also considered. Our proposed model shows good agreements with experimental data in solvent activity estimations for ordinary and associated binary polymer solution.

Molecular thermodynamics for polymer alloys with specific interactions

Abstract In our previous work, we proposed an expression for the Helmholtz energy using universal parameters correlated with energy-of-mixing results from Monte Carlo simulation for binary polymer–solvent solutions. In this study, we obtain new universal parameters for polymer/polymer alloy systems from Monte Carlo simulation data and we extend our previous model to polymer alloy systems. In addition, we introduce a specific interaction term based on a modified double-lattice model. The model includes the secondary lattice as a perturbation term to account for specific interactions. The coexistence curves generated by the proposed model are compared with experimental data.