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

Abstract

ABSTRACT: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 C ␤ and C ␥ in the primary lattice were determined by comparing them with literature Monte Carlo simulation data, which is the only case for r 1 ϭ 1 and r 2 ϭ 100 (case I). In this study we introduce new universal constants, C ␤ and C ␥ , 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 C ␤ and C ␥ .

Solvent quality as reflected in concentration- and temperature-dependent Flory-Huggins interaction parameters

“…The LCT7,8 is a more recent concept that shows some very promising features but appears to be too complicated for practical purposes. Certain simplifications reported in the literature9–11 sacrifice some of the capabilities of the LCT but reduce the number of adjustable parameters to one or two: r stands for the number of segments of the components, c is either a constant11 stemming from Monte Carlo simulation or a quantity that depends on chain length,10 and the ϵ values represent interaction energies. The following relations hold true for the c parameters: The reduced enthalpy effect ϵ˜ is given by Once the system is chosen, the exchange energy ϵ˜ is the only unknown parameter.…”

Group contribution method for the swelling behavior of thermo‐responsive hydrogels

“…The universal constants and are determined by comparing lattice polymer simulation data with chain lengths =1 and =100, respectively. However, it has been reported that the universal constants strongly depend on the chain length and converge to certain values as increases . The values of universal constants for a hydrogel system, however, are difficult to estimate from simulation data because the mixing contribution is determined by interactions between the solvent and a linear polymer with infinite chain length.…”

“…However, it has been reported that the universal constants strongly depend on the chain length and converge to certain values as r i increases. [36][37][38] The values of universal constants for a hydrogel system, however, are difficult to estimate from simulation data because the mixing contribution is determined by interactions between the solvent and a linear polymer with infinite chain length. We therefore revise the universal constants C c and C b to to zero and 0.3, respectively to obtain a mathematically optimized model for a hydrogel system.…”

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

“…Oh and Bae [8] modified the double-lattice model by introducing new universal parameters and simplified the expression of the Helmholtz energy of mixing. In addition, Chang and Bae [9] modified the parameters, which were obtained from limited simulation results, by making them functions of the chain length of a polymer. The resulting model successfully describes liquid-liquid equilibria of binary mixtures with various polymer molecular weights and provided a better understanding of dependency on the chain length of the polymer.…”