Composition Dependence of the Flory-Huggins Interaction Parameter in Polymer Blends: Structural and Thermodynamic Calculations

Flory-Huggins Theory has been the basis for understanding polymer solvent and blended polymer thermodynamics for much of the last 60 years. Within this theory, a parameter (χ) [chi] was included to quantify the enthalpic energy of dispersion between distinct components. Thin film self-assembly of polymer melts and block copolymers depends critically on this parameter, and in application, χ has generally been assumed to be independent of the concentrations of the individual components of the system. However, Small-Angle Neutron Scattering data on isotopic polymer blends, such as polyethylene and deuterated polyethylene, have shown a roughly parabolic concentration dependency for χ. Therefore, an investigation of this concentration dependency was undertaken from both thermodynamic (χ_T) [chi T] and structural (χ_S) [chi S] theories. Thermodynamic information was obtained through thermodynamic integration with χ_T defined using the original Flory-Huggins theory, and structural calculations for χ_S were based on the Random Phase Approximation of de Gennes. Comparison of the two theories revealed that χ_T and χ_S possess unique composition dependencies; however, via an expression developed within the Random Phase Approximation involving the second derivative of the Gibbs free energy function with respect to composition, χ_T can be transformed into χ_S while sacrificing some information related to system specificity.

Having investigated the composition dependencies of χ_T and χ_S, simulations were then performed to address the effects of wavenumber selection and chain length on the observed composition dependencies of χ_T and χ_S. Lastly, simulations on a polymer melt and its corresponding diblock copolymer were completed to investigate the differences in the characteristics of their interaction parameter composition dependencies. This study was inspired due to a desire to extend the original Flory-Huggins Theory to include a composition dependency for χ, thereby producing more accurate morphological data for polymeric systems, and develop more precise methods for calculation of the interaction parameter in polymer systems.