Prediction of χ Parameter of Polymer Blends by Combining Molecular Simulations and Integral Equation Theory

A combination of molecular simulations and integral equation theory is applied to predict the χ parameter for polymer blends. The inter- and intramolecular structures of the polymer blends are obtained from molecular dynamics (MD) simulations with atomistic models, which, in turn, are used to calculate the χ parameter using the integral equation theory (χ_I). This approach was employed to determine the temperature and concentration dependence of χ_I in the binary blends of atactic polypropylene (aPP)-head-to-head polypropylene (hhPP) and polyethylene (PE)-isotactic polypropylene (iPP), respectively. The χ parameter calculated from this approach (χ_I) is compared with the χ parameter estimated in the literature from phase equilibrium simulation data for aPP-hhPP blends. In the case of PE-iPP blends, χ_I is compared with the χ parameter obtained from fitting the structure factor to the random phase approximation. Our approach for calculating χ does not require any fitting, and the only input required for the approach is the radial distribution function which can be calculated from MD simulations. Thus, using this approach in conjunction with atomistic models provides a general methodology for predicting χ parameter of polymeric systems of any chemistry.