Composition Dependency of the Flory-Huggins χ Parameter in Isotopic Polymer Blends

Flory-Huggins Theory has been the basis for understanding polymer/solvent and blended polymer thermodynamics for much of the last 50 years. Within this theory, a parameter (χ) was developed to account for the energy of dispersion between distinct components. Thin film self-assembly of diblock copolymers and polymer melts depends critically on this parameter, and in application, χ has generally been assumed to be independent of the concentrations of individual components in the system. However, Small Angle Neutron Scattering (SANS) data on isotopic polymer blends, such as polyethylene (PE) and deuterated polyethylene (dPE), have shown a parabolic concentration dependency for χ. In order to understand better the nature of χ and develop more accurate morphological data for polymer systems, an investigation of this concentration dependency was undertaken.

The focus of this research was to use Molecular Dynamics and Configurational Bias Monte Carlo simulations to test the Flory-Huggins interaction parameter in the PE-dPE system via both its structural (χ_S) and thermodynamic (χ_T) definitions. Structural calculations for χ_S were based on the Random Phase Approximation developed by de Gennes, which assumes that the structure factor (S(Q)) is linked to the Flory-Huggins parameter as shown in equation 1.

                                                                                                                                    1.

Here, g_D is the familiar Debye function,

                                                                                                                                    2.

and R_g is the radius of gyration of the polymer. Q is the wavenumber, and Φ and N are the volume fraction and chain length, respectively.

Thermodynamic information was obtained through thermodynamic integration of the free energy with χ_T defined using the original Flory-Huggins Theory, as shown in equation 3.

                                                                                                                                    3.

Here, k_B is the Boltzmann constant; T is the absolute temperature of the system, and DG is the change in Gibbs free energy.

Calculation of the structural and thermodynamic interaction parameters allowed X_S and X_T to be compared for internal consistency and then examined with respect to the experimental SANS data for the PE/dPE system.