(222bd) Composition Dependency of the Flory-Huggins ? 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_Dis the familiar Debye function,

                                                                                                                                    2.

and R_gis 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_Bis 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.