Reliably Estimating Bare Chi from Compressible Blends in the Grand Canonical Ensemble

TL;DR

This paper investigates how to reliably estimate the bare chi parameter in polymer blends from experimental data, identifying which effective chi measures are accurate and how they are influenced by thermodynamic factors like density fluctuations.

Contribution

The study introduces a theory-independent method to identify effective chi measures that reliably estimate the bare chi in polymer blends, accounting for thermodynamic effects.

Findings

Conventional effective chi is not a reliable estimator of the bare chi.

A density fluctuation-free effective chi provides a good estimate of the bare chi.

Effective chi's show weak composition dependence and do not diverge at composition extremes.

Abstract

The bare chi characterizing polymer blends plays a significant role in their macroscopic description. Therefore, its experimental determination, especially from small-angle-neutron-scattering experiments on isotopic blends, is of prime importance in thermodynamic investigations. Experimentally extracted quantity, commonly known as the effective chi is affected by thermodynamics, in particular by polymer connectivity, and density and composition fluctuations. The present work is primarily concerned with studying four possible effective chi's, one of which is closely related to the conventionally defined effective chi, to see which one plays the role of a reliable estimator of the bare chi. We show that the conventionally extracted effective chi is not a good measure of the bare chi in most blends. A related quantity that does not contain any density fluctuations, and one which can be easily extracted, is a good estimator of the bare chi in all blends except weakly interacting asymmetric blends (see text for definition). The density fluctuation contribution is given by (Delta v^bar)**2/2TK_T, where Delta v^bar is the difference of the partial monomer volumes and K_T is the compressibility. Our effective chi's are theory-independent. From our calculations and by explicitly treating experimental data, we show that the effective chi's, as defined here, have weak composition dependence and do not diverge in the composition wings. We elucidate the impact of compressibility and interactions on the behavior of the effective chi's and their relationship with the bare chi.