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Spinodal decomposition in filled polymer blends exhibiting upper critical solution temperature behavior

A. I. Chervanyov

TL;DR

The study addresses how solid fillers alter the thermodynamic stability and UCST-type phase behavior of binary polymer blends. It advances the Sanchez–Lacombe lattice-fluid framework to include finite-sized fillers, deriving filler-induced corrections to pressure and chemical potentials, and yielding both exact and low-compressibility spinodal conditions. A key contribution is the three-component stability criterion $S\ge 0$ with explicit $m_{ij}$ expressions, and a simple incompressible-limit form $S_{inc}$ that agrees with exact results within a few kelvin. The approach, validated against UCST data for EVA/HDPE with nanoclay, provides a computationally efficient tool for predicting and tuning miscibility in polymer–filler nanocomposites and highlights the role of osmotic effects and cross-interactions in filler-induced compatibilization.

Abstract

By extending the Sanchez-Lacombe lattice-fluid model for mixtures to the case of polymer blends containing solid fillers, we calculate the excess thermodynamic quantities arising from the presence of fillers. These results are then used to derive the spinodal stability condition of a filled polymer blend. In the low-compressibility limit, this condition reduces to a remarkably simple analytical expression that is derived self-consistently within the present framework. Comparison between the exact and approximate spinodal curves shows excellent agreement, with deviations in the spinodal temperature of less than 4 K, thereby validating the proposed approximation. The obtained analytical approximation enables a straightforward evaluation of the spinodal temperature without the extensive numerical calculations required to determine the exact spinodal condition. Both the exact and approximate spinodal conditions yield good quantitative agreement with experimental data for filled and unfilled blends.

Spinodal decomposition in filled polymer blends exhibiting upper critical solution temperature behavior

TL;DR

The study addresses how solid fillers alter the thermodynamic stability and UCST-type phase behavior of binary polymer blends. It advances the Sanchez–Lacombe lattice-fluid framework to include finite-sized fillers, deriving filler-induced corrections to pressure and chemical potentials, and yielding both exact and low-compressibility spinodal conditions. A key contribution is the three-component stability criterion with explicit expressions, and a simple incompressible-limit form that agrees with exact results within a few kelvin. The approach, validated against UCST data for EVA/HDPE with nanoclay, provides a computationally efficient tool for predicting and tuning miscibility in polymer–filler nanocomposites and highlights the role of osmotic effects and cross-interactions in filler-induced compatibilization.

Abstract

By extending the Sanchez-Lacombe lattice-fluid model for mixtures to the case of polymer blends containing solid fillers, we calculate the excess thermodynamic quantities arising from the presence of fillers. These results are then used to derive the spinodal stability condition of a filled polymer blend. In the low-compressibility limit, this condition reduces to a remarkably simple analytical expression that is derived self-consistently within the present framework. Comparison between the exact and approximate spinodal curves shows excellent agreement, with deviations in the spinodal temperature of less than 4 K, thereby validating the proposed approximation. The obtained analytical approximation enables a straightforward evaluation of the spinodal temperature without the extensive numerical calculations required to determine the exact spinodal condition. Both the exact and approximate spinodal conditions yield good quantitative agreement with experimental data for filled and unfilled blends.
Paper Structure (8 sections, 22 equations, 4 figures)

This paper contains 8 sections, 22 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. Stability of pure polymer blend
  4. Contribution of fillers to the thermodynamics and stability of a polymer blend
  5. Low-compressibility limit of a polymer blend
  6. Comparison with experiment
  7. Conclusions
  8. Derivation of the spinodal stability condition

Figures (4)

  • Figure 1: Comparison between experimental and theoretical spinodals of unfilled (EVA/HDPE) and filled (EVA/HDPE/NC) polymer blends. Symbols represent experimental data Hemmati2014, while solid and dashed lines correspond to the theoretical predictions obtained from Eqs. (\ref{['spin']}) and (\ref{['Eq2_1']}) for unfilled ($\varphi=0$) and filled blends, respectively. The presence of nanoclay (NC) lowers the spinodal temperature by approximately $5~\mathrm{K}$, in quantitative agreement with experimental observations.
  • Figure 2: Dependence of the free volume, defined as $1 - \eta$, on the EVA fraction $\phi$ at the spinodal for unfilled and filled polymer blends. The solid and dashed lines correspond to the theoretical predictions for the unfilled and filled blends, respectively.
  • Figure 3: Comparison between the exact and approximate spinodals for unfilled (EVA/HDPE) and filled (EVA/HDPE/NC) polymer blends. The exact spinodals (solid and dash-doted lines) are obtained from the full numerical solution of Eqs. (\ref{['spin']}) and (\ref{['Eq2_1']}), whereas the approximate spinodals (dashed and dash-dot-doted lines) are calculated from the analytical incompressible-limit expression, Eq. (\ref{['spin_inc']}).
  • Figure 4: Comparison between the experimental spinodals and the approximate theoretical spinodals obtained from Eq. (\ref{['spin_inc']}) for unfilled (EVA/HDPE) and filled (EVA/HDPE/NC) polymer blends. Symbols represent the experimental data Hemmati2014, while the solid and dashed lines correspond to the approximate theoretical spinodals for the unfilled and filled blends, respectively.