Growth Kinetics for a System with Conserved Order Parameter: Off Critical Quenches

TL;DR

This paper extends growth kinetics theory for systems with conserved order parameters to off-critical quenches, incorporating a new parameter M, and provides explicit scaling functions and predictions consistent with simulations.

Contribution

The paper introduces a generalized growth kinetics theory for off-critical quenches with a conserved scalar order parameter, including explicit scaling functions depending on M and dimensionality.

Findings

Scaling law L ~ t^{1/3} holds for all M.

Structure factor exhibits Porod's law at large Q.

Oscillations in the scaling function are suppressed near the coexistence curve.

Abstract

The theory of growth kinetics developed previously is extended to the asymmetric case of off-critical quenches for systems with a conserved scalar order parameter. In this instance the new parameter $M$, the average global value of the order parameter, enters the theory. For $M=0$ one has critical quenches, while for sufficiently large $M$ one approaches the coexistence curve. For all $M$ the theory supports a scaling solution for the order parameter correlation function with the Lifshitz-Slyozov-Wagner growth law $L \sim t^{1/3}$. The theoretically determined scaling function depends only on the spatial dimensionality $d$ and the parameter $M$, and is determined explicitly here in two and three dimensions. Near the coexistence curve oscillations in the scaling function are suppressed. The structure factor displays Porod's law $Q^{-(d+1)}$ behaviour at large scaled wavenumbers $Q$, and $Q^{4}$ behaviour at small scaled wavenumbers, for all $M$. The peak in the structure factor widens as $M$ increases and develops a significant tail for quenches near the coexistence curve. This is in qualitative agreement with simulations.