⅔ -Power Law for Copolymer Lamellar Thickness Implies a ⅓ -Power Law for Spinodal Decomposition

Abstract

We demonstrate the relation $\ensuremath{\theta}=2\ensuremath{\varphi}$. Here the exponent $\ensuremath{\theta}$ is defined as $D\ensuremath{\sim}{N}^{\ensuremath{\theta}}$, where $D$ is the equilibrium lamellar thickness of the diblock copolymer ordered phase and $N$ is the molecular weight. The exponent $\ensuremath{\varphi}$ is defined as $l\ensuremath{\sim}{t}^{\ensuremath{\varphi}}$, where $l$ is the pattern size of the spinodally decomposing system (say, a binary alloy) and $t$ is the time.