Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

TL;DR

This paper analyzes the nucleation process of stable cylinders from a metastable lamellar phase in diblock copolymer melts, providing an analytical model for interfacial free-energy and critical droplet characteristics.

Contribution

It introduces an analytic expression for the anisotropic interfacial free-energy between cylinders and lamellae, and characterizes the shape and size of critical droplets near the phase boundary.

Findings

Interfacial free-energy is anisotropic and lower when cylinders are perpendicular to the interface.

Critical droplets are lens-shaped with aspect ratios of 4-10.

Nucleation barriers range from 30 to 40 k_B T near the phase boundary.

Abstract

The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet interfacial profile, an analytic expression for the interfacial free-energy of an interface of arbitrary orientation between cylinders and lamellae is found. The interfacial free-energy is anisotropic, and is lower when the cylinder axis is perpendicular to the interface than when the cylinders lie along the interface. Consequently, the droplet shape computed via the Wulff construction is lens-like, being flattened along the axis of the cylinders. The size of the critical droplet and the nucleation barrier are determined within classical nucleation theory. Near the lamellar/cylinder phase boundary, where classical nucleation theory is applicable, critical droplets of size 30--400 cylinders across with aspect ratios of 4--10 and nucleation barriers of 30--40 k_B T are typically found. The general trend is to larger critical droplets, higher aspect ratios and smaller nucleation barriers as the mean-field critical point is approached.