A Universal Scaling Analysis of Nonisothermal Kinetics in Block Copolymer Phase Transitions

Recently, Farjas and Roura (FR) have proposed a universal scaling law to describe nonisothermal crystallization kinetics based on a modification of the conventionally used Avrami model. In this letter, we apply the approach of Farjas and Roura to analyze the kinetics of an order-order phase transition in a diblock copolymer solution. We present an analysis of kinetics of the hexagonally packed cylinders (HEX) to gyroid transformation in polystyrene-b-polyisoprene (SI) diblock copolymer solutions in dimethyl phthalate using time-resolved small-angle X-ray scattering (SAXS) measurements. By shifting and scaling time in terms of the time at which the transformation rate is maximal, data for samples at two different concentrations at different ramp rates collapse onto the single universal curve predicted by Farjas and Roura. The activation energy for this process was estimated by fitting to the FR model. An estimate of the activation energy was also obtained by Avrami analysis of temperature jump experiments on the same sample. These two estimates differ by a factor of 2, suggesting that the two methods probe different stages of the phase transformation.