A numerical method for the study of nucleation of ordered phases

Authors:
Ling Lin;Xiuyuan Cheng;Weinan E;An-Chang Shi;Pingwen Zhang
Affiliations:
School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, PR China;School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, PR China;Department of Mathematics and PACM, Princeton University, Princeton, NJ 08544, USA;Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1;School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, PR China
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

A numerical approach based on the string method is developed to study nucleation of ordered phases in first-order phase transitions. Among other things, this method allows an efficient computation of the minimum energy path (MEP) during the nucleation process. The MEP provides information about the size, shape and free energy barrier of the critical nucleus. To improve the efficiency of the string method, a special initialization process is proposed. Constraints from physical models are treated using two methods, a generalized coordinates method and a projection method. Strategies for choosing the computational domain and defining the nucleus boundary are also introduced. The validity of our approach is illustrated by two nontrivial examples from soft condensed matter physics, namely the nematic-isotropic transition of liquid crystals and the ordered-to-ordered phase transition of diblock copolymers.