NUMERICAL STUDY OF PHASE TRANSITION PROBLEMS USING STRING METHOD

Abstract

String method is a powerful mathematical tool on numerical study of the phase transition problems. In this thesis, I develop the climbing string method in collective variables, which is a novel variation of the string method, focusing on the study of saddle point on the free energy landscape. Three types of phase transition problems are investigated using the new method and the existing ones. The phase transitions include (1) the vapor-to-liquid vapor condensation on hydrophobic surfaces patterned with pillar structures, (2) the Wenzel-to-Cassie phase transition of a liquid droplet on a grooved solid surface, (3) the isotropic-nematic phase transition of the collision of hard spherocylinders. The first problem is studied using the phase field model and the last two problems are studied on the free energy landscape in atomistic system. New phenomenons for phase transitions are observed and discussed.