A numerical method for the study of nucleation of ordered phases

Ling Lin; Xiuyuan Cheng; Weinan E; An Chang Shi; Pingwen Zhang

doi:10.1016/j.jcp.2009.11.009

A numerical method for the study of nucleation of ordered phases

Ling Lin, Xiuyuan Cheng, Weinan E, An Chang Shi, Pingwen Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1797-1809
Number of pages	13
Journal	Journal of Computational Physics
Volume	229
Issue number	5
DOIs	https://doi.org/10.1016/j.jcp.2009.11.009
State	Published - Mar 1 2010

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

Keywords

Block copolymer
Critical nuclei
Liquid crystal
Minimum energy path (MEP)
Nucleation
Ordered phase
String method

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10.1016/j.jcp.2009.11.009

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title = "A numerical method for the study of nucleation of ordered phases",

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.",

keywords = "Block copolymer, Critical nuclei, Liquid crystal, Minimum energy path (MEP), Nucleation, Ordered phase, String method",

author = "Ling Lin and Xiuyuan Cheng and Weinan E and Shi, {An Chang} and Pingwen Zhang",

note = "Funding Information: All the computing was carried out on the HP Linux Cluster CCSE-I (HP DL360 G4). We would like to express our deepest gratitude to the substantial help of computer center and CCSE. A.-C. Shi would like to thank Peking University and Prof. Pingwen Zhang for their hospitality, and NSERC for financial support. The work of E is partially supported by ONR under Contract No. N00014-01-1-0674 . PWZ would like to thank the financial support by the special funds for Major State Research Projects ( 2005CB321704 ), and National Natural Science Foundation of China ( 50930003 ).",

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T1 - A numerical method for the study of nucleation of ordered phases

AU - Lin, Ling

AU - Cheng, Xiuyuan

AU - E, Weinan

AU - Shi, An Chang

AU - Zhang, Pingwen

N1 - Funding Information: All the computing was carried out on the HP Linux Cluster CCSE-I (HP DL360 G4). We would like to express our deepest gratitude to the substantial help of computer center and CCSE. A.-C. Shi would like to thank Peking University and Prof. Pingwen Zhang for their hospitality, and NSERC for financial support. The work of E is partially supported by ONR under Contract No. N00014-01-1-0674 . PWZ would like to thank the financial support by the special funds for Major State Research Projects ( 2005CB321704 ), and National Natural Science Foundation of China ( 50930003 ).

PY - 2010/3/1

Y1 - 2010/3/1

N2 - 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.

AB - 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.

KW - Block copolymer

KW - Critical nuclei

KW - Liquid crystal

KW - Minimum energy path (MEP)

KW - Nucleation

KW - Ordered phase

KW - String method

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A numerical method for the study of nucleation of ordered phases

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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