A Catastrophe-Theoretic Approach to Tricritical Points with Application to Liquid Crystals

A criterion to locate tricritical points in phase diagrams is proposed. The criterion is formulated in the framework of elementary catastrophe theory and encompasses all the existing criteria in that it applies to systems described by a generally nonsymmetric free energy which can depend on one or more order parameters. We show that tricritical points are necessarily given by free energies which are not 4-determined. An application to smectic-C liquid crystals is briefly discussed.

[1]  M. Calderer,et al.  Landau-de Gennes theory of isotropic-nematic-smectic liquid crystal transitions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Nair,et al.  Mean-field to tricritical crossover behavior near the smectic-A-smectic-C tricritical point. , 1988, Physical review letters.

[3]  R. Griffiths.  Proposal for Notation at Tricritical Points , 1973 .

[4]  B. Fung,et al.  Relation between the orientational ordering and the tricritical behavior for smectic‐A to smectic‐C phase transition , 1995 .

[5]  Robert Gilmore,et al.  Catastrophe Theory for Scientists and Engineers , 1981 .

[6]  Michel Demazure,et al.  Bifurcations and Catastrophes: Geometry Of Solutions To Nonlinear Problems , 2000 .

[7]  Epifanio G. Virga,et al.  Variational Theories for Liquid Crystals , 2018 .

[8]  L. Longa.  On the tricritical point of the nematic–smectic A phase transition in liquid crystals , 1986 .

[9]  L. Longa.  Invited Lecture. Order-parameter theories of phase diagrams for antiferroelectric smectic-A phases , 1989 .

[10]  G. de Matteis,et al.  Tricritical points in biaxial liquid crystal phases. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Cheng-Cher Huang.  The existence of a tricritical point in the smectic A-smectic C transition line , 1982 .

[12]  P. Mukherjee,et al.  Tricritical behavior of the smectic-A to smectic-C phase transition in a liquid crystal mixture. , 2008, The Journal of chemical physics.

[13]  A. Sonnet,et al.  Universal mean-field phase diagram for biaxial nematics obtained from a minimax principle. , 2006 .

[14]  Akhlesh Lakhtakia,et al.  The physics of liquid crystals, 2nd edition: P.G. De Gennes and J. Prost, Published in 1993 by Oxford University Press, Oxford, UK, pp 7,597 + xvi, ISBN: 0-19-852024 , 1995 .

[15]  G. de Matteis,et al.  Bifurcation analysis and computer simulation of biaxial liquid crystals. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  A. Sonnet,et al.  Dielectric shape dispersion and biaxial transitions in nematic liquid crystals. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  J. Straley,et al.  Ordered phases of a liquid of biaxial particles , 1974 .

[18]  E. Virga,et al.  Criterion for Tricritical Points in Liquid Crystal Phases , 2006 .

[19]  Martin Golubitsky,et al.  An Introduction to Catastrophe Theory and Its Applications , 1978 .

[20]  B. Widom,et al.  Multicomponent-Fluid Tricritical Points , 1973 .

[21]  Garland Cw,et al.  Nematic-smectic-C heat capacity near the nematic-smectic-A-smectic-C point. , 1987 .

[22]  E. Virga,et al.  Constrained stability for biaxial nematic phases , 2007 .