Introduction to Q-tensor theory

Nigel Mottram, C.J.P. Newton

Research output: Working paper

Abstract

This paper aims to provide an introduction to a basic form of the Q-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has been driven by investigations into the fundamental nature of defects and new applications of liquid crystals such as bistable displays and colloidal systems for which a description of defects and disorder is essential. The work in this paper is not new research, rather it is an introductory guide for anyone wishing to model a system using such a theory. A more complete mathematical description of this theory, including a description of flow effects, can be found in numerous sources but the books by Virga and Sonnet and Virga are recommended. More information can be obtained from the plethora of papers using such approaches, although a general introduction for the novice is lacking. The first few sections of this paper will detail the development of the Q-tensor approach for nematic liquid crystalline systems and construct the free energy and governing equations for the mesoscopic dependent variables. A number of device surface treatments are considered and theoretical boundary conditions are specified for each instance. Finally, an example of a real device is demonstrated.
LanguageEnglish
Publication statusPublished - 12 Sep 2014

Fingerprint

Tensor
Liquid Crystal
Defects
Surface Treatment
Modeling
Disorder
Free Energy
Governing equation
Display
Liquid
Boundary conditions
Dependent
Model
Form

Keywords

  • q-tensor model
  • q-tensor theory
  • liquid crystals

Cite this

Mottram, N., & Newton, C. J. P. (2014). Introduction to Q-tensor theory.
@techreport{09097abcb672450aa659cbf01670548d,
title = "Introduction to Q-tensor theory",
abstract = "This paper aims to provide an introduction to a basic form of the Q-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has been driven by investigations into the fundamental nature of defects and new applications of liquid crystals such as bistable displays and colloidal systems for which a description of defects and disorder is essential. The work in this paper is not new research, rather it is an introductory guide for anyone wishing to model a system using such a theory. A more complete mathematical description of this theory, including a description of flow effects, can be found in numerous sources but the books by Virga and Sonnet and Virga are recommended. More information can be obtained from the plethora of papers using such approaches, although a general introduction for the novice is lacking. The first few sections of this paper will detail the development of the Q-tensor approach for nematic liquid crystalline systems and construct the free energy and governing equations for the mesoscopic dependent variables. A number of device surface treatments are considered and theoretical boundary conditions are specified for each instance. Finally, an example of a real device is demonstrated.",
keywords = "q-tensor model, q-tensor theory, liquid crystals",
author = "Nigel Mottram and C.J.P. Newton",
year = "2014",
month = "9",
day = "12",
language = "English",
type = "WorkingPaper",

}

Introduction to Q-tensor theory. / Mottram, Nigel; Newton, C.J.P.

2014.

Research output: Working paper

TY - UNPB

T1 - Introduction to Q-tensor theory

AU - Mottram, Nigel

AU - Newton, C.J.P.

PY - 2014/9/12

Y1 - 2014/9/12

N2 - This paper aims to provide an introduction to a basic form of the Q-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has been driven by investigations into the fundamental nature of defects and new applications of liquid crystals such as bistable displays and colloidal systems for which a description of defects and disorder is essential. The work in this paper is not new research, rather it is an introductory guide for anyone wishing to model a system using such a theory. A more complete mathematical description of this theory, including a description of flow effects, can be found in numerous sources but the books by Virga and Sonnet and Virga are recommended. More information can be obtained from the plethora of papers using such approaches, although a general introduction for the novice is lacking. The first few sections of this paper will detail the development of the Q-tensor approach for nematic liquid crystalline systems and construct the free energy and governing equations for the mesoscopic dependent variables. A number of device surface treatments are considered and theoretical boundary conditions are specified for each instance. Finally, an example of a real device is demonstrated.

AB - This paper aims to provide an introduction to a basic form of the Q-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has been driven by investigations into the fundamental nature of defects and new applications of liquid crystals such as bistable displays and colloidal systems for which a description of defects and disorder is essential. The work in this paper is not new research, rather it is an introductory guide for anyone wishing to model a system using such a theory. A more complete mathematical description of this theory, including a description of flow effects, can be found in numerous sources but the books by Virga and Sonnet and Virga are recommended. More information can be obtained from the plethora of papers using such approaches, although a general introduction for the novice is lacking. The first few sections of this paper will detail the development of the Q-tensor approach for nematic liquid crystalline systems and construct the free energy and governing equations for the mesoscopic dependent variables. A number of device surface treatments are considered and theoretical boundary conditions are specified for each instance. Finally, an example of a real device is demonstrated.

KW - q-tensor model

KW - q-tensor theory

KW - liquid crystals

UR - http://arxiv.org/abs/1409.3542

M3 - Working paper

BT - Introduction to Q-tensor theory

ER -

Mottram N, Newton CJP. Introduction to Q-tensor theory. 2014 Sep 12.