Continuum theory of nematics

In conclusion, the theoretical model explains the main features of the experimental observations and provides a reliable numerical value for the threshold. This proves the underlying idea, i.e. that the observed phenomena is due to a Fredericks transition in optical field, which can be described by the continuum theory of nematics, taking into account the finite size of the deforming light beam. 

The hydrodynamic continuum theory of nematic liquid crystals was developed by Leslie [1,2] and Ericksen [3, 4] in the late 1960s. The basic equations of this theory are presented in Vol. 1, Chap. VII, Sec. 8. Since then, a great number of methods for the determination of viscosity coefficients have been developed. Unfortunately, the reliability of the results has often suffered from systematic errors leading to large differences between results. However, due to a better understanding of flow phenomena in nematic liquid crystals, most of the errors of earlier investigations can be avoided today. 

Eqs. [5] and [6] are the fundamental equations of the elastic continuum theory of nematic and cholesteric liquid crystals (for nematics Xo in Eq. [5] is set equal to ). In the following section we use the fundamental equations to solve four examples as illustrations for their applications. 

Oseen [1] and Frank [2] far before the development of LCD technology. The dynamic continuum theory of nematics, which is frequently called the nematodynamics, was developed by Ericksen [3] and Leslie [4] (hereafter referred to as E-L theory) based on the classical mechanics just in time for the upsurge of LCD technology. In conjunction with the electrodynamics of continuous media, the static and dynamic continuum mechanics of Oseen-Erank and E-L theory provided theoretical tools to analyze quantitatively key phenomena, e.g., Freedericksz transition of various configurations and associated optical switching characteristics. For the details of E-L theory [5-7] and its development [9,10], please refer to the articles cited. 

To characterize the diffraction properties of the LC grating, we estimated the director distribution in the cell based on the elastic continuum theory of nematic LCs. The elastic energy density of a deformed nematic LC, u, is given by... 

In general, the classical Fredericks transition in nematics can be fairly well-explained using continuum theory of nematic liquid crystals developed by Frank, Ericksen and Leslie. Before we present a detailed analysis on the optical Fredericks transition, which couples the interaction between the applied electromagnetic field of a light wave and the orientation of hquid crystals, we would like to briefly review the classical results (de Geimes and Frost 1993 Virga 1994 Stewart 2004). Many of our ideas here are borrowed from Stewart (2004). 

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