Showing papers by "S. Chandrasekhar published in 1975"

The role of permanent dipoles in nematic order

Abstract: We propose a new model for the statistical description of short range order in nematic liquid crystals of positive dielectric anisotropy. We consider the molecules to be cylindrically symmet- ric and assume the pair potential to be of the form A*P 1 ,(cos θ ij ) - B*P 2 ( cos θ ij ) which favours an antiparallel arrangement of the perma- 11 nent dipoles. From physical considerations, antiferroelectric long range ordering is not expected to be present in nematics. Applying the Krieger-James approximation, solutions are obtained with an apolar or P 2 (cos θ) type of long range order, but allowing for antiferro- electric short range order. Two important consequences of the theory arc ( i ) the mean dielectric constant should increase slightly on passing from the nematic to the isotropic phase, (ii) the magnetic and electr~c birefringence in the isotropic phase should both vary approximately as ( T-T* ) -1 , where T* is the hypothetical second order transition point, except when the dipolar interactions are very strong, in which case the electric birefringence should exhibit a slower variation at tempe- ratures well above T*. Choosing values of A*/B*, illustrative calculations are given of the long range and short range order parameters, dielectric properties, electric and magnetic birefringence. The results are in general agreement with the experimental data for such compounds.

Flow of cholesteric liquid crystals—I: Flow along the helical axis

Abstract: It is shown that the essential features of Helfrich’s permeation model for flow along the helical axis of a cholesteric liquid crystal can be derived approximately on the basis of the Ericksen-Leslie theory

Dynamical theory of reflexion from cholesteric liquid crystals

Abstract: The analogy between the optical phenomena exhibited by cholesterics and the diffraction of x-rays from perfect crystals is empha-sized and some of its consequences are discussed. Difference equations similar to those formulated by Darwin in his dynamical theory lead to simple analytical expressions for the reflexion coefficient, rotatory power and circular dichroism which are shown to be in good agree-ment with the results of the rigorous electromagnetic treatment. An extension of the theory to absorbing systems at once yields the relevant formulae for the Borrmann effect in cholesterics. It is pointed out that this simple approach should be sufficient for most practical calculations.