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*P₁,(cos θ_ij) - B*P₂( 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 P₂(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.