GENERAL ANALYSIS OF LINEAR NEMATIC ELASTICITY

A. I. Leonova and V. S. Volkovb 

UDC 532.584 + 612.117

The results of a general analysis of linear nematic elasticity 
on the basis of the five-parameter thermodynamic potential of de Gennes 
(DG) have been presented. It has been shown that, depending on the 
similarity of the material parameters to the conditions of marginal 
(limiting) stability, the DG potential describes the entire diversity 
of soft, semisoft, and harder behavior of weakly elastic nematic solids. 
It has been established that an additional soft mode of longitudinal 
stretching, acting along the director, can also exist alongside the 
known shear soft modes. A theorem on the special rotational invariance 
of the stress-tensor components, which is close to the principle of 
rotational invariance postulated earlier by Olmsted, has been proves. 
It has been shown that the stress tensor is symmetric if the shear 
modes are soft. In this case the reduced DG potential is reduced to 
a one-parameter nematic potential. If the mode of longitudinal stretching 
is also soft, this dimensionless parameter contains no additional 
parameters. Simple shear and simple tension have been considered as 
an illustration of the theory elaborated.

a The University of Akron, Akron, Ohio 44325-0301, USA; 
email: leonov@uakron.edu; b Institute of Petrochemical Synthesis,
Russian Academy of Sciences, 29 Lenin Ave., Moscow, 119991, Russia; 
email: vsvolk@ips.ac.ru. 
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 77, No. 4, 
pp. 36-45, July-August, 2004. Original article submitted 
October 29, 2003.