K. Kawasaki et Hr. Brand, LIFETIME RENORMALIZATION IN CRITICAL-DYNAMICS AS APPLIED TO THE ISOTROPIC-NEMATIC TRANSITION IN SIDE-CHAIN LIQUID-CRYSTALLINE POLYMERS, Physica. A, 208(3-4), 1994, pp. 407-422
We study the dynamic behavior near the isotropic-nematic transition in
liquid crystalline sidechain polymers using a mode coupling technique
as applied to the life-time. renormalization. To lowest order in mode
coupling we find for the dynamical critical exponent z for the relaxa
tion time of the order parameter the value z = 1.5, while in mean fiel
d approximation one obtains z = 1. This result is in agreement with re
cent experiments done in Martinoty's group on two different classes of
sidechain liquid crystalline polymers using electric and acoustic bir
efringence measurements. This qualitative difference in behaviour betw
een low molecular weight systems and sidechain polymers can be traced
back to nonlinear (cubic) cross coupling terms in the generalized ener
gy between the order parameter and the strain associated with the tran
sient network. The importance of such nonlinear cross coupling terms i
s corroborated further by recent measurements of the dynamic stress-op
tical coefficient in sidechain elastomers.