*J. Phys. II France* **5**, 397
(1995)

# Periodic Pattern Formation in Side-Group Polymer Nematic
Solutions at the Twist Frederiks Transition

## E. E. Pashkovsky*, W. Stille and G. Strobl

### *Institute of Macromolecular Compounds, Academy of
Sciences of Russia, Bolshoi pr. 31, St. Petersburg, 199004, Russia

### Fakultät für Physik, Universität Freiburg,
Hermann-Herder-Str. 3, 79104 Freiburg, Germany

#### Abstract

Periodic pattern formation at the Frederiks transition in the magnetic
field has been studied for dilute solutions of a polymethacrylate with
mesogenic side groups in a nematic solvent, pentylcyanobiphenyl (5CB). For
this purpose, a combination of dielectric measurements and direct pattern
observations was used to determine the twist elastic constant
*K*_{2}, the rotational viscosity γ_{1}, and the
wavelength of the periodic distortion λ. For polymer concentrations
0 ≤ *w* ≤ 1 % the values of λ were found to
follow a power law
λ ∼ (*B* - *B*_{c})^{-β} with
β ≈ 1/2, where *B*_{c} is the critical field for
formation of periodic patterns. A strong effect of the polymer molecules on
*B*_{c} has been observed, due to the contribution of the
macromolecules to the shear Miesowicz viscosity coefficient η_{a}
being large compared to the effect on γ_{1}. In a simple
phenomenological model, which is constructed analogous to the Landau theory
for second order phase transitions, and uses an expansion of the growth rate
of the patterns in powers of the wavenumber
*k* = 2π / λ, we describe correctly the observed
power law.