J. Phys. II France
Volume 5, Numéro 3, March 1995
Page(s) 397 - 411
DOI: 10.1051/jp2:1995140
J. Phys. II France 5 (1995) 397-411

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

E.E. Pashkovsky1, W. Stille2 and G. Strobl2

1  Institute of Macromolecular Compounds, Academy of Sciences of Russia, Bolshoi pr. 31, St. Petersburg, 199004, Russia
2  Fakultät für Physik, Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany

(Received 4 October 1994, accepted in final form 25 November 1994)

Periodic pattern formation at the Frederiks transition in the magnetic field has been studied 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 K2, the rotational viscosity $\gamma_1$, and the wavelength of the periodic distortion $\lambda$. For polymer concentrations $0\leq w \leq 1 \%$ the values of $\lambda$ were found to follow a power law $\lambda \propto (B-B_{\rm c})^{-\beta}$ with $\beta \approx 1/2$, where $B_{\rm c}$ is the critical field for formation of periodic patterns. A strong effect of the polymer molecules on $B_{\rm c}$ has been observed, due to the contribution of the macromolecules to the shear Miesowicz viscosity coefficient $\eta_{\rm a}$ being large compared to the effect on $\gamma_1$. 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 $k=2\pi / \lambda$, we describe correctly the observed power law.

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