Abstract:
We consider a continuum theoretical description of a Smectic C monolayer
made of molecules that can undergo cis-trans isomerization when subject to
photo-activation. We use analytical and numerical methods to investigate the
dynamics of this system. We show that this system exhibits self-regulation
and the existence of propagating solitary waves, central features of an
active fluid. Thus we demonstrate that this system can serve as an
experimental platform to investigate the physics of this inherently
out-of-equilibrium class of materials. The specific results obtained in this
study are as follows : a) An equilibrium Smectic C monolayer can exist in
one of two states - a homogeneous state and a striped state. b) In the
presence of photo-activation the system develops propagating orientation
waves. These waves are not a pattern but are rather solitary waves resulting
from the self-regulating nature of the dynamics of the system. c) The
properties of these waves are characterized as a function of two system
parameters, the strength of spontaneous splay and the relaxation rate for
the equilibration process of the molecular isomerization. We find that the
speed of propagation increases as a function of both these parameters. c) We
localize the activation by illuminating the monolayer using slits of various
widths. In this case we find that the localization leads to the formation of
a domain wall at the edge of the activated region and propagating waves are
set up moving away from this domain wall. In the absence of diffusion, the
waves remain confined to the slit of illumination. When diffusion is ramped
up, the waves penetrate into the dark regions of the system and hence can
potentially serve for controlled pattern generation and stabilization in
this liquid crystal system.
