499 research outputs found
Contributions of Repulsive and Attractive Interactions to Nematic Order
Both repulsive and attractive molecular interactions can be used to explain
the onset of nematic order. The object of this paper is to combine these two
nematogenic molecular interactions in a unified theory. This attempt is not
unprecedented; what is perhaps new is the focus on the understanding of
nematics in the high density limit. There, the orientational probability
distribution is shown to exhibit a unique feature: it has compact support on
configuration space. As attractive interactions are turned on, the behavior
changes, and at a critical attractive interaction strength, thermotropic
behavior of the Maier-Saupe type is attained.Comment: 14 pages, 4 figure
Predicting phase equilibria in polydisperse systems
Many materials containing colloids or polymers are polydisperse: They
comprise particles with properties (such as particle diameter, charge, or
polymer chain length) that depend continuously on one or several parameters.
This review focusses on the theoretical prediction of phase equilibria in
polydisperse systems; the presence of an effectively infinite number of
distinguishable particle species makes this a highly nontrivial task. I first
describe qualitatively some of the novel features of polydisperse phase
behaviour, and outline a theoretical framework within which they can be
explored. Current techniques for predicting polydisperse phase equilibria are
then reviewed. I also discuss applications to some simple model systems
including homopolymers and random copolymers, spherical colloids and
colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like
colloidal particles; the results surveyed give an idea of the rich
phenomenology of polydisperse phase behaviour. Extensions to the study of
polydispersity effects on interfacial behaviour and phase separation kinetics
are outlined briefly.Comment: 48 pages, invited topical review for Journal of Physics: Condensed
Matter; uses Institute of Physics style file iopart.cls (included
Dynamics of the Ericksen-Leslie Equations with General Leslie Stress I: The Incompressible Isotropic Case
The Ericksen-Leslie model for nematic liquid crystals in a bounded domain
with general Leslie and isotropic Ericksen stress is studied in the case of a
non-isothermal and incompressible fluid. This system is shown to be locally
well-posed in the -setting, and a dynamic theory is developed. The
equilibria are identified and shown to be normally stable. In particular, a
local solution extends to a unique, global strong solution provided the initial
data are close to an equilibrium or the solution is eventually bounded in the
topology of the natural state manifold. In this case, the solution converges
exponentially to an equilibrium, in the topology of the state manifold. The
above results are proven {\em without} any structural assumptions on the Leslie
coefficients and in particular {\em without} assuming Parodi's relation
Computers and Liquid State Statistical Mechanics
The advent of electronic computers has revolutionised the application of
statistical mechanics to the liquid state. Computers have permitted, for
example, the calculation of the phase diagram of water and ice and the folding
of proteins. The behaviour of alkanes adsorbed in zeolites, the formation of
liquid crystal phases and the process of nucleation. Computer simulations
provide, on one hand, new insights into the physical processes in action, and
on the other, quantitative results of greater and greater precision. Insights
into physical processes facilitate the reductionist agenda of physics, whilst
large scale simulations bring out emergent features that are inherent (although
far from obvious) in complex systems consisting of many bodies. It is safe to
say that computer simulations are now an indispensable tool for both the
theorist and the experimentalist, and in the future their usefulness will only
increase.
This chapter presents a selective review of some of the incredible advances
in condensed matter physics that could only have been achieved with the use of
computers.Comment: 22 pages, 2 figures. Chapter for a boo
- …