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Membranes
Motivation
Understanding the properties of two-dimensional interfaces and membranes
has become an important goal for many fields of science. Indeed the study
of such systems embraces disciplines as diverse as chemical physics, biology,
chemistry and theoretical physics. It is fascinating that the
behavior of red blood cells in the body can be described by theories which
are also used to explain the structure of the Universe at the earliest instants
after the Big Bang - the string theories of particle physics. We believe
that this simulation will fascinate undergraduates as their explorations range
from cosmology through materials to the biology of their life processes.
Much of our growing understanding of these systems has arisen from the use of
numerical simulation to model accurately the underlying microscopic dynamics -
calculations that are too lengthy to perform without the use of high performance
computers.
One of the most important applications of these ideas has been to amphiphilic
membranes.
Living cells possess a large number of such membranes, for example the
nuclear double membrane which separates the nucleus from the rest of the cell.
Existing Research Simulations
Real Membranes
Artificial amphiphilic membranes have recently become a lively research
field stimulated by their applications in industry, in medicine and in cosmetics. One can form from
them tunable filters which mimic the action of the biological membranes. They are able to close in
on themselves forming vesicles (small closed surfaces), which may act as drug carriers, designed
to open up and release their load when the `correct' physical and chemical conditions are found.
The surface tension of these membranes is typically very small, so that the shapes taken up by
such surfaces are determined by a `bending' energy which puts a penalty on large curvatures.
Furthermore, there are two main classes of such surface - fluid surfaces in which the molecules
can freely flow around each other for any shape of the membrane surface and polymerized
systems where the molecules are held in place by strong covalent bonds. At any finite
temperature these membranes undergo thermal fluctuations and the physical properties of the
surface depend on the interplay between these disordering effects and the ordering associated
with a curvature-suppressing energy term. Complex phase structures exist between `smooth'
surfaces, `crumpled' surfaces and other more exotic possibilities.
Particle Physics
As elementary particle physicists our own interest in these systems originated
from the realization that the string theories that have been actively investigated
recently as candidates for a unified description of fundamental particles and their
interactions can be thought of as theories of random surfaces. The thermal fluctuations
which drive possible phase transitions in the biological context are then replaced by
quantum fluctuations.
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This page is maintained by Simeon Warner
Last updated 3 June 1996