Cylindrical colloids on a fluid membrane
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Date
2009-05-22T14:48:03Z
Authors
Mkrtchyan, Sergey
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
We theoretically study the adhesion and membrane-mediated interaction of cylindrical
colloids to a flat fluid membrane. There are two ways to approach this
problem. The first way, based on energy, requires finding the equilibrium shape of
the membrane given the placement of the particle(s). In order to do so, we need to
know how the energy of the surface depends on its shape (i.e. the surface Hamiltonian),
as well as how the adhered colloid deforms the membrane. The second
way to approach this class of problems is “geometrical”, where forces between the
membrane-adhered particles are related directly to the geometry of the deformed
membrane via the surface stress tensor. The surface Hamiltonian allows finding the
stress at any point on the membrane in terms of local geometry. The force acting
on the colloid can then be found by integrating this surface stress tensor along any
contour enclosing the colloid.
In this thesis, using the approach based on free energy calculations, we look into
the problem of cylindrical colloids adhering to a membrane with fixed constant adhesion
energy between the membrane and the colloids. Angle-arclength parameterization
is used in order to treat the problem beyond small gradient approximation.
We present three different cases here: single cylinder adhering on a membrane, two
cylinders adhering on the same side of the membrane, and two cylinders adhering
on different sides of the membrane. For the single cylinder case we present a structural
phase diagram to separate no wrapping, partial wrapping and closure states
and we compare it to the phase diagram obtained for a related system of spherical
colloids. For two cylinders adhered on the same side of the membrane we obtain
repulsive interaction and transition from shallow to deep wrapping as the cylinders
move apart from each other. We also look into a phase where two cylinders are
vertically stacked and discuss its energetics. For two cylinders adhering to the opposite
sides of the membrane, attractive interaction is obtained in accordance with
previous results and we further show that in that case two cylinders are generally
in contact and a first-order transition from shallow to full wrapping is possible. In
the last section, we put a framework for the class of problems where the particle
is between the membrane and the supporting interface, where adhesion is assumed
between the interface and the membrane.
Description
Keywords
colloid, adhesion, membrane, interaction