1109.6555 (Jemal Guven et al.)

Confinement of semiflexible polymers    [PDF]

Jemal Guven, Pablo Vázquez-Montejo

A variational framework is developed to examine the equilibrium states of a
semi-flexible polymer that is constrained to lie on a fixed surface. As an
application the confinement of a closed polymer loop of fixed length $2\pi R$
within a spherical cavity of smaller radius, $R_0$, is considered. It is shown
that an infinite number of distinct periodic completely attached equilibrium
states exist, labeled by two integers: $n=2,3,4,...$ and $p=1,2,3,...$, the
number of periods of the polar and azimuthal angles respectively. Small loops
oscillate about a geodesic circle: $n=2$, $p=1$ is the stable ground state;
states with higher $n$ exhibit instabilities. If $R\ge 2R_0$ new states appear
as oscillations about a doubly covered geodesic circle; the state $n=3, p=2$
replaces the two-fold as the ground state in a finite band of values of $R$.
With increasing $R$, loop states alternate between orbital behavior as the
poles are crossed and oscillatory behavior upon collapse to a multiple cover of
a geodesic circle, (signalled respectively by an increase in $p$ and an
increase in $n$). The force transmitted to the surface does not increase
monotonically with loop size, but does asymptotically. It behaves
discontinuously where $n$ changes. The contribution to energy from geodesic
curvature is bounded. In large loops, the energy becomes dominated by a state
independent contribution proportional to the loop size; the energy gap between
the ground state and excited states disappears.

View original: http://arxiv.org/abs/1109.6555