Polymers in Curved Boxes

Details Polymers in Curved Boxes Polymers in Curved Boxes

1996-08-05

arxiv.org/abs/mtrl-th/9608003v1

Physics

Condensed Matter

Materials Science

20 pages RevTeX, epsf; 4 figures; submitted to Macromoledules

Scientific paper

10.1021/ma961088x

We apply results derived in other contexts for the spectrum of the Laplace operator in curved geometries to the study of an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D and conclude that the free energy compared to its value for an uncurved box of the same thickness and volume, is lower when $D < 3$, stays the same when $D = 3$, and is higher when \mbox{$D > 3$}. Thus confining an ideal polymer chain to a cylindrical shell, lowers the effective bending elasticity of the walls, and might induce spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned results show that {\em {any}} shell in $D = 3$ induces this effect, except for a spherical shell). We compute the contribution of this effect to the bending rigidities in the Helfrich free energy expression.

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