Cross-link induced shrinkage of grafted Gaussian chains

The statistical mechanics of polymers grafted on surfaces has been the subject of intense research activity because of many potential applications. In this paper, we analytically investigate the conformational changes caused by a single cross-link on two ideal (Gaussian) chains grafted on a rigid planar surface. Both the cross-link and the surface reduce the number of allowed configurations. In the absence of the hard substrate, the sole effect of the cross-link is a reduction in the effective Kuhn length of a tethered chain. The cross-link induced shrinkage (collapse) of the grafted chains (mushrooms) turns out to be a reduction in the variance of the distribution of the height of the chain rather than a reduction of the height itself.

Bundling in brushes of directed and semiflexible polymers

We explore the effect of an attractive interaction between parallel-aligned polymers, which are perpendicularly grafted on a substrate. Such an attractive interaction could be due to, e.g., reversible cross-links. The competition between permanent grafting favoring a homogeneous state of the polymer brush and the attraction, which tends to induce in-plane collapse of the aligned polymers, gives rise to an instability of the homogeneous phase to a bundled state. In this latter state the in-plane translational symmetry is spontaneously broken and the density is modulated with a finite wavelength, which is set by the length scale of transverse fluctuations of the grafted polymers. We analyze the instability for two models of aligned polymers: directed polymers with a line tension and weakly bending chains with a bending stiffness.

Orientational order and glassy states in networks of semiflexible polymers

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order or are frozen in random directions depending on the value of the crossing angle, the crosslink concentration and the stiffness of the polymers. A crossing angle $thetasim 2pi/M$ leads to long range $M$-fold orientational order, e.g., hexatic or tetratic for $theta=60^{circ}$ or $90^{circ}$, respectively. The transition is discontinuous and the critical cross-link density depends on the bending stiffness of the polymers and the cross-link geometry: the higher the stiffness and the lower $M$, the lower the critical number of cross-links. In between the sol and the long range ordered state, we always observe a gel which is a statistically isotropic amorphous solid (SIAS) with random positional and random orientational localization of the participating polymers.

Stretching semiflexible filaments with quenched disorder

We study the effect of quenched randomness in the arc-length dependent spontaneous curvature of a wormlike chain under tension. In the weakly bending approximation in two dimensions, we obtain analytic results for the force-elongation curve and the width of transverse fluctuations. We compare quenched and annealed disorder and conclude that the former cannot always be reduced to a simple change in the stiffness of the pure system. We also discuss the effect of a random transverse force on the stretching response of a wormlike chain without spontaneous curvature.