On the adsorption of a polymer chain with positive or negative bending stiffness onto a planar surface

Abstract

Adsorption of a single homopolymer chain with bending stiffness on a homogeneous planar surface is studied theoretically in the framework of the lattice model and the generating functions approach. The stiffness is introduced by assigning a statistical weight to a trans-isomer (a straight segment) with respect to a gauche-isomer (a kink). This statistical weight is related to the bending energy εbend associated with a kink: k=exp(εbend∕kBT) and depends on the temperature but one can also treat k as a temperature-independent parameter. Both positive and negative values of the bending energy corresponding to stiff (εbend>0, k>1, positive stiffness) and “quasi-zigzag” (εbend<0, 0<k<1, negative stiffness) chains are considered. The dependence of the adsorption transition temperature on εbend and k is non-monotonic and has a minimum for flexible chains at εbend=0 and k=1. At the same time, at moderate and strong adsorption, the fraction of adsorbed units is a strictly increasing function of the bending energy or the stiffness parameter. Adsorption is accompanied by the straightening of the chain in the case of positive εbend and its “zigzaging” in the case of negative εbend. In contrast, when k is temperature independent, a decrease in temperature leads to the increase in the fraction trans-isomers at any positive k. The temperature dependence of the specific heat can exhibit one or two maxima in addition to the jump in at the adsorption (second order) transition point.