Phase transition and winding properties of a flexible polymer adsorbed to a rigid perioidic copolymer

Motivated by the noncovalent binding of polypeptides to DNA, the adsorption of a flexible polymer to a rigid periodic copolymer is studied in two dimensions and three dimensions. The fraction of adsorbed monomers, the specific heat, and the Binder cumulant are analyzed and compared with analytical results for an ideal chain. As the interaction strength ε increases, a second-order phase transition occurs from a nonadsorbed state to an adsorbed state, in two dimensions, and a higher-order transition occurs in three dimensions. The transition point is estimated as ε0∼2.2 for d=2 and ε0∼2.1 for d=3, where ε is given in units of kBT. The dependence of the number of adsorbed monomers Nads on the chain length L of the flexible polymer shows a power law scaling relation Nads∼Lϕ, with ϕ∼0.46,0.42 for d=2,3, respectively. We also find an optimal ε∼2.8 for the winding of the flexible polymer around the rigid one in three dimensions. Compared to the adsorbed monomers, the successive nonadsorbed monomers contribute more to the winding. When the interaction is strong, ε>3.5, the winding value or the number of winding turns of the flexible polymer becomes linearly dependent on the chain length.