Adsorption of a periodic heteropolymer onto a periodic heterogeneous surface: a directed walk model

The adsorption of a periodic heteropolymer onto a periodic heterogeneous surface is studied using the two-dimensional partially directed walk model of the polymer. We show how the generating function approach developed by Polotsky (2012 J. Phys A: Math. Theor. 45 425004) for the adsorption of a random copolymer onto a random surface can be extended to the case of an arbitrary periodic heteropolymer and a chemically heterogeneous surface: the main equation remains unchanged and the transition probability matrices acquire the special form of circulant matrices of a dimension equal to the corresponding sequence and surface periods, while the particular structure of periods in the polymer and on the surface is encoded in the diagonal 'interaction matrix'. The developed approach is applied to study the adsorption of a symmetric multiblock copolymer onto a symmetric multiblock two-letter surface. Analysis of the adsorption transition point dependence on polymer and surface block sizes and different sets of polymer–surface interaction parameters reveals interesting 'odd–even' and 'recognition' effects. Beyond the transition point, temperature dependences of the main conformational and thermodynamic characteristics demonstrate that adsorption can occur as a two-stage process, where binding of the polymer chain to the surface is followed by 'tuning' the chain conformations in order to maximize the number of energetically favourable contacts. The two-stage adsorption is characterized by the appearance of the maximum on the heat capacity curves. (paper)