A simple and exactly solvable model for a semiflexible polymer chain interacting with a surface

We use the lattice model of directed walks to investigate the conformational as well as the adsorption properties of a semiflexible homopolymer chain immersed in a good solvent in 2D and 3D. To account for the stiffness in the chain we have introduced energy barrier for each bend in the walk and have calculated the persistent length as a function of this energy. For the adsorption on an impenetrable surface perpendicular to the preferred direction of the walk we have solved the model exactly and have found the critical value of the surface attractions for the adsorption in both 2D and 3D. We have also enumerated all possible walks on square and cubic lattices for the number of steps N⩽30 for 2D and N⩽20 for 3D and have used ratio method for extrapolation. The transition located using this method is in excellent agreement with the results found from the analytical method. We have compared the results of surface adsorption for two different surface orientations. In one of the orientation, surface is considered parallel to the preferred direction and in another it is perpendicular to the preferred direction. Results found in both the cases indicate that for stiffer chains adsorption transition takes place at higher temperature compared to that of flexible chain