Directed walk models of adsorbing semi-flexible polymers subject to an elongational force

We consider several directed path models of semi-flexible polymers. In each model we associate an energy parameter for every pair of adjacent collinear steps, allowing for a model of a polymer with tunable stiffness. We introduce weightings for vertices or edges in a distinguished plane to model the interaction of a semi-flexible polymer with an impenetrable surface. We also investigate the desorption of such a polymer under the influence of an elongational force and study the order of the associated phase transitions. Using a simple low-temperature theory, we approximate and study the ground state behaviour of the models.