POLYMER-MOLECULES AT CHEMICALLY RANDOM SURFACES

We consider the adsorption of polymers on the surface of a solid, occu pying the region z < 0 The usual approach to the problem is the one du e to de Gennes. We show that the propagator of this approach can be re presented in terms of path integrals, where the paths are unconstraine d and can enter the region z < 0 too. Using this approach, we consider adsorption on a flat, but random surface-where the randomness causes the adsorption energy to be a random function of position. Using the r eplica trick and variational formalism, we study the size of the adsor bed polymer. To simplify the calculations, we use the ground-state dom inance approximation. The calculations revealed a sudden decrease in t he size of the polymer, in both the parallel and perpendicular directi ons, as randomness is increased beyond a certain value. Further, the s ize of the polymer in the perpendicular direction is found to become z ero at a larger value of the randomness. To verify whether these are a rtifacts of the ground-state dominance approximation, we also did exac t calculations for test cases. It was found that the sudden change in size was absent in the exact calculations. Increasing randomness leads to a smooth, continuous decrease in the size. Ultimately, however, th e polymer was found to collapse in the perpendicular direction.