Static and dynamic properties of tethered chains at adsorbing surfaces: a Monte Carlo study

We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain's extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength epsilon(c) one has M(c) approximately N(phi), and we find (using the above results) as best candidate phi to equal 0.59. However, slight changes in the estimation of epsilon(c) lead to large deviations in the resulting phi; this might be a possible reason for the difference in the phi values reported in the literature. We also investigate the dynamical scaling behavior at epsilon(c), by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at epsilon(c) the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum.