Density profile of terminally anchored polymer chains: a Monte Carlo study

We present results of a detailed Monte Carlo simulation study of a system of a large num- ber of polymer chains terminally anchored or end-grafted on a flat surface. We study this system on a three-dimensional lattice for several different values of the surface coverage and the chain length. We also consider several different distributions for the chain lengths. For monodisperse chains, we find that the monomer density profile shows a depletion layer near the grafting plane in agreement with phenomenolog- ical theories. Beyond this depletion layer, the density profile can be represented by a parabolic form. This result is in agreement with recent self-consistent-field (SCF) calculations rather than with the scaling argu- ments that predict a plateau region for the density profile. The chain-end density is also found to be con- sistent with the SCF calculations; Le., we find that the free ends of the chains are not excluded from regions near the grafting surface. We also study the effect of polydispersity in the chain lengths. In the case of a system consisting of two species of polymers of length N and 2N, we find that there is a region in which the density profile matches that of the monodisperse case with chain length N, in agreement with another recent self-consistent-field calculation. The width of this region, however, is narrower than that predicted by the theory. We have also considered a uniform distribution of chain lengths and compared the density profile with the functional form obtained by intergrating the equations derived in the SCF formalism. The agreement between the Monte Carlo data and the theory is remarkable except, again, for the presence of a depletion layer near the grafting plane.