One-Dimensional Model of Polymer Adsorption

A detailed treatment of the conformations of a one-dimensional polymer molecule adsorbed to a surface is given. The average number of contacts of the chain with the surface, the end-to-end length, and the distribution of segments ρ(z) with respect to distance z from the surface are computed as functions of the chain length (N) of the polymer and the attractive energy of the surface. Both theoretical and Monte Carlo calculations are used. A transition is found at an attractive energy of kT ln 2. For attractive energies less than this value, the average number of contacts of the chain with the surface approaches a finite value as N approaches infinity, while the end-to-end length vaires as N½. However, above the transition the number of contacts is proportional to N and the end-to-end length is independent of N. The distribution of segments ρ(z) also shows a marked change as we go through the transition. The one-dimensional model is shown to correspond to the projection of a three-dimensional model on the direction normal to the surface. Therefore, these results are believed to represent the distribution normal to the surface for real systems.