Conformational statistics for model polymer chain in interfacial layer

Based on the model of random walk on the simple cubic lattice, the distribution function of conformation of a polymer chain in an interfacial layer was deduced. If the model chain was consisted of N segments, it was possible to form both the tall chain, when the terminal segments were adsorbed at the interface, and the adsorbed chain with the non-terminal group. The conformational number Omega(tail) of a tail chain is equal to Omega(free)/(6piN)(1/2), where Omega(free) is the conformational number of a chain in free state and equals to 6(N) for this random walk model. It was found from theoretical analysis that, for the set of a chain attached non-terminally to the interface, the total conformational number Omega(tot) is equal to Omega(free)/6. As an result, the average conformational number Omega(m). for the chain attached non-terminally to the interface is Omega(free)/6N. In the case of short chain, for instance N is equal to about 10, the conformational number Omega(tail) of tail chain is even larger than the total number Omega(tot). In the limitation of long chain, however, the conformational number Omega(tail) for tail chain is nuch large than Omega(m), but smaller than Omega(tot). The conclusion is that the distribution function of conformation for chains in the interfacial layer is not uniform, but has a special distribution form described in this paper.