On the conformational transition of a self-avoiding walk adsorbed at an interface

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Abstract
The conformational transition of a self‐avoiding walk at an interface, between nonadsorbed and adsorbed states, is investigated by means of extended numerical data in the asymptotic limit, for five‐choice and four‐choice walks on the simple cubic lattice, up to 14 and 16 steps, respectively. Given x = exp(βε), where ε is the energy per adsorbed segment (β = 1/kT), the location of the transition is found to be x* = 1.485 (five choice) and x* = 1.502 (four choice). The nature of the transition is also investigated and it is shown that the mean fraction of adsorbed segments y n (x), in the limit of infinite n, tends to 0 below x* and to A[ln(x/x*)]α above x*, with α?0.35–0.40. The mean thickness (perpendicular to the surface) and the mean spread (parallel to the surface) of the walks are also discussed.

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