Abstract
We study the transition from infinite to finite-sized loops of Gaussian chains adsorbed onto a regular patterned surface as a function of sticking energy, E, sticker concentration, C, and surface lattice constant, m. Three cases are studied in the limit of infinite chain length. In the first case, which corresponds to a finite substrate, the ratio of the maximum surface dimension to the chain length, R/N, is zero as N→∞. In the second and third cases, the number of possible sticking sites is infinite in one and two dimensions, respectively. In the first case, we find that there is a first order transition from infinite to finite loop sizes, and there exists a range of average loop size that is inaccessible. In the second and third cases no such gap exists, and the transition is continuous.
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