Theoretical and Monte Carlo studies have been carried out on selfhyphen;avoiding random walks confined to relatively narrow strips or tubes. Such walks are used to simulate the behavior of macromolecular chains subject to corresponding external boundary constraints. It is proved that, if a chain is confined to a strip or tube of a width small compared to the contour length of the chain, the mean square endhyphen;tohyphen;end separation of the chain is asymptotically proportional ton2, wherenis the number of links in the chain. In addition, Monte Carlo results are reported for strips of three and eight layers and for thin tubes with four and five connected channels. The results so obtained are consistent with the theory. It is conjectured that chains confined to a thin surface, not necessarily monomolecular, will behave as if the chains were limited to a plane, but with parameters different from those for the strictly twohyphen;dimensional problem.
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