Statistics of self-avoiding walks confined to strips and capillaries

A long self-avoiding chain confined to a narrow strip or thin tube tends to be elongated in the direction of the strip or tube. The mean end-to-end separation of a long chain so confined becomes asymptotically proportional to the number of links in the chain as the contour chain length becomes infinite. By use of scaling arguments, it is shown that the mean end-to-end separation also becomes proportional to D(-1/3) for chains confined to two-dimensional strips and proportional to D(-2/3) for three-dimensional capillaries, where D is the width or diameter of the strip or capillary. These predictions have been verified by Monte Carlo studies of self-avoiding walks. The agreement is excellent for two-dimensional systems, but less certain for those of three dimensions since less data are available for verification.