SHAPES AND SIZES OF LINEAR AND CIRCULAR MULTIPLE-RING MACROMOLECULES

The shapes and sizes of linear and circular multiple-ring macromolecul es in the framework of the Gaussian model have been numerically invest igated in terms of shape factors, asphericity and prolateness factors and parameters, and shrinking factors. Simple analytic expressions for the eigenpolynomials of the Kirchhoff or architecture matrices for bo th linear and circular multi-rings in the Iii-nit of an infinitely lar ge individual ring have been obtained via a new recursion method. It i s found that for both types of multiple rings, shape asymmetry increas es while size decreases as the number of rings increases, and that asp hericity and prolateness parameters for a circular 99-ring macromolecu le or it doubly stranded closed random walk have stronger dependence o n dimensionality of the space in which the molecule is embedded than t hose of its linear counterpart. (C) 1997 by John Wiley & Sons, Ltd.