Segment Distribution around the Center of Gravity of a Triangular Polymer

Abstract

The segment distribution around the center of gravity is investigated for a special comb polymer (triangular polymer) having the side chains of the same generation number, g, as the main backbone. Common to all the other polymers, the radial mass distribution is expressed as the sum of the distribution functions for the end-to-end vectors, { r Gh }, from the center of gravity to the monomers on the hth generation; the result being, for a large g, N 1/2 0 ∝ N 1/4 , giving the same exponent as observed for the randomly branched polymer. On the basis of the present result, we put forth that all the known polymers obey the equality: s 2 N 0 = A g l 2 , where A is a polymer-species-dependent coefficient and also depends on the choice of the root monomer. We discuss the extension of this empirical equation.