COMPUTED PROBABILITY DENSITY FUNCTIONS OF RADII OF GYRATION OF LONG RANDOM-FLIGHT CHAINS

Probability density functions for the orthogonal components of the radius of gyration, Si, of a randomflight chain were computed using an indirect numerical integration algorithm which was based upon a multiple convolution proposed by Forsman and Hughes. Computations were performed for relatively long chains of 100-1000 statistical segments t. By using a reduced radius of gyration ξi= (π/2√3) Si(Si2) -1/2 the distributions converged to a limiting function at about 2=500, except for extremely small radii, ξi≤[10(2t)1/2] -1. Additional computations using the one-dimensional distributions yielded the corresponding probability densities for both the two- and three-dimensional (polar) radii. The computed functions were in excellent agreement with all their limiting properties previously determined by analytical methods.