Persistency properties of models of polymers on simple cubic and face-centred cubic lattices

The first four odd moments of the persistence lengths of trails and silhouettes are studied on two different 3D lattices, the simple cubic lattice and the face-centred cubic lattice. Variations of the averaged persistence lengths with chain lengths (l) and inverse temperatures ( theta ) are systematically examined. It is found that the averaged persistence lengths scale with a scaling law of the form (Xl2k+1( theta )) approximately lpk nu ( theta ) f(l) where nu is the correlation exponent, p is a parameter, k=0, 1, 2, . . . and f(l) approximately constant, in contrast to the results in 2D where f(l) approximately loge l.