An investigation of the shape and crossover scaling of flexible tangent hard-sphere polymer chains by Monte Carlo simulation

Results are presented from our simulation study of flexible, tangent hard-sphere polymer chains, using a Monte Carlo technique with a reptation algorithm. We examine the crossover region from the swollen (dilute) region to the semidilute regime using chains of degree up to N=2000. The (average) chain end-to-end distance is analyzed as a function of the number of chain links, as is a correlation function for the internal separation of segments, expressed in terms of their connectivity. We study the structure of the polymer chains using scattering functions, which are presented in addition to the segment–segment distribution functions from which they are calculated. Not surprisingly, the Flory exponent ν changes gradually from the dilute value of ν≈0.59 to ≈12 at high density. We find that for chains of 2000 segments, this transition begins at the very low molecular volume fraction of about 0.1%. An analysis of the correlation function for internal segments provides a similar but more detailed picture, in that the role of the screening length ξ becomes explicit. The pair distribution and scattering functions in the swollen, crossover, and melt regions are determined and the scaling behavior is reexamined in the context of these functions. The system considered will form a reference system for subsequent studies in which the model will be broadened to include a network and/or attractive interactions. In this paper we seek first of all to establish that reference, and to relate our work to previous studies in this area of interest. As an important technical point, we also note that the use of an inappropriate random number generator can cause the complete failure of simulations of this type.