Correlations among interpenetrating polymer coils : the probing of a fractal

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Abstract
We use renormalization group and ε-expansion to calculate the density distribution in a polymer coil of polymerisation index N2, interpenetrating a coil of polymerisation index N1. The distance of the coils is controlled by fixing the center of mass distance or by fixing the center of mass of coil N2 with respect to the central segment of coil N1. The effective free energies of the two-coil system in both situations are universal functions which tend to some finite limit as N1 →∞, N 2/N1 fixed. This is in sharp contrast to the prediction of mean field models which lead to hard sphere behaviour. Besides free energies we calculate the radius of gyration and the density distribution of coil N2. For N2 ⪡ N1 all our results show a pronounced dependence on the position of the probe coil N2 relative to coil N1, thus proving the strong inhomogeneity of the density of coil N1 characteristic for a fractal object. We carry through off-lattice Monte Carlo simulations which nicely confirm our analytical results