Density Autocorrelations at Finite Overlap

Abstract

The density autocorrelation function Id,a(q) measures the conformation of a probe chain in a solution containing an arbitrary concentration of other chains. In the dilute limit it of course coincides with the density correlation function of a single chain, as analyzed in Chap. 15. In the semidilute limit it reflects the basic features of the concentration blob model. As has been discussed in Sect. 9.1 we may view the chain as a sequence of concentration blobs of typical spatial extension ξE. This blob size or screening length measures the range of nontrivial excluded volume correlations in the solution. Roughly speaking, in the excluded volume limit two segments j1, j2 found within spatial distance ∣rj2 − rj1∣< ξ E most likely are part of the same chain. ξ E depends on concentration and temperature, but is independent of the chain length. It thus defines a new scale, characteristic of the semi dilute limit and small compared to the radius of gyration R g . According to the blob model correlations on scale r≫ ξ E are Gaussian, since the interaction among the blobs is screened. Pairs of segments deep inside a blob, however, feel the full interaction and show excluded volume correlations like in an isolated chain.