Correlation hole effect

This function also gives an accurate description of the behavior of a linear chain in a good solvent (the expansion of the chain size is scaled by the x variable) except for very high values of x, corresponding to short distances between units. These short distances are dominated by the correlation hole effect due to EV [16,26]. 

FIG. 19 Schematic representation of the radial pair distribution function g(r) and corresponding solution structure factor S(q) for two cases discussed in the text liquidlike structure (left) and correlation hole effect (right). See text for more details. 

The inter-chain pair distribution function g(r) from the bulk simulation for the n-tetracosane system at 450 K and 0.1 MPa is shown as the solid curve in Fig. 11a. Unlike the pair density function, the distribution function has an asymptotic value of unity. Even for this short-chain system, we can see the beginnings of the so-called correlation hole effect. At small distances, c[Pg.264]

At this point, it is appropriate to critically reexamine to what extent the Flory-Huggins description (Eqs. 5-7) is valid as a phenomenological model. One important qualitative effect that is neglected completely is the correlation hole effect (14) For an effective monomer of a chain it is more likely to have other monomers in the neighborhood that belong to the same chain rather than to other chains. Of course, only interchain interactions and no intrachain interaction contribute to macroscopic phase separation, and hence the effective coordination number z that enters the Flory-Huggins parameter / gets reduced. It turns out (78) that this leads to H /N corrections in d = 3, z = z o + const/v, and similarly /c = Xoo + const/ /iV, + const/ /iV, etc. In d = 2, however, this... 

The second contribution to g(r) in Eq. (3.2) is called the correlation hole effect by deGennes and is associated with the longer wavelength universal aspects of chain connectivity and interchain repulsive forces. On intermediate length scales it has a critical power law form due to chain conformation self-similarity, and this simple analytic form remains an excellent representation even for chemically realistic models when intersite separations exceed an intrinsic (/V-independent) distance of the order of 3-5 site diameters... 

The quality of the quasi-instantaneous field approximation and the ability of SCM F simulations to capture nontrivial correlation effects is illustrated by studying deviations from the Gaussian chain statistics due to the correlation hole effect in polymer solutions [94] and melt [95,96]. These intermolecular correlations result in a power-law decay of the intramolecular, bond-bond correlation function [95, 96] in a one-component melt as shown in Figure 5.4. 

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