The Short-Range-Force Assumption

In Table 1 it can be seen that the intermolecular force contnbutions to the stress tensor and heat flux involve the forces between beads on different molecules. We assume that this force is negligibly small unless bead v of molecule a and bead /x of molecule / are extremely close (see Fig. (18.1-1) of DPL). That is, we state that 

When this assumption is made, the intermolecular force contributions in Eqs. (7.19) and (8 21) are both zero. This means that there is no need to know the pair distnbution function that appears in these two expressions. It should be 

The above reasoning has been used to eliminate the need for knowing the pair distribution function in the kinetic theory of polymer melts [9,14a]. 

For dilute solutions, one generally considers the solvent to be a continuum, and polymer-solvent interactions are not explicitly considered. As a result the terms contaimng the pair distribution functions (in Eqs. (7.19), (8.11), and (8.21)) are not needed, since polymer-polymer interactions occur only rarely. On the other hand, if one wishes to study polymer-solvent effects explicitly, then it will be necessary to consider in detail the terms containing the pair distribution function. 

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In order to make use of the flux expressions in Sects. 6, 7, and 8, it is necessary to have the singlet distribution function and - unless the short-range force assumption is used - the doublet distribution function as well. Virtually nothing is known about the doublet distribution function. If we knew how to make a reasonable guess of this function (possibly obtainable from molecular or Brownian dynamics), then we could estimate the contributions to the fluxes in Table 1 that involve the molecule-molecule interactions. 

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