Screening in dense polymer systems

Let us start with a molten system of chains (degree of polymerization N ) to which we add a very weak concentration of solvent molecules. We assume that the stem isothermal— i.e., the solvent-monomer interaction is exactly equal to the moiHMner-monomer interaction. Of course, if the solvent molecules are extremely dilute, they behave as a gas of independent particles. However, here we go one step further to consider the interactions between two solvent molecules. 

When averaged over all sites j different from i, the shift ASy is positive. Our reader may acquire a qualitative feeling for this sign by inspection of a (comparatively) simple case—namely, dimers (N = 2) on a square lattice. If we look at two distant units (/) and (j) (Rg. II.4a), we see that each has four neighbors where a dimer molecule is restricted in orientation starting on any of these neighbors the dimer can point only in three directions (a /3 y). On the other hand, if (i) and (/) are adjacent, there are only six sites 

Returning to the general form of 5y, we may also translate it into an effective interaction f/y between sites (/) and (/) putting 

For = J we must take (7 j as repulsive and infinitely large because we do not allow two solvent molecules on the same site. The resulting aspect of Ut is shown in Fig. II.S. At finite Ra, the interaction oscillates in sign, but it is predominantly attractive. At / o the interaction drops to zero. 

The repulsive core is what we might call the bare interaction it would be present even in the absence of polymer chains on surrounding sites. The attractive part is due to the chains and tends to reduce or screen out the bate interaction. This notion of screening was first introduced— in a somewhat different context— for semi-dilute solutions by S. F. Edwards.  

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