The hydrophobic interaction at zero separation

This section presents some information of a more theoretical nature on the problem of HcpO interaction. In the next section, we also show how such considerations can be used to extract information on the HcpO interaction at real distances, but for the moment we focus our attention on the formal aspect of the problem. 

Consider first the case of two simple solute particles such as argon, methane, or even hard-sphere particles. We recall the general expression for the indirect part of the work required to bring the two solute particles from infinite separation to the final configuration Ri,R2 (the process being carried out at 

From a practical point of view, the interesting question concerning the H0O interaction is for R = IR2 — R2I cr, with a being the diameter of the solute. However, since we are interested in the solvent properties, and since the expression in (4.4.39) does not include the direct solute-solute pair potential, we can ask for the value of 8A at any distance R a. This section is devoted to one particular distance, R = 0. 

We can apply a cyclic process similar to the one depicted in Fig. 4.7 and obtain 8A 0), expressed as a difference between the work required to bring the two real solutes to R = 0 in the liquid and in the gas. We will avoid such a cyclic process, however, since it compels us to subtract two quantities of the order of infinity to obtain a finite quantity. Instead, we regard 8A 0) as the total work required to bring the two fields of force from infinity to zero separation. In such a process, we do not encounter any repulsive forces that originate from the direct solute-solute interaction. 

Suppose the solutes are hard-sphere particles. Clearly, two hard spheres of diameter ans cannot be brought to a distance R CTHS- However, in (4.4.39), we need only be concerned with the field of force produced by two hard spheres the latter may be referred to as two cavities in the solvent.  

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