Hydrophobic interaction At zero separation

This section presents some information of theoretical value pertinent to the problem of HI. In the next section, we also indicate how such information can be employed to extract information on HI 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 Rj, Rg (the process being carried out at constant T, F, N) 

We have already noted that from the practical point of view, the interesting question concerning the HI is for R = Rg — Ri =5 a, with a the diameter of the solute. However, since we are now interested in the solvent properties, and since in (8.82) we have no trace of the direct pair potential for solute-solute interaction, we can search for the value corresponding to the HI at any distance R a. This section is devoted to the one particular distance R = 0. 

We can apply a cyclic process similar to the one depicted in Fig. 8.9 and obtain (0) as the difference between the work required to bring the two 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 adhere to the point of view suggested by (8.82), i.e., we regard 5 (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 strong repulsive forces that originate from the direct solute-solute interaction. 

We start with the simplest solutes, hard-sphere particles. Clearly, two hard spheres of diameter cths cannot be brought to a distance R a. However, in (8.82), we need only be concerned with the field of force produced by the two hard spheres the latter may be referred to as two cavities in the solvent.  

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