Application of One-Dimensional Models to Study Hydrophobic Interactions

Application of One-Dimensional Models to Study Hydrophobic Interactions 

The first application of a 1-D model to study H(f)0 interactions was carried out by Elkoshi and Ben-Naim (1979). The model used in this study was a generalized 1-D lattice model for water proposed by Bell (1969). Although it was not stated explicitly by Bell, it was noted by Elkoshi and Ben-Naim that the success of the Bell model in exhibiting some of the outstanding behavior of liquid water was due to the implementation of the principle, namely that water molecules strongly bound to their environment (by hydrogen bonds ) are also those which experience a relatively low local density. 

Elkoshi and Ben-Naim (1979) attempted to study the problem of the H(pO interaction within this model, hoping that the fact that the principle is a built-in feature of Bell s model would be helpful in clarifying the molecular reasons for the phenomenon of the H(pO interaction. At that time it was not known whether or not the HtpO interaction was a result of the principle. As we noted in Sec. 3.9, the hydrophobic interaction is nothing but the difference in solvation Gibbs energies. Therefore, since the solvation Gibbs energy is not a result of the principle, we can also expect that the H(f)0 interaction will not depend on the principle. 

Without going into the details of the model, we note here that the study of Elkoshi and Ben-Naim focused on the function yss at contact distance (i.e. when two solutes s become nearest neighbors). This function is related to the solvent-induced part of the change in the Gibbs energy for the process of bringing the two solutes from infinite separation to the distance of nearest neighbors  

A more detailed study of the HtpO was carried out recently by Widom and his collaborators using a similar 1-D model that was originally described by Ben-Naim (1992). The general idea is that particles placed on lattice points have different orientations (relative to the 1-D axis) and that in one of these states the particles can form a hydrogen bond (HB). A simple solute can occupy only the interstitial sites between two molecules that are in the HBing state. 

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