Dipolar Solutes at an Aqueous Interface

In this second example, we examine simple systems near the water-hexane interface. Specifically, we calculate the difference in the free energy of hydrating a hard-sphere solute of radius a, considered as the reference state, and a model solute consisting of a point dipole p located at the center of a cavity [11]. We derive the formula for A A assuming that the solute is located at a fixed distance z from the interface, and subsequently we examine the dependence of the free energy on z. The geometry of the system is shown in Fig. 2.3. 

For the model solutes, the difference in the potential energy is equal to the electrostatic energy of solvating a dipole 

we consider the second-order perturbation approximation. Since (AU)0 averaged over dipolar orientations vanishes 

Equation (2.39) leads to the prediction that AA should be proportional to p2. For a bulk solvent, this can be considered as a molecular equivalent of the well-known Onsager formula derived for the continuum dielectric model [12], 

Indeed, both expressions predict quadratic dependence of AA on the dipole moment of the solute. As in the previous example, it is of interest to test whether this prediction is correct. Such a test was carried out by calculating AA for a series of model solutes immersed in water at different distances from the water-hexane interface [11]. The solutes were constructed by scaling the atomic charges and, consequently, the dipole moment of a nearly spherical molecule, CH3F, by a parameter A, which varied between 0 and 1.2. The results at two positions - deep in the water phase and at the interface - are shown in Fig. 2.3. As can be seen from the linear dependence of A A on p2, the accuracy of the second-order perturbation theory 

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