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400 temperature

Fig. 5 Thermodynamic functions for the hydration of apolar molecules, quasichemical approximation; lattice with orientation-dependent interactions after Besseling (1993)

400 temperature

### 500 K

respectively. Here, nafj is the number of contacts between face a of one molecule and face fi of the other with which it is in contact, and ua/i is the corresponding energy (see above), na/3(<x>) is the value that naj, would assume if all contacts were random, i.e., if there would not be orientation correlations. Further, k is Boltzmann's constant, nA is the number of molecules of type A and a>A is the number of distinguishable orientations that A can have.

From (9) and (10) the Helmholtz energy is obtained and from that all relevant mechanical and thermodynamic quantities, including the pressure, density and the chemical potential of each component, the properties of water near surfaces, etc.

By way of example, Fig. 5 gives the thermodynamic functions for the hydration of vacancies. At given TAbyirSm, Ahydr//„, can be adjusted to obtain the corresponding parameters for small apolar molecules. The inverse functions relate to dehydration, as happens for instance in hydrophobic bonding. The theory can be extended to dissolved chain molecules like tails of surfactants, but even in the present picture it is seen that the switch from endothermal AHm for hydrophobic bonding at low temperature to exothermal AHm at higher temperatures is well predicted. However, the endothermic nature of AHm at low temperature is not due to additional hydrogen bond formation, as in traditional iceberg models, but to an increase of the number of repulsive water-water interactions, induced by the dissolution of vacancies or foreign apolar molecules. This last conclu

Fig. 5 Thermodynamic functions for the hydration of apolar molecules, quasichemical approximation; lattice with orientation-dependent interactions after Besseling (1993)

sion simply follows from counting nHb and «nHb. It is further noted that AH is relatively small, as observed. In agreement with observation, TASm is positive but decreasing with T above room temperature. At very high temperatures TASm even becomes negative; then AGm passes through a maximum. The occurrence of such a maximum was recently put forward by Privalov and Gill [28].

Finally, it is noted that AHm and TASm depend rather strongly on T, whereas A Gm is much less dependent on it. In other words, the new model also accounts for the entropy-enthalpy compensation.

Hence, it is concluded that the new model can at least semi-quantitatively account for all the main features for hydrophobic bonding. In forthcoming papers, we hope to return to all of this in more detail.

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