Solvent molecules (typically water) at or near a solid substrate often experience a hindered rotation relative to those far from the interfacial region. If liberated from the surface via, for example, displacement by an adsorbed protein, a net entropy gain results. An estimation of the rotational contribution to the entropy is given by the statistical mechanical result for an ideal gas rigid rotor, Srot = Nk ln qrot where N is the number of molecules, k is the Boltzmann constant, and qrot is the rotational partition function. For water at 300 K, qrot ~ 30, so the contribution per mole of water liberated from the surface is about 28 J/Kmol. An average-sized protein might result in the liberation of 50 water molecules, so the contribution to the overall free energy of adsorption at 300 K from the solvent rotation would be about -420 kJ/mol. Of course, this is an upper limit since the molecules at the surface do possess some rotational freedom. This estimate would most accurately apply to water at a neutral, hydrophobic surface, where the molecules are expected to be very ordered. As the magnitude of surface charge is increased, the water becomes more disordered (i. e., they may experience enhanced rotation), and the free energy gain from its liberation is thus diminished. As several of the aforementioned studies show trends consistent with these thoughts, the role of solvent structure in the overall influence of an applied electric field cannot be discounted.
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