Entropy Changes in Aqueous Solutions of Non-polar Substances and in Bio-complex Formation

The entropy changes, ΔSapp, (i) for dissolution in water of non-polar substances and (ii) for protein-ligand complexation show linear dependences on the logarithm of the absolute temperature. For every compound, the slope m(S)=ΔCp for the line ΔSapp=f(ln T) depends on the size of the molecule and is exactly equal to the slope m(H)=ΔCp found in the diagram ΔHapp=f(T). This means that the slopes are rigorously proportional (with a ratio m(S)/nw=Cp,w) where nw is the number of involved water molecules as determined from the enthalpy change ΔHapp=f(T). It is also worth noting that the value of nw is positive (as well as m(S) and m(H)) in the dissolution of non-polar substances, whereas it is negative (as well as m(S) and m(H)) in bio-complex formation and in micelle formation. The number nw (nw>0) involved in the dissolution of non-polar substances depends on the size of the cavity (excluded volume) formed in the structure of water. These water molecules that have been excluded from the structure of the solvent absorb thermal energy that compensates for the negative enthalpy change, whereas the formation of the cavity implies there should be a large negative entropy contribution. The low solubility of non-polar substances in water depends on the highly negative entropy effect due both to cavity formation and to loss of configurational entropy by the gas trapped in a cage of water molecules. In processes involving association, as in micelle formation and in protein complexation, the cavities surrounding the separate units coalesce and the resultant cavity is smaller than the sum of the previous ones. The nw water molecules (nw<0) needed to fill the excess cavity return to the structure of the bulk solvent and release thermal energy, which compensates for the endothermic enthalpy. The affinity in the association processes is bound, for the most part, to the entropy produced by occupation of part of the cavity by condensation of water molecules. The association processes are therefore entropy driven.