Born charging entropy

In the case of such large ions as the metalloporphyrin complexes with their rigid planar structure, to a first approximation the entropy change will be given by the difference in the Born charging entropy of the two valency forms. The Born charging entropy of an ion is given by ... 

If we view our process as charging the sphere such that we go from a single strand to a double strand then we have a Born charging model of the Free Energy, G, of binding DNA near a surface. This can be adjusted for both dielectric and metallic surfaces. Given the free energy we can then calculate entropy and enthalpy via the familiar derivatives,... 

The Born coefficients of the HKF model for the various organic species are simply related to their standard partial molal entropies at 25 °C and 1 bar through the effective charge (Shock et al., 1989). 

The second term in the square brackets is the Born expression applicable at distances n + Ari, i.e., beyond the first hydration shell of thickness Ar. The first term describes the electrostatic interaction inside this shell, characterized by a relative permittivity e now, approximated by the square of the refractive index of water at the sodium D line. With the relevant de /rfT and de/tfT values for water at 25 °C, the enthalpy of hydrationEq. (2.28)is AHeh+A//ei2 = -69.5z2[(0.35(Ari/ri)+1.005)/(ri+Ari)] kJ mor The entropy is then A5eu + A5ei2 = —4.06z [(1.48(Ari/ri)+1.00)/(ri + Ari)] J mol The thickness of the first hydration shell, Ar, depends on the number of water molecules, hi, in it, the hydration number. According to the model (Marcus 1987) hi = 0.36 zi /(r/nm), that is, it is proportional to the charge number of the ion and inversely proportional to its radius. The volume occupied by hi water molecules is nhid l6, where cfw = 0.276 nm is the diameter of a water molecule. Hence the volume of the first hydration shell is given by ... 

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