Born expression

The classical Born expression for the polarization free energy of a spherical ion of net charge q can be written as82 ... 

In 1920, Bom wrote to G. N. Lewis about the reprint he had received of Lewis s 1916 paper on the "atom and the molecule." The "cubic" distribution of electrons, Born cautioned, had no general usefulness, and Lewis should look at how Born treated the problem in his new work, which he had sent Lewis. 3 Born expressed some humility about his knowledge of chemistry, confessing to Lewis a few years later, with respect to the new Lewis and Randall textbook on chemical thermodynamics, that he could not speak as well to the chemical side as to the physical side.4... 

Attempts 34 to improve on the simple Born expression by allowing for ion—dipole interactions and consideration of the solvent structure in the case of a redox couple of the type M2+/M led to extensions of equation (27) to such as (29), which included terms for these factors ... 

Use of a More Rigorous Expression for the Repulsive Energy. The simple Born expression (equation 2-3) for the repulsive energy is not strictly correct from quantum-mechanical considerations. More refined expressions do not greatly change the results, however. 

The thermodynamic cycle (Figure 4) showed that changes in redox potential in various solvents were a consequence of the different interaction of the solvent with the dissolved redox couple. One model that has been used to quantify these changes is the electrostatic model, which is based on treating the ion as an ideal sphere in a continuous dielectric the model ignores the effect of any transfer of charge that may occur. The Born expressions for the free energy of solvation of... 

An instructive, albeit partly inconclusive, exercise toward understanding the effect of solvent properties on cesium selectivity in transfer from water to an organic solvent can be obtained from the electrostatic approach already outlined. An estimate of AG°r has often been obtained by applying the modified Born expression in Eq. (4) to calculate values of AG% and for substitution into Eq. (13). Rearrangement then gives an expression applicable to both cations and anions ... 

From distribution experiments at 25°C [150] water and nitrobenzene are mutually saturated. Calculated from the modified Born expression for single-ion transfer [Eq. (17)] with = 34.8 (Table 5) and A, = 0.080 nm. 

Corrected radius equal to r + used in the modified Born expression, Eq. (4)... 

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 ... 

Then Eq. (3.17) will coincide with the rigorous Born expression ... 

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