Enthalpy Born model

You can calculate the enthalpies of ion solvation from the vapor phase to water (dielectric constant D) from the Born model by using the Gibbs-Helmholtz Equation (13.41) ... 

It should be born in mind, however, that the activation parameters calculated refer to the sum of several reactions, whose enthalpy and/or entropy changes may have different signs from those of the decrystalUzation proper. Specifically, the contribution to the activation parameters of the interactions that occur in the solvent system should be taken into account. Consider the energetics of association of the solvated ions with the AGU. We may employ the extra-thermodynamic quantities of transfer of single ions from aprotic to protic solvents as a model for the reaction under consideration. This use is appropriate because recent measurements (using solvatochromic indicators) have indicated that the polarity at the surface of cellulose is akin to that of aliphatic alcohols [99]. Single-ion enthalpies of transfer indicate that Li+ is more efficiently solvated by DMAc than by alcohols, hence by cellulose. That is, the equilibrium shown in Eq. 7 is endothermic ... 

The Langmuir model first assumes the adsorption sites are energetically identical. Actually, this assumption is not borne out when adsorption occurs predominantly by physisorption. The spread of A/Tads values between the various sites can be as high as 2 kJmol-1, which is often a significant fraction of the overall enthalpy of adsorption when physisorption is the sole mode of adsorption. By contrast, energetic discrepancies between sites can be ignored when adsorption occurs by chemisorption. 

The lattice energy of zinc sulfide (Born-Lande) is 3136 kJ mol the enthalpy of lattice formation is -3136 - 6 = -3142 kJ mol. The calculated standard enthalpy of formation of zinc sulfide is 187 kJ mol clearly at odds with the ionic model. The solid is considerably covalent. 

Born (1) and later Bjerrum (2) developed a theoretical approach to ion-solvent interactions based on a rather simple electrostatic model. Ions are considered as rigid spheres of radius r and charge z in a solvent continuum of dielectric constant e. Changes in enthalpy AH av) and in free energy AG av), respectively, associated with the transfer of the gaseous ions into the solvent are represented by the following equations ... 

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,... 

Another semi-empirieal approach, based on an electrostatic hydration model for the primary sphere and a Born continuum treatment for the secondary solvation effects, was used by Goldman and Morss (1975) and by Tremaine and Goldman (1978). The value of the hydration number was taken as an adjustable parameter to fit the experimental free energy (AG ) and enthalpy (A//h) of hydration. This gave an estimate of n across the lanthanide series of 5.6 which seems to be too small in view of the experimental data reviewed in earlier sections. 

Use of the Born equation for the calculation of free energies and enthalpies of solvation is based on a model of a continuous dielectric... 

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 ... 

Despite the simplifying assumptions in the derivation, such as assuming that the medium, water, is a continuum with no structure, and that the only work is electrostatic, and even more assumptions in calculating the properties of individual ions from the measured properties of electrolytes, as estimated by the Born function comes reasonably close to the measured Gibbs energy of ion solvation, as shown in Figure 6.7. Other thermodynamic properties such as the volume, entropy and enthalpy of solvation can also be obtained by appropriate differentiation of Equation (6.5). As a result, ever since its inception the Born equation has been used as a primitive model for the electrostatic contribution to the properties of an ion in a dielectric solvent. 

Since the lattice enthalpy for ionic crystals cannot be determined experimentally in any simple way, it has to be determined from other experimental numbers. Below we describe a model for calculating the reaction enthalpy, AH , for the formation of the LiF ionic crystal, referred to as the Born-Haber cycle developed by Max Bom and Fritz Haber (Figure 6.5). 

The choice of the adjustable parameters used in conjunction with classical potentials can result to either effective potentials that implicitly include the nuclear quantization and can therefore be used in conjunction with classical simulations (albeit only for the conditions they were parameterized for) or transferable ones that attempt to best approximate the Born-Oppenheimer PES and should be used in nuclear quantum statistical simulations. Representative examples of effective force fields for water consist of TIP4P (Jorgensen et al. 1983), SPC/E (Berendsen et al. 1987) (pair-wise additive), and Dang-Chang (DC) (Dang and Chang 1997) (polarizable, many-body). The polarizable potentials contain - in addition to the pairwise additive term - a classical induction (polarization) term that explicitly (albeit approximately) accounts for many-body effects to infinite order. These effective potentials are fitted to reproduce bulk-phase experimental data (i.e., the enthalpy at T = 298 K and the radial distribution functions at ambient conditions) in classical molecular dynamics simulations of liquid water. Despite their simplicity, these models describe some experimental properties of liquid... 

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