Solute cavity

The liquid phase of saturated saltwater muds is saturated with sodium chloride. Saturated saltwater muds are most frequently used as workover fluids or for drilling salt formations. These muds prevent solution cavities in the salt formations, making it unnecessary to set casing above the salt beds. If the salt formation is too close to the surface, a saturated saltwater mud may be mixed in the surface system as the spud mud. If the salt bed is deep, freshwater mud is converted to a saturated salt water mud. 

In this contribution, we describe and illustrate the latest generalizations and developments[1]-[3] of a theory of recent formulation[4]-[6] for the study of chemical reactions in solution. This theory combines the powerful interpretive framework of Valence Bond (VB) theory [7] — so well known to chemists — with a dielectric continuum description of the solvent. The latter includes the quantization of the solvent electronic polarization[5, 6] and also accounts for nonequilibrium solvation effects. Compared to earlier, related efforts[4]-[6], [8]-[10], the theory [l]-[3] includes the boundary conditions on the solute cavity in a fashion related to that of Tomasi[ll] for equilibrium problems, and can be applied to reaction systems which require more than two VB states for their description, namely bimolecular Sjy2 reactions ],[8](b),[12],[13] X + RY XR + Y, acid ionizations[8](a),[14] HA +B —> A + HB+, and Menschutkin reactions[7](b), among other reactions. Compared to the various reaction field theories in use[ll],[15]-[21] (some of which are discussed in the present volume), the theory is distinguished by its quantization of the solvent electronic polarization (which in general leads to deviations from a Self-consistent limiting behavior), the inclusion of nonequilibrium solvation — so important for chemical reactions, and the VB perspective. Further historical perspective and discussion of connections to other work may be found in Ref.[l],... 

To calculate the surface charge densities c p and <3%r eq [cf. (2.11)], one has to solve numerically the integral equations on the solute cavity surface domain[ll]... 

All of the interaction mechanisms described above are expected to produce electric fields in the solute cavity. In the case of specific interactions and reaction field effects these electric fields are expected to have some specific orientation with respect to the solute coordinate system. Dispersion forces and Stark effects are not expected to have any specific orientation with respect to the solute. Magnetic field effects seem unlikely to be important in light of the well-known invariance of coupling constants to changes of the external magnetic field. However, it is conceivable that a solvent magnetic reaction field might... 

This situation can be somewhat ameliorated by choosing a regular ellipsoid instead of a sphere for the solute cavity. In that case, Eq. (11.17) can still be solved in a simple fashion, with the reaction field factors depending on the ellipsoidal semiaxes (Rinaldi, Rivail, and Rguini 1992). However, while this is clearly an improvement on a spherical cavity, the small number of solutes that may be well described as ellipsoidal does not make this a particularly satisfactory solution. 

To rationalize the effect of polar groups on and Sj, we can imagine that polar interactions with the water molecules around the solute cavity replace some of the hydrogen bonds between the water molecules. As indicated by the experimental data, this loss of water water interaction enthalpy seems to be compensated by the enthalpy gained from the organic solute water polar interactions. At this point it should also be mentioned that additional polarization effects could enhance the interaction between the organic solute and the water molecules in the hydration shell... 

Similarly, the reaction field, R (88-90), associated with a group of solvent molecules with cholesteric phase order is much larger when operating on a triplet of BN R increases with increasing a. Hie limitations of the Onsager model to the very anisotropic environment experienced by 2BN preclude a reasonable quantitative discussion. The solute cavity Is not spherical BN may be described better for the purposes of elucidating its interactions with neighboring solvent molecules as a quadrupole... 

This chapter is divided into three main parts one presents and comments the main aspects related to the definition of the solute cavity and the solvent-solute boundary, the second focuses on the numerical techniques to obtain boundary elements while the third part describes the main numerical procedures to solve the integral equations. 

Let us consider the nonlocal Poisson equation V(sW) = -4irp in the uniform space. The singular boundary condition on the surface of the solute cavity is neglected. Note that this condition furnishes the mechanisms of the excluded volume effect. The solute is charged and spherical, i.e. p(r) = p(R). The solution T (A ) is obtained by using Fourier transform [6,16] it is valid outside the cavity (R > a),... 

When one solute atom moves, the solute-solvent interface (the solute cavity ) changes. We have seen that the cavity is described in terms of tesserae , i.e. small elements on the surface of the spheres that form the cavity the first derivatives of all the tesserae geometrical elements (position, shape and size) can be computed analytically with respect... 

While powerful contemporary techniques permit the use of molecular cavities of complex shape [3], it is instructive to note a few cases based on idealized representations of solute cavity and charge density. Cavities are typically constructed in terms of spherical components. Marcus popularized two-sphere models, [5,38] which can be used to model CS, CR, or CSh processes (see Section 3.5.2), where the two spheres are associated with the D and A sites, and initial and final charge densities are represented by point charges (qD and qA) at the sphere origins. If a single electron is transferred, Ap corresponds to A = 1 in units of electronic charge (e), and Aif is given by [5,38]... 

A three-zone DC model for treating electrochemical ET at a self-assembled monolayer (SAM) film-modified metal electrode surface [49] is displayed in Figure 3.27, where zones I, II, and III, defined by parallel infinite planes, correspond, respectively, to an aqueous electrolyte, a hydrocarbon film, and the metal, and the ET-active redox group is represented by a point charge shift (Aq) in a spherical solute cavity [22]. The Poisson equation has been solved for this system, and the results analyzed in terms of image charge contributions to As [22] (see below). 

The Poisson-Boltzman (PB) equation relates the electric displacement to the charge density (see Equation (4.28)). The total charge distribution includes the solute charge inside the solute cavity (pint) and that generated by the ion atmosphere outside the cavity (Pext) The external charge density can be represented as shown in Equation (4.30), which leads to the expanded form of the PB equation (Equation (4.31)), which can be simplified for low (Equation (4.32)) and zero (Equation (4.33)) ionic strengths. 

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