Solvent radius

The modification by method 2 is more acceptable. Although several types of modifications have been reported, Abraham and Liszi [15] proposed one of the simplest and well-known modifications. Figure 2(b) shows the proposed one-layer model. In this model, an ion of radius r and charge ze is surrounded by a local solvent layer of thickness b — r) and dielectric constant ej, immersed in the bulk solvent of dielectric constant ),. The thickness (b — r) of the solvent layer is taken as the solvent radius, and its dielectric constant ej is supposed to become considerably lower than that of the bulk solvent owing to dielectric saturation. The electrostatic term of the ion solvation energy is then given by... 

Figure 5. The relative solvent accessible areas (SAA) of the five most common faces on the sucrose crystal. Solvent radius 0 A.

Figure 8. The solvent accessible areas (SAA) of five sucrose ciystal faces in angstroms per unit cell and their mesh areas (same units). Solvent radius 15 A.

Figure 10. Solvent accessible area of three faces of Adipic acid solvent radius 1.5 A.

One should also mention the so-called mean spherical approximation (MSA) treatment of solvent reorganization [25]. McManis and Weaver [125] considered how the solvent radius and dielectric parameters affect the electron transfer within the frame of this theory. The frequency dependence of the effective radius should cause significant deviations from the Marcus expression for the activation energy of... 

This approach, then, accounts for the electrostatic and solvent polarization (but not the solute polarization) portions of the ENP term, using force field atomic partial charges. Still et al. also included a part of the CDS energy term in their formalism by employing a SASA approach (i.e., Equation [5]), where the SASA is evaluated for the OPES van der Waals surface plus solvent radius, and the surface tension cr is defined to be a constant of 7.2 cal mol ... 

Fig. 6.2 Plot on logarithmic scales of the Debye relaxation time Xq for aprotic solvents against the product where p is the viscosity and r, the molecular solvent radius.

Fig. 6.11 Plots of the Stokes radii for Na+ and TEA+ estimated using equation (6.10.2) against the effective solvent radius r. The data for TEA have been shifted vertically by 300 pm for the sake of clarity.

The results for the Stokes radii of anions are more eomplex and are eonsidered separately for protic and aprotie solvents. In the ease of aprotie solvents, the value of fsT decreases in the aprotie solvents with inerease in solvent radius (fig. 6.12). Since the interaction between the anion and solvent is weak, the number of solvent molecules which move with the ion decreases with inerease in solvent size. This trend is weaker for the larger CIO4 ion than for the smaller CP ion, demonstrating that the CP anion is more strongly solvated in solvents of the smallest molecular size. In the case of protic solvents, hydrogen bonding is involved in anion solvation. Data are available in only a few solvents so that a detailed analysis is not possible at present. 

The results presented here demonstrate elearly that the solvent radius is the important parameter to be considered in diseussing the solvent dependence of the... 

Estimate the missing data points for Cs in table 6.4 using a linear correlation between the Stokes radius and the solvent radius as illustrated in fig. 6.11. 

While the Stokes-Einstein equation is strictly applicable only in cases where the diffusing particle is large when compared to the surrounding solvent molecules (so that the fluid can be considered a continuum), it has proven to be useful for solute-solvent pairs in which the radius, a, is only two to three times the solvent radius. For a solute with radius comparable to the solvent radius, the 6 in Equations 4-3 and 4-4 should be replaced by a 4, since the assumption of no slip at the solute surface is no longer valid [48]. 

Fig. 3.1. Visualization of a drug molecule N-(4-hydroxy-phenyl)-acetamide (Tylenol or acetaminophen) computerized with different levels of graphic representations. (A) Molecular structure of the drug Tylenol. (B) Ball-stick model showing atomic positions and types. (C) Ball-stick model with van der Waals dot surfaces. (D) Space-filled model showing van der Walls radii of the oxygen, nitrogen, and carbon atoms. (E) Solvent accessible surface model (solid) (solvent radius, 1.4A). (See black and white image.)...

Hexane, the least spherical molecule in the list, behaves as if its molar volume is much less, in fact more closely equivalent to the volume corresponding to the axial radius. For more general purposes, a more elaborate treatment might therefore recast Eq. (25) in terms of a solvent radius parameter rather than Vs, where a cross-sectional radius is more appropriate for elongated shapes. 

Effective ionic radius from crystallographic data (nm) Solvent radius in nm defined as rs = [(Vs x 10 )/(8Nav)] Molar refractivity of an ion... 

Sample Solvent Radius of gyration (nm) Morphological diameter (nm)... 

As examples of the level of accuracy obtainable for TEMPO we basically use two papers from 2006 [86, 90]. As an example of particular methods development, aiming also at other redox shuttle families, the first of these papers also includes the systematic variation of CPCM parameters (B3LYP/6-31G ), something we do not observe in any other papers. Both the solvent radius and the dielectric constant were varied and TEMPO applied as the probe by varying the radius between 4.0 and 6.0 A, for a dielectric constant of 60.0, and the dielectric constant between 40.0 and 80.0, for a radius of 5.0 A, the TEMPO is shown to vary between 3.63 and 3.65 V, and thus being rather insensitive to this variation. 

AG(s) given in Equation 13.3 represents the situation after some time when the solvent has had time to relax around the new charges. It is of great interest to study also the situation immediately after excitation. The problem is that there are no reduction potentials for that situation. We first derive the relationship between E (D) and 1(D) with the help of the Bom equation. The ionization energy I is the oxidation potential in a medium with dielectric constant c = 1, while E is the same oxidation potential in a medium with the dielectric constant c after a sufficiently long time for the solvent to polarize (Hgure 13.4). We have (a is a solvent radius around the charge)... 

For computation of ASA the computer program SURFAC was used. It requires geometry of a molecule and van der Waals radii of every atom and the solvent moleculeas the main input. Standard tabulated values (Weast 1974) of van der Waals radii of atoms were used. For water, the radius used was 1.5A (Pearlman 1981). In order to calculate SA, the solvent radius is assumed to be zero (Bultsma 1980). For chlorophenols, the geometry, optimized by MNDO MO calculations (Gombar Richards 1985), was input to SURFAC whereas for chlorobenzenes and acyclic chlorocarbons, planar and fully staggered conformations, respectively, were assumed and standard angles and distances used to generate the cartesian co-ordinates. 

Although not necessarily related to the central COSMO idea, the COSMO implementations have a special efficient way of cavity construction, which is illustrated schematically in Figure 1. The cavity is assumed to be a kind of SES. To construct this surface, in a first step the SAS is built as the exterior of all spheres of radius R, -F / soiv, where the / , are the radii of the atoms, usually defined as element specific radii, and Rsoiv is some radius representing a typical maximum curvature of solvent molecular surfaces.The default for Rsoiv is set to 1 A, and this has turned out to be a good choice for a great variety of solvents. R oiv should not be misinterpreted as a mean solvent radius, nor modified for different solvents. All spheres are... 

This is similar to equation (II) in that it contains corresponding terms, shown here as effectively an area times a surface tension y and a curvature correction to the surface tension, and a pressure-volume term, but does not have the point particle contribution term involving Kp which is important for microscopic cavities. The constant S is about half a solvent radius. 

The diffusion coefficient varies inversely with viscosity when the ratio of solute to solvent radius exceeds five. This behavior is reassuring because the Stokes-Einstein equation is derived by assuming a rigid solute sphere diffusing in a continuum of solvent. Thus, for a large solute in a small solvent, Eq. 5.2-1 seems correct. 

In closing this section, we add that the Stokes-Einstein equation breaks down when the ratio of the solute-to-solvent radius becomes less than 5. Errors become quite large in high-viscosity solvents, and we find that the product tends to become a constant [4Q. 

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