Solvated volume

For the mechanistic interpretation of activation volume data for nonsymmetrical electron-transfer reactions, it is essential to have information on the overall volume change that can occur during such a process. This can be calculated from the partial molar volumes of reactant and product species, when these are available, or can be determined from density measurements. Efforts have in recent years focused on the electrochemical determination of reaction volume data from the pressure dependence of the redox potential. Tregloan and coworkers (139, 140) have demonstrated how such techniques can reveal information on the magnitude of intrinsic and solvational volume changes associated with electron-transfer reactions of transition... 

With these assumptions, the distribution of boron species (among boric acid, borate anion, borate esters, and borate diesters) reduces to a function of boron concentration, polymer concentration, radius of gyration and solvated volume fraction of a polymer unit, solution pH, and the association constants for the borate esters of the functional groups employed. 

If a polymer molecule in solution behaves as a random coil, its average end-to-end distance is proportional to the square root of its extended chain length (see page 25) - i.e. proportional to Ai 5, where Mr is the relative molecular mass. The average solvated volume of the polymer molecule is, therefore, proportional to M 5 and, since the unsolvated volume is proportional to A/r, the average solvation factor is proportional to (i.e. Af 5). The intrinsic viscosity of... 

For the case of constant valence, the counterion of higher atomic number (lower hydrated radius or smaller solvated volume) at low concentration and ordinary temperature. Thus,... 

Here, we use straight derivatives to indicate differentiation along the equilibrium line. The two derivatives of AG on the rhs of equation (7.108) are identified as the solvation entropy and the solvation volume, respectively thus,... 

Van Krevelen [20] examined various equations for solution viscosity. He recommended the use of the following two equations [24,25] for the r ss of dilute polymer solutions (at polymer concentrations above the limit of c—>0 but with low values of c, especially c<0.01 g/cc). In these equations, Solv denotes the solvated volume fraction (see Section l.D for conversions between volume, weight and mole fractions) of the polymer, and p is the polymer bulk density. 

Figure 12.3. Solvated volume fraction intrinsic viscosity [r ] in cc/g (used as curve labels) and concentration c for a polymer of density p=l g/cc. The dilute solution approximation should be most accurate for <3>soiv<0.156 (below lower dashed line), become increasingly less accurate with increasing Solv for 0.156<soiv<0.2854 (between the two dashed lines), and certainly be invalid for Osoiv>0.2854 (above upper dashed line). 

The interpretation of pressure effects on the photochemistry of metal complexes in solution is in some cases limited by information on the partial molar volume of ES species and the difficulty to separate intrinsic and solvational volume contributions. The latter can be resolved in more detail by performing systematic solvent-dependence studies, through which corrections via the application of appropriate solvent parameters can be made in order to extract the intrinsic volume changes that, for instance, control the nature of the photosubstitution mechanism. Other difficulties are the fragmentary nature of much of the published pressure data and the need for a better understanding of the effect of pressure on the rates of photophysical processes. 

In some of the simplest cases (namely, solvent exchange and self-exchange reactions), the experimental data could be supported by theoretical calculations. Significant developments are expected to occur in this area, such that the theoretical optimization of transition state structures will become standard practice in mechanistic studies. Here again volume of activation data will play a crucial role, since they present an experimental measure of the intrinsic and solvational volume changes in the transition state and form a basis for comparison with theoretical predictions. It will be an ideal situation when volume profiles can be constructed for more complex reaction sequences, for instance for catalytic cycles in enzymatic processes. This will, as in the case of more simple reactions, enhance our understanding of complex chemical processes and improve our ability to tune them. 

Picosecond laser spectroscopy offers direct access to molecular vibrational (T,) and phase (Tj) relaxation as well as orientational dynamics of molecules, t,< . In contrast to experiments on vibrational relaxation in liquids, all those on the reorientational process have been confined to large polyatomic molecules, particularly dye molecules in probe solvents for pragmatic reasons. Since the slip boundary conditions are also a sensitive function of the shape of the molecules and solute-solvent interactions, there is some uncertainty in deciding whether or not it is the local interaction in terms of the solvation volume, or the boundary condition, or both, that varies for a given molecule in a range of liquids such as the... 

Thus, intrinsic and solvational volume contributions affect the partial molar volumes of the product and transition states in a similar manner and are governed by the nature of Rjdien and X"". It is also deduced that the transition state is more compact than either the reactant or product ground state. 

Porphyrin complex Z Unit cell volume (A ) Porphyrin volume/unit cell°(A ) Solvate volume/unit cell°(A ) Void volume/unit cell (A ) Total channel volume/unit cell (A )... 

Porphyrin and solvate van dcr Waals volumes were calculated from Quanta for each unit cell. Void volume is defined as the unit cell volume minus the sum of the porphyrin volume and the solvate volume. For the inetalloporphyrins, the volumes of the coordinated ligands were counted as pan of the poiphyrin volume. 

Total channel volume is defined as the sum of void and solvate volume, in A. Values in brackets refer to the percentage of total channel volume in the unit cell. 

A larger solvated volume and therefore a lower diffusion (through the liquid phase) coefficient. 

Generally, the experimental data in Table 5.3 are consistent with these hypotheses. Firstly, the surface partition coefficient, is the ratio of the surface saturation concentration (T ) to the overall amount of surfactant needed to saturate the surface (keeping in mind that a significant amount of the surfactant remains solubilised). Therefore, at relatively constant T , should decrease as the solubility of the copolymer increases. This can be seen in Table 5.3. Secondly, the solvated volumes were not directly measured however, the diffusion coefficients were measured and they decreased as X increased. It is generally known that the diffusion coefficient varies as the inverse of the solvated volume [49]. From this relationship, one would conclude that the solvated volumes of the copolymers increased with X. Thirdly, the interfacial areas of the copolymers generally increased as X increased. Finally, we were not able to measure the surface viscosities of these materials in solution. ITowever, all of them yielded mobile-surfaced films. This means that their surface viscosities were relatively low, as expected. 

Fig. 1.48 (a) Solvation volumes, and (b) partial molar heat capacity of... 

We shall now estimate the conditional solvation Gibbs or Helmholtz energy per arm of a water molecule. This quantity is useful in various applications in the theory of aqueous solutions. Since PAV, where A is the solvation volume, is usually negligible compared with AG, we shall actually compute the solvation Helmholtz energy and assume that AG... 

The last quantity we shall discuss here is the solvation volume. The volume of solvation of a solute is defined as... 

Finally, we note that the solvation volume (here in the T, P, N ensemble) of a solute s in very dilute solutions may be... 

In (3.4.22), the solvation volume is viewed as consisting of two terms an average Voronoi polyhedron of the solute and a change in the volume of the solvent due to solute induced changes in the distribution of the volumes of the Voronoi poly-hedra of the solvent molecules. 

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