Volume of solvation

Strictly speaking, Eq. (2.1) is an approximation, since it should be taken at the constant pressure P°, but actually is obtained experimentally at the variable pressurep. However, this introduces a negligible error, SAG (P° - p) AV. The volume of solvation of the solvent is given by the molar volume V, corrected for the isothermal compressibility kt ... 

Concentrative refractivity — This is the first derivative of the refractive index of a solution over the concentration of a given species (dn/dC). The variations of the refractive index due to the inhomogeneous spatial concentration of chemical species can be decoupled as (dn/dC) = (dn/dp)c(dp/dC) + (dn/dC)p where the first term is related to the molecular (or ionic) volume of solvated species and the second one is associated to the electronic structure of such species [i]. The value of (dn/dCj) can be considered a constant for rather diluted aqueous solutions and therefore, it is characteristic for each solvated species [ii]. 

Note that the universal calibration relations apply to polymeric solutes in very dilute solutions. The component species of whole polymers do indeed elute effectively at zero concentration but sharp distribution fractions will be diluted much less as they move through the GPC columns. Hydrodynamic volumes of solvated polymers are inversely related to concentration and thus elution volumes may depend on the concentration as well as on the molecular weights of the calibration samples. To avoid this problem, the calibration curve can be set up in terms of hydrodynamic volumes rather than molecular weights. A general relation [20] is... 

Note that the volume changes for the last two processes are identical. We note also that for the liquid phases at room temperature k1t is much smaller than 1 atm-1 (e.g., for water at 0°C, kTxT 1 cm3 mol-1, AV 20 cm3 mol-1, and kT / atm w2x 104cm3 mol-1). Similarly, in equation (7.73) k1t < i P-1 (the limit of an ideal-gas phase). Thus, the volume change for the three standard processes is dominated by the terms which originate from the ideal-gas compressibility. Because of this undesirable feature, it is common to abandon these processes when studying the volume of solvation. Almost all researchers who study the solvation phenomena apply one of these standard processes for quantities like the Gibbs energy, entropy and enthalpy of... 

Partial molal volumes of aqueous ionic species vary considerably with changes in pressure and temperature. The molar volume of an aqueous species can be split into a Coulombic and a non-Coulombic term. The non-Coulombic term consists of the intrinsic volume of the ion. The Coulombic term consists of the volume of solvation and the volume of collapse. The volume of solvation is related to the orientation of water dipoles around the aqueous species, and the volume of collapse is the component of the partial molal volume related to the collapse of the water structure in the vicinity of the aqueous species. The pressure and temperature dependence of the molar volume of aqueous species arises from a similar change in the electrostatic properties of the solvent... 

The volume change is the sum of terms due to the charge, the dipole, and the quadrupole. Each term is the sum of two subterms, one in 8t- j8p, which is usually but not necessarily negative and which describes an electrostriction of the solvent, and one in d In aJ8p, which is necessarily negative or zero and which describes a compression of the cavity. The electrostatic volume of solvation is therefore the sum of the electrostriction of the solvent and the compression of the cavity. 

Electrostatic Oibbs Free Energies and Volumes of Solvation... 

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

The constants K depend upon the volume of the solvent molecule (assumed to be spherica in slrape) and the number density of the solvent. ai2 is the average of the diameters of solvent molecule and a spherical solute molecule. This equation may be applied to solute of a more general shape by calculating the contribution of each atom and then scaling thi by the fraction of fhat atom s surface that is actually exposed to the solvent. The dispersioi contribution to the solvation free energy can be modelled as a continuous distributioi function that is integrated over the cavity surface [Floris and Tomasi 1989]. 

If the solute molecule is solvated, then any bound (subscript b) solvent (subscript 1) must be added to the volume of the unsolvated solute (subscript 2) that is. 

Continuum models of solvation treat the solute microscopically, and the surrounding solvent macroscopically, according to the above principles. The simplest treatment is the Onsager (1936) model, where aspirin in solution would be modelled according to Figure 15.4. The solute is embedded in a spherical cavity, whose radius can be estimated by calculating the molecular volume. A dipole in the solute molecule induces polarization in the solvent continuum, which in turn interacts with the solute dipole, leading to stabilization. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

The volumes of activation for some additions of anionic nucleophiles to arenediazonium ions were determined by Isaacs et al. (1987) and are listed in Table 6-1. All but one are negative, although one expects — and knows from various other reactions between cations and anions — that ion combination reactions should have positive volumes of activation by reason of solvent relaxation as charges become neutralized. The authors present various interpretations, one of which seems to be plausible, namely that a C — N—N bond-bending deformation of the diazonium ion occurs before the transition state of the addition is reached (Scheme 6-2). This bondbending is expected to bring about a decrease in resonance interaction in the arenediazonium ion and hence a charge concentration on Np and an increase in solvation. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Electroviscous effect occurs when a small addition of electrolyte a colloid produces a notable decrease in viscosity. Experiments with different salts have shown that the effective ion is opposite to that of the colloid particles and the influence is much greater with increasing oxidation state of the ion. That is, the decrease in viscosity is associated with decreased potential electrokinetic double layer. The small amoimt of added electrolyte can not appreciably affect on the solvation of the particles, and thus it is possible that one of the determinants of viscosity than the actual volume of the dispersed phase is the zeta potential. 

Figure 4. Schematic description of the swelling process. The molecules of the swelling liquid start to penetrate inside the polymer framework from its surface (a) and to solvate the polymer chains. The polymer chain start to stretch out and to move away from one another the apparent volume of the polymer increases and the first nanopores are formed (b). Swelling stops when increasing elastic forces set up by the unfolding of the polymer chains counterbalance the forces which drive the molecules of the swelling agent into the polymer framework (c).

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