The Solvation Process

It is impossible to follow by measurements an actual experimental process of the transfer of a single ion from its isolated state in the gas phase to its fully solvated state in a solntion. Such a process, however, may be dealt with as a thought process and theoretical considerations may be applied to it. 

Ben-Naim and Marcus [1] discussed a process termed solvation that applies to a particle of a (non-ionic ) substance transferring from its isolated state in the gas phase into a liquid irrespective of the concentration. The particle would then be surrounded by solvent molecules only in an ideally dilute solution (infinite dilution), or by solvent molecules as well as by molecules of its own kind at any arbitrary mole fraction with regard to the solvent, and by molecules identical with itself only on condensation into its own liquid. The interactions involved and their thermodynamics are aU covered by the same concept of solvation. The solvation process of a solute S is defined [1] as the transfer of a particle of S Ifom a fixed position in the (ideal) gas phase (superscript G) to a fixed position in a liquid (superscript L) at a given temperature T and pressure P. Statistical mechanics specifies the chemical potential of S in the ideal gas phase as  

Ions in Solution and Their Solvation, First Edition. Yizhak Marcus. 

Here is the internal partition function of S (=1 for a strnctureless particle, such as a noble gas atom), is its number density, and Ag is its momentum partition function. The qnantity p in either phase pertains to the particle at a fixed position where it is devoid of the translational degrees of freedom, and kj In pJl expresses its liberation from this constraint. The Gibbs energy of solvation, is expressed as the change in the chemical potential of S at equilibrium, where is then  

The quantity Ap is called also the coupling work of the solute S with its surroundings. If the internal partition function q is modified by the presence of the solvent in the liquid, then these changes are absorbed into Ap and are part of the solvation interactions measured by it. The molar Gibbs energy of solvation is AG = N Ap and the corresponding molar entropy and enthalpy of solvation are  

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An empirical solution of Eq. (1) consists of analysis of the solvation process of the target molecule in solute, finding descriptors, which govern each phase and using them to calculate logP. This was done, for example, in the LSER approach which considered that the process of any solvation involves (i) endoergic creation of a cavity in the solvent and (ii) incorporation of the solute in the cavity with consequent setting up of various solute-solvent interactions [4—6]. Each of these steps... 

Abstract This chapter reviews the theoretical background for continuum models of solvation, recent advances in their implementation, and illustrative examples of their use. Continuum models are the most efficient way to include condensed-phase effects into quantum mechanical calculations, and this is typically accomplished by the using self-consistent reaction field (SCRF) approach for the electrostatic component. This approach does not automatically include the non-electrostatic component of solvation, and we review various approaches for including that aspect. The performance of various models is compared for a number of applications, with emphasis on heterocyclic tautomeric equilibria because they have been the subject of the widest variety of studies. For nonequilibrium applications, e.g., dynamics and spectroscopy, one must consider the various time scales of the solvation process and the dynamical process under consideration, and the final section of the review discusses these issues. 

With taken into account, that the constants of the reaction rates are determined via the equilibrium constants of the activated reactive complex formation, and the last in part depend on the solvation processes, it was proposed by Koppell and Palm [22] the following equation in order to determine the influence of medium properties on the reaction rates of processes proceeding in it ... 

Generally, the solubihty characteristics of organic compounds depend on several properties of the participating components. For the solute, these properties are the molecular size and structure, polarity, dipole moment, va-por/sublimation pressure, and, in the case of a sohd solute, also its melting characteristics. When using SCCO2 as the solvent, mainly its dipole moment and quadrupole moment influence the solvatation process (Sect. 2.2). 

These expressions appear more applieable to nonpolar solvents or mixtures than to polar solvents. The nature of the solvation process (and the radii and so forth of the solvated reactants) may stay approximately constant in the first situation but almost certainly will not in the seeond. The function (E>op A ) features in the reorganisation term Xq which is used for estimating rate constants for redox reactions (Eqn. 5.23). is the optical dielectric constant and Dj the static dielectric constant (= refractive index ). 

When a solute particle is introduced into a liquid, it interacts with the solvent particles in its environment. The totality of these interactions is called the solvation of the solute in the particular solvent. When the solvent happens to be water, the term used is hydration. The solvation process has certain consequences pertaining to the energy, the volume, the fluidity, the electrical conductivity, and the spectroscopic properties of the solute-solvent system. The apparent molar properties of the solute ascribe to the solute itself the entire change in the properties of the system that occur when 1 mol of solute is added to an infinite amount of solution of specified composition. The solvent is treated in the calculation of the apparent molar quantities of the solute as if it had the properties of the pure solvent, present at its nominal amount in the solution. The magnirndes of quantities, such as the apparent molar volume or heat content, do convey some information on the system. However, it must be realized that both the solute and the solvent are affected by the solvation process, and more useful information is gained when the changes occurring in both are taken into account. 

One can consider two facets of the solvation process, the energetics and the kinetics. Clearly, the kinetics will not matter if reactions take place on a time scale that is much faster or much slower than the solvation process. However, if reaction and solvation occur on the same time scale, the considerable energy changes that the solvation process can engender will affect the reaction. In fact, exactly what solvent motions take place during the solvation process may well be important. Thus, it is of interest to understand the kinetics of the solvation process. 

The solvation processes for the anion systems were simulated using both simple ball models and more representational models of the solvent and solute [14,22]. 

Anion solvation has been studied by observing the shift in the absorption spectrum of the benzophenone anion in various solvents and as a function of temperature. The benzo-phenone anion was formed from the reaction of the benzophenone molecule and a precursor to the solvated electron. Approximately 0.25 M benzophenone is put into the solution so that all the presolvated electrons will react with the benzophenone and virtually none will form the solvated electron. This process occurs much more quickly than the solvation processes that are observed [14,20]. 

It is important to stress that not only the direct solute-solvent interactions are taken into account in the solvation process, but also the other changes mentioned. Excluded from consideration are effects due to translational degrees of freedom of the solute, which are due to the different volumes at the disposal of the solute particle in these phases. 

Current work with supercritical fluids can also illustrate the importance of cosolvents. Cosolvent effects in supercritical fluids can be considerable for systems where the cosolvent interacts strongly with the solute. A correlation suggests that both physical and chemical forces are important in the solvation process in polar cosolvent supercritical CO2 mixtures. The model coupled with the correlation represents a step toward predicting solubilities in cosolvent-modified supercritical fluids using nonthermody-namic data. This method of modeling cosolvent effects allows a more intuitive interpretation of the data than either a purely physical equation of state or ideal chemical theory can provide (Ting et al., 1993). 

The assumption underlying continuum solvation models, which are the subject of this chapter, is that one may remove the huge number of individual solvent molecules from the model, as long as one modifies the space those molecules used to occupy so that, modeled as a continuous medium, it has properties consistent witli those of the solvent itself. To determine how to define such a medium, one must consider the solvation process itself. 

Another physical effect associated with solvation is cavitation. It is again helpful to visualize the solvation process as a stepwise procedure. Here, we imagine the first step as being creation of a cavity of vacuum within the solvent into which the solute will be inserted as a second step. The energy cost of the cavity creation is the cavitation energy. Note that energy is always required to create the cavity - if it were favorable to create bubbles of vacuum in the liquid, the solvent would not remain in the liquid phase. 

Other energetic components associated widi the solvation process include non-electrostatic aspects of hydrogen bonding and solvent-structural rearrangements like the hydrophobic effect. Despite many years of study, the fundamental physics associated with both of these processes remains fairly controversial, and physically based models have not been applied with any regularity in the context of continuum solvation models. 

To proceed further it is necessary to make some assumptions about the interrelations of the - G terms. Such assumptions will be extrathermodynamic in nature. It will be assumed that each Hi term can be split into an intrinsic contribution from the bare ion and a term from the solvation process. Thus... 

It is immediately apparent that because only differences in chemical potential between states can be measured, the intrinsic term will always disappear. It will be further assumed that long-range and short-range contributions to the solvation process may be separated out. Thus... 

In this work we presented the results of Molecular Dynamics simulations performed to study the solvatochromism and the dynamic stokes-shift of coumarin 153 in mixtures of solvents. We showed the ability of MD to reproduce available data of the time-dependent Stokes-shifts. Moreover, MD allowed us to interpret these dynamics in benzene-acetonitrile mixtures in terms of motions of benzene around the coumarin or rotation of acetonitrile. The role of benzene in the solvation process of Cl53 seems to be more important than usually assumed. 

Such a time scale separation between system and bath may often be appropriate when dealing with intramolecular vibrational motions of molecules but is likely never appropriate for electronic transitions in solution near room temperature. In the past 10 years much effort has been devoted to dynamical aspects of the solvation process in polar liquids utilizing experiments [2-4], theory [5, 6], and computer simulations of molecular dynamics [7-10]. The... 

The analysis of the transient fluorescence spectra of polar molecules in polar solvents that was outlined in Section I.A assumes that the specific probe molecule has certain ideal properties. The probe should not be strongly polarizable. Probe/solvent interactions involving specific effects, such as hydrogen-bonding should be avoided because specific solute/solvent effects may lead to photophysically discrete probe/solvent complexes. Discrete probe/solvent interactions are inconsistent with the continuum picture inherent in the theoretical formalism. Probes should not possess low lying, upper excited states which could interact with the first-excited state during the solvation processes. In addition, the probe should not possess more than one thermally accessible isomer of the excited state. 

Unfortunately, the procedure just described to determine C(t) can consume many hours of spectrometer time, since several transients must be acquired and processed. Recently, an alternative timesaving procedure for measuring C(t) was developed [23,31], The procedure, which is approximate, requires a single emission transient and certain photophysical data on the probe. It is based on a simple photodynamic model, in which it is assumed that the spectrum of the probe is a simple function of a single solvent parameter, X, denoted as the solvent polarization. During the solvation process, X is time-dependent, such that C(t) = [X(t) — A (oo))]/ [X(0) - X(oo)]. 

Alternatively, the solvent dependence of X(t = oo) can be estimated from the equilibrated fluorescence maximum hvfl of the probe in each solvent. Thus the dependence of the photophysical properties of the probe, on its fluorescence maximum hvfl, can be established. This is demonstrated in Figure 14. The usefulness of the curves in Figure 14 is clear if one considers Eq. (23) and the fact that in the subpicosecond solvation experiments, the excited state population Se can be assumed to be a constant during the solvation process. It follows that the curves in Figure 10 represent how the fluorescence intensity at different wavelengths should change as the emission maximum... 

Recently, several authors have studied solvation dynamics of aqueous solutions using molecular dynamics (MD) computer simulations [36, 57, 58, 112], The simulations offer a detailed molecular approach to interpreting the experimental results, as they focus particularly on the microscopic, molecular aspects of the solvation process. 

Ion exchange from organic solvents and mixed organic aqueous solvents offers interesting possibilities for the extraction and separation of metals because of the different nature of the solvation processes in these systems. Only cation solvation is significant in dipolar, aprotic, organic... 

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