Constant of Solvents

Rates of degradation between ions and dipoles in solutions depend on the bulk properties of the solvent, such as the dielectric constant. Variation in the dielectric constant of a solvent can cause A 3 in Eq. (2.7) to vary, leading to a variation in rate constants with changes in dielectric constant. For example, ion-dipolereaction rate constants have been related to the dielectric constant D of the solvent through Eq. (2.1 10), which was developed by Amis.396 

kD= is the rate constant at infinite dielectric constant, ZA, p, and r are ion charge, dipole moment and the shortest ion-dipole distance, respectively, and k is the Boltzmann constant. The term 0 represents the alignment of reactants, and cos 0 is unity in the case of head-on alignment. Thus, as the dielectric constant decreases, the rates of anion-dipole reactions decrease and the rates of cation-dipole reactions increase. As indicated by a linear relationship with a positive slope in log k versus 1/D plots (Fig. 84), the hydrolysis rate constant for chloramphenicol in water-propylene glycol mixtures increases with decreasing dielectric constant, suggesting a hydronium ion-dipole reaction.397 

The dependence of ion-ion reaction rate constants on the dielectric constant of the solvent is given by 

A complication in interpreting the effect of solvent dielectric constants on kinetic data is that the dissociation constants of various species can change with changing solvent properties. Also, the possible role that a solvent modifier plays in the reaction must be considered. For example, an alcohol or glycol or some other co-solvent might be used to modify the dielectric constant of water. The co-solvent molecule may react with the drug in question, thus complicating the interpretation of the solvent dielectric effect. 

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Table 1.5 Self-ionization constants of solvents. (According to B. Tremillon)... 

K = electrical conductivity of solution Vf = flow rate volume/time of solution through ES capillary y = surface tension of solvent e = permitivity of solvent Co = permitivity of vacuum e/ o = dielectric constant of solvent... 

Chain Transfer Constants of Solvent to Styrene in Free Radical Chain Polymerization at 60°C... 

Figure 3.11 Catalytic efficiency, (fcca,/K ,)app ( ), of salt-activated subtilisin Carlsberg in hexane, THF, and acetone in comparison with T2 (transverse relaxation constant) (O) of mobile deuterons as a function of dielectric constant of solvent [103].

Eluting power roughly parallels the dielectric constants of solvents. The series also reflects the extent to which the solvent binds to the column material, thereby displacing the substances that are already adsorbed. This preference of alumina and silica gel for polar molecules explains, for example, the use of percolation through a column of silica gel for the following purposes-drying of ethylbenzene, removal of aromatics from 2,4-dimethylpentane and of ultraviolet absorbing substances from cyclohexane. 

Figure 4.9 Effect of refractive index and dielectric constant of solvent on O—O transitions of a polar molecule.

In the homogeneous mechanism, the reaction is assumed to start by protonation of one of the reactants, either ester (mechanisms denoted as Aac1 and Aac2 [397,398]) or, less frequently, alcohol (mechanism Aal1). It seems likely that protonation of reactants is an important step in esterification catalysed by ion exchangers, too. This follows from all that has been said above about the effect of the acidic properties of ion exchangers on their catalytic activity and is further supported by the effect of the dielectric constant of solvents (Fig. 18), which indicates that the reaction mechanism involves a positive ion and a dipolar molecule [454]. 

It is interesting to note that this relation was verified for polymerizations of styrene, p-methoxystyrene, and isobutylvinylether with iodine by Kanoh and Higashimura (19). They have demonstrated that the apparent rate constants of termination, propagation, and monomer transfer increased with increasing dielectric constant of solvent, and the rates of the increase for these three rate constants were of the order of Eq. (21). 

Fuoss (40) has improved Bjerrum s original treatment (37) of this situation and, although a number of other sophistications have been introduced, his formulation (41) is the one most used today. In fact rather fortuitously the relatively low dielectric constants of solvents employed in organic chemical reactions, particularly ionic polymerisations, are ideal media for the application of these theories. The analysis carried out by Fuoss leads not surprisingly to an equation... 

Table 4. Reaction rates and dielectric constants of solvents and reaction mixtures for the copolymerization of ethylene glycol carbonate (0.1 mol) with phthalic anhydride (0.1 mol) in, 100 ml of solvent initiated with KC1 (0.001 mol-%) at 200 °C. 541 (Reproduced by courtesy of Hiithig and...

The medium in which a species is dissolved or on which it is adsorbed may exert considerable influence on the intensity and wavelength of the fluorescence. Polar materials such as alcohols or esters frequently increase the intensity of the fluorescence relative to non-polar hydrocarbon solvents. The solvent environment often prevents or inhibits intersystem crossing to a triplet state in favour of excitation to a singlet state and fluorescence, while in many cases the opposite is true. The dielectric constant of solvents has been shown to influence the fluorescence intensity and wavelength maxima of some compounds [33,34]. Fig.2.9 shows the effect of solvent dielectric constant on the fluorescence intensity of DNS-phenol, while Table 2.4 shows the corresponding effect on the fluorescence wavelength [34]. For DNS-phenol, solvents of low dielectric constants result in the most intense fluorescence and shift the wavelength maxima to lower values. 

Figure 20 Relation between diastereomer excess (De%) and dielectric constant of solvent.

Phenomenology of the thermal decomposition, 765 Phonon model, 646 Photochemical degradation, 779 Photo-doping, 341 Photooxidation, 781, 783 Physical ageing, 438 Physical constants of solvents, 904 Physical data of simple gases, 657, 658 Physical properties of polymers, 920 Physical quantity, 52 Pilling, 881 tester, 881... 

Where e is the elementary electric charge, r is the radius of ions, and e is the dielectric constant of solvent. 

The failure of the solvent relative permittivity to represent solute/solvent interactions has led to the definition of polarity in terms of empirical parameters. Such attempts at obtaining better parameters of solvent polarity by choosing a solvent-dependent standard system and looking at the changes in parameters of that system when the solvent is changed e.g. rate constants of solvent-dependent reactions or spectral shifts of solvatochromic dyes) are treated in Chapter 7. 

The aforementioned macroscopic physical constants of solvents have usually been determined experimentally. However, various attempts have been made to calculate bulk properties of Hquids from pure theory. By means of quantum chemical methods, it is possible to calculate some thermodynamic properties e.g. molar heat capacities and viscosities) of simple molecular Hquids without specific solvent/solvent interactions [207]. A quantitative structure-property relationship treatment of normal boiling points, using the so-called CODESS A technique i.e. comprehensive descriptors for structural and statistical analysis), leads to a four-parameter equation with physically significant molecular descriptors, allowing rather accurate predictions of the normal boiling points of structurally diverse organic liquids [208]. Based solely on the molecular structure of solvent molecules, a non-empirical solvent polarity index, called the first-order valence molecular connectivity index, has been proposed [137]. These purely calculated solvent polarity parameters correlate fairly well with some corresponding physical properties of the solvents [137]. 

It is obvious that such a definition of solvent polarity cannot be measured by an individual physical quantity such as the relative permittivity. Indeed, very often it has been found that there is no correlation between the relative permittivity (or its different functions such as l/sr, (sr — l)/(2er + 1), etc.) and the logarithms of rate or equilibrium constants of solvent-dependent chemical reactions. No single macroscopic physical parameter could possibly account for the multitude of solute/solvent interactions on the molecular-microscopic level. Until now the complexity of solute/solvent interactions has also prevented the derivation of generally applicable mathematical expressions that would allow the calculation of reaction rates or equilibrium constants of reactions carried out in solvents of different polarity. 

By plotting log d[M]/dt( vs. log[I]o it could be shown that the order with respect to initiator is indeed one. However, the order with respect to monomer depends on the polymerization solvent being above two in solvents with dielectric constant below the monomers and only equal to two when dielectric constants of solvent and monomer are equal. 

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