Dielectric constant of medium

R = factor for electrical relaxation D = dielectric constant of medium F = factor for size of spheres and = zeta potential. 

S Dielectric constant of medium surrounding particle, dimensionless... 

Fig. 18. Calculated influence of dielectric constant of medium surrounding the complex on the preference of K+ over Baa+...

Figure 15-7. Interaction energies (kcal/mol) between imidazole and water molecule, at each of various sites defined in Figure 15-4, within context of solvent. Horizontal axis F0 is defined as (e—l)/(e+2) where represents dielectric constant of medium...

Fig. 20.—Critical Micelle Concentration (at Room Temperature), Rate Constant (at 60°), and Maximum Amount of Solubilizing Water (at Room Temperature)asa Function of Dielectric Constant of Medium for the Process of Hydrolysis of Elextrin by Means of Dodecylben-zenesulfonic acid. (1, in hexane 2, in cyclohexane 3, in CCI4 4, in benzene S, in toluene and 6, in o-xylene.)...

Dielectric Sedimentation Method. The measurement relies upon the sensing of changes in the dielectric constant of medium between a pair of capacitance sensing plates placed around the sedimentation tube. 

Vr = electrostatic repulsive energy between two like particles e = dielectric constant of medium a = particle radius... 

Strong electrolytes are dissociated into ions that are also paired to some extent when tlie charges are high or the dielectric constant of the medium is low. We discuss their properties assuming that the ionized gas or solution is electrically neutral, i.e. 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

The angles ot, p, and x relate to the orientation of the dipole nionient vectors. The geonieti y of interaction between two bonds is given in Fig. 4-16, where r is the distance between the centers of the bonds. It is noteworthy that only the bond moments need be read in for the calculation because all geometr ic features (angles, etc.) can be calculated from the atomic coordinates. A default value of 1.0 for dielectric constant of the medium would normally be expected for calculating str uctures of isolated molecules in a vacuum, but the actual default value has been increased 1.5 to account for some intramolecular dipole moment interaction. A dielectric constant other than the default value can be entered for calculations in which the presence of solvent molecules is assumed, but it is not a simple matter to know what the effective dipole moment of the solvent molecules actually is in the immediate vicinity of the solute molecule. It is probably wrong to assume that the effective dipole moment is the same as it is in the bulk pure solvent. The molecular dipole moment (File 4-3) is the vector sum of the individual dipole moments within the molecule. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

The signal is reflected from the product surface because there is an abmpt impedance change in the sensor at the air—product interface. Because the electromagnetic field extends outside the two sensor conductors, the sensor impedance depends on the dielectric constant of the surrounding medium. In... 

Studies have shown that, in marked contrast to carbanionic polymerisation, the reactivity of the free oxonium ion is of the same order of magnitude as that of its ion pair with the counterion (6). On the other hand, in the case of those counterions that can undergo an equiUbrium with the corresponding covalent ester species, the reactivity of the ionic species is so much greater than that of the ester that chain growth by external attack of monomer on covalent ester makes a negligible contribution to the polymerisation process. The relative concentration of the two species depends on the dielectric constant of the polymerisation medium, ie, on the choice of solvent. 

The dielectric constant of the medium affects the equilibria where charges are generated in the dissociations e.g. AH A -I- H" " and therefore affects the pK values. However, its effect on dissociations where there are no changes in total charge such as BH B -1- H" " is considerably less, with a slight decrease in pK with decreasing dielecuic constant. 

The magnitude of the anomeric effect depends on the nature of the substituent and decreases with increasing dielectric constant of the medium. The effect of the substituent can be seen by comparing the related 2-chloro- and 2-methoxy-substituted tetrahydropy-rans in entries 2 apd 3. The 2-chloro compound exhibits a significantly greater preference for the axial orientation than the 2-methoxy compound. Entry 3 also provides data relative to the effect of solvent polarity it is observed that the equilibrium constant is larger in carbon tetrachloride (e = 2.2) than in acetonitrile (e = 37.5). 

The Self-Consistent Reaction Field (SCRF) model considers the solvent as a uniform polarizable medium with a dielectric constant of s, with the solute M placed in a suitable shaped hole in the medium. Creation of a cavity in the medium costs energy, i.e. this is a destabilization, while dispersion interactions between the solvent and solute add a stabilization (this is roughly the van der Waals energy between solvent and solute). The electric charge distribution of M will furthermore polarize the medium (induce charge moments), which in turn acts back on the molecule, thereby producing an electrostatic stabilization. The solvation (free) energy may thus be written as... 

The simplest reaction field model is a spherical cavity, where only the net charge and dipole moment of the molecule are taken into account, and cavity/dispersion effects are neglected. For a net charge in a cavity of radius a, the difference in energy between vacuum and a medium with a dielectric constant of e is given by the Bom model. ... 

Some recent studies have underlined the effect that certain physical properties of the reaction medium have in governing the nature and yields of the products obtained when indole Grignard reagents react with alkyl or alkynyl halides. Such factors include the basicity and dielectric constant of the medium and its ability to solvate any of the reacting species. ... 

If a piece of metal, such as silver, is dipping into a solvent, and a positive atomic core is taken from the surface into the solvent, the ion is again surrounded by its electrostatic field but free energy has been lost by the dielectric, and a relatively small amount of work has had to be done. The corresponding potential-energy curve (Fig. 96) is therefore much less steep and has a much shallower minimum than that of Fig. 9a. For large distances d from a plane metal surface this curve is a plot of — c2/4td where t is the dielectric constant of the medium at the temperature considered The curve represents the work done in an isothermal removal of the positive core. 

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