Molar polarizability

It is clear from the equation that the molar polarizability is proportional to —, the... 

Molar polarizability, P, can be evaluated from measurements of D by Eq. (18), and a critical test of the Debye theory (Debye, 1954) is provided by a plot of P against 1/T, which gives a straight line of slope... 

A vast amount of data based on dielectric constant measurements of substances in dilute solution in nonpolar solvents indicate that the theory is correct, but it looses validity and breaks down completely in the case of strongly polar media. It is interesting to notice that such a breakdown can be shown by the concept of the Curie point, introduced in connection with studies of magnetism but directly applicable to the case of dielectric constants. The dielectric constant can be related to the molar polarizability P and the molar concentration c by q. (21) and the value of P itself is given by Eq. (22). It is obvious that P increases as T dimin-... 

Dielectric polarization is the polarized condition in a dielectric resulting from an applied AC or DC field. The polarizability is the electric dipole moment per unit volume induced by an applied field or unit effective intensity. The molar polarizability is a measure of the polarizability per molar volume thus it is related to the polarizability of the individual molecules or polymer repeat unit. 

Polarizability-Kow Relationships Molar polarizabilities can be derived from molecular orbital (MO) calculations by the complete neglect of differential overlap (CNDO) method [42]. The following correlation has been found for polar compounds that contain either hydrogen-bond-accepting or hydrogen-bond-donating groups (alkanols, alkanones, dialkyl ethers, alkanenitriles) ... 

Lewis, D. F. V., The Calculation of Molar Polarizabilities by the CNDO/2 Method Correlation with the Hydrophobic Parameter, Log P. J. Comput. Chem, 1989 10, 145-151. 

There is no obvious reason why oA should express Pearson s scale of softness. Nevertheless, it is evident that it succeeds much better than for instance the molar polarizabilities a given in Table 2. The border-line cases between hard and soft central atoms have aA around 3 eV, whereas typical hard behaviour is found when oA is below 2 eV. A mild criticism is that oA has a tendency to increase more with the oxidation number z than appropriate for the chemical softness, producing aA =... 

As the molar polarizabilities represent an easily available experimental set of data, the expressions above become important for the theoretical evaluation of molecular response properties in fact they represent the most direct quantities to compare with the computed results obtained applying a given model for the solvent effects. 

As a result the definition of the molar polarizability for the third-order EFISHG process given in Equation (2.177) for a solution has to be modified as follows ... 

In this section, we investigate the relations between the macroscopic susceptibilities and the molecular polarizabilities. Consistent microscopic interpretations of many of the non-linear susceptibilities introduced in Section 2 will be given. Molar polarizabilities will be defined in analogy to the partial molar quantities (PMQ) known from chemical thermodynamics of multicomponent systems. The molar polarizabilities can be used as a consistent and general concept to describe virtually all linear and non-linear optical experiments on molecular media. First, these quantities will be explicitly derived for a number of NLO susceptibilities. Physical effects arising from will then be discussed very briefly, followed by a survey of experimental methods to determine second-order polarizabilities. 

It follows with (18)-(21) that the units for the quantities are Cm" V "mole i.e. those of an nth-order polarizability per mole. Therefore, we refer to as an nth-order molar polarizability of the constituent J. These quantities have to be calculated on the basis of a specific molecular model and appropriate local field corrections have to be taken into account. To simplify the notation, we will drop the index J in the following. A summation according to (99) is implied if the system consists of more than one constituent. 

The calculation of the molar polarizabilities, often involves statistical mechanical averaging over orientational distributions of the molecules. An important example is the distribution function w caused by dipole orientation in an externally applied static electric field E° because it describes the process of electric poling of NLO-phores. To second order in the field, the dipolar contributions to this (normalized) function are given by (100),... 

In the following we present explicit relations for the molar polarizabilities for a number of important macroscopic susceptibilities. These equations will be used subsequently as a basis for the experimental determination of molecular polarizabilities. 

The second-order susceptibility of a molecular crystal can be represented in terms of the macroscopic molar polarizabilities by the relation (106),... 

The susceptibility x —2w,o),w,0) is determined in the EFISHG experiment [electric-field-induced second harmonic generation see below (Levine and Bethea, 1974, 1975)]. In order to measure the two independent components and x cxz of this susceptibility, the experiment can be performed under two polarization conditions, the incident IR photons being polarized parallel and perpendicular to the externally applied field (Wortmann et al., 1993). For theoretical treatments see also Andrews and Sherborne (1986), Wagniere (1986) and Andrews (1993). A concentration series finally yields the molar polarizabilities (Kleinman symmetry assumed) through (109),... 

The quadratic effect of an externally applied field on the refractive index n is described by the third-order susceptibility (- ) w,0,0) (Kerr susceptibility). The two independent components Yilzz and x ixx can be interpreted in terms of molar polarizabilities. The results for 2 symmetric molecules with only one significant component of the second-order polarizability are expressed in (113) and (114),... 

For typical NLO-phores the (ju, ) 6a term is much larger than the p,gl3 term. The molar polarizabilities (113) and (114) were recently used to derive a molecular figure of merit (FOM) for NLO-phores for organic photorefractive (PR) materials with low glass-transition temperature (Wortmann et al., 1996). Rational design of NLO-phores based on this FOM led to organic PR-materials with unprecedented performance (Wtirthner et al., 1997). 

For an isolated electronic transition between a ground state g) and an excited state a), the molar polarizabilities can be represented by (120) and (121). 

Table 1 Mean dielectric constants and molar polarizabilities of simple oxides...

---