Debye electric moment

In the original treatment of Debye and Hiickel these constants were determined under the assumption that the ion had a point charge at r = 0 and that the interior of the ion had the same dielectric constant D as the solvent. In the On-sager (5) theory of dipolar liquids it is assumed that the molecule is represented by a spherical cavity in the liquid with a singularity at its center. The characteristics of the molecule are its electric moment in vacuum po and its polarizability a. This is to be related to an internal refractive index n by... 

The Debye Equation for Dielectric Constant.—The Debye equation for the dielectric constant of a gas whose molecules have a permanent electric moment no is... 

Here, Eq is the permittivity of free space. For a simple Debye-type relaxation process, Eq. (4), and owing to the incorrect representation of the high-frequency limit inherent in any expression for K (to) consistent with an exponential decay function for the electric moment, one obtains for the high-frequency limit of a(to) from Eqs. (4) and (6) (30) ... 

The unit of pressure in the constants above is the dyne per square centimeter, the unit of volume is cubic centimeters per mole. The electric moments are expressed in absolute electrostatic units. Data for Van der Waals constants and volumes are taken from Landolt s Tables for the electric moments from Debye, Polare Molekeln, Leipzig, 1929. 

Electric moment M Electrostatic cgs unit Electromagnetic cgs unit Debye = 1CT18 esu cm... 

Quadratic Permittivity Variations in Gases and Liquids. -Gases and Dilute Dipolar Media. We shall calculate Ae within the framework of the classical Langevin-Debye theory. The total electric moment of a dipolar molecule having the permanent electric moment p and linear electric polarizability a immersed in a field E is ... 

All the results confirm the fact (required by Debye s law) that the dielectric constant is a linear function of the reciprocal of the temperature. The electric moments (/x) of the molecules calculated from the slopes of the lines are in each case given under the table. 

As Stuart worked with very small densities which were determined experimentally, and in addition the values of the molecular polarization calculated from the measured values of the dielectric constants and the corresponding densities are strictly in accordance with Debye s law, the values of the electric moment obtained from the variation of the molecular polarization with temperature must be regarded as being very accurate. We should therefore expect that the results we obtained should agree with Stuart s within the range of experimental error, if the methods used are genuinely successful. 

Debye s theory on the whole in particular, the papers by Zahn Watson f, and Stuart J may be mentioned. The measurements were carried out for various temperatures the pressures and densities of the gas were chosen at random, i.e. were quite independent of each other. The electric moment [x was calculated from Debye s law... 

Some years ago, at Professor Debye s suggestion, I set up in the Zurich laboratory an apparatus by means of which the temperature variation of dielectric constants can be measured for a constant number of molecules. Various defects in the apparatus, in particular the use of ordinary brass condensers, prevented the dielectric constants being determined with the accuracy necessary for an accurate calculation of the electric moment, so that the moments could only be determined to about o i. io e.s.u. 

Qualitatively, it is clear that the d values are correlated with the dipole moments of the solute molecules. For -amino acids, electric moments may be approximately estimated on the assumption that a charge + e (e = 4.8 e. s. u.) is concentrated at the N atom of the — NH group, and a charge —e is located midway between the two oxygens of the COO groups. Consideration of a space model of an a-amino acid [see Cohn and Edsall (16), Chapters 6 and 14] indicates that the distance between the two charges is very nearly 3 A, giving a moment of 3 4.8 - 10 = 14.4 10 e. s. u. = 14.4 Debye units. 

The foundations for our present understanding of intermolecular forces were laid in the first decades of this century. First, Keesotn Debye and Falckenhagen elucidated the role played by permanent electric moments and polarizabilities. After the advent of quantum mechanics, Heitler and London S identified the exchange forces which keep molecules apart, and London discovered the dispersion forces which explained such puzzling phenomena as the condensation of noble gases. 

The trans form is symmetrical and therefore is expected to have zero electric moment. It is found experimentally that the compound which the chemists had previously selected as the tram form does in fact have zero moment, whereas the cis form has a moment of about 1.74 X 10-18 e.s.u. (The unit 10 18 e.s.u. is sometimes called a Debye unit.) Strong evidence for the plane structure of benzene is also provided by electric-moment data, and many other problems of interest to chemists have been attacked in this way. 

In this relation m is an electric moment. If we may use the electric moment obtained from the dielectric constant by means of the Debye classical equation, by may be evaluated. Substituting the value 1.034 X 10-18 c.g.s.u. which Zahn5 obtained from his investigation on the dielectric constant of HC1, we obtain for 65,6 the result, 1.12 X 1018. 

While much of his reputation was based on nonpolymeric accompHshments, such as demonstrated by the Debye-Huckel theory, the Debye-Scherrer x-ray diffraction technique, the Debye-Sears effect in liquids, the Debye temperature, the Debye shielding distance, the Debye frequency and the Debye unit of electric moment, his development of the hght scattering technique for the determination of the molecular weight of polymers resulted in his also being recognized as a world class polymer scientist. 

This induced moment is added to the permanent electric moment of the second molecule and Debye showed that the interaction energy between two molecules, due to this polarizability effect, is independent of temperature and takes the form ... 

The value of the relaxation time is based on dielectric constant studies of Oncley (140) at 25 , who showed that the protein underwent anomalous dispersion and conformed nicely to the simple Debye curve, exhibiting a single critical frequency ve — 1.9 X 10 cycles sec"S a low frequency dielectric increment of -f 0.33 g. liter and a high frequency increment of —0.11 g." liter. The data just presented have been discussed by Oncley (141) and by Wyman and Ingalls (241) with the aid of their nomograms. It appears from their analyses that the facts might reasonably well be reconciled with the assumption either of oblate ellipsoids with p = 3 and A = 0.3 — 0.4 or of prolate ellipsoids with p = H and = 0.3 — 0.4. On the assumption of prolate ellipsoids, however, it would be necessary to assume that there was no component of the electric moment parallel to the long axis (axis of revolution). In either case the two dielectric increments correspond to an electric moment of about 500 Debye units (140). 

The symbols 5+ and 5- indicate polarity of the two ends or poles of the electrically neutral molecule. Such a polar molecule constitutes a permanent dipole, i.e., two equal and opposite charges (e) separated by a distance (d) in space. A quantitative measure of the polarity of a molecule is the dipole moment (p in Debye units), which is defined as the product of the charge (e in electrostatic units) and the distance (d in cm). 

Incomplete Dissociation into Free Ions. As is well known, there are many substances which behave as a strong electrolyte when dissolved in one solvent, but as a weak electrolyte when dissolved in another solvent. In any solvent the Debye-IIiickel-Onsager theory predicts how the ions of a solute should behave in an applied electric field, if the solute is completely dissociated into free ions. When we wish to survey the electrical conductivity of those solutes which (in certain solvents) behave as weak electrolytes, we have to ask, in each case, the question posed in Sec. 20 in this solution is it true that, at any moment, every ion responds to the applied electric field in the way predicted by the Debye-Hiickel theory, or does a certain fraction of the solute fail to respond to the field in this way In cases where it is true that, at any moment, a certain fraction of the solute fails to contribute to the conductivity, we have to ask the further question is this failure due to the presence of short-range forces of attraction, or can it be due merely to the presence of strong electrostatic forces ... 

One important stracture in molecules are polar bonds and, as a result, polar molecules. The polarity of molecules had been first formulated by the Dutch physicist Peter Debye (1884-1966) in 1912, as he tried to build a microphysical model to explain dielectricity (the behaviour of an electric field in a substance). Later, he related the polarity of molecules to the interaction between molecules and ions. Together with Erich Hiickel he succeeded in formulating a complete theory about the behaviour of electrolytes (Hofimann, 2006). The discovery of the dipole moment caused high efforts in the research on physical chemistry. On the one hand, methods for determining the dipole momerrt were developed. On the other hand, the correlation between the shape of the molectrle and its dipole moment was investigated (Estermanrr, 1929 Errera Sherrill, 1929). 

The linear polarizability, a, describes the first-order response of the dipole moment with respect to external electric fields. The polarizability of a solute can be related to the dielectric constant of the solution through Debye s equation and molar refractivity through the Clausius-Mosotti equation [1], Together with the dipole moment, a dominates the intermolecular forces such as the van der Waals interactions, while its variations upon vibration determine the Raman activities. Although a corresponds to the linear response of the dipole moment, it is the first quantity of interest in nonlinear optics (NLO) and particularly for the deduction of stracture-property relationships and for the design of new... 

When a constant electric field is suddenly applied to an ensemble of polar molecules, the orientation polarization increases exponentially with a time constant td called the dielectric relaxation time or Debye relaxation time. The reciprocal of td characterizes the rate at which the dipole moments of molecules orient themselves with respect to the electric field. 

Methods for determining permanent dipole moments and polarizabilities can be arbitrarily divided into two groups. The first is based on measuring bulk phase electrical properties of vapors, liquids, or solutions as functions of field strength, temperature, concentration, etc. following methods proposed by Debye and elaborated by Onsager. In the older Debye approach the isotope effects on the dielectric constant and thence the bulk polarization, AP, are plotted vs. reciprocal temperature and the isotope effect on the polarizability and permanent dipole moment recovered from the intercept and slope, respectively, using Equation 12.5. 

---