Debye electric moment frequency

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) ... 

B. Protein Solutions. The dielectric properties of proteins and nucleic acids have been extensively reviewed (10, 11). Protein solutions exhibit three major dispersion ranges. One occurs at RF s and is believed to arise from molecular rotation in the applied electric field. Typical characteristic frequencies range from about 1 to 10 MHz, depending on the protein size. Dipole moments are of the order of 200-500 Debyes and low-frequency increments of dielectric permittivity vary between 1 and 10 units/g protein/100 ml of solution. The high-frequency dielectric permittivity of this dispersion is lower than that of water because of the low dielectric permittivity of the protein leading to a high-frequency decrement of the order of 1 unit/g protein/... 

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. 

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 first term, which contains the the static dielectric permittivities of the three media , 2, and 3, represents the Keesom plus the Debye energy. It plays an important role for forces in water since water molecules have a strong dipole moment. Usually, however, the second term dominates in Eq. (6.23). The dielectric permittivity is not a constant but it depends on the frequency of the electric field. The static dielectric permittivities are the values of this dielectric function at zero frequency. 1 iv), 2 iv), and 3(iv) are the dielectric permittivities at imaginary frequencies iv, and v = 2 KksT/h = 3.9 x 1013 Hz at 25°C. This corresponds to a wavelength of 760 nm, which is the optical regime of the spectrum. The energy is in the order of electronic states of the outer electrons. 

The first process prevails at relatively low frequencies. The electric component E of radiation orients dipole moments p along the field direction, while chaotic molecular motions hinder this orientation p and E are the vectors, and the field E is assumed to vary harmonically with time t. Due to inertia of reorienting molecules the time dependence of the polarization lags behind the time dependence E(f), so that heating of the medium occurs (the heating effect is not considered in this work). The dielectric spectrum obeys the Debye relaxation, for which the absorption monotonically increases with frequency. 

The dielectric constant at angular frequency to is e (ai) = e (u>) — ie" u>). The limiting dielectric constants arc e, (sometimes written e ) and e, (sometimes written e,). In Debye s model the relaxing clement (which represents a polar molecule) is a sphere of radius a containing an electric dipole of dipole moment p = qd (see Fig. 4.36). The sphere is immersed in a liquid of viscosity q. Under an electric field E the torque on the dipole is pE sin 0. The rotation of the dipole under this torque is resisted by the Stokes frictional torque Xnt/cr tl. The dipole will follow the field for low U biit not for high. The relaxation time is... 

Dielectric analysis measures two fundamental characteristics of a material—permittivity e and conductivity o (or resistivity p)—as functions of time, temperature, and AC radial frequency (O. As was discussed above, permittivity and conductivity are two parameters characteristic of respective abilities of analyzed material to store electrical energy and transfer electric charge. Both of these parameters are related to molecular activity. For example, a "dielectric" is a material whose capacitive current (out of phase) exceeds its resistive (in phase) current. An "ideal dielectric" is an insulator with no free charges that is capable of storing electrical energy. The Debye Equation (Eq. 1-12) relates the relative permittivity e to a concept of material polarization density P [C/nP], or electrical dipole moment [C/m] per unit volume [m ], and the applied electric field V ... 

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