Robert H. Cole

Dielectric Relaxation in Glycerol, Propylene Glycol, and n‐Propanol

Complex dielectric constants have been measured at frequencies from below 20 c/s to 5 mc/s over the temperature range −40° to −75°C in glycerol, −45° to −90° in propylene glycol, and −80° to −140° in n‐propanol. The results for n‐propanol are described by the Debye equation, but the values for the other two require a modified equation corresponding to a broader range of dispersion at higher frequencies. In all three liquids, evidence is found for a second dispersion region at still higher frequencies, which accounts for much of the difference between the radio frequency and optical dielectric constant. The relaxation times are quantitatively described over wide ranges by an empirical rate equation of a form which also fits viscosity data. The significance of the various results is discussed.

Dielectric Properties of Ice and Solid D2O

Complex dielectric constants have been measured for ice from the melting point to −65°C, and for solid D2O to −35°C, by a combination of bridge and transient methods. For both, the dispersion is described by the simple Debye formula, and the relaxation times τ by the simple rate expression τ = A exp(B/RT). For ice, A = 5.3×10−16 sec, B = 13.2 kcal/mole; and for solid D2O, A = 7.7×10−16 sec, B = 13.4 kcal/mole. The equilibrium dielectric constant for ice is 91.5 at 0°C and increases at lower temperatures; the values for solid D2O are only slightly smaller. Measures taken to minimize errors from voids in the sample and direct current conductance are discussed.

Time domain reflection methods for dielectric measurements to 10 GHz

Total reflection methods and instrumentation for their use are described for measurements of dielectric permittivity and loss at frequencies to 10 GHz or more. Several cell designs are shown, together with analyses of their performance. Procedures are given for correcting effects of wave propagation in the cells and residual reflections in the cells by bilinear analysis with calibrations using dielectrics of known permittivity. Representative results are presented for highly polar liquids, dilute solutions of polar molecules in nonpolar solvents, electrolyte solutions, and ionic glasses with appreciable ohmic conduction.

Dielectric Constants of Imperfect Gases. III. Atomic Gases, Hydrogen, and Nitrogen

A modified cyclic‐expansion method has been used to determine dielectric constants as a function of relative density with a precision of less than 1 ppm for He, Ne, Ar, Kr, H2, and N2 at 49°C and pressures below 150 atm, which with data at measured pressures below 7 atm determine the first and second dielectric virial coefficients, and can also be used to determine pressure second virial coefficients.Dielectric second virial coefficients are for all six gases less than values predicted by present theories of fluctuations and pair polarizabilities, an effect believed to result from overlap interactions at short range. The low‐density values of the Clausius—Mossotti function are in good agreement with other recent determinations.

Correlation Function Theory of Dielectric Relaxation

The Kubo formalism is developed for polarizable dipolar molecules treated as harmonic oscillators in the relaxation counterpart of Kirkwoods equilibrium theory. Treatment of reaction field induced moments as in Onsagers model gives a generalization of the relaxation time ratio 3e0/(2e0+e∞) proposed by Powles. The correlation function expression for relaxation is evaluated for several models: rotational transition probabilities including diffusion, nonequivalent dipole orientation sites, and flexible molecules with internal dipole reorientations.

Dielectric Properties of Liquid Butyl Alcohols

Measurements of static dielectric constant were made for all except t‐butyl alcohol from the boiling points to —140°C; dispersion and loss were measured below 0°C in the range 20 cy/sec to 2 Mc/sec. Multiple dispersions were found as in other alcohols. The temperature dependences of static values are examined in terms of finite extent of chainwise molecular coordination by hydrogen bonding, and the rate laws of the dispersions are discussed.

Dielectric Properties of Liquid Ethanol and 2‐Propanol

Abstract : Dielectric constant and loss measurements of liquid EtOH and 2-PrOH were obtained from room temperature to -160 deg C for the pure liquids and mixtures with small amounts of H2O to facilitate supercooling. Two distinct dispersion regions were found below -100 deg C in the range from 1 c to 5 mc. The temperature dependances were similar and described by rate laws of the form found for similar measurements in 1-PrOH. The magnitudes and temperatures dependances of the equilibrium dielectric constants are discussed in terms of Kirkwoods theory. An explanation of the multiple dispersions is discussed in terms of H bond breaking to permit reorientation fo alkyl and hydroxyl groups. The dielectric constants and loss of trimethylene glycol were measured in the range 1 to -70 deg C at frequencies below 5 mc. The results indicate that the complex dielectric constant is not represented by a Debye function, but can be fitted by an empirical dispersion function of the same form describing measurements for glycerol and propylene glycol. The measured properties are intermediate between those for the latter 2.

Dielectric and Pressure Virial Coefficients of Imperfect Gases. II. CO2–Argon Mixtures

Dielectric and pressure second virial coefficients of five mixtures and the pure gases have been determined at 49.7°C, the values for CO2 at 29.4°C. The pressure coefficients are in reasonably good agreement with values predicted from combining rule Lennard‐Jones parameters derived from viscosities of the pure gases. The large effect of quadrupole interaction energy on the dielectric coefficient of pure CO2 has been calculated numerically, and analytical treatments of the smaller effects of reaction fields of induced moments, quadrupole‐induced dipole energy, and anisotropy energy have also been made. These result in a calculated molecular quadrupole moment of CO2 of 4.3 × 10−26 esu cm2 from the data for pure CO2. For CO2–Ar pairs, the effects in addition to the direct quadrupole‐induced dipole contribution are much smaller, and the value 4.1 × 10−26 esu cm2 for the quadrupole moment of CO2 is derived from the dielectric coefficient. Both values are in good agreement with the Buckingham–Disch result and w...

On the Analysis of Dielectric Relaxation Measurements

Convenient methods of analyzing dielectric dispersion and loss data satisfying the Debye equations are described and illustrated. The similarities and differences of the Fuoss‐Kirkwood and circular arc representations of symmetrical, non‐Debye‐type dispersions are considered. Interpretations given by various writers to the asymmetric dispersion found by D. W. Davidson and the writer for glycols are discussed. Finally, the possibilities and limitations of reduced representations of dielectric measurements are examined

Dielectric Properties of Methanol and Methanol‐1‐Propanol Solutions

Measurements of dispersion in the solutions show that at all concentrations the principal dispersion is a simple relaxation process, while the higher frequency behavior gives evidence of overlapping dispersions. As in other alcohols, the temperature dependences of relaxation times differ markedly from simple rate laws, especially for temperatures below 200°K. The significance of the results in relation to reorientation of hydroxyl and alkyl groups and intermolecular hydrogen bonds is discussed. Difficulties in measurements on solid methanol are described and their possible origins examined.