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 Relaxation in Glycerol, Propylene Glycol, and n-Propanol

The α-dispersion in many polymer systems is the process to be associated with the glass transition temperature where many physical properties undergo drastic changes. We have measured and analyzed the complex dielectric behavior of the α-dispersions for five polymers [i.e., polycarbonate and polyisophthalate esters of bisphenol A, isotactic poly-(methyl methacrylate), poly(methyl acrylate), and a copolymer of phenyl methacrylate and acrylonitrile] and have found that the usual methods of analysis cannot be used to represent the data. However, it is possible to represent the relaxation process as the sum of two dispersions but there is no evidence to support this contention. An empirical expression is proposed to represent the data. This expression which takes the form of 



appears to be a general representation for the three known dispersions, i.e., Debye, circular arc, and skewed semicircle. The complex dielectric constants calculated with the aid of this expression and the parameters for each polymer system which was determined graphically were found to be in excellent agreement with the experimental complex dielectric constants. This method of representation was extended to sixteen α-dispersions reported in the literature always with excellent results.

A complex plane analysis of α‐dispersions in some polymer systems

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.

Dielectric Properties of Ice and Solid D2O

Chapter 6 – determination of biological impedances1

The dielectric relaxation study of glass‐forming liquids show the presence of two relaxation regions at temperatures above TQ. The low frequency relaxation is attributed to the cooperative rearrangement of molecules. The high frequency relaxation, which continues to exist in the glassy state, is suggested to arise from the hindered rearrangement of the molecules encaged by large regions which have been made relatively immobile by the stringent requirement of a cooperative motion. The hindered reorientation of dipoles in liquids at low viscosity has about the same Arrhenius energy as the β process seen in glasses. The results emphasize the role of intermolecular potential barriers in producing relaxation characteristics which have been generally accepted to arise from intramolecular rearrangement.

Intrinsic mobility of molecular glasses

The bridge described has been developed for reasonably accurate measurement by direct balance of capacitance and conductance in the frequency range 50 c/sec. to 5 mc/sec., and over most of this range is essentially direct reading in the two admittance components with negligible unbalance from lead effects or guard circuits of the unknown. These properties are realized by using two circuits developed from the work of others. The first employs inductively coupled ratio arms to minimize residual impedance effects and unbalance by guard circuits, the second, a conductance shifter wye network with good high frequency properties and an essentially linear conductance reading. Design considerations and limitations of these circuits are discussed, as are suitable test cells and auxiliary equipment.

A Wide Range Capacitance‐Conductance Bridge

The null method described permits either guarded three‐terminal or four‐terminal potential probe measurements of conductance from 1 kHz to dc and of capacitance to frequencies as low as 0.01 Hz. Sample currents to a null detector are balanced by adjustable currents derived from dc voltage inverter and follower circuits which drive fixed standards of conductance and capacitance. Procedures for minimizing errors from circuit residuals and results of representative measurements are described.

Low Frequency Bridge for Guarded Three‐Terminal and Four‐Terminal Measurements of Admittance

A dielectric plunger displaces liquid filling a short section of coaxial line, and dielectric constant and loss are determined from changes in measured capacitance and conductance with displacement. Corrections for imperfect plunger fit, lead capacitance, and inductance are small and well defined, and procedures for making them are given. Dielectric constants from 3 to 300 and high losses can be measured from −70 to 100°C with 3 cc or less of sample.

Coaxial Displacement Dielectric Cell for Liquids Usable to 250 Mc

An instrument similar in principle to one developed by Kohaut but suitable for absolute measurements of large and inhomogeneous fields is described which consists essentially of a d.c. generator with a very small armature coil on the end of a long shaft driven by a synchronous motor, the induced voltage being a direct measure of the field. Typical results are given and the accuracy, relative and absolute, attainable discussed.

A Magnetic Field Meter

A simple method is described for comparison of capacities. It consists of a circuit containing the unknown and standard capacities in series, the potential differences across them being applied directly to the vertical and horizontal deflecting plates of a cathode‐ray tube. Simple methods for calibration of residual circuit capacities and of the cathode‐ray tube are described. The method is capable of an accuracy of the order of 0.5 percent in the range 50 kc to 2 mc and has the advantage that determination of the unknown capacity is unaffected by parallel conductance of the unknown.

Robert H. Cole

Papers

A Wide Range Capacitance‐Conductance Bridge

Low Frequency Bridge for Guarded Three‐Terminal and Four‐Terminal Measurements of Admittance

Coaxial Displacement Dielectric Cell for Liquids Usable to 250 Mc

A Magnetic Field Meter

Use of the Cathode-Ray Tube for Comparison of Capacities