Author

# Robert H. Cole

Bio: Robert H. Cole is an academic researcher from Columbia University. The author has contributed to research in topic(s): Dielectric & Dipole. The author has an hindex of 19, co-authored 26 publication(s) receiving 10077 citation(s).

Topics: Dielectric, Dipole, Relaxation (physics), Solid hydrogen, Polarizability

##### Papers

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TL;DR: In this paper, the locus of the dielectric constant in the complex plane was defined to be a circular arc with end points on the axis of reals and center below this axis.

Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...

7,796 citations

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TL;DR: In this paper, it was shown that the complex dielectric constant, e*, of many liquid and solid dielectrics is given by a single very general formula e*=e∞+(e0−e ∞)/[1+(iωτ0)1−α] In this equation e0 and e∞ are the ''static'' and ''infinite frequency'' dielectoric constants, ω = 2π times the frequency, τ 0 is a generalized relaxation time and α is a constant, 0 < α < 1 The transient current as a

Abstract: In the first paper of this series [J Chem Phys 9, 341 (1941)], it was shown that the complex dielectric constant, e*, of many liquid and solid dielectrics is given by a single very general formula e*=e∞+(e0−e∞)/[1+(iωτ0)1−α] In this equation e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω = 2π times the frequency, τ0 is a generalized relaxation time and α is a constant, 0 < α < 1 The transient current as a function of the time, t, after application of a unit constant potential difference has been calculated from this expression in series form For times much less than τ0, the time dependence is of the form (t/τ0)−α, and for times much greater than τ0, it is of the form (t/τ0)−(2—α) The transition between these extremes occurs for the range in which t is comparable with τ0 The total absorption charge, which is the integral of the exact expression, is always finite Although many transient data for dielectrics are of the predicted form, none have been taken over a suff

728 citations

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TL;DR: In this article, 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.

Abstract: 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.

387 citations

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TL;DR: The Kubo formalism for polarizable dipolar molecules treated as harmonic oscillators in the relaxation counterpart of Kirkwood's equilibrium theory was developed in this article, where the correlation function expression for relaxation was evaluated for several models: rotational transition probabilities including diffusion, nonequivalent dipole orientation sites, and flexible molecules with internal dipole reorientations.

Abstract: The Kubo formalism is developed for polarizable dipolar molecules treated as harmonic oscillators in the relaxation counterpart of Kirkwood's equilibrium theory. Treatment of reaction field induced moments as in Onsager's 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.

185 citations

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TL;DR: In this paper, 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.

Abstract: 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.

169 citations

##### Cited by

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TL;DR: This paper presents a meta-modelling procedure called "Continuum Methods within MD and MC Simulations 3072", which automates the very labor-intensive and therefore time-heavy and expensive process of integrating discrete and continuous components into a discrete-time model.

Abstract: 6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

11,599 citations

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TL;DR: In this paper, the locus of the dielectric constant in the complex plane was defined to be a circular arc with end points on the axis of reals and center below this axis.

Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...

7,796 citations

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TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.

Abstract: Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns. These fractional equations are derived asymptotically from basic random walk models, and from a generalised master equation. Several physical consequences are discussed which are relevant to dynamical processes in complex systems. Methods of solution are introduced and for some special cases exact solutions are calculated. This report demonstrates that fractional equations have come of age as a complementary tool in the description of anomalous transport processes.

6,586 citations

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Rohm and Haas

^{1}TL;DR: In this paper, it was shown that the complex deformation of the same data can be represented by a function of same form but with different values for the constants, which can be interpreted as the decay of the distortion with time of the removal of stress field.

Abstract: In a previous paper it was shown that the complex dielectric constant data of polymers can be represented by an empirical dispersion function. In the present work it is shown that the complex polarization of the same data can be represented by a function of the same form but with different values for the constants. This means that a quantitative evaluation of Scaife's remarks can be made. The dispersion parameters for eighteen polymers were determined for the ϵ∗ (ω) or the ϱ∗ (ω) data. In general, as the ratio ϵ0≥∞ increases, the ϱ∗ (ω) data become broader and faster than the ϵ∗ (ω) data, thus 1 — α, β and τ0 decrease. The normalized loss maximum was found to be temperature dependent [ϵ∗ (ω) data] for eleven polymers where ϵ0≥∞≈2.0. However, the normalized loss maximum [ϵ∗ (ω) data] for the two acetates was found to be independent of temperature while the normalized loss maximum for the ϱ∗ (ω) behaved in a way similar to the other polymers. This observation can be traced to a fortuitous compensation of effects encountered with large dispersions. For those cases where the method of reduced variables is applicable ϵ∗ (ω) calculated from the dispersion function is in good agreement with the shifted values of ϵ∗ (ω). The two parameters α and β are shown to be uniquely related to distribution of relaxation times. The agreement between the distribution function calculated from the dispersion function is in good agreement with the approximate methods used to calculate the function from the shifted data. A complex plane plot of the complex compliance is not at all similar to the dielectric dispersions. An empirical transformation procedure is constructed by analogy with the one used to calculate the complex polarization in order to normalize the mechanical data. The locus of this complex deformation resembles the dielectric dispersion with nearly the same values of α, β and τ0. At very low frequencies, deviations from the assumed behaviour were observed. With polyisobutylene and poly(n-octyl methacrylate) the deviations were in terms of another dispersion. With poly(vinyl acetate) and poly(methyl acrylate) the deviations could be attributed to another low frequency dispersion. The similarity between the dielectric and mechanical dispersions suggests that the following mechanical model can be considered: a spherical inclusion containing the specimen of interest is perfectly bonded to an otherwise continuous homogeneous elastic continuum. Under these conditions the complex distortion of the sphere subjected to a periodic tensile field at infinity is very nearly the empirical complex deformation with Poisson's ratio of 12 for both media. It can also be shown for this model that if the distortion of the sphere is time dependent, then there will be in-phase and out-of-phase components to the distortion in a periodic field. In other words it is not necessary to postulate an internal viscosity to account for a macroscopic viscosity. The equilibrium distortion of the sphere is shown to be related to the square of the asymmetry of the orienting segments. The decay of the distortion with time of the removal of stress field is interpreted in terms of transition probabilities.

2,277 citations

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TL;DR: In this article, it was shown that the electrical double-layer at a solid electrode does not in general behave as a pure capacitance but rather as an impedance displaying a frequency-independent phase angle different from 90°.

Abstract: The electrical double-layer at a solid electrode does not in general behave as a pure capacitance but rather as an impedance displaying a frequency-independent phase angle different from 90°. Ways are indicated how to analyse the interfacial impedance if such a complication arises in the presence of a faradaic process, both on the supposition that the double-layer behaviour is due to surface inhomogeneity and on the supposition that it is a double-layer property per se.
As examples, the equations derived are successfully applied to a totally irreversible and an ac quasi-reversible electrode process at a gold electrode.

2,119 citations