The Distribution of Relaxation Times in Typical Dielectrics

Abstract

K. W. Wagner's treatment of the distribution of relaxation times in dielectrics is reviewed; the effect of the density of distribution upon the frequency variation of the dielectric constant and dielectric loss factor is discussed; and a graphical method of evaluating the constants of Wagner's equation from experimental data is described. These constants have been evaluated for a number of typical dielectrics, and the frequency variations of the dielectric constant and dielectric loss factor as computed from Wagner's equations and from the simple equations for a single relaxation time are compared with the observed behavior. The quantitative correlation obtained between Wagner's equations and the experimental data investigated is viewed as a confirmation of Wagner's theory of a statistical distribution of relaxation times in dielectrics.

Dielectric relaxation in a styrene-acrylonitrile copolymer during and after its polymerization

“…dlogw (7) A ha b een pointed out [15], the use of th e approximation resulting in (7), when used in the calculation of e" from e' , leads to values that are 30 to 40 percent too small. The reason for this discrepancy is that, wh ereas the approximation made in the calculation of (6), namely, (8) is excellent, the approximation which results in (7), namely, …”

“…The curves of fiO"Ul'e 1 b ear a superficial resemblance to the D ebye'" di p ersion curves modified for a d istr ibution of relaxation times [7,8,9] if the time axis is imag ined r eplaced by a Iocr frequency axis. This results from th e fact tha t th~ rate of change of dielectric con stan t with time mu st b e correla ted with the magnitude of th e out-of-:phase component of tlle .complex dielectric constant, 1. e., the loss factor.…”

“…The loss IS therefore attributed primarily 8 to the orien- tation of the eN dipoles. A similar dependence of the magnitudes of the loss-factor maxima on the acrylonitrile concentration is found for the hightenlperature measurements made on the fully cured polymer discussed later (figs.…”

Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master equation formalism

“…However, Matthiessen's rule technically holds only when all mechanisms have the same relaxation time vs energy dependence 59 . Also, employing a single energyindependent relaxation time is generally not a good approximation for systems with pronounced non-Coulomb scattering mechanisms [60][61][62][63] , such as phonons in nonpolar materials; indeed, the use of a single relaxation time has been shown not to accurately capture the loss mechanisms in suspended and, to a lower degree, supported graphene 64 . What is needed is an accurate (and, ideally, computationally inexpensive) theoretical approach that can treat the interaction of light with charge carries in graphene (and in related nanomaterials) in the presence of both interband and intraband transitions due to multiple competing scattering mechanisms, where the transition rates can have pronounced and widely differing dependencies on both carrier energy and momentum.…”

Viscoelastic properties of polymer solutions

“…Philippoff obtained an excellent fit with the relation Tf' = B I[l + (WT) 3/4], \;vhere Band Tare empiricl11 constants of uncertain significance; B was not equal to T} , although of the same order of magnitude. .Al ternatively, a fa ir ly good fit for T}' IT} a a fun ction of WTm , wher e T", is the r eciprocal of the value of W at which T}' ITf = 1/2, is achieved by the Wiechert-Wagner di tl'ibution of r elaxation times [16], with b, th e distribution parameter, chosen as 0. 5 .…”