Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model

Abstract

Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ1(f), the frequency dispersion of the third-order dielectric susceptibility, χ3(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ1(f) and χ3(f) is the characteristic of the many-body relaxation dynamics of interacting systems which are governed solely by the intermolecular potential, and thermodynamic condition plays no role in this respect. Although linked to χ3(f), dynamic heterogeneity is one of the parallel consequences of the many-body dynamics, and it should not be considered as the principal control parameter for the other dynamic properties of glassforming systems. Results same as χ3(f) at elevated pressures had been obtained before by molecular dynamics simulations from the four-points correlation function and the intermediate scattering function. Naturally all properties obtained from the computer experiment, including dynamics heterogeneity, frequency dispersion, the relation between the α- and JG β-relaxation, and the breakdown of the Stokes-Einstein relation, are parallel consequences of the many-body relaxation dynamics governed by the intermolecular potential.

Dynamics of hydrated proteins and bio-protectants: Caged dynamics, β-relaxation, and α-relaxation

“…Since the JG relaxation is also intermolecular in nature, its onset effectively dissolves the cages and terminates the NCL regime. This relation between the NCL and the JG -relaxation has been amply demonstrated by experimental data [24,26,7178], and rationalized by theoretical considerations [29,26,[42][43][44]7178]. The intensity of the NCL change to a stronger temperature dependence when temperature is raised to cross T g from below, reflecting the fact that the caged dynamics and NCL is coupled to density and vitrification.…”

“…The phenomenon and especially the property, T HF T g , is remarkable since T HF is determined usually by measurements of fast caged dynamics at short time scales typically in the ns to ps range by neutron scattering and terahertz (THz) dielectric spectroscopy, while T g characterizes the secondary glass transition at which the Johari-Goldstein (JG) -relaxation time  JG reaches a long time 10 The outstanding property of T HF T g follows as consequence of the coupling of the caged dynamics to density as well as coupling to the density dependent JG -relaxation [24,26,29,33,7178,7885]. The latter originates from the fact that the caged dynamics regime is terminated by the onset of the JG -relaxation.…”

Coupling of Caged Molecule Dynamics to JG β-Relaxation: I

“…However, no effect of the high field was found in the NCL in these high field experiments, as pointed out in a more recent paper. 44 The analyses of these experimental findings also provide additional evidence that ν 0 is a lower bound of the NCL frequency regime. The NCL is terminated when it reaches the critical value, ε max ″ , at the cutoff frequency ν c (T) equal to ν 0 in order of magnitude, by the onset of the primitive relaxation.…”

Investigation of nonlinear effects in glassy matter using dielectric methods

“…In any case, the nonlinearity in this region reported in Ref. [104] is also clearly smaller than for the main relaxation and the overall nonlinear behaviour of the excess wing significantly differs from that of the  relaxation (see also [113] for a detailed discussion of these issues). While glycerol and propylene carbonate are type A glass formers, exhibiting an excess wing, Samanta and Richert [115] have also investigated the nonlinear dielectric response of the type-B glass former sorbitol, which is known to show a well-pronounced  relaxation [64].…”

“…[64] cast some doubts on this finding. Finally, we want to mention that the small or even absent nonlinear effects in the excess-wing region and the contrasting clear nonlinearity found for the  relaxation in sorbitol were consistently explained within the framework of the coupling model [60], where the excess wing is identified with the so-called "nearly constant loss" caused by caged molecular motions [113].…”