Dielectric and shear mechanical relaxations in glass-forming liquids: A test of the Gemant-DiMarzio-Bishop model

Abstract

The Gemant-DiMarzio-Bishop model, which connects the frequency-dependent shear modulus to the frequency-dependent dielectric constant, is reviewed and a new consistent macroscopic formulation is derived. It is moreover shown that this version of the model can be tested without fitting parameters. The reformulated version of the model is analyzed and experimentally tested. It is demonstrated that the model has several nontrivial qualitative predictions: the existence of an elastic contribution to the high-frequency limit of the dielectric constant, a shift of the shear modulus loss peak frequency to higher frequencies compared with the loss peak frequency of the dielectric constant, a broader alpha peak, and a more pronounced beta peak in the shear modulus when compared with the dielectric constant. It is shown that these predictions generally agree with experimental findings and it is therefore suggested that the Gemant-DiMarzio-Bishop model is correct on a qualitative level. The quantitative agreement between the model and the data is on the other hand moderate to poor. It is discussed if a model-free comparison between the dielectric and shear mechanical relaxations is relevant, and it is concluded that the shear modulus should be compared with the rotational dielectric modulus, 1(epsilon(omega)-n2), which is extracted from the Gemant-DiMarzio-Bishop model, rather than to the dielectric susceptibility or the conventional dielectric modulus M=1epsilon(omega).

On the mechanism of the highly viscous flow

“…3 (b) tripropylene glycol 36 as examples for substances without and with visible secondary relaxation peak. In the case of tripropylene glycol one can take position and width from dielectric measurements 36 and replace the parameter γ 2 by the height of the peak, so one has again five parameters.…”

Interconversion algorithm between mechanical and dielectric relaxation measurements for acetate ofcis- andtrans-2-phenyl-5-hydroxymethyl-1,3-dioxane

“…Niss, Jakobsen, and Olsen [8] tested and reformulated the DMB equation for several glass-forming liquids. They relate the induced polarizability to the refractive index through the Clausius-Mossotti approximation, that is, ε ∞ = n 2 .…”

Shear and dielectric spectra in highly viscous liquids

“…5 However, the results can be checked independently by an alternative procedure. One can fit the dielectric data first with a Havriliak-Negami function (adding a Cole-Cole function for the secondary peak if necessary).…”

“…A promising approach for the study of the flow process in highly viscous liquids is its comparison [1][2][3][4][5][6] in different techniques. One usually finds the dielectric absorption peak close to the heat-capacity one, [1][2][3][4] but the shear modulus peak is about half a decade higher in frequency.…”

“…The comparison is done for four samples with a relatively small (smaller than 0.15): TPE (triphenylethylene), squalane, 1,4-polybutadiene, and DC704, a silicon oil used in diffusion pumps. 5 One way to compare is to fit G(ω), then calculate the shear retardation susceptibility from this fit and compare to the dielectric measurement. The fit is better than the data themselves, because small deviations in G(ω) at low ω tend to explode in the calculated retardation spectrum (see, for example, the increasing error bars in Figs.…”