Kristine Niss

Dielectric and shear mechanical alpha and beta relaxations in seven glass-forming liquids.

We present shear mechanical and dielectric measurements taken on seven liquids: triphenylethylene, tetramethyltetra-phenyltrisiloxane (Dow Corning 704 diffusion pump fluid), polyphenyl ether (Santovac 5 vacuum pump fluid), perhydrosqualene, polybutadiene, decahydroisoquinoline (DHIQ), and tripropylene glycol. The shear mechanical and dielectric measurements are for each liquid performed under identical thermal conditions close to the glass transition temperature. The liquids span four orders of magnitude in dielectric relaxation strength and include liquids with and without Johari-Goldstein beta relaxation. The shear mechanical data are obtained by the piezoelectric shear modulus gauge method giving a large frequency span (10(-3)-10(4.5) Hz). This allows us to resolve the shear mechanical Johari-Goldstein beta peak in the equilibrium DHIQ liquid. We moreover report a signature (a pronounced rise in the shear mechanical loss at frequencies above the alpha relaxation) of a Johari-Goldstein beta relaxation in the shear mechanical spectra for all the liquids which show a beta relaxation in the dielectric spectrum. It is found that both the alpha and beta loss peaks are shifted to higher frequencies in the shear mechanical spectrum compared to the dielectric spectrum. It is in both the shear and dielectric responses found that liquids obeying time-temperature superposition also have a high-frequency power law with exponent close to -12. It is moreover seen that the less temperature dependent the spectral shape is, the closer it is to the universal -12 power-law behavior. The deviation from this universal power-law behavior and the temperature dependencies of the spectral shape are rationalized as coming from interactions between the alpha and beta relaxations.

A brief critique of the Adam–Gibbs entropy model

This paper critically discusses the entropy model proposed by Adam and Gibbs in 1965 for the dramatic temperature dependence of glass-forming liquids’ average relaxation time, which is one of the most influential models during the last four decades. We discuss the Adam–Gibbs model’s theoretical bases as well as its reported experimental model confirmations; in the process of doing this a number of problems with the model are identified.

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

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 correlation between fragility and stretching in glass-forming liquids

We study the pressure and temperature dependences of the dielectric relaxation of two molecular glass-forming liquids, dibutyl phthalate and m-toluidine. We focus on two characteristics of the slowing down of relaxation, the fragility associated with the temperature dependence and the stretching characterizing the relaxation function. We combine our data with data from the literature to revisit the proposed correlation between these two quantities. We do this in light of constraints that we suggest to put on the search for empirical correlations among properties of glass-formers. In particular, we argue that a meaningful correlation is to be looked for between stretching and isochoric fragility, as both seem to be constant under isochronic conditions and thereby reflect the intrinsic effect of temperature.

Communication: Identical temperature dependence of the time scales of several linear-response functions of two glass-forming liquids

The frequency-dependent dielectric constant, shear and adiabatic bulk moduli, longitudinal thermal expansion coefficient, and longitudinal specific heat have been measured for two van der Waals glass-forming liquids, tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl-4-ether. Within the experimental uncertainties the loss-peak frequencies of the measured response functions have identical temperature dependence over a range of temperatures, for which the Maxwell relaxation time varies more than nine orders of magnitude. The time scales are ordered from fastest to slowest as follows: Shear modulus, adiabatic bulk modulus, dielectric constant, longitudinal thermal expansion coefficient, and longitudinal specific heat. The ordering is discussed in light of the recent conjecture that van der Waals liquids are strongly correlating, i.e., approximate single-parameter liquids.

Glassy properties and viscous slowing down: An analysis of the correlation between nonergodicity factor and fragility

We present an extensive analysis of the proposed relationship [T. Scopigno et al., Science 302, 849 (2003)] between the fragility of glass-forming liquids and the nonergodicity factor as measured by inelastic x-ray scattering. We test the robustness of the correlation through the investigation of the relative change under pressure of the speed of sound, nonergodicity factor, and broadening of the acoustic exitations of a molecular glass former, cumene, and of a polymer, polyisobutylene. For polyisobutylene, we also perform a similar study by varying its molecular weight. Moreover, we have included new results on liquids presenting an exceptionally high fragility index m under ambient conditions. We show that the linear relation, proposed by Scopigno et al. [Science 302, 849 (2003)] between fragility, measured in the liquid state, and the slope alpha of the inverse nonergodicity factor as a function of T/T(g), measured in the glassy state, is not verified when increasing the data base. In particular, while there is still a trend in the suggested direction at atmospheric pressure, its consistency is not maintained by introducing pressure as an extra control parameter modifying the fragility: whatever is the variation in the isobaric fragility, the inverse nonergodicity factor increases or remains constant within the error bars, and one observes a systematic increase in the slope alpha when the temperature is scaled by T(g)(P). To avoid any particular aspects that might cause the relation to fail, we have replaced the fragility by other related properties often evoked, e.g., thermodynamic fragility, for the understanding of its concept. Moreover, we find, as previously proposed by two of us [K. Niss and C. Alba-Simionesco, Phys. Rev. B 74, 024205 (2006)], that the nonergodicity factor evaluated at the glass transition qualitatively reflects the effect of density on the relaxation time even though in this case no clear quantitative correlations appear.

Streamline topology in the near wake of a circular cylinder at moderate Reynolds numbers

For the flow around a circular cylinder, the steady flow changes its topology at a Reynolds number around 6 where the flow separates and a symmetric double separation zone is created. At the bifurcation point, the flow topology is locally degenerate, and by a bifurcation analysis we find all possible streamline patterns which can occur as perturbations of this flow. We show that there is no a priori topological limitation from further assuming that the flow fulfils the steady Navier–Stokes equations or from assuming that a Hopf bifurcation occurs close to the degenerate flow. The steady flow around a circular cylinder experiences a Hopf bifurcation for a Reynolds number about 45–49. Assuming that this Reynolds number is so close to the value where the steady separation occurs that the flow here can be considered a perturbation of the degenerate flow, the topological bifurcation diagram will contain all possible instantaneous streamline patterns in the periodic regime right after the Hopf bifurcation. On the basis of the spatial and temporal symmetry associated with the circular cylinder and the structure of the topological bifurcation diagram, two periodic scenarios of instantaneous streamline patterns are conjectured. We confirm numerically the existence of these scenarios, and find that the first scenario exists only in a narrow range after the Hopf bifurcation whereas the second one persists through the entire range of Re where the flow can be considered two-dimensional. Our results corroborate previous experimental and computational results.

Communication: Two measures of isochronal superposition

A liquid obeys isochronal superposition if its dynamics is invariant along the isochrones in the thermodynamic phase diagram (the curves of constant relaxation time). This paper introduces two quantitative measures of isochronal superposition. The measures are used to test the following six liquids for isochronal superposition: 1,2,6 hexanetriol, glycerol, polyphenyl ether, diethyl phthalate, tetramethyl tetraphenyl trisiloxane, and dibutyl phthalate. The latter four van der Waals liquids obey isochronal superposition to a higher degree than the two hydrogen-bonded liquids. This is a prediction of the isomorph theory, and it confirms findings by other groups.

Prevalence of approximate t relaxation for the dielectric α process in viscous organic liquids

We present data for the dielectric relaxation of 43 glass-forming organic liquids, showing that the primary (alpha) relaxation is often close to square-root-time relaxation. The better an inverse power-law description of the high-frequency loss applies, the more accurately is square-root-time relaxation obeyed. These findings suggest that square-root-time relaxation is generic to the alpha process, once a common view, but since long believed to be incorrect. Only liquids with very large dielectric losses deviate from this picture by having consistently narrower loss peaks. As a further challenge to the prevailing opinion, we find that liquids with accurate square-root-time relaxation cover a wide range of fragilities.

Beta relaxation in the shear mechanics of viscous liquids: Phenomenology and network modeling of the alpha-beta merging region

Abstract The phenomenology of the beta relaxation process in the shear-mechanical response of glass-forming liquids is summarized and compared to that of the dielectric beta process. Furthermore, we discuss how to model the observations by means of standard viscoelastic modeling elements. Necessary physical requirements to such a model are outlined, and it is argued that physically relevant models must be additive in the shear compliance of the alpha and beta parts. A model based on these considerations is proposed and fitted to data for Polyisobutylene 680.