Bo Jakobsen

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.

Investigation of the shear-mechanical and dielectric relaxation processes in two monoalcohols close to the glass transition

Shear-mechanical and dielectric measurements on the two monohydroxy (monoalcohol) molecular glass formers 2-ethyl-1-hexanol and 2-butanol close to the glass-transition temperature are presented. The shear-mechanical data are obtained using the piezoelectric shear-modulus gauge method covering frequencies from 1 mHz to 10 kHz. The shear-mechanical relaxation spectra show two processes, which follow the typical scenario of a structural (alpha) relaxation and an additional (Johari-Goldstein) beta relaxation. The dielectric relaxation spectra are dominated by a Debye-type peak with an additional non-Debye peak visible. This Debye-type relaxation is a common feature peculiar to monoalcohols. The time scale of the non-Debye dielectric relaxation process is shown to correspond to the mechanical structural (alpha) relaxation. Glass-transition temperatures and fragilities are reported based on the mechanical alpha relaxation and the dielectric Debye-type process, showing that the two glass-transition temperatures differ by approximately 10 K and that the fragility based on the Debye-type process is a factor of 2 smaller than the structural fragility. If a mechanical signature of the Debye-type relaxation exists in these liquids, its relaxation strength is at most 1% and 3% of the full relaxation strength of 2-butanol and 2-ethyl-1-hexanol, respectively. These findings support the notion that it is the non-Debye dielectric relaxation process that corresponds to the structural alpha relaxation in the liquid.

Shear-modulus investigations of monohydroxy alcohols: evidence for a short-chain-polymer rheological response.

In addition to the ubiquitous structural relaxation of viscous supercooled liquids, monohydroxy alcohols and several other hydrogen-bonded systems display a strong single-exponential electrical low-frequency absorption. So far, this so-called Debye process could be observed only using dielectric techniques. Exploiting a combination of broad-band and high-resolution rheology experiments for three isomeric octanols, unambiguous mechanical evidence for the Debye process is found. Its spectral signature is similar to the viscoelastic fingerprint of small-chain polymers, enabling us to estimate the effective molecular weight for the supramolecular structure formed by the studied monohydroxy alcohols. This finding opens the venue for the application of further non-dielectric techniques directed at unraveling the microscopic nature of the Debye process and for an understanding of this phenomenon in terms of polymer concepts.

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).

Supercooled Liquid Dynamics Studied via Shear-Mechanical Spectroscopy

We report dynamical shear-modulus measurements for five glass-forming liquids (pentaphenyltrimethyltrisiloxane, diethyl phthalate, dibutyl phthalate, 1,2-propanediol, and m-touluidine). The shear-mechanical spectra are obtained by the piezoelectric shear-modulus gauge (PSG) method. This technique allows one to measure the shear modulus (10(5)-10(10) Pa) of the liquid within a frequency range from 1 mHz to 10 kHz. We analyze the frequency-dependent response functions to investigate whether time-temperature superposition (TTS) is obeyed. We also study the shear-modulus loss-peak position and its high-frequency part. It has been suggested that when TTS applies, the high-frequency side of the imaginary part of the dielectric response decreases like a power law of the frequency with an exponent -1/2. This conjecture is analyzed on the basis of the shear mechanical data. We find that TTS is obeyed for pentaphenyltrimethyltrisiloxane and in 1,2-propanediol while in the remaining liquids evidence of a mechanical beta process is found. Although the high-frequency power law behavior w(-alpha) of the shear loss may approach a limiting value of alpha = 0.5 when lowering the temperature, we find that the exponent lies systematically above this value (around 0.4). For the two liquids without beta relaxation (pentaphenyltrimethyltrisiloxane and 1,2-propanediol) we also test the shoving model prediction, according to which the relaxation time activation energy is proportional to the instantaneous shear modulus. We find that the data are well described by this model.

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.

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.

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.

Communication: Supramolecular structures in monohydroxy alcohols: Insights from shear-mechanical studies of a systematic series of octanol structural isomers

A recent study [C. Gainaru, R. Figuli, T. Hecksher, B. Jakobsen, J. C. Dyre, M. Wilhelm, and R. Böhmer, Phys. Rev. Lett. 112, 098301 (2014)] of two supercooled monohydroxy alcohols close to the glass-transition temperature showed that the Debye peak, thus far mainly observed in the electrical response, also has a mechanical signature. In this work, we apply broadband shear-mechanical spectroscopy to a systematic series of octanol structural isomers, x-methyl-3-heptanol (with x ranging from 2 to 6). We find that the characteristics of the mechanical signature overall follow the systematic behavior observed in dielectric spectroscopy. However, the influence from the molecular structure is strikingly small in mechanics (compared to roughly a factor 100 increase in dielectric strength) and one isomer clearly does not conform to the general ordering. Finally, the mechanical data surprisingly indicate that the size of the supramolecular structures responsible for the Debye process is nearly unchanged in the series.

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.