Universal wing- and fin-beat frequency scaling.

We derive an equation that applies for the wing-beat frequency of flying animals and to the fin-stroke frequency of diving animals like penguins and whales. The equation states that the wing/fin-beat frequency is proportional to the square root of the animal's mass divided by the wing area. Data for birds, insects, bats, and even a robotic bird-supplemented by data for whales and penguins that must swim to stay submerged-show that the constant of proportionality is to a good approximation the same across all species; thus the equation is universal. The wing/fin-beat frequency equation is derived by dimensional analysis, which is a standard method of reasoning in physics. We finally demonstrate that a mathematically even simpler expression without the animal mass does not apply.

Dielectric and Shear Mechanical Spectra of Propanols: The Influence of Hydrogen-Bonded Structures.

We present a dielectric and shear mechanical study of 1-propanol and three phenylpropanols. Contrary to other monoalcohols, the phenylpropanols do not show a bimodal behavior in their dielectric response, but instead show a single, rather narrow process. Combined dielectric and light scattering spectra (Böhmer, T.; et al. J. Phys. Chem. B 2019, 123, 10959) have shown that this single peak may be separated into a self- and a cross-correlation part, thus indicating that phenylpropanols do display features originating from hydrogen-bonded structures. The shear mechanical spectra support that interpretation, demonstrating a subtle, yet clear, low-frequency polymer-like mode, similar to what is found in other monoalcohols. An analysis of the characteristic time scales found in the spectra shows that shear alpha relaxation is faster than the dielectric alpha and that time scale separation of the dielectric Debye and alpha processes is temperature independent and nearly identical in all the phenylpropanols.

Rheological model for the alpha relaxation of glass-forming liquids and its comparison to data for DC704 and DC705.

Dynamic shear-modulus data are presented for two silicone oils DC704 and DC705 for frequencies between 1 mHz and 10 kHz at temperatures covering more than five decades of relaxation-time variation. Data are fitted to the alpha part of a phenomenological model previously shown to describe well the dynamic shear modulus of squalane, which has a large beta process [Hecksher et al., J. Chem. Phys. 146, 154504 (2017)]. That model is characterized by additivity of the alpha and beta shear compliance and by a high-frequency decay of the alpha process in proportion to ω-1/2, where ω is the angular frequency. The fits of the alpha part of this model to the DC704 and DC705 data are compared to fits by a Havriliak-Negami type model, a Barlow-Erginsav-Lamb model, and a Cole-Davidson type model. At all temperatures, the best fit is obtained by the alpha part of the squalane model. This strengthens the conjecture that so-called t-relaxation, leading to high-frequency loss decays proportional to ω-1/2, is generic to the alpha relaxation of supercooled liquids [J. C. Dyre, Phys. Rev. E 74, 021502 (2006); Nielsen et al., J. Chem. Phys. 130, 154508 (2009); and Pabst et al., J. Phys. Chem. Lett. 12, 3685-3690 (2021)].

Predicting nonlinear physical aging of glasses from equilibrium relaxation via the material time.

The noncrystalline glassy state of matter plays a role in virtually all fields of materials science and offers complementary properties to those of the crystalline counterpart. The caveat of the glassy state is that it is out of equilibrium and therefore exhibits physical aging, i.e., material properties change over time. For half a century, the physical aging of glasses has been known to be described well by the material-time concept, although the existence of a material time has never been directly validated. We do this here by successfully predicting the aging of the molecular glass 4-vinyl-1,3-dioxolan-2-one from its linear relaxation behavior. This establishes the defining property of the material time. Via the fluctuation-dissipation theorem, our results imply that physical aging can be predicted from thermal-equilibrium fluctuation data, which is confirmed by computer simulations of a binary liquid mixture.

Time-scale ordering in hydrogen- and van der Waals-bonded liquids.

The time scales of structural relaxation are investigated on the basis of five different response functions for 1,2, 6-hexanetriol, a hydrogen-bonded liquid with a minor secondary contribution, and 2,6,10,15,19,23-hexamethyl-tetracosane (squalane), a van der Waals-bonded liquid with a prominent secondary relaxation process. Time scales of structural relaxation are derived as inverse peak frequencies for each investigated response function. For 1,2,6-hexanetriol, the ratios of the time scales are temperature-independent, while a decoupling of time scales is observed for squalane in accordance with the literature. An alternative evaluation approach is made on the squalane data, extracting time scales from the terminal relaxation mode instead of the peak position, and in this case, temperature-independent time-scale ratios are also found for squalane, despite its strong secondary relaxation contribution. Interestingly, the very same ordering of response-function-specific time scales is observed for these two liquids, which is also consistent with the observation made for simple van der Waals-bonded liquids reported previously [Jakobsen et al., J. Chem. Phys. 136, 081102 (2012)]. This time-scale ordering is based on the following response functions, from fast to slow dynamics: shear modulus, bulk modulus, dielectric permittivity, longitudinal thermal expansivity coefficient, and longitudinal specific heat. These findings indicate a general relation between the time scales of different response functions and, as inter-molecular interactions apparently play a subordinate role, suggest a rather generic nature of the process of structural relaxation.

Identity of the local and macroscopic dynamic elastic responses in supercooled 1-propanol.

Glass-forming liquids are well known to have significant dynamic heterogeneities, leading to spatially grossly varying elastic properties throughout the system. In this paper, we compare the local elastic response of supercooled 1-propanol monitored by triplet state solvation dynamics to the macroscopic dynamic shear modulus measured by a piezo-electric gauge. The time-dependent responses are found to be identical, which means that the dynamic macroscopic shear modulus provides a good measure of the average local elastic properties. Since the macroscopic shear modulus of a dynamically inhomogeneous system in general is not just the average of the local moduli, there was no reason to expect such a result. This surprising finding not only provides constraints for models of dynamical heterogeneities in glass-forming liquids, but also allows for a fairly straightforward check on elastic models for glassy dynamics.

Long-time structural relaxation of glass-forming liquids: Simple or stretched exponential?

This paper presents data for the physical aging of the density of squalane upon both non-linear and nearly linear temperature jumps from states of thermal equilibrium. Invoking the single-parameter-aging scenario [Hecksher et al., J. Chem. Phys. 142, 241103 (2015); Proc. Natl. Acad. Sci. U. S. A. 116, 16736-16741 (2019)], the linear-response aging relaxation function is extracted from the data. Based on this, it is shown that the relaxation toward equilibrium follows a simple exponential function at long times; a stretched-exponential function provides a poor fit. This demonstrates the existence of a terminal relaxation rate for the physical aging of squalane, corresponding to an effective long-time cutoff in the spectrum of structural relaxation times.

Fast contribution to the activation energy of a glass-forming liquid.

This paper presents physical-aging data for the silicone oil tetramethyl-tetraphenyl trisiloxane. The density and the high-frequency plateau shear modulus [Formula: see text] were monitored following temperature jumps starting from fully equilibrated conditions. Both quantities exhibit a fast change immediately after a temperature jump. Adopting the material-time formalism of Narayanaswamy, we determine from the dielectric loss at 0.178 Hz the time evolution of the aging-rate activation energy. The relative magnitude of the fast change of the activation energy differs from that of the density, but is identical to that of [Formula: see text] In fact, the activation energy is proportional to [Formula: see text] throughout the aging process, with minor deviations at the shortest times. This shows that for the silicone oil in question the dynamics are determined by [Formula: see text] in-as well as out of-equilibrium.

Experimental Evidence for a State-Point-Dependent Density-Scaling Exponent of Liquid Dynamics.

A large class of liquids obey density scaling characterized by an exponent, which quantifies the relative roles of temperature and density for the dynamics. We present experimental evidence that the density-scaling exponent γ is state-point dependent for the glass formers tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl ether (5PPE). A method is proposed that from dynamic and thermodynamic properties at equilibrium estimates the value of γ. The method applies at any state point of the pressure-temperature plane, both in the supercooled and the normal liquid regimes. We find that γ is generally state-point dependent, which is confirmed by reanalyzing data for 20 metallic liquids and two model liquids.

Generalized single-parameter aging tests and their application to glycerol.

Physical aging of glycerol following temperature jumps is studied by dielectric spectroscopy at temperatures just below the glass transition temperature. The data are analyzed using two single-parameter aging tests developed by Hecksher et al. [J. Chem. Phys. 142, 241103 (2015)]. We generalize these tests to include jumps ending at different temperatures. Moreover, four times larger jumps than previously are studied. The single-parameter aging tests are here for the first time applied to a hydrogen-bonded liquid. We conclude that glycerol obeys single-parameter aging to a good approximation.

Perspective: Searching for simplicity rather than universality in glass-forming liquids.

This article gives an overview of experimental results on dynamics in bulk glass-forming molecular liquids. Rather than looking for phenomenology that is universal, in the sense that it is seen in all liquids, the focus is on identifying the basic characteristics, or "stylized facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner.

Toward broadband mechanical spectroscopy.

Diverse material classes exhibit qualitatively similar behavior when made viscous upon cooling toward the glass transition, suggesting a common theoretical basis. We used seven different measurement methods to determine the mechanical relaxation kinetics of a prototype molecular glass former over a temporal range of 13 decades and over a temperature range spanning liquid to glassy states. The data conform to time-temperature superposition for the main (alpha) process and to a scaling relation of schematic mode-coupling theory. The broadband mechanical measurements demonstrated have fundamental and practical applications in polymer science, geophysics, multifunctional materials, and other areas.

Model for the alpha and beta shear-mechanical properties of supercooled liquids and its comparison to squalane data.

This paper presents data for supercooled squalane's frequency-dependent shear modulus covering frequencies from 10 mHz to 30 kHz and temperatures from 168 K to 190 K; measurements are also reported for the glass phase down to 146 K. The data reveal a strong mechanical beta process. A model is proposed for the shear response of the metastable equilibrium liquid phase of supercooled liquids. The model is an electrical equivalent-circuit characterized by additivity of the dynamic shear compliances of the alpha and beta processes. The nontrivial parts of the alpha and beta processes are each represented by a "Cole-Cole retardation element" defined as a series connection of a capacitor and a constant-phase element, resulting in the Cole-Cole compliance function well-known from dielectrics. The model, which assumes that the high-frequency decay of the alpha shear compliance loss varies with the angular frequency as ω-1/2, has seven parameters. Assuming time-temperature superposition for the alpha and beta processes separately, the number of parameters varying with temperature is reduced to four. The model provides a better fit to the data than an equally parametrized Havriliak-Negami type model. From the temperature dependence of the best-fit model parameters, the following conclusions are drawn: (1) the alpha relaxation time conforms to the shoving model; (2) the beta relaxation loss-peak frequency is almost temperature independent; (3) the alpha compliance magnitude, which in the model equals the inverse of the instantaneous shear modulus, is only weakly temperature dependent; (4) the beta compliance magnitude decreases by a factor of three upon cooling in the temperature range studied. The final part of the paper briefly presents measurements of the dynamic adiabatic bulk modulus covering frequencies from 10 mHz to 10 kHz in the temperature range from 172 K to 200 K. The data are qualitatively similar to the shear modulus data by having a significant beta process. A single-order-parameter framework is suggested to rationalize these similarities.

Communication: Linking the dielectric Debye process in mono-alcohols to density fluctuations.

This work provides the first direct evidence that the puzzling dielectric Debye process observed in mono-alcohols is coupled to density fluctuations. The results open up for an explanation of the Debye process within the framework of conventional liquid-state theory. The spectral shape of the dynamical bulk modulus of the two studied mono-alcohols, 2-ethyl-1-hexanol and 4-methyl-3-heptanol, is nearly identical to that of their corresponding shear modulus, and thus the supramolecular structures believed to be responsible for the slow dielectric Debye process are manifested in the bulk modulus in the same way as in the shear modulus.

Communication: Direct tests of single-parameter aging.

This paper presents accurate data for the physical aging of organic glasses just below the glass transition probed by monitoring the following quantities after temperature up and down jumps: the shear-mechanical resonance frequency (∼360 kHz), the dielectric loss at 1 Hz, the real part of the dielectric constant at 10 kHz, and the loss-peak frequency of the dielectric beta process (∼10 kHz). The setup used allows for keeping temperature constant within 100 µK and for thermal equilibration within a few seconds after a temperature jump. The data conform to a new simplified version of the classical Tool-Narayanaswamy aging formalism, which makes it possible to calculate one relaxation curve directly from another without any fitting to analytical functions.

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.

The dynamic bulk modulus of three glass-forming liquids.

We present dynamic adiabatic bulk modulus data for three organic glass-forming liquids: two van der Waal's liquids, trimethyl-pentaphenyl-trisiloxane (DC705) and dibuthyl phtalate (DBP), and one hydrogen-bonded liquid, 1,2-propanediol (PD). All three liquids are found to obey time-temperature superposition within the uncertainty of the measurement in the adiabatic bulk modulus. The bulk modulus spectra are compared to the shear modulus spectra. The time scales of the two responses were found to be similar. The shapes of the shear and bulk modulus alpha loss peak are nearly identical for DBP and DC705, while the bulk modulus spectrum for PD is significantly broader than that of the shear modulus. The data further suggest that a "bulk modulus version of the shoving model" for the temperature dependence of the activation energy using the bulk modulus relaxation strength, ΔK(T), works well for DC705 and DBP, but not PD, while a formulation of the model using the high-frequency plateau value, K∞(T), gave a poor result for all three liquids.

Mechanical spectra of glass-forming liquids. I. Low-frequency bulk and shear moduli of DC704 and 5-PPE measured by piezoceramic transducers.

We present dynamic shear and bulk modulus measurements of supercooled tetraphenyl-tetramethyl-trisiloxane (DC704) and 5-phenyl-4-ether over a range of temperatures close to their glass transition. The data are analyzed and compared in terms of time-temperature superposition (TTS), the relaxation time, and the spectral shape parameters. We conclude that TTS is obeyed to a good approximation for both the bulk and shear moduli. The loss-peak shapes are nearly identical, while the shear modulus relaxes faster than the bulk modulus. The temperature dependence of this decoupling of time scales is constant over the temperature range explored here. In addition, we demonstrate how one can measure reliably the DC shear viscosity over ten orders of magnitude by using the two measuring techniques in combination.