Generic Primary Mechanical Response of Viscous Liquids

On the spectral shape of the structural relaxation in supercooled liquids

Structural relaxation in supercooled liquids is non-exponential. In susceptibility representation, χ″(ν), the spectral shape of the structural relaxation is observed as an asymmetrically broadened peak with a ν1 low- and ν-β high-frequency behavior. In this perspective article, we discuss common notions, recent results, and open questions regarding the spectral shape of the structural relaxation. In particular, we focus on the observation that a high-frequency behavior of ν-1/2 appears to be a generic feature in a broad range of supercooled liquids. Moreover, we review extensive evidence that contributions from orientational cross-correlations can lead to deviations from the generic spectral shape in certain substances, in particular in dielectric loss spectra. In addition, intramolecular dynamics can contribute significantly to the spectral shape in substances containing more complex and flexible molecules. Finally, we discuss the open questions regarding potential physical origins of the generic ν-1/2 behavior and the evolution of the spectral shape toward higher temperatures.

Translational and reorientational dynamics in carboxylic acid-based deep eutectic solvents

The glass formation and the dipolar reorientational motions in deep eutectic solvents (DESs) are frequently overlooked, despite their crucial role in defining the room-temperature physiochemical properties. To understand the effects of these dynamics on the ionic conductivity and their relation to the mechanical properties of the DES, we conducted broadband dielectric and rheological spectroscopy over a wide temperature range on three well-established carboxylic acid-based natural DESs. These are the eutectic mixtures of choline chloride with oxalic acid (oxaline), malonic acid (maline), and phenylacetic acid (phenylaceline). In all three DESs, we observe signs of a glass transition in the temperature dependence of their dipolar reorientational and structural dynamics, as well as varying degrees of motional decoupling between the different observed dynamics. Maline and oxaline display a breaking of the Walden rule near the glass-transition temperature, while the relation between the dc conductivity and dipolar relaxation time in both maline and phenylaceline is best described by a power law. The glass-forming properties of the investigated systems not only govern the orientational dipolar motions and rheological properties, which are of interest from a fundamental point of view, but they also affect the dc conductivity, even at room temperature, which is of high technical relevance.

Solid-that-Flows Picture of Glass-Forming Liquids

This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.

Non-simple flow behavior in a polar van der Waals liquid: Structural relaxation under scrutiny

The non-exponential character of the structural relaxation is considered one of the hallmarks of the glassy dynamics, and in this context, the relatively narrow shape observed by dielectric techniques for polar glass formers has attracted the attention of the community for long time. This work addresses the phenomenology and role of specific non-covalent interactions in the structural relaxation of glass-forming liquids by the study of polar tributyl phosphate. We show that dipole interactions can couple to shear stress and modify the flow behavior, preventing the occurrence of the simple liquid behavior. We discuss our findings in the general framework of glassy dynamics and the role of intermolecular interactions.

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.

Generic α relaxation in a strong GeO_{2} glass melt

The viscoelastic α relaxation in glass-forming GeO_{2} was measured over a range of temperatures near the glass transition using photon correlation spectroscopy. The relaxation in this "strong" glass former exhibits a nonexponential decay identical to that found in a great many simple organic "fragile" liquids. This finding contradicts the longstanding conjecture that nonexponentiality of viscous relaxations near the glass transition are correlated to the liquid's fragility. Instead, the findings offer support for a recent proposal that the nonexponentiality parameter of the α-relaxation in supercooled liquids displays a universal value β(T_{g})=1/2 near the glass transition.

Nongeneric structural-relaxation shape of supercooled liquids: Insights from linear and nonlinear experiments on propylene glycol

Currently, there is a debate whether the structural relaxation of polar liquids is more faithfully reflected (i) by the generically shaped response detected by dynamic light scattering or rather (ii) by the slower, more stretched, system-dependent susceptibility response recorded by dielectric spectroscopy. In this work, nonlinearly induced transients probing structural relaxation reveal that near the glass transition, alternative (ii) is appropriate for propylene glycol. Results from shear rheology and from calorimetry corroborate this finding, underscoring the previously advanced notion (Moch et al., Phys. Rev. Lett. 128, 228001, 2022) that the reorientationally probed structural susceptibility of viscous liquids displays a nongeneric spectral shape.

Predicting Dielectric and Shear-Rheology Properties of Glass-Forming Pharmaceutical Liquids from Each Other: Applications and Limitations

Acetaminophen, nicotine, and lidocaine hydrochloride were investigated in their deeply supercooled liquid states using oscillatory shear rheology. The mechanical spectra of these drugs are presented in modulus, compliance, as well as fluidity formats. Their frequency profiles can be described via models adapted from the field of charge transport. Inspired by the success of this approach, the Barton-Nakajima-Namikawa relation, best known from the same field, was also tested. When adapted to rheology, this approach interrelates static and dynamic characteristics of viscous flow and was found to work excellently. The temperature dependence of the characteristic shear frequencies was checked against the shoving model, which relates them to the temperature-dependent instantaneous shear modulus and acceptable agreement was found. Combined with shear mechanical literature data on ibuprofen and indomethacin, a modified version of the phenomenological model by Gemant, DiMarzio, and Bishop (GDB) was employed to successfully predict the shape and amplitude of the dielectric spectra for all studied liquids, except for lidocaine hydrochloride. For the latter, the modified GDB model is suggested to aid in mapping out the reorientational part of the dielectric response, while the experimental results are strongly superimposed by ionic conduction phenomena. The reverse transformation, the calculation of rheological spectra based on dielectric ones, is also successfully demonstrated. For the example of acetyl salicylic acid, it is shown how dielectric spectra can be used to even predict rheological ones. The limits of the central parameter governing these mutual transformations, the electroviscoelastic material constant, and indications for its correlation with the dielectric relaxation strength are discussed. For pharmaceuticals characterized by a strong dynamical decoupling of the electrical from the mechanical degrees of freedom, the modified GDB model is not expected to be applicable.

Low-frequency dynamics in ionic liquids: Comparison of experiments and the random barrier model

By examining the fine features of dielectric spectra of ionic liquids, we show that the derivative of real permittivity progressively broadens at low frequencies when the glass transition is approached...

Nuclear Spin Relaxation in Viscous Liquids: Relaxation Stretching of Single-Particle Probes

Spin-lattice relaxation rates R₁(ω,T), probed via high-field and field-cycling nuclear magnetic resonance (NMR), are used to test the validity of frequency-temperature superposition (FTS) for the reorientation dynamics in viscous liquids. For several liquids, FTS is found to apply so that master curves can be generated. The susceptibility spectra are highly similar to those obtained from depolarized light scattering (DLS) and reveal an excess wing. Where FTS works, two approaches are suggested to access the susceptibility: (i) a plot of deuteron R₁(T) vs the spin-spin relaxation rate R₂(T) and (ii) a plot of R₁(T) vs an independently measured reference time τ_ref(T). Using single-frequency scans, (i) allows one to extract the relaxation stretching as well as the NMR coupling constant. Surveying 26 data sets, we find Kohlrausch functions with exponents 0.39 < β_K ≤ 0.67. Plots of the spin-spin relaxation rate R₂─rescaled by the NMR coupling constant─as a function of temperature allow one to test how well site-specific NMR relaxations couple to a given reference process. Upon cooling of flexible molecule liquids, the site-specific dynamics is found to merge, suggesting that near T_g the molecules reorient essentially as a rigid entity. This presents a possible resolution for the much lower stretching parameters reported here at high temperatures that contrast with the ones that were reported to be universal in a recent DLS study close to T_g. Our analysis underlines that deuteron relaxation is a uniquely powerful tool to probe single-particle reorientation.

First- and third-order shear nonlinearities across the structural relaxation peak of the deeply supercooled pharmaceutical liquid indomethacin

Nonlinear rheological properties of viscous indomethacin are studied in the frequency range of its structural relaxation, that is, in a range so far inaccessible to standard techniques involving medium-amplitude oscillatory shear amplitudes. The first- and third-order nonlinearity parameters thus recorded using a sequence of small and large shear excitations in a time efficient manner are compared with predictions from rheological models. By properly phase cycling the shear amplitudes, build-up and decay transients are recorded. Analogous to electrical-field experiments, these transients yield direct access to the structural relaxation times under linear and nonlinear shearing conditions. To demonstrate the broader applicability of the present approach, transient analyses are also carried out for the glass formers glycerol, ortho-terphenyl, and acetaminophen.

Rheology based estimates of self- and collective diffusivities in viscous liquids

The self-diffusion coefficient of viscous liquids is estimated on the basis of a simple analysis of their rheological shear spectra. To this end, the Almond-West approach, previously employed to access single-particle diffusivities in ionic conductors, is generalized for application to molecular dynamics in supercooled liquids. Rheology based estimates, presented for indomethacin, ortho-terphenyl, and trinaphthylbenzene, reveal relatively small, yet systematic differences when compared with diffusivity data directly measured for these highly viscous liquids. These deviations are discussed in terms of mechanical Haven ratios, introduced to quantify the magnitude of collective translational effects that have an impact on the viscous flow.

The relationship between charge and molecular dynamics in viscous acid hydrates

Oscillatory shear rheology has been employed to access the structural rearrangements of deeply supercooled sulfuric acid tetrahydrate (SA4H) and phosphoric acid monohydrate, the latter in protonated (PA1H) and deuterated (PA1D) forms. Their viscoelastic responses are analyzed in relation to their previously investigated electric conductivity. The comparison of the also presently reported dielectric response of deuterated sulfuric acid tetrahydrate (SA4D) and that of its protonated analog SA4H reveals an absence of isotope effects for the charge transport in this hydrate. This finding clearly contrasts with the situation known for PA1H and PA1D. Our analyses also demonstrate that the conductivity relaxation profiles of acid hydrides closely resemble those exhibited by classical ionic electrolytes, even though the charge transport in phosphoric acid hydrates is dominated by proton transfer processes. At variance with this dielectric simplicity, the viscoelastic responses of these materials depend on their structural compositions. While SA4H displays a "simple liquid"-like viscoelastic behavior, the mechanical responses of PA1H and PA1D are more complex, revealing relaxation modes, which are faster than their ubiquitous structural rearrangements. Interestingly, the characteristic rates of these fast mechanical relaxations agree well with the characteristic frequencies of the charge rearrangements probed in the dielectric investigations, suggesting appearance of a proton transfer in mechanical relaxation of phosphoric acid hydrates. These findings open the exciting perspective of exploiting shear rheology to access not only the dynamics of the matrix but also that of the charge carriers in highly viscous decoupled conductors.

Generic Structural Relaxation in Supercooled Liquids

One of the unsolved problems of dynamics in supercooled liquids are the differences in spectral shape of the structural relaxation observed among different methods and substances, and a possible generic line shape has long been debated. We show that the light scattering spectra of very different systems, e.g., hydrogen bonding, van der Waals liquids, and ionic systems, almost perfectly superimpose and show a generic line shape of the structural relaxation, following ∝ ω^-1/2 at high frequencies. In dielectric spectra the generic behavior is recovered only for systems with low dipole moment, while in strongly dipolar liquids additional cross-correlation contributions mask the generic structural relaxation.

Isochronal Superposition of the Structural α-Relaxation and Invariance of Its Relation to the β-Relaxation to Changes of Thermodynamic Conditions in Methyl m-Toluate

The dielectric spectra of methyl m-toluate (MMT) in supercooled liquid and glassy states were measured over wide ranges of temperature T at ambient and elevated pressures P. We found that the frequency dispersion of the loss peak contributed by the structural α-relaxation is invariant to changes of P and T, while keeping the loss peak frequency f_α(T,P) constant. This isochronal superposition property of the α-relaxation holds for different choices of f_α(T,P). The invariant frequency dispersions for the same f_α(T,P) are also indicated by the fractional exponent β_KWW in the Fourier transform of the Kohlrausch-Williams-Watts (KWW) function. Similarly, the fragility m index of MMT keeps approximately constant on varying pressure, largely different from H-bonded glass formers. The secondary β-relaxation at a frequency higher than f_α(T,P) is found to shift to lower frequencies by elevating pressure in concert with the α-relaxation. The ratio τ_α(T,P)/τ_β(T,P) is approximately unchanged to variations of T and P while keeping τ_α(T,P) constant. These properties observed in MMT offer experimental evidence of the dynamic correlation between α- and β-relaxations in pure small-molecule glass-formers.

Spectral shape simplicity of viscous materials

A broad survey of viscoelastic data demonstrates that van der Waals, hydrogen-bonded, and ionic liquids, as well as polymeric, inorganic, and metallic melts share a structural relaxation pattern virtually insensitive to their morphological details. This mechanical simplicity is connected with that characterizing the fast reorientation dynamics prevailing in liquids devoid of a distinguishable secondary susceptibility peak. By these means one is able to uncover a generic spectral pattern which rationalizes the recently reported "universality" of relaxation strength vs stretching of the dielectric response of viscous liquids, significantly broadening the framework in which their relaxation behavior is assessed.

Structure and dynamics of short-chain polymerized ionic liquids

Combining experimental results obtained with X-ray scattering and field-gradient nuclear magnetic resonance (NMR) and an assessment of new and previous dielectric and rheology data, our study focuses on the molecular weight (M_w) evolution of local structure and dynamics in a homologous series of covalently bonded ionic liquids. Performed on a family of electrolytes with a tailored degree of ionic decoupling, this study reveals the differences between monomeric and oligomeric melts with respect to their structural organization, mass and charge transport, and molecular diffusion. Our study demonstrates that for the monomeric compound, the broadband conductivity and mechanical spectra reflect the same underlying distribution of activation barriers and that the Random Barrier Model describes fairly well both the ionic and structural relaxation processes in these materials. Moreover, the oligomers with chains comprising ten segments only exhibit both structural and dynamical fingerprints of a genuine polymer. A comparison of conductivity levels estimated using the self-diffusion coefficients probed via NMR and those probed directly with dielectric spectroscopy reveals the emerging of ion correlations which are affecting the macroscopic charge transport in these materials in a chain-length dependent manner.

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.