What is the origin of slow relaxation modes in highly viscous ionic liquids?

Room temperature ionic liquids (RTILs) are molten salts consisting entirely of ions and have over the past decades gained increased interest due to their high potential in applications. These structurally complex systems often display multiple relaxation modes in the response functions at lower frequencies, hinting to complex underlying mechanisms. While the existence of these multimodal spectra in the shear mechanical, dielectric, and light scattering response of RTILs has been confirmed multiple times, controversy still surrounds the origin. This paper, therefore, aims to provide additional insights into the multimodal spectra seen in RTILs by presenting new shear mechanical results on seven different RTILs: Pyr1n-TFSI with n = 4, 6, and 8; Pyr18-TFSI mixed with Li-TFSI in two high concentrations; and Cn-mim-BF4 with n = 3 and 8. Dynamic depolarized light scattering was also measured on one of the Pyr18-TFSI Li-salt mixtures. These specific cases were analyzed in detail and put into a bigger perspective together with an overview of the literature. Recent literature offers two specific explanations for the origin of the multimodal shear mechanical spectra: (1) cation-anion time scale separation or (2) combined cation-anion relaxation in addition to a dynamic signal from mesoscale aggregates at lower frequencies. However, neither of these two pictures can consistently explain all the results on different ionic liquids. Instead, we conclude that the origin of the multimodal spectrum is system specific. This underlines the complexity of this class of liquids and shows that great care must be taken when making general conclusions based on specific cases.

Invariant dynamics in a united-atom model of an ionic liquid.

We study a united-atom model of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethyl)sulfonylamide to determine to what extent there exist curves in the phase diagram along which the microscopic dynamics are invariant when expressed in dimensionless, or reduced, form. The initial identification of these curves, termed isodynes, is made by noting that contours of reduced shear viscosity and reduced self-diffusion coefficient coincide to a good approximation. Choosing specifically the contours of reduced viscosity as nominal isodynes, further simulations were carried out for state points on these, and other aspects of dynamics were investigated to study their degree of invariance. These include the mean-squared displacement, shear-stress autocorrelation function, and various rotational correlation functions. These were invariant to a good approximation, with the main exception being rotations of the anion about its long axis. The dynamical features that are invariant have in common that they are aspects that would be relevant for a coarse-grained description of the system; specifically, removing the most microscopic degrees of freedom in principle leads to a simplification of the potential energy landscape, which allows for the existence of isodynes.

A density scaling conjecture for aging glasses.

The aging rate of glasses has traditionally been modeled as a function of temperature, T, and fictive temperature, while density, ρ, is not explicitly included as a parameter. However, this description does not naturally connect to the modern understanding of what governs the relaxation rate in equilibrium. In equilibrium, it is well known that the relaxation rate, γeq, depends on temperature and density. In addition, a large class of systems obeys density scaling, which means the rate specifically depends on the scaling parameter, Γ = e(ρ)/T, where e(ρ) is a system specific function. This paper presents a generalization of the fictive temperature concept in terms of a fictive scaling parameter, Γfic, and a density scaling conjecture for aging glasses in which the aging rate depends on Γ and Γfic.

Pressing matter: why are ionic liquids so viscous?

Room temperature ionic liquids are considered to have huge potential for practical applications such as batteries. However, their high viscosity presents a significant challenge to their use changing from niche to ubiquitous. The modelling and prediction of viscosity in ionic liquids is the subject of an ongoing debate involving two competing hypotheses: molecular and local mechanisms versus collective and long-range mechanisms. To distinguish between these two theories, we compared an ionic liquid with its uncharged, isoelectronic, isostructural molecular mimic. We measured the viscosity of the molecular mimic at high pressure to emulate the high densities in ionic liquids, which result from the Coulomb interactions in the latter. We were thus able to reveal that the relative contributions of coulombic compaction and the charge network interactions are of similar magnitude. We therefore suggest that the optimisation of the viscosity in room temperature ionic liquids must follow a dual approach.

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.

Quantifying dynamical and structural invariance in a simple molten salt model.

Recent experimental results for the structure in the ionic liquid PYR14 +TFSI- have shown invariance in the main structure factor peak along curves of equal electrical conductivity [Hansen et al., Phys. Chem. Chem. Phys. 22, 14169 (2020)]. The charge peak decreases slightly with increasing temperature at fixed conductivity, however. For simple liquids, curves with invariant dynamics and structure, known as isomorphs, can be identified as configurational adiabats. While liquids with strong-Coulomb interactions do not have good isomorphs, ionic liquids could be an intermediate case with approximate isomorphs along which some aspects of structure and dynamics are invariant. We study a simple molten salt model using molecular dynamics simulations to test this hypothesis. Simple measures of structure and dynamics are investigated along with one transport property, the shear viscosity. We find that there is a substantial degree of invariance of the self-intermediate scattering function, the mean square displacement, and the viscosity along configurational adiabats over a wide range of densities for the three adiabats simulated. The density range studied is more than a factor of two and extends from the strong-Coulomb regime at low densities to the weak-Coulomb regime at high densities. The structure is not invariant over the full range of density, but in the weak-Coulomb regime, we see behavior similar to that seen experimentally over density changes of order 15%. In view of the limited structural invariance but substantial dynamical invariance, we designate the configurational adiabats as isodynes.

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.

Structure and dynamics of highly concentrated LiTFSI/acetonitrile electrolytes.

High salt concentration has been shown to induce increased electrochemical stability in organic solvent-based electrolytes. Accompanying the change in bulk properties is a structural ordering on mesoscopic length scales and changes in the ion transport mechanism have also been suggested. Here we investigate the local structure and dynamics in highly concentrated acetonitrile electrolytes as a function of salt concentration. Already at low concentrations ordering on microscopic length scales in the electrolytes is revealed by small angle X-ray scattering, as a result of correlations of Li+ coordinating clusters. For higher salt concentrations a charge alternation-like ordering is found as anions start to take part in the solvation. Results from quasi-elastic neutron spectroscopy reveal a jump diffusion dynamical process with jump lengths virtually independent of both temperature and Li-salt concentration. The jump can be envisaged as dissociation of a solvent molecule or anion from a particular Li+ solvation structure. The residence time, 50-800 ps, between the jumps is found to be highly temperature and Li-salt concentration dependent, with shorter residence times for higher temperature and lower concentrations. The increased residence time at high Li-salt concentration can be attributed to changes in the interaction of the solvation shell as a larger fraction of TFSI anions take part in the solvation, forming more stable solvation shells.

Pressure and Temperature Dependence of Local Structure and Dynamics in an Ionic Liquid.

A detailed understanding of the local dynamics in ionic liquids remains an important aspect in the design of new ionic liquids as advanced functional fluids. Here, we use small-angle X-ray scattering and quasi-elastic neutron spectroscopy to investigate the local structure and dynamics in a model ionic liquid as a function of temperature and pressure, with a particular focus on state points (P,T) where the macroscopic dynamics, i.e., conductivity, is the same. Our results suggest that the initial step of ion transport is a confined diffusion process, on the nanosecond timescale, where the motion is restricted by a cage of nearest neighbors. This process is invariant considering timescale, geometry, and the participation ratio, at state points of constant conductivity, i.e., state points of isoconductivity. The connection to the nearest-neighbor structure is underlined by the invariance of the peak in the structure factor corresponding to nearest-neighbor correlations. At shorter timescales, picoseconds, two localized relaxation processes of the cation can be observed, which are not directly linked to ion transport. However, these processes also show invariance at isoconductivity. This points to that the overall energy landscape in ionic liquids responds in the same way to density changes and is mainly governed by the nearest-neighbor interactions.

Density scaling of structure and dynamics of an ionic liquid.

Room temperature ionic liquids are salts with low melting points achieved by employing bulky and asymmetrical ions. The molecular design leads to apolar and polar parts as well as the presence of competing Coulomb and van der Waals interactions giving rise to nano-scale structure, e.g. charge ordering. In this paper we address the question of how these nano-scale structures influence transport properties and dynamics on different timescales. We apply pressure and temperature as control parameters and investigate the structure factor, charge transport, microscopic alpha relaxation and phonon dynamics in the phase diagram of an ionic liquid. Including viscosity and self diffusion data from literature we find that all the dynamic and transport variables studied follow the same density scaling, i.e. they all depend on the scaling variable Γ = ργ/T, with γ = 2.8. The molecular nearest neighbor structure is found to follow a density scaling identical to that of the dynamics, while this is not the case for the charge ordering, indicating that the charge ordering has little influence on the investigated 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.

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.

Isochronal superposition and density scaling of the α-relaxation from pico- to millisecond.

The relaxation dynamics in two van der Waals bonded liquids and one hydrogen-bonding molecular liquid are studied as a function of pressure and temperature by incoherent neutron scattering using simultaneous dielectric spectroscopy. The dynamics are studied in a range of alpha relaxation times from pico- to milliseconds, primarily in the equilibrium liquid state. In this range, we find that isochronal superposition and density scaling work not only for the two van der Waals liquids but also for the hydrogen-bonding liquid, though the density scaling exponent is much smaller for the latter. Density scaling and isochronal superposition are seen to break down for intra-molecular dynamics when it is separated in time from the alpha relaxation, in close agreement with previous observations from molecular dynamics simulations.

High-pressure cell for simultaneous dielectric and neutron spectroscopy.

In this article, we report on the design, manufacture, and testing of a high-pressure cell for simultaneous dielectric and neutron spectroscopy. This cell is a unique tool for studying dynamics on different time scales, from kilo- to picoseconds, covering universal features such as the α relaxation and fast vibrations at the same time. The cell, constructed in cylindrical geometry, is made of a high-strength aluminum alloy and operates up to 500 MPa in a temperature range between roughly 2 and 320 K. In order to measure the scattered neutron intensity and the sample capacitance simultaneously, a cylindrical capacitor is positioned within the bore of the high-pressure container. The capacitor consists of two concentric electrodes separated by insulating spacers. The performance of this setup has been successfully verified by collecting simultaneous dielectric and neutron spectroscopy data on dipropylene glycol, using both backscattering and time-of-flight instruments. We have carried out the experiments at different combinations of temperature and pressure in both the supercooled liquid and glassy state.

Mapping Isobaric Aging onto the Equilibrium Phase Diagram.

The linear volume relaxation and the nonlinear volume aging of a glass-forming liquid are measured, directly compared, and used to extract the out-of-equilibrium relaxation time. This opens a window to investigate how the relaxation time depends on temperature, structure, and volume in parts of phase space that are not accessed by the equilibrium liquid. It is found that the temperature dependence of relaxation time is non-Arrhenius even in the isostructural case-challenging the Adam-Gibbs entropy model. Based on the presented data and the idea that aging happens through quasiequilibrium states, we suggest a mapping of the out-of-equilibrium states during isobaric aging to the equilibrium phase diagram. This mapping implies the existence of isostructural lines in the equilibrium phase diagram. The relaxation time is found to depend on the bath temperature, density, and a just single structural parameter, referred to as an effective temperature.

Liquid dynamics in partially crystalline glycerol.

We present a dielectric study on the dynamics of supercooled glycerol during crystallization. We explore the transformation into a solid phase in real time by monitoring the temporal evolution of the amplitude of the dielectric signal. Neither the initial nucleation nor the crystal growth influences the liquid dynamics visibly. For one of the samples studied, a tiny fraction of glycerol remained in the disordered state after the end of the transition. We examined the nature of the α relaxation in this frustrated crystal and find that it is virtually identical to the bulk dynamics. In addition, we have found no evidence that supercooled glycerol transforms into a peculiar phase in which either a new solid amorphous state or nano-crystals dispersed in a liquid matrix are formed.

Communication: High pressure specific heat spectroscopy reveals simple relaxation behavior of glass forming molecular liquid.

The frequency dependent specific heat has been measured under pressure for the molecular glass forming liquid 5-polyphenyl-4-ether in the viscous regime close to the glass transition. The temperature and pressure dependences of the characteristic time scale associated with the specific heat is compared to the equivalent time scale from dielectric spectroscopy performed under identical conditions. It is shown that the ratio between the two time scales is independent of both temperature and pressure. This observation is non-trivial and demonstrates the existence of specially simple molecular liquids in which different physical relaxation processes are both as function of temperature and pressure/density governed by the same underlying "inner clock." Furthermore, the results are discussed in terms of the recent conjecture that van der Waals liquids, like the measured liquid, comply to the isomorph theory.