Dipole-dipole correlations and the Debye process in the dielectric response of nonassociating glass forming 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.

Correlation between entropy fluctuations and the dielectric relaxation of glass-forming systems: The central role of dipolar-dipolar cross correlations

The premise that the dielectric α relaxation has a one-to-one correspondence with entropy fluctuations in equilibrium near the glass transition was experimentally verified in a systematic and quantitative manner for glass-forming systems in general. Validation of this relation was structured at different levels, taking into account various ingredients as the apolar-polar character, macromolecular structure, the presence of hydrogen bonds, or complex structure and dynamics. The results reclaim the suitability of dielectric spectroscopy to echo the primary structural relaxation of glass-forming systems, demonstrating that the dielectric response effectively captures the structural relaxation by reliably correlating with entropy fluctuations. The correlation with entropy fluctuations holds even when the dielectric strength of the systems is high and the dielectric response is narrow and dominated by cross correlations, proving that dipolar intermolecular interactions are fundamental to the structural relaxation and not a particularity of the dielectric probe. This one-to-one correspondence between structural and dielectric α relaxation does not support the existence of a generic spectral shape for the primary structural relaxation valid for all kinds of susceptibility functions.

Specific line shape of the lowest frequency Raman scattering modes of triethylene glycol

For both dielectric spectroscopy and light scattering spectra, the relaxation modes in the microwave region have been characterized by the Debye relaxation model, which is determined by the peak frequency, or by an empirically extended model (e.g., Cole-Davidson and Kohlrausch-Williams-Watts), which has the appropriate line shape. For light scattering from glass-forming liquids, the general line shape is a broader high frequency side in comparison with Debye relaxation. However, for triethylene glycol (TEG) in liquid form at room temperature, the lowest frequency Raman scattering (LFR) mode shows a peak at about 3.0 GHz, which is narrower than that expected for the Debye relaxation. With increasing temperature, this peak exhibits a significant blueshift and begins to resemble the Debye relaxation shape, indicating that the LFR mode of TEG is also a relaxation mode. The narrowing of the LFR mode of TEG is suggested to be caused from the increased non-whiteness of the fluctuation correlations due to increased hydrogen bonding. This is a consequence of breaking the Debye relaxation model's approximation of the overdamping and narrowing limits in the GHz region, which was found in this study by analyzing the relaxation modes of Raman scattering using the multiple random telegraph model for evaluating thermal bath correlation. The analysis results show that the LFR relaxation times of TEG and the main dielectric relaxation overlap only by 333 K. However, the second LFR mode and β-relaxation at higher frequencies coincide over a wide temperature range, suggesting that they are corresponding modes.

Dipolar Order Controls Dielectric Response of Glass-Forming Liquids

The dielectric response of liquids reflects both reorientation of single molecular dipoles and collective modes, i.e., dipolar cross-correlations. A recent theory predicts the latter to produce an additional slow peak in the dielectric loss spectrum. Following this idea we argue that in supercooled liquids the high-frequency power law exponent of the dielectric loss β should be correlated with the degree of dipolar order, i.e., the Kirkwood correlation factor g_{K}. This notion is confirmed for 25 supercooled liquids. While our findings support recent theoretical work the results are shown to violate the earlier Kivelson-Madden theory.

Experimental examination of dipole-dipole cross-correlations by dielectric spectroscopy, depolarized dynamic light scattering, and computer simulations of molecular dynamics

The contribution of cross- and self-correlations to the dielectric and light-scattering spectra of supercooled polar glass formers has recently become a most challenging problem. Herein, we employ dielectric spectroscopy, depolarized dynamic light scattering (DDLS), and rheology to thoroughly examine the dynamics of van der Waals liquid 1,2-Diphenylvinylene. Carbonate (DVC), which is a polar counterpart of canonical glass former ortho-Terphenyl (OTP). We show that the light-scattering data correspond well with the dielectric permittivity function over a wide T range. This pattern is very different from the peaks' separation ω_{max}^{DDLS}/ω_{max}^{BDS}=3.7 reported recently for tributyl phosphate (TBP), despite the same dielectric characteristics of these two glass formers (β_{KWW}=0.75, Δɛ=20 for both TBP and DVC; KWW stands for Kohlrausch-Williams-Watts). This indicates different influence of orientational correlations in both methods for these two systems. We also show the results of the computer simulations of the model, polar molecules, which clearly indicate that the contribution of the cross-term to the correlation function probed in the DDLS experiment can be significant.

Glass spectrum, excess wing phenomenon, and master curves in molecular glass formers: A multi-method approach

The relaxation spectra of glass formers solely displaying an α-peak and excess wing contribution collected by various methods are reanalyzed to pin down their different spectral evolution. We show that master curve construction encompassing both α-peak and emerging excess wing works for depolarized light scattering (DLS) and nuclear magnetic resonance (NMR) relaxometry. It reveals the self-part of the slow dynamics' spectrum. Master curves are to be understood as a result of a more extensive scaling covering all temperatures instead of strict frequency-temperature superposition. DLS and NMR display identical relaxation spectra; yet, comparing different systems, we do not find a generic structural relaxation at variance with recent claims. Dielectric spectroscopy (DS) spectra show particularities, which render master curve construction obsolete. The DS α-peak is enhanced or suppressed with respect to that of DLS or NMR, yet, not correlated to the polarity of the liquid. Attempting to single out the excess wing from the overall spectrum discloses a stronger exponential temperature dependence of its amplitude compared to that below Tg and a link between its exponent and that of the fast dynamics' spectrum. Yet, such a decomposition of α-peak and excess wing appears to be unphysical. Among many different glasses, the amplitude of the excess wing power-law spectrum is found to be identical at Tg, interpreted as a relaxation analog to the Lindemann criterion.

Hydrogen Bonding Exchange and Supramolecular Dynamics of Monohydroxy Alcohols

We unravel hydrogen bonding dynamics and their relationship with supramolecular relaxations of monohydroxy alcohols (MAs) at intermediate times. The rheological modulus of MAs exhibits Rouse scaling relaxation of G(t)∼t^{-1/2} switching to G(t)∼t^{-1} at time τ_{m} before their terminal time. Meanwhile, dielectric spectroscopy reveals clear signatures of new supramolecular dynamics matching with τ_{m} from rheology. Interestingly, the characteristic time τ_{m} follows an Arrhenius-like temperature dependence over exceptionally wide temperatures and agrees well with the hydrogen bonding exchange time from nuclear magnetic resonance measurements. These observations demonstrate the presence of Rouse modes and active chain swapping of MAs at intermediate times. Moreover, detailed theoretical analyses point out explicitly that the hydrogen bonding exchange truncates the Rouse dynamics of the supramolecular chains and triggers the chain-swapping processes, supporting a recently proposed living polymer model.

Orientational dynamics in supercooled glycerol computed from MD simulations: self and cross contributions

The orientational dynamics of supercooled glycerol is probed using molecular dynamics simulations for temperatures ranging from 323 K to 253 K, through correlation functions of first and second ranks of Legendre polynomials, pertaining respectively to dielectric spectroscopy (DS) and depolarized dynamic light scattering (DDLS). The self, cross, and total correlation functions are compared with relevant experimental data. The computations reveal the low sensitivity of DDLS to cross-correlations, in agreement with what is found in experimental work, and strengthen the idea of directly comparing DS and DDLS data to evaluate the effect of cross-correlations in polar liquids. The analysis of the net static cross-correlations and their spatial decomposition shows that, although cross-correlations extend over nanometric distances, their net magnitude originates, in the case of glycerol, from the first shell of neighbouring molecules. Accessing the angular dependence of the static correlation allows us to get a microscopic understanding of why the rank-1 correlation function is more sensitive to cross-correlation than its rank-2 counterpart.

The Debye's model for the dielectric relaxation of liquid water and the role of cross-dipolar correlations. A MD-simulations study

By means of massive (more than 1.2 · 106 molecules) molecular dynamics simulations at 300 K we have disentangled self- and cross-dipolar contributions to the dielectric relaxation of liquid water that cannot be experimentally resolved. We have demonstrated that cross dipolar correlations are of paramount importance. They amount for almost a 60% of the total dielectric amplitude. The corresponding relaxation function is a one-step Debye-like function with a characteristic time, τcross, of the order of the phenomenological Debye time, τD. In contrast, the relaxation function corresponding to the self-contribution is rather complex and contains a fast decay related to dipolar librations and a second relaxation step that can be well described by two exponentials: a low-amplitude fast process (τ0 = 0.31 ps) and a main slow process (τself = 5.4 ps) that fully randomizes the dipolar orientation. In addition to dipolar relaxation functions, we have also calculated scattering-like magnitudes characterizing translation and rotation of water molecules. Although these processes can be considered as "jump" processes in the short time range, at the time scale of about τD-τcross, at which the cross-dipolar correlations decay to zero, the observed behavior cannot be distinguished from that corresponding to uncoupled Brownian translational and rotational diffusion. We propose that this is the reason why the Debye model, which does not consider intermolecular dipolar interactions, seems to work at time t ≳ τD.

Phenol, the simplest aromatic monohydroxy alcohol, displays a faint Debye-like process when mixed with a nonassociating liquid

Solvated in propylene carbonate, viscous phenol is studied using dielectric spectroscopy and shear rheology. In addition, several oxygen-17 and deuteron nuclear magnetic resonance (NMR) techniques are applied to specifically isotope labeled equimolar mixtures. Quantum chemical calculations are used to check the electrical field gradient at phenol's oxygen site. The chosen combination of NMR methods facilitates the selective examination of potentially hydrogen-bond related contributions as well as those dominated by the structural relaxation. Taken together the present results for phenol in equimolar mixtures with the van der Waals liquid propylene carbonate provide evidence for the existence of a very weak Debye-like process that originates from ringlike supramolecular associates.

From Single-Particle to Collective Dynamics in Supercooled Liquids

It has been recognized recently that the considerable difference between photon correlation (PCS) and dielectric (BDS) susceptibility spectra arises from their respective association with single-particle and collective dynamics. This work presents a model that captures the narrower width and shifted peak position of collective dynamics (BDS), given the single-particle susceptibility derived from PCS studies. Only one adjustable parameter is required to connect the spectra of collective and single-particle dynamics. This constant accounts for cross-correlations between molecular angular velocities and the ratio of the first- and second-rank single-particle relaxation times. The model is tested for three supercooled liquids, glycerol, propylene glycol, and tributyl phosphate, and is shown to provide a good account of the difference between BDS and PCS spectra. Because PCS spectra appear to be rather universal across a range of supercooled liquids, this model provides a first step toward rationalizing the more material-specific dielectric loss profiles.

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.

Molecular Mechanism of the Debye Relaxation in Monohydroxy Alcohols Revealed from Rheo-Dielectric Spectroscopy

Rheo-dielectric spectroscopy is employed to investigate the effect of external shear on Debye-like relaxation of a model monohydroxy alcohol, i.e., the 2-ethyl-1-hexanol (2E1H). Shear deformation leads to strong acceleration in the structural relaxation, the Debye relaxation, and the terminal relaxation of 2E1H. Moreover, the shear-induced reduction in structural relaxation time, τ_{α}, scales quadratically with that of Debye time, τ_{D}, and the terminal flow time, τ_{f}, suggesting a relationship of τ_{D}^{2}∼τ_{α}. Further analyses reveal τ_{D}^{2}/τ_{α} of 2E1H follows Arrhenius temperature dependence that applies remarkably well to many other monohydroxy alcohols with different molecular sizes, architectures, and alcohol types. These results cannot be understood by the prevailing transient chain model, and suggest a H-bonding breakage facilitated sub-supramolecular reorientation as the origin of Debye relaxation of monohydroxy alcohols, akin to the molecular mechanism for the terminal relaxation of unentangled "living" polymers.

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.

On the intensity of light scattered by molecular liquids-Comparison of experiment and quantum chemical calculations

The intensity of light scattered by liquids has been studied for over a century since the valuable microscopic information about the molecules can be obtained, such as the anisotropy of the molecular polarizability tensor or preferred orientations of neighboring molecules. However, in modern dynamic light scattering experiments, the scattering intensity is usually disregarded, unlike in dielectric spectroscopy, which can be considered as a complementary experimental method, where the dielectric strength is routinely evaluated. The reason lies partly on the fact that the exact form of the equations relating the macroscopically measured light scattering intensity to the microscopic properties of the molecules is debated in the literature. Therefore, as a first step, we compare anisotropy parameters from the literature, calculated from light scattering intensities using different equations, with quantum chemical calculations for over 150 medium-sized molecules. This allows us to identify a consistent form of equations. In a second part, we turn to the depolarized light scattering spectra of 13 van der Waals liquids and some mixtures thereof, recorded with a combination of Tandem-Fabry-Perót and Raman spectroscopies, giving direct access to the reorientational dynamics of the molecules. We discuss how the strength of the structural α-relaxation is connected to the anisotropy parameter, what implication this has for the shape of the α-relaxation, how the components of a mixture-also for the case of ionic liquids-can be identified in this way, and how orientational correlation parameters can be extracted. Additionally, we point out for the example of n-alkanes that for highly flexible molecules, the reorientational motion might not be the decisive source of the depolarized scattered light. We also show that light scattering might serve as a sensitive tool to check the accuracy of a conformer ensemble obtained by quantum chemical calculations.

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.

One experiment makes a direct comparison of structural recovery with equilibrium relaxation

For a molecular glass-former, propylene glycol, we directly compare the equilibrium fluctuations, measured as "structural" relaxation in the regime of linear response, with structural recovery, i.e., field induced physical aging in the limit of a small perturbation. The two distinct correlation functions are derived from a single experiment. Because the relaxation time changes only 2% during structural recovery, no aging model is needed to analyze the results. Although being conceptually different processes, dielectric relaxation and recovery dynamics are observed to be identical for propylene glycol, whereas single-particle dynamics as seen by photon correlation spectroscopy are significantly faster. This confirms the notion that structural recovery and aging are governed by all modes observed by dielectric spectroscopy, i.e., including cross correlations, not only by single-particle dynamics. A comparison with analogous results for other materials suggests that the relation between relaxation and recovery time scales may be material specific rather than universal.

Glassy dynamics in polyalcohols: intermolecular simplicity vs. intramolecular complexity

Using depolarized light scattering, we have recently shown that structural relaxation in a broad range of supercooled liquids follows, to good approximation, a generic line shape with high-frequency power law ω^-1/2. We now continue this study by investigating a systematic series of polyalcohols (PAs), frequently used as model-systems in glass-science, i.a., because the width of their respective dielectric loss spectra varies strongly along the series. Our results reveal that the microscopic origin of the observed relaxation behavior varies significantly between different PAs: while short-chained PAs like glycerol rotate as more or less rigid entities and their light scattering spectra follow the generic shape, long-chained PAs like sorbitol display pronounced intramolecular dynamic contributions on the time scale of structural relaxation, leading to systematic deviations from the generic shape. Based on these findings we discuss an important limitation for observing the generic shape in a supercooled liquid: the dynamics that is probed needs to reflect the intermolecular dynamic heterogeneity, and must not be superimposed by effects of intramolecular dynamic heterogeneity.

Computational Evidence for the Crucial Role of Dipole Cross-Correlations in Polar Glass-Forming Liquids

In this Letter, we analyze the dipole-dipole correlations obtained from the molecular dynamics simulations for strongly and weakly polar model liquids. As a result, we find that the cross-correlations' contribution to the system's total dipole moment correlation function, which is directly measured in the dielectric spectroscopy experiment, is negligible for weakly polar liquids. In contrast, the cross-correlations' term dominates over the self-correlations' term for the examined strongly polar liquid. Consequently, our studies strongly support the interpretation of the dielectric spectra nature of glass-forming liquids recently proposed by Pabst et al.

Molecular Cross-correlations Govern Structural Rearrangements in a Nonassociating Polar Glass Former

Self- and cross-correlation dynamics of deeply supercooled liquids were recently identified using photon correlation spectroscopy on the one hand and dielectric investigations on the other. These results fueled a controversial discussion whether the "generic" response identified by photon correlation spectroscopy, or rather the nonuniversal dielectric response, reflect the liquid's structural relaxation. The present study employs physical aging and oscillatory shear rheology to directly access the structural relaxation of a nonassociating glass-forming liquid and reveals that collective equilibrium fluctuations of simple liquids and not single-particle dynamics govern their structural relaxation. The present results thus challenge recent views that the glassy response of polar supercooled liquids can generically be decomposed into a Debye-type, supramolecular response and a single-particle dynamics with the latter reflecting the "true" structural relaxation. Furthermore, the current findings underscore the pivotal role dielectric spectroscopy plays in glass science as one of the rare molecular-level reorientation techniques that senses dynamical cooperativity directly.

NMR Relaxometry Accessing the Relaxation Spectrum in Molecular Glass Formers

It is a longstanding question whether universality or specificity characterize the molecular dynamics underlying the glass transition of liquids. In particular, there is an ongoing debate to what degree the shape of dynamical susceptibilities is common to various molecular glass formers. Traditionally, results from dielectric spectroscopy and light scattering have dominated the discussion. Here, we show that nuclear magnetic resonance (NMR), primarily field-cycling relaxometry, has evolved into a valuable method, which provides access to both translational and rotational motions, depending on the probe nucleus. A comparison of ¹H NMR results indicates that translation is more retarded with respect to rotation for liquids with fully established hydrogen-bond networks; however, the effect is not related to the slow Debye process of, for example, monohydroxy alcohols. As for the reorientation dynamics, the NMR susceptibilities of the structural (α) relaxation usually resemble those of light scattering, while the dielectric spectra of especially polar liquids have a different broadening, likely due to contributions from cross correlations between different molecules. Moreover, NMR relaxometry confirms that the excess wing on the high-frequency flank of the α-process is a generic relaxation feature of liquids approaching the glass transition. However, the relevance of this feature generally differs between various methods, possibly because of their different sensitivities to small-amplitude motions. As a major advantage, NMR is isotope specific; hence, it enables selective studies on a particular molecular entity or a particular component of a liquid mixture. Exploiting these possibilities, we show that the characteristic Cole-Davidson shape of the α-relaxation is retained in various ionic liquids and salt solutions, but the width parameter may differ for the components. In contrast, the low-frequency flank of the α-relaxation can be notably broadened for liquids in nanoscopic confinements. This effect also occurs in liquid mixtures with a prominent dynamical disparity in their components.

Temperature dependence of the Kirkwood correlation factor and linear dielectric constant of simple isotropic polar fluids

The theory developed in an accompanying paper [Déjardin, Phys. Rev. E 105, 024109 (2022)10.1103/PhysRevE.105.024109] is used to compute the Kirkwood correlation factor of simple polar fluids of different nature. From this calculation, the theoretical static permittivity is readily obtained, which is compared with experimental values. This is accomplished by fitting only one parameter accounting for induction or dispersion forces and torques, which is necessarily connected with the individual molecular polarizability but not explicitly related to the physical properties due to the nonadditivity of such energies. Excellent agreement between theoretical and experimental static permittivities is obtained over a very broad temperature range for a number of associated and nonassociated liquids. Finally, limitations of the present theory are given.

Two-Step Aging of Highly Polar Glass

Nonequilibrium processes, including physical aging, belong to the most challenging phenomena of glassy dynamics. One of the fundamental problems that needs clarification is the effect of material polarity on the time scale of the structural recovery of glass. The importance of this issue arises from practical applications and recent findings suggesting a substantial contribution of dipole-dipole interactions to the dielectric permittivity spectra of polar glass-formers. Herein, we use dielectric spectroscopy to investigate structural relaxation and aging dynamics of highly polar glass-former 4-[(4,4,5,5,5-pentafluoropentoxy)methyl]-1,3-dioxolan-2-one (FPC), a derivative of propylene carbonate with ε_s = 180 and μ = 5.1. We show that ε″(t_age) data of FPC at T_age < T_g reveal complex behavior resulting from considerable cross-correlation effects. Namely, two characteristic aging time scales, reflecting the evolution of cross-correlation mode and generic structural relaxation toward equilibrium, are obtained at a given T_age. Furthermore, a single stretched exponential behavior of ε″(t_age) has been received for weakly polar carvedilol with negligible dipole-dipole interactions.

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.

Comparative analysis of dielectric, shear mechanical and light scattering response functions in polar supercooled liquids

The studies of molecular dynamics in the vicinity of liquid–glass transition are an essential part of condensed matter physics. Various experimental techniques are usually applied to understand different aspects of molecular motions, i.e., nuclear magnetic resonance (NMR), photon correlation spectroscopy (PCS), mechanical shear relaxation (MR), and dielectric spectroscopy (DS). Universal behavior of molecular dynamics, reflected in the invariant distribution of relaxation times for different polar and weekly polar glass-formers, has been recently found when probed by NMR, PCS, and MR techniques. On the other hand, the narrow dielectric permittivity function ε*(f) of polar materials has been rationalized by postulating that it is a superposition of a Debye-like peak and a broader structural relaxation found in NMR, PCS, and MR. Herein, we show that dielectric permittivity representation ε*(f) reveals details of molecular motions being undetectable in the other experimental methods. Herein we propose a way to resolve this problem. First, we point out an unresolved Johari–Goldstein (JG) β-relaxation is present nearby the α-relaxation in these polar glass-formers. The dielectric relaxation strength of the JG β-relaxation is sufficiently weak compared to the α-relaxation so that the narrow dielectric frequency dispersion faithfully represents the dynamic heterogeneity and cooperativity of the α-relaxation. However, when the other techniques are used to probe the same polar glass-former, there is reduction of relaxation strength of α-relaxation relative to that of the JG β relaxation as well as their separation. Consequently the α relaxation appears broader in frequency dispersion when observed by PCS, NMR and MR instead of DS. The explanation is supported by showing that the quasi-universal broadened α relaxation in PCS, NMR and MR is captured by the electric modulus M*(f) = 1/ε*(f) representation of the dielectric measurements of polar and weakly polar glass-formers, and also M*(f) compares favorably with the mechanical shear modulus data G*(f).

Structural Relaxation and Recovery: A Dielectric Approach

We compare structural relaxation and structural recovery dynamics for molecular glass-formers, both measured by dielectric techniques in the regime of linear responses. It is emphasized that structural recovery restores ergodicity, whereas structural relaxation or α-processes characterize fluctuations of the system in equilibrium (and thus do not involve a change of structure within experimental resolution). Evidence is provided that structural recovery is linked to rate exchange and thus is distinct from structural relaxation dynamics, even in the limit of small perturbations. As a consequence, structural recovery is somewhat slower and more exponential than the equilibrium dynamics as derived, for instance, from low field dielectric relaxation experiments. This contrasts the standard assumption inherent in models of physical aging, which assume the identity of both responses if measured in the limit of a small perturbation. Typical experiments associated with physical aging and scanning calorimetry involve nonlinear responses and are thus even more complex.

The dielectric response of phenothiazine-based glass-formers with different molecular complexity

We examined a series of structurally related glass-forming liquids in which a phenothiazine-based tricyclic core (PTZ) was modified by attaching n-alkyl chains of different lengths (n = 4, 8, 10). We systematically disentangled the impact of chemical structure modification on the intermolecular organization and molecular dynamics probed by broadband dielectric spectroscopy (BDS). X-ray diffraction (XRD) patterns evidenced that all PTZ-derivatives are not 'ordinary' liquids and form nanoscale clusters. The chain length has a decisive impact on properties, exerting a plasticizing effect on the dynamics. Its elongation decreases glass transition temperature with slight impact on fragility. The increase in the medium-range order was manifested as a broadening of the dielectric loss peak reflected in the lower value of stretching parameter β_KWW. A disagreement with the behavior observed for non-associating liquids was found as a deviation from the anti-correlation between the value of β_KWW and the relaxation strength of the α-process. Besides, to explain the broadening of loss peak in PTZ with the longest (decyl) chain a slow Debye process was postulated. In contrast, the sample with the shortest alkyl chain and a less complex structure with predominant supramolecular assembly through π-π stacking exhibits no clear Debye-mode fingerprints. The possible reasons are also discussed.

Dynamics of aqueous peptide solutions in folded and disordered states examined by dynamic light scattering and dielectric spectroscopy

Characterizing the segmental dynamics of proteins, and intrinsically disordered proteins in particular, is a challenge in biophysics. In this study, by combining data from broadband dielectric spectroscopy (BDS) and both depolarized (DDLS) and polarized (PDLS) dynamic light scattering, we were able to determine the dynamics of a small peptide [ε-poly(lysine)] in water solutions in two different conformations (pure β-sheet at pH = 10 and a more disordered conformation at pH = 7). We found that the segmental (α-) relaxation, as probed by DDLS, is faster in the disordered state than in the folded conformation. The water dynamics, as detected by BDS, is also faster in the disordered state. In addition, the combination of BDS and DDLS results allows us to confirm the molecular origin of water-related processes observed by BDS. Finally, we discuss the origin of two slow processes (A and B processes) detected by DDLS and PDLS in both conformations and usually observed in other types of water solutions. For fully homogeneous ε-PLL solutions at pH = 10, the A-DLS process is assigned to the diffusion of individual β-sheets. The combination of both techniques opens a route for understanding the dynamics of peptides and other biological solutions.

Reorientational dynamics in highly asymmetric binary low-molecular mixtures-A quantitative comparison of dielectric and NMR spectroscopy results

Previously, we scrutinized the dielectric spectra of a binary glass former made by a low-molecular high-T_g component 2-(m-tertbutylphenyl)-2'-tertbutyl-9,9'-spirobi[9H]fluorene (m-TPTS; T_g = 350 K) and low-T_g tripropyl phosphate (TPP; T_g = 134 K) [Körber et al., Phys. Chem. Chem. Phys. 23, 7200 (2021)]. Here, we analyze nuclear magnetic resonance (NMR) spectra and stimulated echo decays of deuterated m-TPTS-d₄ (²H) and TPP (³¹P) and attempt to understand the dielectric spectra in terms of component specific dynamics. The high-T_g component (α₁) shows relaxation similar to that of neat systems, yet with some broadening upon mixing. This correlates with high-frequency broadening of the dielectric spectra. The low-T_g component (α₂) exhibits highly stretched relaxations and strong dynamic heterogeneities indicated by "two-phase" spectra, reflecting varying fractions of fast and slow liquid-like reorienting molecules. Missing for the high-T_g component, such two-phase spectra are identified down to w_TPP = 0.04, indicating that isotropic reorientation prevails in the rigid high-T_g matrix stretching from close to T_g ^TPP to T_g1 w_TPP. This correlates with low-frequency broadening of the dielectric spectra. Two T_g values are defined: T_g1 (w_TPP) displays a plasticizer effect, whereas T_g2 (w_TPP) passes through a maximum, signaling extreme separation of the component dynamics at low w_TPP. We suggest understanding the latter counter-intuitive feature by referring to a crossover from "single glass" to "double glass" scenario revealed by recent MD simulations. Analyses reveal that a second population of TPP molecules exists, which is associated with the dynamics of the high-T_g component. However, the fractions are lower than suggested by the dielectric spectra. We discuss this discrepancy considering the role of collective dynamics probed by dielectric but not by NMR spectroscopy.

Dynamics in the plastic crystalline phase of cyanocyclohexane and isocyanocyclohexane probed by 1H field cycling NMR relaxometry

Proton Field-Cycling (FC) nuclear magnetic resonance (NMR) relaxometry is applied over a wide frequency and temperature range to get insight into the dynamic processes occurring in the plastically crystalline phase of the two isomers cyanocyclohexane (CNCH) and isocyanocyclohexane. The spin-lattice relaxation rate, R₁(ω), is measured in the 0.01-30 MHz frequency range and transformed into the susceptibility representation χ_NMR ^″ω=ωR₁ω. Three relaxation processes are identified, namely, a main (α-) relaxation, a fast secondary (β-) relaxation, and a slow relaxation; they are very similar for the two isomers. Exploiting frequency-temperature superposition, master curves of χ_NMR ^″ωτ are constructed and analyzed for different processes. The α-relaxation displays a pronounced non-Lorentzian susceptibility with a temperature independent width parameter, and the correlation times display a non-Arrhenius temperature dependence-features indicating cooperative dynamics of the overall reorientation of the molecules. The β-relaxation shows high similarity with secondary relaxations in structural glasses. The extracted correlation times well agree with those reported by other techniques. A direct comparison of FC NMR and dielectric master curves for CNCH yields pronounced difference regarding the non-Lorentzian spectral shape as well as the relative relaxation strength of α- and β-relaxation. The correlation times of the slow relaxation follow an Arrhenius temperature dependence with a comparatively high activation energy. As the α-process involves liquid-like isotropic molecular reorientation, the slow process has to be attributed to vacancy diffusion, which modulates intermolecular dipole-dipole interactions, possibly accompanied by chair-chair interconversion of the cyclohexane ring. However, the low frequency relaxation features characteristic of vacancy diffusion cannot be detected due to experimental limitations.

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.

Molecular dynamics simulations vs field-cycling NMR relaxometry: Structural relaxation mechanisms in the glass-former glycerol revisited

We combine field-cycling (FC) relaxometry and molecular dynamics (MD) simulations to study the rotational and translational dynamics associated with the glassy slowdown of glycerol. The ¹H NMR spin-lattice relaxation rates R₁(ω) probed in the FC measurements for different isotope-labelled compounds are computed from the MD trajectories for broad frequency and temperature ranges. We find high correspondence between experiment and simulation. Concerning the rotational motion, we observe that the aliphatic and hydroxyl groups show similar correlation times but different stretching parameters, while the overall reorientation associated with the structural relaxation remains largely isotropic. Additional analysis of the simulation results reveals that transitions between different molecular configurations are slow on the time scale of the structural relaxation at least at sufficiently high temperatures, indicating that glycerol rotates at a rigid entity, but the reorientation is slower for elongated than for compact conformers. The translational contribution to R₁(ω) is well described by the force-free hard sphere model. At sufficiently low frequencies, universal square-root laws provide access to the molecular diffusion coefficients. In both experiment and simulation, the time scales of the rotational and translational motions show an unusually large separation, which is at variance with the Stokes-Einstein-Debye relation. To further explore this effect, we investigate the structure and dynamics on various length scales in the simulations. We observe that a prepeak in the static structure factor S(q), which is related to a local segregation of aliphatic and hydroxyl groups, is accompanied by a peak in the correlation times τ(q) from coherent scattering functions.