Primitive Relaxation Research Articles

Noise correlations behind superdiffusive quantum walks.

We study how discrete-time quantum walks behave under short-range correlated noise. By considering noise as a source of inhomogeneity of quantum gates, we introduce a primitive relaxation in the assumption of uncorrelated stochastic noise: binary pair correlations manifesting in the random distribution. Using different quantum gates, we examined the transport properties for both spatial and temporal noise regimes. For spatial inhomogeneities, we unveil noise correlations driving quantum walks from the well-known exponentially localized regime to superdiffusive spreading. This scenario displays an intriguing performance in which the superdiffusive exponent is almost invariant to the degree of inhomogeneity. The time-asymptotic regime and the finite-size scaling also unveil an emergent superdiffusive behavior for quantum walks undergoing temporal noise correlation, replacing the diffusive regime exhibited when noise is random and uncorrelated. However, some quantum gates are insensitive to correlations, contrasting with the spatial noise scenario. Numerical and analytical results provide valuable insights into the underlying mechanism of superdiffusive quantum walks, including those arising from deterministic aperiodic inhomogeneities.

Reconsidering the relation of the JG β-relaxation to the α-relaxation and surface diffusion in ethylcyclohexane

According to the Coupling Model (CM), secondary relaxation belonging to a special class has strong connection to the α-relaxation. These Johari-Goldstein (JG) β-relaxations are predicted to be ubiquitous, and its relaxation time is approximately equal to the primitive relaxation time and the surface diffusion time. These predictions cannot be tested directly in ethylcyclohexane (ECH) because the JG β-relaxation is unresolved and overlapping the α-relaxation to modify its dispersion. To capture the actual dispersion of the α-relaxation we considered surface diffusion data, adiabatic calorimetry data of the JG β-relaxation, and dielectric data of cyanocyclohexane (CNCH). We demonstrated the dispersion of the α-relaxation is actually narrower than known before. The primitive relaxation times calculated are now in agreement with τ JG ( T ) and with τ surface ( T ), and in accord with the CM predictions.

Microscopic understanding of the Johari-Goldstein β relaxation gained from nuclear γ-resonance time-domain-interferometry experiments.

Traditionally the study of dynamics of glass-forming materials has been focused on the structural α relaxation. However, in recent years experimental evidence has revealed that a secondary β relaxation belonging to a special class, called the Johari-Goldstein (JG) β relaxation, has properties strongly linked to the primary α relaxation. By invoking the principle of causality, the relation implies the JG β relaxation is fundamental and indispensable for generating the α relaxation, and the properties of the latter are inherited from the former. The JG β relaxation is observed together with the α relaxation mostly by dielectric spectroscopy. The macroscopic nature of the data allows the use of arbitrary or unproven procedures to analyze the data. Thus the results characterizing the JG β relaxation and the relation of its relaxation time τ_{β} to the α-relaxation time τ_{α} obtained can be equivocal and controversial. Coming to the rescue is the nuclear resonance time-domain-interferometry (TDI) technique covering a wide time range (10^{-9}-10^{-5}s) and a scattering vector q range (9.6-40nm^{-1}). TDI experiments have been carried out on four glass formers, ortho-terphenyl [M. Saito etal., Phys. Rev. Lett. 109, 115705 (2012)10.1103/PhysRevLett.109.115705], polybutadiene [T. Kanaya etal., J. Chem. Phys. 140, 144906 (2014)10.1063/1.4869541], 5-methyl-2-hexanol [F. Caporaletti etal., Sci. Rep. 9, 14319 (2019)10.1038/s41598-019-50824-7], and 1-propanol [F. Caporaletti etal., Nat. Commun. 12, 1867 (2021)10.1038/s41467-021-22154-8]. In this paper the TDI data are reexamined in conjunction with dielectric and neutron scattering data. The results show the JG β relaxation observed by dielectric spectroscopy is heterogeneous and comprises processes with different length scales. A process with a longer length scale has a longer relaxation time. TDI data also prove the primitive relaxation time τ_{0} of the coupling model falls within the distribution of the TDI q-dependent JG β-relaxation times. This important finding explains why the experimental dielectric JG β-relaxation times τ_{β}(T,P) is approximately equal to τ_{0}(T,P) as found in many glass formers at various temperature T and pressure P. The result, τ_{β}(T,P)≈τ_{0}(T,P), in turn explains why the ratio τ_{α}(T,P)/τ_{β}(T,P) is invariant to changes of T and pressure P at constant τ_{α}(T,P), the α-relaxation time.

Why the Brillouin Light Scattering Relaxation Times of Molten Zinc Chloride Are Shorter and Weaker in Temperature Dependence than the Structural Relaxation Times from Depolarized Light and Neutron Spin Echo Spectroscopy

A longstanding problem in the Brillouin light scattering (BLS) study of polymers is the relaxation times τBLS(T) being more than an order of magnitude shorter than the α-relaxation times τα(T) determined by dielectric, depolarized light scattering (DLS), and molecular dynamics simulations. In tackling the problem, τBLS(T) was identified with the relaxation time τ0(T) of the primitive relaxation in the coupling model, which can be calculated from τα(T) and the stretch exponent βK of the Kohlrausch correlation function for the α-relaxation.. The problem was solved by finding that indeed τ0(T) is in good agreement with τBLS(T). A recent work performed the neutron spin echo study of the structural α-relaxation of the network ionic liquid ZnCl2 and found the same anomaly as polymers. The α-relaxation time τNSE(T) from neutron spin echo (NSE) as well as the α-relaxation time τDLS(T) from DLS of ZnCl2 are much longer than τBLS(T) from BLS obtained before by several research groups. The finding of the same anomaly in ZnCl2 and polymers with very different chemical and physical structures offers an opportunity to critically test the explanation given before. The test was carried out by calculating the primitive relaxation times τ0,DLS(T) and τ0,NSE(T) from τDLS(T) and τNSE(T), respectively, in zinc chloride. Good agreements of τBLS(T) from BLS with τ0,DLS(T) and τ0,NSE(T) were found and thus the explanation given for polymers remains valid for ZnCl2. The test was extended to glycerol by comparing τBLS(T) with τ0,ICNS(T) and τ0,CNS(T) calculated from the α-relaxation time τICNS(T) and τCNS(T) from incoherent and coherent neutron scattering, respectively. There is good agreement between τBLS(T) and τ0,ICNS(T) in glycerol. There is also semiquantitative agreement of τBLS(T) with τ0,DS(T) from dielectric spectroscopy as well as τ0,CNS(T). Thus, the explanation for polymers is verified in the two very different glass formers, ZnCl2 and glycerol, and it is an advancement in the application of BLS to study the dynamics of glass formers.

Clarifying the nature of the Johari-Goldstein β-relaxation and emphasising its fundamental importance

ABSTRACT Since 1998 the primitive relaxation time τ 0(T,P) of the Coupling Model (CM) and the Johari-Goldstein (JG) β-relaxation time τJG (T,P) are shown approximately equal in many glass-formers. The CM relation between τ 0(T,P) and τα (T,P) at any T and P is exact. Additionally from the CM relation τα (T,P)/τ 0(T,P) is exactly invariant to variations of T and P while τα (T,P) is kept constant, and τ 0 is exactly a function of ρ γ/T like τα . However, since τJG (T,P) ≈ τ 0(T,P), the exact invariance of τα (T,P)/τ 0(T,P) leads to approximate invariance of τα (T,P)/τJG (T,P), and τJG is approximately a function of ρ γ/T. Notwithstanding, the CM prediction of the approximate relations between τβ and τα were mistaken as exact relations by some researchers. In this paper, we remove this misunderstanding by demonstrating via simulations and experiments that the JG β-relaxation is comprised of processes with different length-scales and degrees of cooperativity, and the process is heterogeneous. The distribution of processes makes τJG (T,P) equivocal, because it is just a single relaxation time used to represent the different processes within the distribution, which may change on varying T and P, at constant τα (T,P). The problem is compounded if the β-relaxation is not resolved, and fitting procedure used to extract τJG (T,P) and τα (T,P). Despite the relations of τJG (T,P) to τα (T,P) are approximate, we show these properties of τJG (T,P) are truly remarkable, fundamental, general, and important.

Influence of the Internal Structure and Intermolecular Interactions on the Correlation between Structural (α) and Secondary (β-JG) Relaxation below the Glass Transition Temperature in Neat Probucol and Its Binary Mixtures with Modified Saccharides.

Broadband dielectric spectroscopy (BDS) has been used to study the molecular dynamics and aging process in neat probucol (PRO) as well as its binary mixtures with selected acetylated saccharides. In particular, we applied the Casalini and Roland approach to determine structural relaxation times in the glassy state of the examined systems (so-called isostructural times, τiso). Next, using the calculated τiso, primitive relaxation times of the coupling model were obtained and compared to the experimental secondary β (Johari-Goldstein (JG) type) relaxation times. Interestingly, it turned out that there is a correlation between the β-JG and the structural (α)-relaxation processes below the glass transition temperature (T < Tg) in each investigated sample. This is a new observation compared to previous studies demonstrating that such a relationship exists only in the supercooled liquid state of neat PRO. Moreover, it was revealed that the stretching parameters obtained from the aging procedure are very close to the ones determined by fitting the dielectric data above the Tg with the use of the Kohlrausch-Williams-Watts function, indicating that the aging process is governed by the α-relaxation. Complementary Fourier transform infrared and X-ray diffraction measurements allowed us to find a possible reason for these findings. It was demonstrated that although there are very weak intermolecular interactions between PRO and modified saccharides, the intra- and intermolecular structure of PRO is practically unaffected by the presence of modified saccharides.

Predicting the α-relaxation time of glycerol confined in 1.16 nm pores of zeolitic imidazolate frameworks.

Uhl et al. [J. Chem. Phys., 2019, 150, 024504] studied the molecular dynamics of glycerol confined in a microporous zeolitic imidazolate framework (ZIF-8) with well-defined pore diameters of 1.16 nm by broadband dielectric spectroscopy. Of interest is a fast process in the central part of the pores identified as the α-relaxation of the confined supercooled glycerol with relaxation times τα,conf(T) reduced from τα,bulk(T) of bulk glycerol and having a temperature dependence different from the super-Arrhenius temperature of the latter. The focus of Uhl et al. was relating the confined molecular dynamics to the cooperativity length scales Lcorr(T) of molecular motion above the glass transition, and deducing the limiting high-temperature value of the correlation length of about 1.22 nm. Not yet considered by anyone are the observed values of τα,conf(T) and temperature dependence. Since the cooperativity length scales Lcorr(T) were found to be larger than the pore size of ZIF-8 over the temperature range studied and the density of the glycerol in the pore is possibly lower than the bulk, the cooperativity of the α-relaxation of glycerol confined in ZIF-8 is drastically reduced. Thus, within the framework of the Coupling Model (CM), τα,conf(T) should be nearly the same as the primitive relaxation time τ0(T) for glycerol when devoid of intermolecular coupling and cooperativity. Consistent with the absence of cooperativity of the glycerol confined in ZIF-8, we find the calculated τα,conf(T) are either the same or slightly longer than the calculated values of τ0(T). The quantitative prediction of the CM is verified. At this time we know of no other theory that can make such a quantitative prediction.

Why the Relaxation Times of Polymers from Brillouin Light Spectroscopy Are Much Shorter than the Primary α-Relaxation Times

Brillouin light spectroscopy (BLS) of polymers recorded much shorter relaxation times over the same temperature range than those obtained from other spectroscopies, including dielectric relaxation, dynamic light scattering, depolarized Rayleigh scattering, NMR, and molecular dynamics simulations. This is an anomaly because a priori BLS is thought to monitor the structural α-relaxation of polymers like all the other techniques. First noted in 1977, the anomaly was repeatedly confirmed, but it has not been explained, and it remains a puzzling finding in amorphous polymers. In this paper, we explain this longstanding anomaly by the Coupling Model (CM), in conjunction with the fact that the α-relaxation of polymers is nonexponential at the relatively high temperatures of BLS measurements. The CM has the primitive relaxation, which is part of the Johari–Goldstein (JG) β-relaxation, and the precursor of the structural α-relaxation. The calculated primitive relaxation times match the BLS relaxation times quantit...

Interpretation of the GHz to THz dielectric relaxation dynamics of water in the framework of the Coupling Model

The microscopic origins of the processes in water observed at temperatures above and below room temperature by dielectric relaxation spectroscopy in the range from GHz to beyond THz are identified by three sequential and interrelated contributions in the framework of the Coupling Model. Appearing after vibration and boson peak is the caged water dynamics. Cage decays with the onset of the primitive relaxation of the Coupling Model (CM), which is practically coincident with the nearly exponential structural α-relaxation. These sequential processes explain the nearly Debye α-loss peak, the high frequency power law (HFPL) associated with it, and the higher frequency dispersion before reaching the vibrational contributions. High frequency and short time experimental data of several glass-formers obtained by different techniques are presented to show the same three processes with the same relationship between them, as proposed for water. Crucial supports of the CM explanation come from neutron scattering experiments on water showing that: (1) caging and decaging indeed occurs in the HFPL regime; (2) the dynamics of the HFPL is independent of the scattering vector Q, in accord with the HFPL is comprised of caged dynamics and decaging; and (3) the terminal process is normal diffusion, justifying the 20 GHz dielectric loss peak originates from the structural α-relaxation, which follows after the completion of decaging, i.e. the end of the HFPL regime.

Relating Ultrastable Glass Formation to Enhanced Surface Diffusion via the Johari-Goldstein β-Relaxation in Molecular Glasses.

Glasses are materials essential for modern technology; they are usually prepared by cooling liquids. Recently, novel ultrastable glasses (SGs) with extraordinary thermodynamic and kinetic stability have been created by vapor deposition at appropriate substrate temperatures. However, the underlying mechanism for the formation of SGs is still not established. For most of the molecular SGs created so far, we demonstrate that the formation of SGs is closely related to the Johari-Goldstein β-relaxation from the fact that the lowest substrate temperatures possible for the formation of SGs match the secondary glass-transition temperatures, where the β-relaxation time reaches 103 s. Theoretically the β-relaxation time via the primitive relaxation time of the coupling model has proven capable of accounting for the enhancement of molecular mobility at the surface. Thus our findings provide evidence to support that the immense enhancement of molecular diffusion at the surface is critical for the formation of SGs. The result has implications in the design and fabrication of SGs.

Characteristics of the secondary relaxation process in soft colloidal suspensions

A universal secondary relaxation process, known as the Johari-Goldstein (J-G) β-relaxation process, appears in glass formers. It involves all parts of the molecule and is particularly important in glassy systems because of its very close relationship with the α-relaxation process. However, the absence of a J-G β-relaxation mode in colloidal glasses raises questions regarding its universality. In the present work, we study the microscopic relaxation processes in Laponite suspensions, a model soft glassy material, by dynamic light scattering (DLS) experiments. α- and β-relaxation timescales are estimated from the autocorrelation functions obtained by DLS measurements for Laponite suspensions with different concentrations, salt concentrations and temperatures. Our experimental results suggest that the β-relaxation process in Laponite suspensions involves all parts of the constituent Laponite particle. The ergodicity breaking time is also seen to be correlated with the characteristic time of the β-relaxation process for all Laponite concentrations, salt concentrations and temperatures. The width of the primary relaxation process is observed to be correlated with the secondary relaxation time. The secondary relaxation time is also very sensitive to the concentration of Laponite. We measure primitive relaxation timescales from the α-relaxation time and the stretching exponent (β) by applying the coupling model for highly correlated systems. The order of magnitude of the primitive relaxation time is very close to the secondary relaxation time. These observations indicate the presence of a J-G β-relaxation mode for soft colloidal suspensions of Laponite.

Understanding the changes in ductility and Poisson's ratio of metallic glasses during annealing from microscopic dynamics

In the paper K. L. Ngai et al., [J. Chem. 140, 044511 (2014)], the empirical correlation of ductility with the Poisson's ratio, νPoisson, found in metallic glasses was theoretically explained by microscopic dynamic processes which link on the one hand ductility, and on the other hand the Poisson's ratio. Specifically, the dynamic processes are the primitive relaxation in the Coupling Model which is the precursor of the Johari–Goldstein β-relaxation, and the caged atoms dynamics characterized by the effective Debye–Waller factor f0 or equivalently the nearly constant loss (NCL) in susceptibility. All these processes and the parameters characterizing them are accessible experimentally except f0 or the NCL of caged atoms; thus, so far, the experimental verification of the explanation of the correlation between ductility and Poisson's ratio is incomplete. In the experimental part of this paper, we report dynamic mechanical measurement of the NCL of the metallic glass La60Ni15Al25 as-cast, and the changes by annealing at temperature below Tg. The observed monotonic decrease of the NCL with aging time, reflecting the corresponding increase of f0, correlates with the decrease of νPoisson. This is important observation because such measurements, not made before, provide the missing link in confirming by experiment the explanation of the correlation of ductility with νPoisson. On aging the metallic glass, also observed in the isochronal loss spectra is the shift of the β-relaxation to higher temperatures and reduction of the relaxation strength. These concomitant changes of the β-relaxation and NCL are the root cause of embrittlement by aging the metallic glass. The NCL of caged atoms is terminated by the onset of the primitive relaxation in the Coupling Model, which is generally supported by experiments. From this relation, the monotonic decrease of the NCL with aging time is caused by the slowing down of the primitive relaxation and β-relaxation on annealing, and vice versa.

Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model.

Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ1(f), the frequency dispersion of the third-order dielectric susceptibility, χ3(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ1(f) and χ3(f) is the characteristic of the many-body relaxation dynamics of interacting systems which are governed solely by the intermolecular potential, and thermodynamic condition plays no role in this respect. Although linked to χ3(f), dynamic heterogeneity is one of the parallel consequences of the many-body dynamics, and it should not be considered as the principal control parameter for the other dynamic properties of glassforming systems. Results same as χ3(f) at elevated pressures had been obtained before by molecular dynamics simulations from the four-points correlation function and the intermediate scattering function. Naturally all properties obtained from the computer experiment, including dynamics heterogeneity, frequency dispersion, the relation between the α- and JG β-relaxation, and the breakdown of the Stokes-Einstein relation, are parallel consequences of the many-body relaxation dynamics governed by the intermolecular potential.

Erratum: “Thermodynamic scaling of α-relaxation time and viscosity stems from the Johari-Goldstein β-relaxation or the primitive relaxation of the coupling model” [J. Chem. Phys. 137, 034511 (2012)

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The behavior and origin of the excess wing in DEET (N,N-diethyl-3-methylbenzamide)

Broadband dielectric spectroscopy along with a high pressure technique and quantum-mechanical calculations are employed to study in detail the behavior and to reveal the origin of the excess wing (EW) in neat N,N-diethyl-3-methylbenzamide (DEET). Our analysis of dielectric spectra again corroborates the idea that the EW is a hidden β-relaxation peak. Moreover, we found that the position frequency of the β peak corresponds to the position of the primitive relaxation of the Coupling Model. We also studied the possible intramolecular rotations in DEET by means of DFT calculation. On that basis we were able to describe the EW as the JG β-relaxation and find the possible origin of the γ-relaxation visible in DEET dielectric spectra at very low temperatures.

Mechanism of fast surface self-diffusion of an organic glass

Zhu et al. [L. Zhu, C. W. Brian, S. F. Swallen, P. T. Straus, M. D. Ediger, and L. Yu, Phys. Rev. Lett. 106, 256103 (2011)] measured the surface self-diffusion for an organic glass former, indomethacin, and found surface diffusion is more than 10(6) times faster than bulk diffusion at temperatures around T(g). With the help of dielectric relaxation and differential scanning calorimetry measurements on bulk indomethacin, and analysis of the data using the coupling model, we provide a quantitative explanation. We find the bulk α-relaxation time is longer than the primitive relaxation time also by about six orders of magnitude in a range of temperature above and below the bulk T(g). Thus, the cause of the fast surface diffusion is the nearly vanishing of intermolecular coupling of relaxation and diffusion at the surface. The results of related experimental studies of enhanced relaxation and diffusion at the surface of other glass formers also have been analyzed and quantitatively explained. Our predictions on surface diffusion from the coupling model are compared with that given by the random first order transition theory.

Thermodynamic scaling of α-relaxation time and viscosity stems from the Johari-Goldstein β-relaxation or the primitive relaxation of the coupling model

By now it is well established that the structural α-relaxation time, τ(α), of non-associated small molecular and polymeric glass-formers obey thermodynamic scaling. In other words, τ(α) is a function Φ of the product variable, ρ(γ)/T, where ρ is the density and T the temperature. The constant γ as well as the function, τ(α) = Φ(ρ(γ)/T), is material dependent. Actually this dependence of τ(α) on ρ(γ)/T originates from the dependence on the same product variable of the Johari-Goldstein β-relaxation time, τ(β), or the primitive relaxation time, τ(0), of the coupling model. To support this assertion, we give evidences from various sources itemized as follows. (1) The invariance of the relation between τ(α) and τ(β) or τ(0) to widely different combinations of pressure and temperature. (2) Experimental dielectric and viscosity data of glass-forming van der Waals liquids and polymer. (3) Molecular dynamics simulations of binary Lennard-Jones (LJ) models, the Lewis-Wahnström model of ortho-terphenyl, 1,4 polybutadiene, a room temperature ionic liquid, 1-ethyl-3-methylimidazolium nitrate, and a molten salt 2Ca(NO(3))(2)·3KNO(3) (CKN). (4) Both diffusivity and structural relaxation time, as well as the breakdown of Stokes-Einstein relation in CKN obey thermodynamic scaling by ρ(γ)/T with the same γ. (5) In polymers, the chain normal mode relaxation time, τ(N), is another function of ρ(γ)/T with the same γ as segmental relaxation time τ(α). (6) While the data of τ(α) from simulations for the full LJ binary mixture obey very well the thermodynamic scaling, it is strongly violated when the LJ interaction potential is truncated beyond typical inter-particle distance, although in both cases the repulsive pair potentials coincide for some distances.

Glass Transition Dynamics of Room-Temperature Ionic Liquid 1-Methyl-3-trimethylsilylmethylimidazolium Tetrafluoroborate

The conductivity relaxation dynamics of the room-temperature ionic liquid 1-methyl-3-trimethylsilylmethylimidazolium tetrafluoroborate ([Si-MIm][BF(4)]) have been studied by broadband conductivity relaxation measurements at ambient pressure and elevated pressures up to 600 MPa. For the first time, several novel features of the dynamics have been found in a room-temperature ionic liquid. In the electric loss modulus M″(f) spectra, a resolved secondary β-conductivity relaxation appears, and its relaxation time τ(β) shifts on applying pressure in concert with the relaxation time τ(α) of the primary α-conductivity relaxation. The spectral dispersion of the α-conductivity relaxation, as well as the fractional exponent (1 - n) of the Kohlrausch-Williams-Watts function that fits the spectral dispersion, is invariant to various combinations of pressure and temperature that keep τ(α) constant. Moreover, τ(β) is unchanged. Thus the three quantities, τ(α), τ(β), and n, are coinvariant to changes in pressure and temperature. This strong connection to the α-conductivity relaxation shown by the β-conductivity relaxation in [Si-MIm][BF(4)] indicates that it is the analogue of the Johari-Goldstein β-relaxation in nonionically conducting glass-formers. The findings have fundamental implications on theoretical interpretation of the conductivity relaxation processes and glass transition in ionic liquids. It is also the first time such a secondary conductivity relaxation or the primitive conductivity relaxation of the coupling model has been fully resolved and identified in M″(f) in any ionically conducting material that we know of.

The role of primitive relaxation in the dynamics of aqueous mixtures, nano-confined water and hydrated proteins

The relaxation scenario in aqueous systems, such as mixtures of water with hydrophilic solutes, nano-confined water and hydrated biomolecules, has been shown to exhibit general features, in spite of the huge differences in structure, chemical composition and complexity. Dynamics, in all these systems, invariably shows at least two relaxations: (i) a slower process, related to cooperative and structural motions of water and solute molecules (in the case of mixtures) or related to interfacial processes in the case of confined water and (ii) a faster process, with non-cooperative character originating from water. The latter has properties including timescale and temperature dependence similar or related in all the aqueous systems. This water-specific relaxation can be identified as the primitive relaxation, or the Johari–Goldstein β-relaxation. The primitive process is the precursor of the many-body relaxation process which increases in length-scale with time until the terminal α-relaxation is reached. Using new experimental data (at atmospheric and high pressure) along with a revision of most of the recent literature on the dynamics of confined water and aqueous mixtures, we show that the two abovementioned relaxation processes are inter-related as evidenced by correlations in their properties. For instance, both relaxation time and dielectric strength of the water-specific relaxation exhibit a crossover from a stronger to a weaker dependence with decreasing T, at the temperature where the slow process attains a very long timescale (> 1 ks) and becomes structurally arrested, exactly analogous to that found for β-relaxation in van der Waals liquids. Moreover, the primitive relaxation of water is shown to play a pivotal role in determining the dynamics of hydrated biomolecules in general, including the “dynamic transition” observed by neutron scattering and Mössbauer spectroscopy. We show that the primitive relaxation of the solvent is responsible for the dynamic transition, even in the case that the solvent is not pure water or an aqueous mixture.

Determining the structural relaxation times deep in the glassy state of the pharmaceuticalTelmisartan

By using the dielectric relaxation method proposed recently by Casalini and Roland(2009 Phys. Rev. Lett. 102 035701), we were able to determine the structuralα-relaxationtimes deep in the glassy state of the pharmaceutical, Telmisartan. Normally, deep in the glassy stateτα is so long that it cannotbe measured but τβ, which is usually much shorter, can be directly determined. Themethod basically takes advantage of the connection between theα-relaxation andthe secondary β-relaxation of the Johari–Goldstein kind, including a relation between their relaxation timesτα andτβ, respectively.Thus, τα of Telmisartan were determined by monitoring the change of the dielectricβ-loss,ε′′,with physical aging time at temperatures well below the vitrification temperature. The values ofτα were compared with those expected by the coupling model (CM). Unequivocalcomparison cannot be made in the case of Telmisartan because itsβ-loss peak is extremely broad, and the CM predicts only an order ofmagnitude agreement between the primitive relaxation frequency and theβ-peak frequency. We also made an attempt to analyze all isothermal and agingsusceptibility data after transformation into the electric modulus representation. Theτα found in the glass state by using the method of Casalini and Roland in themodulus representation are similar to those obtained in the susceptibilityrepresentation. However, it is remarkable that the stretching parameterβKWW − M = 0.51 in the electric modulus representation gives more precise fitsto the aging data than in the susceptibility representation withβKWW = 0.61. Our results suggest that the electric modulus representation may be useful as analternative to analyze aging data, especially in the case of highly polar glassformers havinga large ratio of low frequency and high frequency dielectric constants, such as theTelmisartan studied.