Measuring the configurational heat capacity of liquids

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

Upper bound of fragility from spatial fluctuations of shear modulus and boson peak in glasses

It is shown that the normalized rms fluctuation of the shear modulus on the medium-range order scale in glasses correlates with fragility: the higher fragility, the smaller the fluctuation amplitude. The latter is calculated within the heterogeneous elasticity theory using the data on the boson peak in glasses. On a smaller scale corresponding to cooperative structural relaxation, the normalized rms fluctuation of the infinite-frequency shear modulus was estimated using the data on the decoupling of viscosity and diffusion in supercooled liquids. These fluctuations are much smaller in amplitude, and, in contrast, they increase with increasing fragility. Extrapolation predicts intersection of both rms fluctuations and disappearing of the boson peak at the upper limit to fragility ≈180.

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

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

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

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

Deviations of dynamic parameters characterizing enthalpic and dielectric relaxations in glass forming alkyl phosphates

In our recent study [T. Wu et al., J. Chem. Phys. 147, 134501 (2017)], an alkyl phosphate glass former was studied and it suggested that the enthalpy relaxation involving the motions of all parts of the molecule is global, while the dielectric relaxation detects the local rotation of the polar core. In this work, we study a series of trialkyl phosphates using calorimetric and dielectric measurements over a wide temperature range. The results indicate a departure of the dielectric fragility indexes from the enthalpic ones as the length of the branch chain increases in the trialkyl phosphates. The Kirkwood correlation factor (g _k ) is found to coincide at ∼0.6 at glass transition temperature (T _g ) from triethyl phosphate to tributyl phosphate, indicating a similar structural alignment. The enthalpic relaxation serving as the more fundamental relaxation relevant to the structural relaxation is confirmed. Strikingly, we observed the relation of T _g to the chain length in alkyl phosphates, revealing a minimum T _g behavior, and its explanation assists in the understanding of the glass transition in relation to the structure of the glass-formers.

Interplay of intermolecular interactions and flexibility to mediate glass forming ability and fragility: A study of chemical analogs

We have investigated the enthalpic and dielectric relaxations of four groups of quinoline analogs having similar structural properties (i.e., rigidity, stiffness, and bulkiness) but a different steric character and the nature of intermolecular interactions and flexibility. The dielectric fragility index (m_d) and the enthalpic one (m_H), determined by the Tool-Narayanaswamy-Moynihan-Hodge formalism, are comparable. Generally, for the four sets of molecules of similar structures, both the interactions and flexibility are found to be critical in making the large span of fragility (i.e., from 59 to 131) and glass forming ability. By contrast, individual impacts of the interaction and flexibility can only explain fragility partly among each group of isomers. We found that the molecules with high fragility are of relatively low liquid density, reflecting the joint impact of the interactions and flexibility. An interesting result is observed among the isomers that the molecules which are fragile have enhanced glass forming ability. The results are unveiling the joint impacts of molecular structure (flexibility) and intermolecular interaction on the molecular dynamics.

Unifying different interpretations of the nonlinear response in glass-forming liquids

This work aims at reconsidering several interpretations coexisting in the recent literature concerning nonlinear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate, showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, for both their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these nonlinear susceptibilities. We show that the framework proposed by two of us [J.-P. Bouchaud and G. Biroli, Phys. Rev. B 72, 064204 (2005)PRBMDO1098-012110.1103/PhysRevB.72.064204], where the growth of nonlinear susceptibilities is intimately related to the growth of glassy domains, accounts for all the salient experimental features. We then review several complementary and/or alternative models and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments, which should deepen our understanding of glasses.

Nonlinear dielectric effects in liquids: a guided tour

Dielectric relaxation measurements probe how the polarization of a material responds to the application of an external electric field, providing information on structure and dynamics of the sample. In the limit of small fields and thus linear response, such experiments reveal the properties of the material in the same thermodynamic state it would have in the absence of the external field. At sufficiently high fields, reversible changes in enthalpy and entropy of the system occur even at constant temperature, and these will in turn alter the polarization responses. The resulting nonlinear dielectric effects feature field induced suppressions (saturation) and enhancements (chemical effect) of the amplitudes, as well as time constant shifts towards faster (energy absorption) and slower (entropy reduction) dynamics. This review focuses on the effects of high electric fields that are reversible and observed at constant temperature for single component glass-forming liquids. The experimental challenges involved in nonlinear dielectric experiments, the approaches to separating and identifying the different sources of nonlinear behavior, and the current understanding of how high electric fields affect dielectric materials will be discussed. Covering studies from Debye's initial approach to the present state-of-the-art, it will be emphasized what insight can be gained from the nonlinear responses that are not available from dielectric relaxation results obtained in the linear regime.

Relaxation dynamics in the strong chalcogenide glass-former of Ge22Se78

The enthalpy relaxation is performed in the glassy Ge₂₂Se₇₈ to understand the dynamic behaviors. The structure of the glass is examined by X-ray diffraction and Raman spectra. The dynamic parameters such as the fragility, stretching exponent and non-linear factor are determined. A low fragility of m = 27 is exhibited for the chalcogenide, however, the stretching exponent is found not to have a larger value. The enthalpy relaxation spectra are constructed for various glass formers, and a relationship between the fragility and the symmetry of the spectra is demonstrated. The dynamic results are used to evaluate the structure of the Ge₂₂Se₇₈ glass.

Contrasting dynamics of fragile and non-fragile polyalcohols through the glass, and dynamical, transitions: A comparison of neutron scattering and dielectric relaxation data for sorbitol and glycerol

BACKGROUND

Glycerol and sorbitol are glass-forming hydrogen-bonded systems characterized by intriguing properties which make these systems very interesting also from the applications point of view. The goal of this work is to relate the hydrogen-bonded features, relaxation dynamics, glass transition properties and fragility of these systems, in particular to seek insight into their very different liquid fragilities.

METHODS

The comparison between glycerol and sorbitol is carried out by collecting the elastic incoherent neutron scattering (EINS) intensity as a function of temperature and of the instrumental energy resolution.

RESULTS

Intensity data vs temperature and resolution are analyzed in terms of thermal restraint and Resolution Elastic Neutron Scattering (RENS) approaches.

CONCLUSIONS

The number of OH groups, which are related to the connecting sites, is a significant parameter both in the glass transition and in the dynamical transition. On the other hand, the disordered nature of sorbitol is confirmed by the existence of different relaxation processes.

GENERAL SIGNIFICANCE

From the applications point of view, glycerol and sorbitol have remarkable bioprotectant properties which make these systems useful in different technological and industrial fields. Furthermore, polyols are rich in glassforming liquid phenomenology and highly deserving of study in their own right. The comparison of EINS and calorimetric data on glycerol and sorbitol helps provide a connection between structural relaxation, dynamical transition, glass transition, and fragility. The evaluation of the inflection point in the elastic intensity behavior as a function of temperature and instrumental energy resolution provides a confirmation of the validity of the RENS approach. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo.

Unraveling the success and failure of mode coupling theory from consideration of entropy

We analyze the dynamics of model supercooled liquids in a temperature regime where predictions of mode coupling theory (MCT) are known to be valid qualitatively. In this regime, the Adam-Gibbs (AG) relation, based on an activation picture of dynamics, also describes the dynamics satisfactorily, and we explore the mutual consistency and interrelation of these descriptions. Although entropy and dynamics are related via phenomenological theories, the connection between MCT and entropy has not been argued for. In this work, we explore this connection and provide a microscopic derivation of the phenomenological Rosenfeld theory. At low temperatures, the overlap between the MCT power law regime and AG relation implies that the AG relation predicts an avoided divergence at Tc, the origin of which can be related to the vanishing of pair configurational entropy, which we find occurring at the same temperature. We also show that the residual multiparticle entropy plays an important role in describing the relaxation time.

Revisiting the glass transition and dynamics of supercooled benzene by calorimetric studies

The glass transition and dynamics of benzene are studied in binary mixtures of benzene with five glass forming liquids, which can be divided into three groups: (a) o-terphenyl and m-xylene, (b) N-butyl methacrylate, and (c) N,N-dimethylpropionamide and N,N-diethylformamide to represent the weak, moderate, and strong interactions with benzene. The enthalpies of mixing, ΔH(mix), for the benzene mixtures are measured to show positive or negative signs, with which the validity of the extrapolations of the glass transition temperature T(g) to the benzene-rich regions is examined. The extrapolations for the T(g) data in the mixtures are found to converge around the point of 142 K, producing T(g) of pure benzene. The fragility m of benzene is also evaluated by extrapolating the results of the mixtures, and a fragility m ∼ 80 is yielded. The obtained T(g) and m values for benzene allow for the construction of the activation plot in the deeply supercooled region. The poor glass formability of benzene is found to result from the high melting point, which in turn leads to low viscosity in the supercooled liquid.

Configurational entropy in thermoset polymers

The configurational entropy describes the atomic structure in a material and controls several material properties. Often the configurational entropy is determined through dielectric or calorimetric measurements where the difference between the entropies of the crystalline state and the amorphous state is determined. Many amorphous materials such as thermoset polymers have a high crystallization barrier, greatly limiting the applicability of the existing methods for determining the configurational entropy. In this work, a novel differential scanning calorimetry (DSC) method, based on measurement of the glass transition temperature at different heating rates, for determination of the configurational entropy is introduced. The theory behind the method has a universal character for amorphous materials, as it solely involves measurement of the glass transition temperature. The temperature dependency of the configurational entropy is determined for epoxy resins and PMMA (poly(methyl methacrylate)) to demonstrate the versatility of the method. On the basis of the findings of the introduced method, the influence of the degree of cross-linking and the chemical structure of the network is discussed.

Cooperativity and heterogeneity in plastic crystals studied by nonlinear dielectric spectroscopy

The glassy dynamics of plastic-crystalline cyclo-octanol and ortho-carborane, where only the molecular reorientational degrees of freedom freeze without long-range order, is investigated by nonlinear dielectric spectroscopy. Marked differences to canonical glass formers show up: While molecular cooperativity governs the glassy freezing, it leads to a much weaker slowing down of molecular dynamics than in supercooled liquids. Moreover, the observed nonlinear effects cannot be explained with the same heterogeneity scenario recently applied to canonical glass formers. This supports ideas that molecular relaxation in plastic crystals may be intrinsically nonexponential. Finally, no nonlinear effects were detected for the secondary processes in cyclo-octanol.

Calorimetric determination of fragility in glass forming liquids: T(f) vs. T(g-onset) methods

The calorimetric determination of the fragility m-index is compared using the T f and T g-onset methods for typical metallic and molecular glass forming systems of Pd39Ni10Cu30P21, glycerol, triacetin and propylene carbonate. The results are evaluated by referring to the standard m-values determined from the kinetic measurements of the viscosity or structural relaxation time in the supercooled liquid regimes. The m-indexes derived from the T f method are found to generally agree well with the kinetic measurements for all the systems. However, a large deviation is shown between the m-indexes calculated with the T g-onset method and the kinetic results for the fragile liquids of triacetin and propylene carbonate, indicating the calorimetric determination of the fragility m-indexes in terms of the T f method produces less uncertainty.

Nonlinear dielectric response at the excess wing of glass-forming liquids

We present nonlinear dielectric measurements of glass-forming glycerol and propylene carbonate applying electrical fields up to 671 kV/cm. The measurements extend to sufficiently high frequencies to allow for the investigation of the nonlinear behavior in the regime of the so-far mysterious excess wing, showing up in the loss spectra of many glass formers as a second power law at high frequencies. Surprisingly, we find a complete lack of nonlinear behavior in the excess wing, in marked contrast to the α relaxation where, in agreement with previous reports, a strong increase of dielectric constant and loss is found.

Quantifying the Structural Dynamics of Pharmaceuticals in the Glassy State

Structural dynamics in the glassy state of two protic ionic liquids, carvedilol phosphate and procaine hydrochloride, were characterized from analysis of changes in the conductivity relaxation times during physical aging. The obtained relaxation times, having a magnitude exceeding feasible experimental time scales and thus not directly measurable, are consistent with published data from a method that relies on the presence of a secondary relaxation. We also observe a narrowing of the relaxation dispersion, specific to higher frequencies, that is a consequence of the heterogeneous dynamics of deeply supercooled materials.

Nonlinear response theory for Markov processes: simple models for glassy relaxation

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature T_{0} determined by the value of the asymmetry. In a narrow temperature range around T_{0}, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than T_{0}), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times is considered. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.

Dual field nonlinear dielectric spectroscopy in a glass forming EPON 828 epoxy resin

Results of the dual field nonlinear dielectric spectroscopy (NDS) studies in supercooled glass forming epoxy resin EPON 828 are presented. For the NDS, changes of dielectric permittivity induced by DC (rectangular) or AC (sine-wave) pulses of a strong electric field were probed by a weak radio frequency electric field. A clear stretched exponential (x < 1) decay after switching off the DC pulse and a single exponential decay (x = 1) after switching off the AC pulse were found. The same results are presented for preliminary studies in superpressed low molecular glass former di-isobutyl phthalate. This observation may be considered as an argument for the heterogeneous picture of supercooled glass forming materials. The temperature dependences of the stationary responses related to DC and AC strong electric field excitations are also shown. The sensitivity of the applied set up made it possible to detect NDS outputs even for electric fields E(strong) < 10 kV cm(-1), qualitatively weaker than in similar 'nonlinear, dielectric' experimental studies on glass forming materials carried out so far.

Third harmonics nonlinear susceptibility in supercooled liquids: a comparison to the box model

The box model, originally introduced to account for the nonresonant hole burning (NHB) dielectric experiments in supercooled liquids, is compared to the measurements of the third harmonics P(3) of the polarisation, reported recently in glycerol, close to the glass transition temperature T(g) [C. Crauste-Thibierge, C. Brun, F. Ladieu, D. L'Hôte, G. Biroli, and J.-P. Bouchaud, Phys. Rev. Lett. 104, 165703 (2010)]. In this model, each box is a distinct dynamical relaxing entity (hereafter called dynamical heterogeneity (DH)) which follows a Debye dynamics with its own relaxation time τ(dh). When it is submitted to a strong electric field, the model posits that a temperature increase δT(dh), depending on τ(dh), arises due to the dissipation of the electrical power. Each DH has thus its own temperature increase, on top of the temperature increase of the phonon bath δT(ph). Contrary to the "fast" hole burning experiments where δT(ph) is usually neglected, the P(3) measurements are, from a thermal point of view, fully in a stationary regime, which means that δT(ph) can no longer be neglected a priori. This is why the version of the box model that we study here takes δT(ph) into account, which implies that the δT(dh) of the DHs are all coupled together. The value of P(3), including both the "intrinsic" contribution of each DH as well as the "spurious" one coming from δT(ph), is computed within this box model and compared to the P(3) measurements for glycerol, in the same range of frequencies and temperatures T. Qualitatively, we find that this version of the box model shares with experiments some nontrivial features, e.g., the existence of a peak at finite frequency in the modulus of P(3) as well as its order of magnitude. Quantitatively, however, some experimental features are not accounted for by this model. We show that these differences between the model and the experiments do not come from δT(ph) but from the "intrinsic" contribution of the DHs. Finally, we show that the interferences between the 3ω response of the various DHs are the most important issue leading to the discrepancies between the box model prediction and the experiments. We argue that this could explain why the box model is quite successful to account for some kinds of nonlinear experiments (such as NHB) performed close to T(g), even if it does not completely account for all of them (such as the P(3) measurements). This conclusion is supported by an analytical argument which helps understanding how a "space-free" model as the box model is able to account for some of the experimental nonlinear features.

Kinetic fragility of binary and ternary glass forming liquid mixtures

The experimental studies of liquid fragility in miscible binary and ternary glass forming mixtures reveal a general observation of the negative deviation in fragility upon mixing from the linear average of those of the components. Further analyses from ideal, near ideal to non-ideal mixing modes show that the deviation magnitude does not increase monotonically with mixing enthalpy, and a moderate intermolecular interaction would generate a largest reduction in fragility. Four eutectic systems, methyl-o-toluate-methyl-p-toluate, ZnCl(2)-AlCl(3), glycerol-water, and fructose-water, are studied to locate the composition where the largest fragility deviation occurs in phase diagrams. It is found that the compositions with the fragility minima do not coincide with the eutectic points. The results partly explain the experimental observation that the best glass forming region is not located at the eutectic composition.

An upper limit to kinetic fragility in glass-forming liquids

The kinetic fragility of a liquid is correlated to the magnitude of enthalpy hysteresis in various glass-forming materials during thermal cycling across the glass transition. While the lower bound of liquid fragility is well known, there has been little research into the possibility of an inherent upper limit to fragility. In this paper, we present a theoretical argument for the existence of a maximum fragility and show that the correlation between fragility and enthalpy hysteresis allows for an empirical evaluation of the upper limit of fragility. This upper limit occurs as the enthalpy hysteresis involved in thermal cycling about the glass transition approaches zero, leading to m(max)≈175. This result agrees remarkably well with our previous estimate. The dynamics of maximum fragility liquids are discussed, and a critical temperature of ∼1.5 T(g) (where T(g) is the glass transition temperature) is revealed where a transition from nonexponential to exponential structural relaxation occurs.

Dielectric relaxation dynamics in glass-forming mixtures of propanediol isomers

The relaxation dynamics of 1,2-propanediol-1,3-propanediol mixtures is studied in supercooled liquid regions across a wide composition range. The composition dependences of liquid fragility and nonexponential parameter β(KWW) are presented in the hydrogen-bonded mixtures with ideal mixing. The fragility index and glass transition temperature are shown to develop inversely with β(KWW), in analogy to the dynamic behaviors in mixtures of van der Waals liquids. Negative mixing effects on liquid fragility and β(KWW) are observed, and the strongest dependence of β(KWW on relaxation dynamics is revealed at the equimolar concentration. The glass formation in isomeric liquids is also addressed.

Glass transition and fragility in the simple molecular glassformer CS(2) from CS(2)-S(2)Cl(2) solution studies

With an interest in finding the fragility for a simple, single component, molecular glassformer, we have determined the dielectric relaxation and glass transition behavior for a series of glasses in the CS(2)-S(2)Cl(2) and CS(2)-toluene systems. Crystallization of CS(2) can be completely avoided down to the composition 20 mol% second component, and the fragility proves almost independent of CS(2) content in each system. Since the glass temperature T(g) obtained from both thermal studies and from dielectric relaxation (using T(g,diel)=T(tau=100 s)) is quite linear over the whole composition range in each system, and since relaxation time data for pure CS(2) fall on the same master plot when scaled by the linearly extrapolated T(g) value, we deduce that pure CS(2) has the same high fragility as the binary solutions. The value is m=86, as for ortho-terphenyl (OTP). Based on observations of independent studies for the vibrational density of states (VDoS) (of inherent structures for OTP and instantaneous, at-temperature structures for CS(2)), we attribute the high fragility to an excess vibrational heat capacity (defined by C(p) (vib, excess)=dS(vib, excess)/d ln T) originating in the behavior of the low frequency modes of the VDoS (the boson peak modes). Both low frequency DoS and anharmonicity increase with increasing temperature, augmenting the configurational entropy drive to the top of the system energy landscape. The surprising implication is that fragility is determined in the vibrational, not configurational, manifold of microstates.