Dynamic viscosity of a simple glass-forming liquid

Dual Nature of Large and Anisotropic Glass-Forming Molecules in Terms of Debye-Stokes-Einstein Relation Revealed

The fundamental Debye-Stokes-Einstein (DSE) relation between rotational relaxation times and shear viscosity attracts longstanding research interest as one of the most important characteristics of many glass-forming liquids. Here, we provide strong evidence, missing so far, for the relevance of anisotropy for DSE-related behavior. Dielectric spectroscopy and shear viscosity measurements were employed to get insight into the decoupling between reorientation relaxation times and viscosity for anisotropic glass-formers with dipole moments oriented parallel or perpendicular to the long molecular axis. We found that in the case of large and anisotropic molecules, the breakdown of DSE relation depends on the component of anisotropic rotation contributing to the dielectric response. Specifically, for glass-formers with dipole moment perpendicular to the long molecular axis, the DSE relation was found to be valid throughout the supercooled regime. Contrary, a departure from the DSE predictions in the intermediate supercooled regime, was observed for glass-formers where only short-axes contributions were relevant in dielectric response. MD simulations revealed differences in the mechanism of short and long axes reorientations suggesting that for anisotropic objects, not the reorientation mechanism itself, but the aspect of anisotropic motion, is the key to understanding the behavior of these systems in the context of DSE relation.

Structural relaxation and thermal conductivity of high-pressure formed, high-density di-n-butyl phthalate glass and pressure induced departures from equilibrium state

We report a study of structural relaxation of high-density glasses of di-n-butyl phthalate (DBP) by measuring thermal conductivity, κ, under conditions of pressure and temperature (p,T) designed to modify both the vibrational and configurational states of a glass. Various high-density glassy states of DBP were formed by (i) cooling the liquid under a fixed high p and partially depressurizing the glass, (ii) isothermal annealing of the depressurized glass, and (iii) pressurizing the glass formed by cooling the liquid under low p. At a given low p, κ of the glass formed by cooling under high p is higher than that of the glass formed by cooling under low p, and the difference increases as glass formation p is increased. κ of the glass formed under 1 GPa is ∼20% higher at ambient p than κ of the glass formed at ambient p. On heating at low p, κ decreases until the glass to liquid transition range is reached. This is the opposite of the increase in κ observed when a glass formed under a certain p is heated under the same p. At a given high p, κ of the low-density glass formed by cooling at low p is lower than that of the high-density glass formed by cooling at that high p. On heating at high p, κ increases until the glass to liquid transition range is reached. The effects observed are due to a thermally assisted approach toward equilibrium at p different from the glass formation p. In all cases, the density, enthalpy, and entropy would change until the glasses become metastable liquids at a fixed p, thus qualitatively relating κ to variation in these properties.

Length scales in glass-forming liquids and related systems: a review

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.

Nonlinear viscoelasticity of sorbitan tristearate monolayers at liquid/gas interface

The interfacial rheology of sorbitan tristearate monolayers formed at the liquid/air interface reveal a distinct nonlinear viscoelastic behavior under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes (gamma), the storage modulus (G') decreases monotonically whereas the loss modulus (G'') exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G' and G'' are in the ratio 2:1. The peak in G'' is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence on the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is more general and exhibits many of the features observed in 3D complex fluids.

Molecular mobility, thermodynamics and stability of griseofulvin's ultraviscous and glassy states from dynamic heat capacity

PURPOSE

To determine the calorimetric relaxation time needed for modeling griseofulvin's stability against crystallization during storage.

METHODS

Both temperature-modulated and unmodulated scanning calorimetry have been used to determine the heat capacity of griseofulvin in the glassy and melt state.

RESULTS

The calorimetric relaxation time, tau cal, of its melt varies with the temperature T according to the relation, tau cal [s] = 10(-13.3) exp [2, 292 /(T[K] - 289.5)] , and the distribution of relaxation times parameter is 0.67. The unrelaxed heat capacity of the griseofulvin melt is equal to its vibrational heat capacity.

CONCLUSIONS

Griseofulvin neither crystallizes on heating to 373 K at 1 K/h rate, nor on cooling. Molecular mobility and vibrational heat capacity measured here are more reliable for modeling a pharmaceutical's stability against crystallization than the currently used kinetics-thermodynamics relations, and molecular mobility in the (fixed structure) glassy state is much greater than the usual extrapolation from the melt state yields. Molecular relaxation time of the glassy state of griseofulvin is about 2 months at 298 K, and longer at lower temperatures. It would spontaneously increase with time. If the long-range motions alone were needed for crystallization, griseofulvin would become more stable against crystallization during storage.

Dynamic shear modulus of glycerol: Corrections due to instrument compliance

A recent article by Shi et al. [J. Chem. Phys.123, 174507 (2005)] reports results from mechanical measurements on three simple inorganic glass formers: glycerol, m-toluidine, and sucrose benzoate. The experiments carried out were stress relaxation, aging, and dynamic (all in shear) using a torsional rheometer, an advanced rheometric expansion system (TA Instruments). The original force rebalance transducer (2KFRT) supplied with the system was replaced with a custom-made load cell (Sensotec) that had a capacity of 20 000 g cm in torque and 5000 g in normal force. The replacement of the load cell was done due to the belief that the main source of compliance in this instrument was from the 2KFRT. With this assumption, the authors published their results for the three materials of interest and compared their results with the techniques of Schroter and Donth [J. Chem. Phys.113, 9101 (2000)] for the measurements on glycerol and reported important differences. These differences were disputed by one of the present authors (Schroter), and the present report shows that the results from Schroter and Donth are correct. We show that the reasons have to do with the instrument compliance being greater than originally thought by Shi et al. Here we examine the effects of platen diameter/geometry on the glycerol dynamic moduli, describe a means to correct dynamic data, present a revised comparison of the corrected data with that of Schroter and Donth, and provide a discussion of future work and conclusions.

Effect of silica colloids on the rheology of viscoelastic gels formed by the surfactant cetyl trimethylammonium tosylate

The effects of the addition of submicrometer-sized colloidal silica spheres on the linear and nonlinear rheology of semidilute solutions of a viscoelastic gel are studied. For a 1.4 wt% solution of the surfactant CTAT, a peak in the zero-shear rate viscosity eta(0) is observed at approximately equal weight percents of silica and CTAT. This peak shifts to lower silica concentrations on increasing either the CTAT concentration or the surface charge on silica and disappears when the CTAT concentration is increased to 2.6 wt%. The increases in eta(0) and the high frequency plateau modulus G(0) on the introduction of SiO(2) are explained by considering the increasingly entangled wormlike micelles that are formed due to the enhanced screening of the electrostatic interactions. The observed decrease in the values of G(0) and eta(0) at higher concentrations of silica particles is explained in terms of the formation of surfactant bilayers due to the adsorption of the positively charged cetyl trimethylammonium to the negatively charged silica.

Dielectric and shear mechanical alpha and beta relaxations in seven glass-forming liquids

We present shear mechanical and dielectric measurements taken on seven liquids: triphenylethylene, tetramethyltetra-phenyltrisiloxane (Dow Corning 704 diffusion pump fluid), polyphenyl ether (Santovac 5 vacuum pump fluid), perhydrosqualene, polybutadiene, decahydroisoquinoline (DHIQ), and tripropylene glycol. The shear mechanical and dielectric measurements are for each liquid performed under identical thermal conditions close to the glass transition temperature. The liquids span four orders of magnitude in dielectric relaxation strength and include liquids with and without Johari-Goldstein beta relaxation. The shear mechanical data are obtained by the piezoelectric shear modulus gauge method giving a large frequency span (10(-3)-10(4.5) Hz). This allows us to resolve the shear mechanical Johari-Goldstein beta peak in the equilibrium DHIQ liquid. We moreover report a signature (a pronounced rise in the shear mechanical loss at frequencies above the alpha relaxation) of a Johari-Goldstein beta relaxation in the shear mechanical spectra for all the liquids which show a beta relaxation in the dielectric spectrum. It is found that both the alpha and beta loss peaks are shifted to higher frequencies in the shear mechanical spectrum compared to the dielectric spectrum. It is in both the shear and dielectric responses found that liquids obeying time-temperature superposition also have a high-frequency power law with exponent close to -12. It is moreover seen that the less temperature dependent the spectral shape is, the closer it is to the universal -12 power-law behavior. The deviation from this universal power-law behavior and the temperature dependencies of the spectral shape are rationalized as coming from interactions between the alpha and beta relaxations.

Dielectric and shear mechanical relaxations in glass-forming liquids: A test of the Gemant-DiMarzio-Bishop model

The Gemant-DiMarzio-Bishop model, which connects the frequency-dependent shear modulus to the frequency-dependent dielectric constant, is reviewed and a new consistent macroscopic formulation is derived. It is moreover shown that this version of the model can be tested without fitting parameters. The reformulated version of the model is analyzed and experimentally tested. It is demonstrated that the model has several nontrivial qualitative predictions: the existence of an elastic contribution to the high-frequency limit of the dielectric constant, a shift of the shear modulus loss peak frequency to higher frequencies compared with the loss peak frequency of the dielectric constant, a broader alpha peak, and a more pronounced beta peak in the shear modulus when compared with the dielectric constant. It is shown that these predictions generally agree with experimental findings and it is therefore suggested that the Gemant-DiMarzio-Bishop model is correct on a qualitative level. The quantitative agreement between the model and the data is on the other hand moderate to poor. It is discussed if a model-free comparison between the dielectric and shear mechanical relaxations is relevant, and it is concluded that the shear modulus should be compared with the rotational dielectric modulus, 1(epsilon(omega)-n2), which is extracted from the Gemant-DiMarzio-Bishop model, rather than to the dielectric susceptibility or the conventional dielectric modulus M=1epsilon(omega).

Diluent Effects on the Debye-Type Dielectric Relaxation in Viscous Monohydroxy Alcohols

With the recognition that the Debye-type dielectric relaxation of liquid monohydroxy alcohols does not reflect the structural relaxation dynamics associated with the viscous flow and the glass transition, its behavior upon dilution is expected to differ from that of real alpha-processes. We have investigated the Debye-type dielectric relaxation of binary alcohol/alkane mixtures across the entire concentration range in the supercooled regimes. The focus is on 2-ethyl-1-hexanol in two nonpolar liquids, 3-methylpentane and squalane, which are more fluid and more viscous than the alcohol, respectively. The Debye relaxation is found to occur only for alcohol mole fractions x > 0.2 and is always accompanied by a non-Debye relaxation originating from the alcohol component. Prior to its complete disappearance, the Debye relaxation is subject to broadening. We observe that the Debye dynamics of 2-ethyl-1-hexanol is accelerated in the more fluid 3-methylpentane, while the more viscous squalane leads to longer Debye relaxation times. The present experiments also provide evidence that the breakdown of the Debye relaxation amplitude does not imply the absence of hydrogen-bonded structures.

Shear stress relaxation and physical aging study on simple glass-forming materials

Relaxation and aging behaviors in three supercooled liquids: m-toluidine, glycerol, and sucrose benzoate have been studied by shear stress relaxation experiments in the time domain above and below their nominal glass transition temperatures. For the equilibrium state, the current study provides new data on the behavior of organic complex fluids. The shape of the relaxation function as characterized by the stretching exponent beta is discussed considering that a time-temperature master curve can be constructed even though the beta's for the individual response curves at each temperature vary systematically. In the nonequilibrium state, isothermal physical aging experiments at different glassy structures reveal that the effect of the aging process on the mechanical shear relaxation in these simple glass formers is similar to that observed in polymeric and other systems. Departure from the Vogel-Fulcher-Tamman behavior after the samples have aged back to equilibrium in the glassy state is observed for m-toluidine and, less strongly, for glycerol but not for sucrose benzoate. An inherent structure-based energy landscape concept is briefly discussed to account for the slow dynamics during the physical aging process.

Ideal Mixing Behavior of the Debye Process in Supercooled Monohydroxy Alcohols

Glass-forming monohydroxy alcohols exhibit two dielectric relaxation signals with super-Arrhenius temperature dependence: a Debye peak and an asymmetrically broadened alpha-process. We explore the behavior of these distinct relaxation features in mixtures of such liquids by dielectric measurements. The study focuses on the viscous regime of two binary systems: 2-methyl-1-butanol with 2-ethyl-1-hexanol and 1-propanol with 3,7-dimethyl-1-octanol. We find that the logarithmic relaxation time, log(tau), of the Debye peak follows an ideal mixing law (linear change with mole fraction), even in the case of mixing structurally dissimilar components. By contrast, the log(tau) versus mole fraction curve for the alpha-process is nonlinear, indicative of slower structural relaxation relative to the expectation on the basis of ideal mixing behavior. The latter observation is analogous to the effect of composition on viscosity, heat of mixing, and glass-transition temperature, whereas the ideal mixing of log(tau) seen for the Debye peak is the exception. We conclude that the unusual ideal mixing behavior of dielectric relaxation in monohydroxy alcohols is not a result of structural similarity, but rather yet more evidence of the Debye process being decoupled from other dynamic and thermodynamic properties.

High-frequency dynamics of the glass former dibutylphthalate under pressure

The high-frequency dynamics of a fragile molecular glass former (dibutylphthalate) was studied through inelastic x-ray scattering (IXS), as a function of pressure and temperature. The mesoscopic structural arrest associated with the glass transition process was tracked by following upon cooling the inelastic excitations at fixed Q points in the dispersion curves, at ambient pressure and 2 kbar. The application of pressure to this system induces an offset between the macroscopic glass transition temperature T(g) and the mesoscopic glass transition temperature, as determined from IXS. The concomitant fragility decrease of dibutylphthalate under pressure unveils that the stronger the glass former is, the more its mesoscopic dynamics differ from the macroscopic regime. This trend is interpreted as the signature of a nanoscopic inhomogeneous elastic network. Further aspects of this system are obtained when studying the temperature dependence of its nonergodicity factor f(Q)(T). The chemical specificity of the molecule is suggested to be responsible for the nonobservation of a critical temperature T(c) in dibutylphthalate up to approximately 300 K.

Anomalous stretching in a simple glass-forming liquid

The frequency dependent shear modulus G(omega) for a simple liquid shows strongly stretched behavior and the stretching exponent increases with decrease of temperature. This unconventional behavior was reported earlier in Phys. Rev. Lett. 73, 963 (1994) from experiments on simple liquids. We demonstrate here that this is a feature of the characteristic two-step relaxation process of the self-consistent mode coupling theory of supercooled liquids.

Structural relaxation, self-diffusion, and kinetic heterogeneity in the two-dimensional lattice Coulomb gas

We present Monte Carlo simulation results on the equilibrium relaxation dynamics in the two-dimensional lattice Coulomb gas, where finite fractions f of the lattice sites are occupied by positive charges. In the case of high-order rational values of f close to the irrational number 1-g [g identical with (square root of 5-1)/2 is the golden mean], we find that the system exhibits, for a wide range of temperatures above the first-order transition, a glassy behavior resembling the primary relaxation of supercooled liquids. Single-particle diffusion and structural relaxation show that there exists a breakdown of proportionality between the time scale of diffusion and that of structural relaxation analogous to the violation of the Stokes-Einstein relation in supercooled liquids. Suitably defined dynamic cooperativity is calculated to exhibit the characteristic nature of dynamic heterogeneity present in the system.

The molecular mobility of supercooled amorphous indomethacin as a function of temperature and relative humidity

PURPOSE

To determine the relaxation times of supercooled indomethacin as a function of temperature and relative humidity above Tg, and to analyze the results in the context of being able to predict such behavior at various storage conditions.

METHODS

Dielectric relaxation times were measured in the frequency domain (12 to 10(5) Hz) for amorphous indomethacin equilibrated at 0, 56, and 83% relative humidity. The heating rate dependence of Tg for dry supercooled indomethacin was measured with differential scanning calorimetry and used to determine relaxation times. The results were compared with previously published shear relaxation times and enthalpy recovery data.

RESULTS

Very good agreement was observed between dielectric and shear relaxation times, and those obtained from the heating rate dependence of the Tg, for dry indomethacin as a function of temperature above Tg. The introduction of water lowered the dielectric relaxation times of supercooled indomethacin without significantly affecting its fragility. The relaxation times below Tg, found to be lower than those predicted by extrapolation of the data obtained above Tg, were analyzed in the context of the Adam-Gibbs-Vogel equation.

CONCLUSIONS

The relaxation times of amorphous indomethacin obtained from the heating rate dependence of Tg were in good agreement with those obtained from shear and dielectric measurements, thus validating a relatively simple approach of assessing molecular mobility. The significant molecular mobility of amorphous indomethacin observed below Tg, and the significant plasticizing effects of sorbed water, help to explain why amorphous indomethacin crystallizes well below Tg over relatively short time scales.

Molecular mobility of supercooled amorphous indomethacin, determined by dynamic mechanical analysis

PURPOSE

To determine the viscosity and the frequency-dependent shear modulus of supercooled indomethacin as a function of temperature near and above its glass transition temperature and from these data to obtain a quantitative measure of its molecular mobility in the amorphous state.

METHODS

Viscoelastic measurements were carried with a controlled strain rheometer in the frequency domain, at 9 temperatures from 44 degrees to 90 degrees C.

RESULTS

The viscosity of supercooled indomethacin shows a strong non-Arrhenius temperature dependence over the temperature range studied, indicative of a fragile amorphous material. Application of the viscosity data to the VTF equation indicates a viscosity of 4.5 x 10(10) Pa.s at the calorimetric Tg of 41 degrees C. and a T0 of -17 degrees C. From the complex shear modulus and the Cole-Davidson equation the shear relaxation behaviour is found to be non-exponential, and the shear relaxation time at Tg is found to be approximately 100 sec.

CONCLUSIONS

Supercooled indomethacin near and above its Tg exhibits significant molecular mobility, with relaxation times similar to the timescales covered in the handling and storage of pharmaceutical products.

Dynamics of glass-forming di-n-butyl phthalate as studied by NMR

Spin-lattice relaxation times T1 and nuclear Overhauser effect (NOE) enhancement factors for the individual ring carbons in di-n-butyl phthalate (DBF) show that the reorientational correlation function corresponding to the global dynamics in supercooled liquid can be described by a Davidson-Cole distribution. Measurements of proton spin-lattice relaxation times T1 and T1p, as well as 1H NMR spectra at temperatures below the glass transition temperature, Tg, reveal that the same distribution holds also for description of local dynamics in glassy DBF. The activation parameters of the motions detected are derived.