Non-Debye response for the structural relaxation in glass-forming liquids: test of the Avramov model

The experimentally observed characteristic features of the alpha-relaxation process in glass-forming liquids are the non-Arrhenius behavior of the structural relaxation times and the non-Debye character of the macroscopic relaxation function. The Avramov model in which relaxation is considered as an energy activation process of surmounting random barriers in liquid energy landscape was successfully applied to describe the temperature and pressure dependences of the macroscopic relaxation times or viscosity. In this paper, we consider the dielectric spectrum associated with Avramov model. The asymmetrical broadening of the loss spectra was found to be related directly to dispersion of the energy barrier distribution. However, it turns out that temperature dependence of the spectrum broadening as predicted by the Avromov model is at odds to experimental observation in glass-forming liquids.     

Aging of the Johari-Goldstein relaxation in the glass-forming liquids sorbitol and xylitol

Employing frequency-dependent dielectric susceptibility we characterize the aging in two supercooled liquids, sorbitol and xylitol, below their calorimetric glass transition temperatures. In addition to the alpha relaxation that tracks the structural dynamics, the susceptibility of both liquids possesses a secondary Johari-Goldstein relaxation at higher frequencies. Following a quench through the glass transition, the susceptibility slowly approaches the equilibrium behavior. For both liquids, the magnitude of the Johari-Goldstein relaxation displays a dependence on the time since the quench, or aging time, that is quantitatively very similar to the age dependence of the alpha peak frequency. The Johari-Goldstein relaxation time remains constant during aging for sorbitol while it decreases slightly with age for xylitol. Hence, one cannot sensibly assign a fictive temperature to the Johari-Goldstein relaxation. This behavior contrasts with that of liquids lacking distinct Johari-Goldstein peaks for which the excess wing of the alpha peak tracks the main part of the peak during aging, enabling the assignment of a single fictive temperature to the entire spectrum. The aging behavior of the Johari-Goldstein relaxation time further calls into question the possibility that the relaxation time possesses stronger temperature dependence in equilibrium than is observed in the out-of-equilibrium state below the glass transition.     

Liquid–liquid transition in polymers and glass-forming liquids

It is shown that many simple glass-forming liquids exhibit a phenomenon known in the area of polymer science as the liquid–liquid transition. The phenomenon manifests itself as a third-order transition in the equilibrium liquid-specific heat data around approximately 1.2 T_g and also as a bifurcation of the liquid relaxation into primary and secondry processes. It is stressed that the above phenomenon is due to a smooth changeover of the liquid from one dynamic regime to the other and hence is not due to any real phase transition. It is suggested that a liquid cluster kind of picture for the supercooled liquid regime, is capable of explaining the above phenomenon and is consistent with observation made on polymers and monomeric liquids. © 1993 John Wiley & Sons, Inc.     

Enthalpy,volume and structural relaxation in glass-forming silicate melts

Through structural relaxation, the configuration of a viscous liquid changes to allow the Gibbs free energy to be minimum in response to temperature variations. In this review, the practical importance of relaxation in silicate melts is first illustrated by configurational heat capacity and entropy and their connection with viscosity via Adam-Gibbs theory. Relaxation effects on thermal expansion and compressibility are then examined, and the similarity of the kinetics of structural, enthalpy and volume relaxation is pointed out. Turning to microscopic mechanisms, we finally stress the importance of Si-O bond exchange and its decoupling with the motion of network-modifying elements near the glass transition. This revised version was published online in August 2006 with corrections to the Cover Date.     

Direct computation of characteristic temperatures and relaxation times for glass-forming polymer liquids

Characteristic temperatures and structural relaxation times for different classes of glass-forming polymer liquids are computed using a revised entropy theory of glass formation that permits the chain backbone and the side groups to have different rigidities. The theory is applied to glass formation at constant pressure or constant temperature. Our calculations provide new insights into physical factors influencing the breadth of the glass transition and the associated growth of relaxation times.     

On the relaxation theory of glass transition in liquids

A method for calculating the constant in the main equation of glass transition (which relates the relxation time and the cooling rate near the glass transition temperature) with consideration given to the temperature dependence of the activation energy in this region is proposed. A modification of the main glass transition equation is considered. Application of this equation to the relaxation spectrometry of amorphous polymers and inorganic glasses is discussed.     

Non-exponential non-Arrhenius relaxation in the course of CO rebinding to heme proteins

The dispersive transport model for relaxation of photolyzed heme proteins has been improved to take into account the coupling of the ligand-heme geminate recombination and the non-Gaussian diffusive dynamics of conformational changes in heme proteins. Contrary to the earlier deterministic version of the model, the present more rigorous formulation is based on the stochastic approach to the problem. This implies that the time evolution of protein conformations should be described in terms of the transient distribution which satisfies the Smoluchowski-type differential equation with a time-dependent diffusion coefficient. The obtained analytical solution of this equation enables us to relate main kinetic parameters of the geminate recombination and quantities characterizing the ligand-heme interaction. The derived expressions demonstrate that the reaction barrier shifts with time towards higher values following the near-stretched exponential behavior in agreement with experiment. Such a behavior is governed by the non-exponential non-Arrhenius conformational relaxation. The latter process can be identified by the characteristics “footprint” left on the experimental rebinding curve and is shown to be responsible for some kinetically different phases of the ligand-heme geminate recombination observed within distinct temperature ranges.     

Dynamics of glass-forming liquids. IX. Structural versus dielectric relaxation in monohydroxy alcohols

The prominent Debye-type but non-Arrhenius dielectric relaxation is a feature common to many monohydroxy alcohols in their liquid state. Although this exponential process is often considered to reflect the primary structural relaxation, only a faster, smaller, and nonexponential relaxation peak correlates with viscous flow and mechanical relaxation. We provide dielectric relaxation data for 2-methyl-1-butanol, 2-ethyl-1-hexanol, and 3,7-dimethyl-1-octanol across ten decades in time. Based on these and previous results, we show that there exists a variety of dielectric to mechanical relaxation time ratios in the viscous regime, but a universal value of 100 for that ratio appears to evolve in the high temperature limit. The temperature dependence for both the relaxation time and strength of the Debye peak differs from the typical behavior of structural dynamics in terms of the alpha process. The implications of these findings for rationalizing the Debye-type dielectric process of hydrogen-bonded liquids are discussed.     

The thermoelastic properties and structural relaxation of magnetic liquids

The kinetic equations for one-and two-particle distribution functions were used to study the thermoelastic properties of magnetic liquids in the presence of an external not uniform magnetic field. Dynamic equations for the heat conductivity coefficient λ(ω) and thermal elastic modulus Z(ω) over a wide reduced frequency range were obtained. The asymptotic behavior of λ(ω) and Z(ω) was studied at low and high frequencies; the results were in agreement with those obtained for classic liquids by the method of molecular dynamics. The λ(ω) and Z(ω) values were calculated for a magnetic liquid based on kerosene and Fe₃O₄ magnetic particles. The numerical data on transfer coefficients and elastic properties of magnetic liquids were on the whole in agreement with the general conclusions of the statistical theory of liquids.     

Fragility and thermodynamics in nonpolymeric glass-forming liquids

For nonpolymeric supercooled liquids, the empirical correlation m = 56Tg DeltaCp(Tg)/DeltaHm provides a reliable means of correlating dynamic and thermodynamic variables. The dynamics are characterized by the fragility or steepness index m and the glass transition temperature Tg, while thermodynamics enter in terms of the heat capacity step DeltaCp at Tg and the melting enthalpy DeltaHm. The combination of the above correlation with the 23 rule for the Tg/Tm ratio yields an expression, m = 40DeltaCp(Tg)/DeltaSm, which was rationalized as the correlation of the thermodynamic and kinetic fragilities. Defining a thermodynamic fragility via DeltaCp(Tg)/DeltaSm also reveals that the slopes in Kauzmann's original DeltaS(T)/DeltaSm versus T/Tm plot reflect the fragility concept [Chem. Rev. 43, 219 (1948)], so long as Tm/Tg = 1.5. For the many liquids whose excess heat capacity is a hyperbolic function of temperature, we deduce that the fragility cannot exceed m = 170, unless the Tg/Tm = 2/3 rule breaks down.     

Sensitivity of viscosity Arrhenius parameters to polarity of liquids

Several empirical and semi-empirical equations have been proposed in the literature to estimate the liquid viscosity upon temperature. In this context, this paper aims to study the effect of polarity of liquids on the modeling of the viscosity–temperature dependence, considering particularly the Arrhenius type equations. To achieve this purpose, the solvents are classified into three groups: nonpolar, borderline polar and polar solvents. Based on adequate statistical tests, we found that there is strong evidence that the polarity of solvents affects significantly the distribution of the Arrhenius-type equation parameters and consequently the modeling of the viscosity–temperature dependence. Thus, specific estimated values of parameters for each group of liquids are proposed in this paper. In addition, the comparison of the accuracy of approximation with and without classification of liquids, using the Wilcoxon signed-rank test, shows a significant discrepancy of the borderline polar solvents. For that, we suggested in this paper new specific coefficient values of the simplified Arrhenius-type equation for better estimation accuracy. This result is important given that the accuracy in the estimation of the viscosity–temperature dependence may affect considerably the design and the optimization of several industrial processes.     

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.     

Analysis of dielectric and conductive dispersion above Tg in glass-forming molecular liquids

Dynamics of the nonassociated supercooled liquids N-methyl-epsilon-caprolactam (NMEC) and glycerol in the frequency domain are investigated using full complex-nonlinear-least-squares fitting of immittance spectroscopy data for appreciable temperature ranges above the glass transition. Such fitting, not previously used for these materials, helps to identify physical processes responsible for the data and elements of their common behavior. Several different fitting models were applied to find a physically plausible best-fitting one to distinguish quantitatively between the dielectric effects of dipoles and the conductive effects of mobile ions. The utility of many composite fitting models was investigated, and although a pure conductive-system dispersive (CSD) fitting model led to good but physically unrealistic fits of all data sets, the dielectric-system dispersive (DSD) Davidson-Cole model best fitted the alpha-dispersion part of the responses. Nevertheless, the series combination of such a DSD model and a separate CSD model (one not associated with electrode effects) was found to yield much better fitting of the data for both materials. Although the CSD model plays somewhat the role of the conventional parallel DSD Johari-Goldstein beta-response, it is here in series and arises from mobile impurity-ion effects rather than from dipolar ones. Previous analyses of data of the present and other molecular materials have often involved two DSD models in parallel, but fitting with such a composite model led here to less physically plausible parameter values and ones with appreciably more uncertainties. Surprisingly, the series DSD and CSD composite-model fits led to comparable estimated values of the NMEC and glycerol dielectric strength parameters, as well as to the nearly equal small thermal activation energies of these parameters.     

Dynamics of glass-forming liquids. X. Dielectric relaxation of 3-bromopentane as molecular probes in 3-methylpentane

The glass-forming liquids 3-bromopentane (3BP) and 3-methylpentane (3MP) are readily miscible across the entire composition range, although their polarities differ considerably. As noted by Berberian [J. Non-Cryst. Solids 131-133, 48 (1991)], the nearly matching molar volumes makes this binary system appear ideal for probe-sensitized measurements. We have performed a dielectric study of these mixtures in the range of 3BP mole fractions x from 2 x 10(-4) to 0.75. In the limit of low concentrations, x<0.5%, the dielectric loss peak of 3BP is slower by a factor of 2.5 relative to that of 3MP. Additionally, the relaxation behavior of the guest is more exponential than that of the host liquid. We interpret the distinct dynamics of the guest as a result of temporal averaging over the heterogeneous host dynamics, with the exchange time being near the longest structural time constant of the system.     

Some comments on nature of the structural relaxation and glass transition

We report on an experiment and new formula revealing dynamic and structural heterogeneity observed in liquids and polymeric systems. The formula applied to data obtained by mechanical spectroscopy reveals the glass-forming system behaviour giving the parameters previously postulated. The presented results are compared with data obtained for liquids (oligomers) confined to nanoporous media. To explain the behaviour of the polymeric systems the three-phase model is considered.     

Application of environmental relaxation model to the transport behavior of glass-forming melts

The environmental relaxation model was applied successfully to explain the temperature dependence of viscosity, conductance, and the Walden product of molten Ca(NO₃)₂.3.91H₂O + NiCl₂ system in the non-Arrhenius region. This model was applied to pure melts, binary molten salt systems with ideal solutions marked by the absence of complex ions, and systems in which octahedral or tetrahedral complexes are formed. The values of the glass transition temperature obtained from the free volume and environmental relaxation models are in good agreement. The values of apparent activation energies for viscous and conductance flows derived from these two models are also comparable.     

Correlation between thermodynamic and kinetic fragilities in nonpolymeric glass-forming liquids

A phenomenological relationship between reduced excess heat capacity of supercooled liquid DeltaC(p)(exc)(T(g))DeltaS(m) at the glass transition temperature T(g), fragility index m, and reduced glass transition temperature T(rg)=T(g)T(m), where T(m) is the melting (liquidus) temperature, was derived for fragile nonpolymeric glass-forming liquids under the assumptions that the fragile behavior of these liquids is described by the Vogel-Fulcher-Tammann (VFT) equation; the excess heat capacity of liquid is inversely proportional to the absolute temperature and the VFT temperature T(0) is equal to the Kauzmann temperature T(K). It was found that DeltaC(p)(exc)(T(g))DeltaS(m) is a composite function of m and T(rg), which indicates that the empirical correlation DeltaC(p)(exc)(T(g))DeltaS(m)=0.025m recently identified by Wang et al. [J. Chem Phys. 125, 074505 (2006)] is probably valid only for liquids which have nearly the same values of T(rg).