The disordered nature of glass-forming melts gives rise to non-Arrhenius and non-exponential behaviour of their dynamics. With respect to the microscopic details involved in the structural relaxation, these materials have remained an unsolved puzzle for over a century. The observation of spatial heterogeneity regarding the dynamics provides an important step towards understanding the relation between the macroscopic properties of soft condensed matter and the molecular mechanisms involved. On the other hand, dynamic heterogeneity is the source of several new questions: What is the length scale and persistence time associated with such clusters of relaxation time? What is the signature of heterogeneity at high temperatures and in the glassy state? How do these features depend on the particular material and on the correlation function used for probing these heterogeneities? This work attempts to review the various approaches to heterogeneous dynamics and the generally accepted results, as well as some controversial issues. Undoubtedly, heterogeneity has provoked a number of novel experimental techniques targeted at studying glass-forming liquids at the molecular level. It will be emphasized that the picture of heterogeneity is a requirement for rationalizing an increasing number of experimental observations rather than just an alternative model for the dynamics of molecules.

We compare dielectric relaxation τ(T) data of several low molecular weight glass-forming liquids with the predictions of the Adam–Gibbs theory using experimental data for the configurational entropy Sc(T). Combination of Adam–Gibbs and Vogel–Fulcher equations yields an expression for Sc(T) which can be compared with experimental data. Good agreement is found for a range of temperatures near Tg<T<TB which depends on the fragility of the liquid and on the presence of a β relaxation. For fragile liquids, TB coincides with a qualitative change in the temperature dependence of the relaxation time scale or viscosity, with the temperature Tβ, where Johari–Goldstein-type β processes tend to merge into the α process, and with other crossover temperatures. For nonfragile liquids, TB/Tg increases, and the deviations from the Adam–Gibbs equation weaken or disappear altogether. The significance of TB, and of the Sc(T) temperature dependence implied by the Vogel–Fulcher theory fitting, are discussed in terms of the landscape paradigm.

We have measured the dielectric relaxation times of the α process of phenyl salicylate (salol) covering 11 decades in frequency. Being representative for the class of low molecular weight organic glass forming materials, the highly resolved temperature dependence of the dynamics in salol does not follow a particular function like the Vogel–Fulcher–Tammann (VFT) law over the entire accessible range of temperatures. In order to conduct a detailed and unambiguous analysis of the temperature dependence, we take advantage of the derivatives of the experimental log(fmax) values with respect to temperature, which allow us to either linearize the frequently used temperature laws or to resolve subtle changes in fmax(T) by decreasing the number of free parameters. In this manner we observe that none of the common routes for rationalizing the dynamics like Arrhenius, VFT, Souletie scaling, and idealized mode-coupling theory account for the experimental findings properly. However, we do observe a VFT behavior within the limits 265 K≤T≤320 K, i.e., for temperatures ranging from significantly above the glass transition at Tg=220 K to far above the melting point.

We have studied the temperature dependence of dielectric relaxation times in terms of the peak frequency f max (T) of dielectric loss ⑀Љ͑͒ and the dc-conductivity dc (T) of several glass-forming liquids, covering 12 decades in the peak frequency f max and 9 decades in dc . Although dc-conductivity samples the mobility of ionic tracers, its variation with temperature is similar to that of f max (T). The f max (T) and dc (T) are analyzed using the temperature-derivative method and compared to the viscosity data Ϫ1 (T). While most liquids reveal a common Vogel-FulcherTammann ͑VFT͒ behavior for f max , dc and Ϫ1 in an extended temperature range TуT m , some liquids deviate from this behavior by displaying a crossover at TϭT A to an Arrhenius regime. In these cases the quantity f max (T) decouples from the common curves for dc (T) and Ϫ1 (T) and attains activation energies in excess ͑ϳ40% for alcohols͒ of those related to translational processes. For many samples a departure from the VFT behavior occurs at lower temperatures T B ϽT m which tends to retard the glass transition. The onset of this qualitative change in the temperature dependence at T B turns out to be a characteristic temperature also in other experiments.

We have measured the dielectric relaxation of the glass-former 1-propanol for temperatures between 65 and 350 K in the frequency range 10−2 to 2⋅1010 Hz and the photon correlation spectro-scopy decays near Tg. Attributing the strong Debye-type process of 1-propanol to distinct -OH group effects leaves two faster processes related to the structural relaxation which can be identified as α-relaxation and Johari–Goldstein type β-relaxation characteristic of nonhydrogen-bonding supercooled liquids. From the temperature dependent relaxation times τ(T) regarding the three distinct loss peaks, we can specify an α-β-bifurcation temperature Tβ, which coincides with characteristic qualitative changes in the τ(T) behavior, as also observed for ortho-terphenyl and other glass-forming liquids. This assignment is confirmed by the correla-tion times derived from incoherent quasielastic light-scattering data obtained from the simultaneously measured photon-correlation spectroscopy.

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.

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Near their glass transition temperature T(g), supercooled liquids display dramatic changes regarding the dynamics if subject to geometrical restrictions on the scale of 2 to 200 nm. Confinement-induced shifts of T(g) of 25 K have been reported, equivalent to relaxation times that differ by several orders of magnitude compared with the bulk liquid at the same temperature. Both acceleration and frustration of structural relaxations have been observed, and the effects can depend strongly on the physical and chemical properties of the interface, on soft versus hard confinement, and on the size and dimensionality of the confining topology. This review attempts to extract a unifying picture from the past 20 years of diverse observations that involve experiments, simulations, and model considerations.