The characterlstic features of n-and 9-rdaxarion in the supercooled State of nonnetwork forming liquids and polymers are re.riewed Particular emphasis IS put on properties observed recently by neutron scattering and molecular dynamics studies wthin the mesoscopic time region. The data indicate the exstence of a crossover temperature T,, located above the calorimetric glass transition temperature Tg, where the transport poperties change from those typical for a strongly wupled liquid to factor anomalies, power law divergences of the relaxation scale and a crossover from a-scale universality m dewupling of the various relaxation processes. The p process 1s characterued by a complete absence of correlations between spatial and temporal motion and unconventional scaling laws. There appear two fractal ome decay processes and two divergent hme scdles if the crossovcr temperature I S approached. The results of the mode wupling theory for the supercooled liquid dynamics are reviewed and shown to give a unified and partly quantitative description of the 7:-anomalies Ths review was received m October 1991. those characte:*c 6: 2 g!ass, ) ! ea: T, th.e ~.p--cess s spcr:fi& by Erbye-V)&: W3J-JS8S/92lOW2~IC136$1800 0 1992 IOP Publishing Lid 241 242 1V GOILE andL Sjogren Contents 1. Introduction 2. The a-relaxation process 2.1. General features 2.2. The a-peak intensity 2.3. The a-relaxation scale 2.4. The superposition principle 2.5. von Schweidler relaxation 2.6. a-relaxation stretching 2.7. Double peak phenomena 3. Mode coupling theory of the a-relaxation process 3.1. The basis of the mode coupling theory 3.2. The crossover from iiquid to glass dynamics 3.3. Theoretical results for the a-relaxation 4. The calorimetric glass transition temperature Tg 5. &relaxation phenomena 5.1. General features 5.2. Mode coupling theory for the general &process 5.3. The factorization property and the critical decay 5.4. The minimum of the @-spectrum 5.5. 13-relaxation below 7 , 5.6. The fi-peak scenario 6. Simple modcl systems 6.1. Simple one atomic liquids 6.2. Binary mixtures 6.3. Colloidal suspensions 7. Complex relaxation scenzrios 7.1. General features 7.2. The mode coupling theory of the cusp singularity 7.3. .4 quantitative analysis of some polymer susceptibilities Acknowledgmcnn References 8. Appendix

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An overview is given of recent tests of the mode-coupling theory for the evolution of structural relaxation in glass-forming liquids. Emphasis is put on comparisons between the leading-order asymptotic formulae derived for the dynamics near glass transition singularities and the results of neutron scattering, depolarized light scattering, impulsive stimulated light scattering and dielectric-loss spectroscopy for conventional liquids. The tests based on photon-correlation spectroscopy results for the glassy dynamics of colloids and the findings of molecular dynamics simulations for model systems are also considered.

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third-order bifurcation point, i.e., in a A 3 ͑cusp͒ singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourthorder A 4 ͑swallow-tail͒ singularity at a critical well width. Close to the A 3 and A 4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.

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