The theory of phase-ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase, is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench. How can one determine the growth laws that describe the time dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, for example vector and tensor fields. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings and monopoles) provides a unifying framework for discussing coarsening in these different systems.

Theory of phase-ordering kinetics

Sol-gel chemistry of transition metal oxides

Selected aspects of recent progress in the study of supercooled liquids and glasses are presented in this review. As an introduction for nonspecialists, several basic features of the dynamics and thermodynamics of supercooled liquids and glasses are described. Among these are nonexponential relaxation functions, non-Arrhenius temperature dependences, and the Kauzmann temperature. Various theoretical models which attempt to explain these basic features are presented next. These models are conveniently categorized according to the temperature regimes deemed important by their authors. The major portion of this review is given to a summary of current experimental and computational research. The utility of mode coupling theory is addressed. Evidence is discussed for new relaxation mechanisms and new time and length scales in supercooled liquids. Relaxations in the glassy state and significance of the “boson peak” are also addressed.

Supercooled Liquids and Glasses

We review some recently published methods to represent atomic neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighborhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

/pdf/on-representing-chemical-environments-obdx0bt3dd.pdf

On representing chemical environments

Confocal microscopy was used to directly observe three-dimensional dynamics of particles in colloidal supercooled fluids and colloidal glasses. The fastest particles moved cooperatively; connected clusters of these mobile particles could be identified; and the cluster size distribution, structure, and dynamics were investigated. The characteristic cluster size grew markedly in the supercooled fluid as the glass transition was approached, in agreement with computer simulations; at the glass transition, however, there was a sudden drop in their size. The clusters of fast-moving particles were largest near the α-relaxation time scale for supercooled colloidal fluids, but were also present, albeit with a markedly different nature, at shorter β-relaxation time scales, in both supercooled fluid and glass colloidal phases.

http://science.sciencemag.org/content/sci/287/5453/627.full.pdf

Three-Dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition

The spinodal decomposition of mixtures of poly(ethylenepropylene) (PEP) and perdeuterated poly-(ethylenepropylene) has been studied near the surface using forward-recoil spectrometry. Instead of the composition waves with randomly oriented wave vectors (and random phases) found in the bulk, we observe composition waves with wave vectors normal to, and which propagate inwards from, the surface, maintaining coherence for several wavelengths. We argue that these surface-directed spinodal decomposition waves are caused by the preferential attraction of the d-PEP to the surface.

Surface-directed spinodal decomposition.

The real-space structure of hard-sphere glasses quenched from colloidal liquids in thermodynamic equilibrium has been determined. Particle coordinates were obtained by combining the optical sectioning capability of confocal fluorescence microscopy with the structure of specially prepared fluorescent silica colloids. Both the average structure and the local structure of glasses, with volume fractions ranging from 0.60 to 0.64, were in good agreement with glasses and random close packings generated by computer simulations. No evidence of a divergent correlation length was found. The method used to obtain the three-dimensional particle coordinates is directly applicable to other colloidal structures, such as crystals, gels, and flocs.

/pdf/real-space-structure-of-colloidal-hard-sphere-glasses-2hgf85m01n.pdf

Real-Space Structure of Colloidal Hard-Sphere Glasses

Measurements of the radius of gyration ${\mathrm{R}}_{\mathrm{G}}$ and the hydrodynamic radius ${\mathrm{R}}_{\mathrm{H}}$ of colloidal silica aggregates are reported. These aggregates have fractal geometry and ${\mathrm{R}}_{\mathrm{H}}$ is proportional to ${\mathrm{R}}_{\mathrm{G}}$ for 500 A\r{}\ensuremath{\le}${\mathrm{R}}_{\mathrm{H}}$\ensuremath{\le}7000 A\r{}, with a ratio ${\mathrm{R}}_{\mathrm{H}}$/${\mathrm{R}}_{\mathrm{G}}$=0.72\ifmmode\pm\else\textpm\fi{}0.02. The results are compared with predictions for macromolecules of various shapes. The proportionality of the two radii can be understood with use of the pair correlation function of fractal objects and hydrodynamic interactions on the Oseen level. The value of the ratio remains to be explained.

Hydrodynamic behavior of fractal aggregates.

Classical light-scattering studies of colloidal silica gels show that they have a fractal structure for length scales shorter than a concentration-dependent crossover length $\ensuremath{\xi}$, and behave like a collection of nearly randomly distributed scattering centers for length scales greater than $\ensuremath{\xi}$. Our data show that $\ensuremath{\xi}$ has a power-law concentration dependence, $\ensuremath{\xi}\ensuremath{\propto}{c}^{\ensuremath{-}1.17\ifmmode\pm\else\textpm\fi{}0.1}$.

Gelation of colloidal silica

We present the method and results of two phase-separation experiments performed on the binary polymer blend polyisoprene-poly(ethylene propylene). Elastic light scattering and optical microscopy were used to follow the phase separation after quenches into the coexistence region of the phase diagram.

Pierre Wiltzius

Papers

Surface-directed spinodal decomposition.

Real-Space Structure of Colloidal Hard-Sphere Glasses

Hydrodynamic behavior of fractal aggregates.

Gelation of colloidal silica

Light-scattering experiments on phase-separation dynamics in binary fluid mixtures