Nonergodicity parameters of colloidal glasses

Diffusing-wave spectroscopy of nonergodic media

We introduce an elegant method that allows the application of diffusing-wave spectroscopy (DWS) to nonergodic, solidlike samples. The method is based on the idea that light transmitted through a sandwich of two turbid cells can be considered ergodic even though only the second cell is ergodic. If absorption and/or leakage of light take place at the interface between the cells, we establish a so-called "multiplication rule," which relates the intensity autocorrelation function of light transmitted through the double-cell sandwich to the autocorrelation functions of individual cells by a simple multiplication. To test the proposed method, we perform a series of DWS experiments using colloidal gels as model nonergodic media. Our experimental data are consistent with the theoretical predictions, allowing quantitative characterization of nonergodic media and demonstrating the validity of the proposed technique.

Dynamic structure of thermoreversible colloidal gels of adhesive spheres

The dynamic structure factor f(q,t) of suspensions of adhesive colloidal spheres has been characterized as a function of temperature over the volume fraction range 0.010<phi<0.075. Below a critical temperature that is volume fraction dependent, the suspensions underwent an abrupt, reversible transition in dynamic structure. Below their gel points suspensions became nonergodic, and the time decay of f(q,t) was arrested by as many as five decades. Static light scattering demonstrated that the adhesive spheres formed a fractal cluster gel structure. A recent model of the dynamics of fractal clusters [A. H. Krall and D. A. Weitz, Phys. Rev. Lett. 80, 778 (1998)] was applied to extract the temperature and volume fraction dependence of the characteristic decay times of f(q,t). Immediately above the gel temperature a single stretched exponential decay of f(q,t) was observed. The temperature dependence of the decay time was taualpha approximately epsilon(-1.15+/-0.06), where epsilon=(T-Tgel)/Tgel, and Tgel is the gelation temperature. The argument of the stretched exponential decay p decreased monotonically as the temperature was lowered toward the gel point, until, at gelation, p approximately 0.5. Below the gel temperature, an initial stretched exponential decay of f(q,t) was followed by a plateau. Finally, at long times, an additional exponential decay of the gel f(q,t) was observed. By applying the fractal cluster dynamics model, it was found that the initial decay time, taubeta approximately epsilon(-1.00+/-0.07). The plateau in f(q,t) was due to an upper bound of the mean-squared displacement of gel segments, denoted delta2. The typical magnitude of delta2 was not much greater than the square of the particle radius. The data showed delta2 approximately epsilon(-1.05+/-0.07). The additional exponential decay at long times, taugamma, depended only weakly on epsilon. Its dependence on the scattering vector was taugamma approximately q(-0.53+/-0.06). The argument of the stretched exponential decay of the gel f(q,t) and volume fraction dependence of taubeta and delta2 indicate that the spatial scaling of the gel compliance is consistent with the gel network bonds possessing angular rigidity. The epsilon dependence of the characteristic times taualpha and taubeta could not be fully explained by the fractal cluster dynamics model. The long time decay of f(q,t) exhibited behavior that differed from that recently reported for dilute gels of aqueous colloidal polystyrene [Cipelletti et al., Phys. Rev. Lett. 84, 2275 (2000)]. We hypothesize that the long-time decay in f(q,t) of the gels studied here is due to rare bond disaggregation processes that occur because of the relatively weak interaction between the adhesive spheres (deltaEmin/kT approximately 10) of the thermoreversible gel.

Mechanical properties of a model of attractive colloidal solutions

We review the nature of glass transitions and the glasses arising from a square-well potential with a narrow and deep well. Our discussion is based on the mode coupling theory (MCT), and the predictions of glasses that we make refer to the "ideal" glasses predicted by this theory. We believe that the square-well system well represents colloidal particles with attractive interactions produced by grafted polymers, or depletion interactions. It has been recently shown that two types of glasses, an attractive and a repulsive one, are predicted by MCT for this model. The former can form at quite low densities. Most of our attention is directed at the mechanical properties of the glasses predicted by this theory. In particular we calculate the elastic shear modulus at zero frequency and the longitudinal stress modulus in the long wavelength limit. Results for both are presented along the glass-liquid transition curves and their interesting behavior is explained in terms of the underlying physics of the system.

Higher-order glass-transition singularities in colloidal systems with attractive interactions

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 A3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth-order A4 (swallow-tail) singularity at a critical well width. Close to the A3 and A4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.

Molecular correlations in a supercooled liquid

We present static and dynamic properties of molecular correlation functions S(lmn,l(')m(')n('))(q-->,t) in a simulated supercooled liquid of water molecules, as a preliminary effort in the direction of solving the molecular mode-coupling theory (MMCT) equations for supercooled molecular liquids. The temperature and time dependence of various molecular correlation functions, calculated from 250 ns long molecular dynamics simulations, show the characteristic patterns predicted by MMCT and shed light on the driving mechanism responsible for the slowing down of the molecular dynamics. We also discuss the symmetry properties of the molecular correlation functions that can be predicted on the basis of the C(2v) symmetry of the molecule. Analysis of the molecular dynamics results for the static correlators S(lmn,l(')m(')n('))(q-->) reveals that additional relationships between correlators with different signs of n and n(') exist. We prove that for molecules with C(rv) symmetry this unexpected result becomes exact at least for high temperatures.

Kinetic glass transition in a micellar system with short-range attractive interaction

We show that percolation and structural arrest transitions coexist in different regions of the phase diagram of a copolymer-micellar system and relate them to short-range intermicellar attraction. The intermediate scattering function shows a nonergodic transition along a temperature and concentration dependent line. Analyses show a logarithmic time dependence, attributed to a higher-order glass transition singularity predicted by mode-coupling theory, followed by a power law.

Aspects of the dynamics of colloidal suspensions: further results of the mode-coupling theory of structural relaxation

Results of the idealized mode-coupling theory for the structural relaxation in suspensions of hard-sphere colloidal particles are presented and discussed with regard to recent light scattering experiments. The structural relaxation becomes nondiffusive for long times, contrary to the expectation based on the de Gennes narrowing concept. A semiquantitative connection of the wave vector dependences of the relaxation times and amplitudes of the final alpha relaxation explains the approximate scaling observed by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)]. Asymptotic expansions lead to a qualitative understanding of density dependences in generalized Stokes-Einstein relations. This relation is also generalized to nonzero frequencies thereby yielding support for a reasoning by Mason and Weitz [Phys. Rev. Lett. 74, 1250 (1995)]. The dynamics transient to the structural relaxation is discussed with models incorporating short-time diffusion and hydrodynamic interactions for short times.

Light-scattering microscope

We demonstrate a new design for a light-scattering microscope that is convenient to use and that allows simultaneous imaging and light scattering. The design is motivated by the growing use of thermal fluctuations to probe the viscoelastic properties of complex inhomogeneous environments. We demonstrate measurements of an optically nonergodic sample, one of the most challenging light-scattering applications.