Effect of composition changes on the structural relaxation of a binary mixture

Equilibrium route to colloidal gelation: mixtures of hard-sphere-like colloids

The binodals and the nonergodicity lines of a binary mixture of hard-sphere-like particles with a large size ratio are computed for studying the interplay between dynamic arrest and phase separation in depletion-driven colloidal mixtures. Contrary to the case of hard core plus short-range effective attraction, physical gelation without competition with the fluid-phase separation can occur in such mixtures. This behavior due to the oscillations in the depletion potential should concern all simple mixtures with a nonideal depletant, justifying further studies of their dynamic properties.

MD simulation of concentrated polymer solutions: structural relaxation near the glass transition

We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the mixtures have one glass transition temperature T(g) or critical temperature T(c) of mode-coupling theory (MCT). Both T(g) and T(c) (> T(g)) decrease with increasing solvent concentration φ(S). The decrease is linear for the concentrations studied (up to φ(S) = 25%). Above T(c) we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T(c). Near T(c) we investigate dynamic correlation functions, such as the incoherent intermediate scattering function φ(q)(s)(t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution P(ln r; t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that φ(q)(s)(t) obeys the time-temperature superposition principle and has α relaxation times τ(q)(s) which are compatible with a power law increase close (but not too close) to T(c). In divergence to MCT, however, the increase of τ(q)(s) depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related to the emergence of dynamic heterogeneity at low T. In the time window of the α relaxation an analysis of P(ln r; t) reveals a double-peak structure close to T(c). The first peak corresponds to "slow" particles (monomer or solvent) which have not moved much farther than 10% of their diameter in time t, whereas the second occurs at distances of the order of the particle diameter. These "fast" particles have succeeded in leaving their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation of the cold polymer solution in the vicinity of the extrapolated T(c).

Cooperative activated dynamics in dense mixtures of hard and sticky spheres

The coupled activated dynamics in dense mixtures of repulsive and sticky hard spheres is studied using stochastic nonlinear Langevin equation theory. The effective free energy surface, barriers, saddle point trajectories, and mean first passage times depend in a rich manner on mixture composition, (high) total volume fraction, and attractive interaction strength. In general, there are three types of saddle point trajectories or relaxation pathways: a pure sticky or pure repulsive particle displacement keeping the other species localized, and a cooperative motion involving repulsive and attractive particle displacements. The barrier for activated hopping usually increases with the ratio of sticky to repulsive particle displacement. However, at intermediate values of the displacement ratio it can attain a broad plateau value, and can even exhibit a local maximum, and hence nonmonotonic behavior, at high sticky particle mixture compositions if the attraction strength is modest. The mean first passage, or hopping, times are computed using multidimensional Kramers theory. In most cases the hopping time trends reflect the behavior of the barrier height, especially as the sticky particle attraction strengths become large. However, there are dramatic exceptions associated with cooperative repulsive and attractive particle trajectories where the barriers are high but a greatly enhanced number of such trajectories exist near the saddle point.

Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres

Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.

Theory of dynamic arrest in colloidal mixtures

We present a first-principles theory of dynamic arrest in colloidal mixtures based on the multicomponent self-consistent generalized Langevin equation theory of colloid dynamics [M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E 72, 031107 (2005); M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E76, 039902 (2007)]. We illustrate its application with a description of dynamic arrest in two simple model colloidal mixtures: namely, hard-sphere and repulsive Yukawa binary mixtures. Our results include observation of the two patterns of dynamic arrest, one in which both species become simultaneously arrested and the other involving the sequential arrest of the two species. The latter case gives rise to mixed states in which one species is arrested while the other species remains mobile. We also derive the ("bifurcation" or fixed-point") equations for the nonergodic parameters of the system, which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species. The solution of this system of equations indicates unambiguously which species is arrested (finite localization length) and which species remains ergodic (infinite localization length). As a result, we are able to draw the entire ergodic-nonergodic phase diagram of the binary hard-sphere mixture.

Irreducible memory function and slow dynamics in disordered systems

We show how the irreducible memory function can be obtained in a rather straightforward way, and that it can be expressed in terms of two contributions representing two parallel decay channels. This representation should be useful for treating systems with a slow time dependence and where eventually some internal degrees of freedom enters in the relaxation process, and cuts off an underlying ideal ergodic to nonergodic transition. We also show how the irreducible memory function under certain mild conditions defines a regenerative stochastic process, or a two level stochastic system. This leads to a picture with dynamical heterogeneities, where the statistical properties asymptotically are ruled by limit processes. This can explain the universal behavior observed in many glass-forming systems.

Relaxation scenarios in a mixture of large and small spheres: Dependence on the size disparity

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and small particles. Density-density correlators for the small particles become extremely stretched and display logarithmic relaxation by properly tuning the temperature or the wave vector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated with mode coupling transition lines of the types B and A at, respectively, small and very large size disparities. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent mode coupling theory for fluids confined in matrices with interconnected voids [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)].

Anomalous dynamic arrest in a mixture of large and small particles

We present molecular dynamics simulations of the slow dynamics of a mixture of large and small soft spheres with a large size disparity. The dynamics are investigated in a broad range of temperature and mixture composition. As a consequence of the large size disparity, large and small particles exhibit very different relaxation times. As previously reported for simple models of short-ranged attractive colloids and polymer blends, several anomalous dynamic features are observed: (i) sublinear behavior for mean-squared displacements, (ii) concave-to-convex crossover for density-density correlators, by varying the temperature or wave vector, and (iii) logarithmic decay for specific wave vectors of density-density correlators. These anomalous features are observed over time intervals extending up to four decades and strongly resemble predictions of the mode coupling theory (MCT) for state points close to higher-order MCT transitions, which originate from the competition between different mechanisms for dynamic arrest. For the large particles we suggest competition between soft-sphere repulsion and depletion effects induced by neighboring small particles. For the small particles we suggest competition between bulklike dynamics and confinement, respectively induced by neighboring small particles and by the slow matrix of large particles.

Sensitivity of arrest in mode-coupling glasses to low-q structure

We quantify, within mode coupling theory, how changes in the liquid structure affect that of the glass. Apart from the known sensitivity to the structure factor S(q) at wave vectors around the first sharp diffraction peak q0, we find a strong (and inverted) response to structure at wave vectors below this peak: an increase in S(q0/2) lowers the degree of arrest over a wide q-range. This strong sensitivity to "caged cage" packing effects, on length scales of order 2d, is much weaker in attractive glasses where short-range bonding dominates the steric caging effect.

Tagged-particle dynamics in a hard-sphere system: mode-coupling theory analysis

The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian- and Brownian-dynamics simulations of a polydisperse quasi-hard-sphere system close to the glass transition. After correcting for a 17% error in the dynamical length scale and for a smaller error in the transition density, good agreement is found over a wide range of wave numbers and up to five orders of magnitude in time. Deviations are found at the highest densities studied, and for small wave vectors and the mean-squared displacement. Possible error sources not related to MCT are discussed in detail, thereby identifying more clearly the issues arising from the MCT approximation itself. The range of applicability of MCT for the different types of short-time dynamics is established through asymptotic analyses of the relaxation curves, examining the wave-number and density-dependent characteristic parameters. Approximations made in the description of the equilibrium static structure are shown to have a remarkable effect on the predicted numerical value for the glass-transition density. Effects of small polydispersity are also investigated, and shown to be negligible.

Is there a reentrant glass in binary mixtures?

By employing computer simulations for a model binary mixture, we show that a reentrant glass transition upon adding a second component occurs only if the ratio alpha of the short-time mobilities between the glass-forming component and the additive is sufficiently small. For alpha approximately 1, there is no reentrant glass, even if the size asymmetry between the two components is large, in accordance with the two-component mode-coupling theory. For alpha<<1, on the other hand, the reentrant glass is observed and reproduced only by an effective one-component mode-coupling theory.

Influence of a depletion interaction on dynamical heterogeneity in a dense quasi-two-dimensional colloid liquid

We report the results of digital video microscopy studies of the large particle displacements in a quasi-two-dimensional binary mixture of large (L) and small (S) colloid particles with diameter ratio sigma(L)/sigma(S)=4.65, as a function of the large and small colloid particle densities. As in the case of the one-component quasi-two-dimensional colloid system, the binary mixtures exhibit structural and dynamical heterogeneity. The distribution of large particle displacements over the time scale examined provides evidence for (at least) two different mechanisms of motion, one associated with particles in locally ordered regions and the other associated with particles in locally disordered regions. When rhoL*=Npisigma(L) (2)/4A< or =0.35, the addition of small colloid particles leads to a monotonic decrease in the large particle diffusion coefficient with increasing small particle volume fraction. When rhoL* > or =0.35 the addition of small colloid particles to a dense system of large colloid particles at first leads to an increase in the large particle diffusion coefficient, which is then followed by the expected decrease of the large particle diffusion coefficient with increasing small colloid particle volume fraction. The mode coupling theory of the ideal glass transition in three-dimensional systems makes a qualitative prediction that agrees with the initial increase in the large particle diffusion coefficient with increasing small particle density. Nevertheless, because the structural and dynamical heterogeneities of the quasi-two-dimensional colloid liquid occur within the field of equilibrium states, and the fluctuations generate locally ordered domains rather than just disordered regions of higher and lower density, it is suggested that mode coupling theory does not account for all classes of relevant fluctuations in a quasi-two-dimensional liquid.

alpha-Relaxation processes in binary hard-sphere mixtures

Molecular-dynamics simulations are presented for two correlation functions formed with the partial density fluctuations of binary hard-sphere mixtures in order to explore the effects of mixing on the evolution of glassy dynamics upon compressing the liquid into high-density states. Partial-density-fluctuation correlation functions for the two species are reported. Results for the alpha-relaxation process are quantified by parameters for the strength, stretching, and time scale, where the latter varies over almost four orders of magnitude upon compression. The parameters exhibit an appreciable dependence on the wave vector, and this dependence is different for the correlation function referring to the smaller and that for the larger species. These features are shown to be in semiquantitative agreement with those calculated within the mode-coupling theory for ideal liquid-glass transitions.

Dynamics of colloidal glass-forming mixtures

Recent experimental results from dynamic light scattering on two-component colloidal mixtures close to the glass transition are compared to theory. In the framework of the mode-coupling theory of the glass transition, close agreement is found in general. Discrepancies are identified for the minority-particle correlation function, and possible reasons for them are discussed.

Mixing effects for the structural relaxation in binary hard-sphere liquids

We report extensive molecular-dynamics-simulation results for binary mixtures of hard spheres for different size disparities and different mixing percentages, for packing fractions up to 0.605, and over a characteristic time interval spanning up to 5 orders in magnitude. We explore the changes in the evolution of glassy dynamics due to mixing and discover two opposite scenarios: For large size disparity, increasing the mixing percentage of small particles leads to a speed up of long-time dynamics, while small disparity leads to a slowing down. These results agree with predictions based on the mode-coupling theory for ideal-glass transitions.