On polydispersity and the hard sphere glass transition

Replica theory for the dynamic glass transition of hard spheres with continuous polydispersity

Glassy soft matter is often continuously polydisperse, in which the sizes or various properties of the constituent particles are distributed continuously. However, most of the microscopic theories of the glass transition focus on the monodisperse particles. Here, we developed a replica theory for the dynamic glass transition of continuously polydisperse hard spheres. We focused on the limit of infinite spatial dimension, where replica theory becomes exact. In theory, the cage size A, which plays the role of an order parameter, appears to depend on the particle size σ, and thus, the effective free energy, the so-called Franz-Parisi potential, is a functional of A(σ). We applied this theory to two fundamental systems: a nearly monodisperse system and an exponential distribution system. We found that dynamic decoupling occurs in both cases; the critical particle size σ^{*} emerges, and larger particles with σ≥σ^{*} vitrify, while smaller particles σ<σ^{*} remain mobile. Moreover, the cage size A(σ) exhibits a critical behavior at σ≃σ^{*}, originating from spinodal instability of σ^{*}-sized particles. We discuss the implications of these results for finite dimensional systems.

Measurable structure factors of dense dispersions containing polydisperse optically inhomogeneous particles

Here, it is investigated how optical properties of single scatterers in interacting multi-particle systems influence measurable structure factors. Both particles with linear gradients of their scattering length density and core-shell structures evoke characteristic deviations between the weighted sum 〈S(Q)〉 of partial structure factors in a multi-component system and experimentally accessible measurable structure factors S M(Q). While 〈S(Q)〉 contains only the structural information of self-organizing systems, S M(Q) is additionally influenced by the optical properties of their constituents, resulting in features such as changing amplitudes, additional peaks in the low-wavevector region or splitting of higher-order maxima, which are not related to structural reasons. It is shown that these effects can be systematically categorized according to the qualitative behaviour of the form factor in the Guinier region, which enables assessing the suitability of experimentally obtained structure factors to genuinely represent the microstructure of complex systems free from any particular model assumption. Hence, a careful data analysis regarding size distribution and optical properties of single scatterers is mandatory to avoid a misinterpretation of measurable structure factors.

Decoupling of rotation and translation at the colloidal glass transition

In dense particle systems, the coupling of rotation and translation motion becomes intricate. Here, we report the results of confocal fluorescence microscopy where simultaneous recording of translational and rotational particle trajectories from a bidisperse colloidal dispersion is achieved by spiking the samples with rotational probe particles. The latter consist of colloidal particles containing two fluorescently labeled cores suited for tracking the particle's orientation. A comparison of the experimental data with event driven Brownian simulations gives insights into the system's structure and dynamics close to the glass transition and sheds new light onto the translation-rotation coupling. The data show that with increasing volume fractions, translational dynamics slows down drastically, whereas rotational dynamics changes very little. We find convincing agreement between simulation and experiments, even though the simulations neglect far-field hydrodynamic interactions. An additional analysis of the glass transition following mode coupling theory works well for the structural dynamics but indicates a decoupling of the diffusion of the smaller particle species. Shear stress correlations do not decorrelate in the simulated glass states and are not affected by rotational motion.

Rescaled mode-coupling scheme for the quantitative description of experimentally observed colloid dynamics

We describe experimentally observed collective dynamics in colloidal suspensions of model hard-sphere particles using a modified mode coupling theory (MCT). This rescaled MCT is capable of describing quantitatively the wave-vector and time-dependent diffusion in these systems. Intermediate scattering functions of liquidlike structured dispersions are determined by means of static and dynamic light-scattering experiments. The structure and short-time dynamics of the systems can be described quantitatively employing a multicomponent Percus-Yevick ansatz for the partial structure factors and an effective, one-component description of hydrodynamic interactions based on the semianalytical δγ expansion. Combined with a recently proposed empirical modification of MCT in which memory functions are calculated using effective structure factors at rescaled number densities, the scheme is able to model the collective dynamics over the entire accessible time and wave-vector range and predicts the volume-fraction-dependence of long-time self-diffusion coefficients and the zero-shear viscosity quantitatively. This highlights the potential of MCT as a practical tool for the quantitative analysis and prediction of experimental observations.

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocityv0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case ofv0polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials

A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.

Emerging exotic compositional order on approaching low-temperature equilibrium glasses

The ultimate fate of a glass former upon cooling has been a fundamental problem in condensed matter physics and materials science since Kauzmann. Recently, this problem has been challenged by a model with an extraordinary glass-forming ability effectively free from crystallisation and phase separation, two well-known fates of most glass formers, combined with a particle-size swap method. Thus, this system is expected to approach the ideal glass state if it exists. However, we discover exotic compositional order as the coexistence of space-spanning network-like structures formed by small-large particle connections and patches formed by medium-size particles at low temperatures. Therefore, the glass transition is accompanied unexpectedly by exotic compositional ordering inaccessible through ordinary structural or thermodynamic characterisations. Such exotic compositional ordering is found to have an unusual impact on structural relaxation dynamics. Our study thus raises fundamental questions concerning the role of unconventional structural ordering in understanding glass transition.

Structure ordering and glass transition in size-asymmetric ternary mixtures of hard spheres: Variation from fragile to strong glasses

We investigate the structure and activated dynamics of a binary mixture of colloidal particles dispersed in a solvent of much smaller-sized particles. The solvent degrees of freedom are traced out from the grand partition function of the colloid-solvent mixture which reduces the system from ternary to effective binary mixture of colloidal particles. In the effective binary mixture colloidal particles interact via effective potential that consists of bare potential plus the solvent-induced interaction. Expressions for the effective potentials and pair correlation functions are derived. We used the result of pair correlation functions to determine the number of particles in a cooperatively reorganizing cluster (CRC) in which localized particles form "long-lived" nonchemical bonds with the central particle. For an event of relaxation to take place these bonds have to reorganize irreversibly, the energy involved in the processes is the effective activation energy of relaxation. Results are reported for hard sphere colloidal particles dispersed in a solvent of hard sphere particles. Our results show that the concentration of solvent can be used as a control parameter to fine-tune the microscopic structural ordering and the size of CRC that governs the glassy dynamics. We show that a small variation in the concentration of solvent creates a bigger change in the kinetic fragility which highlights a wide variation in behavior, ranging from fragile to strong glasses. We conclude that the CRC which is determined from the static pair correlation function and the fluctuations embedded in the system is probably the sole player in the physics of glass transition.

Sedimentation path theory for mass-polydisperse colloidal systems

Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here the sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between gravity and polydispersity on sedimentation experiments. Since the theory can be applied to any parent distribution of buoyant masses, it can also be used to study the sedimentation of monodisperse colloidal systems. We find that mass-polydispersity has a strong influence in colloidal systems near density matching for which the bare density of the colloidal particles equals the solvent density. To illustrate the theory, we study crystallization in sedimentation-diffusion-equilibrium of a suspension of mass-polydisperse hard spheres.

Choice of diameters in a polydisperse model glassformer: Deterministic or stochastic?

In particle-based computer simulations of polydisperse glassforming systems, the particle diameters σ=σ_{1},⋯,σ_{N} of a system with N particles are chosen with the intention to approximate a desired distribution density f with the corresponding histogram. One method to accomplish this is to draw each diameter randomly and independently from the density f. We refer to this stochastic scheme as model S. Alternatively, one can apply a deterministic method, assigning an appropriate set of N values to the diameters. We refer to this method as model D. We show that, for sample-to-sample fluctuations, especially for the glassy dynamics at low temperatures, it matters whether one chooses model S or model D. Using molecular dynamics computer simulations, we investigate a three-dimensional polydisperse nonadditive soft-sphere system with f(s)∼s^{-3}. The swap Monte Carlo method is employed to obtain equilibrated samples at very low temperatures. We show that for model S the sample-to-sample fluctuations due to the quenched disorder imposed by the diameters σ can be explained by an effective packing fraction. Dynamic susceptibilities in model S can be split into two terms: one that is of thermal nature and can be identified with the susceptibility of model D, and another one originating from the disorder in σ. At low temperatures the latter contribution is the dominating term in the dynamic susceptibility. Our study clarifies the pros and cons of the use of models S and D in practice.

Deep learning potential of mean force between polymer grafted nanoparticles

Grafting polymer chains on the surfaces of nanoparticles is a well-known route to control their self-assembly and distribution in a polymer matrix. A wide variety of self-assembled structures are achieved by changing the grafting patterns on the surface of an individual nanoparticle. However, an accurate estimation of the effective potential of mean force between a pair of grafted nanoparticles that determines their assembly and distribution in a polymer matrix is an outstanding challenge in nanoscience. We address this problem via deep learning. As a proof of concept, here we report a deep learning framework that learns the interaction between a pair of single-chain grafted spherical nanoparticles from their molecular dynamics trajectory. Subsequently, we carry out the deep learning potential of mean force-based molecular simulation that predicts the self-assembly of a large number of single-chain grafted nanoparticles into various anisotropic superstructures, including percolating networks and bilayers depending on the nanoparticle concentration in three-dimensions. The deep learning potential of mean force-predicted self-assembled superstructures are consistent with the actual superstructures of single-chain polymer grafted spherical nanoparticles. This deep learning framework is very generic and extensible to more complex systems including multiple-chain grafted nanoparticles. We expect that this deep learning approach will accelerate the characterization and prediction of the self-assembly and phase behaviour of polymer-grafted and unfunctionalized nanoparticles in free space or a polymer matrix.

Densest packings from size segregation of particles in geometric confinement

A correlation between density maximization and size segregation for packings of polydisperse particles in geometric confinement has been discovered, through the derivation of a general solution for the densest-packed zigzag arrangements of polydisperse particles. This solution is a size-graded structure in which the larger a particle the closer it is located to either end of the system, such that the smaller particles in the interior are encapsulated by the larger ones away from it. Any pair of different-sized adjacent particles is a grain-boundary-like configuration that reduces the overall packing efficiency of the system, and this solution corresponds to a minimization of excess-volume contributions from grain-boundary-like configurations of different-sized particles as a result of the clustering of equal- or like-sized particles. Our findings provide new insights into how structural order of polydisperse particles emerges in confined settings.

Rheological response of a glass-forming liquid having large bidispersity

Using extensive numerical simulations, we investigate the flow behaviour of a model glass-forming binary mixture whose constituent particles have a large size ratio. The rheological response to applied shear is studied in the regime where the larger species are spatially predominant. We demonstrate that the macroscopic rigidity that emerges with increasing density occurs in the regime where the larger species undergo a glass transition while the smaller species continue to be highly diffusive. We analyse the interplay between the timescale imposed by the shear and the quiescent relaxation dynamics of the two species to provide a microscopic insight into the observed rheological response. Finally, by tuning the composition of the mixture, we illustrate that the systematic insertion of the smaller particles affects the rheology by lowering of viscosity of the system.

Monodisperse patchy particle glass former

Glass formers are characterized by their ability to avoid crystallization. As monodisperse systems tend to rapidly crystallize, the most common glass formers in simulations are systems composed of mixtures of particles with different sizes. Here, we make use of the ability of patchy particles to change their local structure to propose them as monodisperse glass formers. We explore monodisperse systems with two patch geometries: a 12-patch geometry that enhances the formation of icosahedral clusters and an 8-patch geometry that does not appear to strongly favor any particular local structure. We show that both geometries avoid crystallization and present glassy features at low temperatures. However, the 8-patch geometry better preserves the structure of a simple liquid at a wide range of temperatures and packing fractions, making it a good candidate for a monodisperse glass former.

Glassy Behavior of Sticky Spheres: What Lies beyond Experimental Timescales?

We use the swap Monte Carlo algorithm to analyze the glassy behavior of sticky spheres in equilibrium conditions at densities where conventional simulations and experiments fail to reach equilibrium, beyond predicted phase transitions and dynamic singularities. We demonstrate the existence of a unique ergodic region comprising all the distinct phases previously reported, except for a phase-separated region at strong adhesion. All structural and dynamic observables evolve gradually within this ergodic region, the physics evolving smoothly from well-known hard sphere glassy behavior at small adhesions and large densities, to a more complex glassy regime characterized by unusually broad distributions of relaxation timescales and length scales at large adhesions.

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

"Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics

Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.

Entropic long-range ordering in an adsorption-desorption model

We examine a two-dimensional nonequilibrium lattice model where particles adsorb at empty sites and desorb when the number of neighboring particles is greater than a given threshold. In a certain range of parameters the model exhibits entropic ordering similar to some hard-core systems. However, contrary to hard-core systems, on increasing the density of particles the ordering is destroyed. In the heterogenous version of our model, a regime with slow dynamics appears that might indicate formation of some kind of glassy structures.

Diffusion Decoupling in Binary Colloidal Systems Observed with Contrast Variation Multispeckle Diffusing Wave Spectroscopy

In the study of colloidal glasses, crystallization is often suppressed by leveraging size polydispersity, ranging from systems where particle sizes exhibit a continuous distribution to systems composed of particles of two or more distinct sizes. The effects of the disparities in size of the particles on the colloidal glass transition are not yet completely understood. Especially, the question of the existence of a decoupled glass transition between the large and small population remains. In order to measure colloidal dynamics on very long time scales and to disentangle the dynamics of the two populations, we employ contrast variation multispeckle diffusing wave spectroscopy. With this method, we aim to analyze the effect of size ratio, a = rPS/ rpNIPAM, on particle dynamics near the glass transition of a binary colloidal system. We find that both for long-time (α-) and short-time (β-) relaxation, the dynamics of the small particles either completely decouple from the large ones ( a = 0.2), moving freely through a glassy matrix, or are identical to the dynamics of the larger-sized population ( a = 0.37 and 1.44). For a size ratio of 0.37, we find a single-glass transition for both particle populations. The postulated double-glass transition in simulations and theory is not observed.

Structure Dominates Localization of Tracers within Aging Nanoparticle Glasses

We investigate the transport and localization of tracer probes in a glassy matrix as a function of relative size using dynamic X-ray scattering experiments and molecular dynamics simulations. The quiescent relaxations of tracer particles evolve with increasing waiting time, t_w. The corresponding relaxation times increase exponentially at small t_w and then transition to a power-law behavior at longer t_w. As tracer size decreases, the aging behavior weakens and the particles become less localized within the matrix until they delocalize at a critical size ratio δ₀ ≈ 0.38. Localization does not vary with sample age even as the relaxations slow by approximately an order of magnitude, suggesting that matrix structure controls tracer localization.

Super-Arrhenius behavior of molecular glass formers

A theory is developed to calculate values of the potential-energy barriers to structural relaxation in molecular glass formers from the data of static pair-correlation function. The barrier height is shown to increase due to an increase in the number of "stable bonds" a particle forms with its neighbors and the energy of each bond as liquids move deeper into the supercooled (supercompressed) region. We present results for a system of hard spheres and compare calculated values of the structural relaxation time with experimental and simulation results.

Dynamics of liquid-liquid phase separation of wheat gliadins

During wheat seeds development, storage proteins are synthetized and subsequently form dense protein phases, also called Protein Bodies (PBs). The mechanisms of PBs formation and the supramolecular assembly of storage proteins in PBs remain unclear. In particular, there is an apparent contradiction between the low solubility in water of storage proteins and their high local dynamics in dense PBs. Here, we probe the interplay between short-range attraction and long-range repulsion of a wheat gliadin isolate by investigating the dynamics of liquid-liquid phase separation after temperature quench. We do so using time-resolved small angle light scattering, phase contrast microscopy and rheology. We show that gliadins undergo liquid-liquid phase separation through Nucleation and Growth or Spinodal Decomposition depending on the quench depth. They assemble into dense phases but remain in a liquid-like state over an extended range of temperatures and concentrations. The analysis of phase separation kinetics reveals that the attraction strength of gliadins is in the same order of magnitude as other proteins. We discuss the respective role of competing interactions, protein intrinsic disorder, hydration and polydispersity in promoting local dynamics and providing this liquid-like behavior despite attractive forces.

A geometrical criterion for glass transition in soft-sphere fluids

As glass-forming fluids become colder and denser, structural rearrangements become slow and eventually cease. For hard-sphere fluids, percolation of particles unable to change neighbors (T1-inactive particles) signals the glass transition. To investigate this geometrical criterion for mobility in soft-sphere systems, we simulate monodisperse fluids interacting with a generalized Weeks-Chandler-Andersen (WCA) potential in metastable equilibrium, using our previously developed crystal-avoiding method. We find that the vanishing diffusivity as the glass transition is approached can be described by a power law below the onset temperature of super-Arrhenius behavior. By mapping the soft spheres to hard spheres based on mean collision energy, we find that the diffusivity versus effective volume fraction curves collapse onto the hard-sphere curve for all systems studied. We find that the onset of super-Arrhenius behavior and the MCT dynamic glass transition correlate well with temperature when the T1-inactive particles form clusters of two particles on average and when the T1-inactive clusters percolate the entire system, respectively. Our findings provide new insight into the structural origin of glassy dynamics.

Local order and crystallization of dense polydisperse hard spheres

Computer simulations give precious insight into the microscopic behavior of supercooled liquids and glasses, but their typical time scales are orders of magnitude shorter than the experimentally relevant ones. We recently closed this gap for a class of models of size polydisperse fluids, which we successfully equilibrate beyond laboratory time scales by means of the swap Monte Carlo algorithm. In this contribution, we study the interplay between compositional and geometric local orders in a model of polydisperse hard spheres equilibrated with this algorithm. Local compositional order has a weak state dependence, while local geometric order associated to icosahedral arrangements grows more markedly but only at very high density. We quantify the correlation lengths and the degree of sphericity associated to icosahedral structures and compare these results to those for the Wahnström Lennard-Jones mixture. Finally, we analyze the structure of very dense samples that partially crystallized following a pattern incompatible with conventional fractionation scenarios. The crystal structure has the symmetry of aluminum diboride and involves a subset of small and large particles with size ratio approximately equal to 0.5.

Domain size polydispersity effects on the structural and dynamical properties in lipid monolayers with phase coexistence

In lipid monolayers with phase coexistence, domains of the liquid-condensed phase always present size polydispersity. However, very few theoretical works consider size distribution effects on the monolayer properties. Because of the difference in surface densities, domains have excess dipolar density with respect to the surrounding liquid expanded phase, originating a dipolar inter-domain interaction. This interaction depends on the domain area, and hence the presence of a domain size distribution is associated with interaction polydispersity. Inter-domain interactions are fundamental to understanding the structure and dynamics of the monolayer. For this reason, it is expected that polydispersity significantly alters monolayer properties. By means of Brownian dynamics simulations, we study the radial distribution function (RDF), the average mean square displacement and the average time-dependent self-diffusion coefficient, D(t), of lipid monolayers with normally distributed size domains. For this purpose, we vary the relevant system parameters, polydispersity and interaction strength, within a range of experimental interest. We also analyze the consequences of using a monodisperse model to determine the interaction strength from an experimental RDF. We find that polydispersity strongly affects the value of the interaction strength, which is greatly underestimated if polydispersity is not considered. However, within a certain range of parameters, the RDF obtained from a polydisperse model can be well approximated by that of a monodisperse model, by suitably fitting the interaction strength, even for 40% polydispersities. For small interaction strengths or small polydispersities, the polydisperse systems obtained from fitting the experimental RDF have an average mean square displacement and D(t) in good agreement with that of the monodisperse system.

Different scenarios of dynamic coupling in glassy colloidal mixtures

The composition of mixtures determines the mechanism of glass formation and dynamic coupling of different species.

In Silico Synthesis of Microgel Particles

Microgels are colloidal-scale particles individually made of cross-linked polymer networks that can swell and deswell in response to external stimuli, such as changes to temperature or pH. Despite a large amount of experimental activities on microgels, a proper theoretical description based on individual particle properties is still missing due to the complexity of the particles. To go one step further, here we propose a novel methodology to assemble realistic microgel particles in silico. We exploit the self-assembly of a binary mixture composed of tetravalent (cross-linkers) and bivalent (monomer beads) patchy particles under spherical confinement in order to produce fully bonded networks. The resulting structure is then used to generate the initial microgel configuration, which is subsequently simulated with a bead-spring model complemented by a temperature-induced hydrophobic attraction. To validate our assembly protocol, we focus on a small microgel test case and show that we can reproduce the experimental swelling curve by appropriately tuning the confining sphere radius, something that would not be possible with less sophisticated assembly methodologies, e.g., in the case of networks generated from an underlying crystal structure. We further investigate the structure (in reciprocal and real space) and the swelling curves of microgels as a function of temperature, finding that our results are well described by the widely used fuzzy sphere model. This is a first step toward a realistic modeling of microgel particles, which will pave the way for a careful assessment of their elastic properties and effective interactions.

Dramatic slowing of compositional relaxations in the approach to the glass transition for a bimodal colloidal suspension

Molecular dynamics simulation was used to study a model colloidal suspension with two species of slightly different sized colloidal particles in an explicit solvent. In this work we calculated the four interdiffusion coefficients for the ternary system, which were then used to calculate the decay coefficients D_{±} of the two independent diffusive modes. We found that the slower D_{-} decay mode, which is associated with the system's ability to undergo compositional changes, was responsible for the long-time decay in the intermediate scattering function. We also found that a decrease in D_{-} to negligible values at a packing fraction of Φ_{g}=0.592 resulted in an extreme slow-down in the long-time decay of the intermediate scattering function often associated with the glass transition. Above Φ_{g}, the system formed a long-lived metastable state that did not relax to its equilibrium crystal state within the simulation time window. We concluded that the inhibition of crystallization was caused by the inability of the quenched fluid to undergo the compositional changes needed for the formation of the equilibrium crystal.

Size-Dependent Localization in Polydisperse Colloidal Glasses

We have investigated concentrated suspensions of polydisperse hard spheres and have determined the dynamics and sizes of individual particles using confocal microscopy. With increasing concentration, the dynamics of the small and large particles start to differ. The large particles exhibit slower dynamics and stronger localization. Moreover, as the particle size increases, the local volume fraction ϕ_{loc} also increases. In the glass state, the localization length significantly decreases beyond ϕ_{loc}≈0.67. This suggests a link between local crowding and dynamical heterogeneities. However dynamical arrest of subpopulations seems not directly linked to a large value of ϕ_{loc}, indicating the importance of collective effects.

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Strong theoretical evidence shows that dense colloidal mixtures phase-separate in two stages and the denser phase contains long-lived composition heterogeneities.

Structural entropy of glassy systems from graph isomorphism

Configurational entropy plays a central role in thermodynamic scenarios of the glass transition. As a measure of the number of basins in the potential energy landscape, configurational entropy for a glass-forming liquid can be evaluated by explicitly counting distinct inherent structures. In this work, we propose a graph-theory based method to examine local structure and obtain the corresponding entropy of hard-particle systems. Voronoi diagrams of associated clusters are classified using a graph isomorphism algorithm. The statistics of these clusters reveal structural motifs such as icosahedron-like order, and also allow us to calculate the structural entropy SG. We find the structural entropy of an n-particle subsystem grows linearly with n. Thus the structural entropy per particle can be obtained from the slope dSG/dn. Our results are consistent with previous values for configurational entropy obtained via thermodynamic integration. Structural entropies per particle are measured for hard-disk and hard-sphere polydisperse systems, and extrapolated for monodisperse hard disks, all of which are nonzero at the dynamic glass transition.

Dynamics of highly polydisperse colloidal suspensions as a model system for bacterial cytoplasm

There are various kinds of macromolecules in bacterial cell cytoplasm. The size polydispersity of the macromolecules is so significant that the crystallization and the phase separation could be suppressed, thus stabilizing the liquid state of bacterial cytoplasm. On the other hand, recent experiments suggested that the macromolecules in bacterial cytoplasm should exhibit glassy dynamics, which should be also affected significantly by the size polydispersity of the macromolecules. In this work, we investigate the anomalous and slow dynamics of highly polydisperse colloidal suspensions, of which size distribution is chosen to mimic Escherichia coli cytoplasm. We find from our Langevin dynamics simulations that the diffusion coefficient (D_{tot}) and the displacement distribution functions (P(r,t)) averaged over all colloids of different sizes do not show anomalous and glassy dynamic behaviors until the system volume fraction ϕ is increased up to 0.82. This indicates that the intrinsic polydispersity of bacterial cytoplasm should suppress the glass transition and help maintain the liquid state of the cytoplasm. On the other hand, colloids of each kind show totally different dynamic behaviors depending on their size. The dynamics of colloids of different size becomes non-Gaussian at a different range of ϕ, which suggests that a multistep glass transition should occur. The largest colloids undergo the glass transition at ϕ=0.65, while the glass transition does not occur for smaller colloids in our simulations even at the highest value of ϕ. We also investigate the distribution (P(θ,t)) of the relative angles of displacement for macromolecules and find that macromolecules undergo directionally correlated motions in a sufficiently dense system.

Discontinuous nature of the repulsive-to-attractive colloidal glass transition

In purely repulsive colloidal systems a glass transition can be reached by increasing the particle volume fraction beyond a certain threshold. The resulting glassy state is governed by configurational cages which confine particles and restrict their motion. A colloidal glass may also be formed by inducing attractive interactions between the particles. When attraction is turned on in a repulsive colloidal glass a re-entrant solidification ensues. Initially, the repulsive glass melts as free volume in the system increases. As the attraction strength is increased further, this weakened configurational glass gives way to an attractive glass in which motion is hindered by the formation of physical bonds between neighboring particles. In this paper, we study the transition from repulsive-to-attractive glasses using three-dimensional imaging at the single-particle level. We show how the onset of cage weakening and bond formation is signalled by subtle changes in local structure. We then demonstrate the discontinuous nature of the solid-solid transition, which is marked by a critical onset at a threshold bonding energy. Finally, we highlight how the interplay between bonding and caging leads to complex and heterogeneous dynamics at the microscale.

Static lengths in glass-forming monodisperse hard-sphere fluids from periodic array pinning

We explore the static length in glass-forming hard-sphere liquids revealed by the response of dynamical properties (diffusion coefficient D and α relaxation time τα) to a regular array of pinned particles. By assuming a universal scaling form, we find data can be excellently collapsed onto a master curve, from which relative length scales can be extracted. By exploiting a crystal-avoiding simulation method that suppresses crystallization while preserving dynamics, we can study monodisperse as well as polydisperse systems. The static length obtained from dynamical property Q (τα and D) scales as log Q ∼ ξ, with ψ ≈ 1.

How do polydisperse repulsive colloids crystallize?

A modified version of the Gibbs-ensemble Monte-Carlo method reveals how polydisperse charged colloidal particles can build complex colloidal crystals. It provides general rules that are applicable to this fractionated crystallization that stems from size segregation. It explains the spontaneous formation of complex crystals with very large unit-cells in suspensions of nanoparticles with a broad size distribution.

Gelation in mixtures of polymers and bidisperse colloids

We investigated the effects of varying the volume fraction of large particles (r) on the linear rheology and microstructure of mixtures of polymers and bidisperse colloids, in which the ratio of the small and large particle diameters was α=0.31 or α=0.45. Suspensions formulated at a total volume fraction of ϕ_{T}=0.15 and a constant concentration of polymer in the free volume c/c^{*}≈0.7 contained solid-like gels for small r and fluids or fluids of clusters at large r. The solid-like rheology and microstructure of these suspensions changed little with r when r was small, and fluidized only when r>0.8. By contrast, dense suspensions with ϕ_{T}=0.40 and α=0.31 contained solid-like gels at all concentrations of large particles and exhibited only modest rheological and microstructural changes upon varying the volume fraction of large particles. These results suggest that the effect of particle-size dispersity on the properties of colloid-polymer mixtures are asymmetric in particle size and are most pronounced near a gelation boundary.

Convective Cage Release in Model Colloidal Glasses

The mechanism of flow in glassy materials is interrogated using mechanical spectroscopy applied to model nearly hard sphere colloidal glasses during flow. Superimposing a small amplitude oscillatory motion orthogonal onto steady shear flow makes it possible to directly evaluate the effect of a steady state flow on the out-of-cage (α) relaxation as well as the in-cage motions. To this end, the crossover frequency deduced from the viscoelastic spectra is used as a direct measure of the inverse microstructural relaxation time, during flow. The latter is found to scale linearly with the rate of deformation. The microscopic mechanism of flow can then be identified as a convective cage release. Further insights are provided when the viscoelastic spectra at different shear rates are shifted to scale the alpha relaxation and produce a strain rate-orthogonal frequency superposition, the colloidal analogue of time temperature superposition in polymers with the flow strength playing the role of temperature. Whereas the scaling works well for the α relaxation, deviations are observed both at low and high frequencies. Brownian dynamics simulations point to the origins of these deviations; at high frequencies these are due to the deformation of the cages which slows down the short-time diffusion, while at low frequency, deviations are most probably caused by some mild hydroclustering.

T1 process and dynamics in glass-forming hard-sphere liquids

To study the relationship between dynamics and structure in a glass-forming liquid, we introduce a purely geometric criterion for locally mobile particles in a dense hard-sphere fluid: namely, "T1-active" particles, which can gain or lose at least one Voronoi neighbor by moving within their free volume with other particles fixed. We obtain geometrical and dynamical properties for monodisperse hard-sphere fluids with 0.40 < ϕ < 0.64 using a "crystal-avoiding" MD simulation that effectively suppresses crystallization without altering the dynamics. We find that the fraction of T1-active particles vanishes at random close packing, while the percolation threshold of T1-inactive particles is essentially identical to the commonly identified hard-sphere glass transition, ϕg ≈ 0.585.