Mechanical properties of a model of attractive colloidal solutions

Interparticle interaction-dependent jamming in colloids: insights into glass transition and morphology modulation during rapid evaporation-induced assembly

Understanding the role of interparticle interactions in jamming phenomena is essential for gaining insights into the intriguing glass transition behavior observed in atomic and molecular systems. In this study, we investigate the jamming behavior of colloids with tunable interparticle interactions during evaporation-induced assembly (EIA). By manipulating the interaction among charged colloids using cationic polyethyleneimine (PEI) through electro-sorption and subsequent free polymer induced repulsion, we observe distinct jamming behavior in silica colloids during EIA, depending on the interparticle interactions. Silica colloids with strong repulsive interactions exhibit a repulsive colloidal glass state with a volume fraction of silica colloids in supraparticle ϕ ∼ 0.70. On the other hand, PEI-mediated attractive interactions among silica colloids lead to an attractive colloidal glass phase with a significantly lower ϕ ∼ 0.43. Free polymer induced repulsion of colloids at higher PEI concentration once again results in a repulsive glassy state with ϕ ∼ 0.61. Furthermore, we revealed that interparticle interactions not only influence the jamming behavior but also play a significant role in shaping the morphology of self-assembled structures during EIA, and the assembled structure undergoes a morphological reentrant transition from a doughnut-like shape to a spherical form and again back to a doughnut-like configuration. Jamming-dependent evolution of micropores and dynamics of the confined PEI have been probed using positron annihilation lifetime spectroscopy (PALS) and broadband dielectric spectroscopy (BDS). PALS reveals distinct variations in the micropores of the supraparticles with different PEI loadings, confirming the impact of jamming on the evolution of the micropores within the supraparticles. BDS measurements uncover non-monotonic dynamics of PEI molecules confined in the evolved pore network. It is revealed that the reentrant jamming behavior of colloids, modulated by PEI, holds profound significance for the long-term stability of supraparticles.

The Hydrophobic Effect Studied by Using Interacting Colloidal Suspensions

Interactions between nanoparticles (NPs) determine their self-organization and dynamic processes. In these systems, a quantitative description of the interparticle forces is complicated by the presence of the hydrophobic effect (HE), treatable only qualitatively, and due to the competition between the hydrophobic and hydrophilic forces. Recently, instead, a sort of crossover of HE from hydrophilic to hydrophobic has been experimentally observed on a local scale, by increasing the temperature, in pure confined water and studying the occurrence of this crossover in different water-methanol solutions. Starting from these results, we then considered the idea of studying this process in different nanoparticle solutions. By using photon correlation spectroscopy (PCS) experiments on dendrimer with OH terminal groups (dissolved in water and methanol, respectively), we show the existence of this hydrophobic-hydrophilic crossover with a well defined temperature and nanoparticle volume fraction dependence. In this frame, we have used the mode coupling theory extended model to evaluate the measured time-dependent density correlation functions (ISFs). In this context we will, therefore, show how the measured spectra are strongly dependent on the specificity of the interactions between the particles in solution. The observed transition demonstrates that just the HE, depending sensitively on the system thermodynamics, determines the hydrophobic and hydrophilic interaction properties of the studied nanostructures surface.

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.

Designing active particles for colloidal microstructure manipulation via strain field alchemy

Defects in a crystal can exert forces on each other via strain field interactions. Here we explore the strain-field-mediated interaction between an anisotropic interstitial probe particle and dislocation microstructures in a colloidal crystal composed of particles interacting via steep repulsive isotropic potentials. We optimize the interaction between probe particle and dislocation with the anisotropic shape of the probe as a free parameter. Such alchemical optimization is typically carried out upon the explicitly defined interaction potential parameters; instead, we optimize the strain field of the probe and then map back to particle shape. We distinguish this tactic from other alchemical methods as 'strain alchemy'. We report several findings: (1) a robust mapping exists between strain field calculation methods (the method of eigenstrains) and strains produced by an anisotropic interstitial, (2) optimization of strain field interactions in the strain domain permits rapid evaluation of candidate shapes for interstitials, (3) interstitial mobility barriers can be estimated from the strain field, and (4) strongly interacting and highly mobile interstitial particles can be found that are capable of driving dislocation glide with applied force. Active particle-induced dislocation glide is examined for the cases of edge dislocation arrays and extrinsic dislocation loops. For edge dislocations, particle geometries of alternating large and small diameter segments were found to interact most strongly. For dislocation loops, interstitials with a single small radius segment surrounded by large radius segments are best.

α-relaxation, shear viscosity, and elastic moduli of hard-particle fluids from a mode-coupling theory with a retarded vertex

The recently proposed modification of the mode-coupling theory (MCT) in which the static structure used in the vertex is computed at a lower density than the actual one is tested on several dynamics-related properties. The predictions from this modified version of MCT calibrated on the one-component hard-sphere fluid are found in very good agreement with simulation data for one-component and binary hard-sphere fluids. They are also relevant for the stress moduli for models with attractive tails beyond the hard core. The clear improvement observed on several properties should give a new impetus to the use of MCT as a quantitative tool.

Analyses of kinetic glass transition in short-range attractive colloids based on time-convolutionless mode-coupling theory

For short-range attractive colloids, the phase diagram of the kinetic glass transition is studied by time-convolutionless mode-coupling theory (TMCT). Using numerical calculations, TMCT is shown to recover all the remarkable features predicted by the mode-coupling theory for attractive colloids: the glass-liquid-glass reentrant, the glass-glass transition, and the higher-order singularities. It is also demonstrated through the comparisons with the results of molecular dynamics for the binary attractive colloids that TMCT improves the critical values of the volume fraction. In addition, a schematic model of three control parameters is investigated analytically. It is thus confirmed that TMCT can describe the glass-glass transition and higher-order singularities even in such a schematic model.

Bond lifetime and diffusion coefficient in colloids with short-range interactions

We use molecular dynamics simulations to study the influence of short-range structures in the interaction potential between hard-sphere-like colloidal particles. Starting from model potentials and effective potentials in binary mixtures computed from the Ornstein-Zernike equations, we investigate the influence of the range and strength of a possible tail beyond the usual core repulsion or the presence of repulsive barriers. The diffusion coefficient and mean "bond" lifetimes are used as indicators of the effect of this structure on the dynamics. The existence of correlations between the variations of these quantities with the physical parameters is discussed to assess the interpretation of dynamics slowing down in terms of long-lived bonds. We also discuss the question of a universal behaviour determined by the second virial coefficient B ((2)) and the interplay of attraction and repulsion. While the diffusion coefficient follows the B ((2)) law for purely attractive tails, this is no longer true in the presence of repulsive barriers. Furthermore, the bond lifetime shows a dependence on the physical parameters that differs from that of the diffusion coefficient. This raises the question of the precise role of bonds on the dynamics slowing down in colloidal gels.

Aggregation dynamics, structure, and mechanical properties of bigels

Recently we have introduced bigels, inter-penetrating gels made of two different colloidal species. Even if particles with simple short-range isotropic potential are employed, the selective interactions enable the tunability of the self-assembly, leading to the formation of complex structures. In the present paper, we explore the non-equilibrium dynamics and the phenomenology underlying the kinetic arrest under quench and the formation of bigels. We demonstrate that the peculiar bigel kinetics can be described through an arrested spinodal decomposition driven by demixing of the colloidal species. The role played by the presence of a second colloidal species on the phase diagram, as expanded to account for the increased number of parameters, is clarified both via extensive numerical simulations and experiments. We provide details on the realisation of bigels, by means of DNA-coated colloids (DNACCs), and the consequent imaging techniques. Moreover we evidence, by comparison with the usual one-component gel formation, the emergence of controllable timescales in the aggregation of the bigels, whose final stages are also experimentally studied to provide morphological details. Finally, we use numerical models to simulate the bigel response to mechanical strain, highlighting how such a new material can bear significantly higher stress compared to the usual one-component gel. We conclude by discussing possible technological uses and by providing insights on the viable research steps to undertake for more complex and yet tuneable multi-component colloidal systems.

Mode-coupling theory for the glass transition: test of the convolution approximation for short-range interactions

We reexamine the convolution approximation commonly used in the mode-coupling theory (MCT) of nonergodic states of classical fluids. This approximation concerns the static correlation functions used as input in the MCT treatment of the dynamics. Besides the hard-sphere model, we consider interaction potentials that present a short-range tail, either attractive or repulsive, beyond the hard core. By using accurate static correlation functions obtained from the fundamental measures functional for hard spheres, we show that the role of three-body direct correlations can be more significant than what is inferred from previous simple ansatzs for pure hard spheres. This may in particular impact the location of the glass transition line and the nonergodicity parameter.

A spherical model with directional interactions: II. Dynamics and landscape properties

We study a binary non-additive hard-sphere mixture with square well interactions only between dissimilar particles. An appropriate choice of the inter-particle potential parameters favors the formation of equilibrium structures with tetrahedral ordering (Zaccarelli et al 2007 J. Chem. Phys. 127 174501). By performing extensive event-driven molecular dynamics simulations, we monitor the dynamics of the system, locating the iso-diffusivity lines in the phase diagram, and discuss their location with respect to the gas-liquid phase separation. We observe the formation of an ideal gel which continuously crosses towards an attractive glass upon increasing the density. Moreover, we evaluate the statistical properties of the potential energy landscape for this model. We find that the configurational entropy, for densities within the optimal network-forming region, is finite even in the ground state and obeys a logarithmic dependence on the energy.

Elasticity of arrested short-ranged attractive colloids: homogeneous and heterogeneous glasses

We evaluate the elasticity of arrested short-ranged attractive colloids by combining an analytically solvable elastic model with a hierarchical arrest scheme. This new approach allows us to discriminate the microscopic (primary particle-level) from the mesoscopic (cluster-level) contribution to the macroscopic shear modulus. The results quantitatively predict experimental data in a wide range of volume fractions and indicate in which cases the relevant contribution is due to mesoscopic structures. On this basis we propose that different arrested states of short-ranged attractive colloids can be meaningfully distinguished as homogeneous or heterogeneous colloidal glasses in terms of the length scale which controls their elastic behavior.

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.

Third-order thermodynamic perturbation theory for effective potentials that model complex fluids

We have performed Monte Carlo simulations to obtain the thermodynamic properties of fluids with two kinds of hard-core plus attractive-tail or oscillatory potentials. One of them is the square-well potential with small well width. The other is a model potential with oscillatory and decaying tail. Both model potentials are suitable for modeling the effective potential arising in complex fluids and fluid mixtures with extremely-large-size asymmetry, as is the case of the solvent-induced depletion interactions in colloidal dispersions. For the former potential, the compressibility factor, the excess energy, the constant-volume excess heat capacity, and the chemical potential have been obtained. For the second model potential only the first two of these quantities have been obtained. The simulations cover the whole density range for the fluid phase and several temperatures. These simulation data have been used to test the performance of a third-order thermodynamic perturbation theory (TPT) recently developed by one of us [S. Zhou, Phys. Rev. E 74, 031119 (2006)] as compared with the well-known second-order TPT based on the macroscopic compressibility approximation due to Barker and Henderson. It is found that the first of these theories provides much better accuracy than the second one for all thermodynamic properties analyzed for the two effective potential models.

Glass-liquid-glass reentrance in mono-component colloidal dispersions

The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics is employed to describe the ergodic-non-ergodic transition in model mono-disperse colloidal dispersions whose particles interact through hard-sphere plus short-ranged attractive forces. The ergodic-non-ergodic phase diagram in the temperature-concentration state space is determined for the hard-sphere plus attractive Yukawa model within the mean spherical approximation for the static structure factor by solving a remarkably simple equation for the localization length of the colloidal particles. Finite real values of this property signals non-ergodicity and determines the non-ergodic parameters f(k) and f(s)(k). The resulting phase diagram for this system, which involves the existence of reentrant (repulsive and attractive) glass states, is compared with the corresponding prediction of mode coupling theory. Although both theories coincide in the general features of this phase diagram, there are also clear qualitative differences. One of the most relevant is the SCGLE prediction that the ergodic-attractive glass transition does not preempt the gas-liquid phase transition, but always intersects the corresponding spinodal curve on its high-concentration side. We also calculate the ergodic-non-ergodic phase diagram for the sticky hard-sphere model to illustrate the dependence of the predicted SCGLE dynamic phase diagram on the choice of one important constituent element of the SCGLE theory.

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.

Equilibrium and glassy states of the Asakura-Oosawa and binary hard sphere mixtures: effective fluid approach

Motivated by recent experimental results on model binary colloidal mixtures, especially for the glass transition, we investigate the phase diagram of two models of asymmetric binary mixtures: the hard sphere and the Asakura-Oosawa mixtures. This includes the binodals and the glass transition line, computed in the effective one-component representation using the corresponding potentials of mean force at infinite dilution. The reference hypernetted chain approximation is used for computing the static properties and the glass transition line is computed in the mode coupling approximation. The similarities and the differences between the two models are discussed for different size ratios. It is shown that while both models follow a universal behavior at large asymmetry, the hard sphere mixture model leads to more original results at moderate size ratio. These results show that a modeling beyond generic effective potentials might be necessary for an appropriate description of the complete phase diagram.

Glass transition line in C60: a mode-coupling/molecular-dynamics study

We report a study of the mode-coupling theory (MCT) glass transition line for the Girifalco model of C60 fullerene. The equilibrium static structure factor of the model, the only required input for the MCT calculations, is provided by molecular dynamics simulations. The glass transition line develops inside the metastable liquid-solid coexistence region and extends down in temperature, terminating on the liquid side of the metastable portion of the liquid-vapor binodal. The vitrification locus does not show re-entrant behavior. A comparison with previous computer simulation estimates of the location of the glass line suggests that the theory accurately reproduces the shape of the arrest line in the density-temperature plane. The theoretical HNC and MHNC structure factors (and consequently the corresponding MCT glass line) compare well with the numerical counterpart. Our results confirm the conclusion drawn in previous works about the existence of a glassy phase for the fullerene model at issue.

Thermostatistical description of gas mixtures from space partitions

The new mathematical framework based on the free energy of pure classical fluids presented by Rohrmann [Physica A 347, 221 (2005)] is extended to multicomponent systems to determine thermodynamic and structural properties of chemically complex fluids. Presently, the theory focuses on D-dimensional mixtures in the low-density limit (packing factor eta<0.01). The formalism combines the free-energy minimization technique with space partitions that assign an available volume v to each particle. v is related to the closeness of the nearest neighbor and provides a useful tool to evaluate the perturbations experimented by particles in a fluid. The theory shows a close relationship between statistical geometry and statistical mechanics. New, unconventional thermodynamic variables and mathematical identities are derived as a result of the space division. Thermodynamic potentials mu(il), conjugate variable of the populations N(il) of particles class i with the nearest neighbors of class l are defined and their relationships with the usual chemical potentials mu(i) are established. Systems of hard spheres are treated as illustrative examples and their thermodynamics functions are derived analytically. The low-density expressions obtained agree nicely with those of scaled-particle theory and Percus-Yevick approximation. Several pair distribution functions are introduced and evaluated. Analytical expressions are also presented for hard spheres with attractive forces due to Kac-tails and square-well potentials. Finally, we derive general chemical equilibrium conditions.

Kinetic arrest and glass-glass transition in short-ranged attractive colloids

A thermally reversible repulsive hard-sphere to sticky-sphere transition was studied in a model colloidal system over a wide volume fraction range. The static microstructure was obtained from high resolution small angle x-ray scattering, the colloid dynamics was probed by dynamic x-ray and light scattering, and supplementary mechanical properties were derived from bulk rheology. At low concentration, the system shows features of gas-liquid type phase separation. The bulk phase separation is presumably interrupted by a gelation transition at the intermediate volume fraction range. At high volume fractions, fluid-attractive glass and repulsive glass-attractive glass transitions are observed. It is shown that the volume fraction of the particles can be reliably deduced from the absolute scattered intensity. The static structure factor is modeled in terms of an attractive square-well potential, using the leading order series expansion of Percus-Yevick approximation. The ensemble-averaged intermediate scattering function shows different levels of frozen components in the attractive and repulsive glassy states. The observed static and dynamic behavior are consistent with the predictions of a mode-coupling theory and numerical simulations for a square-well attractive system.

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.

Microstructure and rheology near an attractive colloidal glass transition

Microstructure and rheological properties of a thermally reversible short-ranged attractive colloidal system are studied in the vicinity of the attractive glass transition line. At high volume fractions, the static structure factor changes very little but the low frequency shear moduli varies over several orders of magnitude across the transition. From the frequency dependence of shear moduli, fluid-attractive glass and repulsive glass-attractive glass transitions are identified.

Gel to glass transition in simulation of a valence-limited colloidal system

We numerically study a simple model for thermoreversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures T. By studying a large region of T and packing fraction phi we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low phi and T. The former is rather vertical (phi controlled), while the latter is rather horizontal (T controlled) in the phi-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on phi, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in phi along low-T isotherms, seen most strikingly in the behavior of the nonergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.

Viscoelasticity of aqueous telechelic poly(ethylene oxide) solutions: relaxation and structure

We present a rheology study of associating polymers. The associating polymers are telechelic, composed of a water-soluble backbone (polyethylene oxide) terminated by hydrophobic moieties (C16H33). In aqueous solutions, these polymers self-assemble to form micellar structures. Above a critical concentration, approximately 1 wt % of polymer, bridging between the micelles forms a transient network. Traditionally, the viscoelastic response of these polymeric solutions has been described using the Maxwell model. In this work we measure the viscoelastic properties over an extended frequency range (0.01-6000 Hz) using microrheology, and show that at high frequencies the rheology behaves as the square root of the oscillation frequency. To fit the data, we use a combination of the Maxwell model and the Rouse model. The Maxwell model accounts for the hydrophobic associations between the polymeric micelles, and the Rouse model accounts for the microscopic dynamics of the individual micelles.

Noncompact crystalline solids in the square-well potential

We reexamine the phase diagram of the square-well potential, using both theoretical and computer-simulation techniques, for not too short ranges of the potential. The phase diagram turns out to contain a variety of crystalline structures, both compact and, interestingly, also noncompact. The latter result from a large increase in negative energy when pairs of particles come at distances within the interaction range, which more than compensates the entropy loss associated with reduced packing. Transitions between these crystalline structures give rise to a surprisingly rich phase diagram.

Nonlinear elasticity and yielding of depletion gels

A microscopic activated barrier hopping theory of the viscoelasticity of colloidal glasses and gels has been generalized to treat the nonlinear rheological behavior of particle-polymer suspensions. The quiescent cage constraints and depletion bond strength are quantified using the polymer reference interaction site model theory of structure. External deformation (strain or stress) distorts the confining nonequilibrium free energy and reduces the barrier. The theory is specialized to study a limiting mechanical description of yielding and modulus softening in the absence of thermally induced barrier hopping. The yield stress and strain show a rich functional dependence on colloid volume fraction, polymer concentration, and polymer-colloid size asymmetry ratio. The yield stress collapses onto a master curve as a function of the polymer concentration scaled by its ideal mode-coupling gel boundary value, and sufficiently deep in the gel is of an effective power-law form with a universal exponent. A similar functional and scaling dependence of the yield stress on the volume fraction is found, but the apparent power-law exponent is nonuniversal and linearly correlated with the critical gel volume fraction. Stronger gels are generally, but not always, predicted to be more brittle in the strain mode of deformation. The theoretical calculations appear to be in accord with a broad range of observations.

Dynamic yielding, shear thinning, and stress rheology of polymer-particle suspensions and gels

The nonlinear rheological version of our barrier hopping theory for particle-polymer suspensions and gels has been employed to study the effect of steady shear and constant stress on the alpha relaxation time, yielding process, viscosity, and non-Newtonian flow curves. The role of particle volume fraction, polymer-particle size asymmetry ratio, and polymer concentration have been systematically explored. The dynamic yield stress decreases in a polymer-concentration- and volume-fraction-dependent manner that can be described as apparent power laws with effective exponents that monotonically increase with observation time. Stress- or shear-induced thinning of the viscosity becomes more abrupt with increasing magnitude of the quiescent viscosity. Flow curves show an intermediate shear rate dependence of an effective power-law form, becoming more solidlike with increasing depletion attraction. The influence of polymer concentration, particle volume fraction, and polymer-particle size asymmetry ratio on all properties is controlled to a first approximation by how far the system is from the gelation boundary of ideal mode-coupling theory (MCT). This emphasizes the importance of the MCT nonergodicity transition despite its ultimate destruction by activated barrier hopping processes. Comparison of the theoretical results with limited experimental studies is encouraging.

Molecular simulation study of the effect of pressure on the vapor-liquid interface of the square-well fluid

We examine a model system to study the effect of pressure on the surface tension of a vapor-liquid interface. The system is a two-component mixture of spheres interacting with the square-well (A-A) and hard-sphere (B-B) potentials and with unlike (A-B) interactions ranging (for different cases) from hard sphere to strongly attractive square well. The bulk-phase and interfacial properties are measured by molecular dynamics simulation for coexisting vapor-liquid phases for various mixture compositions, pressures, and temperatures. The variation of the surface tension with pressure compares well to values given by surface-excess formulas derived from thermodynamic considerations. We find that surface tension increases with pressure only for the case of an inert solute (hard-sphere A-B interactions) and that the presence of A-B attractions strongly promotes a decrease of surface tension with pressure. An examination of density and composition profiles is made to explain these effects in terms of surface-adsorption arguments.

Barrier hopping, viscous flow, and kinetic gelation in particle-polymer suspensions

The naive mode coupling-polymer reference interaction site model (MCT-PRISM) theory of gelation and elasticity of suspensions of hard sphere colloids or nanoparticles mixed with nonadsorbing polymers has been extended to treat the emergence of barriers, activated transport, and viscous flow. The barrier makes the dominant contribution to the single particle relaxation time and shear viscosity, and is a rich function of the depletion attraction strength via the polymer concentration, polymer-particle size asymmetry ratio, and particle volume fraction. The dependences of the barrier on these three system parameters can be accurately collapsed onto a single scaling variable, and the resultant master curve is well described by a power law. Nearly universal master curves are also constructed for the hopping or alpha relaxation time for system conditions not too close to the ideal MCT transition. Based on the calculated barrier hopping time, a theory for kinetic gel boundaries is proposed. The form and dependence on system parameters of the kinetic gel lines are qualitatively the same as obtained from prior ideal MCT-PRISM studies. The possible relevance of our results to the phenomenon of gravity-driven gel collapse is studied. The general approach can be extended to treat nonlinear viscoelasticity and rheology of polymer-colloid suspensions and gels.

Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths lambda-1 ranging from 0.1 to 1.0, in units of the diameter sigma of the particles. For each one of these widths, several densities rho and temperatures T in the ranges 0.1< or =rhosigma(3)< or =0.8 and T(c)(lambda) less or approximately T less or approximately 3T(c)(lambda), where T(c)(lambda) is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. 100, 3079 (1994); 100, 6665 (1994)] and the nonperturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. 101 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory works for long ranges and high densities.

Thermal vitrification in suspensions of soft colloids: molecular dynamics simulations and comparison with experiments

Dense suspensions of multiarm star polymers are known to develop liquidlike microstructure, which has been attributed to the similarities between high functionality stars and colloidal particles interacting via soft, long ranged potentials. Recent experimental studies reported a counterintuitive solidification of suspensions with f=128 , upon increase of the temperature in marginal solvents. We present our results from molecular dynamics simulations of dense suspensions of multiarm star polymers. Star polymers are modeled as "soft spheres" interacting via a theoretically developed potential of mean field. Our results show a transition towards a "glassy" state at a temperature very close to the one reported experimentally. The features of the transition are consistent with those of ideal glass transitions, as described by ideal mode coupling theory. Furthermore, our findings illustrate the road to vitrification for these soft-colloidal suspensions. Higher temperatures result in arm expansion that causes jamming and more than compensates for faster short time, temperature induced kinetics.

Glass-glass transition and new dynamical singularity points in an analytically solvable p-spin glasslike model

We introduce and analytically study a generalized p-spin glasslike model that captures some of the main features of attractive glasses, recently found by mode coupling investigations, such as a glass-glass transition line and dynamical singularity points characterized by a logarithmic time dependence of the relaxation. The model also displays features not predicted by the mode coupling scenario that could further describe the attractive glasses behavior, such as aging effects with new dynamical singularity points ruled by logarithmic laws or the presence of a glass spinodal line.

Effect of bond lifetime on the dynamics of a short-range attractive colloidal system

We perform molecular dynamics simulations of short-range attractive colloid particles modeled by a narrow (3% of the hard sphere diameter) square well potential of unit depth. We compare the dynamics of systems with the same thermodynamics but different bond lifetimes, by adding to the square well potential a thin barrier at the edge of the attractive well. For permanent bonds, the relaxation time tau diverges as the packing fraction phi approaches a threshold related to percolation, while for short-lived bonds, the phi dependence of tau is more typical of a glassy system. At intermediate bond lifetimes, the phi dependence of tau is driven by percolation at low phi , but then crosses over to glassy behavior at higher phi . We also study the wave vector dependence of the percolation dynamics.

Elasticity and clustering in concentrated depletion gels

X-ray scattering and rheology are employed to study the volume fraction dependence of the collective structure and elastic moduli of concentrated nanoparticle-polymer depletion gels. The nonequilibrium gel structure consists of locally densified nonfractal clusters and narrow random interfaces. The elastic moduli display a power law dependence on volume fraction with effective exponents that decrease with increasing depletion attraction strength. A microscopic theory that combines local structural information with a dynamic treatment of gelation is in good agreement with the observations.

Slow dynamics in gelation phenomena: from chemical gels to colloidal glasses

We here discuss the results of three-dimensional Monte Carlo simulations of a minimal lattice model for gelling systems. We focus on the dynamics investigated by means of the time autocorrelation function of the density fluctuations and the particle mean-square displacement. We start from the case of chemical gelation, i.e., with permanent bonds, and characterize the critical dynamics as determined by the formation of the percolating cluster, as actually observed in polymer gels. By opportunely introducing a finite bond lifetime tau(b), the dynamics displays relevant changes and eventually the onset of a glassy regime. This has been interpreted in terms of a crossover to dynamics more typical of colloidal systems and a connection between classical gelation and recent results on colloidal systems is suggested. By systematically comparing the results in the case of permanent bonds to finite bond lifetime, the crossover and the glassy regime can be understood in terms of effective clusters.

Microscopic theory of gelation and elasticity in polymer–particle suspensions

A simplified mode-coupling theory (MCT) of ergodic-nonergodic transitions, in conjunction with an accurate two-component polymer reference interaction site model (PRISM) theory for equilibrium structural correlations, has been systematically applied to investigate gelation, localization, and elasticity of flexible polymer-hard particle suspensions. The particle volume fraction at the fluid-gel transition is predicted to depend exponentially on reduced polymer concentration and size asymmetry ratio at relatively high colloid concentrations. In contrast, at lower particle volume fractions, a power-law dependence on polymer concentration is found with effective exponents and prefactors that depend systematically on the polymer/particle size ratio. Remarkable power-law and near universal scaling behavior is found for the localization length and elastic shear modulus. Multiple experiments for gel boundaries and shear moduli are in good agreement with the no adjustable parameter theory. The one exception is the absolute magnitude of the shear modulus which is strongly overpredicted, apparently due to nonequilibrium dense cluster formation. The simplified MCT-PRISM theory also captures the qualitative aspects of the weak depletion-driven "glass melting" phenomenon at high particle volume fractions. Calculations based on an effective one-component model of structure within a low particle volume fraction framework yield qualitatively different features than the two-component approach and are apparently all in disagreement with experiments. This suggests that volume fraction and size asymmetry dependent many-body screening of polymer-mediated depletion attractions at finite particle concentrations are important.