Abstract. We study the phase behaviour and structure of model colloid-polymer mixtures. By integrating out the degrees of freedom of the non-adsorbing ideal polymer coils, we derive a formal expression for the effective one-component Hamiltonian of the colloids. Using the twobody (Asakura-Oosawa pair potential) approximation to this effective Hamiltonian in computer simulations, we determine the phase behaviour for size ratios q = σ p /σ c = 0.1, 0.4, 0.6, and 0.8, where σ c and σ p denote the diameters of the colloids and the polymer coils, respectively. For large q, we find both a fluid-solid and a stable fluid-fluid transition. However, the latter becomes metastable with respect to a broad fluid-solid transition for q 0.4. For q = 0.1 there is a metastable isostructural solid-solid transition which is likely to become stable for smaller values of q. We compare the phase diagrams obtained from simulation with those of perturbation theory using the same effective one-component Hamiltonian and with the results of the free-volume approach. Although both theories capture the main features of the topologies of the phase diagrams, neither provides an accurate description of the simulation results. Using simulation and the Percus-Yevick approximation we determine the radial distribution function g(r) and the structure factor S(k) of the effective one-component system along the fluid-solid and fluid-fluid phase boundaries. At state-points on the fluid-solid boundary corresponding to high colloid packing fractions (packing fractions equal to or larger than that at the triple point), the value of S(k) at its first maximum is close to the value 2.85 given by the Hansen-Verlet freezing criterion. However, at lower colloid packing fractions freezing occurs when the maximum value is much lower than 2.85. Close to the critical point of the fluid-fluid transition we find Ornstein-Zernike behaviour and at very dilute colloid concentrations S(k) exhibits pronounced small-angle scattering which reflects the growth of clusters of the colloids. We compare the phase behaviour of this model with that found in studies of additive binary hard-sphere mixtures.

Active colloids exhibit persistent motion, which can lead to motility-induced phase separation (MIPS). However, there currently exists no microscopic theory to account for this phenomenon. We report a first-principles theory, free of fit parameters, for active spherical colloids, which shows explicitly how an effective many-body interaction potential is generated by activity and how this can rationalize MIPS. For a passively repulsive system the theory predicts phase separation and pair correlations in quantitative agreement with simulation. For an attractive system the theory shows that phase separation becomes suppressed by moderate activity, consistent with recent experiments and simulations, and suggests a mechanism for reentrant cluster formation at high activity.

We present a model of spike-driven synaptic plasticity inspired by experimental observations and motivated by the desire to build an electronic hardware device that can learn to classify complex stimuli in a semisupervised fashion. During training, patterns of activity are sequentially imposed on the input neurons, and an additional instructor signal drives the output neurons toward the desired activity. The network is made of integrate-and-fire neurons with constant leak and a floor. The synapses are bistable, and they are modified by the arrival of presynaptic spikes. The sign of the change is determined by both the depolarization and the state of a variable that integrates the postsynaptic action potentials. Following the training phase, the instructor signal is removed, and the output neurons are driven purely by the activity of the input neurons weighted by the plastic synapses. In the absence of stimulation, the synapses preserve their internal state indefinitely. Memories are also very robust to the disruptive action of spontaneous activity. A network of 2000 input neurons is shown to be able to classify correctly a large number (thousands) of highly overlapping patterns (300 classes of preprocessed Latex characters, 30 patterns per class, and a subset of the NIST characters data set) and to generalize with performances that are better than or comparable to those of artificial neural networks. Finally we show that the synaptic dynamics is compatible with many of the experimental observations on the induction of long-term modifications (spike-timing-dependent plasticity and its dependence on both the postsynaptic depolarization and the frequency of pre- and postsynaptic neurons).

Abstract. We investigate stresses and particle motion during the start up of flow in a colloidal dispersion close to arrest into a glassy state. A combination of molecular dynamics simulation, mode coupling theory and confocal microscopy experiment is used to investigate the origins of the widely observed stress overshoot and (previously not reported) super-diffusive motion in the transient dynamics. A link between the macro-rheological stress versus strain curves and the microscopic particle motion is established. Negative correlations in the transient auto-correlation function of the potential stresses are found responsible for both phenomena, and arise even for homogeneous flows and almost Gaussian particle displacements.

We present a density functional theory for mixtures of (hard sphere) colloidal particles and ideal polymers. For this extreme nonadditive system we employ a fundamental measures approach to construct a functional which incorporates the correct dimensional crossover and the exact low density limit. In bulk fluid mixtures the functional yields the same free energy and, therefore, the same gas-liquid (demixing) transition as given by free-volume theory. It generates consistent pair correlation functions; the partial structure factors S(ij)(k) diverge, as k-->0, at the critical point obtained from the free energy. Our results for the structure agree well with those from simulation and Percus-Yevick theory.

Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical many-body systems subject to Brownian dynamics. Our approach is based upon a dynamical functional consisting of reversible free energy changes and irreversible power dissipation. Minimization of this "free power" functional with respect to the microscopic one-body current yields a closed equation of motion. In the equilibrium limit the theory recovers the standard variational principle of DFT. The adiabatic dynamical density functional theory is obtained when approximating the power dissipation functional by that of an ideal gas. Approximations to the excess (over ideal) power dissipation yield numerically tractable equations of motion beyond the adiabatic approximation, opening the door to the systematic study of systems far from equilibrium.

The mode coupling theory (MCT) of glasses, while offering an incomplete description of glass transition physics, represents the only established route to first-principles prediction of rheological behavior in nonergodic materials such as colloidal glasses. However, the constitutive equations derivable from MCT are somewhat intractable, hindering their practical use and also their interpretation. Here, we present a schematic (single-mode) MCT model which incorporates the tensorial structure of the full theory. Using it, we calculate the dynamic yield surface for a large class of flows.arrest | solidification | plasticity T he 20th Century saw formidable advances in the subject known as theoretical rheology-whose aim is to predict or explain the nonlinear flow behavior of materials. Ideally, for each class of material, one wishes to gain a "constitutive equation" that predicts the stress tensor at time t as a functional of the strain tensor at all earlier times (or vice versa). There are two broad approaches to this task. The more traditional one focuses on symmetry, conservation, and invariance principles (often of some subtlety) and then proposes empirical equations that respect these principles (1). In the second approach, the goal is to start from a first-principles analysis of molecular motion and, then, by judicious (though possibly uncontrolled) approximation, arrive at a continuum-level constitutive model. This is clearly far more ambitious, and success has so far been restricted to relatively few classes of material. Perhaps the most striking success has been the Doi-Edwards theory for solutions and melts of entangled linear polymers (2, 3) [extended later to branched (4) or breakable (5) chains]. In their resting state, such polymers are ergodic and therefore attain the Boltzmann distribution: Moreover their local structure is weakly perturbed from this, even under flow.Glasses at rest, in contrast, are nonergodic on experimental time scales. This poses major obstacles to the rheological theory of glasses and is responsible for aging and other phenomena that have been partially addressed by using mesoscopic models (6). The onset of arrest at the glass transition is, familiarly, accompanied by the onset of an elastic modulus. Window glass is a brittle solid: it deforms elastically for low stresses but shatters under large ones. However, some other glasses-most notably in colloidal suspensions (whose glass transition, for hard spheres, is found experimentally at ≈58% volume fraction) are not brittle solids but show continuous yielding behavior. Although experiments suggest a more complex picture (7,8), the simplest explanation is that, above some yield stress, the glass melts. If a steady stress above the yield level is maintained, the resulting fluid can be expected to attain an ergodic (though non-Boltzmann) steady state.This restoration of ergodicity under steady flow offers one motivation for an approach to glass rheology based on mode-coupling theory (MCT). In particular, it mitigates a well-known sho...

Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full tensorial structure of the theory to be identified. Macroscopic deformation measures, such as the Cauchy-Green tensors, thereby emerge. So does a direct relation between the stress and the distorted microstructure, illuminating the interplay of slow structural relaxation and arbitrary imposed flow. We present flow curves for steady planar and uniaxial elongation and compare these to simple shear. The resulting nonlinear Trouton ratios point to a tensorially nontrivial dynamic yield condition for colloidal glasses.