R. M. L. Evans

Delayed sedimentation of transient gels in colloid–polymer mixtures: dark-field observation, rheology and dynamic light scattering studies

The addition of enough non-adsorbing polymer to a hard-sphere suspension causes the particles to aggregate to form a space-filling gel. The integrity of the gel persists for a finite period of time, and then the space-filling structure collapses suddenly to form a denser sediment. This phenomenon of ‘delayed sedimentation’ is ubiquitous in many weakly-flocculated suspensions. In this work, we observe the processes occurring in the bulk of a colloid–polymer gel using dark-field imaging, and probe the arrangement and dynamics of the particles in the system using two-colour dynamic light scattering. The effect of shear is also studied. A number of physical mechanisms relevant to a comprehensive explanation of delayed sedimentation are proposed and discussed.

Measuring storage and loss moduli using optical tweezers: Broadband microrheology

We present an experimental procedure to perform broadband microrheological measurements with optical tweezers. A generalized Langevin equation is adopted to relate the time-dependent trajectory of a particle in an imposed flow to the frequency-dependent moduli of the complex fluid. This procedure allows us to measure the material linear viscoelastic properties across the widest frequency range achievable with optical tweezers.

Optical tweezers: wideband microrheology

Microrheology is a branch of rheology having the same principles as conventional bulk rheology, but working on micron length scales and microlitre volumes. Optical tweezers have been successfully used with Newtonian fluids for rheological purposes such as determining fluid viscosity. Conversely, when optical tweezers are used to measure the viscoelastic properties of complex fluids the results are either limited to the materials high-frequency response, discarding important information related to the low-frequency behaviour, or they are supplemented by low-frequency measurements performed with different techniques, often without presenting an overlapping region of clear agreement between the sets of results. We present a simple experimental procedure to perform microrheological measurements over the widest frequency range possible with optical tweezers. A generalized Langevin equation is used to relate the frequency-dependent moduli of the complex fluid to the time-dependent trajectory of a probe particle as it flips between two optical traps that alternately switch on and off.

Role of metastable states in phase ordering dynamics

We show that the rate of separation of two phases of different densities (e.g. gas and solid) can be radically altered by the presence of a metastable intermediate phase (e.g.liquid). Within a Cahn-Hilliard theory we study the growth in one dimension of a solid droplet from a supersaturated gas. A moving interface between solid and gas phases (say) can, for sufficient (transient) supersaturation, unbind into two interfaces separated by a slab of metastable liquid phase. We investigate the criteria for unbinding, and show that it may strongly impede the growth of the solid phase.

Rules for Transition Rates in Nonequilibrium Steady States

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behavior and, for steady shear, gives rise to stress-mediated long-range interactions.

Detailed balance has a counterpart in non-equilibrium steady states

Transition rates in continuously driven steady states were derived in [Evans R M L, 2005 J. Phys. A: Math. Gen. 38, 293] by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the system be used to describe it. In addition to the mean energy at equilibrium, and unlike them, these driven states have a finite throughput of flux. This implies that the (nonequilibrium) reservoir, to which the system is weakly coupled, is fully characterised by its mean energy and mean flux. While we expect the resulting prescription for the rates in continuous and discretised time versions of models of real systems to be equivalent, it is not trivial to see this from the expression for the rates derived previously. We demonstrate this equivalence for a model of activated processes solved previously for continuous time, thus demonstrating consistency of theory.

Perturbative polydispersity: Phase equilibria of near-monodisperse systems

The conditions of multiphase equilibrium are solved for generic polydisperse systems. The case of multiple polydispersity is treated, where several properties (e.g., size, charge, shape) simultaneously vary from one particle to another. By developing a perturbative expansion in the width of the distribution of constituent species, it is possible to calculate the effects of polydispersity alone, avoiding difficulties associated with the underlying many-body problem. Explicit formulas are derived in detail, for the partitioning of species at coexistence and for the shift of phase boundaries due to polydispersity. Convective fractionation is quantified, whereby one property (e.g., charge) is partitioned between phases due to a driving force on another. To demonstrate the ease of use and versatility of the formulas, they are applied to models of a chemically polydisperse polymer blend, and of fluid–fluid coexistence in polydisperse colloid–polymer mixtures. In each case, the regime of coexistence is shown to be enlarged by polydispersity.

Dynamics of semiflexible polymer solutions in the highly entangled regime.

We present experimental evidence that the effective medium approximation (EMA), [D. C. Morse, Phys. Rev. E 63, 031502 (2001)], provides the correct scaling law of the plateau modulus G0 proportional variantrho4/3Lp(-1/3) (with rho the contour length per unit volume and Lp the persistence length) of semiflexible polymer solutions, in the highly entangled regime. Competing theories, including a binary collision approximation (BCA), instead predict G0 proportional, variantrho7/5Lp(-1/5). We have tested both predictions using F-actin solutions which permit experimental control of Lp independently of other parameters. A combination of video particle tracking microrheology and dynamic light scattering yields independent measurements of G0 and Lp, respectively. Thus we can distinguish between the two proposed laws, in contrast to previous experimental studies focused on the (less discriminating) concentration dependence.

Analysis of the linear viscoelasticity of polyelectrolytes by magnetic microrheometry—pulsed creep experiments and the one particle response

We report experimental measurements on polyacrylamide (flexible polyelectrolytes), actin (semi-flexible polyelectrolytes), and self-assembled peptide (gelled semi-flexible polyelectrolytes) solutions. The measurements were obtained using a two-pole piece magnetic microrheometer based on an upright Olympus microscope with an oil immersion (×100) lens. Pulsed creep experiments produced high quality data over a wide time range with good agreement between passive particle tracking and magnetic microrheology results. This implies a commonality of the one probe particle response to its viscoelastic environment in both passive and active microrheology experiments.

Diffusive growth of polydisperse hard-sphere crystals

Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e., mixtures of infinitely many components with sizes drawn from a continuous distribution. We model the crystallization of hard-sphere colloids (with/without attractions) from an initially amorphous phase. Although the polydisperse hard-sphere phase diagram has been widely studied, it is not straightforwardly applicable to real colloidal crystals, since they are inevitably out of equilibrium. The process by which colloidal crystals form determines the size distribution of the particles that comprise them. Once frozen into the crystal lattice, the particles are caged so that the composition cannot subsequently relax to the equilibrium optimum. We predict that the mean size of colloidal particles incorporated into a crystal is smaller than anticipated by equilibrium calculations. This is because small particles diffuse fastest and therefore arrive at the crystal in disproportionate abundance.