Robin C. Ball

Elasticity of entangled networks

Entanglements are modelled by links which make a sliding contact between polymer networks. A formal solution to this problem is given using the replica formalism and the contribution of an entanglement to the free energy of shear is given by: 12kT∑iλi2(1+η)1 + ηλi2 + kT∑log(1+ηλi2 where λi are the Cartesian extension ratios and η is a measure of the freedom of a link to slide compared with the freedom of movement of a chain. The expression quoted gives correct limits in the (trivial) case of η zero, and η infinity, when it is merely a negative contribution to the osmotic pressure of the network.

The structure of fractal colloidal aggregates of finite extent

Abstract The structure of fractal colloid aggregates formed in both the diffusion- and the reaction-limited regimes is studied by static light scattering experiments. The crossover region of the structure factor of the clusters is measured, and the effects of the finite extent of the fractal structure on the scattering are investigated. The polydispersity of the cluster mass distribution markedly changes the shape of the measured scattering intensity. A form for the structure factor obtained from computer-generated clusters is found to describe the colloidal aggregates very well, for both regimes. Other available models for the crossover region are also discussed. In addition, the effects of the optical plasma resonance in the case of metallic colloids and the effects of cluster restructuring on the static scattering are discussed.

Universality of fractal aggregates as probed by light scattering

Fractal colloid aggregates are studied with both static and dynamic light scattering. The dynamic light scattering data are scaled onto a single master curve, whose shape is sensitive to the structure of the aggregates and their mass distribution. By using the structure factor determined from computer-simulated aggregates, and including the effects of rotational diffusion, we predict the shape of the master curve for different cluster distributions. Excellent agreement is found between our predictions and the data for the two limiting régimes, diffusion-limited and reaction-limited colloid aggregation. Furthermore, using data from several completely different colloids, we find that the shapes of the master curves are identical for each régime. In addition, the cluster fractal dimensions and the aggregation kinetics are identical in each régime. This provides convincing experimental evidence of the universality of these two régimes of colloid aggregation.

Computer simulation of chemically limited aggregation

Cluster-cluster aggregation is studied via a computer simulation in the chemically limited regime. True polydisperse flocculation is compared with idealised monodisperse aggregation in two and three space dimensions in terms of fractal dimensions and the exponents associated with the scaling of the reaction rates with cluster size.

Shear thickening and order–disorder effects in concentrated colloids at high shear rates

The rheology and microstructure of concentrated colloidal suspensions, within the shear thickening regime, are investigated using Stokesian dynamics. We consider systems stabilized by charge and/or polymer layers, at hard core volume fractions above 40%. At φv=0.44, charge stabilized systems show transitions from ordered to disordered flow, with only a small increase in suspension viscosity. At higher φv, we observe larger jumps in viscosity with changes between order and disorder and vice versa. At high shear rates, interparticle gaps can become very small. This work investigates two ways in which these gaps may be controlled: by modifying the charge interaction potential [Dratler et al. (1997)], or by including a model for the presence of a polymer brush [Potanin and Russel (1995)]. The thickening observed is dependent on the gaps of closest approach of particles, but only weakly for hard sphere lubrication forces. Strong thickening is only observed with the presence of an enhanced lubricating force, in...

Social networks – The future for health care delivery

With the rapid growth of online social networking for health, health care systems are experiencing an inescapable increase in complexity. This is not necessarily a drawback; self-organising, adaptive networks could become central to future health care delivery. This paper considers whether social networks composed of patients and their social circles can compete with, or complement, professional networks in assembling health-related information of value for improving health and health care. Using the framework of analysis of a two-sided network--patients and providers--with multiple platforms for interaction, we argue that the structure and dynamics of such a network has implications for future health care. Patients are using social networking to access and contribute health information. Among those living with chronic illness and disability and engaging with social networks, there is considerable expertise in assessing, combining and exploiting information. Social networking is providing a new landscape for patients to assemble health information, relatively free from the constraints of traditional health care. However, health information from social networks currently complements traditional sources rather than substituting for them. Networking among health care provider organisations is enabling greater exploitation of health information for health care planning. The platforms of interaction are also changing. Patient-doctor encounters are now more permeable to influence from social networks and professional networks. Diffuse and temporary platforms of interaction enable discourse between patients and professionals, and include platforms controlled by patients. We argue that social networking has the potential to change patterns of health inequalities and access to health care, alter the stability of health care provision and lead to a reformulation of the role of health professionals. Further research is needed to understand how network structure combined with its dynamics will affect the flow of information and potentially the allocation of health care resources.

A simulation technique for many spheres in quasi-static motion under frame-invariant pair drag and Brownian forces

We report on details of a simulation technique for particles under quasi-static motion determined by a balance of conservative and dissipative interactions acting at the pair level. We develop frame-invariant and linear viscous interactions between pairs of translating and rotating spheres in a form suitable for computation. We report an o(N) method for generating Brownian forces correlated with a pair resistance tensor and show how explicit finite difference schemes lead naturally to an algorithm with Brownian motion and an estimate of the Brownian stress. We justify the algorithm by appeal to the second-order Langevin equation. We discuss the choice of time step and imposition of boundary conditions. We assess a model of this kind as an approximation for colloid spheres concentrated in a fluid medium under shear flow. It is noted that the algorithm is also that required for simulation, in the diffusive limit, of a technique known as dissipative particle dynamics. We report on structural effects in Brownian sphere colloids and their sensitivity to the model details. We argue that the approximation has heuristic value in the study of the rheology in concentrated colloid systems. Its predictions for the rheology of suspensions are in semi-quantitative agreement with experiment.

Dynamics of Colloidal Dispersions

Abstract We review the essential physics underlying the dynamics of colloidal dispersions. The development of the theoretical techniques is discussed in the context of calculations done for both diffusion coefficients and viscosities.

Spinodal decomposition and pattern formation near surfaces

The effects of temperature gradients and boundary conditions at the surface of a system separating into two phases via spinodal decomposition are studied numerically in one and two dimensions. For suitable cooling rates and thermal noise strengths, an off-critical system cooled from an external surface is found to separate by the formation of alternate layers of the two phases near the surface, a very different structure to that formed in the bulk. A similar pattern is found to be generated by a boundary condition associated with a surface free energy. An approximate solution is derived for the evolution of the boundary pattern in this case, allowing an estimate to be made of how far the pattern will propagate into the bulk.

A simplified approach to the interpretation of nuclear spin correlations in entangled polymeric liquids

We derive closed-form expressions for a sine correlation function β(2τ,τ) which is particularly sensitive to modulations of nuclear dipolar (and quadrupolar) interactions caused by slow molecular reorientations. This function is placed in the context of traditional nuclear magnetic resonance (NMR) experiments—the Free Induction Decay R(t) and the solid echo amplitude E(τ) and families of expressions are evaluated for (i) motion governed by an exponential correlation function and (ii) macromolecular motion dominated by reptation. We introduce a simple correlation function for reptation that depends on only two parameters, M2¯, the preaveraged dipolar interaction strength and τd, the tube disengagement time. From proton NMR measurements of β in poly(dimethyl siloxane) melts we estimate M2¯=1.3×106 s−2 and τd=0.019 s at 300 K, in reasonable agreement with a calculated value for M2¯ and an independent NMR estimate of the terminal relaxation time.