Mark Haw

Mesoscopic structure formation in colloidal aggregation and gelation

Abstract Recent small-angle light scattering experiments have revealed that diffusively aggregating spherical particles develop structure on a mesoscopic length scale (∼ tens of particles). The mesoscopic structural length scale persists even when the aggregation proceeds to the formation of a space-spanning network (a gel). We review the technique of small-angle light scattering, survey the experimental evidence for mesoscopic structure formation, discuss attempts at understanding these experimental observations by computer simulation of irreversible and reversible diffusion-limited cluster aggregation (DLCA), and propose a coherent picture for the understanding of non-equilibrium aggregation in the context of phase transitions.

Holographic data storage: The light fantastic

A decade ago, holographic systems promised to revolutionize data storage. The early hype may have evaporated, but the technology quietly progressed, and working devices are now on the market. Mark Haw reports.

Cluster-cluster gelation with finite bond energy

Abstract Aggregation and gelation of colloidal particles in two and three dimensions is simulated using the diffusion-limited cluster-cluster aggregation model with a finite interparticle bonding energy. Particles and clusters break apart due to thermal fluctuations in kinetic energy. The effects on the structure of the aggregating system as a whole are studied via methods analogous to light-scattering in experiments. We consider relatively weak interparticle attractive potentials E of the order of a few times the thermal fluctuation energy k B T . In irreversible aggregation the system of clusters forms a gel, a space-filling connected structure. We find that given strong enough bonding the assembly of clusters still approaches gelation (the assembly fills an increasing fraction of space) but the ‘gel’ structure is markedly different from the case where bonding is irreversible. At lower energies a sol of clusters is formed, the clusters being internally compact with ramified surfaces. At late time one expects the system to evolve to a pattern of coarsening, near-compact droplets familiar from general first-order phase transition and phase separation studies.

STRUCTURE AND CHARACTERISTIC LENGTH SCALES IN CLUSTER-CLUSTER AGGREGATION SIMULATION

The structure of a system of aggregating particle is studied by simulation, in both two and three dimensions, using the on-lattice diffusion-limited cluster aggregation model. We calculate static structure factors S(Q) and pair distribution functions for the aggregating system as a whole. The peak in the scattering function, reported for many experimental aggregating colloidal systems and observed in the simulated structures, is shown to correspond to the characteristic outer radius of a ‘depletion zone’ around clusters. The time-scaling properties of S(Q) are examined. A scaling of the structure factor analogous to the case of spinodal decomposition has been observed in experiments; we find reasonable structure factor scaling at intermediate densities and intermediate times but, due to the relatively small systems studied here, we must be cautious in either confirming or denying the presence of similar structure factor scaling for the simulation model throughout the aggregation, especially at early time and at high density. We examine various ‘characteristic’ length scales in the model system, such as the average radius of gyration of clusters, the radius of the largest cluster, the length scale equivalent to the position of the structure factor peak, and so on, in a more general attempt to determine whether the system can be characterised by a single important length scale. From this there is reasonable indication that approximate scaling is demonstrated over a limited region of time. This is consistent with results from light-scattering experiments. Lastly, an examination of the total perimeter length of the ensemble of clusters in the simulation indicates that we may divide the aggregation into three distinct time regimes, corresponding to a pre-aggregation, a pre-fractal, and a fractal regime.

Gelation Mechanism of Resorcinol-Formaldehyde Gels Investigated by Dynamic Light Scattering

Xerogels and porous materials for specific applications such as catalyst supports, CO2 capture, pollutant adsorption, and selective membrane design require fine control of pore structure, which in turn requires improved understanding of the chemistry and physics of growth, aggregation, and gelation processes governing nanostructure formation in these materials. We used time-resolved dynamic light scattering to study the formation of resorcinol-formaldehyde gels through a sol-gel process in the presence of Group I metal carbonates. We showed that an underlying nanoscale phase transition (independent of carbonate concentration or metal type) controls the size of primary clusters during the preaggregation phase; while the amount of carbonate determines the number concentration of clusters and, hence, the size to which clusters grow before filling space to form the gel. This novel physical insight, based on a close relationship between cluster size at the onset of gelation and average pore size in the final xerogel results in a well-defined master curve, directly linking final gel properties to process conditions, facilitating the rational design of porous gels with properties specifically tuned for particular applications. Interestingly, although results for lithium, sodium, and potassium carbonate fall on the same master curve, cesium carbonate gels have significantly larger average pore size and cluster size at gelation, providing an extended range of tunable pore size for further adsorption applications.

Einstein's random walk

MOST OF US probably remember hearing about Brownian motion in high school, when we are taught that pollen grains jiggle around randomly in water due the impacts of millions of invisible molecules. But how many people know about Einsteins work on Brownian motion, which allowed Jean Perrin and others to prove the physical reality of molecules and atoms?

STRUCTURE FACTORS FROM CLUSTER-CLUSTER AGGREGATION SIMULATION AT HIGH-CONCENTRATION

Aggregation of particles in two dimensions at high concentration is simulated using the diffusion-limited cluster-cluster aggregation model. Static structure factors are calculated from particle configurations. A simple model in which clusters diffuse at rates inversely proportional to their radii of gyration reproduces qualitatively the behaviour observed in experiments. A peak in the structure factor S(Q) is observed at small scattering vectors Q. The intensity of the peak increases, and its Q-value decreases, as the aggregation proceeds. Finally all particles belong to a single system-spanning cluster, the ‘gel’ state, and the scattering peak is ‘frozen’ at a given Q. The gel structure is formed from a random close-packed collection of smaller, ramified clusters.

Void structure and cage fluctuations in simulations of concentrated suspensions

We analyse the mesoscopic structure and structural fluctuations in simulated high-concentration hard sphere colloidal suspensions by means of calculations based on the void space. We show that remoteness, a quantity measuring the scale of spaces, is useful in studying crystallization, since ordering of the particles involves a change in the way empty space is distributed. Calculation of remoteness also allows breakdown of the system into mesoscopic neighbour sets. In the case of crystallizing systems, statistics of mean remoteness and local volume fraction in these neighbour sets are consistent with nuclei forming at locally higher concentration, nucleation involves increased heterogeneity of the system, as previously demonstrated in experiments with model colloidal particles. Meanwhile in dense amorphous systems, local volume fractions in neighbour sets reveal significant details of mesoscale structural fluctuations, indicating that abrupt dilations and compressions of local regions may be important physical components of cage fluctuations in the colloidal glass.

Nanopropulsion by biocatalytic self-assembly.

A number of organisms and organelles are capable of self-propulsion at the micro- and nanoscales. Production of simple man-made mimics of biological transportation systems may prove relevant to achieving movement in artificial cells and nano/micronscale robotics that may be of biological and nanotechnological importance. We demonstrate the propulsion of particles based on catalytically controlled molecular self-assembly and fiber formation at the particle surface. Specifically, phosphatase enzymes (acting as the engine) are conjugated to a quantum dot (the vehicle), and are subsequently exposed to micellar aggregates (fuel) that upon biocatalytic dephosphorylation undergo fibrillar self-assembly, which in turn causes propulsion. The motion of individual enzyme/quantum dot conjugates is followed directly using fluorescence microscopy. While overall movement remains random, the enzyme-conjugates exhibit significantly faster transport in the presence of the fiber forming system, compared to controls without fuel, a non-self-assembling substrate, or a substrate which assembles into spherical, rather than fibrous structures upon enzymatic dephosphorylation. When increasing the concentration of the fiber-forming fuel, the speed of the conjugates increases compared to non-self-assembling substrate, although directionality remains random.

Jamming and unjamming of concentrated colloidal dispersions in channel flows

We investigated the pressure driven flow of concentrated colloidal dispersions in a converging channel geometry. Optical microscopy and image analysis were used to track tracer particles mixed into dispersions of sterically stabilized poly(methyl methacrylate) (PMMA) spheres. The dispersions were drawn into a round 0.5 mm capillary at one of two pump speeds ( applied pressure): v1 = 0.245 ml min−1 and v2 = 0.612 ml min−1. We observed that the dispersions at particle volume fractions ϕ ⩽ 0.50 followed Hagen–Poiseuille flow for a simple fluid; i.e. the mean flow rate 〈V〉 is approximately proportional to pressure drop (pump speed) and inversely proportional to viscosity η. Above this concentration (ϕ 0.505), the dispersions exhibit granular-like jamming behaviour with 〈V〉 becoming independent of the pressure drop. However, at the highest applied pressure (v2), the dispersions are able to unjam and switch from granular-like behaviour back to a simple hard-sphere liquid like system, due to the formation of rotating vortices in the spatial flow pattern. This mechanism is consistent with computer simulations of granular systems and supports for example proposed explanations of anomalously low friction in earthquake faults. We also link this behaviour with the concept of fragile matter (M. E. Cates, J. P. Wittmer, J. P. Bouchaud and P. Claudin, Phys. Rev. Lett., 1998, 81, 1841–1844).