There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Basics of qualitative research: Grounded theory procedures and techniques

Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

Rubbers exhibit enormous extensibility up to several hundred per cent, compared with a few per cent for ordinary solids, and have the ability to recover their original shape and dimensions on release of stress. Rubber elasticity is a property of macromolecules that are either covalently cross-linked or connected in a network by physical associations such as small glassy or crystalline domains, ionic aggregates or multiple hydrogen bonds. Covalent cross-links or strong physical associations prevent flow and creep. Here we design and synthesize molecules that associate together to form both chains and cross-links via hydrogen bonds. The system shows recoverable extensibility up to several hundred per cent and little creep under load. In striking contrast to conventional cross-linked or thermoreversible rubbers made of macromolecules, these systems, when broken or cut, can be simply repaired by bringing together fractured surfaces to self-heal at room temperature. Repaired samples recuperate their enormous extensibility. The process of breaking and healing can be repeated many times. These materials can be easily processed, re-used and recycled. Their unique self-repairing properties, the simplicity of their synthesis, their availability from renewable resources and the low cost of raw ingredients (fatty acids and urea) bode well for future applications.

Self-healing and thermoreversible rubber from supramolecular assembly

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

THE aggregation of colloidal particles is of fundamental importance in colloid science and its applications. The recent application of scaling concepts1,2 has resulted in a much deeper understanding of the structure of colloidal aggregates and the kinetics of their formation. Two distinct, limiting regimes of irreversible colloid aggregation have been identified3. Diffusion-limited colloid aggregation occurs when there is negligible repulsive force between the colloidal particles, so that the aggregation rate is limited solely by the time taken for clusters to encounter each other by diffusion. Reaction-limited colloid aggregation occurs when there is still a substantial, but not insurmountable, repulsive force beween the particles, so that the aggregation rate is limited by the time taken for two clusters to overcome this repulsive barrier by thermal activation. These regimes correspond to the limiting cases of rapid and slow colloid aggregation that have long been recognized in colloid science4. An intriguing possibility suggested by recent work is that each of these limiting regimes of colloid aggregation is universal, independent of the chemical details of the particular colloid system. Here we investigate the aggregation of three chemically different colloidal systems under both diffusion-limited and reaction-limited aggregation conditions. A scaling analysis of light-scattering data is used to compare the behaviour and provides convincing experimental evidence that the two regimes of aggregation are indeed universal.

Universality in colloid aggregation

We study slow, or reaction-limited, colloid aggregation (RLCA) with both static and dynamic light scattering and develop a self-consistent interpretation of the results. Static light scattering is used to determine the fractal dimension of the clusters and the cutoff mass of the power-law cluster-mass distribution. Using this same cutoff cluster mass, we can predict the shape of the temporal autocorrelation function measured by dynamic light scattering. Good agreement with experiments is obtained provided the effects of rotational diffusion are included. In addition, we determine the ratio of the hydrodynamic radius to the radius of gyration of individual RLCA clusters and find \ensuremath{\beta}=1.0. A scaling method is used for the q-dependent first cumulants of the temporal autocorrelation functions to obtain a single master curve for data obtained at different times in the aggregation process. The shape of this master curve is very sensitive to several key features of the process of reaction-limited colloid aggregation. It allows us to unambiguously determine the exponent for the power-law cluster-mass distribution, \ensuremath{\tau}=1.5\ifmmode\pm\else\textpm\fi{}0.05. Furthermore, we show that the master curves for three completely different colloids, gold, silica, and polystyrene, are indistinguishable. In addition, the fractal dimensions of their RLCA clusters, as measured by static light scattering, are all ${d}_{f}$=2.1\ifmmode\pm\else\textpm\fi{}0.05, while the aggregation kinetics for each colloid are exponential. This demonstrates that reaction-limited colloid aggregation is universal, independent of the detailed chemical nature of the colloid system.

Universal reaction-limited colloid aggregation

In recent years considerable interest has developed In the formation of random structures under non-equilibrium conditions. Much of our understanding of the geometry of these structures and its relationship to their formation mechanism has come from the study of simple models by means of both computer simulation and theoretical methods. One of the most fundamental of these models is the ballistic aggregation model in which particles are added to a growing structure via linear (ballistic) trajectories. Other simple models which have been studied intensively include the Eden1 model, diffusion limited aggregation2 (DLA) and diffusion limited cluster-cluster aggregation.3,4

Ballistic Deposition on Surfaces

We use multispeckle dynamic light scattering to measure the dynamic structure factor, f(q,tau), of gels formed by aggregation of colloids. Although the gel is an elastic solid, f(q,tau) nearly completely decays on long time scales, with an unusual form, f(q, tau) approximately exp{-(tau/tau(f))(mu)}, with mu approximately 1.5 and with tau(f) proportional variant q(-1). A model for restructuring of the gel with aging correctly accounts for this behavior. Aging leads to a dramatic increase in tau(f); however, all data can be scaled on a single master curve, with tau(f) asymptotically growing linearly with age. This behavior is strikingly similar to that predicted for aging in disordered glassy systems, offering convincing proof of the universality of these concepts.

/pdf/universal-aging-features-in-the-restructuring-of-fractal-bl7dkwojkh.pdf

Universal Aging Features in the Restructuring of Fractal Colloidal Gels

Black dendritic growths of copper were electrodeposited in steady-state diffusion-limited conditions onto an initially point-like cathode. Their spatial extent R was inferred from the increased current and their mass M from the total charge transferred. Fractal behaviour M∝RD was observed with D = 2.43 ±0.03, in good agreement with computer simulations of diffusion-limited aggregation.

Robin C. Ball

Papers

Universality in colloid aggregation

Universal reaction-limited colloid aggregation

Ballistic Deposition on Surfaces

Universal Aging Features in the Restructuring of Fractal Colloidal Gels

Fractal growth of copper electrodeposits