Lamiae
Mémoire online overview of the structure and the dynamics of attractive spheres, tutoriel & document en PDF.
Chapter 1: Introduction
Generally, matter exists in three forms: solid, liquid and gas although plasma is believed to be the fourth state of matter. Colloidal systems have attracted a lot of interest as models for the liquid. Colloidal suspensions consist of particles of sizes between 10nm−10µm suspended in a liquid. Colloids are orders of magnitude bigger than atoms and molecules and may exhibit different behavior due to their large size.
Their structural relaxation times are large, typically of the order of seconds. They are weak mechanically, and colloidal solids can be shear melted to form a metastable fluid just by shaking. Resolidification may take minutes hours or days giving time to study the crystallization and the meta stable liquid. The spatial scale of the colloids is comparable to the wavelength of light making light scattering an important tool to investigate the structure and dynamics of such systems. The interaction between colloidal particles can be tailored, by various means such as addition of free polymers or modification of the surface coating of the particles. These features allow one to perform experiments with colloidal systems which are not possible with atomistic systems.
Attractive particles diffuse through Brownian motion before they aggregate into clusters. If the attraction is very strong the aggregation process is irreversible. The clusters formed by aggregation are usually fractals as was observed experimentally for example for colloids or proteins. Fractal aggregates were simulated by Kolb et. al and Meakin using a cluster-cluster aggregation model called diffusion limited cluster aggregation (DLCA). Weitz et. al showed that the DLCA model can indeed be used to explain the structure of real particle aggregates, in their case aggregated colloidal gold. Fig.(1.1) shows the structure formed by diffusion limited cluster aggregation (DLCA) from simulations and a aggregate formed by gold colloids.
Another aggregation model is reaction limited cluster aggregation (RLCA) where the sticking probability at a collision goes to zero. Real systems are often closer to RLCA (slow aggregation) than DLCA (fast aggregation), but it is very difficult to simulate RLCA at low volume fraction because very long times are needed to form big clusters.
Both simulations and experiments have shown that structures formed by both types of aggregation are fractals and have a very broad cluster size distribution. This will be discussed in more detail in chapter 2. The aggregates formed by RLCA are denser When the clusters start to inter penetrate their fractal dimension changes. After a cross-over the structure, cluster size distribution and fractal dimension is very well explained by the percolation model. The aggregation proceeds toward a point where a single cluster spans the whole space a phenomena referred to as gelation. Aggregates have a local structure determined by the initial stage of DLCA or RLCA and a large scale structure determined by the percolation process.
Reversible aggregation results in the formation of transient clusters, a phase separated system or a transient percolating cluster depending on the strength and range of attraction. A schematic diagram of these systems is shown in fig(1.3) in which four different regions are identified.
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