Quantitative Confocal Microscopy of Dense Colloidal Systems
This document describes an experimental investigation into dense collections of hard spherical particles just large enough to be studied using a light microscope. These particles display colloidal properties, but also some similarities with granular materials. We improve the quantitative analysis of confocal micrographs of dense colloidal systems, which allows us to show that methods from simulations of granular materials are useful (but not sufficient) in analysing colloidal systems, in particular colloidal glasses and sediments. Collections of spheres are fascinating in their own right, but also make convincing models for real systems. Colloidal systems undergo an entropy-driven fluid-solid transition for hard spheres and a liquid-gas transition for suitable inter-particle attraction. Furthermore, experimental colloidal systems display a so far not well-understood glass transition at high densities, so that the equilibrium state is not achieved. This may be due to limited experimental timescales, but experiments under reduced gravity (both using the Space Shuttle and densitymatching solvents) suggest that it is not. Most colloidal studies have used scattering (i.e. non-microscopical) techniques, which provide no local information. Microscopy (particularly confocal) allows individual particles and their motion to be followed. However, quantitative microscopy of densely-packed, solidlyfluorescent particles, such as colloidal glasses, is challenging. We report, to our knowledge for the first time, a quantitative measure of confidence in individual particle locations and use this measure in an iterative best-fit procedure. This method was crucial for the investigation of the colloidal samples reported in this thesis. One of the disadvantages of microscopy is that it requires particles too large to be truly colloidal; gravity is no longer negligible. The particles used here rapidly sediment to form solid ”plugs”, which are supposedly ”random close packed” (RCP). At least in some cases, this is not the case, since some particles remain free to move. This observation, as well as some literature results, suggest that gravity has some influence on the structure of the sediment. In this document we consider some ideas from literature not normally considered in colloidal studies. Firstly, we discuss the RCP state, and the preferred Maximally Random Jammed state. Secondly, we borrow a technique designed to identify structures known as bridges in simulations of granular materials. Finding bridges, i.e. structures stable against gravity, in colloidal samples is the primary aim of this thesis. Gravity is important in colloidal sphere packings both in sediments and in glasses; its effect is not known but the best available candidate is bridging. The basic results of this analysis, the bridge size distributions, are close to those for granular systems, but differ little for samples of different volume fractions. We identify important stages of the analysis which require more investigation. Whilst questioning the usefulness of the bridge properties, we identify some related packing properties which show interesting trends. No theoretical predictions exist for these quantities. We investigated initially a non-density-matched system, but compare our results with a nearly density-matched system. The results from both systems are similar, despite the particles apparently acquiring a charge in the latter case. This thesis shows that reliable confocal microscopy of very dense systems of solidly-fluorescent particles is possible, and provides a range of unreported properties of dense sedimenting and sedimented nearly-Brownian sphere packings. It provides several suggestions for further analysis of these experimental systems, as well as some to be performed by those who simulate granular matter.