From Triplet Correlations to Triplet Interactions in Colloidal Suspensions

Abstract

In this work, we have been dealing with some of the many aspects that make colloidal systems such an interesting topic in today s physics. One interesting feature, for example, is the ability to observe individual particles with video-microscopy and to study thus phase behaviour and structural properties live on screen. Another feature is the frequent presence of additional components in colloidal suspensions. As one is usually interested in the colloidal particles only, the additional component s degrees of freedom are integrated out which leads to effective interaction potentials between the colloidal particles. These effective interactions will always contain many-body contributions even when all the basic interactions are strictly pair-wise.In particular, we have been dealing with two experimental systems. Both have been observed by video-microscopy and we had therefore access to the full positional data at all times. The first system, the magnetic system, is a simple liquid and interacts with a strictly pair-wise magnetic dipole-dipole potential. The second system, the charged system, is a complex liquid because of the presence of additional micro-ions. The particle interactions thus include also many-body contributions.The numerical calculation of such many-body interactions in my diploma thesis has been the starting point of this work. With this background, we wanted to study the effect of triplet interactions on structural properties. In particular, we wanted to find out, if these triplet interactions can actually be found in experimental data. With video-microscopy, we had access to the full positional data and we could, for the first time, directly extract distribution functions of higher order from experimental data. Thence, the key questions of this work arose: Can we find any traces of triplet interactions in these experimental distribution functions and, subsequently, can we reversely extract triplet interaction potentials from the distribution functions?As a preparation, we have been studying triplet distribution functions first. Contrary to previous investigations, video-microscopy enabled us for the first time to obtain experimental triplet distribution functions. We have been studying the triplet distribution functions regarding the popular superposition approximation of Kirkwood in detail, quantified its errors with the triplet potential of mean force and checked the thermodynamic consistency of the superposition approximation with the Born-Green equation. To clearly separate triplet correlation energies from true triplet interaction energies, we chose to concentrate these investigations on the magnetic system, which is a simple liquid with pair interactions only. We have found that even in a purely pair-wise interacting system, triplet correlation energies can be up to 4kT strong.Subsequent to this important preparatory work on the the magnetic system we turned back to the charged system with possible triplet interactions. To finally extract triplet interactions from triplet distribution functions, we developed two methods. In the first, we were exploiting the limiting behaviour of the distribution functions at low densities. In the second, we have extended the inverse Monte-Carlo method of Almarza and Lomba to triplet interactions. Both methods provided us with the ability to study triplet interactions in situ. We now had the capability to extract the full three-dimensional parameter dependency of the triplet interactions from the positional data of colloidal particles in suspension. This was a major improvement over previous experimental approaches which yield only triplet interactions of isolated particles in limited geometries.We have been applying both methods on reference Monte-Carlo simulations where we could selectively switch triplet interactions on and off. In addition to testing the accuracy and limitations of both methods, we have learned furthermore that we generally need to consider higher order distribution functions to properly extract higher order interactions. Even comparably strong triplet interactions hardly affected the pair distribution function. And even more important, this slightly modified pair distribution function could always be explained with an effective pair potential which hardly differs from the true pair potential. It is therefore essential to go beyond pair distribution functions if one wants to extract many-body potentials from structural data. This justifies and explains the basic idea of this work.Finally, after predicting triplet interactions theoretically, we were able to observe triplet interactions at work in colloidal suspensions. And indeed, we have found an attractive potential of considerable strength in the charged system. It is, however, too short-ranged to significantly influence structural properties.