New mechanisms in the adsorption of colloidal suspensions

Abstract

In this thesis we have studied the influence of transport mechanisms on the adsorption kinetics of colloidal suspensions, as well as in the distribution of colloidal particles at the adsorbed layer. Adsorption of colloidal particles is controlled by the geometric exclusion effects at the surface originated by the finite size of the particles and by the irreversible character of the adsorption in these systems, and is also influenced by the specific transport mechanisms which control the arrival of the colloids from the bulk to the interface. Our main objective has been to elucidate the effects of each contribution, as well as their relative importance and mutual influence in some specific situations.<br/><br/>After a first chapter in which we have introduced the basic kinetic models which have been proposed in the literature to take into account surface exclusion effects (random sequential adsorption (RSA) and ballistic (BM) models), in the second chapter we have studied the adsorption in the presence of an external field parallel to the substrate. Our objective has been to elucidate how surface exclusion effects are sensitive to the imposed external conditions upon which adsorption takes place, showing that they do not arise from purely geometric constrains. Instead of carefully describing the transport process, we have conveniently modified the usual kinetic models. The basic feature now is that a new minimum length at which two particles can approach on the substrate appears, and the kinetics becomes asymmetric in the sense that this minimum distance depends on the side of the preadsorbed disk at which the incoming particle adsorbs. We have observed a decrease of the jamming limit with the strength of this imposed force, and also a tendency to form more locally ordered aggregates when this force increases. New adsorption mechanisms are induced by the external field: a particle may roll over a number of preadsorbed spheres before being either adsorbed or rejected, implying that adsorption becomes non-local in the sense that an incoming particle may interact with many preadsorbed disks. The pair distribution function exhibits a richer structure indicating that the clusters have internal structure since their relative separation is not univocally fixed. If the exclusion distance is a multiple of the diameter, then a resonance is observed when using BM rules, and a highly locally ordered substrate is formed.<br/><br/>In chapter 3 we have studied the effect of the transport on the adsorption of colloidal particles at high Peclet number in the presence of a gravity field, when their diffusion can be neglected. As a new mechanism with respect to previous studies, we have incorporated hydrodynamic interactions (HI) existing between the incoming particle and the adsorbed ones due to the fact that the particles are suspended in a fluid. We have shown that the basic effect of HI is to introduce an effective repulsive interaction between the incoming particle and the preadsorbed ones. Some analytic results obtained in very simplified conditions have helped us to understand the effects of HI, although un general, computer simulations have been carried out to study the adsorption process. We have seen that, although the global quantities obtained with HI do not differ quantitatively from the ones obtained for BM, as for example the coverage as a function of time, the jamming limit, or the available fraction of the line, the local structure differs significantly from the one obtained with BM. The pair correlation function is characterized by having a series of peaks due to the rolling of incoming spheres over preadsorbed ones. The behaviour behind the peaks is different, showing a slower decay with HI, indicating that because of the effective repulsion, larger gaps between the spheres are preferred, which implies that HI induce the formation of looser local structures on the substrate. We have shown that the effective repulsion introduced by HI favours the formation of elongated triplets on the surface where BM would predict more isotropic clusters, meaning that HI changes the structure of the clusters formed at the interface. We have compared with experimental results on the adsorption of mellamine particles. The curves obtained with HI agree better with the experimental ones than those obtained with BM, explaining therefore some of the discrepancies observed when comparing with BM. In particular, the slower decay behind the first peak can be thought of as being due to the effect of HI. This has served to show that BM, which was thought to be a good model to describe the adsorption of heavy colloidal particles, is restricted to situations where inertial effects dominate the transport to the wall.<br/><br/>Finally, in chapter 4 we have developed a thermodynamic theory for the adsorption process. We have focused our analysis on the situation in which adsorption is controlled by a surface energy barrier, which is more realistic for the adsorption of small particles. In this case, the transport to the interface is controlled by the diffusion through the energy barrier. In order to describe this process properly, we have introduced an additional internal variable for the fields at the surface in the thermodynamic description.<br/><br/>The surface exclusion effects at this level are introduced considering that the system at the surface is not ideal. In this way we have derived a local generalized Langmuir equation for the evolution of the surface concentration. If the adsorption is not controlled by an energy barrier, then the local thermodynamic description is different. We have shown how it is possible to obtain global generalized Langmuir equation which describes the evolution of the global surface concentration, using the fact that entropical barriers appear for the incoming particles. We have also studied the fluctuations around steady states in a systematic way. We have shown how to deduce the corresponding fluctuation-dissipation theorem when an internal degree of freedom is introduced, and we have applied the results to analyze the density correlation function of a simple adsorption model with diffusion.