Resumen de Interaction, structure and kinetic properties of colloidal monolayers

Juan Carlos Fernandez Toledano

• The aim of this work is to study the structural and kinetic properties of colloidal monolayers and their relationship with the interparticle interaction potential and with an external force. The main questions that we want to answer here correspond with each one of the chapters of this thesis: 1.- In chapter 2 we present briefly the main theoretical aspects of the colloidal monolayer description that are going to be useful in the develop of this thesis. The analyzed questions are: i.- How is the movement of the colloidal particles at the monolayers We introduce the Langevin and the Fokker-planck equations in order to describe the Brownian motion of the particles.

  ii.- When the particles coagulate between them, how is the structure of the resulting clusters? We will introduce the concept of fractality.

  iii.- After that, the following question is: how are the dynamics of the growing clusters and how dynamics are abetted by the interaction between the particles? To answer this question we introduce the Smoluchowski equation, that depends on the so-called aggregation kernels and we see the relationship between such kernels and the interaction potential.

  2.- In chapter 3 we answer the question: how is the interaction potential between colloidal particles trapped at a polar/non-polar interface? First, we present the typical model for colloids trapped at an interface (due to the surface tension) and how use the interaction potential between infinite half space to calculate the interaction between spheres through the Derjaguin approximation. After that, we analyze the deferent terms of the interaction potential: i.- DLVO interactions: we introduce the electrostatic repulsion and the London-van der Waals attraction which are able to explain the presence of a primary minimum in the total interaction potential.

  ii.- Non DLVO interactions: the impossibility to explain some of the experimental results it make necessary to introduce other interaction terms: a.- Hydrophobic interaction: it is due to the interaction of the colloidal particles with the surrounding molecules of fluid.

  b.- Dipolar and monocular interactions: these are characteristic interactions between particles trapped at a polar/non-polar interface induced by the presence of dipoles (even monopoles) in the non-polar phase. It was necessary to introduce them in order to explain the great stability of the colloids at interfaces in comparison with the three-dimensional case.

  c.- Capillary interactions: these interactions are the result of the distortion of the interface where the colloidal particles are trapped. The capillary interactions can be classified in two different categories: flotation capillary forces, when the interface deformation is provoked by the weight of the particles (and it is considerate negligible for particles with radius ( 5 micrometers) and immersion capillary forces, when the deformation is due to the wetting properties of the particle surface. The last interactions can be important in certain cases for the colloidal stability, 3.- In chapter 4 we show the main mathematical tools used to study the aggregation process from a topological point of view. We define the Voronoi diagram which is used to describe a set of points over the planes (that, in our case, represents the mass center of our clusters) as a tessellation of the plane. Each cluster is represented by a cell which properties (number of sides and area) are directly related with the characteristics of the aggregation process.

  4.- In chapter 5, we use the Voronoi diagrams in order to study the topological properties of systems of colloidal clusters formed in two-dimensional DLCA simulations. Moreover, with the Voronoi diagrams is also possible to observe how the aggregation tends to order the clusters and how this order increases with the surface packing fraction.

  5.- In chapter 6, we study the influence of the interaction range of the repulsive interaction on the colloidal aggregation process. The particles are assumed to interact through a Yukawa potential. Three different kinetic region can be observed in the aggregation process depending on the parameters used on the Yukawa interaction. Moreover, we develop a new method to obtain the kinetic rate constants directly from the simulations.

  Also, introduction the computed kernel in the Smoluchowski equation, we are able to reproduce the simulated cluster size distribution.

  6.- In chapter 7, we show an experimental study of the formation of loosely bound and internally ordered structures (usually called mesostructures) which have been tried to be explained in base of an unknown long-range attractive interaction. We have shown that the formation of such mesostructures is related to the presence of an oily contamination at the interface. The experiments showed that mesostructures can be formed even with very small amounts of contaminant agent (silicon oil). Moreover, we present a simple model, based on oil droplets dispersed at an air-water interface, in order to explain theoretically the formation of such mesostructures. Finally, we have performed some Monte Carlo simulation in order to reproduce some of the colloidal mesostructures obtained in our experiments.