Statistical Mechanics of Superparamegnetic Colloidal Dispersions Under Magnetic Fields

Abstract

Colloidal dispersions, a term coined by the Scottish scientist Thomas Graham in 1861, have been the subject of interest in different scientific areas during more than a century. A colloidal dispersion is characterized by the existence of a dispersed phase uniformly distributed throughout a dispersion medium.

Many different compounds fall in this category like aerosols (smog, fog, clouds or dust), foams, emulsions (mayonnaise or milk) or gels (butter or jelly). Recent improvements in particle synthesis and colloidal stability have boosted the controlled design of new colloids on demand, targeting the required properties for each application. Among the large variety of different colloidal dispersions (either found in nature or man-made), we have studied a singular type of such dispersions where the colloids have a superparamagnetic behavior called superparamagnetic colloidal dispersions. In these dispersions, surprising features arise under the application of an external magnetic field, as a consequence of the interplay between characteristic colloidal interactions and the anisotropic magnetic dipole-dipole interaction between their constituent colloidal particles.

Along this thesis we have used different theoretical and simulation methods to discuss a number of phenomena appearing in superparamagnetic colloidal dispersions. On the one hand, we have shown that the application of a uniform magnetic field to such dispersions may induce the reversible aggregation of superparamagnetic particles. In view of theoretical models and computer simulations, a new criterion based on the physical properties of the colloidal dispersion has been proposed to predict the formation of aggregates, and its validity has been discussed by comparing the predicted behavior with experimental results.

We have provided evidences of the existence of an equilibrium state, where aggregate sizes acquire a steady distribution, an issue previously suggested but unclear up to now. We have also focused our attention on the growth kinetics of the aggregates and its implications in different phenomena observed in experiments. The need to reach the large time scales of some experiments has motivated the development of new models and simulation strategies to overcome the large time consuming calculations required in standard simulations. We have presented a new simulation model that provides a faster and reliable approach to address the formation of chain-like structures in superparamagnetic dispersions.

The model has been validated by direct comparison with standard Langevin Dynamics simulations and has been applied to experimental situations like the T2 relaxation time of protons in aqueous solutions of superparamagnetic nanoparticles.

Let us mention that the simulation model has been implemented and the corresponding computer code is free and available to the scientific community, envisaged as a new modeling tool readily extensible to other problems of interest.

On the other hand, we have analyzed different effects arising as a consequence of the application of inhomogeneous magnetic fields to such superparamagnetic dispersions. Specifically, we have studied the controlled motion of magnetic particles dispersed in a liquid medium by using inhomogeneous magnetic fields, what is known as magnetophoresis. To do so, we have focused the efforts on the description of the magnetic separation of colloids by the application of uniform magnetic field gradients, from superparamagnetic dispersions to mixtures of colloids with different magnetic response. We have validated the theoretical models adopted against computer simulations and we have discussed their usefulness by comparing the predictions obtained with experimental results. The rational analysis of these results provides a proper starting framework to enhance the design and performance of different magnetic separators, as well as to shape new separation strategies, like the cooperative magnetophoretic separation in superparamagnetic dispersions.

There exists, of course, open problems that we hope this work will help to deal with. For instance, a better understanding of the interplay between the induced structures in superparamagnetic dispersions and their aggregation kinetics. This is an important issue in a vast variety of industrial and lab applications as, for example, in magnetic separation-based processes, waste-water treatment and pollutant removal, immunoassays in clinical applications or in the assisted assembly of new supramolecular materials. Nevertheless, we hope that the results presented along this document could encourage further studies in magnetic colloids science, either refining the results and approaches provided here or developing new strategies to face unsolved problems.

There exists, of course, open problems that we hope this work will help to deal with. For instance, a better understanding of the interplay between the induced structures in superparamagnetic dispersions and their aggregation kinetics. This is an important issue in a vast variety of industrial and lab applications as, for example, in magnetic separation-based processes, waste-water treatment and pollutant removal, immunoassays in clinical applications or in the assisted assembly of new supramolecular materials. Nevertheless, we hope that the results presented along this document could encourage further studies in magnetic colloids science, either refining the results and approaches provided here or developing new strategies to face unsolved problems.