Double layer relaxation in colloids

The purpose of the present study is to improve our insight into the relaxation of the electrical double layer around particles in hydrophobic sols. A detailed knowledge of the relaxation mechanisms is required to explain the behaviour of sols under conditions where the double layer is perturbed. Such conditions are frequently encountered in colloid science; for instance when colloidal particles coagulate or when they are subjected to an external field as in electrokinetics.One of the appropriate electrokinetic methods to experimentally study the dynamic properties of double layers is low-frequency dielectric spectroscopy. Previous studies have shown that latices exhibit a large dielectric response. However, these results could not be quantitatively reconciled with either electrophoresis data or existing theory. To discriminate whether the disagreements were due to theoretical or experimental imperfections, dielectric data on inorganic sols were highly desirable. The major aim of this study is to provide such data and, where necessary, to improve the existing theory. The results are described and discussed in chapters 2-5.The stability of sols against coagulation is of crucial importance for their applications. In principle, hydrophobic sols are thermodynamically unstable; they tend to form aggregates due to the attractive Van der Waals forces. However, in many cases the rate of coagulation is slowed down by the presence repulsive electrostatic forces. These occur if double layers overlap.Coagulation is a dynamic process. Particles interact on a certain time scale during which the extent of double layer overlap varies. Consequently, the equilibrium double layer structure will be perturbed, inducing relaxation processes. In principle, the colloid stability depends on the relaxation time of the double layer, which may be well of the same order as the typical time scale of a particle collision. However, the knowledge about the influence of the relaxation processes on the coagulation rate was limited. Therefore, the second aim of this study is to improve that situation. We focussed our attention on those cases where the relaxation rate of the double layer is determined by the adjustment of the surface charge density, see chapter 7. Chapter 6 discusses a related topic.A short summary of the results and main conclusions of each chapter is given below.Chapter 2 gives a description of a newly constructed fourelectrode dielectric spectrometer, designed to measure the dielectric response (or complex admittance) of sols in the frequency range of approximately 500 Hz; to 500 kHz. A four-electrode design is developed to avoid problems related to electrode polarization and, at the same time, to-enable the use of an automatic frequency response analyzer. The device is suitable for fast and accurate data acquisition, the measurement of one complete spectrum taking a few minutes only. Furthermore, it is especially designed to measure frequency-difference spectra.In chapter 3 it is shown that the thin double layer theory for the electrokinetic properties of dilute colloids can be extended to include surface conduction, i.e. a conduction contribution by ions behind the plane of shear. The calculations show that the occurrence of surface conduction leads to a reduction of the electrophoretic mobility and to an increase of the static sol conductivity and the dielectric response. Moreover, it also follows from the theory that an unambiguous interpretation of only one type of experimental data, for example the electrophoretic mobility, is impossible if surface conduction occurs. To assess whether this is the case, one is bound to also measure either the static conductivity or the dielectric response of the sol. The comparison between theory and experiment has been made for literature data on latices. For polystyrene latices, the mobility and static conductivity can be well explained if surface conduction is taken into account. However, the extended theory is not able to provide a quantitative explanation of the extreme dielectric increment of latices.Chapter 4 provides experimental data on the low-frequency dielectric response of dilute aqueous hematite and silica sols of spherical particles as a function of pH, ionic strength and particle size. The pH-sensitivity of the dielectric responses of the two sols shows that this response is a function of the surface charge density. The particle size dependence of the characteristic relaxation frequency is in fair agreement with theoretical predictions. In contrast to the case of latices, the dielectric behaviour of both hematite and silica can be well explained by classical electrokinetic theory yielding reasonable values for the ξ potentials. However, these values are systematically higher than those obtained electrophoretically. This inconsistency indicates the occurrence of surface conduction within the plane of shear, a type of conduction not included into the classical theory. By using the theory as developed in chapter 3, a distinction can be made between the (mobile) counter charge within and that beyond the plane of shear. Application to the hematite and silica data shows that a large fraction of the (mobile) counter charge is located inside this plane. This fraction increases with increasing surface charge density.The experimental and theoretical framework developed in the previous chapters has been applied to a spherical coryneform bacterium suspension in Chapter 5 . According to the preliminary results, approximately 95% of the total (mobile) counter charge in the double layer of the bacterium is located behind the plane of shear, i.e. probably within the cell wall itself. Such a large surface conduction contribution inhibits the possibility to determine the ξpotential of bacteria by electrophoretic measurements only. In this respect. additional information is necessary. The present investigation shows that dielectric spectroscopy is a useful technique to obtain that information.Chapter 6 presents a model to calculate the electrostatic interaction between two colloidal spheres, accounting for their polarizabilities. Under conditions where the potential along the surface varies during interaction, for example under those as discussed in chapter 7, the polarizability of a particle affects the electrostatic repulsion. Results are presented for spheres interacting at constant surface charge density. The calculations clearly show how the electrostatic force decreases with the polarizability of the particle. The decrease becomes larger with stronger double layer overlap, whereas it is relatively insensitive to κa. This insensitivity is a consequence of tangential screening effects inside the particles. It is pointed out that for slowly coagulating sols of particles with a fixed surface charge density, the stability ratio W is sensitive to the polarizability of the particle.Transient deviations from the equilibrium surface charge density during the interaction of colloidal particles and their influence on colloid stability are discussed in chapter 7 . Such deviations cause the process of particle encounter to become a non- first-order Markov process, which complicates the analysis of colloid stability. Two methods are presented to calculate a modified colloid stability ratio, taking such deviations into account in an approximate way. These methods differ by their estimates for the time scale of the Brownian encounter and its dependence on the height of the energy barrier. Despite these differences, both methods show that double-layer dynamics can have major consequences for the stability ratio. However, the predicted dependences of the rate of slow coagulation on the particle radius of the two methods are different. This indicates that double-layer dynamics could explain the experimentally found insensitivity of the stability ratio to the particle size, provided the time scale of the encounter strongly increases with growing height of the energy barrier. However, this proviso is unlikely to be satisfied. A simple statistical analysis indicates that the time scale of any individual encounter should decrease with growing barrier height!This thesis presents experimental and theoretical work related to double layer relaxation of colloids. It is not only of academic interest but also of significant practical importance. The results provide an encouraging basis for further research in the field of electrokinetics and stability of hydrophobic colloids.