Paweł Weroński

Application of the DLVO theory for particle deposition problems

Implications of the DLVO theory for problems associated with colloid particle adsorption and deposition at solid/liquid interfaces were reviewed. The electrostatic interactions between two planar double-layers described by the classical Poisson–Boltzmann (PB) equation were first discussed. Then, the approximate models for calculating interactions of curved interfaces (e.g. spheres) were exposed in some detail, inter alia the extended Derjaguin summation method and the linear superposition approach (LSA). The results stemming from these models were compared with the exact numerical solution for two dissimilar spheres (including the case of sphere/plane interactions) obtained in bispherical coordinate system. The electrostatic interaction energy was used in combination with dispersion interactions for constructing the DLVO energy profiles discussed next. The influence of surface roughness and charge heterogeneity on energy profiles was also discussed. It was demonstrated that in particle deposition problems the monotonically changing profiles determined by the electrostatic interactions played the most important role. In further part of the review the role of these electrostatic interactions in adsorption and deposition of colloid particles was discussed. The governing continuity equation was exposed incorporating the convective transport in the bulk and the specific force dominated transport at the surface. Approximate analytical models aimed at decoupling of these transfer steps were described. It was demonstrated that the surface boundary layer approximation (SFBLA) was the most useful one for describing the effect of electrostatic interaction at initial adsorption stages. A procedure of extending this model for non-linear adsorption regimes, governed by the steric barrier due to adsorbed particles, was also presented. The theoretical results were then confronted with experimental evidences obtained in the well-defined systems, e.g. the impinging-jet cells and the packed-bed columns of monodisperse spherical particles. The experiments proved that the initial adsorption flux of particles was considerably increased in dilute electrolytes due to attractive electrostatic interactions. This was found in a quantitative agreement with the convective diffusion theory. On the other hand, the rate of later adsorption stages was diminished by the electrostatic lateral interactions between adsorbed and adsorbing particles. Similarly, the experimental data obtained by various techniques (AFM, reflectometry, optical microscopy) demonstrated that these interactions reduced significantly the maximum monolayer coverages at low ionic strength. This behaviour was found in good agreement with theoretical MC-RSA simulation performed by using the DLVO energy profiles. The extensive experimental evidences seem, therefore, to support the thesis that the electrostatic interactions play an essential role in adsorption phenomena of colloid particles.

Irreversible adsorption of colloid particles at heterogeneous surfaces

Irreversible adsorption of polystyrene latex particles of micrometer size range at heterogeneous surfaces was studied experimentally. Model substrate surfaces of controlled site coverage (heterogeneity degree) used in these studies were produced by preadsorption of positively charged latex particles on mica sheets. Deposition kinetics of latex was studied as a function of the site coverage, particle to site size ratio λ and ionic strength of the colloid suspension. Particle distributions over surfaces and coverage were quantitatively evaluated by the direct microscope observation techniques using the diffusion cell. In this way, pair correlation function for various coverage degree and particle size ratio was evaluated. It also was determined the dependence of the jamming coverage of colloid particles on site coverage and ionic strength of the suspension. It was demonstrated that the decrease in the ionic strength of the suspension resulted in a significant decrease in the jamming coverage. This was attributed to the effect of the electrostatic field generated by the interface whose range was increased for low ionic strength. These experimental data revealed, in accordance with theoretical predictions derived from numerical simulations, that the multiple site coordination exerted a pronounced effect on the jamming coverage and the structure of adsorbed layers. It also was shown that this effect can be regulated by changes in the ionic strength of particle suspensions. This could allow one to produce particle clusters at the surface of targeted composition.

Role of convection in particle deposition at solid surfaces

Abstract Recent theoretical and experimental data concerning colloid particle deposition from well-defined flows onto solid/liquid interfaces were reviewed. The macroscopic flow fields in the vicinity of the spherical and cylindrical collector (both isolated and forming a structured layer) were presented. Analogous solutions for the impinging-jet cells of (i) radial symmetry (radial impinging-jet cell RIJ) and (ii) plane symmetry (the slot impinging-jet cell SIJ) were also discussed. Similarities and differences between these flows are pointed out. The method of decomposing the macroscopic flows into local flows of simple geometry like shearing and stagnation flows was exposed. The microscopic flows are discussed in some detail, especially those connected with the motion of a spherical particle parallel and perpendicular to a solid wall. Using the local flow distributions the governing continuity equation is formulated, incorporating the convective transport in the bulk and the specific force dominated transport at the surface. Approximate analytical models aimed at decoupling these transfer steps are described, in particular the surface force boundary layer approximation (SFBLA). Limiting analytical solutions for the perfect sink boundary conditions were given. A procedure of extending the convective diffusion theory to non-linear adsorption regimes governed by the steric barrier due to adsorbed particles, was also presented. The role of the electro-hydrodynamic coupling leading to the hydrodynamic scattering effect in the blocking phenomena was discussed. The theoretical results are confronted with experimental data obtained in the well-defined systems, e.g. mostly in the RIJ and SIJ cells using monodisperse polystyrene latex colloids. A good agreement of theoretical and experimental data was found and most of the theoretical predictions were quantitatively confirmed, in particular the significance of the hydrodynamic scattering effect.

Random sequential adsorption on partially covered surfaces

The random sequential adsorption (RSA) approach was used to analyze adsorption of hard spheres at surfaces precovered with smaller sized particles. Numerical simulations were performed to determine the available surface function φl of larger particles for various particle size ratios λ=al/as and surface concentration of smaller particles θs. It was found that the numerical results were in a reasonable agreement with the formula stemming from the scaled particle theory with the modification for the sphere/sphere geometry. Particle adsorption kinetics was also determined in terms of the RSA simulations. By extrapolating the θl vs τ−1/2 dependencies, the jamming concentrations of larger spheres θl∞ were determined as a function of the initial smaller sphere concentration. It was found that θl∞ were considerably reduced by the presence of smaller sized particles, especially for λ≫1. The pair correlation function g of larger particles in the jamming state was also determined, showing more short range ordering ...

Particle deposition at electrostatically heterogeneous surfaces

Abstract Irreversible adsorption of negatively charged polystyrene latex particles (averaged diameter 0.9 μm) at heterogeneous surfaces was studied experimentally. The substrate of controlled heterogeneity was produced by covering freshly cleaved mica sheets by positively charged polystyrene latex (averaged diameter of 0.47 μm) to a desired surface coverage. Positive latex deposition was carried out under convection and diffusion-controlled transport conditions and the coverage (defined as heterogeneity degree) was determined by direct particle counting using the optical and electron microscopy. Deposition kinetics of larger latex particles at heterogeneous surfaces produced in this way was studied by using the direct optical microscope observations in the impinging-jet and diffusion cells. It was demonstrated that the initial adsorption rate under the convection-controlled transport attained the limiting value pertinent to homogeneous surfaces for heterogeneity degree of a few per cent. This effect was even more pronounced for diffusion-controlled transport conditions. This behaviour was quantitatively interpreted in terms of the theoretical model considering the coupling between surface and bulk transport of particles. Similarly, the experimental results obtained for higher surface coverage of latex (long adsorption times) were in a good agreement with the generalised random sequential adsorption (RSA) model.

Particle adsorption under irreversible conditions: kinetics and jamming coverage☆

Irreversible adsorption of protein and colloid particles at solid/liquid interfaces was analysed theoretically. The expression describing the surface mass balance equation was discussed which can be used as boundary condition for the bulk mass transfer equation. Analytical kinetic equations were derived in the limit of short and long adsorption time. It was shown that the crucial role in the long-time expressions plays the maximum (jamming) coverage which can be derived numerically by applying the random sequential adsorption approach. The results obtained by using this model were discussed in the case of spheres and spheroids. Methods of extending results obtained for hard (noninteracting) particles to interacting particles were also presented. It was demonstrated that the electrostatic double-layer interactions decreased considerably the maximum coverage and influenced the structure of the adsorbed particle mono-layer analysed quantitatively in terms of the pair correlation function.

Limiting diffusion current at rotating disk electrode with dense particle layer.

Exploiting the concept of diffusion permeability of multilayer gel membrane and porous multilayer we have derived a simple analytical equation for the limiting diffusion current at rotating disk electrode (RDE) covered by a thin layer with variable tortuosity and porosity, under the assumption of negligible convection in the porous film. The variation of limiting diffusion current with the porosity and tortuosity of the film can be described in terms of the equivalent thickness of stagnant solution layer, i.e., the average ratio of squared tortuosity to porosity. In case of monolayer of monodisperse spherical particles, the equivalent layer thickness is an algebraic function of the surface coverage. Thus, by means of cyclic voltammetry of RDE with a deposited particle monolayer we can determine the monolayer surface coverage. The effect of particle layer adsorbed on the surface of RDE increases non-linearly with surface coverage. We have tested our theoretical results experimentally by means of cyclic voltammetry measurements of limiting diffusion current at the glassy carbon RDE covered with a monolayer of 3 μm silica particles. The theoretical and experimental results are in a good agreement at the surface coverage higher than 0.7. This result suggests that convection in a monolayer of 3 μm monodisperse spherical particles is negligibly small, in the context of the coverage determination, in the range of very dense particle layers.

Particle monolayers formed under irreversible conditions: jamming coverages and structure

The random sequential adsorption (RSA) approach was used for modelling irreversible adsorption phenomena of polyatomic particles at homogeneous interfaces. Particles of spherical and spheroidal shape, characterised by various axis ratio parameter A, were considered. In the latter case, the flat (side-on) and unoriented adsorption was discussed. The sticking probability (available surface function) was determined for various particle shapes together with “jamming” coverages for clean and precovered surfaces. The structure of adsorbed particle monolayers (under transient and jammed states) was analysed quantitatively in terms of the pair correlation functions. Methods of extrapolation of these results to interacting (soft) particle systems were also discussed. The theoretical predictions were confronted with existing experimental results derived for monodisperse spherical particles. A good agreement with theory was found both in respect of jamming coverages and the monolayer structure. These theoretical and experimental studies demonstrated that minor amounts of small particles (nanometer size range) exert decisive influence on adsorption of larger particles. This phenomenon can be treated as analogous to the surface poisoning effect occurring in heterogeneous catalytic systems.

Fluctuations in the number of irreversibly adsorbed particles

Fluctuations in the number of colloid particles adsorbed irreversibly under pure diffusion transport conditions were determined as a function of surface density and ionic strength of the suspension. The experiments were carried out for monodisperse polystyrene latex particles of micrometer size range adsorbing irreversibly at mica surface. The surface density of adsorbed particles at various areas was determined using the direct microscope observation method. A new experimental cell was used enabling in situ observations of particles adsorption under conditions of negligible gravity effects. It was found that the particle density fluctuations for high ionic strength were in a good agreement with the theoretical results derived from the random sequential adsorption (RSA) model. Also, the theoretical results stemming from the equilibrium scaled particle theory reflected the experimental data satisfactorily. For lower ionic strength a deviation from the hard sphere behavior was experimentally demonstrated. T...

Wet formation and structural characterization of quasi-hexagonal monolayers.

We have presented a simple and efficient method for producing dense particle monolayers with controlled surface coverage. The method is based on particle sedimentation, manipulation of the particle-substrate electrostatic interaction, and gentle mechanical vibration of the system. It allows for obtaining quasi-hexagonal structures under wet conditions. Using this method, we have produced a monolayer of 3 μm silica particles on a glassy carbon substrate. By optical microscopy, we have determined the coordinates of the particles and surface coverage of the obtained structure to be 0.82. We have characterized the monolayer structure by means of the pair-correlation function and power spectrum. We have also compared the results with those for a 2D hexagonal monolayer and monolayer generated by random sequential adsorption at the coverage 0.50. We have found the surface fractal dimension to be 2.5, independently of the monolayer surface coverage.