Dennis C. Prieve

Measurement of colloidal forces with TIRM

During the last 10 years, we have developed a new experimental technique called Total Internal Reflection Microscopy. Using TIRM we can monitor the separation distance between a single microscopic sphere immersed in an aqueous solution and a transparent plate. Because the distance is calculated from the intensity of light scattered by the sphere (3–30 μm in diameter) when illuminated by an evanescent wave, this technique provides a sensitive, non-intrusive, and instantaneous measure of the distance between the sphere and the plate. Changes in distance as small as 1 nm can be detected. From the equilibrium distribution of separation distances sampled by Brownian motion, we determine the potential energy profile in the vicinity of the minimum formed by gravitational attraction and double-layer repulsion or steric repulsion caused by an adsorbed soluble polymer. Forces as small as 0.01 pN can be detected. We have also measured van der Waals attraction, the radiation pressure exerted by a focused laser beam, receptor-mediated interaction between antigen and antibodies, and steric repulsion due to adsorbed polymer layers. From the autocorrelation of the temporal fluctuations in scattering intensity, we have inferred the value of the normal component of the diffusion coefficient, which is approximately two orders of magnitude smaller than the bulk value owing to the close proximity of the sphere to the wall. This provides the first experimental test of Einstein’s equation (relating mobility and diffusion coefficient) in a colloidal force field.

Hindered diffusion of colloidal particles very near to a wall: Revisited

Total internal reflection microscopy is a technique for monitoring changes in the distance between a single microscopic sphere and a flat plate by measuring the intensity of light scattered by the sphere when illuminated by an evanescent wave. A histogram of scattering intensities can be used to construct the potential energy profile as a function of distance relative to the most probable distance. Thus potential energies can be measured to within a fraction of kT while changes in distance can be measured to within 1 nm. An autocorrelation of the scattering intensities can be used to deduce an average diffusion coefficient of the sphere, which is found to be only a few percent of the Stokes–Einstein value, owing to the close proximity of the plate. The analysis of the intensity-autocorrelation function presented here can be used to deduce an absolute value for the most probable separation distance, without a priori knowledge of the functional form of the PE profile and in the presence of a constant backgr...

Rate of deposition of Brownian particles under the action of London and double-layer forces

The rate of collection of Brownian particles under the influence of interaction forces between the collector surface and the particles is calculated by (a) incorporating the interaction forces in the rate constant of a virtual, first order, chemical reaction taking place on the surface of the collector, and by (b) solving the convective diffusion equation subject to that chemical reaction as a boundary condition. Several geometries (sphere, cylinder, rotating disc) are considered for the collector.An Arrhenius type equation is obtained for the apparent reaction rate constant. Equations for the apparent activation energy and for the frequency factor are established as functions of Hamakers constant, ionic strength, surface potentials and particle radius.

Scattering of an evanescent surface wave by a microscopic dielectric sphere.

A ray-optics scattering model has been developed to determine if multiple reflections between the sphere and the plate could alter the exponential relationship between the scattering intensity and the separation distance as contact is approached. Results indicate that the effect of multiple reflections is dependent on sphere size, refractive indices, and the penetration depth of the evanescent wave. An experimental validation of the model was performed with polystyrene spheres (diameters 7-30 microm) immersed in an alcohol mixture and resting on an MgF(2) film that had the same refractive index. Film thicknesses varied between 0 and 300 nm. No significant effect of multiple reflections was measured at an incident angle approximately 2 degrees above the critical angle, which was in agreement with the predictions of the ray-optics model. By contrast, the scattering intensity from a 300-microm sphere was predicted to be much more sensitive to the separation distance at separations below one penetration depth when the incident a ngle was increased to over 6 degrees above the critical angle.

Simplified predictions of Hamaker constants from Lifshitz theory

Abstract Approximations to Lifshitz theory are developed to estimate the van der Waals interaction of coated and uncoated nonmetallic half spaces as a function of separation distance. Using a three-parameter representation of the dielectric spectrum of each material, based only on refractive index data from the visible part of the spectrum and the static dielectric constant, the approximations yield nonretarded Hamaker constants within an average error of 4% of corresponding values computed from rigorous evaluation of Lifshitz theory with the complete dielectric spectra. The effects of retardation and a coating on one of the half-spaces can also be estimated from the approximations but with less accuracy. These approximations should be useful in semiquantitative applications requiring a very large number of such evaluations but not a high level of precision (e.g., to screen materials to be used as a coating or to assess stability to flocculation).

The surface potential of and double-layer interaction force between surfaces characterized by multiple ionizable groups.

By considering that the electrostatic charge on biological surfaces arises from the presence of multiple ionizable groups, the surface potential of and double-layer force between two plane surfaces, separated by an electrolyte solution, were evaluated by numerically solving the non-linear Poisson-Boltzmann equation. Boundary conditions were formulated by assuming the groups of the surfaces are always in ionic equilibrium with the solution. Comparisons are made between the force numerically calculated as above and analytical expressions obtained by (a) linearly superimposing the non-interactive electrostatic potential profiles of each surface, or by solving the linearized Poisson-Boltzmann equation with (b) fixed surface potential or with (c) fixed surface charge density. Surface characteristics used for the comparisons were deduced from electrophoretic data on erythrocyte or leucocyte surfaces.

Role of colloidal forces in hydrodynamic chromatography

Abstract Double-layer and van der Waals forces, acting between solute particles and the wall of a capillary in which an aqueous carrier solution undergoes Poiseuille flow, influence the radial distribution of particle centers. If the elution time is sufficient to allow the Brownian particles to sample all radial positions then the radial distribution is shown to be a Boltzmann one. Choosing the capillary radius so as to match the hydraulic radii of the packed column and capillary, predicted average particle residence times agreed reasonably well with all the experimental results obtained by Small (3). A parameter sensitivity study suggests that at low ionic strengths (∼10 −4 mole/liter) the average particle residence time is nearly independent of the chemical nature of the particle (i.e., Hamakers constant and surface potential). However, at high ionic strengths (∼0.1 mole/liter) the particles chemical nature is also important. Under the latter conditions, the secondary minimum in the particle—packing interaction energy profile becomes appreciably larger than the particles thermal energy ( kT ), causing the particles to sample the slow region near the packing surface more frequently and significantly increasing the average residence time.

Adsorption of brownian hydrosols onto a rotating disc aided by a uniform applied force

Abstract The interaction-force boundary layer method is employed to estimate the steady-state rate of deposition under the action of a spatially uniform, applied force field. A simple algebraic equation was derived which predicts values of the rate within ±20% of those computed from a numerical solution of the complete transport equation—including van der Waals attraction, double-layer repulsion, an externally applied force field, fluid motion, diffusion, and the position-dependence of the particles mobility and diffusion coefficient. This approximation provides a good estimate of the rate whenever the diffusion boundary layer is thick compared to the range of the interaction forces or when aU/ D ∞ ≤ 0.01, where a and D ∞ are the particles radius and diffusion coefficient, respectively, and U is the normal component of the undisturbed fluid velocity evaluated one particle radius from the discs surface.

Diffusiophoresis of a rigid sphere through a viscous electrolyte solution

Numerical predictions of the migration velocity are presented for slightly non-uniform aqueous solutions of KCl or NaCl over a wide range of zeta potential (ζ) and particle radius divided by Debye length (κa). The characteristic speed of migration is comparable in magnitude to the ensemble mean diffusion velocity of ions forming the concentration gradient. In the absence of a macroscopic electric field induced by the gradient, the particle usually migrates toward higher salt concentration (the chemiphoretic contribution). However, for moderate values of κa, the particle reverses direction when |ζ| becomes sufficiently large. With an induced electric field, competition between electrophoresis and chemiphoresis can result in as many as four reversals in direction over the range of ζ. In some cases, the direction of migration was found to depend on the magnitude of the ionic drag coefficients, which seems to preclude predicting the direction on the basis of equilibrium thermodynamics.

Diffusiophoresis: Migration of Colloidal Particles in Gradients of Solute Concentration

Abstract When a rigid colloidal particle is placed in a solution which is not uniform in the concentration of some solute that interacts with the particle, the particle will be propelled in the direction of higher or lower concentration of the solute. The resulting locomotion is called diffusiophoresis. Experimental observations and theoretical predictions of the migration velocity of hydrosoIs are reviewed. Present commercial applications include the formation of rubber gloves and the deposition of paint films onto a steel surface. New applications to the analysis of colloidal mixtures and solid-liquid separation are suggested.