Electrophoretic mobility of a spherical colloidal particle
01 Jan 1978-Journal of the Chemical Society, Faraday Transactions (The Royal Society of Chemistry)-Vol. 74, pp 1607-1626
TL;DR: In this article, it was shown that for a colloidal particle of any shape the mobility is independent of the dielectric properties of the particle and the electrostatic boundary conditions on the particle surface.
Abstract: The equations which govern the ion distributions and velocities, the electrostatic potential and the hydrodynamic flow field around a solid colloidal particle in an applied electric field are reexamined. By using the linearity of the equations which determine the electrophoretic mobility, we show that for a colloidal particle of any shape the mobility is independent of the dielectric properties of the particle and the electrostatic boundary conditions on the particle surface. The mobility depends only on the particle size and shape, the properties of the electrolyte solution in which it is suspended, and the charge inside, or electrostatic potential on, the hydrodynamic shear plane in the absence of an applied field or any macroscopic motion.New expressions for the forces acting in the particle are derived and a novel substitution is developed which leads to a significant decoupling of the governing equations. These analytic developments allow for the construction of a rapid, robust numerical scheme for the solution of the governing equations which we have applied to the case of a spherical colloidal particle in a general electrolyte solution. We describe a computer program for the conversion of mobility measurements to zeta potential for a spherical colloidal particle which is far more flexible than the Wiersema graphs which have traditionally been used for the interpretation of mobility data. Furthermore it is free of the high zeta potential convergence difficulties which limited Wiersema's calculations to moderate values of ζ. Some sample computations in typical 1:1 and 2:1 electrolytes are exhibited which illustrate the existence of a maximum in the mobility at high zeta potentials. The physical explanation of this effect is given. The importance of the mobility maximum in testing the validity of the governing equations of electrophoresis and its implications for the colloid chemist's picture of the Stern layer are briefly discussed.
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TL;DR: It is demonstrated that electrical charges on sterically stabilized nanoparticles determine B NSL stoichiometry; additional contributions from entropic, van der Waals, steric and dipolar forces stabilize the variety of BNSL structures.
Abstract: The assembly of nanoparticles of two different materials into a binary nanoparticle superlattice is a promising way of synthesizing a large variety of materials (metamaterials) with precisely controlled chemical composition and tight placement of the components. In theory only a few stable binary superlattice structures can assemble from hard spheres, potentially limiting this approach. But all is not lost because at the nanometre scale there are additional forces (electrostatic, van der Waals and dipolar) that can stabilize binary nanoparticulate structures. Shevchenko et al. now report the synthesis of a dozen novel structures from various combinations of metal, semiconductor, magnetic and dielectric nanoparticles. This demonstrates the potential of self-assembly in designing families of novel materials and metamaterials with programmable physical and chemical properties. Assembly of small building blocks such as atoms, molecules and nanoparticles into macroscopic structures—that is, ‘bottom up’ assembly—is a theme that runs through chemistry, biology and material science. Bacteria1, macromolecules2 and nanoparticles3 can self-assemble, generating ordered structures with a precision that challenges current lithographic techniques. The assembly of nanoparticles of two different materials into a binary nanoparticle superlattice (BNSL)3,4,5,6,7 can provide a general and inexpensive path to a large variety of materials (metamaterials) with precisely controlled chemical composition and tight placement of the components. Maximization of the nanoparticle packing density has been proposed as the driving force for BNSL formation3,8,9, and only a few BNSL structures have been predicted to be thermodynamically stable. Recently, colloidal crystals with micrometre-scale lattice spacings have been grown from oppositely charged polymethyl methacrylate spheres10,11. Here we demonstrate formation of more than 15 different BNSL structures, using combinations of semiconducting, metallic and magnetic nanoparticle building blocks. At least ten of these colloidal crystalline structures have not been reported previously. We demonstrate that electrical charges on sterically stabilized nanoparticles determine BNSL stoichiometry; additional contributions from entropic, van der Waals, steric and dipolar forces stabilize the variety of BNSL structures.
1,981 citations
TL;DR: The present review critically investigates to what extent self-assembly can be directed, enhanced, or controlled by either changing the energy or entropy landscapes, using templates or applying external fields.
Abstract: Within the field of nanotechnology, nanoparticles are one of the most prominent and promising candidates for technological applications. Self-assembly of nanoparticles has been identified as an important process where the building blocks spontaneously organize into ordered structures by thermodynamic and other constraints. However, in order to successfully exploit nanoparticle self-assembly in technological applications and to ensure efficient scale-up, a high level of direction and control is required. The present review critically investigates to what extent self-assembly can be directed, enhanced, or controlled by either changing the energy or entropy landscapes, using templates or applying external fields.
1,938 citations
Cites background from "Electrophoretic mobility of a spher..."
...polarization as well.(70) In the far-field, the induced field surrounding a polarized particle takes the form of a dipole and leads to a strong, anisotropic dipole dipole interaction between particles....
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TL;DR: The response of a model microelectrochemical system to a time-dependent applied voltage is analyzed, including electrochemistry, colloidal science, and microfluidics, including surface conduction, multicomponent electrolytes, and Faradaic processes.
Abstract: The response of a model microelectrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate blocking electrodes, which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter epsilon= lambdaD/L, where lambdaD is the screening length and L the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of lambdaDL/D (not lambdaD2/D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduces multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L2/D. In the "strongly nonlinear" regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multicomponent electrolytes, and Faradaic processes.
938 citations