Analytical Ultracentrifugation of Inorganic Colloids; Sedimentation Velocity of Interacting and Non-Interacting Particles

Several case studies of the sedimentation velocity of non-interacting, attractive and repulsive colloids are discussed. After a brief introduction that highlights historical facts, basic analytical ultracentrifugation theory, some instrument issues and experiments are reviewed. The existence of discrete single molecular molybdenum Keplerate-type clusters in aqueous solution is demonstrated. Starting from a discrete spherical molybdenum cluster the formation of an 'open' basket type molybdenum defect structure is shown for the first time in solution. A method to determine the particle size distribution via analytical ultracentrifugation without a priori knowledge of the particles is presented with which the average particle size, variance, standard deviation and relative polydispersity can be obtained from a single sedimentation velocity (SV) analytical ultracentrifugation (AUC) run. SV AUC interference optical data also yield the specific particle volume, such that distributions of sedimentation coefficients for colloidal spheres can be converted directly to particle size distributions. A sedimentation velocity analytical ultracentrifugation study on spherical polyoxometalates that exhibit supramolecular structure formation is reported. The particle shape and absolute molar weight of the molybdenum-iron monomers and trends in the sedimentation coefficient distributions for 'giant' vesicles are determined from sedimentation velocity experiments. Combined with dynamic light scattering data, the sedimentation velocity experiments reveal that after 3 years at room temperature, the vesicles are constituted of two molybdenum-iron monomers layers. An equation is derived for the linear concentration dependent sedimentation velocity of attractive colloids that reversibly associate into dimers. Within our approach that is based on an anisotropic interaction potential, the magnitude of this concentration dependence is primarily determined by the dimerization equilibrium constant. We also show how this dimerization affects the osmotic equation of state and conclude that both the sedimentation velocity and the sedimentation-diffusion equilibrium can be used to determine the binding energy from the equilibrium constant for associating colloids or macromolecules, at concentrations low enough for only dimerization to occur. The model for the concentration dependent sedimentation velocity of attractive colloids is used to interpret experimental results from SV AUC measurements on magnetic colloids. A systematic analytical ultracentrifugation study on the concentration dependent sedimentation velocity of magnetic iron oxide colloids as a function of magnetic dipole moment, tuned by adjusting the particle volume is presented. On increase of the dipole moment, a sharp transition occurs after which the sedimentation velocity increases with concentration. We compare our observations with calculations based on a pair-distribution function, as well as a phenomenological model for reversible colloid-colloid association. A system of colloidal repulsive rods is investigated that is very different from the systems in the previous case studies. The effect of ionic strength on the concentration dependent sedimentation velocity for a dispersion of rigid boehmite-silica rods is investigated. Experimental results are compared to predictions from theory for hard rods. Addition of salt lowers the sedimentation velocity concentration dependence, which is eventually similar to the prediction from theory for uncharged rigid rods. Above 50 mM NaCl the rods gel into a fine network that tends to settle in the earth's gravitational field

Model independent determination of colloidal silica size distributions via analytical ultracentrifugation

We report a method to determine the particle size distribution of small colloidal silica spheres via analytical ultracentrifugation and show that the average particle size, variance, standard deviation, and relative polydispersity can be obtained from a single sedimentation velocity (SV) analytical ultracentrifugation (AUC) experiment. The particle size distribution (psd) from the enhanced van Holde-Weischet (vHW) analysis accounts for the dynamic light scattering results quite well. In addition, the vHW psd equals the psd from a continuous distribution of sedimentation coefficients analysis where whole sedimentation velocity boundaries are fitted. The SV AUC interference optical data also yield the specific particle volume such that distributions of sedimentation coefficients for colloidal spheres can be converted directly to particle size distributions. Our results show that SV AUC experiments may yield a quantitative particle size distribution without a priori knowledge of the particle size and the shape of the size distribution

Ultracentrifugation of single-domain magnetite particles and the De Gennes-Pincus approach to ferromagnetic colloids in the dilute regime.

We report an analytical ultracentrifugation study on sedimentation in dilute stable dispersions of uniform, magnetic iron oxide (Fe3O4) colloids. On increase of the dipolar coupling constant, tuned by the average particle size, the linear concentration dependence of the sedimentation velocity shows an abrupt transition from the hindered sedimentation expected for hard spheres to a marked acceleration already for weak dipolar interactions. This transition is not reproduced by sedimentation theory derived from an effective, isotropic pair correlation function of the type proposed by De Gennes and Pincus, for reasons which are made clear. Accelerated settling, instead, follows a scaling based on the mass action law for dimer formation with dipoles in head-to-tail configuration. Our work illustrates that orientational averaging of dipole interactions of ferromagnetic colloids in the dilute regime is inapplicable, with an obvious implication for the possible existence of isotropic gas-liquid criticality for such colloids

Direct evidence on the existence of [Mo132] Keplerate-type species in aqueous solution

We demonstrate the existence of discrete single molecular [Mo132] Keplerate-type clusters in aqueous solution. Starting from a discrete spherical [Mo132] cluster, the formation of an open-basket-type [Mo116] defect structure is shown for the first time in solution using analytical ultracentrifugation sedimentation velocity experiments

Ultracentrifugation of single-domain magnetite particles and the De Gennes-Pincus approach to ferromagnetic colloids in the dilute regime.

We report an analytical ultracentrifugation study on sedimentation in dilute stable dispersions of uniform, magnetic iron oxide (Fe3O4) colloids. On increase of the dipolar coupling constant, tuned by the average particle size, the linear concentration dependence of the sedimentation velocity shows an abrupt transition from the hindered sedimentation expected for hard spheres to a marked acceleration already for weak dipolar interactions. This transition is not reproduced by sedimentation theory derived from an effective, isotropic pair correlation function of the type proposed by De Gennes and Pincus, for reasons which are made clear. Accelerated settling, instead, follows a scaling based on the mass action law for dimer formation with dipoles in head-to-tail configuration. Our work illustrates that orientational averaging of dipole interactions of ferromagnetic colloids in the dilute regime is inapplicable, with an obvious implication for the possible existence of isotropic gas-liquid criticality for such colloids