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Register a new userSize Distribution of Superparamagnetic Particles Determined by Magnetic Sedimentation
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Added by
Jean-Francois Berret
Publication date
2006
fields
Physics
and research's language is
English
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We report on the use of magnetic sedimentation as a means to determine the size distribution of dispersed magnetic particles. The particles investigated here are i) single anionic and cationic nanoparticles of diameter D = 7 nm and ii) nanoparticle clusters resulting from electrostatic complexation with polyelectrolytes and polyelectrolyte-neutral copolymers. A theoretical expression of the sedimentation concentration profiles at the steady state is proposed and it is found to describe accurately the experimental data. When compared to dynamic light scattering, vibrating sample magnetometry and cryogenic transmission electron microscopy, magnetic sedimentation exhibits a unique property : it provides the core size and core size distribution of nanoparticle aggregates.
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We investigate the sedimentation of initially packed paramagnetic particles in presence of a homogeneous external magnetic field, in a Hele-Shaw cell filled with water. Although the magnetic susceptibility of the particles is small and the particle-particle induced magnetic interactions are significantly smaller compared to the gravitational acceleration, we do observe a measurable reduction of the decompaction rate as the amplitude of the applied magnetic field is increased. While induced magnetic dipole-dipole interactions between particles can be either attracting or repulsive depending on the particles relative alignment, our observations reveal an effective overall enhancement of the cohesion of the initial pack of particles due to the induced interactions, very likely promoting internal chain forces in the initial pack of particles. The influence of the magnetic field on the particles once they disperse after being decompacted is on the other hand found to remain marginal.
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel, used to study e.g. rain initiation and particle distributions in the atmosphere. We solve the kinetic equation analytically to obtain steady state and self-similar solutions in time and in height, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.
We report on calculations of the reduced sedimentation velocity $U/U_{0}$ in homogenous suspensions of strongly and weakly charged colloidal spheres as a function of particle volume fraction $phi$. For dilute suspensions of strongly charged spheres at low salinity, $U/U_{0}$ is well represented by the parametric form $1-pphi^alpha$ with a fractional exponent $alpha=1/3$ and a parameter $psimeq 1.8$, which is essentially independent from the macroion charge $Z$. This non-linear volume fraction dependence can be quantitatively understood in terms of a model of effective hard spheres with $phi$-dependent diameter. For weakly charged spheres in a deionized solvent, we show that the exponent $alpha$ can be equal to 1/2, if an expression for $U/U_0$ given by Petsev and Denkov [J. Colloid Interface Sci. 149, 329 (1992)] is employed. We further show that the range of validity of this expression is limited to very small values of $phi$ and $Z$, which are probably not accessible in sedimentation experiments. The presented results might also hold for other systems like spherical proteins or ionic micelles.
Soft elastic composite materials can serve as actuators when they transform changes in external fields into mechanical deformation. Here, we address the corresponding deformational behavior of magnetic gels and elastomers, consisting of magnetizable colloidal particles in a soft polymeric matrix and exposed to external magnetic fields. Since many practical realizations of such materials involve particulate inclusions of polydisperse size distributions, we concentrate on the effect that mixed particle sizes have on the overall deformational response. To perform a systematic study, our focus is on binary size distributions. We systematically vary the fraction of larger particles relative to smaller ones and characterize the resulting magnetostrictive behavior. The consequences for systems of various different spatial particle arrangements and different degrees of compressibility of the elastic matrix are evaluated. In parts, we observe a qualitative change in the overall response for selected systems of mixed particle sizes. Specifically, overall changes in volume and relative elongations or contractions in response to an induced magnetization can be reversed into the opposite types of behavior. Our results should apply to the characteristics of other soft elastic composite materials like electrorheological gels and elastomers when exposed to external electric fields as well. Overall, we hope to stimulate the further investigation on the purposeful use of mixed particle sizes as a means to design tailored requested material behavior.
For suspensions of permeable particles, the short-time translational and rotational self-diffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a uniformly permeable sphere of a given permeability, with the internal solvent flow described by the Debye-Bueche-Brinkman equation. The particles are assumed to interact non-hydrodynamically by their excluded volumes. The virial expansion of the transport properties in powers of the volume fraction is performed up to the two-particle level. The first-order virial coefficients corresponding to two-body hydrodynamic interactions are evaluated with very high accuracy by the series expansion in inverse powers of the inter-particle distance. Results are obtained and discussed for a wide range of the ratio, x, of the particle radius to the hydrodynamic screening length inside a permeable sphere. It is shown that for x >= 10, the virial coefficients of the transport properties are well-approximated by the hydrodynamic radius (annulus) model developed by us earlier for the effective viscosity of porous-particle suspensions.
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