## Determination of the Exact Particle Radius Distribution for Silica Nanoparticles via Capillary Electrophoresis and Modeling the Electrophoretic Mobility with a Modified Analytic Approximation

journal contribution

posted on 14.02.2017 by Anna Fichtner, Alaa Jalil, Ute Pyell#### journal contribution

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In
this study, we use aqueous dispersions of amorphous silica nanoparticles
of various sizes to investigate whether electropherograms recorded
from capillary electrophoresis experiments can be converted directly
into exact number-based particle radius distributions, provided that
there is a relaxation effect-based size selectivity of the electrophoretic
mobility and provided that the electrokinetic potential ζ of
the particles can be regarded to be homogeneous over the surface of
the particles, independent of the particle size. The results of this
conversion procedure are compared with number-based particle radius
distributions obtained from a large set of transmission electron microscopy
(TEM) data. For this specific example, it is shown that the modified
analytic approximation developed by Ohshima adequately describes the
mobility-dependent relaxation effect and the electrophoretic mobility of the particle as a function
of the reduced hydrodynamic radius and electrokinetic potential, which
is a prerequisite for the presented procedure. Simultaneously, we
confirmed that for the given Debye length/particle diameter ratio
the electrokinetic surface charge density can be regarded to be size-invariant
(including spherical geometry and planar limiting case). It is shown
that the accuracy of the results of the developed method is comparable
to that gained by a large set of TEM data, which is important when
a precise description of the particle size distribution is needed
to deduce conclusions regarding the underlying mechanism(s) of particle
growth. The values obtained for the dispersion (width) of the distribution
show only a small negative deviation, when compared with the TEM data
(4–16%).

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electrokinetic surface charge densityrelaxation effect-based size selectivityModified Analytic Approximationnumber-based particle radius distributionsTEMcapillary electrophoresis experimentsparticle size distributiontransmission electron microscopyExact Particle Radius Distributionmobility-dependent relaxation effectdataelectrophoretic mobility

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### Keyword(s)

electrokinetic surface charge densityrelaxation effect-based size selectivityModified Analytic Approximationnumber-based particle radius distributionsTEMcapillary electrophoresis experimentsparticle size distributiontransmission electron microscopyExact Particle Radius Distributionmobility-dependent relaxation effectdataelectrophoretic mobility