A critical problem in materials science
is the accurate characterization
of the size dependent properties of colloidal inorganic nanocrystals.
Due to the intrinsic polydispersity present during synthesis, dispersions
of such materials exhibit simultaneous heterogeneity in density ρ, molar mass M, and particle diameter d. The density increments ∂ρ/∂d and ∂ρ/∂M of these
nanoparticles, if known, can then provide important information about
crystal growth and particle size distributions. For most classes of
nanocrystals, a mixture of surfactants is added during synthesis to
control their shape, size, and optical properties. However, it remains
a challenge to accurately determine the amount of passivating ligand
bound to the particle surface post synthesis. The presence of the
ligand shell hampers an accurate determination of the nanocrystal
diameter. Using CdSe and PbS semiconductor nanocrystals, and the ultrastable
silver nanoparticle (M4Ag44(p-MBA)30), as model systems, we describe a Custom Grid method implemented
in UltraScan-III for the characterization of nanoparticles and macromolecules
using sedimentation velocity analytical ultracentrifugation. We show
that multiple parametrizations are possible, and that the Custom Grid
method can be generalized to provide high resolution composition information
for mixtures of solutes that are heterogeneous in two out of three
parameters. For such cases, our method can simultaneously resolve
arbitrary two-dimensional distributions of hydrodynamic parameters
when a third property can be held constant. For example, this method
extracts partial specific volume and molar mass from sedimentation
velocity data for cases where the anisotropy can be held constant,
or provides anisotropy and partial specific volume if the molar mass
is known.
A method for fitting sedimentation velocity experiments using whole boundary Lamm equation solutions is presented. The method, termed parametrically constrained spectrum analysis (PCSA), provides an optimized approach for simultaneously modeling heterogeneity in size and anisotropy of macromolecular mixtures. The solutions produced by PCSA are particularly useful for modeling polymerizing systems, where a single-valued relationship exists between the molar mass of the growing polymer chain and its corresponding anisotropy. The PCSA uses functional constraints to identify this relationship, and unlike other multidimensional grid methods, assures that only a single molar mass can be associated with a given anisotropy measurement. A description of the PCSA algorithm is presented, as well as several experimental and simulated examples that illustrate its utility and capabilities. The performance advantages of the PCSA method in comparison to other methods are documented. The method has been added to the UltraScan-III software suite, which is available for free download from http://www.ultrascan.uthscsa.edu.
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