Properties of nanoparticles are influenced by various parameters like size, shape or composition. Comprehensive high throughput characterization techniques are urgently needed to improve synthesis, scale up to production and make way for new applications of multidimensional particulate systems. In this study, we present a method for measuring two-dimensional size distributions of plasmonic nanorods in a single experiment. Analytical ultracentrifuge equipped with a multiwavelength extinction detector is used to record the optical and sedimentation properties of gold nanorods simultaneously. A combination of sedimentation and extinction properties, both depending on diameter and length of the dispersed nanorods, is used to measure two-dimensional distributions of gold nanorod samples. The length, diameter, aspect ratio, volume, surface and cross-sectional distributions can be readily obtained from these results. As the technique can be extended to other non-spherical plasmonic particles and can be used for determining relative amounts of particles of different shapes it provides complete and quantitative insights into particulate systems.
Hydrodynamic and thermodynamic non-ideality are important phenomena when studying concentrated and interacting systems in analytical ultracentrifugation (AUC). Here we present an extended Brownian Dynamics (BD) based algorithm which incorporates hydrodynamic and thermodynamic non-ideality. It can serve as an independent and versatile approach for the theoretical description of interparticulate interactions in AUC, as it allows tracking the trajectory of individual particles. Concentration dependencies of the sedimentation and diffusion coefficient have been implemented and validated for the extended BD model. For monodisperse systems, it is shown that profiles obtained by BD are in excellent agreement with well-established Lamm equation solvers. Moreover, important limits and restrictions of current Lamm equation based analysis methods are discussed. In particular, BD allows modeling and evaluation of AUC data of non-ideal polydisperse systems. This is relevant as most nanoparticulate systems are polydisperse in size. Here, a simulation for a polydisperse system including concentration effects is presented for the first time.
Particle science and technology evolve toward ever increasing complexity with respect to the multidimensional particle properties of size, shape, surface, internal structure, and composition. In this study, the theoretical background is elaborated for multidimensional particle size distributions (PSDs) by transferring the concepts known from 1D size distributions to anisotropic particles comprising at least two different length dimensions, e.g., nanorods and platelets. After introducing 2D PSDs, the calculation of differently weighted probability density functions including their interconversion is presented. This is necessary in order to compare data resulting from different measurement techniques which probe different physical properties and thus provide differently weighted PSDs. In addition, it is shown how 1D distributions with reduced content of information can be deduced from 2D PSDs. As a proof‐of‐concept and for illustration purposes, this approach is applied to a 2D Gaussian size distribution. Furthermore, a generalized scheme is suggested which outlines the conversion of number, surface, and volume weighted densities within the 2D space. The application of these methods to the more general n‐dimensional case is straightforward.
Brownian dynamics
(BD) has been applied as a comprehensive tool to model sedimentation
and diffusion of nanoparticles in analytical ultracentrifugation (AUC)
experiments. In this article, we extend the BD algorithm by considering
space-dependent diffusion and solvent compressibility. With this,
the changes in the sedimentation and diffusion coefficient from altered
solvent properties at increased pressures are accurately taken into
account. Moreover, it is demonstrated how the concept of space-dependent
diffusion is employed to describe concentration-dependent sedimentation
and diffusion coefficients, in particular, through the Gralen coefficient
and the second virial coefficient. The influence of thermodynamic
nonideality on diffusional properties can be accurately simulated
and agree with well-known evaluation tools. BD simulations for sedimentation
equilibrium and sedimentation velocity (SV) AUC experiments including
effects of hydrodynamic and thermodynamic nonideality are validated
by global evaluation in SEDANAL. The interplay of solvent compressibility
and retrieved nonideality parameters can be studied utilizing BD.
Finally, the second virial coefficient is determined for lysozyme
from SV AUC experiments and BD simulations and compared to membrane
osmometry. These results are in line with DLVO theory. In summary,
BD simulations are established for the validation of nonideal sedimentation
in AUC providing a sound basis for the evaluation of complex interactions
even in polydisperse systems.
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