Determination of 2D Particle Size Distributions in Plasmonic Nanoparticle Colloids via Analytical Ultracentrifugation: Application to Gold Bipyramids. - Frank, Uwe; Drobek, Dominik; Sánchez-Iglesias, Ana; Wawra, Simon; Nees, Nico; Walter, Johannes; Pflug, Lukas; Apeleo Zubiri, Benjamin; Spiecker, Erdmann; Liz-Marzan, Luis M.; Peukert, Wolfgang (ACS nano, 2023)
Multidimensional particle properties determine the product properties in numerous advanced applications. Accurate and statistically meaningful measurements of complex particles and their multidimensional distributions are highly challenging but strongly needed. 2D particle size distributions of plasmonic nanoparticles of complex regular shape can be obtained from analytical ultracentrifugation experiments via the optical back coupling method. A workflow for the calculation of frictional properties of arbitrarily shaped nanoparticles was developed based on bead shell models and applied to gold bipyramids with a pentagonal cross-section. The obtained 2D particle length-diameter distributions and the reduced cumulative 1D length and diameter distributions were compared to transmission electron microscopy measurements. While we find very good agreement for most measurements, the obtained length and diameter distributions were shifted by a few nanometers for some samples. Transmission electron microscopy, energy-dispersive X-ray spectroscopy, electron tomography, and finite element modeling indicate that the shift originated from a slight mismatch between the assumed shape of the simulated perfect bipyramids and the real particle shape and composition due to the presence of silver in the particles. This study demonstrates the feasibility of the applied techniques for complex shape analysis of nanoparticle ensembles with unmatched particle count numbers.
Keywords: analytical ultracentrifugation; bead modeling; electron tomography; extinction cross section; gold bipyramids; optical back coupling; particle shape distribution

Development of an advanced multiwavelength emission detector for the analytical ultracentrifuge - Lautenbach, Vanessa; Onishchukov, Georgy; Wawra, Simon; Frank, Uwe; Hartmann, Lukas; Peukert, Wolfgang; Walter, Johannes (Nanoscale Advances, 2024)
An advanced design of the analytical ultracentrifuge with multiwavelength emission detection (MWE-AUC) is presented which offers outstanding performance concerning the spectral resolution and range flexibility as well as the quality of the data acquired. The excitation by a 520 nm laser is complemented with a 405 nm laser. An external spectrograph with three switchable tunable gratings permits optimisation of the spectral resolution in an order of magnitude range while keeping the spectral region broad. The new system design leads also to a significant reduction of systematic signal noise and allows the assessment and control of inner filter effects. Details regarding the very large signal dynamic range are presented, an important aspect when studying samples in a broad concentration range of up to five orders of magnitude. Our system is validated by complementary studies on two biological systems, fluorescent BSA and GFP, using the commercial Optima AUC with absorbance detection for comparison. Finally, we demonstrate the capabilities of our second generation MWE-AUC with respect to multiwavelength characterisation of gold nanoclusters, which exhibit specific fluorescence depending on their structure. Overall, this work depicts an important stepping stone for the concept of multiwavelength emission detection in AUC. The MWE-AUC developed, being to our knowledge the first and sole one of its kind, has reached the development level suitable for the future in-depth studies of size-, shape- and composition-dependent emission properties of colloids.
CRIS-Team Scopus Importer:2024-03-22

Estimation of bivariate probability distributions of nanoparticle characteristics, based on univariate measurements - Furat, Orkun; Frank, Uwe; Weber, Matthias; Wawra, Simon; Peukert, Wolfgang; Schmidt, Volker (Inverse Problems in Science and Engineering, 2020)
The properties of complex particle systems typically depend on multivariate distributions of particle properties, like size and shape characteristics. Multidimensional particle property distributions can be a powerful tool to describe these systems. However, only few techniques exist which are able to simultaneously measure more than one property of individual particles in fast and efficient ways. It is shown how two-dimensional property spaces can be constructed by the combination of two univariate measurements to obtain bivariate particle size distributions. The proposed method is a general approach, which can be applied to a wide spectrum of particle systems and measurement devices. In this paper, the results of a case study are presented, which allow the estimation of bivariate distributions of length and diameter of nanorods, solely using univariate distributions of their particle mass and extinction-weighted sedimentation coefficient distributions. These quantities contain joint information about the particle lengths and diameters, which is used for the reconstruction. The method is validated in a simulation study in which the bivariate distribution to be reconstructed and the reconstruction parameters are varied. In addition, regularization techniques are introduced to reduce methodical errors. This approach can be transferred to other particle systems and measurement techniques, for which functional relationships between particle properties and measured quantities are well describe
Keywords: particle size distributions; reconstruction; inverse problem; Multidimensional characterization; copulas

Multidimensional Fractionation of Particles - Frank, Uwe; Dienstbier, Jana; Tischer, Florentin; Wawra, Simon; Gromotka, Lukas; Walter, Johannes; Liers-Bergmann, Frauke; Peukert, Wolfgang (Separations, 2023)
The increasing complexity in particle science and technology requires the ability to deal with multidimensional property distributions. We present the theoretical background for multidimensional fractionations by transferring the concepts known from one dimensional to higher dimensional separations. Particles in fluids are separated by acting forces or velocities, which are commonly induces by external fields, e.g., gravitational, centrifugal or electro-magnetic fields. In addition, short-range force fields induced by particle interactions can be employed for fractionation. In this special case, nanoparticle chromatography is a recent example. The framework for handling and characterizing multidimensional separation processes acting on multidimensional particle size distributions is presented. Illustrative examples for technical realizations are given for shape-selective separation in a hydrocyclone and for density-selective separation in a disc separator.
Keywords: multidimensional separation; two-dimensional property distribution; size; shape; composition

Multidimensional Particle Size Distributions and Their Application to Nonspherical Particle Systems in Two Dimensions - Frank, Uwe; Wawra, Simon; Pflug, Lukas; Peukert, Wolfgang (Particle & Particle Systems Characterization, 2019)
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.
CRIS-Team Scopus Importer:2019-06-04
Keywords: 2D distributions; multidimensional characterization; particle size distributions; particle technology

Progress in Multidimensional Particle Characterization - Frank, Uwe; Uttinger, Maximilian; Wawra, Simon; Lübbert, Christian; Peukert, Wolfgang (KONA Powder and Particle Journal, 2021)
The properties of particle ensembles are defined by a complex multidimensional parameter space, namely particle size, shape, surface, structure, composition and their distributions. Macroscopic product properties are a direct result of these disperse particle properties. Therefore, the comprehensive multidimensional characterization of particle ensembles is a key task in any product design. However, the determination of complex property distributions is major challenge. We provide a broad overview of the current tools for multidimensional particle characterization. First, the mathematical handling of multidimensional (nD) property distribution is outlined as a necessary framework for the correct handling of nD particle size distributions (PSDs). Then, well-established techniques as well as recent developments with the potential to extract nD property distributions are reviewed. Exsitu imaging techniques like electron tomography or Raman spectroscopy with AFM co-localization, for instance, provide a resolution on the level of single particles but are limited in terms of sample statistics. A particular focus lies therefore on methods in the gas and the liquid phase, which provide multidimensional particle properties either directly or by a combination of one-dimensional technique