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Multidimensional Particle Size Distributions and Their Application to Nonspherical Particle Systems in Two Dimensions
Author(s) -
Frank Uwe,
Wawra Simon E.,
Pflug Lukas,
Peukert Wolfgang
Publication year - 2019
Publication title -
particle and particle systems characterization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.877
H-Index - 56
eISSN - 1521-4117
pISSN - 0934-0866
DOI - 10.1002/ppsc.201800554
Subject(s) - statistical physics , particle (ecology) , particle size , nanorod , gaussian , anisotropy , probability density function , physics , probability distribution , mathematics , materials science , nanotechnology , chemistry , statistics , optics , quantum mechanics , oceanography , geology
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.