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Computing the 3D Radial Distribution Function from Particle Positions: An Advanced Analytic Approach

Title data

Kopera, Bernd A. F. ; Retsch, Markus:
Computing the 3D Radial Distribution Function from Particle Positions: An Advanced Analytic Approach.
In: Analytical Chemistry. Vol. 90 (2018) Issue 23 . - pp. 13909-13914.
ISSN 1520-6882
DOI: https://doi.org/10.1021/acs.analchem.8b03157

Official URL: Volltext

Project information

Project financing: Deutsche Forschungsgemeinschaft
VolkswagenStiftung

Abstract in another language

The radial distribution function, g(r), is ubiquitously used to analyze the internal structure of particulate systems. However, experimentally derived particle coordinates are always confined to a finite sample volume. This poses a particular challenge on computing g(r): Once the radial distance, r, extends beyond the sample boundaries in at least one dimension, substantial deviations from the true g(r) function can occur. State of the art algorithms for g(r) mitigate this issue for instance by using artificial periodic boundary conditions. However, ignoring the finite nature of the sample volume distorts g(r) significantly. Here, we present a simple, analytic algorithm for the computation of g(r) in finite samples. No additional assumptions about the sample are required. The key idea is to use an analytic solution for the intersection volume between a spherical shell and the sample volume. In addition, we discovered a natural upper bound for the radial distance that only depends on sample size and shape. This analytic approach will prove to be invaluable for the quantitative analysis of the increasing amount of experimentally derived tomography data.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties > Faculty of Biology, Chemistry and Earth Sciences > Department of Chemistry
Faculties > Faculty of Biology, Chemistry and Earth Sciences > Department of Chemistry > Chair Physical Chemistry I
Faculties > Faculty of Biology, Chemistry and Earth Sciences > Department of Chemistry > Chair Physical Chemistry I > Lehrstuhl Physikalische Chemie I - Univ.-Prof. Dr. Markus Retsch
Profile Fields > Advanced Fields > Polymer and Colloid Science
Research Institutions > Research Centres > Bayreuth Institute of Macromolecular Research - BIMF
Research Institutions > Research Centres > Bayreuth Center for Colloids and Interfaces - BZKG
Research Institutions > Collaborative Research Centers, Research Unit > SFB 840 Von partikulären Nanosystemen zur Mesotechnologie
Faculties
Faculties > Faculty of Biology, Chemistry and Earth Sciences
Profile Fields
Profile Fields > Advanced Fields
Research Institutions
Research Institutions > Research Centres
Research Institutions > Collaborative Research Centers, Research Unit
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 540 Chemistry
Date Deposited: 09 Jan 2019 09:34
Last Modified: 09 Jan 2019 09:34
URI: https://eref.uni-bayreuth.de/id/eprint/46839