The Effect of Orientation on the Mobility and Dynamic Shape Factor of Charged Axially Symmetric Particles in an Electric Field

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. The mobility of a nonspherical particle is a function of both particle shape and orientation. Thus, unlike spherical particles, the mobility, through its orientation, depends on the magnitude of the electric field. In this work, we develop a general theory, based on an extension of the work of Happel and Brenner (1965), for the orientation-averaged mobility applicable to any axially symmetric particle for which the friction tensor and the polarization energy are known. By using a Boltzmann probability distribution for the orientation, we employ a tensor formulation for computing the orientation-averaged mobility rather than a scalar analysis previously employed by Kim et al. (2007) for nanowires. The resulting equation for the average electrical mobility is much simpler than the expression based on the scalar approach, and can be applied to any axially symmetric structures such as rods, ellipsoids, and touching spheres. The theory is applied to the specific case of nanowires and the experimental results on the mobility of carbon nanotubes (CNT). A set of working formulas of additional mobility expressions for nanorods and prolate spheroids in the free molecular , continuum, and transition regimes are also presented. Finally, we examine the expression of dynamic shape factor common in the literature, and propose a clearer definition based on the tensor approach. Mathematica codes for the electrical mobility evaluations for five cases are provided in the Supplemental Information. 1. INTRODUCTION The differential mobility analyzer (DMA) is widely used for measuring the size distribution of nanoparticles in the aerosol phase (Kim et al. 2007; Li et al. 2011a, b). For a spherical particle , the electrical mobility diameter is equivalent to its geometric diameter. However, for nonspherical particles, the measured