Understanding ion-mobility and transport properties of aerosol nanowires

In a previous experimental study, we demonstrated that gas phase electrophoretic mobility separation enables one to classify diameter-selected carbon nanotubes (CNTs) by length [Kim, S. H. & Zachariah, M. R. (2005). In-flight size classification of carbon nanotubes by gas phase electrophoresis. Nanotechnology, 16, 2149–2152] and have subsequently used this capability to track the growth rate of CNTs in free-flight [Kim, S. H. & Zachariah, M. R. (2006). In-flight kinetic measurements of the aerosol growth of carbon nanotubes by electrical mobility classification. Journal of Physical Chemistry B, 110, 4555–4562]. In this paper, we develop a theoretical model to describe the behavior of nanotubes (or nanowires) undergoing Brownian rotation in an electric field, and provide a more rigorous interpretation of the experimental results. The Boltzmann expression for the orientation probability includes both the free charge energy as well as the polarizability energy. In the theoretical model, we computed the orientation-averaged electrical mobility and the precipitating time of a rotating nanowire in DC electric field in the free-molecular limit. This analysis was used to obtain the precipitation time of a nanowire in a differential mobility analyzer (DMA). Based on the theoretical model and its comparison with experimental measurement, we found that: (i) a stronger electric field was required to select longer nanowires for a given diameter and (ii) shorter nanowires with the aspect ratio of freely rotate for applied electric field up to , while longer nanowires (β> 30) were aligned by the electric field. The experimentally determined nanowire length was in fair agreement with that computed by our theoretical model, in which the effect of the nanowireʹs alignment on mobility classification in various electric fields was accounted for. The over prediction of the model for longer nanowires is shown to result from the bent structure of the longer nanowires. The methodology should be generic to other nanostructures with high aspect ratio.