On this page, you will find links to codes (for ion mobility calculations and for size distribution function inversions) that we make use of extensively in studying nanoparticles and molecular clusters in the gas phase.

**Ion Mobility Calculations:**

Prof. Carlos Larriba, Indiana University-Purdue University-Indianapolis, developed IMoS, i.e. the Ion Mobility Spectrometry Suite, to better facilitate calculations of mobility and collision cross sections for ionized clusters, macromolecules, proteins, multiprotein complexes, as well as coarse grained models of non-spherical nanoparticles in the free molecular regime. The publications describing the development of this package are noted here; it tracks individual gas molecule trajectories and computes the rate of momentum transfer from impinging and reemitted gas molecules to a candidate structure (as depicted in the figure to the right). Approximations assuming that the momentum transfer collision cross section is proportional to the projected area are also calculable and both ballistic, straight line gas molecule trajectories as well as those affected by potential interactions can be modeled. IMoS can be freely downloaded from Professor Larriba’s **website**. It is an .exe file, but please follow the instructions provided on the website to get the software to function. In addition, if you use IMoS to generate data for submission of a peer-reviewed manuscript, we recommend you cite the starred (“**”) manuscripts below.

**Relevant Publications:**

**Shrivastav V., Nahin M., Hogan C. J., & Larriba C. (2017) Benchmark Comparison for a Multi-Processing Ion Mobility Calculator in the Free Molecular Regime. *J. Amer. Soc. Mass Spectrom. 28: 1540-1551. *10.1007/s13361-017-1661-8

Larriba-Andaluz C., Fernandez Garcia J., Ewing M. A., Hogan C. J., & Clemmer D.E. (2015). Gas Molecule Scattering & Ion Mobility Measurements for Organic Macro-ions in He versus N_{2} Environments. *Phys Chem Chem Phys. 17, 15019-15029. *10.1039/C5CP01017A

Larriba-Andaluz C., & Hogan C. J. Collision Cross Section Calculations for Polyatomic Ions Considering Rotating Diatomic/Linear Gas Molecules. (2014). *J. Chem. Phys. 141: 194107. *10.1063/1.4901890

Ouyang H., Larriba-Andaluz C., Oberreit D. R., & Hogan C. J. (2013). The Collision Cross Sections of Iodide Salt Cluster Ions in Air via Differential Mobility Analysis-Mass Spectrometry. *Journal of the American Society for Mass Spectrometry. 24:1833-1847. 10.1007/s13361-013-0724-8 *

**Larriba, C. & Hogan C. J. (2013). Free Molecular Collision Cross Section Calculation Methods for Nanoparticles and Complex Ions with Energy Accommodation. *J. Computational Phys. 251:344-363. *10.1016/j.jcp.2013.05.038

**Larriba C. & Hogan C. J.** **(2013). Ion Mobilities in Diatomic Gases: Measurement vs. Prediction with Non-Specular Scattering Models. *J. Phys. Chem. A. 117:3887-3901 (Cover Article). *10.1021/jp312432z

**Differential Mobility Analyzer-Mass Classification Data Inversion Codes:
**Our group has developed two dimensional size distribution function inversion routines (based upon the Twomey-Markowski algorithm) to infer the number based size-mass distribution function from differential mobility analyzer-aerosol particle mass analyzer-condensation particle counter measurements. Details on the two dimensional inversion code are found in:

Buckley D. T., Kimoto S., Lee M-. H., Fukushima N., & Hogan C. J.** **(2017) Technical Note: A Corrected Two Dimensional Data Inversion Routine for Tandem Mobility-Mass Measurements. *Journal of Aerosol Science. 114: 157-168. *10.1016/j.jaerosci.2017.09.012

MATLAB compile-able codes and a README.txt file are available as supplemental information with this manuscript. The code files can also be downloaded **HERE**.

In addition, we have adapted this algorithm for Differential Mobility Analyzer-Centrifugal Particle Mass Analyzer-Condensation Particle Counter measurements using a CPMA transfer function provided by **Prof. Jason Olfert. **This code can be downloaded **HERE**. We caution it has not yet undergone the testing our DMA-APM-CPC inversion code has, though the only change to the code is the change from the APM transfer function to the CPMA transfer function. If you use either code in a manuscript or conference presentation, please cite the manuscript noted above (Buckley et al, 2017, Journal of Aerosol Science). In addition, we are happy to answer any questions that might come up while running these codes, so feel free to contact Chris regarding them.

**Fractal Aggregate Projection Properties:**

In several studies, we utilized electron microscope (EM) images of aggregated particles to determine their most probable fractal dimension *D _{f}*, number of primary particles N, and pre-exponential factor k (with the primary particle radius a

_{p }measured manually. In doing so, we assume that each aggregate approximately obeys the relationship: where

*R*is the radius of gyration. EM images yield projections of aggregates, not three dimensional structures. To infer the most probable aggregate structure (from a finite-set) as well as the weighted average aggregate properties, for each projection we compute the visible area normalized by the projected area of a primary particle), the visible perimeter normalized by the primary particle radius, the longest end-to-end distance normalized by the primary particle radius, and the 2-dimensional radius of gyration normalized by the primary particle radius. These four values are compared to those calculated for computationally generated projections of aggregates with

_{g}*D*in the 1.2-2.9 range, k in the 1.2-2.0 range, and N in the 10-1000 range, with three orthogonal projections calculated for each aggregate, and 10 aggregates generated for each fractal dimension-pre-exponential factor-number of primary particles set. Aggregate generation was accomplished via the cluster-cluster algorithm of Filippov et al. The method of comparison between EM imaged aggregates and computationally generated aggregates is described in the references noted below. In addition, the database of projected properties for computationally generated aggregates, where their projected areas and hydrodynamic radii are also noted is downloadable HERE. With this database our image analysis method can be duplicated. Should this database be used in the preparation of any manuscripts for peer review, please cite Thajudeen et al, 2015 (full citation info below).

_{f}**Figure 1.**An example of aggregate image analysis results. Adapted from Thajudeen et al, 2015, Journal of Aerosol Science.

**Relevant Publications:**

Thajudeen T., Jeon S., & Hogan C. J. (2015). The Mobility of Flame Synthesized Aggregates/Agglomerates in the Transition Regime. *J. Aerosol Sci. 80: 45-57. *10.1016/j.jaerosci.2014.11.003

Jeon S., Hurley K.R., Bischof J. C., Haynes C. L. & Hogan C. J. (2016) Quantifying Intra- and Extracellular Aggregation of Iron Oxide Nanoparticles and its Influence on Specific Absorption Rate. *Nanoscale. 8: 16053-16064.* 10.1039/C6NR04042J

**Coming Soon:** One Dimensional DMA-CPC data inversion codes based upon the Twomey-Markowski Algorithm, Brownian Dynamics Algorithms for Collision Kernel Calculations, and Random Aggregate Generation Codes (the Cluster-Cluster Algorithm).