(468b) Diffusion Coefficients of Fullerene and Silica Nanoparticles (<10 nm) in Air By Fully Atomistic Molecular Dynamics.

Given the advances in molecular dynamics and their impact on aerosol science (Mavrantzas and Pratsinis, 2019), a more accurate way to obtain diffusion coefficients for NPs with sizes less than 20 nm is through detailed atomistic simulations by employing accurate forcefields and shapes for the NPs and the surrounding gases. To this end, we have employed all-atom molecular dynamics (MD) simulations to study the diffusion coefficients of small fullerene and silica NPs with diameters from 0.4 to 7 nm in air at room temperature (T = 298 K) and pressure (P = 1 atm) by fully accounting for the diatomic shape and force field of air molecules (Tsalikis et al., 2023).

The MD results are averaged over several independent simulations to enhance sampling and decrease the statistical uncertainty of simulations. The MD-extracted diffusion coefficients are then compared to nearly all theoretical expressions widely used in the literature for NP diffusivity from the classic Cunningham-Millikan (CM) equation to the Fernández de la Mora et al. (2003) one, as well as that by the elementary kinetic theory of gases. We have also studied the diffusivity of a single silica molecule and several of the fullerene NPs modeled here as a function of temperature from 100 to 600 K.

The present MD-calculated diffusion coefficients show systematic deviations, already reported in the literature (e.g., by Fernández de la Mora et al., 2003, Li and Wang, 2003, Rudyak et al., 2002, Tammet, 1995), from the CM equation, especially as the NP diameter becomes comparable to the size of air molecules. This is justified because the CM equation was based mainly on experimental data with much larger particles at low pressures. Especially for the simulated NPs with diameter smaller than 2 nm, the diffusivity in air cannot be captured even by modifications of the CM equation that accounts for the size of gas molecules, as proposed by Tammet (1995) to account for the collision diameter and the transition from the elastic to inelastic collisions or by Fernández de la Mora et al. (2003) including an “effective” particle diameter instead of the true geometric particle diameter or even the reduced mass in a hybrid Epstein formula.

By comparing the present MD-derived diffusion coefficients with the above formulae and also the predictions of the kinetic theory of gases and the empirical formula by Fuller et al. (1966), we obtain a better understanding of how the NP size should be treated in these formulations. More specifically, we propose a new modification to the Cunningham-Millikan equation that captures quite well the data in the free molecular and transient regimes.

In addition, we provide new simulation data for the temperature dependence of the NP diffusivity in the free molecular and transient regimes, which allows us to evaluate existing scaling laws as well as to check if the exponents in these laws depend on NP size as has been reported by Rudyak et al. (2019).

References

J. Fernández de la Mora, L. de Juan, K. Liedtke, A. Schmidt-Ott, Mass and size determination of nanometer particles by means of mobility analysis and focused impaction, J. Aerosol Sci. 34, (2003) 79-98, doi.org/10.1016/S0021-8502(02)00121-0.

N. Fuchs, The mechanics of aerosols, (Dover Publications Inc, New York, 1964).

S. Fuller, P.D. Schettler, J.C. Giddings, A new method for predictions of binary gas-phase diffusion coefficients, Ind. Eng. Chem. 58 (1966) 18-27, doi.org/10.1021/ie50677a007.

Z. Li, H. Wang, Drag force, diffusion coefficient, and electric mobility of small particles. I. Theory applicable to the free-molecule regime, Phys. Rev. E 68 (2003) 061206, doi.org/ 10.1103/PhysRevE.68.061206.

V.G. Mavrantzas, S.E. Pratsinis, The impact of molecular simulations in gas-phase manufacture of materials, Curr. Opinion Chem. Eng. 23 (2019) 174-183, doi.org/10.1016/j.coche.2019.04.006.

V.Ya. Rudyak, S.L. Krasnolutskii, A.G. Nasibulin, E.I. Kauppinen, Methods of measuring the diffusion coefficient and sizes of nanoparticles in a rarefied gas, Dokl. Phys. 47 (2002) 758-761, doi.org/10.1134/1.1519325.

V.Ya. Rudyak, S.N. Dubtsov, A.M. Baklanov, Measurements of the temperature dependent diffusion coefficient of nanoparticles in the range of 295–600 K at atmospheric pressure, Aerosol Sci. 40 (2019) 833-843, doi.org/10.1016/j.jaerosci.2009.06.006.

H. Tammet, Size and mobility of nanometer particles, clusters and ions, J. Aerosol Sci. 26 (1995) 459-475, doi.org/10.1016/0021-8502(94)00121-E.

D.G. Tsalikis, V.G. Mavrantzas, S.E. Pratsinis, Dynamics of molecular collisions in air and its mean free path, Phys. Fluids. 35, (2023) 097131, doi.org/10.1063/5.0166283.