#23 - Collisions between Air Molecules and their Mean Free Path

Autor: Dimitris G. Tsalikis (ETH Zurich, Switzerland), Vlasis G. Mavrantzas (U. Patras, Greece), Sotiris E. Pratsinis (ETH Zurich, Switzerland)

Description: For eons, the kinetic theory (KT) of gases has been used to determine the MFP assuming elastic collisions between spherical gas molecules [1]. However, is this so with what we know about molecular shape and force fields today? Having reached a state of maturity now, molecular dynamics (MD) simulations can elucidate the fundamentals of basic gas-phase (aerosol) processes that lead to a) better understanding of natural phenomena and b) accelerating process scale-up [2]. Here the mechanics of gas collisions are elucidated for plain air at room temperature by thoroughly-validated atomistic MD treating O2 and N2 as true diatomic molecules accounting for their shape and force field, for the first time to our knowledge [3]. So it is revealed that their trajectories are no longer straight, and collision frequencies are much higher due to the attractive part of the force field and the diatomic, thus more voluminous, shape of N2 and O2 as shown by the respective videos. Detailed analysis of the latter trajectories revealed that molecular collisions involve strong interactions between colliding molecules. These interactions lead to multi-body collisions, something not expected by the classic kinetic theory [1]. Such collisions increase with decreasing temperature and increasing pressure. For example, even 6-body ones are observed for air at 100 K and 5 atm [4].

Furthermore, colliding molecules can split from each other but soon return to collide again and again without interacting with any other molecule in between by the so-called spurious collisions [3] resulting in orbiting collisions as had been envisioned, at least, 60 years ago [5]. A direct result of the enhanced interactions between air molecules when treated as true diatomic molecules having attractive and repulsive potential components is that their mean free path (MFP) comes out to be considerably smaller than that from the classic kinetic theory. The new MFP for air is 38.5 nm, almost 43% smaller than that in textbooks of 67.3 nm at 300 K & 1 atm [3].

Aside from its fundamental value for tiny (< 5 nm) aerosol particle (TNP) dynamics (i.e. diffusion, nucleation of subcritical clusters, coagulation etc.), such a result is significant in gas-phase synthesis of tiny (< 5 nm) nanoparticles where asymptotic (self-preserving) particle size distributions and (fractal-like) structure have not been attained yet to simplify the corresponding process design [6]. The TNPs have many potential applications and play a pivotal role in the atmosphere. Atmospheric TNPs grow into larger aerosol particles that reduce visibility and adversely affect air quality, human health and climate. For example, formation and growth of atmospheric TNPs from 1.7 to 3.0 nm leads to a 50% increase in the predicted concentrations of cloud condensation nuclei, having important implications on climate [7]. With respect to applications is worth noting that TNPs hold most of the promises of nanotechnology as in that size range is where the drastic changes of material properties take place. For example, the melting point of gold decreases by just about 10% from its bulk value for particles having sizes down to 5 nm, but by 50% when their size drops to 3 nm [8].

1. J.C. Maxwell, V. Illustrations of the dynamical theory of gases.—part i. On the motions and collisions of perfectly elastic spheres. The London, Edinburgh, and Dublin Philos. Mag. and J. of Science 19:19-32 (1860). doi: 10.1080/14786446008642818.

2. Mavrantzas, V. G. and S. E. Pratsinis. 2019. The impact of molecular simulations in gas-phase manufacture of nanomaterials. Curr. Opin. Chem. Eng. 23:174-183. doi: 10.1016/j.coche.

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

4. D. Tsalikis, V.G. Mavrantzas, S.E. Pratsinis, A new equation for the mean free path of air, Aerosol Sci. Technol., 58, 930-941 (2024). doi.org/10.1080/02786826.2024.2333859

5. J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases & Liquids, Wiley, 1964.

6. S.E.Pratsinis, Aerosol-based technologies in nanoscale manufacturing: From functional materials to devices through core chemical engineering. AlChE J. 56:3028-3035 (2010). doi: 10.1002/aic.12478.

7. J. Tröstl, W. K. Chuang, H. Gordon, M. Heinritzi, C. Yan, U. Molteni, L. Ahlm, C. Frege, et al., “The role of low-volatility organic compounds in initial particle growth in the atmosphere,” Nature 533, 527 (2016). https://doi.org/10.1038/nature18271

8. P. Buffat, and J. P. Borel, “Size effect on melting temperature of gold particles,” Phys. Rev. A 13, 2287 (1976). https://doi.org/10.1103/PhysRevA.13.2287