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Formation of Argon Cluster with Proton Seeding !"#$%"& '()"!) !#&*' + ,+--. --+! / , + , *../. 01.2 02.3 456.7. ,+ 8 !"!"#$ %& ' ()& & & ) * (( +,))-$ ."."/"0""!1/231!"!".313/.4 84 ! "# $% &# ! ' ( ' ) * +,-) . '' ' #. . ' ' ( /. 0( ) 1 MOLECULAR PHYSICS e1767813 https://doi.org/10.1080/00268976.2020.1767813 RESEARCH ARTICLE Formation of argon cluster with proton seeding O. C. F. Browna,b, D. Vrinceanu c, V. Kharchenkoa,d and H. R. Sadeghpour a aITAMP,Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA; bDepartment of Physics and Astronomy, University of Southampton, Southampton, UK; cDepartment of Physics, Texas Southern University, Houston, TX, USA; dDepartment of Physics, University of Connecticut, Storrs, CT, USA ABSTRACT ARTICLE HISTORY We employ force-field molecular dynamics simulations to investigate the kinetics of nucleation to Received 17 February 2020 new liquid or solid phases in a dense gas of particles, seeded with ions. We use precise atomic pair Accepted 7 May 2020 interactions, with physically correct long-range behaviour, between argon atoms and protons. Time KEYWORDS dependence of molecular cluster formation is analysed at different proton concentration, tempera- Cluster formation; molecular ture and argon gas density. The modified phase transitions with proton seeding of the argon gas are dynamics simulations; identified and analysed. The seeding of the gas enhances the formation of nano-size atomic clus- protonated argon gas ters and their aggregation. The strong attraction between protons and bath gas atoms stabilises large nano-clusters and the critical temperature for evaporation. An analytical model is proposed to describe the stability of argon-proton droplets and is compared with the molecular dynamics simulations. 1. Introduction Recent interest in optical and physical properties of Gas phase clusters are weakly bound aggregates com- gas phase clusters has been partly stimulated by the prised of either atoms or molecules, and often display discovery of exoplanets and analysis of absorption and chemical and physical properties that are quite distinct emission spectra of their hazy atmospheres. Optical and from those of their atomic constituents or associated infrared spectra observed from planetary and exoplane- bulk materials [1,2]. To synthesise catalysts or thin films, tary atmospheres, comets, and natural satellites are some- size-selected gas clusters can be delivered to substrates times unusually featureless, which are attributed to the to obtain materials with desired individual or collective presence of atmospheric dust, ice, haze and aerosol par- properties [3,4]. Thermodynamics of gas phase clusters, ticles [5–7]. Haze is mostly formed by small (submicron) aerosols and clouds bears on the nature of nanoparti- cluster particulates that can produce a broad continuum cle formation in the atmosphere and in the interstellar opacity to light. Interaction between haze particles and medium [2]. radiating atoms or molecules can dramatically modify CONTACT D. Vrinceanu [email protected] Department of Physics, Texas Southern University, Houston, TX 77004, USA Supplemental data for this article can be accessed here. https://doi.org/10.1080/00268976.2020.1767813 © 2020 Informa UK Limited, trading as Taylor & Francis Group 2 O. C. F. BROWN ET AL. absorption spectra of exoplanets [5,8–11] and used as a thermodynamically metastable state to a stable state markers for the simulation of atmospheric constituents. occur in the homogeneous gas due to microscopic fluctu- Recent laboratory experiments simulating hazy environ- ations. Fluctuations produce nano-size clusters in a liquid ments for super-Earths and mini-Neptunes atmospheres or solid phase. These clusters are relatively stable and suggestthatsomeoftheseatmospherescontainthick become centres of growth of a new phase, if the typical photochemically generated hazes [12]. cluster size R is larger than some critical value Rc.Clus- Compositions and parameters of haze particle and ters with R < Rc are unstable and disappear back into atmospheric gases are expected to vary considerably for the gas phase [37]. Ions and other seed particles may different exoplanets. The most realistic atmospheric haze stimulate the formation of critical clusters arising in the materials are water and CO2 ice and liquid droplets early stage of nucleation. Modelling of production of crit- for the terrestrial atmospheres and methane or hydro- ical clusters is the most difficult part in investigations carbons for the Jupiter-type exoplanets and Titan [13]. of nucleation processes. We performed MD simulations Investigation of the haze formation in most impor- aimed at clarifying the kinetics of short-term nucleation, tantatmosphericgases,suchasCO2,H2O, CH4,isa which initiates sub-critical and critical clusters. The long- formidable task due to a complexity of molecular quan- term stages of haze formation, such as coalescence, when tum interaction in polyatomic gases. Cluster formation growth of larger clusters occurs due to ‘swallowing up’ in noble gases represents an ideal environment for the of small ones [37], can then described with standard laboratory simulations and theoretical modelling of spec- kinetics of the first order phase transition. tral changes induced by ultra-small haze particles and Charge particles can catalyse short-term cluster for- aggregates. mation in the gas phase. A main goal of this work is to Argonisapotentialtargetspeciesinsearchfornatu- study argon nucleation with and without proton seed- rally occurring, noble gas compounds. Argon is known to ing, based on the most accurate quantum-mechanical be polarisable with the proper ligands [14]. While argon binary potentials for classical MD simulations. We will clusters are some of the simplest chemical systems to show how small concentrations of positive ions acceler- study, experimental investigations of the structure and ate nucleation process, but high ionic densities prevent stability of neutral rare-gas clusters and nano-size liq- the formation of the gas phase clusters. The phase tran- uid droplets are extremely challenging. Charged clusters sitions in clusters due to the temperature change and are on the other hand, easily studied using mass spectro- proton contribution are studied by analysing the pair metric techniques [15,16]. The first noble gas molecule correlation functions (the radial distribution function – observed in nature is the simple argon–proton cation RDF) and the size of nucleation clusters. Other order (argonium, Ar-p)[17]. Argonium has been detected in parameters, or discriminating quantities such as mean the interstellar medium (ISM) toward various astronom- square displacement, or diffusion coefficient, are more ical objects [18,19]. Also, the existence of the proton- adapted to studying bulk transformations because their bound dimer Ar-p-Ar has been proved by spectroscopic dependence on cluster size makes these parameters less evidence in argon matrix [20,21]. Ion–molecule com- unique. In future extensions of this work for larger clus- plexes of the form Arnp are detected in pulsed-discharge ters and aggregates, these complementary measures will supersonic expansions containing hydrogen and argon be investigated. [22] and studied theoretically [23]. The nucleation stim- ulated by proton seeding is unique because proton has no 2. Simulation procedure and details core electrons, and from the chemical point of view it can be seen as a point charge [24]. The Large Atomic/Molecular Massively Parallel Simula- Considerable effort has been devoted to obtaining a tor (LAMMPS) [38]isemployedtoperformsimulations better understanding of the nucleation [25,26], struc- of the dynamics of cluster formation in an Ar gas when tural properties [27], collision dynamics [28] and phase seeded with protons. The classical force fields are cal- transitions [29,30] of argon clusters by means of clas- culated from the quantum mechanical pair interaction sical Molecular Dynamics (MD) [31]. The dependence potentialswhicharedescribedindetailbelow.Theresults of argon phase transformations on the size of clusters is are visualised using Visual Molecular Dynamics software investigated experimentally by using electron diffraction (VMD) [39]. analysis [32–34] and was predicted theoretically using MD simulations [35]. Phase diagram of argon nanoclus- 2.1. Binary interaction potentials ters up to 400 atoms has been reported by means of constant energy molecular dynamics simulations [36]. The dynamics of cluster formation, stability and struc- The cluster nucleation in atomic and molecular tural properties with ion seeding are obtained from MD gases occurs in several stages. Phase transitions from simulations that use classical force fields deduced from MOLECULAR PHYSICS 3 accurate quantum calculation of pairwise interaction potentials. Ar–Ar interaction. The binary Ar–Ar potential is mod- elled by a Lennard–Jones 6-12 (LJ) potential [36,40,41]. σ 12 σ 6 V − (r) = 4ε − , (1) Ar Ar r r where parameters, ε = 1.23 × 10−2 eV and σ = 3.357 Å, are deduced from gas and matrix spectroscopy. The phys- ically correct weak van der Waals (vdW) asymptotic behaviour is evident from the LJ potential. Ar–p interaction. The Ar–p Born–Oppenheimer (BO) potential energy curves for the ground and excited elec- tronic states were calculated by Sidis [42]. The BO poten- Figure 1. Potential energy curves of pair interactions for the tials were subsequently used for the
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