On the Influence of Rotational Motion of Oxygen Molecules on the

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On the Influence of Rotational Motion of Oxygen Molecules on the Scattering from Graphite Surface Maria Rutigliano, and Fernando Pirani J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01966 • Publication Date (Web): 04 Apr 2019 Downloaded from http://pubs.acs.org on April 4, 2019

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The Journal of Physical Chemistry

On the Influence of Rotational Motion of Oxygen Molecules on the Scattering from Graphite Surface Maria Rutigliano*,1 and Fernando Pirani2

1CNR-NANOTEC

2

(P.LAS.M.I. Lab), Via G. Amendola 122/D, 70126 Bari, Italy

Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, Via Elce di Sotto 8, Perugia 06123, Italy

*corresponding author e-mail: [email protected]; phone: +39 080 5929512

1 Environment ACS Paragon Plus

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract

A new analytical potential energy surface is proposed to investigate, by semiclassical Molecular Dynamics calculations, the scattering of O2 molecules in well-defined initial roto-vibrational (vi, ji) states from graphite under a variety of conditions of applied interest. The reaction dynamics appears to be dominated by the coupling between translational and rotational internal degrees of freedom of molecule, that, at low-medium collision energies, can be also triggered by the energy exchange with the surface phonons. The final states (vf, jf) of backscattered molecules are characterized and carefully analyzed. Most important results are: 1) after the interaction with the surface molecules are backscattered mainly in a direction very close to the specular one; 2) vi is preserved, except for high initial vibrational states; 3) the surface temperature plays a minor role; 4) the final jf states exhibit non-Boltzmann distributions with the main peak nearby jf =ji and a secondary maximum at very high jf. Moreover, the features of rotational distributions suggest a close correlation between the initial rotational configuration of impinging molecules and the final state achieved after the scattering. These findings, complementary to those from Molecular Beam experiments, cast light on relevant selectivities in elastic and inelastic collision events that control the stereo-dynamics of several elementary processes occurring both in gaseous and condensed phase for low energy (as those meet in the Interstellar Medium) as well as for high energy (as those of interest for aerospace applications).


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1. Introduction The molecular reactivity under thermal and hyper-thermal conditions is triggered often by the formation of energetically activated species by means of collisions. These species follow a chemistry rather different respect to that of molecules in their ground state. Collisions at low energy and involving ground state molecules are, instead, of great interest for sub-thermal phenomena, as those occurring in cold environments of the Interstellar Medium1,2. Among the different elementary processes promoted under a variety of conditions and storing energy in molecular roto-vibrational states, those occurring at the gas-surface interface certainly play a primary role. In particular, chemi-/physi-sorptions of diatomic molecules can lead to their dissociation as well as to backscattering in gas-phase, depending selectively on the rotovibrational excitation degree suffered by the molecules. The dynamics of elementary processes involved directly controls the energy exchange mechanism between the surface and the internal degrees of freedom of incident molecules. As stressed above, under some conditions molecular dissociation at the surface can also occur: it produces two atoms that if trapped on the surface modify its chemical and thermal properties, or if diffused into the gas-phase they can act as very effective collision quenchers. In light of these considerations, the interaction of oxygen molecules with a graphite surface appears to be of fundamental relevance. Moreover, the role of this interaction has also a wide interest in different applicative fields, spanning from the assessment of burning phenomena in nature to the control of oxygen reduction reactions in fuel cells3, from thermal protection systems of space vehicles, made of carbon-based materials4, to the preparation of single-wall carbon nanotubes (SWNT) for electronics5. Very often in the same applicative fields elementary processes involving O atoms interacting with graphite 6, 7 are also of interest.



Recently, the scattering of O2 from graphite surface has been investigated by Molecular Beam (MB) experiments for surface temperature ranging from 150 to 500 K, selecting the incident translational energy between 0.291 to 0.614 eV3, 8, and for surface temperature of 300K and at collision energy of 0.09, 0.32 and 0.65 eV9. Obtained results were interpreted with hard cube model8, with classical rigid molecular scattering theory3 or using chemical dynamics simulations9. Moreover, in Ref. [4] the reaction was studied, for surface temperature between 100K and 900K and collision energy between 0.2 eV and 1.2 eV: the investigation was performed by using quasi-classical trajectory calculations on a Potential Energy Surface (PES) based on Density Functional Theory (DFT), for which the limitations in the description of longrange interactions are well-known (see for example Ref. [5]). In that dynamical study results in line with the experiments8 were obtained, when the same conditions were assumed. In spite of the cited experimental and theoretical investigations on oxygen molecule-graphite processes, a systematic study of the effect on the collision dynamics of initial vibrational states, different from the ground-one (or from the low-lying levels), coupled with that of different initial rotational states, still does not exist. In previous works only the interaction mechanism, the angular distributions of the scattered molecules and their energy exchanges with the surface were characterized. In two recent papers10, 11, we simulated the interaction of H2, HD and D2 molecules, in welldefined initial roto-vibrational (vi, ji) states, with a graphite surface. The investigation was conducted by using Molecular Dynamics (MD) calculations, based on a PES, formulated in terms of a recently proposed Improved Lennard Jones (ILJ) model12, suitable to describe noncovalent long-range interactions in the full space of the relative configurations. The collision energy was considered ranging from 0.001 eV and 2.0 eV and the surface temperature varying


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between 10K and 800K. These studies pointed out that while the vibrational state is preserved, some selectivities and propensities exist in the final rotational states’ distributions, being these latter independent of the surface temperature. In this paper, we propose a new PES for the interaction O2/graphite, formulated again in terms of the ILJ model, useful to investigate if some selectivities exist also for oxygen molecules scattered from a graphite surface. In particular, the obtained PES has been exploited to study this reaction by MD calculations based on a state-to-state semi-classical collision treatment13. The adopted theoretical approach, incorporating the state-to-state dynamics, is proper to resolve the roto-vibrational states of the scattered molecules. Obtained spectra highlight not only some selectivities in the final distributions of O2 molecules that diffuse in gas-phase after the interaction with graphite surface, but they cast light also on the microscopic mechanisms underlying the interaction, which appear closely triggered by the initial rotational configuration of molecules with respect to the surface. According to our knowledge, both variety of initial roto-vibrational states and range of collision energies taken into account in this work are the wider considered up to now for the system under study. The paper is organized as follows: in Section 2 MD calculations are described, with the focus on formulation and features of the new PES; in Section 3 the main obtained results are presented, while a detailed discussion is found in Section 4. Finally, some conclusions are drawn in Section 5.



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2. Computational Details This study reports on some basic features of the scattering of oxygen molecules in selected initial roto-vibrational states from graphite. As indicated before, the investigation has been carried out exploiting MD calculations, based on a semiclassical collision treatment13 successfully used in the past to describe the dynamics of elementary gas-surface processes (see for example Refs. [10], [14]-[16] and references therein). The method, based on the assumption that each collision event can be characterized by solving the relevant 3D Hamilton’s equations of motion self-consistently with the dynamics of the lattice phonons, includes also a state-to-state approach for the evaluation at each time of internal degrees of freedom of the molecular species. The complete Hamiltonian for a diatomic molecule interacting with the surface is given by:

1

P2i

H = 2∑imi +V(rO ― O) + ΔEph + Veff(t, TS)

i=1,2

(1)

where Pi is the momentum of each atom i having mass mi in the impinging molecule, V(rO-O) is the intramolecular potential for O2 molecule in gas-phase and Eph is the energy exchanged with the surface phonons. Veff(t, TS) represents the effective potential of mean field type, depending on interaction time (t) and surface temperature (TS), and obtained as the expectation value of the phonons wave function on the interaction potential Vint, given by the next Eq. (2). Details on the calculations of this term can be found in Ref. [13]. The adopted method treats the molecular translational motion classically, while populated rotational and vibrational states (the latter, represented as Morse oscillators17) of scattered molecules are analyzed in terms of the action-angle variables by using the semi-classical quantization rules18. Accordingly, at each time the internal energy of the interacting molecule is


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partitioned into vibrational and rotational contributions by using equations that include rotational angular momentum and related spectroscopic constants. Therefore, we are unable to predict some features due to quantum effects and selection rules. However, at least in the choice of the initial molecular states, we can account for the fact that the roto-vibrational ground-state is (0, 1) and that, because of its symmetry and open-shell nature, O2 can exist only in odd rotational states. Before to proceed in the integration of Hamilton’s equation it is necessary to determine both the dynamics of phonons for a 3D crystal of considered material and an accurate PES driving the reaction under study. Here, we consider the same graphite crystal used in Ref. [10] and, therefore, the same phonon frequencies are adopted. Instead, the PES is formulated as:

N

Vint(rO ― O , R) =

2

∑∑V

N

O2 ― graphite(Rik)

i = 1k = 1

∗ fsw(rO ― O) +

∑V

O ― graphite(Ri)

∗ (1 ― fsw(rO ― O))

i=1

(2)

where VO2 ― graphite and VO ― graphite represent the interaction potential between the O2 molecule and O atom, respectively, obtained as a sum of pair-wise interaction contributions. R is the distance between carbon atom i in the lattice and the k-th O atom in the molecule, for the first term on the right side of Eq.(2), while it represents the distance between carbon atom i in the lattice and the O atom, for the second term. N is the number of C atoms in the graphite lattice. 𝑓𝑠𝑤(rO ― O) is a function of intramolecular distance rO-O, which switches the interaction potential between VO2 ― graphite and VO ― graphite components. The analytical expression of 𝑓𝑠𝑤(rO ― O) is:



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𝑓𝑠𝑤(rO ― O) = ―0.5 ∗ (tanh (1.65 ∗ rO ― O ― 4.8) ― 1.0)

(3)

This is a weight function, chosen to provide quick switching between 1 and 0 preserving the values of VO2 ― graphite and of VO ― graphite for rO ― O lower and higher, respectively, of the intramolecular distance considered critical for O2 molecule dissociation. In the range of distances in which the switching occurs, the potential is obtained as a sum of both components weighted according to the 𝑓𝑠𝑤(rO ― O) value. Molecular oxygen interacting with a graphite surface is only physisorbed with an adsorption energy of ~ 0.1eV, as determined in various studies performed with different methods and at a different degree of accuracy19-22. The dynamics of the elementary processes studied in this work is then determined by the non-covalent intermolecular interactions, dominant at intermediate and large separation distances between gas-phase species and surface, which are the same controlling the physical adsorption. Accordingly, VO2 ― graphite is obtained as a sum of effective atomeffective atom pair interaction contributions, each one represented by an Improved Lennard Jones (ILJ) formulation12, depending on the pair distance R and having the following analytical expression:

[

VILJ(R) = ε

Rm n(R) m n(R) ― m R

( )

―

Rm m n(R) n(R) ― m R

( )

]

(4)

with R 2 R𝑚

( )

𝑛(R) = 𝛽 +4

(5)

The first term of the Eq. (4) describes the size repulsion, while the second one the attraction.


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The parameters  and Rm, which represent the potential well depth and its location, respectively, for the considered pair, define the strength of both terms in Eq. (4).  is an additional parameter depending on the “hardness” of the two partners, and its modulation, within limited ranges, allows to include indirectly the role of other less important interaction components (see for instance Refs. [23], [24]). For the neutral-neutral interactions, as the present ones, m=6 must be used: in these cases, the ILJ function provides for each interacting pair an asymptotic dispersion attraction associated to a C6 coefficient defined as C6= Rm6. The parameters used here to describe the interaction O2-graphite have been calculated (see Refs. [12], [25], and references therein) by exploiting the polarizability of the single O atom (0.8 Å3), the effective polarizability values of O in O2 (0.8Å3) and of C atom in the graphite (1.3 Å3), which are the fundamental physical properties controlling both the size repulsion and the dispersion attraction. The values of the parameters so obtained and used in this work are reported in Table 1. Although in this particular case the involved polarizability components of oxygen atoms are the same, the slight differences in the parameter values arise from small differences both in the number of polarizable electrons and in many body effects affecting the behavior of O and of O(O2) 25, 26.

Table 1. ILJ parameters used in the calculations (meV)

Rm(Å)



O(O2)-C interaction

4.410

3.638

8.0

O-C interaction

4.616

3.616

8.0



From the parameters reported in Table 1, we determined the dispersion coefficient C6 for O(O2)-C and O-C pair interactions obtaining 10228 meVÅ6 and 10327 meVÅ6, respectively. The global C6 value obtained by us for O2-C is lower by about 30% if compared with the value reported in Ref. [20]. However, in that work, this coefficient was estimated by dividing the C6 determined for O2-benzene interaction by a factor 6. Therefore, that value also includes the contribution of the O2-H interaction, which roughly contributes to 30-40 %. Moreover, by using the well-known relation27 between C6 and C3, the C3 value obtained by us for O2-graphite is 1214 meVÅ3 in good agreement with the value of 1157 meVÅ3 reported in Ref. [28], while on the contrary, the C6 value determined in Ref. [20] would give a very larger value for C3. The interaction potential, evaluated for O2 molecule impinging with its bond in the perpendicular and parallel configuration on the three high symmetry sites of graphite, namely on top of a C atom, on a bridge site and above the center of the hexagonal cell, is shown in Figure 1(b) – (c). It appears that in both configurations, the interaction is almost independent on the considered site, the minimum energy value for the perpendicular one is ~ -85meV while for the parallel one is ~ -120meV, in quite agreement with data from literature20, 21. VO ― graphite for each one of the three sites mentioned above is represented as a Morse-like function by taking, binding energy and minimum position values of Ref. [29], where they were obtained by using first-principles wave-method. Thus, a term of ILJ type (Eq. (4)), whose parameters are given in Table 1, is added to this potential for the proper description of the longrange interaction between the oxygen atom and graphite substrate. Figure 1(a) reports the interaction potential so obtained that includes also the short-range behavior.


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Figure 1. Interaction potential for the O-graphite system (a) (including the long range ILJ contribution) and the ILJ potential for O2 molecule impinging (b) perpendicular and (c) parallel on three selected graphite sites. (d) 2D contour plot of PES (see Eq. 2), in eV, used in the simulations. Figure 1(d) shows the 2D contour plot of the complete PES for O2 that impinges with the bond parallel on the bridge site. The interaction is plotted as a function of rO-O and Z, the cartesian coordinate of the molecular center of mass normal to the X-Y surface plane in the assumed reference frame. Note also that in Eq. (2) the zero of the complete PES is set for R∞ and rO-O=re, where re is the equilibrium bond distance of O2 molecule.



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The simulations involve integrating the complete Hamiltonian of Eq. (1) describing the interaction for fixed initial conditions. We propagate and analyze 15000 trajectories for each considered initial roto-vibrational state and collision energy, assuming a fixed value for polar and azimuthal angles of the impinging molecule (==0° define the selected normal approach) and for the surface temperature (TS=100K). The initial coordinates of both atoms in the molecule are chosen randomly in an aiming area on the surface, enough large and at the same time such as to prevent the edge effects during trajectory propagation. The integration step is of 0.25 fs and the accuracy required in the integration procedure is of 10− 8. In the calculations, in addition to the ground-state, we have considered excited states covering low and medium-high values for both vibrational and rotational degrees of freedom. The collision energy has been spanned on a wide range of values, going from 0.01eV (thermal conditions) up to 2.0 eV (hyper-thermal conditions). Only for the ground-state and for some energies we have also investigated the effect of surface temperature, by increasing this latter up to 800K. The same number of trajectories have been propagated, each trajectory having the same initial kinematic conditions, to avoid spurious effects due to different initial conditions. The adopted PES enables to describe and follow the different elementary surface processes occurring when an O2 molecule impinges on the surface, that is:

O2(vf, jf) + graphite

molecular scattering

(6.1)

[O2(vf, jf)]*graphite

molecular adsorption

(6.2)

O2(vi,ji) + graphite ----> Oad*graphite+Oad*graphite dissociative adsorption Oad*graphite + Ogas Ogas + Ogas + graphite

dissociative adsorption/desorption atomic desorption


(6.3) (6.4) (6.5)

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The criteria adopted in the present analysis, that lead to the assignment of a given trajectory to one of the channels in Eq. s (6), are similar to those used in Ref. [10]. So that, molecular scattering (Eq. (6.1)) occurs if, after the interaction with graphite surface, the intramolecular distance (rO-O) is

On the Influence of Rotational Motion of Oxygen Molecules on the

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