Chemical Physics at Interfaces within a Refrigerant-Lubricated Contact

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Chemical Physics at Interfaces Within a Refrigerant-Lubricated Contact: From Electronic Structure to Large Scale Molecular Dynamics Simulations Stéphane Tromp, Laurent Joly, Manuel Cobian, and Nicolas Fillot J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11267 • Publication Date (Web): 14 Feb 2018 Downloaded from http://pubs.acs.org on March 2, 2018

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The Journal of Physical Chemistry

Chemical Physics at Interfaces within a Refrigerant-Lubricated Contact: from Electronic Structure to Large Scale Molecular Dynamics Simulations Stéphane Trompa,b, Laurent Jolyb, Manuel Cobianc, Nicolas Fillota,* a

LaMCoS – INSA Lyon, Université de Lyon, Villeurbanne 69621, France

b

ILM, Université de Lyon, Villeurbanne 69621, France

c

LTDS – ECL, Université de Lyon, Ecully 69134, France

Corresponding Author *E-mail: [email protected] Telephone number: (+33) 4 72 43 82 89

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Abstract The adsorption phenomenon of refrigerant − 1233( ) molecules on a hematite 2) surface is studied at the quantum level thanks to Density Functional Theory + (011 U (DFT+U) calculations employing a van der Waals functional combined with a spin-polarized system. The results show different adsorption sites on the solid surface depending on orientations of the molecule, characterizing strong interactions between the refrigerant molecule and both iron and oxygen atoms. A range of binding energy values of −0.92 to −0.22 is observed. These ab-initio results are used to parametrize a force field at the refrigerant-hematite interface for larger scale Molecular Dynamics simulations. Effects of these ab-initio considerations on density and velocity profiles are studied, in the case of a confined fluid between two surfaces as in a lubricated contact. The high binding energy values induce a locking effect of the − 1233( ) molecules close to the hematite surface, showing a resistance to compression ( = 500) and shearing ( = 20/ ).


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1. Introduction In large refrigeration systems, compressors include rolling bearings. In these systems the bearings inside compressors are usually lubricated with an oil-refrigerant mixture.1 For decades and until now many research groups have tried to determine the lubricating properties of these refrigerant-oil mixture.2–7 However and as a consequence of environmental aspects, maintenance and manufacturing costs, compressors and bearings manufacturers have an increasing interest for oil-free pure refrigerant lubricated systems.6,8,9 Because they contribute to depleting the ozone layer10,11, phase-out of chlorofluorocarbon (CFC) and hydrochlorofluorocarbons (HCFC) has been planned during the Montreal Protocol in 1987. Following the Kigali amendment in 2016, hydrofluorocarbons (HFC) are also phased down due to their characterization as greenhouse gases.12 Hydrofluoroolefins (HFOs) are developed as alternative refrigerants in order to replace them.13,14 The trans-1-chloro-3,3,3-trifluoropropene 1233zd(E), also called − 1233( ), is an example of this fourth generation of refrigerants and belongs to the Hydrochlorofluoroolefin (HCFO) family. Even though this molecule contains a chlorine atom, it still has a low Ozone Depletion Potential (ODP), due to its short atmospheric lifetime of around 26 days15,16 caused by the double carbons bond of the − 1233( ).17 The nonflammable − 1233( ) is considered as an alternative refrigerant to replace the R245fa for Organic Rankine Cycle and for high temperature heat pump, or the R123 for low pressure centrifugal chiller18–21, as approved by the U.S. Environmental Protection Agency.22,23

Morales-Espejel et al.24 studied experimentally the lubricating capability of − 1233( ) in elastohydrodynamic lubrication (EHL) regime, characterized by severe conditions (high pressure, thin lubricant film thickness).25 By measuring with an optical interferometer the film thickness in a glass-steel contact, a thick solid layer was observed on the steel ball surface, suggesting that chemical reactions could occur during the experiments. Some research groups investigated experimentally the formation of a tribolayer with other refrigerants interacting on different iron surfaces.26–30 However, concerning the !" − 1233( ) in a steel contact no experimental or numerical result about the formation of a tribolayer was found in the literature except the paper published by Morales-Espejel et al.24 Thanks to the enhancement of experimental tools at the nanoscale, it could now be possible to determine the chemical composition of this tribolayer, for instance with X-ray photoelectron spectroscopy analysis.27,31 But the physicochemical phenomena occurring at the refrigerant-surface interface during tribological process cannot be determined experimentally yet and it is crucial to be able to study the effects of shearing and severe pressure and temperature conditions on this deposited layer. Such information can however be obtained from molecular simulations. The study performed by Morales-Espejel et al. was under EHL conditions and hence following atomistic simulations are performed under similar conditions to try to understand the macroscopic experimental behavior from the atomic scale. On the one hand, Density Functional Theory (DFT) can describe matter at the quantum level, but its high computational costs precludes its use to consider a whole elastohydrodynamic (EHD) contact. DFT provides accurate adsorption information at the atomic level but is



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generally limited to static calculations. On the other hand, classical non-equilibrium molecular dynamics (NEMD) simulations, which are based on empirical force fields (FF), are widely used for large systems to describe the rheology as well as the molecular structure of lubricants over reasonable timescales in some nanometric patch inside lubricated contacts.32–36. Ab-initio Molecular Dynamics (AIMD) methods become affordable on certain systems37,38 but remain too demanding for other materials, e.g. those involving magnetic order. Ewen et al.35 used NEMD simulations in order to study the behavior of stearic acid molecules adsorbed on a hematite surface while Doig et al. considered the structures and friction of different fatty-acids adsorbed on iron-oxide surfaces.39 Ta et al.40 used DFT calculations to parametrize a classical force field for the adsorption of n-alkanes on iron and iron oxide surfaces. Then, this force field was implemented into molecular dynamics simulations to study the tribological behavior of alkanes confined by iron and iron oxide surfaces under shear.36,41 Vega et al.42 and Lísal et al.43 used MD simulations for some HFC and HCFC refrigerants in order to predict thermophysical properties. However, to the best of our knowledge, no numerical study of adsorption phenomena was achieved with any refrigerant. Moreover, no MD simulations with confined refrigerants was found in the literature. In that context, we developed a multiscale numerical methodology where DFT calculations, describing matter at the level of its electronic structure, are combined with large scale molecular dynamics simulations, using empirical force fields adapted on the basis of the DFT results. Both methods and “Results and discussions” sections are divided into three main subsections. First, the results obtained with DFT are detailed and the interactions between refrigerant and hematite are explained. DFT calculations are used to obtain accurate binding energies under different conformations. Then, the methodology used to parametrize a force field at the refrigerant-surface interface based on these DFT results is discussed. Finally, this force field is implemented in NEMD simulations to study structure and flow behavior in a system of interacting refrigerant molecules confined between two hematite surfaces.

2. Numerical methods a. Density Functional Theory Density Functional Theory calculations are used to study the adsorption of refrigerant molecules at the quantum level by considering a set of positions and orientations of one molecule near the surface. This aims to mimic probable situations in an elastohydrodynamic contact. In order to represent an oxidized steel surface located in a rolling bearing, an iron oxide is considered. As shown in Figure 1, in this study the surface of iron oxide is described with hematite (# − ), which is the most thermodynamically stable form of iron oxide under ambient environment and thus, the most common on earth. The (x,y,z) dimensions of the relaxed hematite is approximately of 10 Å x 11 Å x 10 Å. The choice was made to consider the (0112) orientation because of the presence of both iron and oxygen atoms on the upper layer. Therefore a representative set of interactions between atoms of the refrigerant and the surface will be considered. Moreover, as represented in Figure 1, the 4 ACS Paragon Plus Environment

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− 1233 ( ) molecule is composed of a " group next to a double-carbon bond. The sp2 carbon in the middle is linked to a hydrogen named !2 and the second sp2 carbon to one hydrogen !1 and one "$ atom.

2) relaxed surface (left) and trans-1-chloro-3,3,3Figure 1: hematite # − (011 trifluoropropene 1233zd(E) molecule (right). In order to study the adsorption of − 1233( ) molecules on hematite (# − ) surfaces, we used the CP2K/QUICKSTEP code44 (version 3.0) to perform Density Functional Theory (DFT) calculations in the Born-Oppenheimer approximation. Because van der Waals (vdW) dispersion forces are of primary importance to describe liquids and the interfacial behavior, the exchange-correlation term is calculated within the generalized gradient approximation (GGA) with the non-local optB88-vdW functional.45 Dabaghmanesh et al. showed that this functional is accurate for methane and benzene adsorption on hematite surface.46 The pseudopotentials of Goedecker-Teter-Hutte were employed.47 The aim is to find the lowest energy value of the whole system composed of one molecule of the 1233 and one surface formed with 120 atoms. Because the surface is already relaxed, iron and oxygen atoms remain fixed during the geometry optimization and only the molecule of refrigerant can move in a box of 10.24 Å x 10.93 Å x 25 Å. This leaves a vacuum gap of ca. 1 nm between the top of the molecule and the bottom of the periodic image of the solid surface. With the standard DFT method, the 3d strong correlated electrons are not well described. Therefore the DFT-GGA+U method, in which a Hubbard-type on-site Coulomb repulsive term is added to the Hamiltonian, was used. The challenging point we face here is to employ a van der Waals functional combined with a spin-polarized system by using the named GGA+U method. The convergence of a geometry optimization process is much more difficult with the DFT+U method and it is often necessary to use different methods (standard DFT followed by DFT+U) to perform this convergence.

Standard DFT method

For calculations without DFT+U method, geometry optimizations were carried out in order to solve the Kohn-Sham equations. The short range molecularly optimized double-ζ valence polarized (m-DZVP) Gaussian basis functions were used. A cutoff value of 300 Ry was used for the plane wave expansion. The Kohn-Sham matrix is iteratively diagonalized with the Orbital Transformation method.

DFT+U method 5 ACS Paragon Plus Environment


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All calculations using the DFT+U method were performed spin-polarized by solving the unrestricted Kohn-Sham equation. A value % = 5 predicts correctly the hybridization of 3d-electrons of iron atoms.48,49 Therefore, an angular momentum quantum number of 2 is chosen for iron atoms in this method. A ramping method is used from a threshold value of the self-consistent field (SCF) convergence of 10&' to incrementally increase the U value to target U (5eV) value with an increment of 0.5eV. Different values were tested and these latter did show the best capacity to converge the calculus. The short range molecularly optimized single-ζ valence polarized (m-SZV) Gaussian basis functions were used for every atom and the final plane-wave cutoff was set to 500 Ry. The modified Broyden mixing method is used in order to improve the convergence behavior of the SCF procedure.50 Moreover, due to the antiferromagnetic behavior of the hematite this convergence is enhanced by setting an initial multiplicity value to one. The Fermi-Dirac smearing method was used with an electronic temperature of 3000 K. Since smearing can lead to occupied molecular orbitals (MOs) in conduction band, additional empty MOs were added to represent the initially unoccupied orbital in this band. Finally, the Kohn-Sham matrix was diagonalized with standard methods.

Binding Energy

2) #- was studied and the The adsorption behavior of − 1233( ) on the (011 binding energy values ( were calculated with the following formula:

) = {+,-./01234567899:; } − +,-./0 − 234567899:;

(1)

where {+,-./01234567899:;} is the total energy of the relaxed adsorbate-substrate system, +,-./0 is the energy of the clean surface slab and 234567899:; is the energy of the isolated − 1233( ) molecule. The two last terms are calculated by using the same geometry as the { =>?@ + 1B$C2 D } system optimized one. A negative value of the binding energy means that the obtained geometry is more stable than the unbounded state. To estimate the basis set superposition error, we calculated the total energy of the molecule for 6 representative orientations by considering two basis sets: first, the basis set of the isolated molecule, and second, the basis set of the whole system. The difference in energy was always lower than 47meV, this maximum value corresponding to a flat orientation of the molecule. After DFT calculations are completed, a parametrization of the interfacial force field will be performed. In the next subsection, the methods used to calculate the interfacial potential parameters are presented. b. Interfacial potential parametrization An adapted force field of the interface between the refrigerant and the surface will be derived from this ab-initio behavior. In this section the ab-initio post processing is described and the force field parameters used at the interface for large scale molecular dynamics simulations are determined. Because no periodic boundary condition is used in this section, we have to consider a larger surface than the one presented above. Indeed, electrostatic 6 ACS Paragon Plus Environment

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interactions have to be included with a large amount of pairs between the surface and the refrigerant molecule. By using the periodicity of the small surface composed of 120 atoms, a new bigger one was built multiplying by three in x and y the smaller one. Hence the new surface used for ab-initio post processing is composed of 1080 atoms and the molecule of refrigerant is placed upon the central small surface with the position obtained at the end of ab-initio geometry optimization process. In this study 16 different positions and orientations of the refrigerant molecule on the surface are used and an algorithm detailed in Figure 2 is performed in order to determine the interfacial parameters. Ta et al.40 studied the adsorption of normal-alkanes on various kinds of iron oxide surfaces and they used a trial-and-error approach in order to adjust the force field parameters to the DFT results. They ran the adsorption energy calculations repeatedly until they obtained a good agreement between ab-initio and MD results. They also published an interfacial potential between an aqueous copolymer solution and an iron surface, by deriving parameters from DFT calculations.51 Here, the choice was made to transcript the refrigerant-surface interactions by using pairwise Coulombic and Lennard-Jones (LJ) 12-6 potentials between each atom pair i and j with atomic charges EF and EG respectively, >FG the distance between two atoms, HFG the welldepth energy and IFG the distance corresponding to a zero value of the potential between both atoms. The following formula represents the model we used for the interfacial interactions.

EF EG IFG = JK + 4HFG OP Q 4MHN >FG >FG

2

F,G

IFG − P Q ST >FG R

(2)

HFO compounds have been in the market for only a few years and therefore experimental data for these molecules are rare.52,53 That is why Raabe et al. developed a force field in order to study this kind of refrigerants54. In 2015 an extension of this force field was published for the − 1233( ) refrigerant in order to study its thermophysical properties.19 In the next section, we will use this empirical FF to represent the bulk refrigerant behavior. In order to remain consistent by using the FF of Raabe for the refrigerant with large-scale MD calculations, the partial charges of Raabe19 will be used for the ab-initio postprocessing and only the LJ 12-6 parameters between the fluid and the surface will be adjusted. For hematite surface, a partial charge of iron is fixed of EV0 = +0.6 and of oxygen to EX = −0.4. Because LJ parameters have to be distinguished depending on atom types, sp2 and sp3 carbons are named " and "Y, respectively.

Analyzing situations where − 1233( ) molecules adsorbed at least partially either with O-Cl or with Fe-Cl interactions, IV0&Z5 and IX&Z5 are fixed to 2.46Å and 2.53Å, respectively, only on the basis of adsorption distances obtained from ab-initio calculations. Moreover, I values for interactions including carbons remain fixed as explained below. The values of ε for LJ potential including carbon sp3 will be adapted in order to take into account the strong



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interactions obtained between fluorine atoms and the surface. The ε values for LJ potential including carbon sp2 will be fixed. Sixteen unknown LJ parameters remain to be determined. Since we could not obtain physical solutions by solving the global system of 16 equations and 16 unknown parameters, the solving process is split into 9 different steps. In every step, only a smaller amount k of optimized geometries are taken into account by choosing them for being relevant to the parameters calculated in this step. For each of the k corresponding equations, we calculate each distance between the 9 atoms of the molecule and the 1080 atoms of the surface. A system composed of k nonlinear equations named ?\ with an amount of unknown LJ parameters smaller than k is obtained. The (\ is the binding energy associated to the geometry optimization number k, while >\FG represents the distance between both atoms i and j for this geometry k. The vector x is composed of the 16 LJ-parameters including the unknown, the determined ones on previous steps, and the ones initially fixed as detailed below, which will be calculated on next steps. By using a trust-region reflective method we solve the following least squares problem for each step and we find the x vector minimizing the following sum:

min aJ ?\ (b) c `

With

(3)

\

EF EG IFG ?\ = (\ − J K + 4HFG OP Q 4MHN >\FG >\FG

2

F,G

IFG − P Q ST >\FG R

(4)


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Figure 2: Postprocess algorithm in order to obtain LJ 12-6 parameters between − 1233( ) molecule and hematite surface. Because of physical considerations both initial points and boundary conditions for the solutions are fixed for each postprocessing step higher than 1 Angström and lower than 5 Angströms for every sigma value. Concerning the values of epsilon they are in both cases fixed positives and lower than 1eV. Indeed the maximum value of binding energy obtained with ab-initio calculations remains lower than 1eV for the whole set of position possibilities and thus the energy represented by epsilon between only two atoms cannot exceed this value. For each step of this process numbered from 1 to 9, 100 initial points are randomly chosen within these boundary conditions. The Lennard-Jones parameters still not obtained at the step i, are fixed by using the Lorentz-Berthelot mixing rules:

HFG = dHF HG and IFG =

ef 1eg

,

(5)

where we used Raabe force field parameters for the refrigerant molecule and the Consistent Valence Force Field (CvFF) for iron and oxygen atoms.55–57 From ab-initio results it is possible to find four converged geometries related to the case 1 in which the Chlorine atom is directly placed upon the iron and oxygen atoms. Therefore we used these four results in order to find in step 1 the interactions between Chlorine and the surface. Then four other converged geometries describing a molecule adsorbed thanks to Chlorine and Hydrogen H1 are used within steps 2 and 3 in order to obtain the interactions between this Hydrogen and the surface. Afterwards the parameters between Fluorine and the surface are found within steps 4 and 5. Then the interactions parameters between the Hydrogen H2 and the surface are found by using four optimized geometries in steps 6 and 7. In order to reproduce the binding energies obtained with horizontal positions of the 9 ACS Paragon Plus Environment


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molecule, ε values between surface and the carbon "h are adapted as well within steps 8 and 9. The optimized interfacial force field will be used in larger scale Molecular Dynamics simulations and the methods concerning this following step are presented in the next subsection. c. Large-scale Molecular Dynamics

System Setup

All MD calculations in this section are performed by using the LAMMPS software (version: 2) slabs of hematite with (x,y,z) dimensions of around 30 Å x 33 Å x May 14th 2016).58 (011 10 Å are used in all MD calculations. In this MD study the hematite surface built by using abinitio calculations was used and duplicated considering periodic boundaries. Moreover, each atom is bonded with a spring to a virtual atom located at its equilibrium position. A value of 200 kcal/mol for the spring stiffness is chosen to ensure thermal conduction between thermostatted regions and the liquid. The upper surface is built by rotating the lower surface of 180°. Each surface is composed of 1080 atoms (not including the virtual atoms). 192 molecules constitute the refrigerant liquid. Raabe force field introduced in the previous section is used to represent the refrigerant in a bulk behavior.19,51 The Lorentz-Berthelot mixing rules are applied to determine LJ parameters between different atoms in the bulk refrigerant (Equation (5)). Surface-refrigerant interactions are represented with LJ and coulomb potentials. LJ parameters obtained with the postprocessing and partial charges exposed in the previous section are implemented. No LJ interaction are considered within the surface. The Verlet integration algorithm is used with a time step of 1 fs. The non-bonded interactions are represented by the Lennard-Jones 12-6 potential coupled with the longrange Coulombic interactions including a cutoff value of 12 Å for both non-bonded kinds of interactions. Intramolecular nonbonded interactions between atoms separated by one or two bonds are set to zero. Scaling factors of 1/2 and 1/1.2 are applied to nonbonded LJ and electrostatic interactions respectively, between atoms separated by exactly three bonds. Electrostatic interactions were determined using the particle-particle particle-mesh (PPPM) algorithm. A slab correction is used for the PPPM solver because of the non-periodic system in z direction.59

Compression and Shearing

All initial systems are obtained with the Moltemplate software.60 An initial vacuum gap of around 30 Å in z direction between refrigerant molecules and the surface is set up, in order not to disrupt energy minimization and refrigerant bulk stabilization before applying the normal load. The pressure = 500 is controlled by applying an additional external force to the virtual surface in such way that every virtual atom experiences the same force, so that the virtual surface moves rigidly. After the compression stage, a velocity of ` = ± ⁄2 is implemented in x direction for all virtual atoms with a shearing velocity = 20 m/s while the normal load remains fixed. A Langevin thermostat with a time 10 ACS Paragon Plus Environment

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relaxation of 0.1ps is applied to the two third outermost layer of atoms in the hematite slabs, in order to keep them at a temperature of 283K during all the MD calculations. During the sliding stage, the Langevin thermostat is applied in both hematite surfaces but only perpendicularly to sliding and compression directions, thus only in y direction.61 Indeed, it was shown that direct thermostatting the confined fluid can lead to unrealistic properties.62 Figure 3 is a representation of a − 1233( ) fluid confined between two hematite surfaces where mechanical conditions, as well as thermostats, are outlined. The shearing step lasted for 10ns and results are averaged upon the last 2ns for the velocity and density profiles.

Figure 3: Representative system setup for the NEMD simulations of R1233zd (E) confined between two hematite surfaces In the next section, results are gathered and divided into three subsections. First, the results obtained with DFT are detailed and the interactions between refrigerant and hematite are explained. Then, the optimized interfacial force field is determined and discussed. Finally, results obtained with large scale molecular dynamics simulations regarding density and velocity profiles in the contact and using this optimized force field are presented. 3. Results and discussions a. Determination of the adsorption behavior with ab-initio calculations In this subsection, results are obtained with DFT calculations. Sixteen different initial configurations have been obtained by translating and rotating randomly the refrigerant molecule with respect to the three directions. As shown in Table 1 below, the adsorption possibilities are classified into six different molecule positions associated to six ranges of binding energy values. Every adsorption results is visualized with the visual molecular dynamics (VMD) software.63



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Table 1: Six different kinds of adsorption possibility with the ranges of binding energy values combined with the geometry optimization number (see the energy values of the 16 optimizations in the next section) !1

"$

"

!2

Case 1

) ⋲ m−0,45; −0,22o( ) ) 4, 12, 13, 14

Case 2

) ⋲ m−0,57; −0,50o( ) ) 2, 10, 11, 16

Case 4

) ⋲ m−0,92; −0,82o( ) ) 6, 7, 8

!1

"$

!2

"$

Case 5

) r −0,70 ( ) ) 1

!1

"$

Case 3

) ⋲ m−0,66; −0,64o( ) ) 5, 9, 15 "s

Case 6

) r −0,47 ( ) ) 3

The first important result is that chlorine atoms strongly interact with iron atoms, as shown in the first case. The chlorine can interact with the oxygen atoms as well. However, it involves to decrease the distance between iron and chlorine and the binding energy will decrease. Therefore we can conclude that the "$ − interaction is of major importance. During geometry optimization process, it is also possible that the molecule of refrigerant leans and the hydrogen H1 located near the chlorine will play a non-negligible role of stabilization, as shown in the second case. In the third one, it is shown that the fluorine has to be taken into account, with a lower energy value of around -0.65eV. The assumption of possible interaction between iron and fluorine atoms had been raised28, although it was with another refrigerant. We obtained the strongest interaction for the fourth case. Indeed, the binding energies 6-7-8 with refrigerant molecules parallel to the hematite surface are higher than the ones with vertical orientations of the molecule. Therefore it means that the horizontal positions of the refrigerant molecules are more stable than the vertical ones. By considering extreme values of energy in both case 1 and 4, we have a lowest difference of around 0.37eV and a biggest one of around 0.7eV. Indeed both interactions between Fluorine – surface and between Chlorine – surface will play a role. Moreover, the π-bonding 12 ACS Paragon Plus Environment

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of the double carbons bond could play a role. For the fifth case, the molecule rotated along the double-carbon bond axis and both chlorine and fluorine, as well as the hydrogen H2 bonded with the carbon located in the middle of the molecule, interact with the surface. In the sixth case, only the fluorine atoms interact with the surface. This latter orientation of the molecule was actually the most difficult to obtain and the geometry optimization process did not converge easily. It is also interesting to observe that we could obtain the same binding energy value with one molecule adsorbed either thanks to the three fluorine atoms or with only the chlorine atom. It shows what was hypothesized in the paper of Na et al.30 with the former refrigerant dichlorodifluoromethane CFC-12 about an iron-chloride coating formation. Indeed, chlorine and iron atoms strongly interact and the − 1233( ) molecule can be adsorbed with a major contribution of van der Waals interactions between these two atoms and of course because of all coulombic interactions. Moreover, Akram et al. reported the formation of a fluorine-enriched film for the HFO-1234yf.26 Therefore it is possible to link this observation to our sixth optimized geometry case. It could happen that organic molecules decompose by approaching a metal surface64 and build an amorphous film mostly composed of the molecule atoms. It would be problematic here because it would mean that the refrigerant would not be able to interact with any iron or oxygen atoms because of presence of an amorphous phase at the interface. Furthermore, because of the double-carbon bonds it could be firstly thought that − 1233( ) does not remain stable when approaching the surface. However, in this study no dissociation phenomenon was observed.

In this ab-initio study, we have shown that the − 1233( ) molecule could strongly adsorb on an iron oxide surface. Moreover, this adsorption was characterized by considering a set of position and orientation of the molecule upon the surface, describing a lubricated contact. These information about reactivity of the surface with the refrigerant obtained from DFT calculations are then retained in a force field in order to study much larger systems.

b. From the quantum behavior of matter to larger molecular scale

In the previous section, adsorption ability of the − 1233( ) on hematite surface was observed. An adapted force field of the interface between the refrigerant and the surface will be derived from this ab-initio behavior. The results obtained for the parametrization of interfacial potential are summarized in Table 2. Table 2: LJ 12-6 parameters for the interactions between hematite surface and − 1233( ) Pairwise O-Cm O-Ct Fe-Cm Fe-Ct

HFG Kcal/mol 0.149 0.196 1.090 0.479

IFG Å 3.13 3.13 2.86 2.86



O-H1 O-H2 O-Cl O-F Fe-H1 Fe-H2 Fe-Cl Fe-F

0.408 0 0.618 0.174 0.068 0 1.147 0.740

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2.34 1.00 2.53 2.95 3.70 1.00 2.46 1.97

Iron atoms play a major role of the adsorption process with strong ε values of pairwises − "$ and − . Moreover, the strong interaction observed for horizontal orientation is described with a high ε value between iron and carbon sp2-hybridized atoms. The hydrogen !2 bonded to the second carbon is well described by zero well-depth energy values with both oxygen and iron. The binding energy values obtained with this optimized interfacial force field are compared with the ones determined from ab-initio calculations. The results summarized in Table 3 show a maximal difference value of 54meV. This latter value enables to be confident with these new LJ 12-6 parameters values. The highest difference between MD and ab-initio results is of around 10%.

Table 3: Comparison between binding energies obtained with the optimized force field and the ab-initio ones for every system geometry. Absolute Binding energies [eV] Absolute difference Value [%] N° MD with modified FF ab-initio [meV] ) 1 -0.728 -0.696 4.56 32 ) 2 -0.507 -0.521 2.63 14 ) 3 -0.421 -0.468 10.06 47 ) 4 -0.376 -0.393 4.21 17 ) 5 -0.680 -0.663 2.48 16 ) 6 -0.903 -0.874 3.29 29 ) 7 -0.869 -0.922 5.83 54 ) 8 -0.840 -0.825 1.71 14 ) 9 -0.649 -0.639 1.54 10 ) 10 -0.487 -0.507 4.00 20 ) 11 -0.530 -0.551 3.80 21 ) 12 -0.361 -0.343 5.26 18 ) 13 -0.479 -0.446 7.55 34 ) 14 -0.219 -0.224 2.24 5.0 ) 15 -0.629 -0.649 3.08 20 ) 16 -0.534 -0.572 6.59 38


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In the following section, we will consider a larger system representative of what could occur in a bearing when roughness peaks of ball bearings are close enough with a distance of few nm.

c. Molecular Dynamics simulations In this subsection, results are obtained with large-scale MD simulations. Density and velocity profiles of this confined refrigerant between two hematite surfaces are plotted in Figure 4 and Figure 5 for both optimized and non-optimized force fields.

Figure 4: Flow velocity profile with Pz=500MPa, Vx=±10m/s and wall temperature T=283K. The blue points represent the velocity profile in the x direction with the optimized FF and the orange crosses with the non-optimized FF. Each point is an average over a 2 Å thick layer in z direction. The red crossed lines give the refrigerant boundary where the surface is located. Figure 4 shows that the − 1233( ) molecules close to the surface are locked. It means that effective shearing will occur within a smaller film thickness. This locking effect is reminiscent of experimental observations made by Morales-Espejel et al. and detailed in the introduction about formation of a thick solid layer on the steel ball surface.24 This layer resists under high pressure (500) and high shearing with ` = ±10 m/s. It could lead to protect the bearing surfaces against wear when two asperities are closed, what was firstly assumed by Morales-Espejel et al.24 The velocity profile does not vary much by using either the optimized FF or the non-optimized one. However, as shown in the following Figure 5, the density profiles is affected.



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Figure 5: Number density profiles in the contact, with Pz=500MPa, Vx=±10m/s and wall temperature T=283K. The case a) obtained with the non-optimized FF, thus obtained with classical Lorentz-Berthelot mixing rules and case b) with the optimized FF. Figure 5 compares the classical interfacial FF (a) obtained thanks to Lorentz-Berthelot mixing rules and the optimized FF (b). This underlines a difference in the refrigerant molecules structure at the surface. In case (b) of the Figure 5, a high concentration of refrigerant molecules is observed next to the surfaces. Specifically, in case (b), hydrogens H2 are localized close to the surface and the density of chlorine atoms at the interface becomes higher than in case (a). In contrast, H1 atoms are repelled from the surface. This high presence of chlorine at the interface reproduces well the ab-initio results. Indeed, it was concluded that the refrigerant molecule could be strongly adsorbed on the surface thanks to chlorine atoms. The nonsymmetrical features of the density profiles suggest that desorption timescales are much higher than the 10 ns of this shearing stage, so that molecules locked at the surface do not have the time to equilibrate with the bulk. However, it does not change the qualitative observations done in this section. The presence of hydrogen !2, chlorine and a non-negligible amount of fluorine atoms near the surface suggests that the fifth ab-initio adsorption case is the most representative here at the interface. This case 5 owns the second highest binding energy ( ) r −0,70 ( )) just following case 4 obtained with 16 ACS Paragon Plus Environment

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horizontal positions of the molecule ( ) ⋲ m−0,92; −0,82o( )) (see Table 1). The ab-initio studies were all single molecule studies and the preference for case 4 over case 5 is more likely a coverage effect in large scale MD simulations. A preference for tilted over flat conformations has also be observed in MD simulations of organic friction modifiers.39,65 In real conditions (high pressure, small film thickness, rough surfaces), this structural organization might have a large impact on tribological behavior (wear and fatigue resistance).

4. Conclusion In this work, two distinct approaches where used to study a refrigerant-iron oxide interface. The conclusion is then split into two subsections to distinguish DFT and large scale MD findings.

Ab-initio calculations have been carried out in order to study the adsorption of − 1233( ) on iron oxide surface. This work is an ideal complement to answer some experimental gaps observed in the literature. The challenging point was to employ a vdW functional combined with a spin-polarized system by using the GGA+U method. The main findings can be summarized as follows: -

a range of surface-refrigerant molecule binding energy values of −0.92 to −0.22 is observed, the iron atoms play a major role of the adsorption process represented by strong ε energy values of pairwises − "$ and − for Lennard-Jones potential, the hydrogen !1 located near the chlorine will play a non-negligible role of stabilization, as observed in DFT calculations, the horizontal positions of the refrigerant molecules are the most stable with a binding energy value of around −0.92 , no dissociation phenomenon of the refrigerant on hematite was observed.

Furthermore, postprocessing methodology is developed to parametrize a force field at the refrigerant-surface interface on the basis of ab-initio results. The information about reactivity of the surface with the refrigerant obtained from DFT calculations are retained in an optimized force field in order to study much larger systems. Moreover, larger scale MD simulations including this optimized force field were analyzed. A locked layer of refrigerant on hematite surface was observed and resisted to compression ( = 500) and shearing ( = 40/ ). Moreover, the high binding energy values could in fine lead to the initial formation of a tribolayer. As a consequence the adsorbed molecules of refrigerant could be able to protect the surface against wear in a lubricated contact. Our results motivate experimental characterization of the tribolayers using for instance X-ray photoelectron spectroscopy analysis. More generally the optimized force field developed in this study provides the opportunity to study complex systems, for instance with a more representative analysis of lubricated contact. 17 ACS Paragon Plus Environment


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Acknowledgments

This work was supported by the LABEX iMUST (ANR-10-LABX-0064) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). Moreover, L.J. is supported by the Institut Universitaire de France. We are also grateful for HPC resources from GENCI/TGCC (Grants t2016087230 and A0010807230). We also thank P2CHPD computer center (Université Claude Bernard Lyon 1) for the allocation of computational resources. Finally we want to thank Guillermo E. Morales-Espejel for fruitful discussions.

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Figure 3: Representative system setup for the NEMD simulations of R1233zd (E) confined between two hematite surfaces 77x61mm (96 x 96 DPI)

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Figure 4: Flow velocity profile with Pz=500MPa, Vx=±10m/s and wall temperature T=283K. The blue points represent the velocity profile in the x direction with the optimized FF and the orange crosses with the nonoptimized FF. Each point is an average over a 2 Å thick layer in z direction. The red crossed lines give the refrigerant boundary where the surface is located. 101x94mm (96 x 96 DPI)



Figure 5: Number density profiles in the contact, with Pz=500MPa, Vx=±10m/s and wall temperature T=283K. The case a) obtained with the non-optimized FF, thus obtained with classical Lorentz-Berthelot mixing rules and case b) with the optimized FF. 102x139mm (96 x 96 DPI)


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Chemical Physics at Interfaces within a Refrigerant-Lubricated Contact

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