A 2d model of the dynamic of the collision: i2-polymeric liquid surfaces of perfluorinatedpolyether (PFPE), polydimetilsiloxane (PDMS) and squalane

ARTICLE

A 2d model of the dynamic of the collision: i₂-polymeric liquid surfaces of perfluorinatedpolyether (PFPE), polydimetilsiloxane (PDMS) and squalane

Alexandre S. LealI, ^*; Claudio G. dos Santos^II; Cristina M. Quintella^III; Heloiza H. R. Schor^IV

^IComissão Nacional de Energia, Centro de Desenvolvimento de Tecnologia Nuclear, Universidade Federal de Minas Gerais Campus, 30.123.970 Belo Horizonte-MG, Brazil

^IIDepartamento de Química do Instituto de Ciências Exatas e Biológicas, Universidade Federal de Ouro Preto, 35.400-000 Ouro Preto-MG, Brazil

^IIIDepartamento de Química, Universidade Federal da Bahia, 40.170-280 Salvador-BA, Brazil

^IVDepartamento de Química, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 31.270-901 Belo Horizonte-MG, Brazil

ABSTRACT

This paper presents two dimension classical trajectory calculations for the scattering of an I₂ molecule in the liquid polymeric surfaces of perfluorinatedpolyether (PFPE), polydimethyl-siloxane (PDMS) and squalane. The potential function describing the interaction of the gas molecule with the liquid surface is formulated as a modified LEPS potential. Each diatomic I₂ molecule and the I-surface potential are represented as a Morse function, with parameters adjusted from experimental data of scattering experiments. The surface was modeled as a typical effective mass with two harmonic vibrational degrees of freedom. This dynamics of the scattering process is in good agreement with experimental dynamical data. The experimentally observed inelastic scattering (IS) and the trapping and desorption (TD) processes were characterized and the determined I₂ vibrational temperatures showed good agreement with experimental values.

Keywords: gas-liquid scattering, perfluorinatedpolyether, polydimethylsiloxane, squalane

RESUMO

Este artigo apresenta um modelo em duas dimensões para o espalhamento de I₂ pela superfície de líquidos poliméricos: poliéterperfluorado (PFPE), polidimentilsiloxano (PDMS) e esqualano. A função energia potencial adotada para descrever a interação do gás com a superfície líquida formulada é do tipo LEPS. Cada molécula diatômica I₂ e o potencial I-superfície são representados como uma função de Morse, com parâmetros ajustados de dados experimentais do espalhamento sobre as referidas superfícies. A superfície líquida foi modelada como um oscilador harmônico bidimensional. Os resultados obtidos com este modelo simplificado da superfície reproduzem, satisfatoriamente, os dados experimentais da dinâmica do espalhamento, em que os processos de espalhamento inelástico e captura e desorção são caraterizados. A temperatura vibracional da molécula de I₂ espalhada foi determinada em concordância com os resultados experimentais.

Introduction

Collisions of gas molecules with liquid surfaces are involved in many physical and chemical phenomena that occur in the gas-liquid interface such as evaporation, condensation, dissolution and reaction. Despite that, very little is known about the dynamics of the gas-liquid interaction. Knowledge of the mechanisms of interaction between atoms, molecules and ions with liquid surfaces is a fundamental step towards a complete understanding of the phenomena occurring at those interfaces. When gaseous species, an atom or a molecule, strike a surface of a low vapor pressure liquid, inelastic collision, adsorption followed by a desorption or a complete dissolution of the colliding species in the liquid can all take place. The important questions are the determination of the rate of the surface processes of adsorption, trapping, desorption and reaction and the efficiency of the energy conversion processes between the gas molecules and the liquid.¹

Recently a number of spectroscopic methods have been employed to probe the dynamics of interface processes. Experiments of scattering of atoms and molecules from liquid surfaces, some in association with molecular dynamics simulations have been used to elucidate the dynamics of inelastic collision, the trapping and desorption processes and the reaction between gaseous species and liquids of low vapor pressure^1-11 and liquid crystals.¹²

In this work, we have simulated a scattering experiment of I₂ molecules from the liquid polymeric surfaces of PFPE (perfluorinatedpolyether, F[CF(CF₃)CF₂O]_nCF₂CF ₃), PDMS (polydimethylsiloxane, (CH₃)₃SiO[Si(CH₃)₂O] _nSi(CH₃)₃ ) and squalane (2,6,10,15,19,23-hexamethyltetracosane, C₃₀H₆₂) in vacuum, in the energy range of 10 kJ mol^-1 to 40 kJ mol^-1. In the related experiments, the processes in which the molecules are scattered directly from the surface could be distinguished from those in which they are adsorbed at the surface. Also the amount of energy transferred during the collision as vibrational excitation of the gas molecule was determined and shown to depend on the chemical nature of the surface.^10,11

Here, we present a calculation of the dynamic of these scattering processes aiming at characterization of the gas-liquid interaction and a molecular description of the collision processes. The model presented here was extended to describe a three dimensional atom-liquid surface scattering with some changes.¹²

Methods

The classical trajectory method was employed to solve the dynamics of the scattering of the I₂ gas molecule from a model liquid surface, in the energy range of 10 kJ mol^-1 to 40 kJ mol^-1. The liquid polymeric surfaces are modeled as two-dimensional coupled harmonic oscillators as it is illustrated in Figure 1. The values of the respective parameters are presented in Table 1.

This simple model of a liquid surface is adequate for a preliminary investigation of the dynamics of the gas-liquid interaction in this energy range. Experiments have shown that PDMS, squalane and PFPE have axial protruding –CH₃ and –CF₃ groups, respectively, in a trans configuration and the orientation of these groups also suggests some degree of order in the liquid surface.^12-15 Therefore, we describe in this model the oscillations of the protruding groups, taken as a –CH₃ group in PDMS and squalane and a –CF₃ group in PFPE, as the oscillations of a set of three coupled harmonic oscillators of mass M corresponding to the mass of each group. The frequencies n₁ and n₂ of the oscillators are the two lowest frequencies observed in the Raman spectra of these compounds.¹⁶ The lowest frequencies n₁ are taken as the frequencies of molecular rocking modes of the groups –CH₃ and –CF₃ of the polymer chain and the higher frequencies n₂ are approximated as the frequencies of the stretching mode of the periodic C–C and C–O bonds in squalane and PFPE surfaces and the frequency of Si–O stretching in the chain of PDMS.^16,17 In Table 1, a represents the length of C–CF₃ bond in PFPE and C–CH₃ bond in PDMS and squalane while the value of b is the horizontal projection of the C–CF₂O bond in PFPE, Si–O bond in PDMS and C–CH₂ bond in squalane. A similar surface model has also been suggested to describe atomic vibrations in metallic atomic surfaces in order to accurately describe the exchange of energy occurring in the scattering of atoms from metallic surfaces.¹⁸

The potential representing the interaction between the I₂ and the model liquid surface is a LEPS (London-Eyring-Polanyi-Sato) potential employed in many gas phase reaction studies¹⁹ and gas-solid interaction.^20,21 This potential can be easily calculated and is also appropriate to describe the asymptotic atomic configurations in processes were the scattered diatomic molecule is dissociated. V_LEPS is a non-pairwise potential for a molecule and a surface S of the following form:

where

are empiric functions describing the Coulomb Q_i(R_i) and exchange J_i(R_i) integrals for each one of the three i pairs, I_a – I_b , I_a – S and I_b – S, where I_a and I_b are the two iodine atoms and S represents the surface.

The parameters De, a and D for the I₂ molecule are well known from spectroscopic data and R₀, the length of I–C bond in equilibrium, was taken as 2.132 Å.^{16, 22} The remaining parameters for the I₂-surface interaction were determined interactively from the present calculation fitting the results to experimental data and are presented in Table 2. The initial value of De parameter for each pair of I–S interaction was arbitrarily chosen as 0.029 a.u., corresponding to half of the dissociation energy of I₂ molecule and varied from 0.022 to 0.036 in steps of 0.001 a.u. This range is also arbitrary but compatible with acceptable values of dissociation energy of I–C bond in polyatomic molecules. The initial value of a_i was assumed as 0.99 a.u., the same value as the one of the I₂ molecule and it was also determined interactively in the calculation, changing its value in the range from 0.91 to 0.99 in steps of 0.02. For each pair of fixed values of De and a, D was varied from 0.2 to 0.6 in steps of 0.1. A total of 750 different sets of parameters values were employed in the calculation.

The initial conditions of the trajectories were the same as established in the related experiment:¹⁰ the molecules of I₂ are in the ground vibrational and rotational states, the surface is in the ground vibrational state, the initial kinetic energy of I₂ is 40 kJ mol^-1 and the molecular beam is normal to the surface. In order to check the consistency of our results, we have also employed an initial energy of 10 kJ mol^-1. The trajectories are calculated by fourth order Runge-Kutha method with steps of integration of 0.5 a.u. from the initial conditions up to the point where the final I₂–S distance is larger than 20.0 a.u.

For each set of potential parameters, 2500 trajectories were calculated with a standard Monte Carlo error l lower than 1%, as defined in equation 2. In this expression, p_a = N_a /N, is the probability of adsorption, and N_a is the number of trajectories in which the gas is adsorbed in the surface and N is the total number of trajectories.

The value of l calculated for this set of trajectories is 0.6% for all three surfaces, which ensures the statistical accuracy of the obtained results.

In the experiment,¹⁰ the vibrational temperatures of I₂ after the collision were obtained from the spectra assuming a Boltzmann distribution for the vibrational population proportional to the rate of the intensities peaks in the laser induced fluorescence spectra of the scattered I_2. Here, we calculate the vibrational temperature by equation 3, where P₀ and P₁ are the population of the ground and first excited vibrational states, respectively.

The two different ways of interaction between the incident molecule and the surface, inelastic collision (IS) and the trapping and desorption (TD), are distinguished by the total time of the trajectory. A particular trajectory is classified as belonging to an IS or TD processes if its time of duration is lower or larger, respectively, than the average trajectory time for a set of 2500 trajectories. This criterion is arbitrary but it can be considered adequate for this bi-dimensional model of the surface proposed here. The same criterion was employed by these authors in a similar model for describing the atom-surface scattering with satisfactory results.¹²

Results

The optimal values of the parameters De, a, and D, which best reproduced the experimental results of the I₂ vibrational temperatures are shown in Table 2.

Figure 2 shows the minimum path into the potential energy for the approximation of the I₂ molecule with the molecular axis parallel to the surface. Figures 3 and 4 show, respectively, the corresponding minimum energy path in the PDMS, PFPE and squalane potential surfaces.

The depth of the well in the path is due to the value of De, larger in the PFPE and squalane, than in PDMS, Figure 2. The height of barrier, related to the Sato parameter D, can be observed in Figures 3 and 4. The parameter a determines the width of the well and affects the dynamics of the rotation of the molecule.²³ Changes in this latter parameter affect slightly the results compared with De and D. Some general comparative results, between the surfaces, presented in Table 3, show how they are related by different potential energy surfaces.

Table 3

Experimental results of gas-liquid scattering ^6,9,10,18 have shown that for higher values of incident energy E of the atom or molecule, the IS process dominates and for the lower values of E a significant amount of the incident gas species is temporarily adsorbed. This result, demonstrated in a previous study of the dynamic of I₂ - PFPE scattering¹⁴ is confirmed by the simulation. This is showed in Figure 5, in which the temporal variation of the parameter r, as defined in Figure 1, is plotted for the surface models of PDMS (5a and 5d), PFPE (5b and 5e) and squalane (5c and 5f), for a particular set of 10 consecutive trajectories randomly chosen with initial energy of 40 kJ mol^-1 (Figures 5a, 5b and 5c) and 10 kJ mol^-1 (Figures 5d, 5e, and 5f). It can be verified that for the same particular set, the amount of trajectories classified as TD grows when E_i = 10 kJ mol^-1, in 5d, 5e and 5f cases. On the other hand, when E_i = 40 kJ mol^-1, in 5a, 5b and 5c, the IS process dominates and the dynamic differences between the surfaces are not so evident.

Experimentally, this result can be interpreted in terms of the probability of excitation of some of the several modes of the protruding groups of the surface –CH₃ and –CF₃,⁹ when the gas molecule strikes the surfaces with lower kinetic energy.

The dynamics of the two distinct modes of interaction between the incident I₂ molecule and the model of the liquid surface, the IS and TD, can also be investigated by following a typical trajectory for each case. The behavior of the molecule in both situations is illustrated in Figures 6a, 6b and 6c, corresponding to an IS process and in Figures 6d, 6e and 6f, corresponding to a TD process. Figures 6a and 6d it is shown the temporal evolution of I₂–surface distance and the embedded vertical vibration of the surface. It is evident from the figures the difference of the time in which the molecule remains adsorbed in the surface before being desorbed in each case. This difference is not so evident when the incident energy is 40 kJ mol^-1, as shown in Figure 5. This is a consequence of the low percentage of the kinetic energy of the molecule transferred to the surface. The vibrational and rotational excitation of the molecule are shown in Figures 6b and 6c, for an IS process, and in Figures 6e and 6f for a TD process. The average distance of I–I bond remains the same in the typical trajectory shown in Figure 6b but increases two times in the trajectory illustrated in Figure 6e. The different probabilities of temporary uptake by the surface and the degrees of vibrational and rotational excitation of the molecule depend on to the geometry of approximation, as can be seen in Figures 6c and 6f. In both cases the molecule is rotationally cold before the collision, and the occurrence of an IS or an TD process is due to the different relative position between the I–I axis bond and the surface. As a consequence, the conversion of initial translational energy to vibrational and rotational modes is more effective in a TD process due to the transfer of momentum to the molecule while trying to escape from the surface. The IS process is characterized by a slight loss of the initial translational kinetic energy of the gas molecule.

The main goal of the experimental work of the scattering of a beam of I₂ molecules from the liquid polymeric surfaces^9,10 was to validate the method of using the vibrational spectra of a molecule as a probe to get information about the structure of the surface. The obtained vibrational temperature allows one to infer a qualitative and comparative analysis of the surfaces rather than detailed features of each one.

The vibrational temperatures, calculated according to the equation (3), obtained here are compared with the experimental values in Table 4. The average percent error calculated is between 13% for the squalane (TD) and 21% for PDMS (TD) and can be considered satisfactory regarding the simplicity of the model of the surface employed and also it is not so discrepant from those encountered in the literature for similar simulations.²⁴

Conclusion

The qualitative results presented here suggest that the simple two dimensional model of representation of a liquid surface as set of harmonic oscillators can correctly reproduce some important dynamic and experimental features observed in the scattering of gas species from high density liquid surfaces. The model could distinguish between IS and TD modes of gas-liquid interaction and reproduce, with a good agreement, the experimental vibrational temperatures of the I₂.

Acknowledgments

The thors wish to acknowledge financial support from CNPq and FAPEMIG.

Received: March 9, 2006

Web Release Date: April 27, 2007

• 1. Nathanson, G. M.; Annu. Rev. Phys. Chem. 2004, 55, 231.
• 2. Jayne, J. T.; Worsnop, D. R.; Kolb, C. E.; Swartz, E.; Davidovits, P.; J. Phys. Chem. 1996, 100, 8015.
• 3. Klassen, J. K.; Nathanson, G. M.; Science 1996, 273, 333.
• 4. Tribe, L.; Manning, M.; Morgan, J. A.; Stephens, M. D.; Ronk, W. R.; Treptow, E.; Nathanson, G. M.; Skinner, J. L.; J. Phys. Chem. B 1998, 102, 206.
• 5. Nathanson, G. M;. Davidovits, P.; Worsnop, D. R.; Kolb, C. E.; J. Phys. Chem. 1996, 100,13007.
• 6. Morgan, J. A.; Nathanson G. M.; J. Chem. Phys 2001, 114, 1958.
• 7. Tomassone, M. S.; Couzis, A.; Maldarelli, C. M.; Banavar, J. R.; Koplik, J.; J. Chem. Phys 2001, 115, 8634.
• 8. Chase, D.; Manning, M.; Morgan, J. A.; Nathanson, G. M.; J. Chem. Phys 2000, 113, 9279.
• 9. Zhao, M. S.; Chemarev, D.; Rice, S.A.; J. Chem. Phys 1998, 108, 5055.
• 10. Quintella, C.M.; McCaffery, A. J.; Zidan, M. D.; Chem. Phys. Lett. 1993, 214, 563.
• 11. Keynon, A. J.; McCaffery, A. J.; Quintella, C.M.; J. Chem. Soc., Faraday Trans. 1993, 89, 3877.
• 12. Leal, A. S.; Schor, H. H. R.; Rodrigues, I.; Quim. Nova 2004, 27, 483.
• 13. Waclawik, E. R.; Cynthia Gon, M.; Donaldson, D. J.; J. Chem. Phys 1999, 110, 8098.
• 14. Leal, A.S.; dos Santos, C.G.; Quintella, C. M.; Schor, H.H.R.; J. Braz. Chem. Soc 1999, 10, 359.
• 15. Pattai, Z. In The Organic Chemistry of Organic Silicon Compounds, J. Wiley and Sons: New York, 1989, ch. 3-6.
• 16. Leal, A. S.; Ph.D Thesis, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil 2001.
• 17. Ramasamy, S.; Pradeep, T.; J. Chem. Phys 1995, 103, 485.
• 18. Pradeep, T.; Chem. Phys. Lett. 1995, 243, 125.
• 19. Benjamin, I.; Wilson, M.; Pohorille, A.; J. Chem. Phys 1994, 100, 6500.
• 20. Levine, R.D.; Bernstein, R.B. In Molecular Reaction Dynamics; Oxford University Press: New York, 1994, ch. 5-6.
• 21. Pazzi, V. I.; Tantardini, G.G.; Surf. Sci 1997, 377, 572.
• 22. Herzberg, G. In Spectra of Diatomic Molecules; Van Nostrand Reinhold: New York, 1950, ch.5.
• 23. Schor, H. H. R.; Chapman, S.; Zare, R.N.; J. Chem. Phys. 1978, 69, 3790.
• 24. Lipkin, N.; Gerber, R. B.; Moiseiev, N.; Nathanson, G. M.; J. Chem. Phys. 1994, 100, 8048.

Publication Dates

• Publication in this collection
  28 June 2007
• Date of issue
  2007

History

• Accepted
  27 Apr 2007
• Received
  09 Mar 2006