Picosecond dynamics of gas-phase dimers in liquid carbon dioxide

Chemical Physics Letters 464 (2008) 177–180

Contents lists available at ScienceDirect

Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett

Picosecond dynamics of gas-phase dimers in liquid carbon dioxide E. Guarini a,f,*, M. Sampoli b,f, U. Bafile c, F. Formisano d,f, M. Jiménez-Ruiz d, A. Orecchini e,f, G. Venturi a,f, F. Barocchi a,f a

Dipartimento di Fisica, Università di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy Dipartimento di Energetica, Università di Firenze, Via S. Marta 3, I-50139 Firenze, Italy c Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy d Institut Laue Langevin, BP 156, F-38042 Grenoble, France e Dipartimento di Fisica, Università di Perugia, Via A. Pascoli, I-06123 Perugia, Italy f CNR-INFM CRS-Soft, c/o Dipartimento di Fisica, Università di Roma ‘La Sapienza’, I-00185 Roma, Italy b

a r t i c l e

i n f o

Article history: Received 18 April 2008 In final form 14 September 2008 Available online 20 September 2008

a b s t r a c t An inelastic neutron scattering and molecular dynamics simulation study of the interaction properties of liquid CO2 is reported. By means of an interaction-based interpretation of neutron scattering and simulation results for the dynamic structure factor we also show that ðCO2 Þ2 equilibrium dimers characteristic of the gas phase are present in dense liquid carbon dioxide and predominantly contribute to the observed picosecond dynamics. Such a memory of the gas-phase structures was not observed in liquid methane. The role of anisotropy and strength of interactions on these important differences is discussed. Ó 2008 Elsevier B.V. All rights reserved.

Exploring the existence, origin, and kind of ‘long-living’ twobody structures in molecular liquids is crucial for a deeper understanding of the dynamic properties and relaxation phenomena of disordered systems. Actually, if temporary aggregates take place in a liquid, relaxation processes can likely be interpreted in terms of the continuous decay and restoration of such structures at the rhythm of their characteristic lifetimes. Simple systems offer important opportunities to enquire into the physical reasons at the basis of the heuristic relaxation concept. Here we address the case of liquid carbon dioxide, a fluid of fundamental interest in science and applications, and of still unknown dynamic behaviour. Experimental and simulation studies of the static pair distribution functions of CO2 at liquid densities [1–6] suggest, without exceptions, the presence of preferential two-body short-range orientations mainly driven by the anisotropy of the intermolecular potential. Debate is open, instead, about the favoured pair geometry that static analyses are able to discern. In particular, the preferential T-like configurations deduced in Refs. [2–5] have been recently quite strongly excluded by reverse Monte Carlo techniques applied to existing diffraction data [6]. Indeed, the CO2 case long remained unsettled even as far as the equilibrium geometry of the free ðCO2 Þ2 dimer was concerned [7]. Stable structures of the gas phase could finally be accurately identified with the slipped-parallel (SP) planar configuration (with a C– C-O angle of 58.2°) by infrared measurements [8], later confirmed by ab initio-based calculations [9,10]. * Corresponding author. Address: Dipartimento di Fisica, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy. Fax: +39 055 457 2136. E-mail address: guarini@fi.infn.it (E. Guarini). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.09.036

To gain insight into the still controversial results for liquid CO2, dynamic investigations are essential, as they provide unique information on the lifetimes of existing correlations which remain out of reach of static studies. The range of lifetimes that can be probed obviously depends on the adopted experimental technique. Neutron Brillouin scattering is suited to study the dynamics of molecular pairs with correlation times in the picosecond range. Here we demonstrate that the gas-phase stable configuration of the ðCO2 Þ2 dimer, i.e., the SP one, has a leading role in the measured picosecond dynamics of the dense liquid. This fact provides a precious hint for the exploration of the possible mechanisms which may or may not favour the persistence, in disparate liquids, of pre-existing equilibrium structures of the cold gas phase. A combination of inelastic neutron spectroscopy (INS) and molecular dynamics (MD) simulations is used to probe the dynamics of liquid carbon dioxide at the nanometer and picosecond length- and time-scales. This twofold approach, recently applied to liquid D-methane (CD4) [11], indeed revealed that dynamic structure factor, SðQ ; xÞ, determinations offer a precious access to the interaction law, with special sensitivity to its anisotropic character. Moreover, the Q-evolution of MD spectra obtained with different potentials was found to have a strong correspondence with the short- and medium-range behaviour of the interaction– energy curves pertaining to a particular CD4–CD4 configuration. An unconventional analysis of dynamical data in terms of the underlying anisotropic interactions is therefore able to point at the pair geometries which mostly contribute in the probed picosecond range. This novel discriminating method can thus be usefully applied to liquid CO2. Carbon dioxide is practically a ‘perfect’ sample for neutrons, thanks to the low absorption and, mainly, to the negligible

178

E. Guarini et al. / Chemical Physics Letters 464 (2008) 177–180

incoherent-to-coherent ratio of neutron cross sections (<103) for both carbon and oxygen, which greatly simplifies the neutron access to SðQ ; xÞ. The INS experiment was carried out using the IN3 three-axis spectrometer of the Institut Laue-Langevin in Grenoble. Constant-Q energy scans with fixed final energy (Ef ¼ 14:7 meV) were performed at eight Q-values between 3 and 17 nm1, i.e., up to 0.9 Q p , with Q p the position of the main peak in the static structure factor [12]. The sample was condensed at T = 221.9 ± 0.3 K inside a vanadium container, and slightly pressurized as to reach a molecular number density n = 15.88 ± 0.01 nm3 [13]. The empty vanadium-cell data needed for background evaluation also provided us with an estimate of the elastic energy resolution: a Gaussian-shaped spectrum of 0.74 meV full width at half maximum. Raw neutron intensities were corrected for background, attenuation, and multiple scattering following methods very similar to those detailed in Ref. [14]. Besides proper consideration of energy resolution effects, the corrected data [15] are proportional to the neutron-weighted version of the dynamic structure factor, here named ~ SðQ ; xÞ. This, in the totally coherent case of CO2, is

Q = 3 nm-1

0.2 0.15 0.1 0.05 0 -6 0.1

-4

-2

0

2

4

6

Q = 5 nm-1 0.08 0.06

pffiffiffi 2 ~SðQ; xÞ ¼ bðCÞ SCC ðQ ; xÞ þ 2 2bðCÞ bðOÞ SCO ðQ ; xÞ þ 2bðOÞ2 SOO ðQ ; xÞ coh coh coh coh ð1Þ

0.04

ðaÞ bcoh

0.02

~ S(Q,ω) [barn ps]

where is the coherent scattering length of either C or O, and the usual definition [16,17] of the partial dynamic structure factors, Sab ðQ ; xÞ, was adopted. Each Sab ðQ ; xÞ can be accessed by MD simulations, for which we used six potential models, i.e., those of Murthy et al. (MSM) [18,19], of Harris and Yung (EPM2) [20], of Tsuzuki and Tanabe (TT) [21], of Bock et al. (BBV) [22], of Potoff and Siepmann (TraPPE) [23], and of Zhang and Duan (ZD) [5]. Two of these, TT and BBV, are based on ab initio calculations. For each model, the dynamics was simulated in a constant-NVE ensemble of 500 rigid molecules, with a force cutoff distance of 1.6 nm ( half the box length). The equations of motion were integrated with a time step of 1.67 fs. The Verlet and Fincham [24] algorithms were used for translations and rotations, respectively. Energy conservation was achieved within a 2  105 relative drift over 1000 time steps. After a suitable thermalization, the evolution of the system was followed for about 1 ns and configurations stored every 10 fs. The Sab ðQ ; xÞ were calculated from the power density spectrum of the corresponding signals, and combined following Eq. (1). Detailed-balance asymmetry and instrumental resolution broadening were applied to the MD results before comparison with the neutron data. Since the MSM and ZD models provide hardly distinguishable MD spectra in the explored Q-range, the MSM data will not be presented. Fig. 1 shows the experimental ~ SðQ ; xÞ and the corresponding simulation results at selected Q values. Four models (EPM2, TraPPE, ZD, and, though not reported, MSM) are, on the whole, equivalent and effectively describe the overall dynamics, with EPM2 showing a superior performance at the highest Q. Conversely, serious disagreements with the measured quasi-elastic peak characterize the small- and medium-Q spectra of the BBV and TT models, though with opposite tendencies. The BBV potential produces evident low-Q overestimates which progressively reduce with increasing wave vector, and eventually reverse into an underestimate at the highest Q. The TT results underestimate the central line at most Q values, and finally predict an excess intensity at 17 nm1. The equivalence of the EPM2, TraPPE, and ZD (MSM) predictions of liquid CO2 experimental spectra, as well as the clear anomalies in the BBV and TT ones, can be explained by looking at the potential curves of the above models for some of the CO2 dimers. Fig. 2 shows the potential–energy curves of the various models in five example pair configurations: crossed (C), linear (L), parallel

0 -10 0.06

-5

0

5

10

Q = 9 nm-1

0.05 0.04 0.03 0.02 0.01 0 -15

-10

-5

0

5

10

15

Q = 17 nm-1

0.6 0.5 0.4 0.3 0.2 0.1 0 -15

-10

-5

0

5

10

15

ω [ps ] -1

Fig. 1. Experimental ~ SðQ ; xÞ of liquid CO2 (circles with error bars) at selected Q values, compared with the corresponding MD results for the BBV (solid), EPM2 (full dots), TraPPE (dotted), ZD (dot-dashed), and TT (dashed) potentials. Uncertainties on the MD data (not shown) are of the size of the EPM2 symbols.

179

E. Guarini et al. / Chemical Physics Letters 464 (2008) 177–180

recall those of the RP potential in CD4 (larger r, shallower minimum). Indeed, an underestimate of the Rayleigh line is observed in both cases. Moreover, the various MD peak-intensities of CO2 at low and medium Q are found to strictly follow the order of the collision parameters in the SP curves: a sequence which is not respected in other configurations. The same thing happened in CD4. Finally, the TraPPE and TT models are those predicting higher repulsive energies between SP pairs at very short distances, though just appreciable in Fig. 2 for the TraPPE curve. The correspondence between stronger repulsion and, as a more marked effect, higher SðQ ; xÞ appears as another comcentral peaks in the close-to-Q p ~ mon feature of the CD4 and CO2 cases, here qualitatively accounting for the results at 17 nm1. As far as repulsive properties and spectral shapes are concerned, the analogy between CO2 and CD4 is however not complete. In fact here we have, in the SP case, potential curves which have (sometimes slightly) different r, but comparable repulsive steepness, the TT hard-core behaviour being only a little softer. Thus, in the present CO2 potentials repulsion-energy values differ mainly because of r. Instead, in CD4 we could also observe the combined effect of different collision parameters and/or slope in the hard-core region. Here the second effect is practically absent. The similar steepness of the present CO2 potentials explains, in our view, the Q-evolution of the BBV spectra and why discrepancies tend to vanish with increasing wave vector. Indeed, the high-Q dynamics of a dense molecular liquid appears to be mainly influenced by the derivative, rather than by the absolute value, of the repulsive energy. In this sense, the slightly softer character of the TT hard-core might give reason of the limited differences between TraPPE and TT at 17 nm1.

(P), T-shaped (T), and slipped parallel (SP). The changes due to anisotropy are evident with varying geometry. Moreover, for each of the C, L, P and T dimers, the ZD, EPM2, and TraPPe models show rather different behaviours, incompatible with the results of Fig. 1, and with the high sensitivity of ~ SðQ ; xÞ. Conversely, nearly coincident curves pertain to the above three potentials [25] in the SP dimer, with only minor deviations in the TraPPE case. In particular, for SP pairs, quite close values for configuration-dependent parameters as the depth and position (r m ) of the attractive well, the collision parameter (r), and the hard-core steepness, characterize the three potentials. We note in passing that the nearest neighbour C– O distance of the free dimer (0.314 nm) determined in Ref. [8] is the same that can be calculated back from the EPM2 and ZD (MSM) curves of the SP case when r CC ¼ rm ¼ 0:359 nm. Finally, only in SP geometry TT and BBV display the (opposite) differences from the common behaviour of ZD, EPM2, and TraPPe, that are witnessed by the neutron spectra. These facts indicate that SP-like pairs largely influence the neutron-detected picosecond dynamics of liquid CO2. More precisely, they reveal that molecular pairs of this kind have average correlation lifetimes which match the explored time-window. Focusing on the medium- and short-range (rCC 6 r m ) properties of the potentials in the SP case, the correspondence between potential features and details of the resulting spectra has direct analogies with that found in CD4 for base–vertex geometry [11]. In particular, BBV departs from the other models in the same way the RMK model does in methane (quite smaller r, much deeper attractive well). Actually, identical effects influence the respective MD spectra, with enormous overestimates of the low-Q central peaks. Similarly, the present TT deviations from the other curves

1000

1000 1

800

600

-0.5

400

0 Y -1 -1

1 X

0

2

600

-1 1

4

3

Y

-1 -1

-200

0

0.4

0

1

2

3

-1 1

4 0 Y

X

-1 -1

400

linear (L) 200

0.35

0

400

0

0.45

0.5

2 X

1

3

4

parallel (P)

0

0.55

0.5

0.55

1000

0.6

0.65

0.3

0.35

0.4

0.45

0.5

0.55

1000 BBV TT TraPPE ZD EPM2

1

Z

0.5 0

-0.5

500

500

-1 1 Y

0 -1 -1

1

0

2

3

1

0

-1 1 4

0.5

4

3

0 Y

X

2 1

-0.5 -1 -1

0

X

slipped parallel (SP)

T-like (T)

0

0

-500

-500 0.35

0

200

Z

0.3

0

-0.5

crossed (C)

0.25

0.5

0

-0.5

600

-1 1

200

1

800

0.5

0

Z

Z

0.5

Z

800

E [K]

1000

1

0.4

0.45

0.5

0.55

0.6

0.3

0.35

0.4

0.45

0.5

0.55

rCC [nm] Fig. 2. Five significant geometries of carbon dioxide pairs (3D plots in the reference frame XYZ, reported as insets) and total potential energy in units of kB , as a function of the CC distance along the X-axis of the coordinate system. Different curves refer to the BBV(solid), EPM2 (full dots), TraPPE (dotted), ZD (dot-dashed), and TT (dashed) models.

180

E. Guarini et al. / Chemical Physics Letters 464 (2008) 177–180

Fig. 3. Three-dimensional representation of the CC pair distribution function g CC ðr CC ; cos hÞ of liquid CO2, as obtained from the MD simulation using the EPM2 potential. Similar trends are found with other potential models. The dependence on the carbon–carbon intermolecular distance rCC and on cosh, with h the angle between the axes of the two molecules in the pair, are reported.

The above comparison of the carbon dioxide and methane cases shows that, at least for simple molecules, a common interpretation scheme qualitatively works, disclosing the presence of some general features. On the other hand, details may of course differ from a fluid to another, as a consequence of their specific interaction properties. This study confirms the effectiveness of dynamic approaches to the interaction law of molecular liquids. Anisotropic CO2 potentials able to account for SðQ ; xÞ data are confidently discerned here from less realistic ones. Moreover, our MD-aided method shows that close-to-SP molecular pairs play an important role on the measured neutron spectra. This experimental observation allows to assign to SP-like geometries an average correlation time within the picosecond range we accessed by INS. The sensitivity of the neutron dynamical spectra to SP pairs does not imply that other ðCO2 Þ2 configurations are absent or present only to a negligible extent in the liquid static structure. For example, in Fig. 3 we show the EPM2-based MD results for the angle-dependent pair distribution function g CC ðrCC ; cos hÞ, where h denotes the angle between the axes of the two molecules. The h dependence of g CC ðrCC ; cos hÞ is rather flat at any distance, hence all mutual orientations are nearly equiprobable in a static picture of liquid CO2. With the present dynamic investigation we obtain additional information about the system configurations able to produce a signal at the picosecond scale, finding in particular that these contain pairs with nearly SP geometries. Lifetimes of SP-like pairs turn out to be at least one order of magnitude longer than the Enskog time between collisions evaluated for our sample. Therefore, dimers with the gas-phase equilibrium structure are able to survive, in liquid CO2, for times quite longer than the inverse collision rate, i.e. they can experience tens of collisions with negligible effects on average. This result differs considerably from that of CD4, where the stablest isolated dimer

(‘base–base’, according to the well-depth of the TUT potential in Fig. 2 of Ref. [11]) is not the picosecond-living ‘base–vertex’ pair detected in the liquid. Comparison of the curves of reliable potentials for CO2 and CD4 clearly witnesses two fundamental facts: (i) the well-known much stronger anisotropy of interactions in CO2, and, (ii) the far larger binding energy of the ðCO2 Þ2 free dimer. The first point can partly account for the existence of a pair configuration easily recurrent throughout all phases of carbon dioxide. In other terms, the weaker anisotropy of CD4 less effectively selects given geometries, thus the persisting dimer structures in this liquid may depend more on other conditions. The second observation justifies the weaker effect of collisions on SP gas-dimers of CO2 even at liquid densities. Clearly, packing properties and overall steric effects may also play a role in the differences between the two molecular liquids. In conclusion, we showed that INS spectra provide a clear-cut selection among available potentials for CO2. Two body shortrange structures living for picoseconds exist in dense fluids and this work on CO2 reveals that their configurations depend on the degree of anisotropy and energy of the interactions. Memory of the free dimer structure clearly emerges from the ps dynamics of liquid CO2. Weakly anisotropic systems are instead less evidently reminiscent, as density grows, of the gas-phase situation. Acknowledgement The valuable support of the ILL staff is gratefully acknowledged. References [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]

A.K. Adya, C.J. Wormwald, Mol. Phys. 74 (1991) 735. I.I. Fedchenia, J. Schröder, J. Chem. Phys. 106 (1997) 7749. P. Cipriani, M. Nardone, F.P. Ricci, M.A. Ricci, Mol. Phys. 99 (2001) 301. M. Saharay, S. Balasubramanian, J. Chem. Phys. 120 (2004) 9694. Z. Zhang, Z. Duan, J. Chem. Phys. 122 (2005) 214507. L. Temleitner, L. Pusztai, J. Phys.: Condens. Matter 19 (2007) 335203. K.W. Jucks, Z.S. Huang, D. Dayton, R.E. Miller, W.J. Lafferty, J. Chem. Phys. 86 (1987) 4341. K.W. Jucks, Z.S. Huang, R.E. Miller, G.T. Fraser, A.S. Pine, W.J. Lafferty, J. Chem. Phys. 88 (1988) 2185. M. Welker, G. Steinebrunner, J. Solca, H. Huber, Chem. Phys. 213 (1996) 253. S. Tsuzuki, T. Uchimaru, M. Mikami, K. Tanabe, J. Chem. Phys. 109 (1998) 2169. E. Guarini, M. Sampoli, G. Venturi, U. Bafile, F. Barocchi, Phys. Rev. Lett. 99 (2007) 167801. J.B. van Tricht, H. Fredrikze, J. van der Laan, Mol. Phys. 52 (1984) 115. E.W. Lemmon, M.O. McLinden, D.G. Friend, Thermophysical properties of fluid systems, in: P.J. Linstrom, W.G. Mallard (Eds.), NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Gaithersburg, MD, 2005. E. Guarini et al., J. Phys.: Condens. Matter 17 (2005) 7895. Detailed account of the measurements and data treatment will be given elsewhere. N.W. Ashcroft, D.C. Langreth, Phys. Rev. 156 (1967) 685. C. Liao, S.-H. Chen, Phys. Rev. E 64 (2001) 021205. C.S. Murthy, K. Singer, I.R. McDonald, Mol. Phys. 44 (1981) 135. L.C. Geiger, B.M. Ladanyi, M.E. Chapin, J. Chem. Phys. 93 (1990) 4533. J.G. Harris, K.H. Yung, J. Phys. Chem. 99 (1995) 12021. S. Tsuzuki, K. Tanabe, Comput. Mater. Sci. 14 (1999) 220. S. Bock, E. Bich, E. Vogel, Chem. Phys. 257 (2000) 147. We thank the authors for providing the correct að5Þ ¼ 1:3578  105 a.u. parameter for the CC interaction which was misprinted in Table 1 of the original paper.. J.J. Potoff, J.I. Siepmann, AIChE J. 47 (2001) 1676. D. Fincham, CCP5 Quart. 10 (1983). . The MSM curve (not shown in Fig. 2) also practically coincides, in SP geometry, with the ZD and EPM2 ones.