Structure and Single Proton Dynamics of Bulk Supercooled Water

Journal of Molecular Liquids 136 (2007) 236 – 240 www.elsevier.com/locate/molliq

Structure and Single Proton Dynamics of Bulk Supercooled Water A. Botti a,⁎, F. Bruni a , M.A. Ricci a , A. Pietropaolo b , R. Senesi b , C. Andreani b Dipartimento di Fisica “E. Amaldi”, Università di Roma Tre, via della Vasca, Navale 84, 00146 Roma, Italy Dipartimento di Fisica, Universita ` degli Studi di Roma “Tor Vergata” via della, Ricerca Scientifica 1, 00133, Roma, Italy a

b

Available online 30 August 2007

Abstract Neutron diffraction measurements with isotopic substitution (NDIS) and Deep In- elastic Neutron Scattering (DINS) experiments have been performed on bulk liquid water in the supercooled regime. Supercooling of ultra-pure water has been obtained thanks to a PTFE coating of the sample container. From the structural point of view the effect of supercooling at ambient pressure results in a slight change of the water coordination shells with respect to the structure of ambient water, although similarities with Low Density Water can be observed. As a matter of fact, the present data compare well with previous results obtained at about the same temperature, applying external pressure and can be interpreted within the second critical point scenario. DINS measurements have been carried out on this system with the aim of determining the anharmonic character of the momentum distribution of the protons, complementing the structural information on supercooled bulk water. © 2007 Elsevier B.V. All rights reserved. Keywords: Supercooled water; Neutron diffraction; Neutron scattering; Momentum distribution PACS: 61.12.-q; 25.40.Fq; 61.20.Qg; 64.60.My

1. Introduction The thermodynamic, structural and dynamic properties of bulk water in its supercooled state is an ongoing issue, that have been approached mostly theoretically and computationally [1], due to the experimental difficulties in keeping bulk water in a metastable state, below its melting point. From the experimental side, different approaches have been adopted in order to circumvent this practical obstacle. Among all the possible choices, pressurization[2,3] and confinement [4–6] have played an important role; in the experiments presented here instead we have obtained supercooling of the bulk liquid at ambient pressure, by using PTFE coated containers. The result of the theoretical and experimental effort so far is rationalized in two opposite theories, namely the second critical point scenario and the singularity free hypothesis [7]. Despite their differences, both theories share the idea that molecules can organize in at least two different ways, giving origin to two water polymorphs: a high-specific volume and low entropy structure, called low density water (LDW), and a low-specific

⁎ Corresponding author. E-mail address: [email protected] (A. Botti). 0167-7322/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2007.08.017

volume and high entropy structure, called high density water (HDW). These are the liquid counterpart of the low density amorphous (LDA) and very high density amorphous (VHDA) solid water, i.e. the glassy phases found below the temperature of glass transition, Tg. The existence of two water polymorphs in the supercooled liquid state, originally formulated after the Mishima et al. experiments [8], has been further supported by two recent experiments, namely a neutron diffraction study of supercooled water under pressure [2,3] and measurements of the density of a quasi-liquid layer at the interface between amorphous SiO2 and ice Ih [4]. At thermodynamic states accessible to the experiments, that are well above the hypotized second critical point, water is assumed to continuosly evolve between the two extreme structures of LDW and HDW. Structural studies can be coupled to dynamical studies performed on the same bulk supercooled water sample towards a complete picture of this challenging system. In particular the Deep Inelastic Neutron Scattering technique allows to investigate the single-particle proton dynamics [9]. This technique is of great relevance for an accurate description of the microscopic interactions between water molecules. Indeed, it reflects both the role of the hydrogen bond network in determining the mean kinetic energy of the proton, bEk N, and the influence of the molecular symmetry on its momentum distribution, n(p).

A. Botti et al. / Journal of Molecular Liquids 136 (2007) 236–240

237

Fig. 1. Panel A: distance dependence of the coordination number n(r), between two oxygen atoms. Panel B: Oxygen–Oxygen site–site radial distribution function. For both panels thin line refers to Low Density Water (LDW), thick line to supercooled bulk water T = 267 K and P = 1 bar (SPR) and dotted line to ambient water (RT). The arrows evidence the main changes in the RDF.

Here we revisit the first experimental determination of the site–site distribution functions of supercooled pure bulk water at 1bar [10], and present the first measurements of the single proton momentum distribution at the same thermodynamic conditions. These experiments provide new information for a thorough comprehension of the behavior of water in the supercooled regime. 2. Structure The experiment was performed at the SANDALS [11] diffractometer installed at the ISIS spallation source. In order to apply the hydrogen/deuterium isotopic substitution method in the neutron diffraction experiment, we have used these samples, namely ultra pure H2O and D2O from Aldrich and an equimolar mixture of these two (hereafter labeled HDO) [12]. Three independent measurements of the neutron differential crosssection (DCS) are needed to extract the partial structure factors (PSF) of water, namely SOO, SOH, and SHH, following the procedure outlined in Ref 10. These PSF are defined as Fourier transforms of the three site–site radial distribution functions of water, which describe the microscopic structure of the liquid as a function of the modulus of distance r between two atomic sites. The three experiments have been performed at slightly different temperatures, namely T = 266.60K for H2O, T = 274.16K for D2O and T = 268.96K for HDO, in order to account for the differences in the PVT data of the two water isotopes [13]. The temperature was controlled via a thermostatic bath with an accuracy of ±0.1 K. The sample container was made of two vanadium plates coated with PTFE by Isoflon [14]. The total

external thickness of the container was 3.4 mm, of which 1.1 mm occupied by the sample. The sealing of the two plates was achieved by means of a PTFE gasket. The three samples have been exposed to the neutron beam for about ten hours each. Measurements were also recorded for the empty container, empty instrument and a standard vanadium slab. Data have been corrected for absorption, multiple scatting, inelasticity effects, and calibrated to an absolute scale, according to the standard procedure described in Ref. [15]. The site–site radial correlation functions for each pair of atoms in the system, namely gOO, gOH and gHH, have been obtained from the PSF through the EPSR code [16–21]. More details about the experiment and data analysis can be found in Ref. [10]. Fig. 1 reports the comparison of LDW [2], ambient water at P = 1 bar T = 298 K (RT) [22] and supercooled water at P = 1 bar T = 267 K (SPR) [10], as far as the gOO (r) function (panel B) and running coordination number (panel A), nOO , are concerned, being: Z r noo ðrÞ ¼ 4pqo r V2 goo ðr VÞdr V ð1Þ 0

where ρO is the atomic number density of oxygen atoms. We notice a better definition of the first peak at ∼ 2.9 Å in the case of LDW compared to RT, suggesting a molecular arrangement closer to that of ice in the first neighbor shell. This is confirmed by the lower first minimum, and by the behavior of the nOO function (shown in panel A), that is more intense than that of RT water in the range 2.5 b r b 3.7 Å. The same trend, although not so evident, is shown by the nOO of SPR water, which is always

238

A. Botti et al. / Journal of Molecular Liquids 136 (2007) 236–240

Fig. 2. Oxygen-Hydrogen site–site radial distribution function, gOH , and corresponding coordination number. The thick line refers to SPR water, the thin line to LDW and the dottet line to RT water. In the inset the first intermolecular peak of the gOH is enlarged and the arrow indicates the shift of the peak with respect to RT water.

intermediate between the two states. Moreover the number of water molecules in the first coordination shell is larger than 4, confirming the presence of interstitial molecules at all three thermodynamic states. The modifications of the Hydrogen Bond (HB) network is displayed by the shift of the position of

the second peak of the gOO which moves toward smaller distances in the case of the LDW and the SPR sample with respect to RT water. On the contrary, the third peak of LDW moves towards larger distances, while SPR water data overlap quite well with RT ones in this region.

Fig. 3. Hydrogen–Hydrogen site–site radial distribution function, gHH, and corresponding running coordination number. The thick line refers to SPR water, the thin line to LDW and the dottet line to RT water. In the inset the first intermolecular peak of the gHH is enlarged. The arrows evidence the changes of the RDF.

A. Botti et al. / Journal of Molecular Liquids 136 (2007) 236–240

The HB length, as shown by the position of the first intermolecular peak of the Oxygen–Hydrogen site–site radial distribution function of Fig. 2 (enlarged in the inset), becomes slightly longer upon supercooling (1.79 Å) and in the LDW (1.81 Å) if compared with water at ambient conditions (1.77 Å). This change implies the existence of more linear hydrogen bonds. The differences in the intensities are compensated by the changes in density, so that, as it can be seen in the nOH [23], the number of HB per oxygen atom are in the average a bit less than 2 for all data sets. The second intermolecular peak is related to the tetrahedral coordination of water molecules, which appears better defined in LDW because the peak shows a steep rise between 2.5 and 3 Å; this feature is not shared by the supercooled and RT data. Moreover, LDW shows between 4 and 4.5 Å an extra peak, absent in SPR and RT water. In the case of the gHH function, reported in Fig. 3, differences between SPR and RT water are minor, suggesting that in both states the relative orientations of water molecules are more disordered compared to LDW. Nevertheless we notice that the first intermolecular peak position moves from 2.33 Å in the case of RT water to 2.35 Å for supercooled water, up to 2.38 Å for LDW (see the inset). Interestingly, the LDW and the supercooled water have a small extra shoulder ar 5 Å which doesn't show up in RT water. In the same Fig. the corresponding nH H functions are shown for completeness. These findings suggest that in SPR water the first coordination shell has a more pronounced tetrahedral symmetry compared to RT water, which suggest similarities with LDW, although the longer range correlations still evidence a higher degree of disorder.

239

longitudinal momentum y, the atomic momentum component along the direction of the wave vector transfer q between y and y ± Δy. In an isotropic system there is no dependence on qˆ, and the response function is given by: Z l pnð pÞdp: ð4Þ JIA ð yÞ ¼ 2p jyj

For finite q values, deviation from IA can be accounted for in terms of additive corrections to the asymptotic form [28], in the form J(y, q) = JIA(y) + ΔJ (y, q). Experimental data at T = 269 K and T = 271 K have been acquired in the standard Resonance Filter configuration, employing the Single Difference (SD) and the Double Difference (DD) methods [26,27], the latter providing a narrow instrumental resolution, with the aim of carrying out a detailed line–shape analysis of the proton NCP. The time of flight (TOF) spectra were acquired through an array of 32 fixed-angle detectors, placed in the angular range 32° ≤ 2ϑ ≤ 70°, 2ϑ being the scattering angle. Standard data reduction procedures have been employed to correct time of flight data for multiple scattering, sample container and other spurious signals. The corrected TOF data have been transformed into spectra in the y domain, thus obtaining the so-called Experimental Compton Profile, Fexp(y, q) = J(y, q) ⊗ R(y, q), for each fixed-angle detector, R(y, q) being the fixed-angle resolution function.

3. Single proton short-time dynamics The intense flux of epithermal neutrons (E ≥ 500 meV) provided by the ISIS spallation source is exploited on the VESUVIO inverse geometry spectrometer where Deep Inelastic Neutron Scattering (DINS) measurements allow the direct measurement of proton momentum distribution [9]. The high energy (Jω) and wave vector (q) transfers achieved in DINS experiments, allow to describe the scattering process within the framework of the Impulse Approximations (IA) [9,24]. In the IA framework the dynamical structure factor is related to the single particle momentum distribution through the relation: SIA



 Y q; w ¼

Z

    pd Yq Y Jq2 Y Y  n p d w d p; M 2M

ð2Þ

J2 q2 2M being the recoil energy of the struck atom of mass M and q is the

wave vector transfer. In the DINS regime, Jw and q are not independent, but are related by a scaling law, so that [25]: JIA ð y;qÞ̂ ¼

Jq Y  SIA q; w M 

ð3Þ



M where y ¼ Jq w  Jq is the West scaling variable [25]. The 2M function JIA ð y;qÞ̂ referred to as the Neutron Compton Profile (NCP), represents the probability to find an atom with a 2

Fig. 4. (a) Single detector response function, averaged over the whole set of detector elements: (a) T = 300 K (open dots) and T = 269 K (close squares); (b) T = 269 K (open dots) and T = 271 K (close squares).

240

A. Botti et al. / Journal of Molecular Liquids 136 (2007) 236–240

The analysis of the experimental DINS data is still in progress. A preliminary result is shown in Fig. 4, where data relative to the experimental response function F exp(y, q) for T = 269 K and T = 271 K are plotted and compared with room temperature bulk water [29]. This figure suggests that the single particle dynamics in supercool water differs quantitatively from that observed in RT water. 4. Conclusion The radial distribution functions of supercooled water at P = 1bar, determined after a neutron diffraction experiment with H/D isotopic substitution, suggest that the structure of water at these thermodynamic conditions is intermediate between that of ambient water and the extremal structure of the Low Density polymorph. In particular the first neighbor peaks of all three RDF are sharper than those of ambient water, suggesting a better localization of the atomic sites and of protons in particular. When the same thermodynamic state is studied in terms of the distribution of the proton momentum, via a DINS experiment, then evident differences in the single proton dynamics show up. The analysis is still in progress and it will aim to investigate the differences in the momentum distribution line shapes in supercooling and room temperature thermodynamical conditions, also related to the structural and dynamical changes of the local proton environment. Acknowledgments This work has been performed within the Agreement No.01/ 9001 between CCLRC and CNR, concerning collaboration in scientific research at the spallation neutron source ISIS and with partial financial support of CNR. References [1] P.G. Debnedetti, J. Phys. Condens. Matter 15 (2003) R1669. [2] A.K. Soper, M.A. Ricci, Phys. Rev. Lett. 84 (2000) 2881. [3] M.A. Ricci, A.K. Soper, Pysica A 304 (2002) 43.

[4] S. Engemann, H. Reichert, H. Dosch, J. Bilgram, V. Honkimaki, A. Snigirev, Phys. Rev. Lett. 92 (2004) 205701. [5] J.M. Zanotti, M.C. Bellissent-Funel, S.H. Chen, Europhys. Lett. 71 (2005) 91. [6] L. Liu, S.H. Chen, A. Faraone, C.W. Yen, C.Y. Mou, A.I. Kolesnikov, E. Mamontov, J. Leao, J. Phys. Condens. Matter 18 (2006) S2261–S2284. [7] H. Stanley, S. Buldyrev, G. Franzese, N. Giovanbattista, F.W. Starr, Phil. Trans. R. Soc. A 363 (2005) 509. [8] O. Mishima, H. Stanley, Nature 392 (1998) 164. [9] C. Andreani, D. Colognesi, J. Mayers, G.F. Reiter, R. Senesi, Adv. Phys. 54 (2005) 377. [10] A. Botti, F. Bruni, A. Isopo, M.A. Ricci, J. Chem. Phys. 117 (2002) 6196. [11] A.K. Soper, in: D.K. Hyer (Ed.), Advanced Neutron Sources 1988, IOP Conference Series, vol. 97, IOP Publishing, Bristol, 1989. [12] F. Bruni, M.A. Ricci, A.K. Soper, J. Chem. Phys. 114 (2001) 8056. [13] Zahlenwerte und Functionen aus Ohysik, Chemie, Astronomie, Geophysik und Technik, Landolt-Bornstein Series (Springer, New York 1967), 6. Aufl., Bd II/f, pp. 449. [14] More details about PTFE coatings may be obtained from Isoflon, Zone d'Activites. 38790 Diemoz (France). [15] A.K. Soper, W.S. Howells, A.C. Hannon, RAL Report No. RAL-89–046, 1989. [16] A.K. Soper, Chem. Phys. 202 (1996) 295. [17] A.K. Soper, J. Mol. Liq. 78 (1998) 179. [18] A.K. Soper, Chem. Phys. 258 (2000) 121. [19] A.K. Soper, Molec. Phys. 99 (2001) 1503. [20] A. Botti, F. Bruni, S. Imberti, M.A. Ricci, A.K. Soper, J. Chem. Phys. 121 (2004) 7840. [21] A.K. Soper, Empirical Potential Structure Refinement - User Manual, 2006 http://www.isis.rl.ac.uk/disordered/dmgroup_home.htm. [22] A.K. Soper, Chem. Phys. 258 (2000) 121–137. [23] The definition of nOH and nHH is analogous to that of nOO, provided that rH is substituted to qO. [24] P.C. Hoemberg, P.M. Platzman, Phys. Rev. 152 (1966) 198. [25] G.B. West, Phys. Rev. 18 (1975) 263.E. Pace, G. Salme', G. West, Phys. Lett.B 273. [26] R.J. Newport, M.P. Paoli, V.T. Pugh, R.N. Sinclair, A.D. Taylor, W.G. Williams, ICANS VIII- Proceedings of the eighth Meeting of the International Collaboration on Advanced Neutron Sources, RAL-85–110 Rutherford Appleton Laboratory, 1985, p. 562. [27] C. Andreani, D. Colognesi, E. Degiorgi, A. Filabozzi, M. Nardone, E. Pace, A. Pietropaolo, R. Senesi, Nucl. Instr. Meth. A 497 (2003) 535. [28] R. Senesi, D. Colognesi, A. Pietropaolo, T. Abdul-Redah, Phys. Rev. B 72 (2005) 054119. [29] G.F. Reiter, J.C. Li, J. Mayers, T. Abdul-Redah, P. Platzman, Bras. J. Phys. 34 (2004) 142.