Percolation and three-dimensional structure of supercritical water M. Bernabei, 1 A. Botti, 1 F. Bruni, 1 M. A. Ricci, 1 and A. K. Soper 2,3 1 Dipartimento di Fisica “E. Amaldi”, Università degli Studi “Roma Tre”, Via della Vasca Navale 84, 00146 Roma, Italy 2 Isis Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX110QX, United Kingdom 3 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom Received 22 October 2007; revised manuscript received 18 January 2008; published 28 August 2008 It is well established that at ambient and supercooled conditions water can be described as a percolating network of H bonds. This work is aimed at identifying, by neutron diffraction experiments combined with computer simulations, a percolation line in supercritical water, where the extension of the H-bond network is in question. It is found that in real supercritical water liquidlike states are observed at or above the percolation threshold, while below this threshold gaslike water forms small, sheetlike configurations. Inspection of the three-dimensional arrangement of water molecules suggests that crossing of this percolation line is accompa- nied by a change of symmetry in the first neighboring shell of molecules from trigonal below the line to tetrahedral above. DOI: 10.1103/PhysRevE.78.021505 PACS numbers: 61.05.fm, 61.20.Ja, 61.25.-f I. INTRODUCTION In the late 1970s, Stanley 1 proposed the correlated-site polychromatic percolation model, as a useful tool for inter- preting the anomalous properties of ambient and supercooled water. Since then this model has been corroborated by sev- eral tests on experimental data and computer simulations 2–4. According to this model, liquid water can be consid- ered as a “transient gel” or percolating H-bond network, which continuously reconstructs itself on the picosecond time scale of the H bonds. Recently the concept of percola- tion has been applied to analyze the structure of supercritical water 5,6, in order to identify a percolation line, which separates two structurally different fluids, respectively below and above the so-called percolation threshold. This threshold is defined as the locus of thermodynamic states where the distribution of cluster size, Pn, obeys the power law Pn n - 1 with the universal exponent  = 2.19 in three-dimensional systems 7,8. In ambient and supercooled states water is a fully percolating system, since the average number of H bonds per molecule exceeds the critical value n c = 1.55 4 in these conditions. The existence of low-density and low- connectivity states instead below the percolation threshold has recently been predicted in the supercritical fluid by Pár- tay and co-workers 5,6. As a matter of fact, the percolation theory seems a natural framework for describing the density fluctuations and clustering of molecules in supercritical flu- ids including simple ones 9, and the persistence of a small H-bond peak in the radial distribution function of supercriti- cal water 10–14 unambiguously defines a bound pair, based on a geometrical criterion. Thus water, even in supercritical states, is a paradigmatic sample for percolation studies 15,16. We notice also that, although the concept of perco- lation implies in principle formation of an infinite cluster, which may only occur in an infinite system, Eq. 1 defines a percolation threshold also in a finite system, such as a simu- lation box. So far studies of percolation phenomena have been used to qualitatively justify the behavior of experimental data and quantitative tests have been limited to model systems, through the analysis of the outcome of molecular dynamics or Monte Carlo simulations. Since the development of the empirical potential structure refinement EPSR 17–20 code for the analysis of neutron and x-ray diffraction data from liquid and amorphous materials, experimentalists also have access to a collection of molecular configurations. These can be investigated and represented in the same man- ner as for the output of a classical computer simulation, with the advantage of being compatible with an experiment per- formed on a real sample. Consequently a test of the H-bond percolation model based on experimental data is now fea- sible. In this work we present the EPSR analysis of new and old 13 neutron diffraction data from supercritical water, in the framework of the percolation model, with the aim of inves- tigating the structural differences between gaslike and liquid- like states and the possible location of the percolation line of real water. The crossing of this line determines important changes in the connectivity of the fluid, which may influence the properties of supercritical water as a solvent and oxidiz- ing medium for organic and toxic waste 21. II. EXPERIMENTAL METHODS AND DATAANALYSIS The thermodynamic states investigated have been chosen to be as close as experimentally feasible to the thermody- namic states investigated in Ref. 5 and labeled after that work, as shown in Table I. All experimental points are at pressures and temperatures above water critical values, namely, P c = 220.64 bar and T C =647.096 K, while only the state point A expt corresponds to a density lower than the criti- cal one  c =332 kg / m 3 , as shown in Fig. 1. Neutron dif- fraction measurements were performed on the SANDALS 23 diffractometer, installed at the ISIS facility 24U.K.. The sample container was a Ti-Zr cell designed to withstand a pressure of 3 kbar: it consists of five cylindrical holes 1.7 mm internal diameter drilled in a slab 0.75 cm thickness, PHYSICAL REVIEW E 78, 021505 2008 1539-3755/2008/782/0215059 ©2008 The American Physical Society 021505-1