J. Phys. Chem. 1996, 100, 403-408
403
Temperature Dependence of Hydrogen Bonding in Supercritical Water Tahmid I. Mizan, Phillip E. Savage,* and Robert M. Ziff Department of Chemical Engineering, UniVersity of Michigan, Ann Arbor, Michigan 48109-2136 ReceiVed: June 6, 1995; In Final Form: August 22, 1995X
The effect of temperature on hydrogen bonding in supercritical water is investigated at densities of 257 and 659 kg/m3 and at temperatures in the range 773-1073 K using molecular dynamics simulations with a flexible simple point charge water potential. An energetic criterion is used to distinguish hydrogen-bonded pairs from non-hydrogen-bonded pairs. The number of hydrogen bonds per water molecule decreases as the temperature is increased. Hydrogen-bonded clusters in supercritical water consist of fewer than five members. Cluster size distributions are not strongly influenced by temperature at the higher density, although a slightly broader distribution is obtained at lower temperatures for the lower density. Hydrogen bond persistence time functions and autocorrelation functions exhibit faster decay at higher temperatures. The rupture of hydrogen bonds appears to be primarily temperature dependent, although the frequency of bond breakage is slightly higher at the higher density. The flexible water model exhibits slower hydrogen bond rupture rates than the corresponding rigid water model.
I. Introduction Hydrogen bonding influences many important characteristics of a solvent, including its structure, dielectric constant, and the molecular relaxation processes that occur within it. Understanding the nature of hydrogen bonding in supercritical water (SCW) from a molecular perspective would shed light on the nature of this solvent, which shows promise as a reaction medium.1,2 Currently, there is considerable controversy surrounding the question of hydrogen bonding in SCW. Although spectroscopic evidence suggests that some form of hydrogen bonding is present, some neutron diffraction experiments seem to contradict this assertion. At the same time, X-ray diffraction studies apparently do not rule out the possibility that hydrogen bonds exist in SCW.3,4 The spectroscopic studies referred to above include the infrared (IR) absorption studies by Franck and Roth5 of the O-D stretch in dilute mixtures of HDO in H2O at supercritical conditions. At 673 K and a very low density of 16.5 kg/m3 they observed distinct R-, Q-, and P- branches of the O-D vibrations corresponding to the vibration-rotation structures observed for the free HDO molecule. At densities above 100 kg/m3 they no longer observed the Q-branch but did find an absorption peak indicative of hydrogen bonding. Since they did not notice a separate absorption frequency at 2700 cm-1, the characteristic frequency for free O-D groups, above 100 kg/m3, it be may concluded that some form of hydrogen bonding exists above this density. A very recent report by Gorbaty and Kalinichev3 has confirmed and extended the earlier results of Franck and Roth.5 In addition, Raman studies of SCW (HDO in H2O) at 673 K by Kohl et al.6 show a shift in the O-D stretching band from 2727 cm-1 at 40 kg/m3 to 2668 cm-1 at 800 kg/m3, again indicative of the existence of hydrogen bonding at least in the dense supercritical states. On the other hand, Postorino et al.7 have interpreted their neutron diffraction with isotopic substitution (NDIS) results for the oxygenhydrogen pair correlation function, gOH, of SCW at 673 K and 660 kg/m3 to imply the absence of hydrogen bonding. This conclusion is based on the absence of a peak in gOH at approximately 2 Å, which is present for ambient water and is taken as an indicator of hydrogen bonding. NDIS experiments X
Abstract published in AdVance ACS Abstracts, December 1, 1995.
0022-3654/96/20100-0403$12.00/0
are, however, very difficult,8 and additional independent confirmation of these results is awaited. Furthermore, as Kalinichev9 and Chialvo and Cummings10 have pointed out, using gOH as the sole determinant of the presence of hydrogen bonding in SCW may lead to erroneous conclusions. While the presence of a gOH peak at around 2 Å may be sufficient evidence for the existence of hydrogen bonding in liquid water, the energetic and structural features of SCW are vastly different.11 Therefore, the relative orientations of molecular pairs and their energetic interactions must be examined in addition to gOH to provide conclusive answers to the question of hydrogen bonding in SCW. In the backdrop of such conflicting information, a molecular dynamics investigation of hydrogen bonding should add to a fundamental understanding of the processes involved and thus contribute to a clarification of the issues referred to above. Previously, we examined hydrogen bonding in SCW at a single temperature (773 K) and studied the effect of density not only on hydrogen bonding but also on the energetic aspects that influence it.11 Although there have been a number of other computer simulation studies of hydrogen bonding in SCW,9,12,13,14 only Mountain12 has systematically investigated its temperature dependence. Mountain used 108 rigid TIP4P15 water molecules in simulations of only 3.32 ps duration at state conditions extending over a wide range of temperatures and densities from the vapor-liquid coexistence curve to 1100 K and from 100 kg/m3 to 1000 kg/m3. He found that the average number of intermolecular hydrogen bonds per water molecule, nHB, decreased with increasing temperature. He also noticed a definite temperature scaling trend for the ratio nHB/n, where n is the number density, except at supercritical densities below 450 kg/m3. In determining whether a hydrogen bond exists between a pair of molecules, Mountain used a simple geometric criterion in which only the O‚‚‚H distance specification was considered. Such a simple criterion may not, however, be suitable for SCW. As Kalinichev16 has noted, the hydrogen bonding peak of gOH is very diffuse at supercritical conditions. Moreover, the first two coordination spheres exhibit a considerable degree of overlap. This suggests that a simple geometric criterion for hydrogen bonding is insufficient. Furthermore, Chialvo and Cummings10 observed that even for a hypothetical water © 1996 American Chemical Society
404 J. Phys. Chem., Vol. 100, No. 1, 1996 molecule with almost zero dipole moment (which they assert should not exhibit any hydrogen bonding), the geometrically defined hydrogen bonding component to gOH is still relatively strong. They used a more involved definition of hydrogen bonding that included a specification of not only interatomic separations but also the relative orientations of the molecules.8 They concluded that a definition of hydrogen bonding based only on geometric considerations was inadequate. An alternative is to use an energetic criterion to identify hydrogen-bonded pairs. This criterion has been judged to be more effective, at least for SCW.9 According to the energetic criterion,17 a hydrogen bond exists if the pair interaction energy, Epair, between two molecules is less than a negative threshold value, EHB,cut, usually taken to be the minimum between the two peaks of the bimodal pair energy distribution of liquid water. In this work, we use such an energetic criterion to determine hydrogen bonding. For the flexible potential model used in our study, EHB,cut is -13.2 kJ/mol,11 whereas for the rigid version of this model EHB,cut is -12.5 kJ/mol. Since SCW pair energy distribution curves are unimodal, however, there is no unequivocal definition of an energetic threshold value for this phase. Thus, the precise value of this energetic cutoff is arbitrary. The values we used were chosen because they are unequivocal in the liquid water limit. Changing the value of EHB,cut slightly will affect the quantitative results, but the qualitative features will remain the same. In addition to our use of the energetic hydrogen-bonding criterion, our work is different from that of Mountain in that we examine how Epair varies with molecular separation and orientation and also report the distribution of pair energies. This gives a more detailed picture of the energetic environment experienced by a water molecule under supercritical conditions. Moreover, we use a flexible water model that allows for intramolecular vibrations as opposed to the rigid TIP4P model used by Mountain. Flexibility might be important because dynamic properties such as orientational correlation times are better reproduced by flexible water models than by rigid water models, at least for ambient water.18 Also, flexibility allows the HOH angle, and thus the dipole moment, to respond to the molecular environment.11 Our results will demonstrate that the inclusion of flexibility in the water model may be important in supercritical water also, particularly for dynamic properties. We also report, for the first time, the effect of temperature on the size distribution for hydrogen-bonded clusters in SCW. Since molecules are directly hydrogen bonded to nearest neighbors only, cluster sizes are indicators of the spatial extent of hydrogen bonding in SCW. Phenomena that have length scales similar to that of a cluster are likely to be affected by hydrogen bonding. Without examining the temporal nature of hydrogen bonding in SCW, but based only on time-averaged pair correlation function results, Mountain asserted that the disappearance of the peak in gOH at around 2 Å indicates that the lifetime of the hydrogen bond in SCW is quite short. In this study, we address the issue of hydrogen bond lifetimes by directly examining the survival or persistence of hydrogen bonds. Moreover, we determine the effect of temperature on the persistence of hydrogen bonds and on the hydrogen bond autocorrelation function under supercritical conditions. Knowledge of the time scales over which hydrogen bonds exist is important in evaluating the influence of hydrogen bonding on solvation or reaction processes. Obviously, any process that has a time scale on the order of the lifetime of a hydrogen bond may potentially be influenced by it.
Mizan et al. II. Simulation Method A detailed description of the simulation methodology used in this study is given elsewhere.11,19 Our system consisted of a cubic cell containing 256 water molecules. Standard molecular dynamics techniques20 were used for the simulations. The reversible reference system propagator algorithm (r-RESPA)21 was used to integrate the equations of motion. The water potential we used was the flexible simple point charge water (SPC) potential of Teleman et al.,22 which will be identified as the TJE (Teleman, Jo¨nsson and Engstro¨m) model. All systems were equilibrated for at least 100 ps prior to production runs, which were also of 100 ps duration (in contrast to 3.32 ps for those of Mountain). Atomic coordinates were saved every 50 fs and were analyzed after the run was completed. Dimer energies for each pair of molecules were calculated for each configuration, and these energies were then used to establish a connectivity matrix based on whether or not the dimer energy was below the threshold energy, EHB,cut. The elements of this connectivity matrix correspond to all possible combinations of molecular pairs and have a logical value of true if a hydrogen bond exists between the molecules of a pair and false otherwise. This connectivity matrix was used for determining cluster size distributions, hydrogen bond persistence times, and autocorrelation functions. We also conducted simulations with a rigid water model to investigate the effect of incorporating flexibility on dynamic aspects of hydrogen bonding in SCW. We used the SPC water model of Berendsen et al.23 for rigid water simulations. The method used for the rigid SPC simulations is identical to that used for the flexible water simulations except that the equations of motion were integrated using the RATTLE method.24 A time step of 2 fs was used. III. Results The dimer energy distributions, cluster size distributions, hydrogen bond persistence times, and autocorrelation functions of simulated water were calculated at densities of 257 and 659 kg/m3 and at temperatures between 773 and 1073 K. The effect of density on hydrogen bonding at 773 K has been reported elsewhere;11 in this paper we focus on the effect of temperature. All results reported herein are for the flexible water model unless otherwise indicated. Figure 1 shows the distribution of pair energies, Epair, for SCW at the two densities. It is clear that temperature has little effect on the repulsive or positive branch of the distributions for 257 kg/m3. On the other hand, the area under the attractive or hydrogen-bonding branch appears to increase slightly with decreasing temperature for this density. This trend is reflected in an increase in the number of hydrogen bonds per water molecule with decreasing temperature. The differences between the isotherms at 659 kg/m3 are less clear. At both densities the peaks of the pair energy distributions centered at 0 kJ/mol extend up to about 70 mol % (not shown in the figure), although this number has no particular significance but simply reflects the size of the simulation system. The shape of the dimer energy distributions at supercritical conditions is in general agreement with the distributions obtained by Kalinichev in Monte Carlo simulations of supercritical TIP4P water.16 Our use of an energetic criterion to determine hydrogen bonding makes it incumbent on us to investigate the energetic environment that a water molecule experiences. We describe this environment by plotting the trajectory-averaged dimer energies, Epair, as a function of molecular separation, r, and dipole-dipole angle, θµµ, in Figures 2 and 3, respectively. Figure 2 indicates that the well depth of the Epair(r) curves for SCW
Hydrogen Bonding in Supercritical Water
J. Phys. Chem., Vol. 100, No. 1, 1996 405
Figure 3. Pair energies of supercritical water as a function of dipoledipole angle for nearest neighbor pairs at different temperatures: (a) at 257 kg/m3; (b) at 659 kg/m3. Figure 1. Pair energy distributions of supercritical water at various temperatures: (a) at 257 kg/m3; (b) at 659 kg/m3.
TABLE 1: Hydrogen Bond Analyses at 257 kg/m3 property
773 K
873 K
973 K
1073 K
nHB 〈EHB,Coulomb〉, kJ/mol 〈EHB,LJ〉, kJ/mol 〈EHB〉, kJ/mol
0.80 -23.48 4.22 -19.27
0.67 -23.08 4.07 -19.26
0.57 -22.76 3.92 -18.85
0.50 -22.59 3.87 -18.72
TABLE 2: Hydrogen Bond Analyses at 659 kg/m3
Figure 2. Pair energies of supercritical water as a function of molecular separation at different temperatures: (a) at 257 kg/m3; (b) at 659 kg/m3.
decreases with increasing temperature. The dimer energy as a function of molecular separation, Epair(r), has contributions of Lennard-Jones type and Coulombic type. While the LennardJones contribution, which is spherically symmetric, is independent of both temperature and density, the Coulombic contribution is not because it depends upon the orientations of the molecular pairs and because Epair(r) is averaged over orientations. At higher temperatures, each molecular pair possesses the energy to visit a larger variety of orientational configurations so that the Coulombic contribution to Epair(r) is less negative, resulting in the decrease in well depth observed in Figure 2. The dimer energies, Epair, for the nearest neighbor interactions are plotted as a function of dipole-dipole angle, θµµ, in Figure 3. We consider only the nearest neighbor pairs because, as Figure 1 shows, a large majority of the pairs are at such great separations that they have nearly zero energy of interaction and hence have no strong energetically preferred orientation with respect to each other. For this reason we choose to average over the first solvation shell only. The maximum extent of this
property
773 K
873 K
973 K
1073 K
nHB 〈EHB,Coulomb〉, kJ/mol 〈EHB,LJ〉, kJ/mol 〈EHB〉, kJ/mol
1.44 -24.12 4.65 -19.47
1.32 -23.77 4.52 -19.26
1.22 -23.51 4.41 -19.10
1.14 -23.33 4.34 -18.99
shell determined from the position of the minimum following the first peak of the gOO curve11 is 4.4 Å. Therefore, nearest neighbors are molecules separated by 4.4 Å or less. As Figure 3 shows, the Epair(θµµ) curves have a shallow minimum at around 0° for all conditions, indicating that SCW molecular pairs in the first solvation shell somewhat prefer a parallel dipolar alignment. Another noticeable trend is that the higher the temperature the less negative the pair energy becomes and the flatter the profile becomes. This trend is essentially another representation of the decrease in well depth with increasing temperature apparent in Figure 2. The number of hydrogen bonds per water molecule, nHB, was calculated by counting the number of pairs of molecules that have dimer energies below the cutoff value, EHB,cut, averaging over configurations, and dividing by the number of water molecules. Tables 1 and 2 give nHB for each state point. At the 257 kg/m3 density supercritical state, nHB ranges from 0.80 to 0.50, while at the higher density it ranges from 1.44 to 1.14. Thus, the average number of hydrogen bonds depends both on the density and on the temperature. The decrease in the degree of hydrogen bonding with increasing temperature is a result of the increasing orientational disorder at higher temperatures. This trend is clearly reflected in Figure 4 which shows a semilog plot of nHB against the reciprocal temperature. The simple linear dependence of the logarithm of nHB on the reciprocal temperature is apparent. The slope of the higher density curve is less steep, indicating that density moderates the effect of temperature on the degree of hydrogen bonding. This moderating effect of density is essentially the scaling and nonscaling behavior observed by Mountain at densities above and below 450
406 J. Phys. Chem., Vol. 100, No. 1, 1996
Mizan et al.
Figure 4. Variation of nHB with reciprocal temperature.
kg/m3, respectively. The same trend becomes clearer in the inset to Figure 4, which shows the same data points plotted as nHB/n vs temperature. The low-density state curve has a steeper slope, in agreement with the results of Mountain. Table 1 shows that the average hydrogen-bonding energy at 257 kg/m3 changes from -19.27 kJ/mol at 773 K to -18.72 kJ/mol at 1073 K. This energy has a Coulombic part, 〈EHB,Coulomb〉, and a Lennard-Jones part, 〈EHB,LJ〉. The Coulombic part becomes less negative with increasing temperature. The higher temperatures facilitate greater orientational disorder and hence result in a less negative 〈EHB,Coulomb〉 because this energy depends upon the relative orientations of the molecular pairs. The Lennard-Jones component of the hydrogen bonding energies, 〈EHB,LJ〉, decreases with increasing temperature, indicating that those pairs that are hydrogen bonded (that is, pairs that have a pair energy below the EHB,cut) are at greater average separations at higher temperatures than those at lower temperatures. Since a molecule can be hydrogen bonded to several other molecules, which in turn can be hydrogen bonded to other molecules, a cluster of hydrogen-bonded molecules may exist in a fluid. We devised the following method of counting hydrogen-bonded clusters using the connectivity matrix described previously. Cluster sizes were established by generating a list of the identifying indices of molecules constituting a given cluster. We checked all molecules to see if the current molecule belonged to a previously counted cluster. If it did not, we put it at the top of the list. We then checked all other molecules and, provided that these molecules had not been previously counted in a cluster, used the connectivity matrix to determine whether a molecule was hydrogen bonded to the current molecule. If it was connected, we appended it to the list. We then made the next molecule in the list the current molecule and checked its neighbors for hydrogen bonding. In this way we checked each molecule, its neighbors, the neighbors of its neighbors, and so on until the indices of all the molecules in the cluster had been put on the list. The number of molecules on the list was equal to the size of the cluster. A new list was then created for the next cluster, and the next uncounted molecule was considered. In this way the size of each cluster in a particular configuration was determined. Figure 5 depicts the cumulative size distributions of hydrogen-bonded clusters at 257 and 659 kg/m3. The ordinate SN represents the fraction of clusters that have N or fewer molecules in them. For the lower density state, very few clusters have a size greater than five at any of the temperatures. At the higher density state larger clusters are observed, although about 90% of the clusters have sizes of four or less. It is clear from Figure 5 that temperature
Figure 5. Cumulative size distributions for hydrogen-bonded clusters in supercritical water at various temperatures: (a) at 257 kg/m3; (b) at 659 kg/m3.
Figure 6. Hydrogen bond persistence functions for supercritical water at various temperatures: (a) at 257 kg/m3; (b) at 659 kg/m3.
has little influence on the cluster size distribution for the higher density states. At 257 kg/m3, however, a slightly broader distribution is obtained at lower temperatures. These results clearly indicate that hydrogen bond cluster size distributions are not strongly affected by temperature, while our earlier results11 as well as a comparison of parts a and b of Figure 5 show that these size distributions do depend strongly on density. For all conditions reported here, we are clearly below the percolation threshold and a majority of the clusters have five or fewer members. A complete understanding of hydrogen bonding in SCW requires an investigation of the temporal nature of this phenomenon. The dynamics of hydrogen bonding may be characterized by how long a particular bond survives before a rupture occurs. This interval of time may be called the persistence time or lifetime of a hydrogen bond. If a hydrogen bond is present at time 0 and exists continuously (within the resolution of the data-sampling period) until time t, it is said to persist at time t. Figure 6 shows hydrogen bond persistence curves at 257 and 659 kg/m3 at various temperatures. The ordinate gives the ratio of the number of original hydrogen bonds still present at any time t, NHB(t), to the number of hydrogen bonds initially present at time 0, NHB(0). It appears from Figure 6 that hydrogen bonds
Hydrogen Bonding in Supercritical Water
J. Phys. Chem., Vol. 100, No. 1, 1996 407
Figure 8. Variation of continuous hydrogen bond autocorrelation function decay times with temperature for flexible TJE and rigid SPC water models under supercritical conditions.
Figure 7. Continuous hydrogen bond autocorrelation functions for supercritical water at different temperatures: (a) at 257 kg/m3; (b) at 659 kg/m3.
decay faster at higher temperatures. This is understandable since at a higher temperature, the higher kinetic energy allows for more frequent disruption of hydrogen bonds. Figure 6 may be compared with Figure 9 of Mizan et al.,11 which shows hydrogen bond persistence curves for different densities at a supercritical temperature of 773 K. Based on these figures, the effect of temperature on hydrogen bond persistence appears to be stronger than the effect of density. The curves in Figure 6 are, however, not very smooth, and this leads to some ambiguity in our conclusions. We, therefore, employ another measure of hydrogen bond persistence used earlier by Rapaport25 and defined by the autocorrelation function
CHB(t) )
∑〈i,j〉 si,j(t0)si,j(t0 + t) ∑〈i,j〉 si,j(t0)
(1)
where the set of values {sij(t)} form the connectivity matrix at time t with the true and false values being replaced in this case by unity and zero, respectively. Two types of hydrogen bond autocorrelation functions may be defined: continuous and intermittent, identified customarily by c and i subscripts, respectively. In the continuous case, if a bond exists between molecules i and j at time t0 and exists continuously until time t, at which point it breaks, for all subsequent times si,j(t) is considered to be zero even though the bond may re-form. In the intermittent case, however, si,j(t) reverts to unity if the bond is re-formed. The continuous hydrogen bond autocorrelation function, CHB,c(t), is essentially a measure of the distribution of hydrogen bond lifetimes and is the only one reported in this study. It may be considered to be a trajectory-averaged version of NHB(t)/NHB(0). Figure 7 shows CHB,c(t) at 257 and 659 kg/m3. Both the upper and lower panels of curves show that CHB,c(t) decays in a manner very similar to the hydrogen bond persistence function. However, in this case the averaging process results in smoother curves from which a number of different trends may be discerned. Like the hydrogen bond persistence curves, these curves also show that hydrogen bonds decay faster at higher temperature. The insets in Figure 7 display the same data with logarithmic ordinates. Clearly, the decay is nearly exponential:
CHB,c(t) ) exp(-t/τHB)
(2)
Figure 9. Comparison of continuous hydrogen bond autocorrelation functions of flexible TJE and rigid SPC water models at 773 and 1073 K: (a) at 257 kg/m3; (b) at 659 kg/m3.
The continuous hydrogen bond autocorrelation function decay constant, τHB, was calculated by a least squares fit of the corresponding CHB,c(t) curve. These decay constants are plotted against temperature (as filled symbols) in Figure 8. The estimated uncertainties in τHB are less than (6% at a 95% confidence level. Figure 8 demonstrates that the decay times decrease monotonically with increasing temperature. At the same time the figure shows that the density has a small but discernible effect on decay times: at higher densities decay times are smaller. There is no overlap between the lower and higher density points at a given temperature even if the uncertainties at a 95% confidence level are included, so the effect of density on decay times is statistically significant. This density effect is reasonable since higher densities at a given temperature imply a greater number of collisional encounters and hence more frequent breaking of hydrogen bonds. The density dependence of hydrogen bond decay constants is a new finding. Previously, we had calculated decay times for the hydrogen bond persistence function but did not find the decay times to be substantially different at different densities, primarily because the resolutions of the persistence curves were poor.11 We also determined the continuous hydrogen bond autocorrelation functions for rigid SPC23 water at all eight state points. For the sake of clarity the CHB,c(t) curves at only four state points are shown in Figure 9 along with the corresponding flexible TJE water curves. The slopes of the CHB,c(t) curves are steeper
408 J. Phys. Chem., Vol. 100, No. 1, 1996 for the rigid water cases than for the flexible water ones. The hydrogen bond decay times for the rigid SPC simulations extracted from these slopes are also plotted in Figure 8 as crossed-open symbols. These decay times, which have uncertainties of less than (5%, are consistently lower than the corresponding values for flexible water model simulations. This means that for the rigid water model, hydrogen bonds tend to rupture more rapidly than for the flexible water model under the same conditions. Since the flexible model allows for distortions in the molecular geometry, it permits a greater departure of hydrogen-bonded configurations from the equilibrium (or minimum energy) geometry than a rigid model would permit. For rigid model simulations, a slight perturbation increases the pair energy of a hydrogen-bonded pair above the cutoff value because those regions of phase space in which contorted molecular geometries have pair energies below the cutoff value are not accessible to it. Flanagin et al.26 have examined lifetimes of hydrogen bonds between rigid SPC23 water molecules and a chloride ion as it participates in the SN2 reaction of methyl chloride with a chloride ion in SCW. They used a definition of hydrogen bonding in which a bond is said to exist if a hydrogen atom is 2.95 Å distant from the chloride ion. Since their focus was on hydrogen bonds between the chloride ion and water molecules and not among water molecules themselves as in our case, no direct comparison between the two studies is possible. However, it is noteworthy that they observed the stability of hydrogen bonds to decrease with decreasing density and with increasing temperature. Our results confirm the latter assertion, but contradict the former. Figure 8 clearly shows that the decay times are smaller, and hence, hydrogen bonds are less stable at the higher density for both the flexible and rigid SPC water models. Whether this reversal in the density dependence of hydrogen bond lifetimes observed by Flanagin et al. is a unique feature of hydrogen bonding with a strong structure-breaking moiety such as a chloride ion is uncertain. Further investigation of this conundrum is clearly warranted. IV. Conclusions and Summary In this study we investigated the temperature dependence of some measures of hydrogen bonding in SCW through molecular dynamics simulations using a flexible SPC water potential. Our work is the first such study of hydrogen bonding in SCW using a flexible water model. We employed an energetic criterion for determining the existence of a hydrogen bond between a pair of molecules as opposed to geometric criteria used by some previous studies. Pair energies distributions were reported at densities of 257 and 659 kg/m3 and temperatures from 773 to 1073 K. We reported the dependence of the trajectory-averaged dimer energies, Epair, on molecular separation, r, and dipole-dipole angle, θµµ. At nearest neighbor distances Epair(θµµ) became less negative with increasing temperature. The parallel alignment of the dipoles of molecular pairs was found to be more energetically favorable in the first solvation shell at the supercritical conditions studied. The number of hydrogen bonds per water molecule decreased from 0.80 to 0.50 as the temperature was increased from 773 to 1073 K at a density of 257 kg/m3 while this number changed from 1.44 to 1.14 at a density of 659 kg/m3 over the same temperature range. Thus, the degree of hydrogen bonding decreases with increasing temperature although the effect of temperature appears to be modified by the density. Additionally, ours is the only study to date to report the effect of temperature on hydrogen bond cluster size distributions in SCW. We found that cluster size distributions did not appear
Mizan et al. to be strongly influenced by temperature. At the supercritical conditions we investigated, water molecules exist largely as single entities or small clusters of five or fewer members. Another aspect of our investigation is a study of hydrogen bond dynamics. We examined hydrogen bond persistence and hydrogen bond autocorrelation functions at various temperatures at the two densities. Our results show that hydrogen bond rupture is essentially a temperature dependent process as indicated by the more rapid decay of hydrogen bond persistence curves and hydrogen bond autocorrelation functions at higher temperatures. Density does, however, appear to play a small but discernible role. We found that the flexible water model shows slower rupture rates of hydrogen bonds than does the rigid water model. This is because the flexible model increases the region of phase space accessible to the system by allowing for contorted molecular geometries, some of which may have pair energies below the hydrogen-bonding threshold value. This is the first direct comparison of a flexible water model and its corresponding rigid version at supercritical conditions. In summary, from an energetic perspective at least, SCW is weakly hydrogen bonded and the degree of hydrogen bonding decreases with increasing temperature. This study demonstrates the need to look not only at average hydrogen-bonding tendencies in SCW but also at the temporal and spatial aspects of hydrogen bonding. References and Notes (1) Savage, P.; Gopalan, S.; Mizan, T.; Martino, C.; Brock, E. AIChE J. 1995, 41, 1723-1778. (2) Tester, J.; Holgate, H.; Armellini, F.; Webley, P.; Killilea, W.; Hong, G.; Barner, H. In Emerging Technologies in Hazardous Waste Management III; American Chemical Society: Washington, DC, 1993; pp 35-76. (3) Gorbaty, Y.; Kalinichev, A. J. Phys. Chem. 1995, 99, 5336-5340. (4) Yamanaka, K.; Yamaguchi, T.; Wakita, H. J. Chem. Phys. 1994, 101, 9830-9836. (5) Franck, E.; Roth, K. Faraday Discuss. Chem. Soc. 1967, 43, 108114. (6) Kohl, W.; Linder, H.; Franck, E. Ber. Bunsenges. Phys. Chem. 1991, 95, 1586-1593. (7) Postorino, P.; Tromp, R.; Ricci, M.-A.; Soper, A.; Neilson, G. Nature 1993, 366, 668-670. (8) Beveridge, D.; Mezei, M.; Mehrotra, P.; Marchese, F.; RaviShanker, G.; Vasu, T.; Swaminathan, S. In Molecular-Based Study of Fluids; American Chemical Society: Washington DC, 1983; pp 281-351. (9) Kalinichev, A.; Bass, J. Chem. Phys. Lett. 1994, 231, 301-307. (10) Chialvo, A.; Cummings, P. J. Chem. Phys. 1994, 101, 4466-4469. (11) Mizan, T.; Savage, P.; Ziff, R. InnoVations in Supercritical Fluids: Science and Technology; Hutchenson, K. W., Foster, N. R., Eds.; ACS Symposium Series 608; American Chemical Society: Washington, DC, 1995; pp 47-64. (12) Mountain, R. J. Chem. Phys. 1989, 90, 1866-1870. (13) Cochran, H.; Cummings, P.; Karaborni, S. Fluid Phase Equilib. 1992, 71, 1-16. (14) Cummings, P.; Chialvo, A.; Cochran, H. Chem. Eng. Sci. 1994, 49, 2735-2748. (15) Jorgensen, W.; Chandrasekhar, J.; Madura, J.; Impey, R.; Klein, M. J. Chem. Phys. 1983, 79, 926-935. (16) Kalinichev, A. Z. Naturforsch. 1991, 46A, 433-444. (17) Rahman, A.; Stillinger, F. J. Chem. Phys. 1971, 55, 3336-3359. (18) Wallqvist, A.; Teleman, O. Mol. Phys. 1991, 74, 515-533. (19) Mizan, T.; Savage, P.; Ziff, R. J. Phys. Chem. 1994, 98, 1306713076. (20) Allen, M.; Tildesley, D. Computer Simulation of Liquids; Oxford University Press: Oxford, UK, 1987. (21) Tuckerman, M.; Berne, B.; Martyna, G. J. Chem. Phys. 1992, 97, 1990-2001. (22) Teleman, O.; Jo¨nsson, B.; Engstro¨m, S. Mol. Phys. 1987, 60, 193203. (23) Berendsen, H.; Potsma, J.; van Gunsteren, W.; Hermans, J. In Intermolecular Forces; D. Reidel Publishing Co.: Dordrecht, Netherlands, 1981; pp 331-342. (24) Andersen, H. J. Comput. Phys. 1983, 52, 24-34. (25) Rapaport, D. Mol. Phys. 1983, 50, 1151-1162. (26) Flanagin, L.; Balbuena, P.; Johnston, K.; Rossky, P. J. Phys. Chem. 1995, 99, 5196-5205.
JP951561T
