Simulation of supercritical water and of supercritical...

Simulation of supercritical water and of supercritical aqueous solutions P. T. Cummings Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia, 22901

H. D. Cochran, J. M. Simonson, and R. E. Mesmer Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831

S. Karaborni Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22901

(Received 1 November 1990; accepted 4 January 199 1)

Molecular dynamics (MD) calculations have been performed to determine equilibrium structure and properties of systems modeling supercritical (SC) water and SC aqueous solutions at two states near the critical point using the simple point charge (SPC) potential model of Berendsen et al. for water. Both thermodynamic and dielectric properties from the simulations for pure water are accurate in comparison with experimental results even though the SPC model parameters were fitted to properties of ambient water. Details of the near- critical clustering in SC water have been predicted which have not been measured to date. MD studies have also been undertaken of systems that model sodium and chloride ions and neutral argon in SC water at the same states. The first solvation shell in SC water is observed to be similar to that in ambient water, and long-range solvation structures in SC water are similar to those observed for simple SC solvents. An excess of water molecules is observed clustering around ionic solutes which behave attractively and a deficit is observed around neutral atomic solutes which behave repulsively. These results should be helpful in developing a qualitative understanding of important processes that occur in SC water.

I. INTRODUCTION

Dense fluids at temperatures slightly above the vapor- liquid critical temperature [ supercritical (SC) fluids] have attracted industrial interest ‘-’ as solvents for separation processes and as reaction media, e.g., and dilute SC solutions have received considerable recent research attention.“’ SC water has been proposed as a medium for extraction of coal and oil shale, for regeneration ofsorbents used in wastewater treatment, for hazardous waste decontamination of soils or equipment, and for oxidation of hazardous chemicals. In addition, SC water is an important solvent in power generation and in many geochemical processes.

al orders of magnitude is not uncommon. Furthermore, solubility may be caused to vary in a controlled fashion over two to three orders of magnitude by small changes in pressure or temperature near the critical point (CP). The transport properties of solutions in SC solvents typically fall between those of gaseous mixtures and liquid solutions; thus, compared with liquid solvents, SC solvents may exhibit improved mass and heat transfer performance.

The aim of this work was to use molecular dynamics (MD) calculations to study the equilibrium structure and properties of systems modeling SC water and SC aqueous solutions. We wish to answer the following questions: ( 1) To what extent is SC water similar to or different from other SC solvents? (2) To what extent is SC water similar to or different from ambient water? and (3) What is the structure of SC water in the vicinity of a solute particle? In the remainder of this section, we shall briefly discuss prior work (including prior molecular simulations) related to SC solutions and to SC water. Section II details the simulation methodology. Section III includes results for pure SC water, for ions in SC water, and for neutral atoms in SC water. Finally, we present some concluding remarks in Sec. IV.

A. Supercritical solutions

With the development of new experimental techniques, there is an extensive and expanding literature on measured bulk thermodynamic properties of aqueous solutions ex- tending through the critical region. This experimental infor- mation, reviewed recently by Wood et al.,” Mesmer et al.,” and Simonson et al.” has been shown to be consistent with the concept of clustering of solvent molecules around solute molecules or ions. A simple two-state model, in which the solvent is assumed to have a higher density in a cluster around an attractive solute moiety as compared with the bulk value, ’ ’ may be used to represent qualitatively the observed bulk thermodynamic properties. This simple model has been shown by HahnI to give a nearly quantitative correlation of ?z, the partial molar volume of the aqueous ion B at infinite dilution, with radial distribution functions measured by neutron diffraction near ambient conditions, and to be applicable to a wide variety of aqueous ions of different charges. Near the solvent CP, this approximate treatment leads to divergence of the number of water molecules in the cluster with the divergence of the infinite-dilution partial molar volume ?;“, .

For over a century, it has been knownxv9 that low volatil- The general nature of the clustering phenomenon, in- ity solids exhibit markedly enhanced solubility in dense SC cluding clustering in nonaqueous solvents, is demonstrated gases compared with the solubility that would be predicted in recent studies.‘4-‘5 Biggerstaff and Wood I6 have calculat- for an ideal gas mixture; enhancement of solubility by sever- ed the number of excluded solvent molecules in a shell

5606 J. Chem. Phys. 94 (8), 15 April 1991 0021-9606/91/085606-i 6$03.00 0 1991 American Institute of Physics

around a repulsive solute (argon, xenon, ethylene) in near- critical aqueous solutions. Eckert and co-workers” inferred the collapse of - 100 solvent molecules about a solute molecule from the large, negative partial molar volume of solutes in SC solutions. Likewise, Kim and Johnston” determined a local solvent density surrounding a solute molecule more than 50% greater than the bulk solvent density from the frequency shift in the ultraviolet (UV) absorption maximum for phenol blue dissolved in SC ethylene. Debene- detti” and, independently, Kim and Johnston2’ calculated that a solute molecule is solvated to form clusters of - 100 solvent molecules near the CP using the fluctuation theory of Kirkwood and Buff to interpret experimental partial molar volume data” (for naphthalene dissolved in SC CO*, for example). Additional experimental evidence for the clustering phenomenon is provided by several recent studies.2’.22 The clustering of solvent molecules around a solute molecule in SC solution and the resulting solution properties are related by Kirkwood-Buff theory; e.g., in a dilute, binary mixture of solute B in SC solvent A, the number of excess A molecules surrounding a B (beyond the bulk average) is given by the following integral:

s cc rm =P?% =d dr4rr2[ k4,(d), - 117 (1)

0

where p is the number density, G is the Kirkwood fluctuation integral, g is the pair correlation function, r is the intermolecular separation, ( * ), represents averaging over all orientations, and superscript ’ represents the value at infinite dilution of B.

The infinite dilution partial molar volume of B is given by the following Kirkwood-Buff expression:

p;?ij = 1 +p”A (GO,, - G:B) and the isothermal compressibility by

(2)

p”, kTx$ = 1 + p”, GOAR. (3) The relation between equilibrium properties and structure of solutions is evident from these expressions. The dramatic changes in properties of dilute SC solutions result from the divergence of the fluctuation integrals as the pair correlation functions become long ranged. The G’s become large and positive as do the cluster size and the compressibility on approaching the CP of the pure solvent; the partial molar volume becomes large and negative. Such solutions have been called dilute, attractive SC solutions.

Wheeler” and Debenedetti and Mohamed’” showed that when the solute-solvent attraction is not as strong as the solvent-solvent attraction, the partial molar volume becomes large and positive and the solute-solvent cluster size becomes large and negative. Such cases have been called dilute, repulsive SC solutions.

Previous molecular simulations of SC solutions have been consistent with this description. Monte Carlo calculations with quadrupolar Lennard-Jones (LJ + Q) mixtures by Shing and ChungZs simulated naphthalene in SC CO,; unfortunately, this work suffered from lack of knowledge of the location of the CP for the LJ + Q fluid and from the effects of large fluctuations. Petsche and Debenedettiz4 per-

formed molecular dynamics simulations of a single LJ solute particle in a bath of LJ solvent particles modeling both attractive and repulsive SC solutions. In order to accommodate the long range of the pair correlation functions, they studied relatively large systems of 864 particles. Nouacer and Shing*’ studied LJ + Q particles and LJ + dipole (LJ + D) particles in the grand ensemble to accommodate the large fluctuations.

6. Supercritical water

The critical temperature and density of water are, respectively,26 T, = 373.98 “C = 647.10 K andp, = 322 kg/ m3, so that SC aqueous states correspond to T> 374 “C, with dense SC states corresponding to densities greater than pc. The critical pressure of water is PC = 220.55 bar.

In contrast to the many studies of aqueous systems at or near ambient conditions (density near 1000 kg/m3, temperature near 25 “C), relatively few structural or simulation studies have been made of pure SC water and, to our knowledge, none have been made of SC aqueous solutions. This is in spite of the many technologically important applications of SC aqueous systems and the increasing number and quali- ty of bulk thermodynamic measurements summarized above. Moreover, these systems are easier to study than ambient aqueous systems because many of the difficulties en- countered in molecular simulation of aqueous systems at ambient conditions (mostly caused by the very long orientational relaxation time) are absent at SC state conditions. Thus, despite their importance and relative ease of study, there have been few molecular simulations of SC aqueous systems, and even fewer scattering experiments.

Gorbaty and Demianets” performed x-ray scattering experiments on SC and liquid water at high pressure (1000 bar) in the temperature range 25 to 500 “C. In addition to computing the water-water distribution function from the scattering data, Gorbaty and Demianets computed the co- ordination number (number of water molecules in the nearest-neighbor shell) as a function of temperature. Lisichkin et aZ.28 performed neutron scattering experiments on subcriti- cal ( T = 360 “C) and SC ( T = 400 “C) water in the density range 50 to 320 kg/m3, thus including some low-density SC states. These results have been reported in terms of total scattering function only.

Kalinichev” undertook a study of dense SC water (T = 500 “C, or reduced temperature T, = T/T, = 1.19) at pressures of 1000, 10 000, and 30 000 bar using a constant number of molecules N, pressure, and temperature (NPT) ensemble Monte Carlo simulation with 64 water molecules interacting via transferable intermolecular potential set (TIPS2)30 intermolecular potential. The 1000 bar simulation corresponds to the highest temperature for which Gor- baty and Demianets performed x-ray scattering, so Kalini- chev was able to compare the oxygen-oxygen distribution functions with experiment. Very good agreement was found. The simulation results for thermodynamic properties (en- thalpy, molar volume, heat capacity, compressibility, and thermal expansivity) all agreed acceptably well with experimental data. Kataoka3’ calculated the thermodynamic

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5608 Cummings eta/: Simulation of supercritical water

properties of the Carravetta-Clementi potential, a modifica- tion of the Matsuoka-Clementi-Yoshimine3* (MCY) potential, using molecular dynamics in constant molecule number, volume, and temperature (NVT) ensemble at 347 state points including many SC ones. The simulation results were used to develop an equation of state for the MCY potential. However, structural properties are not reported.

II. DETAILS OF THE SIMULATIONS A. Potential models

We have used the simple point charge (SPC) model of Berendsen et aZ.33 for the water molecule. The model pic- tures a water molecule as a Lennard-Jones (LJ) sphere corresponding to the oxygen atom with a partial negative charge ( - 0.82e) at the sphere center and two partial positive charges ( + 0.41e) each 1 A from the center and forming an angle of 109.47“. The SPC water-water interaction is given by

%vw (r,*,fl,,R,) = =$, $* 9 If

+4%#3’*-(33], (4)

where the subscript ww represents water-water interactions, the subscript oo represents oxygen-oxygen interactions, r,* is the vector between the centers of molecules 1 and 2, R, and fi, are the angles describing the orientation of molecules 1 and 2, qp is the charge on site a on molecule i, r$ is the distance between site a on molecule 1 and site p on molecule 2, E is the LJ energy parameter, and (T is the LJ size parameter.

Our choice of the SPC potential is based on previous studies34 which have shown tht the SPC model yields properties (including the dielectric constant) for ambient water that are in good agreement with experimental values. An additional motivation for using the SPC potential is that the critical point of SPC water has been determined using Gibbs ensemble simulation by de Pablo et aZ.34

For sodium-water and chloride-water interactions, we have used the potential models given by Pettitt and Rossky35 which picture the ion as an LJ sphere with a central unit charge. The ion-water potential is given by three interactions-one ion-oxygen and two ion-hydrogen interactions-according to

3

II IW = 4 &cJ=l

f$+%w[($)‘2-(~y],, (5)

where the subscript iw represents the ion-water interaction, the superscripts * and w represent ion and water, respectively, and the index p represents the oxygen and two hydrogen sites in the water molecule. Strictly speaking, Pettitt and Rossky derived these ion-water potentials by fitting ab initio ion-water energy surfaces to a water model whose charge distribution differs very slightly from the SPC model. Refit- ting of this potential using the SPC charge distribution would therefore lead to slightly different values of cIW and alp . For the present purposes of investigating the qualitative structure of the SC solvent in the vicinity of an ionic solute, we regard the Pettitt-Rossky potentials as sufficiently accurate. For the argon-water interaction, we have used the LJ model derived by Straatsma et aZ.36 for noble gas-SPC water interactions. The solute-water potential is given by

usw = 4&s, [(2)‘2- ()I * (6)

where the subscript sw represents the solute-water interaction.

The parameters for the potential models are summarized in Table I.

B. Calculation method

The technique used for the simulation involves solving Newton’s laws of motion using Gear’s fourth-order predic- tor-corrector method which has been detailed previously- 37*38 The simulations have been performed in the canoni- cal-isokinetic (NVT) ensemble in which the total kinetic energy of the simulated system is kept constant. During code

TABLE I. Parameters for interaction potentials.

Species 44) E(erg/molecule) Charge (e) Mass (amu)

Water”

Sodiumh

Chloridt?

Argon’

Oxygen Hydrogen

Ion-oxygen Ion-hydrogen

Ion-oxygen Ion-hydrogen

Solute-water

. 3.166

.

. . . 2.720 0.9303 1.310 0.9303

. . . t.. 3.550 4.1679 2.140 4.1679

. . . . . 3.228 1.2144

. . . 1.0800

. . .

. . .

. . . - 0.82 + cl.21 f 1.00

. . .

18.0 . . . . .

23.0 . . .

- 1.ocl 35.5 . . . . . . . . . . .

0.00 39.9 . . . . . .

’ Berendsen et al. ( Ref. 33). bPettitt and Rossky (Ref. 35). ’ Straatsma et al. (Ref. 36).

J. Chem. Phys., Vol. 94, No. 8, 15 April 1991

Cummings eta/: Simulation of supercritical water

TABLE II. Parameters for the simulations.

5609

case State N,.” Solute L /cQoob teqc(Ps) f,“,d (PS) At’(p)

216 256 215 255 215 255 215 255 863

. . .

. . Na+ Na+ Cl- cl- A r Ar Ar

1.95 15 9.63 15 1.95 15' 9.63 15' 7.95 15' 9.63 15' 7.95 15' 9.63 15'

14.45 15

30 30 30 30 30 30 45 45 30

lo-’ lo-’ 10-a 1o-3 1o-3 lo-’ lo-’ lo-’ lo-’

‘Number of SPC water molecules. b Dimensionless length of simulation cell. ’ Equilibration time. d Simulation time. ‘Time step. ‘The solute replaced one SPC water molecule in SPC water that had been run previously for 45 ps.

development, each simulation code was tested for energy conservation in the absence of the isokinetic constraint. For the present simulations, we have been concerned only with systems at equilibrium. To compute the longe-range contributions to the force and energy, the simulation cell is surrounded by identical images of itself (periodic boundary conditions), and the truncated long-range charge-charge interactions are corrected using the reaction field technique. We imagine that the periodically replicated system forms a large sphere with dielectric constant E surrounded by a dielectric continuum of dielectric constant E’. For r > R,, we assume the Coulombic interaction is zero and that systems interact with the continuum. This gives for a charge-charge interaction”’

- I

for r=cR,,

u,,(r) = 0 for r> R,. (7)

For the states studied, which are near the CP of SPC water (see below), we have to give careful consideration to the correlation length gin comparison to the length of the simulation cell, L. Sengers and Sengers4’ give the following equation for the correlation length of water along the critical isochore:

{=&(An “11 +.&(AT)-*+ **.I, (8)

where AT= (T - T,)/F, v = 0.630, and A = 0.51 are uni- versal exponents; and &, = 0.13 x 10 -9 m and 6, = 2.16 are specific for water. For T, = 1.05, g = 12.9 A and {/go0 = 4.07. The length of the simulation cell was chosen to be

TABLE III. Equilibrium properties of r, = l.O,p, = 1.5.

approximately twice the correlation length. Of course, it would be desirable to use an even larger simulation cell, but practical constraints prohibited this; for L > 4(, a simulation of 1280 SPC water molecules would have been required. Our simulations required more than 3 h of central processing unit (CPU) time on the Oak Ridge Cray XMP for the cases with 216 or 256 particles and more than 12 h for the case with 864 particles. In future work, we plan to test the effects of system size at various distances from the CP.

C. Cases studied

For SPC water, de Pablo et aZ.34 have established the following CP: T, = 578 K, pc = 270 kg/m3. We have chosen state points at T, = 1.0, pr = 1.5 (state 1) and T, = 1.05, pr = 1.0 (state 2), corresponding to T = 578 K, ’

p = 405 kg/m” and T = 616 K, p = 270 kg/m3, respectively. We performed simulations at each state for systems consisting of pure SPC water, sodium ion in SPC water, chloride ion in SPC water, and argon atom in SPC water. Parameters for the simulations are summarized in Table II.

Ill. RESULTS In the following three subsections we present the results

for equilibrium properties and structure of pure SC SPC water, ions in SC SPC water, and argon atoms in SC SPC water, respectively.

A. Pure supercritical SPC water Table III compares some of the equilibrium properties

of SPC water at T,. = 1 .O, pr = 1.5 with experimental values

p(kg/m’) T(K) E’ U,,,,,,- (kcal/gmol jh U,,,, (kcal/gmol)’ &bar)

SPC 405 578 14.7 & 1.5 - 4.83 + 0.09 - 3.39 f 0.09 220+ 30 Expt. 483 647.1 9.6 - 4.64 234.7

I’ Dielectric constant. hConligurational energy. ’ Total internal energy.



TABLE IV. Equilibrium properties of r, = 1.05, p, = 1.0.

p(kg/m”) r(K) E” Ucqnr (kcal/gmol ) b U,,, (kcal/gmol )’ P( bar)

SPC 270 616 8.8 * 0.9 - 3.83 f 0.09 - 2.39 0.09 270 30 Expt. 322

f 679.45

f 5.1 - 3.52 . . . 310

“Dielectric constant. bConfigurational energy. ‘Total internal energy.

for water. Note that the experimental water properties are at T, = 1 .O, pr = 1.5 for real water (647.1 K and 483 kg/m3). Table IV makes a similar comparison for T, = 1.05, p, = 1.0. In Table IV, the real water state is 679.5 K and 322

kg/m3. The dielectric constant was calculated in the simulations using the reaction field technique (described above) from the average value of the square of the total dipole moment (M’), where

M=& (9) r=l

and P, is the (vector) dipole moment of molecule i. Then, the dielectric constant E is calculated from4’

(E- 1)(2&‘+ 1) 3 (E + 2E’)

=gT (M2), (10)

where V is the cell volume and k is Boltzmann’s constant. The error estimates given in Table III are based on breaking the production runs (30 ps in cases A-F and case I, 45 ps in cases G and H) into ten blocks, regarding the averages of the computed properties over each block as ten independent samples, and calculating the standard deviation based on these ten samples.

Given that the SPC parameters were fitted for water properties at ambient conditions, the substantial agreement between calculated and experimental equilibrium properties is remarkable.

Figure 1 presents the oxygen-oxygen correlation function for ambient SPC water4’ and for SPC water at state 1 (T, = l.O,p, = 1.5)andatstate2 (T, = 1.05,~~ = l.O).In comparison with ambient SPC water, the high density state exhibits a lower, broader first maximum and a broad second maximum at substantially greater distance. The near-critical state exhibits a first maximum of comparable magnitude to that of ambient water, but substantially broader. Broadened peaks indicate that at the lower density the molecules are not as localized as at the higher, ambient density where the molecules are forced together into much closer packing. The long-range correlation [go0 (r) > 1.01 is evidence of near criticality, but the simulation cell size appears to be sufficiently large. The number of nearest neighbors, calculated out to the first minimum, R,, according to

RNN n NN = 4qp I

go0 (r) r %r (11) 0

decreases only slightly form the ambient value (see Table VI.

3.00

2.50 -..-.---........__._..-.-..--.

2.00

0.00 ~~~~~~~~~I~~~.~~~~~I~.~~~~ll~i 0.00 0.50 1.00 1.50 2.00 2.50 3.00

FIG. 1 Oxygen-oxygen correlation functions for SPC water [ambient results are from Beil et al. (Ref. 42) 1.


Cummings et al.: Simulation of supercritical water 5611

Figure 2 presents the oxygen-hydrogen correlation functions of SPC water for the same states. The hydrogen- oxygen correlations, calculated independently, were virtual- ly indistinguishable from the oxygen-hydrogen functions (as required) and have not been presented. In comparison with ambient SPC water, both the high density state (state 1) and the near-critical state (state 2) exhibit a substantially

TABLE V. Nearest-neighbor numbers.

R NN

Ambient l.l%l State 1 State 2

4x-i

5.2 4.2 1.30,

1.40,, 3.9

3.00 8 a + 8 / 1s 0 ’ , ’ “1 1 “1’ Q 1” 1 16 ’ ”

2.50 - . . . .._._..____._.....----.....

2.00 -

G 5 1.50 -

6

1.00 -

0.50 -

0.00 ’ ’ ’ ’ I,,,,I,‘,,I,,,,I,,,,- 0.00 0.50 1.00 1.50 2.00 2.50 3.00

FIG. 2. Oxygen-hydrogen correlation functions for SPC water [ambient results are from Beil et al. (Ref. 42) 1.

3.00 t 3 8 1, 8 1 ’ “1 “1 1” ) ’ ” ‘1, 11 11 1

2.50 -

2.00 -

E I2 1.50 -

Ml

1.00 -T

0.50 -

0.00 I ’ * ’ 1,,,,1,,,,1,,,,1,,,,- 0.00 0.50 1.00 1.50 2.00 2.50 3.00

FIG. 3. Hydrogen-hydrogen correlation functions for SPC water [ambient results are from Beil et al. (Ref. 42)].


5612 Cummings et&: Simulation of supercriticai water

0.80 - 0.80 -

0.60 - 0.60 -

0.40 - 0.40 -

0.20 - 0.20 -

0.00 ’ ’ ’ ’ ’ ’ n. OOOt------ . 0.00 0.00 0.50 0.50

1 I”“I”“I’“‘I”“_

Ambient

pr=1.5, T,=l.OO 1 j

1.00 1.50 2.00 2.50 3.00

FIG. 4. Orientational correlation functions for SPC water [ambient results are from Beil et al. (Ref. 42) 1.

lower, broader first maximum and a large, broad second maximum. The hydrogen-hydrogen correlation functions are shown in Fig. 3.

In Fig. 4, we consider the orientational structure in the cluster of SPC water molecules around an SPC water molecule for the two SC states compared with the orientational structure of ambient water. Plotted for the three states is the ratio of the correlation function g, (I) to the correlation function g, (r), where g, ( r) is defined by

g,(r) =-J-- 647T4 J-J g(r,,,%WD( 12MfWf% (12)

and D ( 12) is the dipole-dipole tensor D( 12) = 3S,.i,,&.i,, -3,-Z, , (13)

where 3, is the unit vector giving the orientation of molecule 1, Z2 is the unit vector giving the orientation of molecule 2, and ?,, is the unit vector along the line joining the centers of molecules 1 and 2. Thus, the range of g, (r)/g, (r) is from - 2, where all molecules rare aligned head to head or tail to

tail through - 1 which corresponds to the molecules at r being aligned parallel, 0 where alignment is uncorrelated, + 1 which corresponds to the molecules at r being aligned

antiparallel, to + 2 where all molecules at rare aligned head to tail or tail to head. The repulsive configurations (head to head and parallel) will give negative values of D, the attractive ones (antiparallel and head to tail) will give positive values of D.

Additional results from analysis of the simulations of SC SPC water will be included in a forthcoming paper.43

B. Ions in supercritical SPC water

Equilibrium properties of sodium and chloride ions in SPC water are summarized in Table VI for state 1 and in Table VII for state 2, respectively. For comparison, Pettitt and Rossky 35 found the configurational energy due to ion- water interactions U,, to be - 166 and - 190 kcal/gmol for ambient aqueous Na+ and Cl-, respectively.

The thermodynamic properties of these simulated ionic solutions already suggest strong effects of water-ion interac-

TABLE VI. Equilibrium properties at T, = 1.0, p, = 1.5.

Uconr (kcal/gmol)” lf,, (kcal/gmol ) h U,, (kcal/gmol)’ P( bar)

Na’ - 5.55 f 0.08 - 4.57 - 216.3 - 107 f 50 Cl- - 5.54 * 0.08 - 4.67 - 189.8 660&50

“Configurational energy. “Configurational energy due to water-water interactions. ‘Configurational energy due to ion-water interactions.


Cummings eta/: Simulation of supercritical water 5613

TABLE VII. Equilibrium properties of r, = l.O5,p, = 1.0.

U,,,, (kcal/gmol )’ VW, ( kcal/gmol )’ U,, (kcal/gmol)’ P( bar)

Na’ -4.53f0.13 - 3.68 + 0.04 - 220.6 f 0.8 103 f 07 Cl- - 4.41 0.09 * - 3.71 f 0.02 - 182.4 + 0.9 417 f 30

‘Configurational energy. bConfigurational energy due to water-water interactions. ‘Configurational energy due to ion-water interactions.

I 20 E

a li 1: I.. : : ; :

n

FIG. 5. Sodiumaxygen correlation functions for Na+ in SPC water.

121 b 3 I I, I t I I ,I I I t, I I IS, I1 1 t ,t L I 91

lp,=1.5, T,=l.OO 1

6-

: J’ ” ’ I ’ t ” ” ’ I ” ” ” 11

0.00 0.50 1.00 1.50 2.00 2.50 3.00

FIG. 6. Chloride-oxygen correlation functions for Cl- in SPC water.


5614 Cummings et al.: Simulation of supercritical water

25 r

20 -

15 F

10 +-

57

-5-"""I""""")"t"""~"""""I- 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

L/o FIG. 7. Number of excess SPC water molecules surrounding a sodium ion.

tion for both the high density SC state (state 1) and the near- critical SC state (state 2). The strong effects on pressure at state 1 (negative pressure for Na+ and high pressure for Cl-) are indicative, we believe, of the relatively high ion concentration (mole fraction 0.004 65) plus other possible effects of the small system size which are discussed further below. The effects observed at state 2 exhibit qualitatively similar but smaller departures from the properties of pure

SPC water at these states. Figures 5 and 6 present the sodium-xygen (oxygen

represents the water center) and chloride-oxygen pair correlations, respectively, for the two SC states of SPC water. The very large first maximum in each case is indicative of the strength of the ion-water interaction. Figures 7 and 8 present the number of excess water molecules, above the bulk average, surrounding each ion within a radius L of the ion,

FIG. 8. Number of excess SPC water molecules surrounding a chloride ion.


Cummings et&: Simulation of supercritical water 5615

40, I1 I I, I I I1 ’ I I I I ’ I I1 I ’ 1 I I ‘I,,” I I

I I

3Ol- I #-l --- n-l n l”f:5: z::; 1

/

/ / / / /’ /’ / / /

/ / i

“0.0 0.5 1.0 1.5 2.0 2.5 3.0

FIG. 9. Number of nearest-neighbor SPC water molecules surrounding a sodium ion.

calculated by [see Eq. ( 1) ] maximum due to the shell of first nearest neighbors is dis-

I

L tinctly evident. The maximum at longer range (14 excess NW,(L) =p 4n-r ‘[go, (r) - l]dr. (14) water molecules within a shell of radius 3ooo for state 1; 25

0 within 4aoo for state 2) is the cluster characteristic of at- The clustering of SPC water molecules around each ion for tractive solutes in SC solutions. In addition, however, these both SC states is quite evident. The minimum is due to the figures suggest further possible effects of the relatively small excluded volume effect (water displaced by the ion). The system size for these simulations. In particular, the decrease

FIG. 10.

0 I 0.0 0.0 0.5 0.5 1.0 1.0 Lg 2.0 2.0

Number of nearest-neighbor SPC water molecules surrounding a chloride ion. Number of nearest-neighbor SPC water molecules surrounding a chloride ion.

‘I I 2.5 2.5 3.0 3.0


5616 Cummings eta/.: Simulation of supercritical water

in NW, (L) at longe range is, we believe, an artifact of the small system size. At constant N and V, the formation of a cluster of relatively high density around the ion necessarily creates a region of reduced density elsewhere. Despite the evidence of system size effects in these results, we believe that the structures we have observed are realistic at short range and are likely to be valid to distances approaching the long-range maxima (say to 3 or 4000 ) .

Figures 9 and 10 show conventional nearest-neighbor plots for sodium and chloride, respectively, for the two SC

TABLE VIII. Nearest-neighbor numbers.

R NN hN

Ambient* Na+ l.ou~o 4.3 State 1 Na+ l.lu,, 6.5 State 2 Na+ 1.4u, 10.0 Ambient” Cl- 1.4u, 11.7 State 1 Cl- l.lu, 6.5 State 2 Cl- 1.5u, 10.5

‘Pettitt and Rossky (Ref. 35).

0.00 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

FIG. 11. Charge-dipole correlation functions for Na+ in SPC water.

-6.00

““I’ * ” ’ ““I B ” ” ’ ” B I”’ I ’ 8 ” ’ I”” 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

rb FIG. 12. Charge-dipole correlation functions for Cl- in SPC water.

.



-loo0 -

2

7z 5

-2000 -

-3ooo” I’ u”“““~.“~““““l~“‘,“,“‘~“““’ 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

L/cr FIG. 13. Contributions of successive neighborhoods to the ion-water configurational energy for Na+ in SPC water.

states of SPC water. Table VIII summarizes the number of where 3Z is the unit vector giving the orientation of water nearest neighbors as defined analogously to Eq. ( 11). molecule and F,, is the unit vector from the center of the ion

Figures 11 and 12 show the charge-dipole correlation to the center of water molecule. The orientational correla- around sodium and chloride, respectively, for the two SC tion of water molecules in the first solvation shell is very states of SPC water. The charge-dipole correlation is defined strong even at SC conditions. The decrease in orientational by correlation at longer range, we suspect, is due to thermal

effects, but some correlation is still evident.

&D tr) = & s

81W (rdb)~12’%dn2, (15) Figures 13 and 14 show the contributions by water molecules at increasing distance from the sodium and chloride

0 ,,,“““,““““‘,‘““““‘““,““,‘“’

-1000 -

=i‘

3 -20Qo -

ii\ : ~;ztG.:;, / 1 : a

___....-.....-.- _.._.....----. .--e-e..*.*-

I

-3ooo’“““““‘~““““~““~“~‘~“~“““~“~~ 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

Us FIG, 14. Contributions of successive neighborhoods to the ion-water configurational energy for Cl- in SPC water.



ions, respectively, to the ion-water configurational energy for the two SC states of SPC water. U(L) is the configurational energy of interaction of the solute with all of the water molecules located within a sphere of radius L centered on the solute particle.

C. Neutral argon in supercritical SPC water

Equilibrium properties are summarized in Table IX for argon atoms in SPC water at the two SPC states.

Figure 15 shows the argon-oxygen pair correlation for the SC state of water at pr = 1 .O and T,. = 1.05 for a simulation with 864 particles. The results at this state and at pr = 1.5 and T, = 1.00 with 256 and 216 particles, respective-

ly, could not be distinguished, within the relatively high noise, from the result shown. The apparently higher noise level in these correlation functions compared with those presented previously is predominantly the result of the greatly expanded scale of Fig. 15. The very small first maximum (less than 1) and the long-range negative correlation [gAro (r) < 1.01 is representative of the behavior of repulsive solutes in SC solution. At both SC states, the argon atom is surrounded by a sphere of reduced solvent density compared with the bulk average. Figure 16 shows the deficit of water molecules, below the bulk average, surrounding the argon atom within a radius L, calculated analogously to Eq. ( 14). There is apparently a larger deficit, -five water molecules, at p, = 1.5 and T, = 1.00 than at the near-critical state, pI = 1.0 and T, = 1.05 where the deficit is -three water molecules. This may be a result of the low signal-to- noise ratio seen in Fig. 15, or else it is unexplained. Again there is evidence of system-size effects and our explanation is

TABLE IX. Equilibrium properties for Ar in SPC water.

State 1 State 2

Kc,d a (kcal/gmol)

- 4.89 - 3.91

u h u SW c (kcalyimol ) (kcal/gmol ) P( atm)

- 4.92 - 0.56 268 - 3.93 - 0.44 263

“Configurational energy. bConfigurational energy due to water-water interactions. ‘Configurational energy due to ion-water interactions.

similar to the one given above. The decrease in the magnitude of the deficit at long range is a system-size artifact; because there is a region of lower than average density surrounding the argon atom, in a system of constant N and V there must be higher than average density elsewhere. Again, we believe that the structures we have observed are realistic at short range and are likely to be valid only to distances approaching the long-range minima.

Figure 17 shows that argon-dipole orientational correlation [defined analogously to Eq. ( 15) ] is absent for the argon-water system at pr = 1.0 and T, = 1.05 with 864 particles. The results at this state and at p, = 1.5 and T, = 1.00 with 256 and 216 particles, respectively, could not be distinguished, within the relatively high noise, from the result shown.

Figure 18 shows the contributions by water molecules at increasing distance from the argon atom to the argon-water configurational energy for the two SC states. The positive contribution by the shell offirst nearest neighbors is striking. It appears that the water-water interactions are sufficiently strong to result in a small overlap (leading to a repulsive

pr=l .O, T,=l .OS (864 particles)

0.00 0.00 0.50 1.00 1.5.0 2.00 2.50 3.00

r/o

FIG. 15. Argon-oxygen correlation function for argon in SPC water.



-1

-2

-3

-4

-5

1.5 2.0 2.5 3.0 3.5 4.0

r/o

FIG. 16. Deficit of SPC water molecules surrounding an argon atom.

interaction) with the argon atom, an interaction similar to that with a cavity.

IV. CONCLUDING REMARKS

We have presented new results from MD simulations for the structure and properties of pure SPC water and solu-

tions of sodium ions, chloride ions, and argon atoms in SPC water for two SC states. Compared with water and aqueous solutions at ambient conditions, SC conditions are relatively easy to simulate because of the absence at SC conditions of orientational correlations with a long time constant.

The thermodynamic and dielectric properties we have calculated for pure SPC water at a dense SC state and at a

I.00 “““““““““““““““““,“”

pI=l .O, T,=l.O5 (864 particles)

LOO-““““““m ~‘~~“‘~“““~“‘~“““’ 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

r/o

FIG. 17. Argon-dipole correlation function for argon in SPC water.


5620 Cummings et a/.: Simulation of supercritical water

FIG. 18. Contributions of successive neighborhoods to the argon-water configurational energy for argon in SPC water.

pr=l.5, Tr=l .OO

pr=l .O, T,=l.O5 . . . . ..-......--............ o.=l .O. T,=l.O5 (864 Darticles)

-4 ” ” ” ” ” ” ” ” ” ” ” ’ “““‘I ” ’ I”” 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

r/o

near-critical SC state are in reasonable agreement with measured properties. Even in the SC states, each SPC water molecule is surrounded by about four nearest neighbors which are oriented tetrahedrally; the H-bonding structure of the nearest-neighbor shell appears little different from that of ambient water. The SC states of SPC water exhibit reduced positional and orientational correlation, compared with ambient states, for the second and succeeding solvation shells. However, like simple fluids, the range of the centers correlation function increases as the CP is approached. The correlation length of SPC water for the SC states studied appears to have been well within the cell size chosen for the simulations.

The thermodynamic properties of systems consisting of a single sodium or chloride ion in a bath of SPC water molecules at SC states suggested that the small system sizes used in these studies may have introduced some artifacts. Sodium and chloride ions in SC SPC water behave as attractive solutes, collapsing clusters of SPC water molecules around themselves to create a region of locally high density. As an artifact of the small system size, the portions of the simulation cell at long range from the ion exhibited reduced density. We believe the structure of the cluster around the sodium or chloride ion has not been seriously distorted within the range of the long-range maximum in the plot of the number of excess SPC water molecules within a sphere of a given size (Figs. 7 or 8). Compared with ambient conditions, the ionic solutions at SC states exhibit effects of strong ion-water interactions, the ion disrupting the H-bonded structure.

The thermodynamic properties of systems consisting of a single argon atom in a bath of SPC water molecules at SC states also suggested that the small system sizes used in these studies may have introduced some artifacts. The argon atom

behaved as a repulsive solute in SC SPC water, forming around itself a shell of reduced local density. As a conse- quence of the small system size, other parts of the simulation cell exhibited increased density. The interaction of the water molecules with the argon atom is similar to that with a cavity. The center-dipole-dipole projection of the solute-solvent-solvent triplet correlation function could be examined to see if structures around the argon atom are also similar to those around a cavity.44

These results may lead to improved understanding of the qualitative behavior the equilibrium structure and properties of solutions in SC water which are of importance in both technological and natural processes. Perhaps similar understanding of kinetic processes might be gained from future dynamic simulations.

ACKNOWLEDGMENTS This work has been supported by the Division of Chemi-

cal Sciences, Office of Basic Energy Sciences, Office of Ener- gy Research of the U.S. Department of Energy and by the ORNL Exploratory Studies Program under Contract No. DE-AC-05-840R21400 with Martin Marietta Energy Sys- tems, Inc. and through Grant No. DE-FG-05-88ER13943 with the University of Virginia. PTC is grateful for a summer at ORNL under the aegis of the Oak Ridge Associated Uni- versities.

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