Table Of ContentStructural Properties of High and Low Density Water in a Supercooled Aqueous
Solution of Salt
∗
D. Corradini, M. Rovere and P. Gallo
Dipartimento di Fisica, Universita` “Roma Tre”,
Via della Vasca Navale 84, I-00146 Roma, Italy
We consider and compare the structural properties of bulk TIP4P water and of a sodium chloride
aqueoussolutioninTIP4Pwaterwithconcentrationc=0.67mol/kg,inthemetastablesupercooled
region. In a previous paper [D. Corradini, M. Rovere and P. Gallo, J. Chem. Phys. 132, 134508
(2010)] we found in both systems the presence of a liquid-liquid critical point (LLCP). The LLCP
is believed to be the end point of the coexistence line between a high density liquid (HDL) and a
low density liquid (LDL) phase of water. In the present paper we study the different features of
water-water structure in HDL and LDL both in bulk water and in the solution. We find that the
ionsareabletomodifythebulkLDLstructure,renderingwater-waterstructuremoresimilartothe
1 bulk HDL case. By the study of the hydration structure in HDL and LDL, a possible mechanism
1
forthemodificationofthebulkLDLstructureinthesolutionisidentifiedinthesubstitutionofthe
0
oxygen bythe chloride ion in oxygen coordination shells.
2
n PACSnumbers: 61.20.-p,64.60.My,65.20.Jk
a
J
7 I. INTRODUCTION are also indications from experiments of the existence of
2 theLLCPinbulk water16–19. Itwouldbeapproximately
The possible existenceofa secondcriticalpoint ofwa- located at T ∼220 K at P ∼100 MPa.
]
t ter in the liquid supercooled metastable phase has been Becauseofthedifficultiesofperformingexperimentsin
f
o the subject of a long debate in the literature. The first the region where the LLCP would reside in bulk water,
s hypothesisofitsexistenceoriginatedfromtheresultsofa the possibility of observing the LLCP of water in aque-
.
t computersimulationonwatermodeledwiththeST2po- ous solutions that can be more easily supercooled20 has
a
tential1. Onthebasisofthoseresultsthethermodynamic been recently explored theoretically21 and in computer
m
anomaliesofwateruponsupercoolingwereinterpretedin simulations22,23. Results compatible with the existence
-
d termsofthelongrangefluctuationsinducedby thepres- of a LLCP have been also found in aqueous solutions of
n ence of a second critical point. This critical point would salts through thermometric experiments24–27.
o bealiquid-liquidcriticalpoint(LLCP)locatedattheend Inarecentpaper22,bymeansofacomputersimulation
c ofthecoexistencelinebetweenalowdensityliquid(LDL)
study of the phase diagram, we indicated the possible
[
phase and a high density liquid (HDL) phase of water. detectionin thermometricexperiments ofthe LLCPin a
1 In the LLCP scenario, these liquid phases would be the NaCl(aq) solution.
v counterpartathighertemperatureofthewell-knownlow
1 density amorphous (LDA) and high density amorphous Since the detection of low and high density forms of
1 watercanalsoofferaviablepathtotheexperimentalde-
(HDA)phasesofglassywater. ThehypothesisofaLLCP
3 tection of a LLCP, structural properties of supercooled
scenario for water motivated a large number of experi-
5 mental, computational and theoretical investigations2,3. water and aqueous solutions are of extreme interest in
.
1 Different interpretations of the origin of the thermo- this context. The structure of water and of aqueous so-
0 lutions,canbestudiedwithneutrondiffractionusingiso-
dynamic anomalies of water have been also proposed as
1 topic substitution28,29 or by X-ray scattering30.
alternativestotheLLCPscenario. Inthesingularityfree
1
scenario4 the anomaliesof water are due to local density In the present paper we focus on the structural prop-
:
v fluctuations and no critical phenomena take place. Re- erties of bulk TIP4P water and of the NaCl(aq) solution
Xi cently a critical point free scenario5 has also been pro- with c = 0.67 mol/kg, in order to analyze and compare
posed in which the transition between HDL and LDL theresultsinHDLandLDLespeciallyclosetotheLLCP.
r
a is seen as an order-disorder transition without a critical Thepaperisorganizedasfollows. InSec.IIthedetailsof
point. the computer simulations are given. In Sec. III we sum-
A number of computer simulations, performed on su- marizethemainresultsobtainedonthethermodynamics
percooled water with different model potentials, con- ofbulkwaterandNaCl(aq)andwepresentthepotential
firmed the plausibility of the LLCP scenario6–15. There energy of the systems. The new results for the struc-
tural properties of the systems are presented in Sec. IV.
This section is divided in two parts: water-water struc-
ture is discussed in subsection IVA, while the hydration
∗ Author to whom correspondence should be addressed, e-mail: structureofionsisaddressedinsubsectionIVB. Finally,
gallop@fis.uniroma3.it conclusions are given in Sec. V.
2
II. COMPUTER SIMULATION DETAILS decreasing temperature. The total running times span
from0.15nsforthehighesttemperaturesto30nsforthe
Molecular dynamics (MD) computer simulations were lowest ones. The parallelized version of the DL POLY
performed on bulk water and on NaCl(aq) with concen- package35wasemployedtoperformthesimulations. The
tration c = 0.67 mol/kg. The interaction potential be- total simulation time is circa 6 single CPU years.
tween pairs of particles is given by the sum of the elec-
trostatic and the Lennard-Jones (LJ) potentials.
III. THERMODYNAMICS IN THE
U (r)= qiqj +4ǫ σij 12− σij 6 (1) SUPERCOOLED REGION
ij ij
r (cid:20)(cid:16) r (cid:17) (cid:16) r (cid:17) (cid:21)
In this section we start by summarizing the main re-
Water molecules were modeled using the TIP4P poten-
tial31. The details about this potential are reported in sults on the thermodynamic behavior in the supercooled
regionofbulk waterandofNaCl(aq)obtainedinRef.22
theAppendix. TIP4Ppotentialisknowntowelldescribe
waterpropertiesinitsliquidsupercooledstate31andalso and then we analyze the behavior of the potential en-
ergy of the systems studied at different temperatures.
to be able to reproduce the very complex ices phase dia-
gram32. Fromextensivesimulationsonbulk TIP4Pwaterandon
NaCl(aq)withconcentrationc=0.67mol/kg,welocated
The LJ interactionparametersfor the ions were taken
from Jensen and Jorgensen33 and the ion-water inter- inboth systems the LLCP.Details aboutthe calculation
of the position of the LLCP are given in Ref. 22.
action parameters were calculated by using geometrical
mixing rules ǫ = (ǫ ǫ )1/2 and σ = (σ σ )1/2. The InFig.1wereportacomparisonofthephasediagrams
ij ii jj ij ii jj
ofthesupercooledregionsofbulkwaterandNaCl(aq)as
ion-ionandion-waterparametersarereportedinTableI.
obtained directly from MD. Together with the LLCP of
TheseparameterswereoptimizedforusewithTIP4Pwa-
the two systems, we show the Widom lines, the temper-
terandtheywellreproducestructuralcharacteristicsand
free energies of hydration of the ions33. ature of maximum density (TMD) lines and the liquid-
gas limit of mechanical stability (LG-LMS) lines. The
Although the presence of ions would suggest the use
Widomlinecanbeconsideredanextensionofthecoexis-
of polarizable potentials, at the moment no joint set of
tenceline inthe one-phaseregion36,37. Inbulkwaterthe
polarizable potentials for water and ions are tested as
position of the LLCP is T =190 K and P =150 MPa.
reliable for very low temperatures. c c
In a very recent paper38 another estimate of the LLCP
for bulk water has been performed with a TIP4P po-
TABLEI.Ion-ionandion-waterLJinteractionparameters33. tential with modified parameters39. The values that the
authors obtained for the critical point, T = 193 K and
c
Atom pair ǫ(kJ/mol) σ(˚A) Pc =135MPa,andtheWidomlineappearssubstantially
the same as the values that we found with the original
Na-Na 0.002 4.070
TIP4P22.
Na-Cl 0.079 4.045
Coming back to Fig. 1 we can see that in NaCl(aq)
Cl-Cl 2.971 4.020
the position of the LLCP moves to lower pressure and
Na-O 0.037 3.583 higher temperature, appearing at T = 200 K and P =
c c
Cl-O 1.388 3.561 −50 MPa. The TMD line of the solution lies circa 10 K
below intemperature andatslightlylowerpressurewith
respecttobulkwater. TheLG-LMSinsteadisalmostun-
Periodicboundaryconditionswereapplied. Thecutoff changed with respect to the bulk. From the comparison
radius was set at 9 ˚A. Standard long-range corrections of the phase diagrams for these two systems, we found
were applied for the calculation of the potential energy thatthemaineffectofthepresenceoftheionsistoshrink
and the virial. The long-range electrostatic interactions the region of existence of the LDL22, consistent with an
were handled with the Ewald summation method. The observed increased solubility of ions in HDL water27,40.
integration time step was fixed at 1 fs. Importantly, we also found that with a rigid shift in
The totalnumber of particles containedin the simula- temperatureandpressureofthephasediagramofTIP4P
tion box is N = 256. For bulk water N = N = bulk water(not shown), that broughtthe TMD curveto
tot wat tot
256 while in the case of NaCl(aq) with concentration coincide with the experimental TMD values, the LLCP
c = 0.67 mol/kg, Nwat = 250 and NNa+ = NCl− = 3. in bulk water appears at Tc = 221 K and Pc =77 MPa,
Extensive sets of simulations were run both for bulk wa- close to the experimental value estimated by Mishima
ter and for NaCl(aq). The range of densities investi- and Stanley16 T ∼ 220 K and P ∼ 100 MPa. We
c c
gated spans from ρ = 0.83g/cm3 to ρ = 1.10g/cm3 note that this shift in temperature is compatible with
and the range of temperatures goes from T = 350 K the shift between the melting line of TIP4P41 and the
to T = 190 K. Temperature was controlled using the melting line of real water. Recently Mishima published
Berendsen thermostat34. Equilibration and production a new estimate of the LLCP in the bulk at T ∼ 223 K
c
simulation times were progressively increased with the and P ∼ 50 MPa19 also compatible with our findings.
c
3
-46
200 Bulk LLCP -40 Bulk NaCl(aq)
NaCl(aq) LLCP
T = 300 K -48
100 TMD -42 T = 300 K
-50
)
0 mol-44
Pa) kJ/ T = 245 K -52
M U ( T = 235 K
(-100 -46
P
LMS -54
-200 -48 T = 190 K T = 200 K
-56
-300 -50
0.85 0.9 0.95 1 1.05 1.1 0.85 0.9 0.95 1 1.05 1.1
ρ (g/cm3) ρ (g/cm3)
-400
175 200 225 250 275 300 325
FIG. 2. Potential energy per molecule as a function of the
T (K)
densityofthesystematconstanttemperature. Forbulkwater
(leftpanel)theisothermsofthepotentialenergyarereported
FIG. 1. Comparison between the thermodynamic features of
atT =300K,T =245KandT =190K.ForNaCl(aq)(right
bulk water and NaCl(aq) in the supercooled region, based
panel) the isotherms of the potential energy are reported at
on the results shown in Ref. 22. We report the position of
T =300 K, T =235 K and T =200 K. Continuous lines are
theLLCP and of theWidom linefor bulkwater (dot-dashed
a polynomial best fits tothe simulated points.
line)andforNaCl(aq)(dottedline). TheTMDandLG-LMS
linesarealsoshownforbulkwater(solidlines)andNaCl(aq)
(dashed lines).
NaCl(aq). We show the behavior of potential energy for
These results confirmthat TIP4Pis a goodpotentialfor ambient temperature T = 300 K, for the first tempera-
describing the supercooled water phase diagram. The tureshowinganegativecurvatureofU,T =245Kinthe
same shift applied to our ionic solution led us to predict bulk and T = 235 K in the solution, and for the LLCP
a LLCP in NaCl(aq) located at T ∼ 231 K and P ∼ temperature, T = 190 K in the bulk and T = 200 K in
c c
−123 MPa. These last values appear to be in a region the solution. In both systems, at high temperature the
accessiblebyexperiments,being abovethe homogeneous potential energy is a positively curved function of the
nucleation temperature of the solution20,42. density and it decreases monotonically (becomes more
Generallyspeaking,fromthe behaviorofthepotential negative) as density increases. When the temperature
energyU it isalsopossibleto extractinformationonthe is decreased, a minimum is formed after which the cur-
thermodynamics of a system close to a phase transition. vature of the potential energy becomes negative. The
As already pointed out in Ref. 8 and 15 if we examine minimum corresponds to the presence of a tetrahedrally
thecurvatureoftheconfigurationalpartoftheHelmholtz ordered liquid with an energetically favorable configura-
free energy A=U −TS, tion15. Forthe temperature correspondingto thatofthe
LLCP,weseethatinbothsystemstheminimumbecomes
∂2A ∂2U ∂2S verydeepandamaximumissuggestedathighdensities,
= −T (2)
(cid:18)∂V2(cid:19) (cid:18)∂V2(cid:19) (cid:18)∂V2(cid:19) indicating the possible occurrence of a second minimum
T T T
at higher densities. This second minimum has been pre-
it must be positive in the regionof stability of an homo- viouslyobservedforconfinedbulkwater43 andforhigher
geneousphase. Whenthe curvatureofU is negative,the concentrationNaCl(aq)solutions44 andconnectedtothe
system can still be stable due to the contribution of a existence of two distinct liquid phases in the system, as
dominant entropic term in Eq. (2). At supercooled low atverylowtemperaturesthe entropiccontributionisde-
temperatures, the stabilization induced by the entropic pressed and the behavior of the free energy A can be
term can be less effective as the factor T in front of the approximatedwiththatofthepotentialenergyU. Com-
second derivative of the entropy in Eq. 2 becomes pro- paringthe behaviorofthepotentialenergyofbulkwater
gressively smaller. Thus, at low temperatures the range and NaCl(aq), we can notice that apart from the shift
of volumes where (∂2U/∂V2) < 0, corresponds to a in the absolute value due the presence of ions, their be-
T
region of reduced stability for the homogeneous liquid, havior is quite similar. Nonetheless the minimum at low
where separation in two distinct phases with different density becomes more shallowin the solution,indicating
densities may occur. that this phase is made less stable by the presence of
In Fig. 2 the isotherms of the potential energy are ions, consistent with the fact that ions stabilize the high
reported for three temperatures for bulk water and density phase22.
4
6
5 ρ = 1.10 g/cm3 ρ = 1.10 (HDL)
5 ρ = 0.92 (LDL)
ρ = 1.06
ρ = 0.86 (LG-LMS)
4 ρ = 1.02 4
ρ = 0.98
)
(r)O3 ρρ == 00..9942 g(rOO3
gO ρ = 0.88 2
2 ρ = 0.86 (LG-LMS)
1
1
2.5
0
2 3 4 5 6 7 8
2
r (Å)
)
r
(H1.5
FIG. 3. O-O RDFs of bulk water at T =190 K for densities O
from ρ=1.10g/cm3 toρ=0.86g/cm3 (LG-LMS). g 1
0.5
IV. STRUCTURAL RESULTS
As discussed in the previous section, the study of the
2.5
phase diagram of bulk water and of the aqueous solu-
tion shows the presence of a LLCP in the supercooled
2
region. We now discuss the structural properties of the
)
r
systems. In the following subsection, we analyze water- (H1.5
water structure both in the bulk and in the solution. H
g
Then we study the hydration (ion-water) structure. 1
0.5
A. Water-water structure
0
1 2 3 4 5 6 7 8 9
In Fig. 3 we report the O-O radial distribution func- r (Å)
tions(RDFs)ofbulkwaterattheLLCPtemperaturefor
decreasingdensitiesfromρ=1.10g/cm3totheLG-LMS
FIG. 4. O-O (top panel), O-H (centralpanel) and H-H (bot-
densityρ=0.86g/cm3. Accordingtoourphasediagram, tom panel) RDFs for bulk water at T = 190 K. Solid lines:
theLLCPinbulkwaterislocatedatρ=1.06g/cm3. As ρ=1.10g/cm3 (HDL);dashedlines: ρ=0.92g/cm3 (LDL);
ageneraltrend,thereisanincreaseofthefirstpeakwith dot-dashed lines: ρ=0.86g/cm3 (LG-LMS).
decreasing density. We note that the second peak from
ρ = 0.86g/cm3 to ρ = 0.98g/cm3 does not substan-
tiallychangeposition. As theLLCPisapproached,from density ρ = 0.86g/cm3 that represents, at this temper-
ρ=1.02g/cm3 it starts to shift to lower distances. ature, the LG-LMS of bulk water are also reported for
The LLCP is located at ρ = 0.99g/cm3 in NaCl(aq); comparison. WeobservefortheO-ORDFthattheheight
thus in order to study the structural differences be- ofthefirstpeakdecreasesgoingfromLDLtoHDL while
tween the LDL and the HDL both in bulk water and its position does not change. The second peak instead is
in NaCl(aq), we will take into account, in the follow- markedly different. In HDL its position shifts to lower
ingdiscussion,the RDFsattwodensityvalueswhichare distances, its height decreases and its shape broadens,
wellaboveandwellbelowtheestimatedcriticaldensities, with respect to the LDL. For the g (r) the height of
OH
namely ρ = 1.10g/cm3 for HDL and ρ =0.92g/cm3 for the first peak decreases in HDL and it moves to slightly
LDL. lower distances. This slight shift is conserved between
In Fig. 4 we compare the water-water RDFs g (r), the first and the second shell, while the position and the
OO
g (r)andg (r)ofbulkwaterobtainedatthethermo- height of the second shell are fairly similar for HDL and
OH HH
dynamicconditionsinwhichwateriseitherintheLDLor LDL, apart from the appearance of a shoulder between
inthe HDLregion. TheRDFsareplottedforT =190K the second and the third shell in HDL. It can be also
atdensitiesρ=0.92g/cm3andρ=1.10g/cm3represen- notedthatwhiletheLDLshowsaverywell-definedthird
tative of LDL and HDL respectively. The RDFs at the shell, it disappearsin HDL. For the g (r) alsothe first
HH
5
6 validity of the TIP4P model also for the study of the
Bulk ρ = 1.10 (HDL)
structural properties in the supercooled region.
5 NaCl(aq) ρ = 1.10 (HDL)
In Fig. 5 we compare the HDL and LDL water-water
Bulk ρ = 0.92 (LDL) RDFs for bulk water and for NaCl(aq). In NaCl(aq) the
4 NaCl(aq) ρ = 0.92 (LDL) overall shape and positions of the peaks remain similar
)
(rO3 tothoseofbulkwaterinbothcases,butsomedifferences
O can be noted for the LDL. The height of the first peak
g
2 of gOO(r), gOH(r) and gHH(r) is slightly lower for the
NaCl(aq) LDL with respect to the correspondent phase
1 in bulk water. Furthermore in the g (r) the first min-
OO
imum moves to lower distances in the solution and the
height of the second peak is reduced. In the g (r) the
OH
firstandthesecondshellremainsimilarbuttheheightof
2.5
the third shell is damped in the NaCl(aq). These results
indicate that at this concentration the effect of ions on
2
water-water structure is not strong and all the features
)
(rH1.5 found in bulk water are preserved. Nonetheless, LDL
O seems to be more affected by the presence of ions than
g
1 HDL. This can be due to a certain degree of disruption
ofhydrogenbondsinducedbytheions. Infact,asshown
0.5 in Fig.5 we see that the effect ofions is that of reducing
the LDL character of water-water structure and making
it more similar to the one of the HDL. These results are
in agreement with that observed in our study the ther-
2.5 modynamics of these systems22. In fact, it was found
that the range of existence of the LDL phase is reduced
2
when ions are added to bulk water.
)
(rH1.5 To complete the comparison between HDL and LDL
H in bulk water and in NaCl(aq) we report in Fig. 6 the
g
1 quantity
h(r)=4πρr[0.092g (r)+0.422g (r)+0.486g (r)−1]
0.5 OO OH HH
(3)
This correlation function has been obtained in neutron
0
1 2 3 4 5 6 7 8 9 diffractionexperimentsontheamorphousHDAandLDA
r (Å) phases of water45,46. The qualitative agreement shows
the existing relation between the LDA/HDA phases of
FIG. 5. O-O(top panel),O-H (central panel) and H-H(bot- ice with the corresponding LDL/HDL phases of water
tom panel) RDFs for bulk water at T = 190 K and for as already pointed out in simulations of bulk water with
NaCl(aq) at T = 200 K. Solid lines: bulk ρ = 1.10g/cm3 theST2potential15. We observeagainthatLDL ismore
(HDL); dashed lines: NaCl(aq) ρ = 1.10g/cm3 (HDL); long influenced by the presence of ions. The modifications
dashed lines: bulk ρ = 0.92g/cm3 (LDL); dot-dashed lines: to h(r) in fact appear larger in LDL with a significant
NaCl(aq) ρ=0.92g/cm3 (LDL). reduction of the peak at about 4.6 ˚A and the different
behaviorforlong distances, r >6.5˚A. This confirms the
behaviorthatweobservedforLDL,lookingatthepartial
peak ofthe HDL is less intense than the one ofLDL and water-water RDFs.
slightly shifted to lower distances. It can also be noted To conclude the analysis of water-water structure we
a widening of the second shell in the HDL. The overall reportinFig.7theoxygen-oxygenfirstshellcoordination
trend of water-water RDFs and in particular the differ- numbers as a function of density, at constant tempera-
ence in the second shell of the O-O RDF clearly shows ture. We report them at the same temperatures that
the disruption of hydrogen bonds between the first and we show in Fig. 2 for the potential energy, T = 300 K,
secondshellofwatermoleculesthatoccursinHDL,caus- T =245KandT =190KforbulkwaterandT =300K,
ingittohaveacollapsedsecondshellwithrespecttothe T = 235 K and T = 200 K for NaCl(aq). The first shell
tetrahedrally coordinated LDL28. coordination numbers can be calculated integrating the
The resultsfor HDL andLDL RDFs inbulk waterare radial distribution function until the first minimum is
ingoodagreementwiththosefoundinexperiments28. It reached, and thus they represent the average number of
has been shown that the TIP4P model is a very reliable firstneighbors aroundan oxygenatom. At high temper-
model for the study of the thermodynamics of solid32 atures the coordinationnumbers decrease monotonically
and supercooled liquid water22. Our results confirm the with the density, without reaching the value of 4 typical
6
ofLDL15 inthe spannedrangeofsimulatedstatepoints.
0.4
Astemperatureisdecreased,theisothermsofthecoordi-
nationnumbers approachanasymptotic value of4 when
0.2 density decreases. For the lowest temperature, the co-
ordination number reaches the value 4 already at quite
]
-2Å 0 highdensitiesinbulkwateranditactuallydropsslightly
[ below4 inNaCl(aq). Inthe caseofthe firstshellcoordi-
)
(r nation numbers, HDL and LDL seem to be affected in a
h-0.2
similarwaybythepresenceofions,withaslightdecrease
Bulk HDL of the average number of first neighbors. Nonetheless,
-0.4 NaCl(aq) HDL the weakening of the ordered tetrahedral configuration
Experimental HDA of LDL in the first shell induced by the ions may allow
for a reorganization of the bonds that leads to a more
packed, HDL-like structure, as we have seen looking at
0.2 the RDFs.
] 0 B. Hydration structure
2
-Å
[
r) -0.2 The hydration structure in NaCl(aq) at ambient tem-
(
h perature and in the moderately supercooled region has
beenthesubjectofseveralexperimental29,47,48 andcom-
Bulk LDL
-0.4 NaCl(aq) LDL puter simulation works49–59. Nonetheless, the hydration
Experimental LDA behavior close to the LLCP has never been studied pre-
viously.
2 3 4 5 6 7 8 Inorderto study the generalfeatures ofthe hydration
r (Å) shellsweshowinFig.8theNa-waterandCl-waterRDFs
for ρ = 1.00g/cm3 at ambient temperature T = 300 K
andinthe deepsupercooledregion,atT =200K,corre-
FIG.6. Functionh(r),seetextfordefinition. Toppanel: bulk
sponding to the LLCP temperature in the solution. For
HDL(solidline),NaCl(aq)HDL(dashedline)andexperimen-
tal HDA (dotted line). Bottom panel: bulk LDL (solid line), all the four couples we can observe that there are two
NaCl(aq) LDL (dashed line) and experimental LDA (dotted well-definedhydrationshells. Theheightofboththefirst
line). and second peak tends to increase greatly upon super-
cooling. In the case of Na-O and Cl-O we observe also
7 7 for the second peak also a shift of its position to slightly
Bulk NaCl(aq) lower distances at the lowesttemperature. These results
seem to indicate that upon supercooling the hydration
6.5 T = 300 K 6.5 T = 300 K
T = 245 K T = 235 K shells tend to stabilize and to become more compact. In
T = 190 K T = 200 K the case of the chloride ion, the Cl-O first and second
6 6
peaks are very well separated from the respective Cl-H
peaks, by roughly 1 ˚A. In the case of the sodium ion the
OO5.5 5.5 distanceisreducedtoroughly0.6˚Aandthereisactually
n
an overlap of the Na-O and Na-H hydration shells. For
5 5
the chloride ion the hydration structure of the shells is
similar to the case of O-O and O-H structure (see Fig. 4
4.5 4.5
and Fig. 5). Thus, we argue that chloride can substitute
oxygen in the hydration shells forming linear hydrogen
4 4 bondswithoxygenatomsasindicatedbythe sharp,first
0.9 0.95 1 1.05 1.1 0.9 0.95 1 1.05 1.1 Cl-H peak. The Na+ ion cannot simply substitute the
ρ (g/cm3) ρ (g/cm3) oxygen atom. Its positive charge induces a major rear-
rangement of the hydration shells that results in more
FIG. 7. O-O first shell coordination numberas a function of packed structure. The behavior of the hydration shells
density, at constant temperature, for bulk water (left panel) of Na+ and Cl− ions is in good agreement with those
and NaCl(aq) (right panel). The temperatures reported are found experimentally for ambient temperature in recent
T = 300 K, T = 245 K and T = 190 K for bulk water and neutron diffraction experiments29,47.
T =300 K,T =235 K and T =200 K for NaCl(aq).
In Fig. 9 we report the Na-water and Cl-water RDFs
for the HDL, at ρ = 1.10g/cm3 and the LDL at ρ =
0.92g/cm3 and at T = 200 K. We can see that the hy-
7
9
8 Na-O T = 300 K Na-O HDL
Na-O T = 200 K 8 Na-O LDL
7 Na-H T = 300 K Na-H HDL
Na-H T = 200 K 7 Na-H LDL
6
6
5
g(r) 4 g(r) 45
3
3
2
2
1
1
5 Cl-O T = 300 K 5 Cl-O HDL
Cl-O T = 200 K Cl-O LDL
Cl-H T = 300 K Cl-H HDL
4 Cl-H T = 200 K 4 Cl-H LDL
g(r) 3 g(r) 3
2 2
1 1
0 0
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
r (Å) r (Å)
FIG. 8. Na-water (top panel) and Cl-water (bottom panel) FIG. 9. Na-water (top panel) and Cl-water (bottom panel)
RDFsatρ=1.00g/cm3 andattemperaturesT =300Kand RDFs for ρ=1.10g/cm3 (HDL) and ρ=0.92g/cm3 (LDL),
T =200 K.
at T =200 K.
dration shells of sodium ions are not much affected by tically imperceptible. The second shell appears already
the HDL or LDL environment of the solvent. An in- sensitive to the HDL and LDL environment as we can
creaseofthe firstandsecondpeakoftheNa-ORDFand deduce from the decrease of hydration numbers in going
of the first peak of the Na-H RDF is observed in LDL from HDL to LDL.
with respect to HDL but the position of the peaks re-
mains unaltered apart from a very slight shift to higher
TABLE II. First shell, n1, and second shell, n2, hydration
distances of the second shell of Na-O for the LDL. In numbers for sodium and chloride ions in HDL and LDL at
the case of the chloride ion, the Cl-H RDF remains un- theLLCP temperature, TC =200 K.
changed in HDL or LDL but the Cl-O RDF show some
differences. In the LDL the first peak is higher than in
Atom pair n1 HDL n1 LDL n2 HDL n2 LDL
HDL and the second peak is both higher and shifted to
Na-O 5.975 5.957 18.490 15.898
longerdistances. WereportinTableIIthefirstshelland
Na-H 15.912 15.364 49.474 43.521
secondshellhydrationnumbersforthe sodiumandchlo-
Cl-O 7.214 7.032 23.193 19.378
rideionsattheLLCPtemperature. Thesenumbershave
been calculated by numerical integrationof the first and Cl-H 6.983 7.002 33.177 27.069
second peak of the RDFs plotted in Fig. 9. The integra-
tion range spans form zero to the first minimum for the
firsthydrationshellandfromthefirsttothesecondmin- As shown in Fig. 5 and Fig. 6, the ions seem to affect
imum for the second hydration shell. The modifications the LDL more than the HDL. The most significant dif-
of the first shell in going from HDL to LDL are prac- ference in the hydration shells of the ions is noticed in
8
the region of existence of the LDL phase shrinks in the
5 O-O HDL NaCl(aq) with respect to bulk water.
Cl-O HDL
O-O LDL
4
Cl-O LDL
V. CONCLUSIONS
3
)
r
(
g
BytheuseofMDcomputersimulations,wehavestud-
2
iedthestructuralpropertiesofTIP4Pbulkwaterandofa
sodiumchloridesolutioninTIP4Pwaterwithconcentra-
1 tionc=0.67mol/kg. Inparticular,wewereinterestedin
the structural differences between the two phases of wa-
ter, HDL and LDL, that appear in the deep supercooled
0.5 1 1.5 2 2.5 3 region. From our previous work22 we knew accurately
r (Å)/σ the phase diagrams of these systems and in particular
LJ the position of the LLCP.
Our results showed that the TIP4P model can repro-
FIG.10. Comparison of HDLandLDLO-OandCl-O RDFs
with distances rescaled by theLennard-Jones parameter σ. duce well the structural properties of the two phases of
supercooledliquidwaterinadditiontobeingaverygood
potentialforthestudyofliquid22 andsolid32 waterther-
modynamics. Comparing water-waterRDFs in bulk wa-
the second shell of the Cl-O RDF. We have also already
terandinNaCl(aq)wehaveseenthattheLDLisaffected
mentionedthat the hydrationstructurearoundthe chlo-
by the presenceof ions more thanthe HDL, as indicated
ride ion resembles the O-O and O-H structures (Fig. 8)
also by the shrinkage of the LDL phase observed in the
with the chloride ion able to substitute oxygen in shells
study of the thermodynamics.
ofotheroxygenatoms. Tofurtherinquirethispossibility
and to assess the effect of the chloride ion hydration on The study of the hydration structure of ions in HDL
HDL/LDL weplottogetherinFig.10the O-OandCl-O and LDL revealed that a disturbance to the LDL struc-
RDFs for HDL and LDL with distances rescaled by the ture is inducedby the substitution ofoxygenby chloride
respective LJ interaction distance parameter σ. For the ions in coordination shells of other oxygen atoms. The
O-O pair σ = 3.154 ˚A as given in the TIP4P model31, chloride ions in fact pull inward its second shell of oxy-
for the Cl-O pair σ =3.561 ˚A as reported in Table I. genatoms,disrupting the LDL structure. This, together
InbothLDLandHDLthefirstandthesecondshellof with the hydrogen bond breaking caused by the sodium
oxygenatomsarecloserinthecaseoftheCl-ORDF(see ion, causes the LDL phase to be less stable in NaCl(aq)
also Fig. 5 and Fig. 9). To make a quantitative compar- solutions and its region of existence in the thermody-
ison we can look at the distance between the first peak namic plane to reduce, with a consequent shift of the
and the second peak of the RDFs ∆R. In HDL, for the liquid-liquid coexistence line and of the LLCP to lower
O-O pair ∆R = 0.49, for the Cl-O ∆R = 0.42. In LDL, pressures with respect to bulk water.
for the O-O pair ∆R = 0.55 and for Cl-O ∆R = 0.44 Since from our thermodynamic results we hypothesize
(distances in real units are obtained multiplying ∆R by thatthe LLCP regionis abovethe nucleationline inthis
the respective σ). Thus we see that in LDL the chloride solution, an observation of the structural features pre-
ion has the major effect in pulling inward its second hy- sented in this paper in X-ray and neutron scattering ex-
dration shell of oxygens. As shown in Fig. 4 and Fig. 5 periments, can also represent a viable route for experi-
themaindifferenceinthestructureoftheHDLandLDL mentalists to solve the quest of the LLCP in bulk wa-
is in the position of the second shell of the O-O RDFs, ter. Along this line experimental indications of a HDL
therefore, a possible explanation for why the presence of andLDLphasecoexistenceandLLCPhavebeenrecently
ionsaffecttheLDLmorethantheHDL.Infactthechlo- found60.
ride ion cantake the place ofthe centraloxygenatomin
oxygen shells and can be accommodated in water-water
structure at the price of bending hydrogen bonds and
pullingthesecondshellofoxygenclosertothefirstshell.
ACKNOWLEDGMENTS
ThiscanbetoleratedinHDLwherethe molecularstruc-
ture is already collapsed in the second shell28 but the
LDL structure results instead disrupted. In essence, the We gratefully acknowledge the computational re-
substitution of oxygenatoms by chloride atoms together sources offered by CINECA for the “Progetto Calcolo
withthehydrogenbonddisruptioncausedbyNa+ forces 891”, by the INFN RM3-GRID at Roma Tre University
the LDL structure to become more HDL-like. Hence, we and by the Democritos National Simulation Center at
can understand also from a structuralpoint of view why SISSA (Trieste, Italy).
9
APPENDIX tance 0.9752˚A. The anglebetween the bonds is 104.52◦.
The site of the oxygen is neutral while a fourth site car-
ries the negative charge of the oxygen q =−2q . This
O H
The TIP4P model for water is a nonpolarizable po- site is located in the same plane of the molecule at a
tential where three sites are arranged according to the distance 0.15 ˚A from the oxygen with an angle 52.26◦
molecular geometry. The two sites representing the hy- from the OH bond. The intermolecular interactions are
drogens are positively charged with q = 0.52 e; each represented by Eq. 1. The LJ parameters are given by
H
oneformsarigidbondwiththesiteofthe oxygenatdis- σ =3.154 ˚A and ǫ =0.64852 kJ/mol.
OO OO
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