molecular dynamics simulations of water conﬁned in graphene nanochannels

8/13/2019 Molecular dynamics simulations of water confined in graphene nanochannels

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Molecular dynamics simulations of water conned in graphene nanochannels: Fromambient to supercritical environments

J. Mart , J. Sala, E. GurdiaDepartament de Fsica i Enginyeria Nuclear, Universitat Politcnica de Catalunya, B4-B5 Campus Nord, 08034 Barcelona, Catalonia, Spain

a b s t r a c ta r t i c l e i n f o

Available online 14 October 2009

Keywords:

LiquidHigh-temperatureSupercritical waterMolecular dynamicsHydrophobic connementGraphene slab

We report results of molecular dynamics simulations of water at ambient, high-temperature andsupercritical conditions inside a graphene slab 3.1 nm wide. The potential models we employed include aexible SPC water force eld, especially adjusted to reproduce the main features of the infrared spectrum ofwater at room temperature, and Lennard-Jones like forces between oxygen and carbon atoms. A thoroughanalysis of the structure, hydrogen bonding, dielectric, diffusion and spectroscopical properties of the systemis presented. The main aim of the present work has been to compare all collected properties within a widerange of temperatures and densities and to explore the inuence of thermodynamic and hydrophobicconnement effects on the microscopic structure and dynamics of the system. In route from ambient tosupercritical environments, we observed structural weakening due to massive hydrogen-bond breaking,reduction of permittivity and residence times in selected regions, a gradual rise of water self-diffusioncoefcients and the presence of spectral shifts related to changes in molecular and atomic vibrations.

2009 Elsevier B.V. All rights reserved.

1. Introduction

Water at interfaces and, in particular, near hydrophobic surfaceshas generated a great amount of work since long time ago[1,2]. Morerecently, microscopical properties of water conned at the nanoscalereceived a lot of interest because of the importance of such anubiquitous solvent for the understanding of many biological processes[3], such as the dynamics and function of membranes [4], thestructure of ion channels[5]or the formation of micelles due to thehydrophobic effect, rst noted by Kauzmann[6], which is regardedtoday as a multifaceted phenomenon [7] still worth to be investigated.

At any physical or (bio)chemical situation, it has been widelyaccepted that the presence of a hydrophobic surfacewill have a stronginuence in the structure and dynamics of water, especially ofinterfacial molecules, compared to those of the bulk liquid. Never-theless, in a liquid phase the inuence of hydrophobicity will affectnot only the nearest local environment but several molecular shells,getting deep enough to modify properties of water in the bulk phase.This fact was already analyzed in previous communications for waternearby a hydrophobic surface at room temperature[8] and at hightemperatures[9]. In this paper, we will compare a wide variety ofthermodynamical states, including supercritical states, since the studyof supercritical water (SCW) at interfaces is a hot topic, with specialrelevance for elds of technological interest, such as the treatment oforganic wastes[10]or in the generation of power in nuclear reactors

[11]. A Monte Carlo study of water adsorbed in porous carbons,including experimental measurements was reported by Striolo et al.

[12]for sub-critical temperatures between 298 and 600 K.This contribution will investigate the structure, dielectric permit-tivity and microscopic dynamics of sub- and supercritical waterconned in a slit pore formed by two parallel graphene sheets at axed distance. The study of water in carbon pores with graphite-likesurfaces has been recently carried out by means of Monte Carlo[13,14]and Molecular Dynamics (MD) simulations[15]. Connementeffects due to carbon and silica walls have been recently studied byArgyris et al.[16]. We will describe the molecular models employedand computational details of the simulations in Section 2, then wewillreport and analyze the set of results in Section 3to draw the mostrelevant conclusions inSection 4.

2. Computational details

We consideredNwater molecules embedded into two at parallelgraphene plates with no defects, in order to model single sheets ofhighly oriented pyrolytic graphite (HOPG). The two graphene layerswere placed along the XYplane. Our simulation box lengths in thexand y directions were of 34.4 and 34.1 , respectively. These valuescorrespond to the geometry of HOPG measured in experiments [17].We assumed the z coordinate to be perpendicular to the graphenelayers, with a constant distance between the two graphene plates setup to 31 . The usual periodic boundary conditions were consideredonly in thex andy directions. The temperature of the system varied inbetween 298 K (ambient conditions) and 673 K (supercritical states).

Journal of Molecular Liquids 153 (2010) 7278

Corresponding author.E-mail address:[email protected](J. Mart).

0167-7322/$ see front matter 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.molliq.2009.09.015

Contents lists available at ScienceDirect

Journal of Molecular Liquids

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A different number of molecules were considered, ranging fromN=100 to 1089, to cover a wide set of densities, from =0.08 to1 gcm3. Full details of the molecular dynamics (MD) simulations,including temperature, density, particle number and effective atomiccharges are presented inTable 1.

Waterwater interactions, including intramolecular forces, weremodeled by means of a exible simple-point-charged (SPC) potential,which was specically reparameterized to reproduce the positions of

the main bands of the experimental infrared spectrum of liquid waterat ambient conditions[18]. This potential model has a critical point(Tc= 643 K, c=0.32 gcm

3), which is markedly close to theexperimental one (Tc=647 K, =0.322 gcm

3)[19]. Nevertheless,we should point out that connement may signicantly alter thelocation of a critical point, up to the point that the mere existence ofsuch critical point is unclear[20,21].

Watercarbon forces were assumed to be of Lennard-Jones type,with the same parameterization employed in previous studies ofwater in carbon nanotubes [22,23], near graphite [24] or in a grapheneslab [8,9,25]. Concerning effective atomic charges for this watermodel,we should emphasizethat they were parameterized to work atambient conditions, leading to an averaged molecular dipole momentof water of 2.44D[26]. However, the molecular dipole moment ofwater in the gas phase is about 1.85 D, a much lower value. For thisreason, when we are interested in the simulation of low densitysupercritical states, values of effective charges must be reduced (seeref. [27] for more details). The set of atomic effective chargesemployed in this work is reported inTable 1.

To carry out the simulations we employed the integrationalgorithm of Berendsen et al. [28]with a time step of 0.5 fs and athermal bath coupling parameter of 10 fs. Short-ranged forces weretruncated at half the box length and the Ewald summation techniquewas applied to account for the long-ranged Coulomb interaction.It should be pointed out that when one deals with systems possessing2-dimensional periodicity, the treatment of long-ranged interactionsis a delicate issue[29]. The correct way to introduce Ewald sums inconned systems where a given direction is constrained is through a2Dversion of the method, as it was proposedby Heyes et al. [30],orby

Hautman and Klein[31], among others. Nevertheless, the use of the3D Ewald sum routine with elongated box length in the constraineddirection is equivalent to the 2D versions indicated above, as it hasbeen demonstrated by Spohr [32]. This author proved that theenlargement of thezcoordinate of the simulation box by at least vetimes those of thexand ydirections produces results asymptoticallyequivalent to those from the 2D version. In the present work, we setup the z-direction box length to 170 and employed the usual 3D

Ewald routine. Finally, each run consisted of an initial equilibrationperiod of 50 ps and a production period of 300 ps to collectstatistically meaningful properties.

3. Results

3.1. Density proles

Snapshots of typical MD con

gurations are depicted in Fig. 1. Therewe can observe how density plays a crucial role in determining thestructure of the system: we can deal with packed systems, i.e. in thewhole temperature range (298673 K) and at densities larger than0.5 gcm3, systems are occupying the full available space. Mean-while states at low density, say below 0.3 gcm3, show gas-likestructures mostly formed by water monomers together with smallwater clusters composed by a few H-bonded molecules.

We will investigate the structural organization of our system bymeans of oxygen density proles along thezcoordinate, displayed inFig. 2. We compared the reference oxygen density prole at ambientconditions versus a set of proles obtained at selected thermody-namical states. These proles are qualitatively similar to thosereported by Cicero et al. [33] by means of rst principle MDsimulations at 400 K and by Brovchenko et al. [34]at temperaturesaround 600 K.

A typical depletion layer of excluded volume (width 2.5 ) isobserved at the two interfaces, in good agreement with ref.[33]. Thisis a region characteristic of water near hydrophobic surfaces, as it wasobserved in other studies (see for instance refs.[16,35]). At rst sight,we observe two distinguishable classes of regions existing at allthermodynamical states: interfaces and bulk-like regions. The formerare well dened as thin layers with a width of2.5 , besides thegraphene sheets, whereas the rest of the system can be roughlyconsidered bulk-like[36].Hence, we assumed that water moleculeslocated at z


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additional angular cut-off is appropriated when the selection ofparticular congurations, say linear HB, is in order. In the presentwork it was chosen to be of 30. Other authors [38]have reportedresults where several classes of HBs can be distinguished, but this is

out of the scope of this work.As it can be seen fromFig. 3, the number of hydrogen bonds per

moleculenHB(z) as a function of the thermodynamical state reveals ahuge HB destruction as temperature increases. This is a well knownfeature since at high temperatures, still in a condensed phase, waterstructure is basically formed by monomers, dimers and small clusters,whereas in steam hydrogen bonds have mostly disappeared [39]. Atambient conditions, our model produced an amount of3.55 HBs permolecule in a bulk-like region, compared to the value of 3.7 [27]obtained for unconstrained bulk water modeled with the same model.At interfaces, the amount of hydrogen bonding decreases to valuesbetween 33.5 HBs per molecule, due to the particular orderinginduced by the hydrophobic surface, as it has been explained above.

The increase in temperature produced smaller amounts of HBs,

both at interfaces and in the central areas of the system. In all cases,

thepresenceoftheconning walls reducedthe amount of H-bondingobtained without connement:for instance, at thestate of 673 K and0.66 gcm3 we collected1.75 HBs per molecule, comparedto 2.1 inthe unconstrained bulk system[27]. In all cases but at the lowest

density at the supercritical isotherm (=0.08 gcm3

), hydrogenbonding at interfaces is about 715% lower than at bulk-like regions.The reason is the orientational order induced by the graphenesurface,which forces partof thehydrogen atoms to point out towardsthe wall (dangling HBs). Finally,the supercriticalstate at 0.08 g cm3

has a at prole, indicating the existence of few dimers and amajority of water monomers, very close to the structure of watersteam.

3.3. Dielectric permittivity

The relative dielectric permittivity (called static dielectric constantas well) 0controls the dielectric solvent behavior and the possibilityof salts to ionic dissociation, so it is very useful to describe dielectric

properties of a liquid. For a system with long range interactions,

Fig. 1.Snapshots of the simulation box with the water molecules and the graphene walls at different temperatures and densities: (a) 298 K, 1 gcm3; (b) 473 K, 0.863 gcm3;(c) 673 K, 0.66 gcm3; and (d) 673 K, 0.08 gcm3.

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treated through the Ewald sum rule, with conducting boundaryconditions0is given by[40,41]:

0= 1 + 4NM2

3VkBT ; 1

Nbeing the number of water molecules, Vthe accessible volume, kBtheBoltzmann constant and

Mt= Ni = 1itthe total dipole moment

of the system. Here t is the molecular dipole moment of water.Brackets indicate statistical average over independent congurations.

Our results for 0 as a function of temperature and density aredisplayed in Fig.4, where we used logarithmicaxis for0, since therangeof values covering ambient, sub-criticaland supercritical statestogetherisverywide.Itiswellknown[42] thatpermittivity of SCWis in therange

of1025, somewhat lower than that of sub-critical ambients. The valueof0obtained with our model revealed to be in good agreement withexperimental data when bulk unconstrained water is considered[41].Now, under connement new features will appear, since two classes ofwater and, correspondingly, two values of permittivity arise; one forinterfacial water and a second one for bulk-like water.

As a general feature, permittivities of interfacial water are largerthan those of water at the bulk-like regions. This nding agreesqualitatively well with the results reported by Ballenegger andHansen [43] for slab and spherical geometries, who observed ageneral increase of permittivity when moving from bulk-like tointerfacial regions. The explanation of this fact can be twofold: on onehand, it may be due to a larger extent the orientational order at theinterface, as it was pointed out above, and on the other hand, to thelarge uctuations of the electrostatic potentialbesides the two watergraphene interfaces (seeFig. 5b of ref.[9]).

Ourselection of representative statesreveals twokinds of regimes:a quasi-linear behavior for sub-critical states (between 298 and633 K), which in linear axis corresponds to a quasi-exponentialregime and a pure linear behavior for SCW states. A quasi-exponential

dependence of0as a function of density was also observed in SCW[41]. It should be pointed out that at low density SCW permittivitytends to be extremely small (below 1), since we are very close to gas-like ambients, where microscopic structure is basically the same forwater molecules belonging to the interfaces and for those located in

Fig. 2.Oxygen density proles for supercritical and liquid water for a set of selectedthermodynamical states.

Fig. 3.Number of hydrogen bonds per water molecule in several sub- and supercritical

states.

Fig. 4. Static dielectric constant of water 0 at several temperatures for water atinterfaces and in bulk. Dashed lines are simply an aid to the eye.

Fig. 5.Normalized residence times of water molecules in a variety of states and inselected regions: interfaces and bulk. Arrow indicates decreasing densities (0.66, 0.33

and 0.08 gcm3

) for SCW states.

75J. Mart et al. / Journal of Molecular Liquids 153 (2010) 7278


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the bulk-like region. As density rises, structure tends to beprogressively more complex, including trimers and short waterchains, leading to different values for 0in the two water sets.

3.4. Residence time of water molecules in selected regions

A way to measure characteristic times for a microscopic process isby means of the so-called residence time. In the case of water, itsresidence time in a given sub-system is dened as the time spent by awater molecule in such particular space beforemoving away. As it wasdened by Impey et al. [44], the residence time can be computedallowing multiple re-entrance of water moleculesuntil they denitely

leave the given region for a period of time of innite

length.However, for practical purposes such innite length in timeis taken tobe of the order of picoseconds. We will analyze its behavior throughthe results reported inFig. 5.

We have computed the values offor water for the interfacial andbulk-like water classes. Such raw values do not take into account the

huge difference in size between the two regions: interfaces have a zspan of about 2.5 whereas the bulk-like region is about an order ofmagnitude longer. We can take this fact into account by normalizingwith the width of the considered zone, obtaining a parameter nearlyindependent of the size of the water slab. This is the normalizedtime presented in Fig. 5. There we can observe an enormous differencefor computed at room temperature (22 psat the interface,8 ps inthe bulk) and the corresponding values at high-temperature states

(1

6 ps). Further, as temperature increases does not changesignicantly, being almost constant in SCW, in the range of 24 psfor both interfacial and bulk-like water, regardless of density. Insummary, normalized residence times of water at interfaces arehigherthan those in bulk at sub-critical conditions, whereas they tendto even decrease as temperature rises towards SCW.

3.5. Translational water diffusion

Transport properties of liquids such as molecular diffusion maysuffer considerable variations from those of the unconstrained liquidbulk when the liquid is conned in restricted geometries. Thesechanges have been observed in the particular case of liquid water [37]and they are different for interfacial and bulk-like areas[45]. In this

work, we report results from calculations of the translational self-diffusion coefcientDOof oxygens for water at interfaces and in bulk.We considered diffusion coefcientsonly for oxygens, since thecenterof mass of the water molecule is roughly located on the oxygen site.All DO were calculated by means of time integration of the oxygenvelocity autocorrelation functions. This kind of calculation makessense because we can safely dene atomic velocity autocorrelationfunctions (length of 1 ps) in the limited regions during the timeinterval indicated by the residence times presented in Fig. 5(morethan 2.5 ps in all cases). As it was observed by Berne et al. [46], thecalculation of the self-diffusion tensor of liquids with a gasliquid orsolidliquid interface by means of the standard method of the meansquare displacement of oxygens is not valid for systems withinterfaces or for conned uids.

The results are presented inFig. 6in semi-logarithmic axis. There,we can distinguish between sub- and supercritical states, which canbe associated with two different regimes: for the rst group, a quasi-linear dependence ofDOof temperature is observed, what becomesquasi-exponential in linear axis. Then, an Arrhenius-like behavior canbe deducted. For SCW states, the dependence ofDO of density (we

Fig. 6.Self-diffusion coefcients of oxygensDOfor a variety of thermodynamical statesand in selected regions: interfaces and bulk. Arrow indicates decreasing densities forSCW states (full set of densities reported inTable 1,from 0.66 to 0.08 gcm3). Dashedlines are simply an aid to the eye.

Fig. 7. Spectral densities of hydrogen atoms SH() at several thermodynamic

conditions. Fig. 8.Spectral densities of oxygen atomsSO() at several thermodynamic conditions.



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have simulated the supercritical isotherm at 673 K) is roughly linear.The model employed here rendersDO=2.510

5cm2/s for water atambient conditions and DO=39.410

5 cm2/s at 673 K and0.66 gcm3 [27], in good qualitative agreement with experimentaldata [47] obtained by Lamb et al. by means of NMR-spin echotechniques. Assuming that our model can fairly reproduce the mainfeatures of water diffusion in a wide range of temperatures for bulksystems, we will focus our discussion on the inuence of connement.

From a general point of view, we observe that water inside thegraphene slab shows a tendency to diffuse faster than at uncon-strained conditions and that, in all cases, diffusion of water atinterfaces is slower than that of water in the central bulk-like regions.As a possible cause of such behavior, we can mention the fact thatdiffusion in water within slabs is basically due to molecular motionsalong planes parallel to the walls, since diffusion coefcients ofinterfacial water computed separately for the parallel (xy) andperpendicular to the surface (z) directions revealed Dxy > Dz in allcases[45].In SCW states, connement tends to further increase waterdiffusion, regardless of the location of the water molecules in thesystem (either interfaces or bulk region). Further, we can see thatwater at low densities diffuses much faster than in closely packedsystems, as expected. This is in good agreement with the neutronscattering data of Tassaing and Bellissent-Funel[48], both concerningthe reported values ofDOand to the density effect.

3.6. Atomic spectral densities

Dynamics of liquidsis usually studied by spectroscopical techniques,such as Raman or infrared spectroscopy. In the case of water, a widefrequency range has been analyzed from a long time ago[39,49,50]. Inthis work, our aim is to give a survey of the most remarkable changesoperated in the infrared region of water spectra when hydrophobicconnement and variable thermodynamical states are considered. Thepotential model employed in the present calculations containsinteraction terms between internal degrees of freedom of the watermolecule, and it has been appropriately adjusted to render a goodagreement with the location of band maxima obtained in experimental

measurements [18]. The physical property which hasdirectrelationshipwith the experimental data is the spectral density of hydrogen atoms SH()[51]. Its calculation is usually performed Fourier-transforming thehydrogen velocity autocorrelation functions vHtvH0, where theaverage should be done over a set of congurations computed atdifferent times along an equilibrated trajectory.

Our results for SH() are reported inFig. 7, where we comparedambient to sub- and supercritical states. The spectral range consideredmay be divided into three parts: librational motions (1001000 cm1),bending vibrations (12002000 cm1) and OH-stretching vibrations(30004000 cm1). At the lowest frequency range, the constant red-shiftof the single band maxima is the main feature observed. The trivialinterpretation of such frequency displacement is the slowdown ofmolecular rotational motions when temperature increases and density

decreases. In second term, no signicant differences appear when highand low density SCW states are considered. Our results are in fairagreementwith thoseof Tassaing and Bellissent-Funel[48], obtained bymeans of neutron scattering experiments, who reported a bandmaximum around 240 cm1 (30 meV), for bulk SCW at 653 K and adensity of 0.59 gcm3. This indicates that inuence of connement isplaying a secondary role, and that the main cause of thereductionin thefrequency of rotational molecular motions must be charged totemperature and density variations.

When the bending region is considered, the most relevant featureobserved is a red-shift of about 140 cm1 between ambient and lowdensity SCW conditions, and the splitting of the main band into twoparts for the supercritical state at lowest density. The former effect canbe properly explained if we take into account the progressive change in

the water structure when we move from ambient to SCW states, i.e. the

evolution from dense, packed structures towards gas-like ones, whichnormally show lower bending frequencies [52]. Thelatter effectis quitehard to explain from ourndings, and it may be attributed to thepoorerstatistics collected at very low densities, which produced a biggeramount of uncertainty in the calculation of the spectral density. A nalremarkconcernsthe value of thered-shift in thebending regionfor SCWat low densities: an experimental value of about 3040 cm1 has beenreported by Tassaing et al. through infrared absorption spectroscopy

measurements [53], i.e., about three times lower than the shift observedin the present work. It makes sense to think that theexible SPC modelemployed in thepresent work tends to overemphasizethe magnitudeoffrequency shifts associated with bending vibrations.

In thefrequency rangecorrespondingto theOH-stretchingvibrationswe observe a qualitatively different behavior, namely blue-shifts forrising temperaturesfromambientto SCWstates, having the largestvaluein the case of SCW at 0.08 gcm3. From the experimental side, neutronscattering measurements by Ricci et al. [54] reported blue-shifts ofsimilar magnitude in unconstrained SCW at 673 K and the high-densityof 0.66 gcm3. More recently, Tassaing et al.[53]reported blue-shiftsclose to those presented in the present work by infrared spectroscopy ina wide study covering a wide variety of thermodynamical statesincluding SCW (298653 K). In the two experimental works, all datasets were obtained for liquid and SCW in bulk with no conningboundaries. In the case of water at interfaces, Gilijamse et al. [55]reported spectra of water dissolved in acetone and CCl4measured byfemtosecond mid-infrared pump-probe experiments, reporting a blue-shift of the OH-stretching main band of about 150 cm1, which is quitecloseto thevalues obtainedin thepresentwork.Fromthe computationalside,TummalaandStriolo[56] mimicked theexperiments of Gilijamseetal. [55], obtaining similar values to those reported in this work. All thesendings are not surprising if we keep in mind that the analyzed statespresent microscopic structures close to those of water steam, where theOH-stretch main band is in the range of 3700 wavenumbers[52].

The low-frequency range between 0 and 400 cm1 can bebasically associated to intermolecular vibrations of water inside theshell of their rst neighbors, either driven by HBs or simply restrictedby the presence of other molecules, which is usually calledcage effect

orrattling in a cage[49]. Such motions can be inspected by means ofthe spectral densities of oxygens, obtained by Fourier-transformingthe atomic oxygen velocity autocorrelation functionsSO()[18]. Ourresults are presented in Fig. 8 for a variety of states including low- andhigh-density SCW states. The main features observed at ambientconditions are a maximum of about 50 cm1 (associated to hinderedtranslations of water in the cageformed by its local environment) anda shoulder of about 220 cm1, which have received differentinterpretations[57], but our point of view is that it has to see withhydrogen-bond-stretch vibrational motions. What happens to SO()when we move from 298 K to the 673 K supercritical isotherm is ageneral weakening of the two main features. First, the low-frequencyband has already vanished at 473 K, leading to the practicaldisappearance of such kind of restricted motions in a cage and

directly related to the loss of structure of water at high temperatures,as reported above (Figs. 2 and 3). In intermediate states between 298and 473 K, the red-shift of this band has been reported[58].Second, aclear weakening of the high-frequency shoulder of about 220 cm1 atroom temperature, which is hardly seen at 473 K and it has fullydisappeared already at 633 K. The physical interpretation is straight-forward, i.e., the absence of intermolecular vibrations mediated viaHB at states above 473 K due again to the loss of structural order.

4. Concluding remarks

A series of molecular dynamics simulations of water conned ingraphene slabs in a wide range of thermodynamical states have beenperformed and analyzed. The potential model has been a exible SPC

potential, able to fairly reproduce the main features of the infrared

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spectrum of liquid water at ambient conditions. Since this model wasinitially set up to model microscopic structure and dynamics of liquidwater at room temperature, subtle corrections of the effective atomiccharge set and, consequently, of the molecular dipole moment wererequired in order to model high-temperature and supercritical waterstates in a constrained geometry. In all states watercarbon forceshave been accounted by means of a 612 Lennard-Jones model. Theproperties under investigation have been structure and hydrogen

bonding, dielectric permittivity and dynamical properties such asresidence times of water in selected regions, translational diffusioncoefcients and spectral densities of hydrogen and oxygen atoms.

Structural organization of water molecules was inspected fromdensity proles of oxygens and revealed two groups of molecules todistinguish: those pertaining to a central, bulk-like region between 5and 25 , containing roughly about 80% of all molecules (in all cases)and a second group composed by water molecules nearby the twointerfaces, i.e., havingz5 orz25 , corresponding to about 20% ofthe total amount of water in all cases. Density proles show a markedtendency of interfacial regions to vanish as temperature increases anddensity decreases. In parallel with this, HBsare systematically destroyedas temperature rises, leading to dilute systems composedby monomersand a few remaining dimers at low density SCW. This effect is commonto interfacial and bulk-like water. Permittivity spans a wide range ofvalues, from85 for water near graphene sheets at ambient conditions toless than 1 for SCW at low densities.

A parameter useful to indicate the persistence of a water moleculein the selected regions indicated above (interfaces, bulk-like) is theresidence time of water. We considered such time divided by the sizeof theconsidered region, which makes it nearlysize-independent.Ourresults indicate that water molecules spend between 2.53.5 ps inSCW, regardless of its location, but when temperature diminishesresidencetimesbecome largerand show a tendency to grow up fast toreach values bigger than 20 ps for interfacial water at 298 K. Waterself-diffusion coefcientsD behave differently whether we considersub- or supercritical states. In theformer case, we found an Arrhenius-like dependence of temperature, whereas in the latter caseD(T)T.Diffusion coefcients in SCW are much larger at low than at high

densities, following the behavior observed in the bulk unconstrainedsystems[27,47]. It is important to remark that diffusion of water atinterfaces has been monitored and observed to happen along planesparallel to the graphene walls.

From spectral densities of hydrogen atoms we have inspected themid-infrared frequency region of water for a variety of thermody-namical states. Two types of features were observed: (1) red-shifts offrequency maxima have been obtained in both librational (associatedto molecular rotations) and bending regions; (2) blue-shifts of themain band maxima were found in the OH-stretch region. Thesefrequency shifts are in qualitative good agreement with availableexperimental data and they are mostly related to temperature anddensity changes, whereas connement effects were revealed to be ofminor inuence. Finally, the study of intermolecular vibrations in the

range of 0400 wavenumbers revealed a drastic destruction, by theeffect of increasing thermal energy, of the two most important modes,namely the one corresponding to restricted translation of a watermolecule in the cage of itsrst neighbors (50 cm1 at 298 K) and themode located about 220 cm1 at ambient conditions, which is usuallyassociated to stretching of hydrogen-bonded dimers.

Acknowledgements

The authors gratefully acknowledge nancial support from theGeneralitat de Catalunya (Grant 2005SGR-00779) and from the

Ministerio de Ciencia e Innovacion of Spain (Grant FIS2006-12436-C02-01). J.S. is a recipient of a FPI Spanish fellowship.

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molecular dynamics simulations of water conﬁned in graphene nanochannels

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