Dynamics of water molecules at liquid–vapour interfacesof aqueous ionic solutions: effects of ion concentration

Sandip Paul, Amalendu Chandra *

Department of Chemistry, Indian Institute of Technology, Kanpur 208016, India

Received 3 December 2002; in final form 29 January 2003

Abstract

The dynamical properties of water molecules at the liquid–vapour interfaces of aqueous NaCl solutions are studied

by means of molecular dynamics simulations. The diffusion coefficients and the orientational relaxation times of the

interfacial molecules of pure water and also the effects of ion concentration on these interfacial dynamical properties of

aqueous solutions are investigated and the results are compared with those of the corresponding bulk phases. The

inhomogeneous density, anisotropic orientational profiles and the surface tension are also calculated in order to

characterize the location, width and the thermodynamic aspects of the interfaces and to explore their effects on the

dynamical properties.

� 2003 Elsevier Science B.V. All rights reserved.

1. Introduction

The microscopic structure and dynamics of

aqueous solutions at liquid–vapour interfaces havebeen a subject of great interest in recent years.

Studies of these interfacial systems are important

not only in chemistry and biology but also in the

areas of environmental and atmospheric sciences.

Earlier experimental studies on liquid–vapour in-

terfaces primarily focused on thermodynamic

quantities such as the surface tension and surface

potential which could provide only a macroscopicdescription of these interfaces. More recent ex-

perimental techniques such as surface second

harmonic [1] and sum frequency generation [2,3]

methods can now provide more detailed molecular

level information of the structure and dynamics ofliquid–vapour interfaces. For aqueous systems,

these techniques have been used rather extensively

in recent years to find the orientational profiles

and kinetics of various chemical processes at air–

water interfaces [1–13]. Many of these properties

have also been investigated by means of molecular

dynamics simulations [14–24]. However, very little

is known about the molecular behaviour of liquid–vapour interfaces of concentrated aqueous solu-

tions of soluble inorganic salts. Only very recently,

a few molecular dynamics studies have considered

the structural aspects of the liquid–vapour inter-

faces of aqueous alkali halide solutions [21–24].

However, the dynamical properties of the inter-

Chemical Physics Letters 373 (2003) 87–93

www.elsevier.com/locate/cplett

* Corresponding author.

E-mail address: amalen@iitk.ac.in (A. Chandra).

0009-2614/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0009-2614(03)00537-2

faces such as the diffusion and orientational re-

laxation of interfacial water molecules have not

yet been investigated for these solutions. The im-

portant issues are the differences between the

interfacial and bulk dynamics at a given ion con-

centration and also the effects of ion concentrationon the dynamical behaviour of such interfaces as

compared to those of the bulk phases. We address

these issues in this Letter by means of molecular

dynamics simulations.

In the present work, we have carried out mo-

lecular dynamics simulations of liquid–vapour in-

terfaces of aqueous NaCl solutions at varying

concentrations. The main focus has been to cal-culate the dynamical properties of the interfacial

water molecules. We have, however, also calcu-

lated the density and orientational profiles and the

surface tension of these systems as the dynamical

properties of the interfaces are intimately related

to these equilibrium quantities. Also, the density

profiles help us to characterize the location and

thickness of the interfaces. The details of the sim-ulations including the construction of the inter-

faces and their characterization in terms of density

profiles are presented in Section 2. In Section 3, we

have discussed the simulation results of the dy-

namics of the interfaces and our conclusions are

briefly summarized in Section 4.

2. Details of simulations and construction of the

interfaces

In this work, we have carried out molecular

dynamics simulations of liquid–vapour interfaces

of pure water and aqueous NaCl solutions of three

different concentrations: 2.1, 3.15 and 4.3 m

(m¼molal). The water molecules are character-ized by the SPC/E potential [25] and the sodium

and chloride ions are modeled as charged Len-

nard–Jones particles [26–28]. In these models, the

interaction between atomic sites of two different

molecules or ions is expressed as

uabðra; rbÞ ¼ 4�abrab

rab

� �12"

� rab

rab

� �6#þ qaqb

rab;

ð1Þ

where rab is the distance between the atomic sites

or ions a and b and qa is the charge of the ath atom

(or ion). The Lennard–Jones parameters rab and

�ab are obtained by using the combination rules

rab ¼ ðra þ rbÞ=2 and �ab ¼ ffiffiffiffiffiffiffiffi�a�b

p. The values of

the potential parameters qa, ra and �a for water

and Naþ and Cl� are available, for example, in

[29].

For each system, we first carried out a bulk

simulation in a cubic box of 864 molecules in-

cluding water and ions, periodically replicated in

all three dimensions. The box length L was ad-

justed according to the experimental density of thebulk solutions. After this bulk solution was prop-

erly equilibrated, two empty boxes of equal size

were added on either side of the original simula-

tion box along the z-dimension and this larger

rectangular box of dimension L� L� Lz with

Lz ¼ 3L was taken as the simulation box in the

next phase of the simulation run. The system was

reequilibrated by imposing periodic boundaryconditions in all three dimensions. This resulted in

a lamella of approximate width L separated by

vacuum layers of approximate width 2L. Some of

the water molecules were found to vapourize to the

empty space to form liquid–vapour interfaces on

both sides of the lamella. In Table 1, we have in-

cluded, for each system, the number of sodium and

chloride ions and water molecules and also thelengths of the simulation box along x and z di-

mensions. In all simulations, the long-range elec-

trostatic interactions were treated by using the

three-dimensional Ewald method [30]. The short-

range Lennard–Jones interactions were calculated

by using a spherical cut-off at distance L=2. We

employed the quaternion formulation of the

equations of rotational motion [30] and, for theintegration over time, we adapted the leap-frog

algorithm with a time step of 10�15 s (1 fs). MD

runs of 300 ps were used to equilibrate each system

in the bulk phase and then MD runs of 400 ps were

used to equilibrate each of the liquid–vapour in-

terfacial systems in rectangular boxes. During the

equilibration, the temperature of the simulation

system was kept at 298 K through rescaling of thevelocities. The simulations of the interfacial sys-

tems were then continued in microcanonical en-

semble for another 600 ps for the calculation of

88 S. Paul, A. Chandra / Chemical Physics Letters 373 (2003) 87–93

various structural and dynamical quantities of theinterfaces.

The density profiles of water and ions for the

4.3 m solution are shown in Fig. 1a. Other systems

show similar density profiles and hence are not

shown here. Following previous work [17], we

define the intrinsic thickness (dlv) of a liquid–

vapour interface as the distance over which the

number density decreases from 90% to 10% of thebulk liquid density. It is seen from Table 1 that

the thickness of the interfaces decreases with

increase of ion concentration. This decrease of

interfacial width can be attributed to the presenceof ions in the liquid region which exert attractive

forces on the interfacial water molecules and is

consistent with an increase of surface tension that

we have observed in this study and also found

experimentally on increase of ion concentration.

We calculated the surface tension by using the

following virial expression which is obtained from

the well-known Kirkwood–Buff theory [31]

c ¼ 1

2A

Xi<j

Xa;b

ouab

orab

1

rabrij � rab

�"*� 3zijzab

#+;

ð2Þwhere uab is the interaction energy between sites aand b on molecules i and j, rij and zij are the centresof mass distance and the distance along z directionbetween molecules i and j and rab and zab are the

corresponding distances between sites a and b. A is

the total surface area which is equal to 2L2. We

calculated the quantity within the third brackets in

the above expression at each MD step and it wascombined with a long-range correction calculated

at each step for the contribution from the Len-

nard–Jones interaction beyond the spherical cut-off

[32] and finally the averaging was done over the

total number of MD steps that were run during the

production phase of the simulations. The average

values of the calculated surface tension of pure

water and the ionic solutions are included in Table1. The standard deviations of the surface tension

data, which were calculated by using block aver-

ages over 100 ps, are about 8% of the average

values reported in Table 1. For pure water, our

calculated value of the surface tension compares

well with the values of 65–66 reported by Taylor

et al. [17] at 298 K for two different system sizes and

also by Alejandre et al. at 328 K [19]. For aqueous

Fig. 1. (a) The number density of water molecules (solid), so-

dium (dashed) and the chloride (dotted) ions for the 4.3 m

aqueous NaCl solution. (b) The probability function of the

orientation of water dipole vectors in the interfacial (dashed)

and bulk (solid) regions. h is the angle between the water dipole

vector and the surface normal.

Table 1

The number of sodium ions (Nþ), chloride ions (N�) and water molecules (Nw), length of the simulation box along x; y (L) and z (Lz)

directions, intrinsic thickness of the liquid–vapour interface (dlv) and the surface tension (c) for each of the systems studied in this work

Concentration

of NaCl

Nþ N� Nw L (�AA) Lz (�AA) dlv (�AA) c

Pure water 0 0 864 29.558 88.674 3.4 69.5

2.1 m 30 30 804 29.227 87.681 3.05 72.0

3.15 m 44 44 776 29.156 87.468 2.95 74.0

4.3 m 58 58 748 29.01 87.03 2.85 75.6

S. Paul, A. Chandra / Chemical Physics Letters 373 (2003) 87–93 89

NaCl solutions, the surface tension is found to in-

crease with increasing ion concentration which is in

good agreement with the known experimental re-

sults [33]. The results of Fig. 1b will be discussed in

Section 3 in the context of orientational relaxationin the bulk and interfacial regions.

We note in this context the recent work of

Jungwirth et al. [21–23] and also of Stuart et al.

[24] on the density profiles of halide ions at the

liquid–vapour interfaces of aqueous ionic solu-

tions. In these work, the polarizable force fields

were used for the ions and water molecules and it

was found that the flouride ions stay mainly in thebulk liquid region, chloride ions stay both in the

liquid and also at the interfaces whereas the bro-

mide and iodide ions were found to act as surf-

actants [23]. This different behaviour of the anion

density profiles was attributed to the varying de-

gree of polarizability of the halide ions. In the

present work, we have used nonpolarizable force

fields and that could be the reason of our notfinding a significant density of the chloride ions at

the surface region. However, the effects of polar-

izability was found to be particularly important

for the bromide and iodide ions than the chloride

ions. For example, the density of chloride ions in

the interfacial region was found to be significantly

lower than that in the bulk solution even after

including the polarization effects [21–23]. Also, in[24], the polarizable chloride ion was always found

to have a full solvation shell. Even when it ap-

proached the interfacial region, it maintained its

solvation shell beneath the surface.

3. Dynamics of water molecules at interfaces

The main objective of this section is to study the

effects of ion concentration on the dynamics of

interfaces and to see how much the dynamics of

interfaces is different from that of the corre-

sponding bulk phases. We denote the ath compo-

nent of velocity of a water molecule by vaðtÞ(a ¼ x; y; z) and its normalized autocorrelation

function Cv;aðtÞ is defined by

Cv;aðtÞ ¼hvaðtÞvað0Þi

hv2ai; ð3Þ

where h� � �i denotes an equilibrium ensemble av-

erage. In Fig. 2a, we have shown the decay of the

parallel (x) and perpendicular (z) components of

the velocity–velocity autocorrelation function of

interfacial water molecules. In these calculations,the average of Eq. (3) is carried out over those

molecules which are found in the interfacial region

at time 0 and also at time t. The results of the

velocity relaxation of bulk water molecules are

also shown in this figure. The results shown here

are for the liquid–vapour interfaces of the 4.3 m

solution, similar results were also found for other

systems studied here. For interfacial molecules, thetwo components of the velocity autocorrelation

function are seen to decay differently which clearly

show the anisotropic nature of the translational

dynamics. It is also found that, upto about 0.2 ps,

both the parallel and the perpendicular compo-

nents of the velocity autocorrelation function of

interfacial molecules decay at a slower rate than

that of the bulk water molecules in the liquidphase. This slower velocity relaxation of interfacial

molecules manifests a reduced collisional effect at

Fig. 2. (a) The time dependence of the x (dashed) and z (dotted)components of the velocity autoccorelation function of water

molecules in the interfacial region of the 4.3 m solution. The

solid curve show the results for bulk water molecules. (b) The

relaxation of the self dipole correlation function at interfaces

(dashed) and in the bulk phase (solid) of the same solution.

90 S. Paul, A. Chandra / Chemical Physics Letters 373 (2003) 87–93

the interfaces due to their lower density and less

number of hydrogen bonds than that of the bulk

liquid water. The somewhat stronger negative

values of the perpendicular velocity correlation

function in the interfacial region at intermediatetimes show, in most likelihood, the rebounce of

water molecules from the surface in the perpen-

dicular direction. This rebounce occurs due to the

inward pull that the surface molecules experience

because of the presence of larger number of mol-

ecules in the liquid side than that in the vapour

side. We have also calculated the diffusion coeffi-

cient Da (a ¼ x; y; z) from the velocity–velocityautocorrelation function by using the following

relation:

Da ¼kBTm

Z 1

0

Cv;aðtÞdt; ð4Þ

where m is the mass of a water molecule and kB is

Boltzmann constant. The values of Dx and Dz ofinterfacial molecules are included in Table 2. We

note that for interfacial molecules Dx ¼ Dy . In this

table we have also included the diffusion coeffi-

cients of bulk water molecules for which

Dx;y ¼ Dz ¼ D. The faster diffusion in the interfa-

cial region is related to the slower relaxation of the

corresponding velocity correlation which occurred

due to the reduced density and less number ofhydrogen bonds in the former region. The rela-

tively smaller value of Dz than Dx in the interfacial

region originates primarily from the stronger

negative region that we found in the relaxation of

perpendicular velocity at intermediate times.

The orientational relaxation of water molecules

at liquid–vapour interfaces is investigated by cal-

culating the time dependence of the self dipolecorrelation function

ClðtÞ ¼hlðtÞ � lð0Þihlð0Þ2i

; ð5Þ

where lðtÞ is the dipole vector of a water moleculeat time t. The results of ClðtÞ are shown in Fig. 2b

for the 4.3 m solution. It is seen that the orienta-

tional relaxation at the interface occurs at a faster

rate than that in the bulk. Similar results have also

been obtained for other solutions. We define the

orientational relaxation time sl as the time integral

of the orientational correlation function where we

have calculated the integral explicitly upto 4 ps byusing the simulation data of ClðtÞ and the contri-

bution of the tail part is obtained by using the

fitted exponential functions. The results of the

orientational relaxation times are also included in

Table 2. The orientational relaxation time of in-

terfacial water molecules is found to be shorter

than that of bulk water molecules for all the sys-

tems studied here although the difference is moresignificant for the concentrated solutions than

pure water. We note that the density is low in the

interfacial region and also interfacial molecules

essentially do not have any solvation shell on the

vapour side of the interface. Because of these re-

duced density and incomplete solvation effects, a

water molecule in the interfacial region has less

number of hydrogen bonds and experiences lessrotational friction than that in the bulk phase. The

second effect is the orientational constraint which

the water molecules face at the liquid–vapour in-

terface. This is illustrated in Fig. 1b where it is seen

that the water dipoles at the interfaces prefer to

orient parallel to the surface although the proba-

bility maximum at cos h ¼ 0 is rather broad which

means the somewhat tilted orientations of thewater dipoles are also present at the interfaces.

Table 2

Values of the diffusion coefficients and orientational relaxation times in bulk solution and at interfaces

Concentration of

NaCl

D (bulk) Dx (interface) Dz (interface) sl (bulk) sl (interface)

Pure water 2.65 4.70 2.90 3.90 3.80

2.1 m 2.05 4.30 2.60 4.55 3.90

3.15 m 1.75 4.05 2.42 4.80 4.10

4.3 m 1.55 3.90 2.15 4.95 4.15

The diffusion coefficients and the relaxation times are expressed in units of 10�5 cm2 s�1 and ps, respectively.

S. Paul, A. Chandra / Chemical Physics Letters 373 (2003) 87–93 91

The bulk molecules do not show any orientational

preference as expected. This orientational struc-

ture imposes a constraint on the rotational motion

of interfacial water molecules. For liquid–vapour

interfaces of aqueous solutions, the effects of re-duced density and less number of hydrogen bonds

prevail and as a result we find an enhanced rate of

orientational relaxation of interfacial water mole-

cules. The more significant difference between the

rates of orientational relaxation of interfacial and

bulk water molecules for concentrated solutions is

due to the greater slowing down of orientational

motion of bulk water molecules as a result of thepreferential presence of ions in the bulk region of

these solutions.

In Fig. 3, we have shown the relative changes of

the diffusion coefficients and orientational relaxa-

tion times with ion concentration. In this figure,

the values of the diffusion coefficients and orien-

tational relaxation times of interfacial and bulk

water molecules of ionic solutions are normalizedby the corresponding values for pure water. It is

seen that the dynamical properties of interfacial

water molecules show a weaker change with ion

concentration than those of bulk molecules. We

note that the density of ions in the liquid region is

significantly higher than that at the interfaces for a

given bulk ion concentration of the ionic solutions.

Also, with increase of bulk ion concentration, the

ion density in the liquid region increases substan-

tially but the increase is much smaller in the in-

terfacial region. Thus, the water molecules in theinterfacial region face a less ionic field and also a

reduced effect of concentration rise for their both

translational and orientation motion. We also find

that the perpendicular diffusion at the interface

depends somewhat stronger on ion concentration

than the parallel diffusion. This behaviour can

again be attributed to the higher density of ions in

the bulk region which drags and enhances therebounce of water molecules from the surfaces in

the perpendicular direction.

4. Conclusion

We have presented molecular dynamics results

for the dynamics of water molecules at liquid–va-pour interfaces of aqueous NaCl solutions of

varying ion concentration ranging from 0 (pure

water) to 4.3 m. The density and orientational

profiles and the surface tension of the interfaces

are also calculated since the dynamics of the in-

terfaces is intimately related to these equilibrium

properties. We found a decrease of the interfacial

width and an increase of the surface tension withincreasing ion concentration. Both these effects are

attributed to a higher concentration of the ions in

the bulk liquid phase than that in the interfacial

region. The water molecules at interfaces are

found to translate and rotate at a faster rate than

that of bulk molecules because of the reduced

density and less number of hydrogen bonds in the

interfacial region. The difference between the ratesof molecular relaxation at interfaces and in the

bulk phase is found to be more significant for the

concentrated solutions which can again be attrib-

uted to the higher ion concentration in the bulk

region that cause a greater slowing down of the

translational and orientational motion of bulk

water molecules. With increase of ion concentra-

tion of the solutions, the ion density in the liquidregion increases substantially but the increase is

found to be much smaller in the interfacial region

Fig. 3. The relative changes of the (a) diffusion coefficients and

(b) dipole orientational relaxation times of water molecules in

the interfacial and bulk regions with increase of ion concen-

tration of the solutions. D0x;z and s0l denote the corresponding

values for pure water.

92 S. Paul, A. Chandra / Chemical Physics Letters 373 (2003) 87–93

or in its vicinity and this causes a weaker depen-

dence of the interfacial diffusion and orientational

relaxation on the ion concentration of the solu-

tions.

The present study of the interfacial dynamics of

aqueous NaCl solutions can be extended in manydirections. For example, it would be interesting to

investigate the dynamics of liquid–vapour inter-

faces of aqueous solutions containing polarizable

bromide and iodide ions which behave as surfac-

tants [23] and thus can modify the interfacial dy-

namics in a different manner. It would also be

interesting to study the dynamics of hydrogen

bonds [34,35] at liquid–vapour interfaces ofaqueous ionic solutions.

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