Molecular dynamics study of n-alcohols adsorbed on an aqueous electrolyte solutionHirofumi Daiguji Citation: The Journal of Chemical Physics 115, 1538 (2001); doi: 10.1063/1.1381056 View online: http://dx.doi.org/10.1063/1.1381056 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/115/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Molecular dynamics study of the n-hexane–water interface: Towards a better understanding of the liquid–liquidinterfacial broadening J. Chem. Phys. 120, 2464 (2004); 10.1063/1.1629278 Molecular dynamics simulations of the adsorption of industrial relevant silane molecules at a zinc oxide surface J. Chem. Phys. 119, 9719 (2003); 10.1063/1.1615491 Static dielectric constant of aqueous electrolyte solutions: Is there any dynamic contribution? J. Chem. Phys. 113, 903 (2000); 10.1063/1.481870 Anomalous conformational behavior of poly(ethylene oxide) oligomers in aqueous solutions. A moleculardynamics study J. Chem. Phys. 109, 8118 (1998); 10.1063/1.477460 A molecular dynamics study of the structure of water layers adsorbed on MgO(100) J. Chem. Phys. 109, 3245 (1998); 10.1063/1.476915

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Molecular dynamics study of n-alcohols adsorbed on an aqueouselectrolyte solution

Hirofumi DaigujiInstitute of Environmental Studies, Graduate School of Frontier Sciences, University of Tokyo,Tokyo 113-0033, Japan

~Received 17 October 2000; accepted 2 May 2001!

The distribution of normal alcohol~n-alcohol! on water and the effect of salt on the structural anddynamical properties ofn-alcohol on aqueous electrolyte solutions were investigated usingmolecular dynamics simulation. The stability of the alcohol distribution was studied for three typesof n-alcohol ~n-propanol, C3H7OH; n-heptanol, C7H15OH; andn-undecanol, C11H23OH), four orfive concentrations of alcohol, and three concentrations of salt. The simulation results reveal thefollowing. The distribution ofn-propanol on water is homogeneous at alln-alcohol concentrationsstudied here and the distribution ofn-heptanol andn-undecanol on water is heterogeneous. Then-alcohol concentration at which fluctuations in the alcohol distribution begin to increase dependson the length of the hydrocarbon chain of then-alcohol. Salt concentration affects the surface excessconcentration ofn-alcohol and the stability of the adsorbed layer ofn-alcohol. The degree of eacheffect depends on the length of the hydrocarbon chain of then-alcohol. Forn-undecanol, the surfacestructure of n-alcohol is independent of salt concentration because interaction between thehydrocarbon chains is sufficiently strong. In absorption refrigeration technology, to enhance theabsorption rate of water vapor into a highly concentrated aqueous electrolyte solution, a smallamount of alcohols is added to the aqueous electrolyte solution, which induces cellular convectionreferred to as Marangoni instability. Among the three types ofn-alcohol studied here, onlyn-heptanol induces strong cellular convection. The simulations reveal two required conditions forMarangoni instability: generation of fluctuations in the alcohol distribution on water, and strongcorrelation between the structural and dynamical properties and salt concentration. Among the threetypes ofn-alcohol studied here, based on the simulations, onlyn-heptanol satisfies both conditions.© 2001 American Institute of Physics.@DOI: 10.1063/1.1381056#

I. INTRODUCTION

The enhancement of interphase mass transfer is a keyissue in liquid–vapor absorption systems and in liquid–liquid extraction systems. A surfactant added to a solutionleads to interfacial turbulence, which increases absorptionrate. In absorption refrigeration technology, LiBr aqueous so-lution is commonly used. To enhance the absorption rate ofwater vapor into ca. 55 wt % LiBr aqueous solution,n-octanol or 2-ethyl-1-hexanol (C8H17OH) is added as a sur-factant to the solution. Our previous experiments show thatas surfactants,n-alcohols with medium-length hydrocarbonchains, such as C7H15OH, C8H17OH, and C9H19OH, aremore effective thann-alcohols with longer- or shorter-lengthhydrocarbon chains.1 From a macroscopic viewpoint, thisdifference in effectiveness can be explained by Marangoniinstability, of which mechanism is that in the transfer of massfrom one phase to another, solute concentration gradients ortemperature gradients can produce surface tension gradients,resulting in cellular convection at the interface.2,3 In the ab-sorption process of water vapor into a LiBr aqueous solutioncontainingn-octanol or 2-ethyl-1-hexanol, a gradient eitherin the alcohol concentration, salt concentration, or tempera-ture can produce a gradient in the surface tension. However,the relationship among these three factors at the liquid–vapor interface is complicated, and the thermodynamic and

dynamic properties ofn-alcohols with medium-length hydro-carbon chains on aqueous electrolyte solutions are not yetclearly understood. The prediction of the thermodynamic anddynamic properties requires an understanding of the molecu-lar level structure of the liquid free surface. The first of twoproblems in understanding this structure is clarifying the dis-tribution of n-alcohols on aqueous electrolyte solutions. Ingeneral, n-alcohols with short-length hydrocarbon chainsmix well with water, whereasn-alcohols with long-lengthhydrocarbon chains do not mix with water, but instead ad-sorb on water. However, the molecular level structure ofn-alcohols with medium-length hydrocarbon chains on wateris not yet clearly understood. In addition, the effect of salt onthe surface structure of alcohols remains unclear. Althoughphysical models of this instability have been proposed from amacroscopic viewpoint,4,5 the mechanism responsible forMarangoni instability can be clarified only if both the distri-bution of n-alcohol on water and the effect of salt on thestructural and dynamical properties ofn-alcohol are clearlyunderstood.

The second problem in understanding the molecularlevel structure is clarifying the generation of fluctuations inthe alcohol distribution on aqueous electrolyte solution. Ma-rangoni instability requires the generation of such fluctua-tions that are due to water vapor absorption. To develop ef-

JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 3 15 JULY 2001

15380021-9606/2001/115(3)/1538/12/$18.00 © 2001 American Institute of Physics

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fective surfactants that induce strong interfacial turbulence,the mechanism and conditions involved in the generation ofsuch fluctuations must be clarified.

The liquid–vapor interfaces of various molecules havebeen studied using molecular simulations.6–8 In the presentwork, molecular dynamics simulations were used to clarify~a! the distribution ofn-alcohol on water,~b! the effect ofsalt on the structural and dynamical properties ofn-alcohol,and ~c! the mechanism and conditions involved in the gen-eration of fluctuations that lead to heterogeneous distributionof n-alcohol on water. The adsorption of three types ofn-alcohol of different lengths of hydrocarbon chain(n-propanol, C3H7OH; n-heptanol, C7H15OH; andn-undecanol, C11H23OH! on water and on LiBr aqueous so-lutions was studied for three salt concentrations is commonlyused in absorption refrigeration technology, was used in thisstudy because the solubility of LiBr aqueous solution is high,about ca. 70 wt % at 373 K, and because the crystallizationof LiBr did not occur in the highest salt concentration stud-ied here.

II. MOLECULAR MODEL AND SIMULATION METHOD

For the three alcohols studied here, the OPLS~optimizedpotential for liquid simulation! models of liquidhydrocarbon9 and liquid alcohol10 developed by Jorgensenwere used. In brief, methyl and methylene units were treatedas united pseudoatoms in which hydrogen molecules werenot explicitly modeled as distinct atoms. All bond lengthswere rigidly constrained to their nominal values. Methyl andmethylene groups were labeledC1 throughCn from the tailgroup, i.e., methyl group, to the head group, i.e., hydroxylgroup. The interaction energy,Eab , between two monomers,a and b, was determined by using Coulomb and Lennard-Jones~LJ! interactions between all intermolecular pairs ofsites as follows:

Eab5(i

on a

(j

on b S qiqje2

r i j14« i j F S s i j

r i jD 12

2S s i j

r i jD 6G D , ~1!

whereqie andqje are the partial charges on united pseudoa-tomsi and j , r i j is the distance between these atoms, ands i j

and« i j are LJ parameters depending on atom type and cal-culated from the combination rules,11 s i j 5(s i i 1s j j )/2, « i j

5(« i i « j j )1/2. The intramolecular potential energy was ex-

pressed by the internal rotational potential function,E(f),and LJ form. For the molecules with a single dihedral angle,the Fourier series in Eq.~2! suffices to describe the potentialenergy for internal rotation:

E~f!5V01 12 V1~11cosf!1 1

2 V2~12cos 2f!

1 12 V3~11cos 3f!, ~2!

wheref is a dihedral angle andVi are Fourier coefficients.n-heptanol andn-undecanol required more complex func-tions because they contained 6 and 10 internal rotations. Thiswas handled by using a Fourier series for each angle plusadditional terms for nonbonded interactions between groupsseparated by more than three bonds. The parameters of in-tramolecular potential functions of the threen-alcohols weredetermined by combining those ofn-alkanes9 andn-propanol.10

For water, the SPC/E model12 was used. The alkali andhalide ions were modeled as LJ spheres with a points chargeat the center.13 The LJ plus Coulomb form potential func-tions were maintained. The parameters of potential functionsare listed in Tables I–V. All bond lengths were rigidly con-strained by using the SHAKE algorithm14,15and electrostaticinteractions were calculated with Ewald method.

In the simulations, the system was enclosed in a boxwhose dimensions wereLx , Ly , Lz with periodic boundaryconditions in all directions. In this box,Lx5Ly525 Å andLz was 4 times larger thanLx andLy to form a rectangularsurface perpendicular to thez axis. Initially, water molecules,or water molecules and ions, were placed at random near thecenter of the simulation box to construct a liquid film, andthen n-alcohol molecules were placed on either side of theconstructed liquid film with hydrocarbon chain axes parallelto the surface of the liquid film, as shown in Fig. 1~a!.

The equations of motion were integrated using the Verletmethod14 with a time step of 1 fs. During the initial 50–200ps of a simulation, the velocity-scaling temperature controlwas used for all molecules until the set temperature of 373 Kwas reached. The velocities of all molecules were rescaledeach 0.1 ps. Figures 1~a!–1~d! show the equilibration pro-cess. After equilibration,n-alcohol molecules were dissolvedin or adsorbed on the water film. Equilibrium was assumedachieved when the time course of the kinetic energy~KE!,potential energy~PE!, and total internal energy~TE! reachedsteady state, as shown in Fig. 2~a!. After equilibration, aNVE simulation was continued for more than 150 ps withoutrescaling. Density, pressure tensors, and energy were mea-sured each 0.1 ps. The density profile, the local surface ten-

TABLE I. Standard geometrical parameters ofn-alcohol.

Bond length,l Å Bond angles,u deg

C–C 1.530 COH 112.0C–O 1.430 CCO 108.0C–H 0.945 CCC 108.5

TABLE II. Values of the charges and the Lennard-Jones parameters for thepseudoatom pair interaction ofn-alcohol.

q s, Å «, kcal/mol

CH3 0.0 3.905 0.175CH2 0.0 3.905 0.118

CH2~COH! 0.265 3.905 0.118O~COH! 20.700 3.07 0.17H~COH! 0.435 0.0 0.0

TABLE III. Values of the Lennard-Jones parameters for the intramolecularinteraction ofn-alcohol.

s, Å «, kcal/mol

C–C 4.0 0.0074C–O~COH! 3.4875 0.0074C–H~COH! 2.6 0.008

1539J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 n-alcohols adsorbed on an aqueous electrolyte solution

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sion profile, and the energies in the simulation box werecalculated using the data of more than 1500 configurations.For all calculation conditions,~a! the average temperatureremained constant without rescaling, and~b! deviation of theaverage kinetic energy (KEav) from the theoretical kineticenergy (KEth), which was calculated from the number ofdegrees of freedom in the simulation box at 373 K, was lessthan 3.7310219J and the standard deviation of the kineticenergy~s! was less than 2.1310219J. The effect of tempera-ture deviation on the energy in the simulation box was muchsmaller than the effect of the number ofn-alcohol molecules,N1 , as shown in Fig. 2~b!. The calculation conditions and thedeviation of kinetic energy are summarized in Table VI.

III. SIMULATION RESULTS: „1… ON WATER

A. n -propanol „C3H7OH…

Figures 3~a!–3~d! show typical instantaneous configura-tions of the mixture of water andn-propanol for four alcoholconcentrations. Alcohols are known to have strong surfaceactivity, which means that alcohol molecules are adsorbed onthe surface of water. The simulation results show that al-

FIG. 1. Instantaneous configurations of an-heptanol and water mixtureduring equilibration:~a! t50 ps~initial state!; ~b! t55 ps; ~c! t540 ps; ~d!t550 ps. The number ofn-heptanol molecules,N1 , is 40, and that of watermolecules,N2 , is 400 ~set III-b!. Black circles show water atoms, graycircles show hydrocarbon chains, and dark gray circles show hydroxylgroups.

FIG. 2. Time course of kinetic energy~KE!, potential energy~PE!, and totalinternal energy~TE! ~left figure!. Av-erage energy in an isolated system as afunction of the number ofn-heptanolmolecules,N1 ~right figure!. Units ofenergy,E, are 10217 J.

TABLE IV. Fourier coefficients for intramolecular rotational potential func-tions of n-alcohol ~units for V’s are kcal/mol!.

Bond V0 V1 V2 V3

C–C 0.0 1.411 20.271 3.145C–C~COH! 0.0 0.702 20.212 3.060

C–O 0.0 0.834 20.116 0.747

TABLE V. Values of the charges and the Lennard-Jones parameters of waterand ions.

q s, Å «, kcal/mol

O 20.8476 3.166 0.1554H 0.4238 0.0 0.0

Li1 1.0 2.37 0.149Br2 21.0 5.04 0.270

TABLE VI. Calculation conditions, the number of each molecule and thedeviations of kinetic energy.

Set H2O Alcohol LiBr(KEth-KEav!/

KEav s/KEav

I 400 0 0 20.012 0.025II-a 400 40~n-propanol! 0 20.020 0.023II-b, b,8 b9 400 80~n-propanol! 0, 50, 100 20.016 0.022II-c 400 120~n-propanol! 0 20.016 0.022III-a 400 20 ~n-heptanol! 0 0.002 0.023III-b 400 40 ~n-heptanol! 0 20.006 0.023III-c, c8, c9 400 60~n-heptanol! 0, 50, 100 20.025 0.022III-d 400 100 ~n-heptanol! 0 20.004 0.020IV-a 400 20~n-undecanol! 0 20.018 0.023IV-b 400 40 ~n-undecanol! 0 20.011 0.021IV-c, c8, c9 400 60~n-undecanol! 0, 50, 100 20.003 0.021IV-d 400 100~n-undecanol! 0 20.037 0.020

1540 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Hirofumi Daiguji

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thoughn-propanol is completely soluble in water, the surfaceadsorption is clearly evident, particularly when the concen-tration is low~set II-a!, as shown in Fig. 3~b!. Figures 4~a!–4~c! show the number density profiles of the pseudoatoms ofn-propanol and the oxygen of the water normal to the inter-face, i.e., along thez axis. Figure 4~a! shows that the hydro-philic parts ofn-propanol face the water surface and that thehydrophobic parts face the gas phase, which means that asoluble monolayer is formed on the water surface. Figures4~b! and 4~c! show that, as the concentration ofn-propanolincreases, the gradients of the number densities of water andn-propanol with respect to thez axis decrease in the surfaceregion. This means that the surface region and the bulk re-gion become increasingly indistinguishable as the concentra-tion of n-propanol increases. In Fig. 4~c!, all of the number

density profiles of the pseudoatoms ofn-propanol are simi-lar. Becausen-propanol and water mix well in the surfaceregion, the head groups ofn-propanol molecules point invarious directions.

FIG. 3. Instantaneous configurations of an-propanol and water mixture as afunction of the number ofn-propanol molecules,N1 : ~a! N150 ~set I!; ~b!N1540 ~set II-a!; ~c! N1580 ~set II-b!; ~d! N15120 ~set II-c!. The numberof water molecules,N2 , is 400.

FIG. 4. Longitudinal number density profiles~number density profile ofeach pseudoatom along the normal to the interface! for n-propanol andoxygen of water as a function of the number ofn-propanol molecules,N1 :~a! N1540 ~set II-a!; ~b! N1580 ~set II-b!; ~c! N15120 ~set II-c!. Thenumber of water molecules,N2 , is 400.

FIG. 5. Instantaneous configurations of an-heptanoland water mixture as a function of the number ofn-heptanol molecules,N1 : ~a! N150 ~set I!; ~b! N1

520 ~set III-a!; ~c! N1540 ~set III-b!; ~d! N1560 ~setIII-c !; ~e! N15100 ~set III-d!. The number of watermolecules,N2 , is 400.

1541J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 n-alcohols adsorbed on an aqueous electrolyte solution

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B. n -heptanol „C7H15OH…

Figures 5~a! and 5~e! show the gas–water interfaces andthen-heptanol-water interfaces, respectively. Both interfacesare clearly evident, and fluctuations at the interfaces aresmall. When monolayers ofn-heptanol are formed on water,fluctuations are also small@Fig. 5~c!#. However, when then-heptanol concentration is slightly higher than that for setIII-b @Fig. 5~c!#, large fluctuations occur@Fig. 5~d!#, whereaswhen the concentration is slightly lower, large fluctuationsdo not occur andn-heptanol molecules move around on thewater surface@Fig. 5~b!#. Figures 6~a!–6~d! show the num-ber density profile of all pseudoatoms ofn-heptanol and ofthe oxygen of water normal to the interface. Figure 6~b!shows that the number density profiles of similar shape liealong thez axis, indicating that the hydrocarbon chain axesof n-heptanol are normal to the water surface. A comparison

between Figs. 6~a! and 6~b! shows that the number densityprofiles ofn-heptanol for set III-a@Fig. 6~a!# are closer to thecenter and in a narrowerz range than those for set III-b@Fig.6~b!#. When then-heptanol concentration is slightly lowerthan that for set III-b, then-heptanol molecules are locatedfurther from the water surface and the chain axes are tiltedfrom the normal to the interface@Fig. 6~a!#. In contrast, whenthe n-heptanol concentration is slightly higher than that forset III-b, the n-heptanol molecules are widely distributednear the surface and the gradients of the number densities ofpseudoatoms ofn-heptanol and water with respect to thezaxis are smaller than those for all other concentrations@Fig.6~c!#. For set III-d, two peaks appear on each surface@Fig.6~d!#. The peak nearer the water surface is defined as the firstpeak, and that farther is defined as the second peak. Thesecond peaks of the head and hydroxyl groups are higherthan the first peaks because the head groups in a layer pointpreferentially in the same direction, but the head groups intwo successive layers point in opposite directions, as shownin Fig. 5~e!. This molecular arrangement is stable in amultilayer ofn-heptanol. Figure 7 shows the profiles of localsurface tension for monolayers ofn-heptanol on water~setIII-b ! and for multilayers ofn-heptanol on water~set III-d!.The local surface tension is defined as the difference betweenthe normal and tangential components of the pressuretensor.7,16 In monomolecular adsorption~set III-b!, one peakappears on each side of the alcohol–water system, whereasin multimolecular adsorption~set III-d!, two peaks appear oneach side. The first peaks are at the interfaces between waterand n-heptanol and the second peaks are at the interfacesbetweenn-heptanol and gas. The peaks for set III-b arehigher than the first peaks for set III-d, indicating that theadsorption ofn-heptanol at the interface between water andn-heptanol is more stable than that between water and gas.The surface tension of water covered with a monolayer ofn-heptanol~set III-b! is 33.8 mN/m, calculated as the integralof the local surface tension over the interface.

C. n -undecanol „C11H23OH…

Water andn-undecanol do not mix at any alcohol con-centration, as shown in Figs. 8~a!–8~e!. Monolayers ofn-undecanol are evident for set IV-b@Fig. 8~c!#. When the

FIG. 6. Longitudinal number density profiles~number density profile ofeach pseudoatom along the normal to the interface! for n-heptanol and oxy-gen of water as a function of the number ofn-heptanol molecules,N1 : ~a!N1520 ~set III-a!; ~b! N1540 ~set III-b!; ~c! N1560 ~set III-c!; ~d! N1

5100 ~set III-d!. The number of water molecules,N2 , is 400.

FIG. 7. Profiles of the local surface tension,g, for a monolayer ofn-heptanol on water~set III-b! and a multilayer ofn-heptanol on water~setIII-d !. Units of local surface tension,g, are 107 N/m2.

1542 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Hirofumi Daiguji

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concentration is lower than that for set IV-b@Fig. 8~c!# andthe water surface is not covered withn-undecanol, then-undecanol molecules tend to cluster in a single region onthe water surface. However, such clusters are not stable. Theformation and break up of a cluster occurs repeatedly@Fig.8~b!#. In contrast, when the concentration is slightly higherthan that for set IV-b@Fig. 8~c!#, the hydrocarbon chain axesare in various directions, but the first adsorbed layer ofn-undecanol is stable and the fluctuations at the interfaceremain small@Fig. 8~d!#. Figures 9~a!–9~d! show the numberdensity profiles normal to the interface. The profiles ofn-undecanol @Fig. 9~a!–9~d!# are similar to those ofn-heptanol@Fig. 7~a!–7~d!#, but the first adsorbed layer ofset IV-c @Fig. 9~c!# is more stable than that of set III-c@Fig.7~c!#. For set IV-c @Fig. 9~c!#, two peaks of the hydroxylgroup occur at interfaces, indicating that the first adsorbedlayer is still stable at this concentration. Forn-heptanol,when the concentration is slightly higher than the concentra-tion at which monolayers are formed, large fluctuations oc-cur and the adsorbed layer cannot be clearly formed. Becausethe hydrocarbon chain ofn-undecanol is long and the inter-actions between hydrocarbon chains are strong,n-undecanoland water are clearly separated andn-undecanol moleculesare always supported on water. For set IV-d@Fig. 9~d!#, themolecular arrangement in a multilayer ofn-undecanol issimilar to that ofn-heptanol, although the second peaks ofthe head groups are lower and broader. This molecular ar-rangement forn-undecanol is less stable than that forn-heptanol.

D. Stability in the n -alcohol distribution on water

The distribution ofn-alcohols on water was studied fromthe viewpoint of stability by using thermodynamics.17 Ac-cording to thermodynamics, a heterogeneous distribution ofn-alcohol on water occurs when the system becomes un-stable with respect to diffusion ofn-alcohol, i.e., a heteroge-neous distribution ofn-alcohol produces an increase in en-tropy. Then the fluctuations in the mole number due to

FIG. 8. Instantaneous configurations of an-undecanoland water mixture as a function of the number ofn-undecanol molecules,N1 : ~a! N150 ~set I!; ~b! N1

520 ~set IV-a!; ~c! N1540 ~set IV-b!; ~d! N1560 ~setIV-c!; ~e! N15100 ~set IV-d!. The number of watermolecules,N2 , is 400.

FIG. 9. Longitudinal number density profiles~number density profile ofeach pseudoatom along the normal to the interface! for n-undecanol andoxygen of water as a function of the number ofn-undecanol molecules,N1 :~a! N1520 ~set IV-a!; ~b! N1540 ~set IV-b!; ~c! N1560 ~set IV-c!; ~d! N1

5100 ~set IV-d!. The number of water molecules,N2 , is 400.

1543J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 n-alcohols adsorbed on an aqueous electrolyte solution

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diffusion in a given volume increase, resulting in a heteroge-neous distribution ofn-alcohol. The condition for instabilitydue to diffusion of components is

d2S52(i , j

]

]NjS m i

T D dNjdNi.0, ~3!

whereNi andm i are the number of moles and the chemicalpotential of componenti , respectively,S is the entropy, andT is the temperature. At a fixedT, for a binary mixture, thiscondition can be written in the explicit form

m11~dN1!21m22~dN2!21m21~dN1!~dN2!

1m12~dN1!~dN2!,0 ~4!

in which

m115]m1

]N1, m225

]m2

]N2, m215

]m2

]N1, m125

]m1

]N2, ~5!

where subscripts 1 and 2 denoten-alcohol and water, respec-tively. The critical parameter for stability of this binary sys-tem is the number ofn-alcohol molecules,N1 , per unit areaon the water surface. In the simulations, because the simula-tion box is fixed and the thickness of the water film is largeenough so that molecules at opposite surfaces cannot interactwith each other across the water film, i.e., the number ofwater molecules is large and the interaction between water

FIG. 10. Effect of the number ofn-alcohol,N1 , on the kinetic energy~KE!, potential energy~PE!, total internal energy~TE!, and theoretical kinetic energy~theoretical KE! at 373 K.~a! n-propanol;~b! n-heptanol;~c! n-undecanol. Units of energy,E, are 10217 J. The theoretical kinetic energy~theoretical KE! wascalculated from the number of degrees of freedom in the simulation box.

FIG. 11. Instantaneous configurations of a mixture ofn-propanol and LiBraqueous solution as a function of the number of LiBr molecules,N3 : ~a!N350 ~set II-b!; ~b! N3550 ~set II-b8!; ~c! N35100 ~set II-b9!. The num-bers ofn-propanol molecules,N1 , is 80, and that of water molecules,N2 , is400. Black circles show water, Li1 and Br2, gray circles show hydrocarbonchains, and dark gray circles are hydroxyl groups.

1544 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Hirofumi Daiguji

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andn-alcohol is weak, the stability of the system is indepen-dent of a small change in the number of water molecule,dN2 . Therefore, the condition for instability can be ex-pressed as follows:

m11,0 ~6!

in which the second derivativem11 is given by

m115]m1

]N1

5]

]N1S ]F

]N1D

V, T

5]

]N1H S ]U

]N1D

V, T

2TS ]S

]N1D

V, TJ

5S ]2U

]N12D

V, T

2TS ]2S

]N12D

V, T

, ~7!

whereF is the Helmholtz free energy,U is the internal en-ergy, andV is the volume. Therefore the conditionm11,0can be written as

S ]2U

]N12D

V, T

,TS ]2S

]N12D

V, T

. ~8!

Because the second derivative of the entropy is positivewhen the system is unstable, the sufficient condition for in-stability can be expressed as follows:

S ]2U

]N12D

V, T

,0. ~9!

Figures 10~a!–10~c! show the effect of the number ofn-alcohol molecules,N1 , on the potential energy, kinetic en-ergy, and total internal energy derived from the moleculardynamics simulations and the theoretical kinetic energy cal-culated from the number of degrees of freedom in the simu-lation box at 373 K. For all calculation conditions, the de-viation of the average simulated kinetic energy from thetheoretical kinetic energy is much smaller than the increasein the kinetic energy with increasingN1 . This means that thereliability of the simulation data is sufficient. Forn-propanol,the total internal energy decreases linearly with increasingnumber ofn-propanol molecules. Becausen-propanol mixeswell with water, the total internal energy of this binary mix-ture decreases linearly. Forn-heptanol, the second derivativeof total internal energy is negative whenN1'60, indicatingthat the system is unstable near this concentration. At thisconcentration, large fluctuations occur on the surface, as seenin Fig. 5~d!. For n-undecanol, the second derivative of thetotal internal energy is negative whenN1'20, indicating thatthe system is unstable near this concentration. At this con-

FIG. 12. Longitudinal number density profiles~number density profile ofeach pseudoatom along the normal to the interface! for n-propanol, oxygenof water, and ions Li1 and Br2, as a function of the number of LiBr mol-ecules,N3 : ~a! N350 ~set II-b!; ~b! N3550 ~set II-b8!; ~c! N35100 ~setII-b9!. The number ofn-propanol molecules,N1 , is 80 and that of watermolecules,N2 , is 400.

FIG. 13. Instantaneous configurations of a mixture ofn-heptanol and LiBraqueous solution as a function of the number of LiBr molecules,N3 : ~a!N350 ~set III-c!; ~b! N3550 ~set III-c8!; ~c! N35100 ~set III-c9!. The num-ber of n-heptanol molecules,N1 , is 60 and that of water molecules,N2 , is400.

1545J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 n-alcohols adsorbed on an aqueous electrolyte solution

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centration,n-undecanol molecules tend to cluster on water,as shown in Fig. 8~b!, but such clusters are not stable. Theformation and break up of such clusters occurs repeatedly.

These simulation results imply that, if the simulation boxis large enough, the distributions ofn-heptanol andn-undecanol on water might be heterogeneous and islands ofalcohol might appear on the water surface. The mechanismresponsible for fluctuations that lead to heterogeneous distri-bution of n-alcohol or to cellular convection at the interfaceis different for each type ofn-alcohol studied here.

IV. SIMULATION RESULTS: „2… ON AQUEOUSELECTROLYTE SOLUTION

A. n -propanol „C3H7OH…

Hozawa et al. concluded that because the interactionsbetween water and salt are stronger than those between waterandn-alcohol, when salt is added to water, somen-alcoholmolecules that are dissolved in the bulk water move towardthe surface and adsorb on the surface.5 This phenomenon iscalled ‘‘salting out’’ and is qualitatively reproduced by thesimulations shown in Figs. 11~a!–11~c!. These simulationsalso show that the solubility ofn-propanol decreases and thesurface excess concentration ofn-propanol increases as salt

concentration increases, and that the gradient of the numberdensity ofn-propanol with respect to thez axis increases inthe surface regions as the salt concentration increases@Figs.12~a!–12~c!#. These results show that salt increases the sur-face excess concentration and stabilizes the adsorbed layer ofn-propanol.

B. n -heptanol „C7H15OH…

Figures 13~a!–13~c! show typical structures ofn-heptanol on aqueous electrolyte solutions for different saltconcentrations based on the simulations. Large fluctuationsare evident at the interfaces between water andn-heptanolfor set III-c @Fig. 13~a!#. By adding salt to water, the fluctua-tions are suppressed and the first adsorbed layers ofn-heptanol are clearly formed on the surfaces of the solution.Figures 14~a!–14~c! show that the number density of the firstadsorbed layer increases with increasing salt concentration.Salt stabilizes the first adsorbed layer ofn-heptanol. On thesurface of water, large fluctuations occur for a certain rangeof n-heptanol concentration@Figs. 5~c!–5~e!#; however, onthe surface of the aqueous electrolyte solution for set III-c9,such fluctuations do not occur within the same range ofn-heptanol concentration. This suggests that salt suppressesthe generation of fluctuations in the distribution ofn-heptanol.

C. n -undecanol „C11H23OH…

Figures 15~a!–15~c! show molecular arrangements ofn-undecanol on aqueous electrolyte solutions for different

FIG. 14. Longitudinal number density profiles~number density profile ofeach pseudoatom along the normal to the interface! for n-heptanol, oxygenof water, and ions Li1 and Br2, as a function of the number of LiBr mol-ecules,N3 : ~a! N350 ~set III-c!; ~b! N3550 ~set III-c8!; ~c! N35100 ~setIII-c 9!. The number ofn-heptanol molecules,N1 , is 60 and that of watermolecules,N2 , is 400.

FIG. 15. Instantaneous configurations of a mixture ofn-undecanol and LiBraqueous solution as a function of the number of LiBr molecules,N3 : ~a!N350 ~set IV-c!; ~b! N3550 ~set IV-c8!; ~c! N35100 ~set IV-c9!. The num-ber ofn-undecanol molecules,N1 , is 60 and that of water molecules,N2 , is400.

1546 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Hirofumi Daiguji

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salt concentrations based on the simulations. The simulationsshow thatn-undecanol does not mix with aqueous electrolytesolutions. Comparison between the number density profilesof n-undecanol for set IV-c@Fig. 16~a!# and those for setIV-c8 @Fig. 16~b!# shows that the density of the first adsorbedlayer of n-undecanol increases with increasing salt concen-tration, indicating that salt stabilizes the first adsorbed layerof n-undecanol. However, comparison between the numberdensity profiles ofn-undecanol for set IV-c8 @Fig. 16~b!# andthose for set IV-c9 @Fig. 16~c!# show that the density of thefirst adsorbed layer does not always increase with increasingsalt concentration. When salt is added,n-undecanol andaqueous electrolyte solution are clearly separated and thefluctuations of the solution surface are reduced. Therefore,n-undecanol molecules form an energy minimum structureon the surface of the aqueous electrolyte solution for setIV-c9, similar to the formation on a solid surface. Becausethe interactions between the hydrophobic parts ofn-undecanol are strong, the hydrophilic parts do not alwaysface the solution surface. Whenn-alcohols with long-lengthhydrocarbon chains are used, the fluctuations of the solutionsurface might promote the stability of the adsorbed layer ofn-alcohol.

V. DISCUSSION

Interfacial turbulence occurs during water vapor absorp-tion into an aqueous electrolyte solution containing amedium-lengthn-alcohol, such asn-heptanol, and strong in-terfacial turbulence does not occur on an aqueous electrolytesolution with either short- or long-lengthn-alcohol. The rea-son is related to the molecular dynamics of these alcohols onwater or on aqueous electrolyte solutions.

The results of the stability analysis done here by usingsimulations show the generation of fluctuations in the distri-bution ofn-heptanol andn-undecanol. Because the system inthe simulation was enclosed in a small box with periodicboundary conditions in all directions, the islands ofn-heptanol orn-undecanol do not appear on water. However,if the system is enclosed in a large box or a box with freeboundary condition, the islands ofn-heptanol orn-undecanolmight appear on water. Forn-heptanol, a heterogeneous dis-tribution @schematically shown in Fig. 17~b!# is more stablethan a homogenous distribution@Fig. 17~a!#. The total inter-nal energy of the system where monolayers and bilayers ofn-heptanol coexist on water is less than that of the systemwhere the same numbers ofn-heptanol molecules are distrib-uted homogeneously on water in the same volume. Forn-undecanol, a monolayer ofn-alcohol with a long hydro-carbon chain breaks up into islands with ordered moleculesat low surface pressure.8 Therefore, a heterogeneous distri-bution of n-undecanol on water@Fig. 18~b!# is more stablethan a homogeneous distribution@Fig. 18~a!#.

The simulation results show that salt concentration af-fects the structural and dynamical properties ofn-alcoholmolecules on the surface of aqueous electrolyte solutions.Salt affects the surface excess concentration ofn-alcohol and

FIG. 16. Longitudinal number density profiles~number density profile ofeach pseudoatom along the normal to the interface! for n-undecanol, oxygenof water, and ions Li1 and Br2, as a function of the number of LiBr mol-ecules,N3 : ~a! N350 ~set IV-c!; ~b! N3550 ~set IV-c8!; ~c! N35100 ~setIV-c9!. The number ofn-undecanol molecules,N1 , is 60 and that of watermolecules,N2 , is 400.

FIG. 17. Adsorbed layer ofn-heptanol at a concentration corresponding toset III-c, showing~a! homogeneous distribution;~b! heterogeneous distribu-tion.

1547J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 n-alcohols adsorbed on an aqueous electrolyte solution

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the stability of the adsorbed layer. The degree of each effectdepends on the length of the hydrocarbon chain. Forn-alcohols with short-length hydrocarbon chains, salt re-duces the solubility and increases the surface excess concen-tration of n-alcohol. For medium-lengthn-alcohols, salt sta-bilizes the adsorbed layer but does not affect the surfaceexcess concentration. However, if the simulation box is largeenough for then-alcohol to form a micelle structure in thebulk liquid, salt might affect the surface excess concentra-tion. For n-alcohols with long-length hydrocarbon chains,salt does not always stabilize the adsorbed layer. Because theinteractions between hydrocarbon chains are strong, somehydroxyl groups do not face the solution surface. The surfacestructure ofn-alcohol with a long hydrocarbon chain couldthus be independent of salt concentration.

In Marangoni instability, interfacial turbulence occursduring water vapor absorption. This absorption reduces saltconcentration, which in turn affects the structural and dy-namical properties of then-alcohol. Changes in the structuraland dynamical properties of then-alcohol on solution due towater vapor absorption requires a strong correlation betweenthe structural and dynamical properties of then-alcohol onsolution and salt concentration. The simulation results sug-gest that salt suppresses the generation of fluctuations in then-alcohol distribution. However, the surface of a highly con-centrated aqueous electrolyte solution during water vapor ab-sorption is not the same as that during liquid–vapor equilib-rium. The mechanism responsible for the generation offluctuations in the distribution ofn-alcohol on a water sur-face might be similar to that on a highly concentrated aque-ous electrolyte solution surface during water vapor absorp-tion. The molecular level structure of a highly concentratedaqueous electrolyte solution surface during water vapor ab-sorption has not been clarified yet.18 Further study is needed.

Two required conditions for Marangoni instability were

revealed by the simulations: generation of fluctuations in then-alcohol distribution on water, and strong correlation be-tween the structural and dynamical properties ofn-alcoholon solution and salt concentration.n-alcohols with long-length hydrocarbon chains satisfy the first required condi-tion, and n-alcohols with short-length hydrocarbon chainssatisfy the second one. Onlyn-alcohols with medium-lengthhydrocarbon chains satisfy both required conditions.

VI. CONCLUSIONS

In the present work, molecular dynamics simulationswere done for three kinds of normal alcohols,n-propanol(C3H7OH), n-heptanol (C7H15OH), and n-undecanol(C11H23OH), on water or on aqueous electrolyte solutions.For then-alcohols and water, the OPLS models and SPC/Emodel were used, respectively. The alkali and halide ionswere modeled as LJ spheres with a points charge at the cen-ter. The LJ plus Coulomb form potential functions weremaintained. The following conclusions could be drawn fromthis work.

The distribution ofn-alcohols on water was studied fromthe viewpoint of stability. The results of the stability analysisshow the possibility of a heterogeneous distribution ofn-heptanol andn-undecanol on water. The mechanism re-sponsible for the generation of fluctuations, which leads toheterogeneous distribution, is different for each kind ofn-alcohol.

Salt concentration affects the structural and dynamicalproperties ofn-alcohol molecules on the surface of aqueouselectrolyte solutions. Salt also affects the surface excess con-centration and the stability of the adsorbed layer. However,for n-alcohols with long-length hydrocarbon chains, thestructure ofn-alcohol could be independent of salt concen-tration because the interactions between the hydrocarbonchains are strong.

Two required conditions for Marangoni instability estab-lished from this work are the generation of the fluctuations inthe n-alcohol distribution on water and a strong correlationbetween the structural and dynamical properties and salt con-centration. Medium-lengthn-alcohols, of which the hydro-phobic interactions and hydrophilic interactions are in bal-ance with each other, are effective surfactants to induceMarangoni instability.

ACKNOWLEDGMENT

This work has been supported by the Grant-in-Aid forEncouragement of Young Scientists from the Japan Societyfor the Promotion of Science under Grant No. 11750154.

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1548 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Hirofumi Daiguji

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1549J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 n-alcohols adsorbed on an aqueous electrolyte solution

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