Molecular Dynamics Study of the Influence of Surfactant Structure on Surfactant-Facilitated Spreading of Droplets on Solid Surfaces

Molecular Dynamics Study of the Influence of SurfactantStructure on Surfactant-Facilitated Spreading of Droplets

on Solid Surfaces

Yangyang Shen,† Alexander Couzis,‡ Joel Koplik,§ Charles Maldarelli,‡ andM. Silvina Tomassone*,†

Department of Chemical and Biochemical Engineering, Rutgers University, Levich Instituteand Departments of Chemical Engineering and Physics, City College of New York, and

Levich Institute and Department of Physics, City College of New York

Received May 20, 2005. In Final Form: August 17, 2005

The spreading of a partially wetting aqueous drop in air on a hydrophobic surface can be facilitated bythe adsorption of surfactants from the drop phase onto the air/aqueous and aqueous/hydrophobic solidinterfaces of the drop. At the contact line at which these interfaces meet, conventional surfactants witha linear alkyl hydrophobic chain attached to a polar group adsorb onto the surfaces, forming monolayerswhich remain distinct as they merge at the contact juncture. The adsorption causes a decrease in theinterfacial tensions and reduction in the contact angle but the angle remains above zero so the drop is stillnonwetting. Trisiloxane surfactants with a T-shaped geometry in which the hydrophobic group is composedof a trisiloxane oligomer with a polar group attached at the center of the chain can give rise to a zero contactangle at the contact line and complete wetting (superspreading). Experimental evidence suggests theadsorption of the T-shaped molecule, in addition to significantly decreasing the tensions of the interfaces(relative to the conventional surfactants), promotes the formation of a precursor film consisting of a surfactantbilayer at the contact line which facilitates the spreading. The aim of this study is to use moleculardynamics to examine if the T-shaped structure can promote spreading by the formation of a bilayer andto contrast this case with that of the linear chain surfactant where complex assembly does not occur. Thesimulation models the solvent as a monatomic liquid, the substrate as a particle lattice, and the surfactantsas united atom structures, with all interactions given by Lennard-Jones potentials. We start with a basecase in which the solvent partially wets a substrate comprised of a lattice of particles. We demonstratethat adsorbed T-shaped surfactant monolayers can, when the interaction between the solvent and thehydrophile particles is strong enough, assemble into a bilayer, allowing the drop to extend to a thin planarfilm. In the case of the flexible linear chain surfactant, there is no interaction between the monolayerson the two interfaces in the case of a strong hydrophile-solvent interaction and less coordination for aweaker interaction. In either case, the monolayers remain distinct, as the surfactant only marginallyimproves wetting.

1. Introduction

Droplets of water placed on nonpolar (hydrophobic)surfaces subtend finite contact angles (as measuredthrough the liquid phase) because the strong hydrogenbonding interactions between water molecules is muchgreater than the attractive van der Waals interactionsbetween water molecules and the nonpolar groups of thesurface, and this imbalance forces the droplet to bead upto maximize the aqueous interaction.1 Many experimentalstudies have shown that surfactant molecules dissolvedin the drop phase can reduce the contact angles andenhance the spreading of aqueous drops on nonpolarsurfaces.2 The simplest mechanism by which surfactantscan facilitate spreading on hydrophobic surfaces is byadsorbing from solution onto the air/aqueous and aqueous/nonpolar solid interfaces and forming monolayers whichreduce the interfacial tensions of these surfaces relative

to their large values in the absence of surfactant; in turn,the reduction in tensions reduces the contact angle andallows area expansion. Certain surfactants can cause areduction of the contact angle to zero and completespreading of water on very hydrophobic surfaces such asParafilm or polyethylene, which subtend contact anglesof 100° or more when pure water is placed on thesesurfaces.3 For these surfaces, conventionally structuredsurfactants having linear alkyl (methylene or -CH2-)chains as their nonpolar group can reduce the equilibriumcontact angle by tens of degrees but do not facilitate thereduction to zero contact angle and complete wetting.4-6

However, surfactants with a trisiloxane group as thenonpolar moiety (Me3-Si-O)2-Si(Me)(CH2)3-) and anoligomeric ethylene oxide (EO) chain (-OCH2CH2-) offour to eight units as the polar group facilitate completewetting (“superspreading”3,4,7). Figure 1 compares themolecular structures of a trisiloxane superspreader withfour EO groups, with a conventional dodecyl-alkyl chainsurfactant with a polar group consisting of the same EOchain (CH3(CH2)11(OCH2CH2)4OH, a polyethoxylated sur-factant).

* To whom correspondence should be addressed.† Rutgers University.‡ Levich Institute and Department of Chemical Engineering, City

College of New York.§ Levich Institute and Department of Physics, City College of

New York.(1) Marmur, A. Adv. Colloid Interface Sci. 1983, 19, 75. de Gennes,

P. Rev. Mod. Phys. 1985, 57, 827. Leger, L.; Joanny, J. Rep. Prog. Phys.1992, 55, 431. Berg, J. Wettability; Marcel Dekker: New York, 1993.

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1996, 12, 337. Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D.; Davis, H.T. Langmuir 1997, 13, 7270.

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12160 Langmuir 2005, 21, 12160-12170

10.1021/la051354c CCC: $30.25 © 2005 American Chemical SocietyPublished on Web 11/24/2005

The origin of superspreading is not completely under-stood, but several studies indicate that an explanationmay lie in the structural differences between the mol-ecules. Ethoxylate chains immersed in water adopt ahelical configuration whose cross section increases withthe number of EO groups. For the superspreaders, thiscross section is less than or approximately equal to thatof the hydrophobic groups, so that the trisiloxane chainacts as an umbrella and its cross section defines thedistance of closest approach of adsorbed molecules on thesurface.8 The linear alkyl chain of polyethoxylate surfac-tants have smaller cross sections relative to the EO chain,9and hence, the ethoxylate chain footprint defines thedistance of closest approach, as is the case for many bulksoluble linear alkyl chain surfactants since the polar groupmust be large to make the surfactant soluble. Thesestructural differences account for differences in the ad-sorbed monolayers, particularly at the aqueous/hydro-phobic solid interface: When the trisiloxane adsorbs athigh bulk concentration onto the aqueous/hydrophobicsolid surface, they can achieve a close-packed arrangementof the hydrophobes in which the trisiloxane moieties adjoineach other side-by-side unimpeded by the hydrophiles.This stacking represents a low-energy structure as itexcludes water (which hydrogen bonds to the hydrophilesor bulk water), and the hydrophobic solid/aqueous inter-facial energy is reduced significantly. At the air/aqueous

interface, a similar structure arises with the layerextending into the air space, and the vapor/aqueousinterfacial energy is reduced. The reduction in the tensionsof the air/aqueous and particularly the aqueous/solidinterfaces can give rise to complete wetting if the sum ofthese energies is smaller than the low air/hydrophobicsolid interfacial energy. In the case of the linear alkylchain surfactants, when these molecules adsorb at thesolid/liquid interface, their polar groups space the mol-ecules apart and hydrophobic chains cannot stack length-wise. Consequently, the adsorbed layer is of higher energy,as water is left to reside between the chains; the lesserreduction at the solid/liquid tension allows for a decreasein contact angle and an improvement in spreading butnot completewetting.Forexample, for thepolyethoxylates,neutron reflectivity, ellipsometry, contact angle measure-ments, and atomic force microscopy measurements at theaqueous/hydrophobic solid interface6,10 indicate that, athigh concentrations, the hydrophobes dangle from thesurface and are separated by water molecules, while atlower concentrations, they lie along the surface.

While the significant reductions in tensionssparticularlythe hydrophobic solid/aqueous tensionsdue to the ad-sorbed trisiloxane monolayer may give rise to completewetting, other factors related to the molecular organizationimmediately at the superspreading front may contributeas well. At the spreading edge, monolayers at the air/aqueous and aqueous/hydrophobic solid interfaces ap-proach to within molecular scales separated by anintervening layer of a limited number of water molecules.Ruckenstein11 has suggested that at the periphery thetrisiloxanesswith their geometry which allows closepacking of the hydrophobes in planar sheetsscan organizeinto a low-energy bilayer structure composed of a hydro-phile/water lamellar phase sandwiched between two densehydrophobic layers originating from the monolayers onthe aqueous/hydrophobic solid and aqueous/air interfaces.Bilayers of conventional surfactants with large polargroups retain water in the hydrophobic layer adjoiningthe solid surface and do not represent a low free energyconfiguration; as a result, at the spreading periphery, theair/aqueous and aqueous/solid monolayers remain sepa-rate, joining with a finite contact angle at the contact line.Similar structure formation tendencies are present in thebulk; where the trisiloxane superspreaders, with theirhydrophobes defining the molecular adsorption footprint,aggregate at a critical concentration in bulk solution inpatch and vesicles structures made up of uni- andmultilamellar molecular assemblies of bilayers,8,12 whilethe conventional surfactants with the packing determinedby the polar group usually form spherical micelles in bulksolution.13 Further evidence for the plausibility of bilayer

(7) Ananthapadnabhan, K. P.; Doddard, E. D.; Chandar, P. ColloidsSurf. 1990, 44, 281. Zhu, S.; Miler, W. G.; Scriven, L. E.; Davis, H. T.Colloids Surf., A 1994, 90, 63. Lin, Z.; Hill, R. M.; Davis, T.; Ward, M.D. Langmuir 1994, 10, 4060. Lin, Z.; Stoebe, T.; Hill, R. M.; Davis, H.T.; Ward, M. D. Langmuir 1996, 12, 345. Svitova, T.; Hoffmann, H.;Hill, R. M. Langmuir 1996, 12, 1712. Rosen, M. J.; Song, L. D. Langmuir1996, 12, 4945. Nikolov, A. D.; Wasan, D. T.; Chengara, A.; Koczo, K.;Policello, G. A.; Kolossvary, I. Adv. Colloid Interface Sci. 2002, 96, 325.

(8) Kunieda, H.; Taoka, H.; Iwanaga, T.; Harashima, A. Langmuir1998, 14, 5113. He, M.; Hill, R. M.; Lin, Z.; Scriven, L. E.; Davis, H. T.J. Phys. Chem. 1993, 97, 8820.

(9) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 7ed.; Wiley: New York, 1999.

(10) Fragneto, G.; Lu, J. R.; McDermott, D. C.; Thomas, R. K.; Rennie,A. R.; Gallagher, P. D.; Satija, S. K. Langmuir 1996, 12, 477. Tidberg,F. J. Chem. Soc., Faraday Trans. 1996, 92, 531. Thritle, P. N.; Li, Z.X.; Thomos, R. K.; Rennie, A. R.; Satija, S. K.; Sung, L. P. Langmuir1997, 13, 5451. Grant, L.; Ducker, W. J. Phys. Chem. B 1997, 101, 5337.Grant, L.; Tidberg, F.; Ducker, W. J. Phys. Chem. B 1998, 102, 4288.Grant, L. M.; Ederth, T.; Tiberg, F. Langmuir 2000, 16, 2285.

(11) Ruckenstein, E. J. Colloid Interface Sci. 1996, 179, 136.(12) Gradzielski, M.; Hoffmann, H.; Robisch, P.; Ulbricht, W.;

Gruning, B. Tenside, Surfactants, Detergents 1990, 27, 366. Hill, R. M.;He, M.; Lin, Z.; Davis, T.; Scriven, L. E. Langmuir 1993, 9, 2789. Versluis,P.; Pas, J. C. v. d.; Mellema, J. Langmuir 1997, 5732. Li, X.;Washenberger, R. M.; Scriven, L. E.; Davis, H. T.; Hill, R. M. Langmuir1999, 15, 2278. Li, X.; Washenberger, R. M.; Scriven, L. E.; Davis, H.T.; Hill, R. M. Langmuir 1999, 15, 2267. Wagner, R.; Strey, R. Langmuir1999, 15, 902.

(13) Mitchell, D. J.; Tiddy, G. J.; Waring, L.; Bostock, T.; MacDonald,M. P. J. Chem. Soc., Faraday Trans. I 1983, 79, 975. Sjoblom, J.; Stenius,P. In Nonionic Surfactants: Physical Chemistry; Schick, M., Ed.;Surfactant Science Series 23; Marcel Dekker: New York, 1987.

Figure 1. Molecular structures of trisiloxane and n-dodecylpolyethoxylate surfactants. Dark (red) atoms are oxygen, light(blue) atoms are hydrogen, and gray (purple) atoms are siliconand carbon.

Molecular Dynamics Study of Surfactant Structure Langmuir, Vol. 21, No. 26, 2005 12161

formation at the spreading periphery of trisiloxanesuperspreaders follows from the spatially resolved ellip-sometric measurements of wetting layer thicknesses inthe complete spreading of pure trisiloxane liquids (witheight ethoxylates) on very low energy hydrocarbon surfacesby Cazabat, Tidberg, and co-workers.14 These authors haveshown that at equilibrium at the spreading edge thereexists a precursor film whose thickness indicates that itis composed of a trisiloxane bilayer. Churaev et al.15

measured the thickness of aqueous drops of trisiloxanesolutions, which have spread to equilibrium pancake-shaped layers micrometers in thickness. They find thatthese flat pancakes, which they note are stabilized fromfurther thinning by vesicular repulsion in the pancakeinterior, are surrounded by a much thinner film of 100nm or less which is in equilibrium with the pancake. Thethickness of the film at its edge was not measured, but theequilibrium of the two films suggests the edge of the drophas assembled into a bilayer, as analogous equilibria existin free-standing phospholipids films.16

The objective of this paper is to examine the surfactantstructure at the spreading periphery. In particular, weintend to demonstrate that T-structured surfactants canform bilayers at the spreading front while linear chainsurfactant molecules retain separate air/liquid and solid/liquid monolayers which co-join at the contact line.Surfactant arrangements at the three-phase contact lineat the edge of a spreading droplet due to surfactantadsorption is most accurately studied using moleculardynamics (MD) simulations since the rearrangementoccurs on the molecular scales at the spreading edge ofthe drop. Several studies have used MD to simulate thespreading of a drop of a pure liquid on a solid surface.Almost all of these investigations have used the Lennard-Jones (LJ) potential to model the interaction between thefluid molecules of the system, while the solid substrate ismodeled as either a lattice of atoms kept in place byharmonic potentials adjoining neighboring atoms andinteracting with the liquid particles (and each other) byan LJ interaction or as the source of an external (“9-3”)potential obtained by integrating the LJ potential over aninfinite half space. The first efforts studied the role of theliquid/solid interactions on the condensation of liquids onsolid surfaces and on equilibrium contact angles.17 Mea-surements of the spreading rate have been obtainedexperimentally by spatially resolved ellipsometry forpolymeric (poly(dimethylsiloxane), PDMS) fluids on solidsof various surface energies.18 These experiments motivateda series of MD simulations of polymeric LJ molecular fluidsspreading on solid substrates.19 De Coninck and co-workers also undertook MD simulations of LJ polymericmolecules spreading on an atomic lattice substrate to

obtain kinetic rate constants for the continuum kineticmodel of spreading20 and to examine spreading onheterogeneous surfaces21 and spreading of liquid mix-tures22 (see also the reviews in De Coninck et al.23). A fewsimulations have studied droplets spreading on substratesusing one of a few models to account for the electrostaticinteractions involved in the intermolecular hydrogenbonding of water molecules. Using the SPC model,Hautman and Klein24 undertook an equilibrium study ofa water cluster of 90 molecules on a surface consisting ofa self-assembled monolayer of alkylthiols terminated ineither a methyl or hydroxyl group and found that thecontact angle on the hydroxyl-terminated surface to besmaller, owing to the stronger interaction of the clusterwith the hydroxyl termination. A second MD study of wateron a graphite surface (modeled as a hexagonally arrayedsingle monolayer of carbon atoms) by Cosgrove et al.25

using the TIP-3P model to account for the hydrogenbonding of water (see also the related investigation by thesame authors on pillared super hydrophobic surfaces26

and the study by Werder et al. of water drops on graphiteusing the SPC/E model27 and Fan and Cagin of waterdrops on crystalline polymer surfaces28). The Cosgrove etal. study also examined the effect of the addition of ethanolto the water and found the contact angle decreased as theethanol molecules form adsorbed monolayers on thehydrophobic and vapor surface and represents one of thefirst efforts to simulate the effect of the adosrption ofsurfactant at the drop interfaces on the contact angle. AnMD simulation with LJ interactions by McNamara,Koplik, and Banavar29 studied cylindrical drops containingsolutions of simple model surfactants based on flexiblechains spreading along only one coordinate direction ona long strip of an atomistic substrate (a computationaldevice to reduce the number of atoms needed). None of anumber of surfactant models led to any improvement inspreading rate or final coverage, but the issue was cloudedby the linear geometry of the system. Unlike radialspreading, in the linear case, the average perimeter of thecontact line does not increase with time, and a tendencyfor surfactant to coagulate there impeded any furtherspreading.

2. Surfactant Models and Simulation Method

In place of simulating genuine aqueous solutions andrealistic molecular models of the trisiloxane and linearchain surfactant molecules discussed above, we studymoderately sized analogous systems on the basis of short-range LJ interactions. The simulations are based onstandard MD techniques in an NVT (constant number ofparticles, volume, and temperature) statistical ensemble,30

(14) Tidberg, F.; Cazabat, A.-M. Langmuir 1994, 10, 2301. Cazabat,A.; Fraysse, N.; Heslot, F.; Levinson, P.; Marsh, J.; Tidberg, F.; Valignat,M. Adv. Colloid Interface Sci. 1994, 48, 1.

(15) Churaev, N. V.; Esipova, N. E.; Hill, R. M.; Sobolev, V. D.; Starov,V. M.; Zorin, Z. M. Langmuir 2001, 17, 1338.

(16) Exerowa, D.; Krugliakov, P. M. Foam and Foam Films: Theory,Experiment, Application; Elsevier: Amsterdam, 1998.

(17) Saville, G. J. Chem. Soc., Faraday Trans. 1977, 12, 1122.Sikkenk, J.; Indekeu, J.; Leeuwen, J.; Vossnack, E.; Bakker, A. J. Stat.Phys. 1988, 52, 23. Nijmeijer, M.; Bruin, C.; Bakker, A.; vanLeeuwen,J. Physica A 1989, 160, 166. Nijmeijer, M.; Bruin, C.; Bakker, A.;vanLeeuwen, J. Phys. Rev. A 1990, 42, 6052. Mar, W.; Klein, M. L. J.Phys.: Condens. Matter 1994, 6, 381.

(18) Heslot, F.; Fraysse, N.; Cazabat, A. Nature (London) 1989, 338,640. Heslot, F.; Cazabat, A.; Levinson, P. Phys. Rev. Lett. 1989, 62,1286. Heslot, F.; Cazabat, A.; Levinson, P.; Fraysse, N. Phys. Rev. Lett.1990, 5, 599.

(19) Nieminen, J.; Ala-Nissila, T. Europhys. Lett. 1994, 25, 593.Nieminen, J.; Ala-Nissila, T. Phys. Rev. E 1994, 49, 4228. Heine, D.;Grest, G.; Webb, E. Phys. Rev. E 2003, 68, 061603.

(20) deRuijter, M.; Blake, T.; De Coninck, J. Langmuir 1999, 15,7836. Blake, T.; Clarke, A.; De Coninck, J.; Ruijter, M. d.; Voue, M.Colloids Surf., A 1999, 149, 123. Blake, T.; Decamps, C.; De Coninck,J.; Ruitjer, M. d.; Voue, M. Colloids Surf., A 1999, 154, 5.

(21) Voue, M.; Semal, S.; De Coninck, J. Langmuir 1999, 15, 7855.(22) Voue, M.; Rovillard, S.; De Coninck, J.; Valignant, M.; Cazabat,

A. Langmuir 2000, 16, 1428.(23) De Coninck, J.; Ruijter, M. d.; Voue, M. Current Opin. Colloid

Interface Sci. 2001, 6, 49. Voue, M.; De Coninck, J. Acta Mater. 2000,48, 4405.

(24) Hautman, J.; Klein, M. Phys. Rev. Lett. 1991, 67, 1763.(25) Lundgren, M.; Allan, N.; Cosgrove, T.; George, N. Langmuir

2002, 18, 10462.(26) Lundgren, M.; Cosgrve, T. Langmuir 2003, 19, 7127.(27) Werder, T.; Walther, J. H. J. Phys. Chem. B 2003, 107, 1345.(28) Fan, C. F.; Cagin, T. J. Chem. Phys. 1995, 103, 9053.(29) McNamara, S.; Koplik, J.; Banavar, J. In Computational

Science - ICCS 2001; Alexandrov, V., et al., Eds.; Springer: New York,2001.

(30) Allen, M.; Tildesley, D. Computer Simulations of Liquids;Claredon Press: Oxford, 1990.

12162 Langmuir, Vol. 21, No. 26, 2005 Shen et al.

and the technical details of the calculation are quite similarto our previous studies of the spreading of liquids on solidsand surfactant phase transitions at an air/fluid interface.31

The basic interaction between any two particle units oftype i and j is given by a LJ potential

Here ε is the energy scale, σ is the approximate diameterof the particle, where a single common value is used forsimplicity, and rij is the separation between particles. Thetwo terms represent repulsion at short distances and anattractive tail at larger separations, respectively. Theinteraction is cut off at a distance 2.5σ, so that thecomputation time is linear in the number of atomic units.The characteristic time unit is the microscopic time scale

for atomic motion, τ ) xmσ2/ε, where m is the (common)mass of an atomic unit. In the remainder of the paper, weuse σ as the unit of length, τ as the unit of time, and ε asthe unit of energy; rough numerical values might beseveral angstroms and several picoseconds for σ and τ,respectively. The coefficientsCij determine the interactionsbetween the various molecular species and control thechemistry of the system. The values will be specified below,but the general convention is to denote particle type 1 asbelonging to the hydrophilic head of a surfactant molecule,particle type 2 as the hydrophobic tail, particle type 3 asthe solvent, and particle type 4 as the solid substrate.

The solvent (particle type 3) is modeled as a monatomicliquid for simplicity, which automatically incorporatessome of the relative size difference between solvent andsurfactant molecules, since as we explain, the models forthe surfactant molecules contain several particles. Wehave considered two model surfactants, each composed ofeight particles, five hydrophobic units and three hydro-philic units, as shown in Figure 2. The particles are boundtogether by the well-studied finitely extensible nonlinearelastic (FENE) potential:32

which acts only between adjoining units. Here r0 ) 1.5 isthe maximum bond length and K ) 30 ε/σ2 is a springconstant. In conjunction with the LJ interaction, any twosuch adjoining atoms experience a confining potential witha well-defined minimum corresponding to the chemicalbond length. The first model surfactant shown schemati-cally in Figure 2 is the model for the trisiloxane andconsists of a T shape of five hydrophobic units and threehydrophilic particles attached to the center hydrophobicparticle. The three central particles of the hydrophobe

group are confined to be linear by using a bond-anglebending potential:

where θ0 is 180°. Again, for computational simplicity, weuse a soft potential rather than a rigid constraint; a forceconstant kθ ) 20ε gives a reasonably stable value of thebond angle. The two end particles, as indicated in thefigure, are freely jointed. The central hydrophobic particle,the hydrophilic particle, which attaches to the centralhydrophobe, and the hydrophobic particle on either sideof the central hydrophobe are confined to a perpendiculararrangement by a bond angle bending potential (θ0 ) 90°;kθ ) 20ε) to form the T shape. The three hydrophilicparticles are also confined to a linear arrangement by abond bending potential. The second model surfactant(Figure 2) is the model for the conventionally structured,linear flexible surfactant and consists of a five-particlehydrophobic group and a three-particle hydrophilic groupall freely jointed and connected by FENE potentialsbetween adjoining particles. The structures of the modelsurfactants mimic in an elementary way the structuralfeatures we have described in the Introduction which givethe trisiloxanes their superspreading/bilayer-formingability and prevent the conventionally structured sur-factants from being effective wetting agents on hydro-phobic surfaces. In the T model, the hydrophilic groupslie within the footprint of the linear hydrophobe umbrella;the linear hydrophobes can adsorb on the solid/liquidsurface and out into liquid/vapor interface in monolayerswith the hydrophilic particles extending perpendicularlyinto the liquid phase. At high concentrations, the hydro-phobes can situate themselves end-to-end. In the flexiblechain model for the conventional surfactant, the hydro-phobic groups can adsorb along the surface (at lowconcentration) or dangle perpendicularly to the surfaceat higher surface concentrations, where interactions ofthe hydrophiles with the solvent prevent close stacking.

The solid is modeled as an fcc atomic lattice with alattice spacing of 0.85σ, with its 001 face exposed to thefluid. The particles in the lattice are tethered to theirlattice sites by harmonic potentials with stiff constants.The particles comprising the surfactant molecules, thesolvent and the solid wall, all interact with each other byLJ potentials; all have the same LJ diameter and the samemass, except for the wall particles which have the samediameter but a mass 100 times that of the other particlesin the system.

We have used two different sets of interaction coef-ficients, Cij, as given in Tables 1 and 2. Note that Cij ) Cjiby Newton’s third law, so the matrix of coefficients issymmetric. For the solvent-solvent attractive interaction,we use a coefficient C33 ) 1.15, a value slightly larger

(31) Tomassone, M. S.; Couzis, A.; Maldarelli, C.; Banavar, J.; Koplik,J. J. Chem. Phys. 2001, 115, 14. Tomassone, M. S.; Couzis, A.; Maldarelli,C.; Banavar, J.; Koplik, J. Langmuir 2001, 17, 6037.

(32) Bird, R. B.; Curtiss, C.; Armstrong, R.; Hassager, O. Dynamicsof Polymeric Liquids; Wiley: New York, 1987; Vol. 2.

Figure 2. Structures of the model surfactants; tan (2) arehydrophobic particles and blue (1) are hydrophilic (a) T-shapedsurfactant, (b) flexible linear chain.

VLJ ) 4ε[( σrij

)12- Cij( σ

rij)6] (1)

VFENE ) - 12

Kr02 ln[1 - (r/r0)

2] (2)

Table 1

Cij 1 2 3 4

1 0.1 0.1 3.0 2.02 0.2 0.8 2.03 1.15 0.84 1.0

Table 2

Cij 1 2 3 4

1 0.1 0.1 2.0 2.02 0.2 0.8 2.03 1.15 0.84 1.0

VBA ) 12

kθ(θ - θ0)2 (3)


than the conventional LJ coefficient of unity, to increasethe cohesiveness of the solvent, to qualitatively model thehydrogen bonding in water, and to ensure that thesurfactants are insoluble. The solid-solid attractiveinteraction, C44, is left at the standard value of 1, and thesolvent-substrate coefficient, C34, is chosen to be 0.8, avalue, which, as we demonstrate below, yields partialwetting.

The attractive interactions between the solvent and thesurfactant’s hydrophilic heads (C13) is chosen to be strong(either 3 (Table 1) or 2 (Table 2)) and the solvent and thehydrophobic tails (C23) weak (0.8), in order that thehydrophilic headgroups extend into the droplet phase andthe hydrophobic groups extend out from the droplet phase,either into the vapor or onto the surface. These coefficientswere also adjusted relative to the value of the solvent-solvent coefficient so that the surfactant remains insoluble.The interactions between the various surfactant unitsthemselves are chosen to be weak, 0.1 or 0.2, to discouragethe separate formation of structures. The interaction ofthe hydrophobic groups with the surface lattice particlesis taken to be large to promote adsorption of surfactantat the hydrophobic solid surface. We consider both verystrong (Table 1) and not-as-strong (Table 2) interactionsof the hydrophiles with the solvent.

In the simulations, a liquid drop containing 112 sur-factant molecules (our standard number) and 8104 solventmonomers is equilibrated in free space at a temperaturekBT ) 0.9ε for 1000τ. The overall number of monomerswas constrained to a moderate value for reasons ofcomputation time since we were required to investigatea large number of choices of interaction coefficients inmapping out the parameter space. The relative numberof surfactant to solvent molecules was dictated by thenecessity for a high surface coverage by surfactant in thefinal spread state. We have also explored variations inthe number of surfactant molecules from our standardvalue of 112, including 126 and 144 molecules, for bothT-shaped and linear chains and Table 1 and 2 interactions.

It is important to note that, as we will see in oursimulations of spreading with the choices of interactionparameters as given in Table 1 and 2, the surfactantmolecules are essentially insoluble, residing on either theliquid/vapor or liquid/solid interfaces (flipping betweeninterfaces is however observed, see below). Experimen-tally, the trisiloxane superspreaders are very soluble, andthis solubility is necessary in order to provide surfactantto the spreading front of the drop where the surfactantsurface concentration is depleted due to the expansion inarea at the front. Owing to the smaller scale of oursimulations, the initial amount of surfactant on the liquid/vapor and liquid/solid interfaces which is present as thedrop contacts the surface (see below) is more than enoughto accommodate the area expansion due to the dropspreading.

A spherical drop forms with the surfactant’s hydrophilicgroups pointing inward toward the solvent bulk and thehydrophobic groups being expelled from the solvent.Typically, about half the solvent molecules are in the vaporunder these conditions. The drop is then translatedadjacent to the vicinity of the solid substrate, whichconsists of 7744 particles and which is also pre-equilibratedfor 1000τ before being placed in the drop’s proximity. Theattraction between liquid and solid atoms draws the dropinto contact with the solid, and spreading commences. Allsimulations are undertaken in a box with x and ycoordinates in the plane of the surface and the z coordinatenormal to the surface. The size of the box is 69σ in x, 80σin z, and 69σ in y, with periodic boundary conditions in

the x and y directions and a repulsive force field at the topof the box. The temperature is kept constant using constantkinetic energy rescaling; test runs using more sophisti-cated thermostats yield essentially equivalent results. Asa test of whether liquid-vapor equilibrium has beenreached, we have computed the number of vapor atomsoutside a cylinder which extends from the top of the dropdown to the substrate, which encloses the drop at all times.The amount of vapor is stable after about 1000τ. Simula-tions are undertaken for a duration of 5000τ from theconfiguration in which the equilibrated drop is firstpositioned in front of the equilibrated solid lattice. Steadybehavior in drop radius and height, as well as molecularconfigurations, is observed after 2000τ, as we demonstratebelow.

3. Results and Discussion3.1. Partial Wetting of Pure Liquid. The reference

point for our surfactant studies is the equilibrium con-figuration of a drop of pure solvent on the substrate. Figure3 gives a snapshot, at t ) 2000τ, of the instantaneousatomic positions of all liquid, vapor, and solid atoms; inthese and most subsequent snapshots, the viewpoint islocated far from the simulation box, along the x axis.Continuing the simulation for longer times does not affectthe interfacial profile or apparent contact angle. Theequilibrium contact angle is approximately 90°, indicativeof partial wetting which is our desired starting point. Thewetting behavior of the pure drop is determined by thevalues for the solvent-solvent and solvent-surfaceinteraction coefficients; here a value of 0.8 for the solvent-surface interaction, coupled with the solvent-solventinteraction coefficient equal to 1.15, provides enoughrelative cohesiveness of the solvent to result in partialwetting. (These values are common to all choices of theinteractions in Tables 1 and 2.). Note the solvent vaporsurrounding the drop representing the establishment ofthe vapor-liquid equilibrium. The relatively large numberof atoms in the vapor phase (approximately one-half ofthe total number of solvent particles) arises because amonatomic LJ fluid is extremely volatile, even at thereduced temperature of this simulation, 0.9, which is justabove the triple point of the fluid (approximately 0.7).Note also that due to the weakness of the solid-liquidinteraction, a continuous condensation layer does not formon the substrate surface.

3.2. Table 1 Coefficients: Bilayer Formation andEnhanced Spreading for T-Shaped Molecules andArrested Spreading for Flexible Linear Chain Sur-factants. In this section, we discuss the effects ofsurfactant adsorption at the fluid and solid drop interfacesfor the Table 1 coefficients. Figure 4a depicts, for theT-shaped molecule, the complete solvent and surfactantconfiguration at the initial time when the pre-equilibrateddrop is translated to the vicinity of the pre-equilibratedsurface, while Figure 4b-d presents the entire time

Figure 3. Spreading of the pure fluid; the white particlesindicate the monatomic solvent, and the yellow the lattice ofsolid surface atoms.


evolution sequence with solvent atoms omitted for clarity.In the initial configuration, the surfactant adsorption atthe surface of the drop is clearly visible from the darkgray hydrophobic tails extending out into the vapor phase(Figure 4a). At t ) 25τ, we see that, as the drop situatesitself on the surface, surfactant molecules remain adsorbedon the vapor/liquid interface facing away from the surface,a cluster of water is located in the interior, and thehydrophobic groups extending originally into the vaporphase and facing the surface have become adsorbed ontothe surface. During the course of the equilibration, thefive hydrophobes of the surface-adsorbed surfactantmolecules remain on the surface while the three hydro-philic groups extend out into the solvent phase. From theseand other snapshots not shown, and more quantitativelyfrom the plot of the spreading radius vs. time presentedbelow, we note that most of the radial spreading is confinedto times less than 500τ, while for later times spreadingis absent but the height of the drop continues to decrease.

The later stages of drop evolution (t larger than 500τ)are shown in Figure 4c and d; surfactant and solventrearrange themselves into a bilayer with the spreadingradius remaining constant and the height decreasing byone-third of its value. During this rearrangement, theupper surfactant monolayer descends toward the surface,so that the hydrophilic groups of the top layer are nearlyin contact with the surface, and the solvent rearrangesitself around these hydrophilic groups. The bilayerstructure which appears at t ) 2000τ optimizes theattractive potential energy in the system by takingadvantage of the T-shaped geometry. The hydrophobeslie flat on the surface, maximizing their large attraction

to it (C24 ) 2), and the hydrophilic groups extending intothe solvent are intercalated and co-joined by solventparticles. This co-joining optimizes the large attractioninteraction between the hydrophilic groups and the solvent(C13 ) 3). Finer details of this structure are displayed inFigure 5, which presents cropped views of the finalconfiguration for the particles contained in slabs a few σin thicknessrunningthroughthecenterof thedropparallelto either the x or y directions. We have extended thesecalculations to 5000τ (note also in Figures 6 and 7), andno further rearrangement of molecules occurs.

The spreading radius as a function of time is given inFigure 6 for the spreading of the pure solvent and for thevarious cases where surfactant is present. The simplestmethod for identifying the drop radius is to calculate the

Figure 4. (a) Deposition of drop with adsorbed T surfactantsonto the substrate surface for Table 1 coefficients. The whiteparticles are the solvent, the tan are the hydrophobic particles,and the blue particles are the hydrophilic particles. Yellowparticles represent the lattice of the substrate. (b-d) Timesequence for the T-shaped surfactant (Table 1 coefficients)adsorbing onto the surface (solvent omitted).

Figure 5. (a) Slab cut parallel to the x axis for a drop withT-shaped surfactant adsorbed onto the interfaces and Table 1coefficients; hydrophobes are colored tan, hydrophiles blue,surface particles yellow, and solvent white. (b) Slab cut parallelto the x axis, without solvent.

Figure 6. Radius as a function of time for the spreading of apure drop and a drop with surfactant adsorbed on the vapor/liquid and solid/liquid interfaces.

Figure 7. Maximum height as a function of time for thespreading of a drop of pure fluid and with surfactant adsorbedonto the vapor/liquid and solid/liquid interfaces.


number density of particles as a function of radial distancefrom the center of mass and to define the radius as thatvalue for which the number of particles drops sharply tozero. In the surfactant-laden case, an alternative methodwhich yields equivalent results is to measure the averagediameter of the region spanned by the surfactant mol-ecules; as seen in the figures, these are located in theinterior or at the boundary of the drop but not in the vaporand, hence, are good indicators of the contour of the spreaddroplet. From Figure 6, it is clear that formation of thebilayer acts to spread the drop into a film with a finalradius larger than the beaded up, hemispherical config-uration of the pure solvent: 20σ vs 13σ. Furthermore, theformer drop has spread about as far as it could, sincethere are not enough surfactant molecules available toextend the bilayer. Figure 6 also shows an increase inspreading of 60% as we compare the effect of the two typesof surfactants considered (linear and T-shaped). Noticethat the linear surfactant (eightmer Table 1 in Figure 6)spreads up to 12.5σ and the T-shaped surfactant producesa spreading of 20σ, showing a 60% increase in spreadingjust by changing the location of the monomers in the modelsurfactants and leaving the number of atoms and thestrength of the interactions the same.

The presence of the surfactant adsorbed on the dropinterface also appears to increase the speed with whichthe drop spreads. For pure solvent, there is a shortinduction period of approximately 100τ from the time thedrop is positioned above the substrate until it begins tospread, while in the presence of T-shaped surfactant,spreading begins almost immediately. This accelerationmay be attributed to the strong interaction of thehydrophobic and hydrophilic groups to the surface, whichdrags them down to the surface and carries the solventfluid along.

The height as a function of time, relative to themonolayer of surface atoms, is given in Figure 7. For puresolvent, the height is computed analogously to the radiusas the value of z where the number density of atoms vsheight drops sharply to zero, or in the presence ofsurfactant, the maximum value of z occupied by asurfactant monomer. The formation of the flat, bilayerfilm clearly reduces the height of the drop from the finalhemispherical configuration of the drop of pure fluid.However, the final bilayer height of approximately 10 isabout double the height expected if the T surfactantmolecules were in perfect registry. The extended heightis due partly to the fact that the hydrophiles of the Tsurfactants adsorbed at the liquid/vapor interface are notextending completely down to the substrate and also tothe fact that the height is a maximum measure and thehydrophobes of the T at the vapor/liquid interface extendout and do not lie flat on the liquid surface.

A markedly different behavior is observed for the flexiblelinear chain surfactant molecules, as seen in the timesequence of snapshots in Figure 8. We note first that abilayer does not form and instead the spreading is verylimited (the drop spreads less than pure solvent, whilemaximum heights are about the same) as a large clusterof solvent remains trapped in the droplet core in the finalstate. At the solid surface, the hydrophobes appear forthe most part to be adsorbed on the surface (due to thelarge 2-4 interaction) as was the case with the bilayer,again with hydrophiles extending into the solvent cluster.Surfactant is also adsorbed at the vapor/liquid interface,as well as with the hydrophobes extending into the vaporphase. These configurations are particularly clear in theslab cut views displayed in Figure 9.

From Figures 6 and 7, it is clear that stable asymptotesare achieved in the radius and height as a function of timeafter 2000τ, for the pure solvent case as well as thesurfactant Table 1 case (and Table 2 cases as well, seebelow), with the possible exception of the height as afunction of time for the eightmer case where the heightdecreases slightly with time. For the majority of cases, wemay therefore conclude that the drop volume is constantand evaporation of the solvent from the drop is notimportant (i.e., the vapor and liquid phases are sufficientlyequilibrated). In the outlying case, the slight reduction inheight is more likely due to extended rearrangements ofthe surfactant molecules, as these (as we explained above)contribute to our height measurement.

Because of the limited number of solvent molecules inour simulation, the molecular configurations depicted forthe T and flexible chain surfactants may be more indicativeof rearrangements at the spreading periphery of realsystems where, as the interfaces approach one another,the number of solvent molecules is limited. Noting this,we may conclude that the T shape drives a bilayerformation, which facilitates the spreading as a precursorfilm, while the flexible chain surfactants force the solventinto a cluster, effectively arresting spreading and creatinga locally large contact angle. Because of the limited numberof molecules (solvent and surfactant) in the simulation,some of the effects present in macroscopic systems, suchas transport of surfactant from the bulk to the periphery,are not faithfully reproduced. As such, the simulationresults reflect the behavior at the contact line and do notgive a complete picture of spreading dynamics.

These results can be interpreted within the context ofde Gennes’ classification of wetting regimes1 (the clearestaccount of superspreading within the context of de Gennes’wetting regimes is the article by Churaev et al.15). In the

Figure 8. Time sequence of a drop with linear flexible chainsurfactant adsorbed on the interfaces and Table 1 coefficients(solvent omitted).

Figure 9. (a) Slab cut parallel to the x axis for drop spreadingwith a flexible linear chain surfactant adsorbed on the interfacesand Table 1 coefficients. (b) Slab cut parallel to thex axis withoutsolvent.


case of only the solvent spreading on the substrate (in theabsence of any surfactant), we formulatedsby the choiceof interaction parameterssa circumstance where the dropdoes not spread and instead forms a finite contact angle(Figure 3). This is partial wetting: The spreading coef-ficient, S (the vapor/solid tension minus the sum of thevapor-solvent and solvent-solid tensions), is negative. Inaddition, since the solvent/solid (3,4) interaction param-eter, C34, is equal to 0.8 and the solvent/solvent (3,3)parameter, C33, is equal to 1.15, the Hamaker constant(A) (proportional to the difference between C33 and C34)is positive and the excess free energy per unit area for athin planar film with thickness h is negative (P(h) ) -A/12πh2). When surfactant is present, two additional effectscome in to play (i) the surfactants lower the bulk tensions,and the spreading coefficient can become positive if theliquid/solid and the liquid/liquid bulk tensions are reducedsufficiently and (ii) the excess free energy can change. Inthe case of the T-shaped surfactant, the spreadingcoefficient can become negative, while the formation ofthe bilayer (as a low free energy structure) wouldcontribute to a lowering of the excess free energy, P(h).Thus, qualitatively the free energy of a flat film as afunction of thickness would decrease from zero at verylarge h, have a minimum (with a negative value) corre-sponding to the optimal bilayer thickness, and then, forsmaller values of h, increase to positive values as thebilayer is compressed. (Correspondingly, the disjoiningpressure (Π(h) ) -dP/dh) would be negative for h largerthan the thickness at the free energy minimum andpositive for h smaller than the minimum.) For S > 0, forvery small drops (which would be the case in oursimulations where the size is limited), Leger and Joanny1

and Churaev et al.15 note that a pancake forms withthickness h* in which a positive spreading coefficient isbalanced by the positive disjoining pressure in the bilayer(corresponding to the compression of the bilayer), thethickness is given by S ) h*Π(h*) + ∫h*

∞ Π(h) dh. This isthe shape we believe is realized in our simulations of theT-shaped formation of the bilayer (Figures 4 and 5). Oursimulations also indicate that, as the surfactant surfaceconcentration increases, the pancake thickness decreasesslightly as the change in surface concentration affects thedisjoining pressure. In the case of the flexible eightmer(with the Table 1 coefficients), the spreading coefficientremains negative and a finite contact angle is retainedand not a pancake shape (Figures 8 and 9).

3.3. Table 2 Coefficients: Solid Substrate Mono-layers Spreading for the T-Shaped Molecules andSolid/Liquid and Liquid/Vapor Monolayers Spread-ing for the Flexible Linear Chain Surfactants. Theresults of the previous section indicate that the interactionof the solvent particles with the hydrophilic chains playsan important role in determining how surfactant structureaffects the adsorption on the drop interfaces, the self-assembly, and ultimately the drop spreading. Specifically,the hydrophile/solvent interaction provided the “glue”which binds the bilayer together and prevents surfactantfrom flipping between monolayers of the bilayer in theT-shaped case and holds the solvent cluster in place inthe flexible linear chain case. In the coefficients of Table2, we reduce the solvent-hydrophile interaction, C13, from3to2 (whilekeeping theremainingcoefficientsunchanged)to understand the effect of decreasing the strength of the“glue” on spreading. Figure 10 presents snapshots forT-shaped surfactant and a reduced 1-3 interaction atlater times (t > 500τ). The surfactant no longer forms abilayer; instead, the liquid/vapor interface is only sparselypopulated with surfactant, and most of the surfactant is

adsorbed, hydrophobic group down, on the solid/liquidinterface. The latter effect leads to an increased spreadingradius (relative to the stronger 1-3 interaction) fromapproximately 18 to 20 (Figure 6) as the additionalsurfactant adsorbed onto the substrate draws solvent withit, while the maximum height has decreased from 10 to8 (Figure 7). This result may be interpreted in the followingway: With the reduced 1-3 interaction, the system doesnot have to configure itself into a bilayer to maximize theinteraction of the solvent particles and the surfactanthydrophiles, as other interactions now become important.Specifically, the system takes advantage of the large (2-4) interaction between the hydrophobe and the surface byadsorbing more surfactant from the top monolayer ontothe solid surface, with the hydrophobic particles down.The depletion of the liquid/vapor interface does come atsome energy cost, since the vapor/liquid interface is nowsparsely populated with surfactant and the tension andenergy of this surface is now large since there areuncoordinated surface solvent particles.

In the Table 2 coefficients, the interaction of thehydrophobic and hydrophilic groups of the surfactant withthe surface are equal (C14 ) C24 ) 2), and the orientationof the surfactant at the interfaces is determined by thefact that the hydrophilic-solvent interaction (C13 ) 2) islarge relative to the hydrophobic-solvent interaction(C23 ) 0.8), so the hydrophobes extend into the vapor oradjoin the solid surface. If the interaction of the hydrophilicgroup with the surface is reduced (C14 ) 0.8 rather than2), we find that the remainder of the surfactant at theliquid/vapor interface becomes adsorbed at the solid/liquidsurface. The reason for this displacement may likely bedue to the fact that when a surfactant is adsorbed at thevapor/liquid interface, the hydrophiles extending into thesolvent are in closer proximity to the surface than in thecase when they are adsorbed at the solid/liquid interface;owing to the nearly complete adsorption of the surfactanton the liquid/solid interface, the solvent accompanies thesurfactant and spreads further than in the cases of Table1 and 2 (although only marginally further than in Table2), and the maximum height is correspondingly thesmallest.

We observe that during the initial spreading phase(t < 250τ) for Table 2 interactions, as the drop spreads,surfactant is layered down on the surface from the vapor/liquid interface at the periphery as a tank treading motion.However, for later times for which spreading has stopped,we note that the movement of the T-shaped surfactantfrom the liquid/vapor to the liquid/solid surface takes placethrough a kinetic route involving the turning around ofthe hydrophobic groups at the vapor/liquid interface andimmersion into the solvent followed by adsorption ontothe solid surface. Execution of this trajectory involvesmovement of the solvent particles including those coor-dinated with the hydrophilic groups of the surfactant. Toillustrate this point, we show in Figure 11 the trajectoriesof two representative molecules, one initially on the

Figure 10. Time sequence of drop spreading for T-shapedsurfactant with Table 2 coefficients (solvent omitted).


liquid-vapor interface and the other on the solid-liquidinterface. The former molecule flips over, and the latterdoes not. The reduction in the 1-3 interaction (i.e., theweakening of the “hydration shell” surrounding thehydrophiles) makes this kinetic route more accessible thanin the case of Table 1 where the 1-3 interaction is muchlarger. From this viewpoint, as mentioned earlier, we seethat, in addition to the co-joining of the hydrophiles fromthe top and bottom monolayers by solvent particles, animportant factor contributing to the stability of the bilayeris the strong coordination of the solvent particles to thehydrophilic groups themselves which makes it verydifficult for the surfactants to “flip” from one interface tothe other.

In the case of the flexible linear chain surfactant, thereduction in the attractive interaction between the hy-drophilic groups and the solvent (C13 ) 2 instead of 3)relaxes the cohesion between the layer of the surfactanthydrophilic groups adjoining the fluid and solid surfacesand the cluster of solvent particles comprising the drop.This cohesion prevents the drop from spreading furtherthan pure solvent. With the cohesion removed, the dropspreads further than pure solvent (Figure 6), and themaximum height decreases as well (Figure 7). As shownin Figure 12, as the drop spreads and comes to equilibrium,surfactant molecules adsorbed at the vapor/liquid andliquid/solid interfaces remain individual monolayersseparated by solvent particles, and the facilitated spread-ing relative to the pure liquid case can be attributed to thereduction in the tensions of the vapor/liquid and liquid/solid interfaces due to the monolayers which allows theseareas to expand. The contact angle at equilibrium in thiscase is markedly reduced relative to that of the puresolvent. This simulation is therefore an example of theclassical explanation of how surfactants facilitate wetting.As was the case with the T-shaped molecule, a change inthe strong attraction of the hydrophilic group to the surface(C14 ) 2 to C14 ) 0.8) has very little influence on thespreading configurations in the flexible linear chain

surfactant case. While the heights of the bilayer of the Tshape using the Table 1 coefficients is the same as thatof the flexible coefficients chain surfactants with thesolvent/hydrophilic interaction reduced, the organizationin the monolayer (as is evident from a comparison ofFigures 4 and 12) is different in that the chains danglinginto the solvent cluster from both interfaces are not nearlyas coordinated for the flexible linear chain surfactant asthey are for the T-shaped surfactant. Figure 6 of thespreading radius as a function of time indicates that theeightmer surfactant with the Table 2 coefficients spreadsalmost as well as that of the T-shaped surfactant with theTable 1 coefficients. While this is true, it does notnecessarily indicate that the eightmer model is a super-spreader. It is important to note that the enhancedspreading behavior of the Table 2 eightmers is stronglyinfluenced by the feature that the interaction between itsheadgroup and the solvent is reduced compared to theTable 1 values. In aqueous systems, this interaction isthat between a polar headgroup and water, which isusually strong. In the more realistic Table 1 case wherethe headgroup/solvent interaction is larger, this greaterinteraction causes the surfactant to bind to the solventand provides a tendency for the drop to ball up ratherthan spread. In this sense, only the T shape has properties

Figure 11. Trajectories of two representative T-shaped Table 2 surfactant molecules during spreading, illustrating a flip fromthe liquid-vapor to the solid-liquid interface.

Figure 12. Time sequence of the drop (solvent not shown)with the linear, flexible chain surfactant adsorbed on theinterfaces of the spreading drop for Table 2 coefficients.


which would encourage spreading when the interactionsare realistic.

It is important to note from the results for the flexiblelinear chain surfactant using Table 2 coefficients that,unlike the T-shaped case, when the attraction of thehydrophilic groups and the solvent is reduced, these chainsurfactants do not show a tendency to flip from the vapor/liquid to the liquid/solid interface. This result may reflecta kinetic limitation in that the flexible chain hydrophobeprovides a wider cross section compared to the T hydro-phobe, and it may be more difficult for the molecule todislocate solvent and adsorb onto the surface.

3.4. Variations in the Surfactant Surface Con-centrations. To explore the sensitivity of the results tothe number of surfactant molecules used in the simulation,we have varied this number from 112 to 126 to 144 for theTable 1 coefficients. The results are shown in the radiusand height vs time plots in Figures13 and 14. For bothtypes of molecules, the radius increases slightly, the heightdecreases slightly, and there is a slight improvement inspreading. There is no significant change in the structureof the surfactant hydrophilic heads, however; in Figure15, we give histograms of the end-to-end length of thehydrophilic parts of the molecule. (More precisely, wemeasure the distance between the end of the hydrophilicgroup and the hydrophobe atom to which it attaches.) TheT shape is typically longer because of the fixed bond angles(the hydrophilic groups are required to lie in a line

perpendicular to the center three hydrophobic groups, seeFigure 2), but bond-length fluctuations are still present.The key feature of this figure is that there is no variationin these length distributions with the amount of surfac-tant. In the eightmer case, in particular, increasingconcentration does lead to a tighter packing which wouldextend the length of the hydrophile.

4. Conclusions and Summary

In this paper, we have undertaken LJ MD simulationsof the spreading of a partially wetting drop of a monatomicliquid on a solid lattice surface when insoluble surfactants(bead and chain models) are adsorbed at the vapor/liquidand liquid/solid interfaces of the drop.

In our MD simulations, the T-shaped surfactant wasmodeledasaneight-particle “molecule”withahydrophobicgroup of five particles and the polar group a string of threeparticles attached to the middle hydrophobe unit of thenonpolar group. The hydrophilic string and the string ofthe center three particles of the hydrophobic group wereconstrained to be linear and intersect perpendicularly.The conventional surfactants were modeled as a flexiblelinear string of five hydrophobic particles followed by threehydrophilic particles. The LJ interaction coefficients forthe solvent and solid particles were chosen so that theliquid only partially wets the lattice surface in the absenceof surfactant, and surfactant interaction coefficients wereselected so that the surfactant straddled the interfaceswith the hydrophiles extending into the drop and thehydrophobes attached to the solid or extended into thevapor. Two different sets of values were used in the MDsimulations; these varied the strength of interactionbetween the hydrophilic particles and the solvent particlesand the hydrophilic particles and the particles of the latticesubstrate. It is worth mentioning that a very largeparametric space was tested and extensive simulationswere performed to find parameter sets that effectivelyrepresent the behavior of surfactants in aqueous systems.

For the base case of a strong interaction between thehydrophilic particles and both the solvent and the surface,the drops with the T-shaped surfactants form a structureresembling a bilayer, with the bilayer formation facilitat-ing the spreading of the drop into a thin lamella. Dropswith the flexible linear chain surfactant, for the samebase set of coefficients, did not spread further than thatof the pure liquid. We observed that the monolayers atthe two interfaces for this case remained distinct and thatthe strong interaction of the hydrophiles, arrayed as apacked inner layer around the cluster of solvent particles,restrained the solvent from spreading. We observe a 60%increase in spreading when going from linear chains toT-shaped chains. This highlights the importance of thestructure of the surfactant conformation in spreading since

Figure 13. Radius as a function of time for the spreading ofdrops with T-shaped (solid lines) and eightmer (dashed lines)surfactants with different numbers of molecules, using Table1 coefficients.

Figure 14. Maximum height as a function of time for thespreading of drops with T-shaped (solid lines) and eightmer(dashed lines) surfactants with different numbers of molecules,using Table 1 coefficients.

Figure 15. Histogram of the end-to-end length of the hydro-philic part (species 1) of the surfactant molecules for the Table1 interactions and various total numbers of surfactant mol-ecules.


the only difference between these two model surfactantsis the way the atoms are distributed in the chain but theyboth have the same the number of atoms in the headgroupand in the hydrophobic tails, as well as the same valuesfor the interaction between like atoms. A schematic of theconclusions of these simulations is shown in Figure 16where (despite the large areas per molecule at theinterfaces in the simulation)) spreading is facilitated bythe T configuration because of the favorable alignmentgeometry to form a more coherent structure resemblinga bilayer (A in Figure 16) than the flexible linear chainsurfactant (B in Figure 16) whose structure is moredisordered.

When the interaction of the hydrophilic groups withthe solvent was reduced (but the hydrophile/solid interac-tion was kept large), drops spreading with a T-shapedsurfactant were observed to form a spread lamella in whichmost of the surfactant was adsorbed to the solid substrate.The final spreading radius was actually larger than thatof the bilayer, as the additional surfactant adsorbed onthe solid surface entrained solvent particles. When theinteraction of the hydrophiles with the solid was reducedas well, all but a few of the T-shaped surfactant was foundto have adsorbed onto the solid substrate, with the finalspreading radius only marginally larger. In both theselater cases, after an initial spreading period wheresurfactant from the vapor/liquid interface was depositedon the substrate at the periphery as the drop spread, thefurther deposition of surfactant from the liquid/vapor tothe solid/liquid interface occurred at constant radius ofspreading by the movement of the surfactant through thethin film. We attributed this direct deposition to the stronginteraction of the hydrophobes for the surface which, whenthe film is thin, drives the surfactant to the surface andthe reduction in the hydrophile/solvent interaction whichincreases the mobility of the molecule through the liquid.For the drops spreading with the linear, flexible chainsurfactant, the reduction in the solvent/hydrophilic in-

teraction allowed the drop to spread into a thin film. Unlikethe case of the spreading of the drop containing T-shapedsurfactant, the monolayer at the vapor/liquid interfaceremained; an effect we attributed to the inability of theflexible chain surfactant, even with a reduced coordinationshell, to maneuver through the film and adsorb onto thesurface. Although the drop spread to a thin lamella, theflexible chain surfactant monolayers at the two interfacesappeared more individual and distinct than in the case ofthe T-shaped surfactant and the strong interaction solvent/hydrophile interaction that produced the bilayer. Furtherreduction of the hydrophilic/surface interaction for theflexible chain surfactant did not affect the spreading.

Considering the small size of our systems, we are carefulin making conclusions. We can still argue that theformation of this bilayer may be due to two effects: Thefirst was the T geometry, which allowed for the conformalassociation of the hydrophiles. The second is a kineticeffect arising from the strong hydrophile/solvent interac-tion, which created a coordination shell of solvent aroundthe hydrophiles. This shell acted to preserve the bilayerby preventing surfactants at the vapor interface fromflipping onto the solid surface. While the MD simulationsdo indicate that that the T-shaped (trisiloxane) geometrycan promote the formation of a bilayer drawing the dropinto a thin lamella, in contrast to the flexible linearsurfactants which formed separate monolayers and ahemispherical unspread shape, the comparison withexperiments cannot be taken too strictly. Aside from thefacts that the MD simulations account only for LJinteractions which do not accurately model the polarinteractions of water and that the surfactant structuresare elementary and the surfactant insoluble, the surfac-tant areas per molecule in the monolayers are relativelylarge compared to the close-packed structures which occurin superspreading. As such, the structures resemblingbilayers in the T-shaped case have much more solventspace then we might expect in a bilayer. Clearly, moresimulations that account for the polar interactions of waterare still needed. Simulations aimed at a more realisticportrayal would not only incorporate aqueous hydrogenbonding but also simulate larger systems at higherconcentrations of surfactant on the surfaces to depict morerealistic area exclusions and molecular arrangements.

Acknowledgment. M.S.T. acknowledges the MerckFoundation, and J.K. acknowledges the NASA ExplorationSystems Mission Directorate for financial support.

LA051354C

Figure 16. Rendering, based on the MD simulations, of thecontrasting solvent/surfactant structures developed with the Tand flexible chain surfactants.


Documents

Molecular Dynamics Study of the Influence of Surfactant Structure on Surfactant-Facilitated Spreading of Droplets on Solid Surfaces