Exploring the Impact of Tail Polarity on the Phase Behavior of SingleComponent and Mixed Lipid Monolayers Using a MARTINI Coarse-Grained Force FieldAla’a F. Eftaiha,*,†,‡ Surajith N. Wanasundara,§ Matthew F. Paige,‡ and Richard K. Bowles‡

†Department of Chemistry, The Hashemite University, P.O. Box 150459, Zarqa 13115, Jordan‡Department of Chemistry, University of Saskatchewan, 110 Science Place, Saskatoon, SK S7N 5C9, Canada§Department of Medical Imaging, University of Saskatchewan, 103 Hospital Drive, Saskatoon, SK S7N 0W8, Canada

ABSTRACT: Coarse-grained molecular dynamics simulationshave been used to investigate the effect of dipalmitoylphos-phatidylcholine (DPPC) tail group polarity on the structuraland phase behavior of both single component and binarymixed monolayers using the MARTINI force field. Surfacepressure−area isotherms of single component systems indicatethat DPPC monolayers become more expanded as a functionof increasing tail group polarity, as observed in experimentalmeasurements in the literature. A combination of radial distribution functions and tilt angle measurements indicate thatincreasing tail group polarity results in the formation of increasingly disordered monolayers. For the mixed monolayer systems,the time dependence of the radial distribution function as well as average cluster size measurements indicate that phaseseparation takes place between components of different tail group polarity when the monolayers undergo phase transition intodisordered configurations.

■ INTRODUCTION

Mixed monolayer films of surfactants are invaluable systems forprobing numerous important physical and chemical phenom-ena, ranging from phase-separation and intermolecularinteractions, to dynamics of surface processes.1−14 The spatialdistribution and organization of surfactants in mixed films is akey area of interest, in part because mixed monolayers (andbilayers) are excellent, albeit highly simplified model systemsfor biological membranes and interfaces, such as the gasexchange interface in lungs and the tear film in eyes, whichexhibit complex spatial distributions of surface-active spe-cies.15−17 A significant effort has been made to understand andcontrol factors that regulate intermolecular interactionsbetween surfactants in complex mixed films, though many ofthese factors are still poorly understood. The development of asimple, minimal model for predicting the spatial distribution ofsurfactants based on the chemical identity of film constituentsand the composition of mixed monolayer systems is animportant but challenging research goal, and efforts to developsuch models are ongoing. In this work, we have explored theinfluence of one key molecular property, surfactant tail grouppolarity, on the structure and spatial distribution of one andtwo-component monolayers, as an incremental step toward thedevelopment of such a model.Computer simulation is a powerful approach for studying the

properties of surfactant films because they provide informationwith a high temporal and spatial resolution that may not befeasible experimentally.17−21 In this regard, molecular dynamics(MD) simulations have been used successfully to study

molecular properties of lipid components in biologicalassemblies, viz., monolayers and bilayers.22−28 While the latterare of fundamental importance as biological membranes, theformer can be used as models to study complex phenomena inbiological systems. Investigations of the structure and dynamicsof lipid architectures via MD simulation have been reported inthe literature using both atomistic and coarse-grained (CG)models.29−35 Although atomistic MD simulations provideinformation about monolayer structure and dynamics, thesekind of simulations are restricted to relatively short time scaleswhich prevents the study of many phase transition process, andthey are prohibitively expensive in terms of computing time forsystems containing a large number of species.36−39 This has ledto the development of more computationally efficient CGsimulation models, which have been able to treat patches ofbilayer membranes up to a few tens of nanometers in lateralextent, over time scales of a few tens of nanoseconds. Inparticular, the MARTINI force field has proven to be useful toinvestigate a wide range of lipid systems covering not onlybilayers but also monolayers, micelles, and vesicles to study self-assembly processes and phase behavior at the microsecondtime-scale as well as to probe protein−lipid interactions ofmembrane-embedded proteins.39−43 The MARTINI force fielduses four main types of interaction sites, referred to as polar(P), nonpolar (N), apolar (C), and charged (Q). Each particle

Received: April 20, 2016Revised: June 11, 2016Published: July 12, 2016

Article

pubs.acs.org/JPCB

© 2016 American Chemical Society 7641 DOI: 10.1021/acs.jpcb.6b03970J. Phys. Chem. B 2016, 120, 7641−7651

type has a number of subtypes that are either distinguished by aletter denoting the hydrogen-bonding capabilities (d = donor, a= acceptor, da = both, and 0 = none), or by a numberindicating the degree of polarity starting from 1 (low polarity)to 5 (high polarity). These subtypes allow tuning ofinteractions on the basis of the chemical nature of atoms.40−42

The MARTINI force field has been shown to reproduce avariety of important structural, dynamic, and thermodynamicproperties of lipid monolayers.44−53 Baoukina et al.44 used theMARTINI force field to explore the behavior of DPPCmonolayers by compressing and expanding two symmetricmonolayers bound to a slab of water. The calculated isothermsrevealed the occurrence of a liquid-expanded (LE)−liquid-condensed (LC) coexistence region, which was in goodagreement with experimental values obtained from captivebubble surfactometer measurements. However, the width of thecoexistence region did not change noticeably with temperatureand the surface pressure in that region was not constant.Duncan and Larson reported that surface pressure−area (π−A)isotherms of MARTINI DPPC monolayers obtained by cyclingsimulations were shifted upward at higher temperatures and theLE−LC coexistence region of both compression and expansionisotherms were shortened. In comparison with experimentallymeasured isotherms, the calculated isotherms were shifted tolarger areas/lipid and the LC−LE coexistence regions occurredat larger pressures.45 In this regard, Tieleman and co-workers44

observed the presence of pores in the LE region of the DPPCmonolayer. This was explained by the low surface tension of thevacuum-water interface, which stabilized pores and preventedthe actual expansion of the monolayer. The influence of lateralpressure profiles on MARTINI lipid monolayers has beenstudied by Tieleman’s group.49 The calculated pressure profilesof DPPC monolayers denoted the presence of repulsiveinteractions between headgroup beads that were balanced bya compensating attraction between headgroup and waters beadsin the LE phase. At higher surface density, the repulsiveelectrostatic interactions between the headgroups beadsprevailed over the attractive headgroup/water interactionsdue to reduced extent of solvation. The aforementioned studiesprovide useful insights into the potential use of the MARTNIforce field to study LE and LC phases of lipid monolayers. Inaddition to characterizing the properties of single-componentmonolayers, the MARTINI force field has proven useful for theexploration of phase separation processes in mixed lipidmonolayers and bilayers.52−56

Our research group and others are particularly interested inunderstanding factors that regulate the organization anddistribution of surfactants in mixed monolayers comprised ofhydrogenated and semi- or perfluorinated surfactants at theair−water and air−solid interfaces.57−60 Interest in these mixedfilms is substantial because of their potential use in industrialand biomedical applications, including, for example, their use asfirefighting foams61 and for lung surfactant mixtures.62 Mixedmonolayer films of fluorinated and hydrogenated surfactants(most commonly mixtures of fluorinated fatty acids withhydrogenated fatty acids or phospholipids) are oftenheterogeneous, with the intrinsic lipophobicity of thefluorinated surfactant contributing significantly to this effect(see the works by Kimura et al.63 and Krafft et al.64 foroverviews of this topic). However, a variety of additionalintermolecular interactions also influence the spatial distribu-tion of film constituents; for example, the influence ofhydrophobic−lipophobic interactions between surfactant tail

groups are a strong function of surface pressure of themonolayer. While the CG simulation studies described abovehave provided important insight into lipid-demixing using theMARTINI force field, fundamental advances are still needed tounderstand the influence of tail polarities on lipid miscibility inmixed monolayers.In this study, the MARTINI force field has been used to

study the effect of lipid tail polarity on the phase behavior ofsingle component and mixed Langmuir monolayers byincreasing the polarity of DPPC tail beads. In this approach,we use C1 beads to model saturated aliphatic tails, and CGbeads with a more polar character are designated by C2, C3, C4,and C5. A detailed description for the interaction between theCn beads and other bead types has been provided (vide inf ra).As a simple model system, we have chosen to study monolayerfilms comprised of either pure DPPC for a single componentsystem or a mixture of two “variants” of DPPC, with eachvariant having a tail group of different polarity, for the mixedfilm. π−A isotherms, radial distribution functions (RDFs) andsurfactant tilt angle calculations for the single componentmonolayer systems indicate that the monolayer becomes moreexpanded and disordered as the tail group polarity is increased.Similar calculations for mixed monolayers have also beencarried out. Results reveal that the lateral heterogeneity withinthe mixed monolayer components is a strong function of thebead polarity.

■ METHODSMARTINI Coarse-Grained Force Field. Scheme 1 shows

the chemical structure and MARTINI GC representation of a

DPPC molecule as adapted from Marrink et al.40 The positivelycharged choline (−NC3

+), the negatively charged phosphate(−PO4

−) and the glycerol ester groups are presented as Q0, Qa,and Na beads, respectively. Each of the lipid tails is modeled byfour hydrophobic particles (C1), representing 16 methyleneunits.Bonded interactions are described by the sum of bond

stretching and angle potentials that are described by weakharmonic potentials. Nonbonded interactions are described bya sum of Lennard-Jones (LJ) 12−6 and Coulomb potentialfunctions given by40

εσ σ

πε ε= − +

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥V

r r

q q

r4

4nb ijij

ij

ij

ij

i j

o r ij

12 6

(1)

Scheme 1. (A) Chemical Structure of DPPC and (B) CGRepresentation of the MARTINI DPPC Molecule

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in which σij is the particle size interaction between species i andj, εij is the strength of their interaction, rij is distance betweenparticles i and j, εo is the dielectric constant in vacuum and εr isthe relative dielectric constant. Here, qi and qj are the chargeson particles i and j, respectively. Generally, the MARTINI CGforce field defines ten levels (0−9) of LJ interactions betweenthe particles based on their chemical identity. The strength ofeach level is determined by the value of εij. The polarinteractions of a compound in the solid state at roomtemperature are described by level I, as are the strong polarinteractions found in materials such as bulk water. Volatileliquids are described by levels II and III. The nonpolarinteractions in aliphatic chains are described by level IV.Various degrees of hydrophobic repulsion between polar andnonpolar phases are described by levels V−VIII. Theinteraction between charged particles and an apolar mediumis described by level IX, which also introduces a longer σij thatincreases the effective repulsion between the components.Molecular Dynamics Details. Our simulation box was

made of two symmetric monolayers (256 molecules in eachlayers) sandwiching a water slab. The box was expanded to 25nm in the direction normal to the water−DPPC interfaces inorder to create a vacuum region in the DPPC tail region. Thesevacuum regions prevent interaction between the DPPC tails ofthe two separate monolayers when periodic boundaryconditions (PBC) were applied.The MARTINI 2.1 CG force field40,41 was used to model the

DPPC monolayer at the vacuum−water interface. All MDsimulations were performed using the Gromacs 4.0.5 softwarepackage45,65 with a time step of 30 fs. The CG simulation timescale was used throughout the paper. The interpretation of thetime scale in CG simulations is not straightforward. Incomparison to atomistic models, the dynamics observed withCG models is faster.40 All nonbonded interactions were treatedusing the standard shift function of Gromacs with a cutoffdistance of 1.2 nm.66 The temperature during simulation waskept constant at 298.15 K using the Berendsen thermostat.Surface tension coupling was applied by using the Berendsenpressure coupling algorithm.66 In this case, surface tension wasapplied to the x/y-plane of the simulation box (parallel to thebilayer surface), and the z component (normal to the surface)of the pressure was coupled to a pressure bath. PBC wasapplied in all directions. In this article, the terms surface tensionand surface pressure have been used to describe the interfacialfree energy of the water slab covered by amphiphiles. Thesurface pressure of a monolayer film is defined as the differencebetween the surface tension of the exposed water slab and thesurface tension of the slab covered by a monolayer. Thus, anincrease in surface tension of the slab results in a decrease insurface pressure. To remove unfavorable contacts betweenatoms, the initial structure of the DPPC−water system was firstrelaxed by energy minimization, followed by a 1 μsequilibration MD run with −50 mN/m surface tension.Negative surface tension was used to create a highly orderedmonolayer system as a starting configuration. The boxconfiguration obtained at the end of the equilibration periodwas then used to perform MD simulations with zero surfacetension for 1 μs. The final configuration was subjected to a newequilibration period for a 100 ns with a surface tension of 10mN/m, followed by a 1 μs simulation period at the samesurface tension. Afterward, the surface tension was systemati-cally increased by 10 mN/m. At each increment, a 100 nssimulation period was performed, followed by a 1 μs simulation

for data collection. This was continued until the surface tensionreached the largest possible value without causing the box sizeto diverge. The process was then reversed by decreasing thesurface tension back to zero. This process, referred to as cyclingthe CG MD simulation, was repeated by changing the CGbeads of the DPPC tails in the final configuration, obtained at−50 mN/m from C1 to C2, C3, C4, and C5. The samemethodology was repeated for 3:1 C1−Cn mixed monolayers.

■ RESULTS AND DISCUSSIONSingle Component Monolayers at the Vacuum−

Water Interface. π−A expansion−compression isotherms ofCn−DPPC monolayers, generated as described above, arepresented in Figure 1. Expansion cycles show that upon

decreasing the surface pressure, the area per molecule of thehighly ordered monolayers is slightly increased. Furtherdecreases result in a substantial change in the area, describedhere by a phase transition from a highly ordered to a disorderedmonolayer. When the surface pressure reaches the lowestpossible value without diverging the box size, the process isreversed; i.e., the monolayers are compressed, going back to π =72 mN/m. As the systems are recompressed, the isothermsexhibit a hysteresis loop.Our calculated C1−DPPC isotherm is consistent with the

simulation results reported previously by Duncan et al.45

However, the phase transition region, identified by a suddenshift to larger mean molecular area, is steeper and shifted tolarger molecular areas than seen experimentally.8−10 Thisdiscrepancy between simulation and experimental results isconsistent with previous reports and has been explained by theMARTINI force field neglecting some degrees of freedoms as itgroups four heavy atoms into a single interaction center.40 Ingeneral, because of these limitations, quantitative comparisonbetween simulated and experimentally generated isotherms isnot common in the literature. Furthermore, while the simulatedisotherms are affected by the selection of force field

Figure 1. (π−A) expansion (dotted)−compression (solid) isothermsof Cn−DPPC monolayers at the water−vacuum interface at 25 °C.The error bars are the standard deviation in mean molecular area atthe surface pressure of interest and were obtained from threeindependent simulations.

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parameters,66 the experimental counterparts are highlyinfluenced by factors such as the subphase temperature andcomposition, the choice of the spreading solvent, and the rateof monolayer compression.45 Because of this, the simulationresults obtained here will only be compared qualitatively withthe experimental results reported in the literature. The standarddeviation of mean molecular area values along the expansionand compression curves were ≤1, except for those pointsobtained after the sudden decrease in area upon compressionthat showed large fluctuations (the last and the second last datapoint along the solid curves).As shown in Figure 1, the onset of the expanded phase

moves to higher pressures as the tail beads change from C1 toC5. The phase transition regions are also shifted to highersurface pressures and take place over a smaller range ofmolecular areas. It is anticipated that noncovalent bondinginteractions between tail−tail and head−tail beads govern thephase behavior of Cn−DPPC monolayers. As described byMarrink and co-workers,40 the interactions between analogoustail beads are modeled by nonpolar interactions in the aliphaticchains and they are similar regardless of bead polarity, i.e., theinteraction between C1−C1 is the same as C2−C2, etc.Therefore, any changes in phase behavior of the singlecomponent monolayers are regulated by the tail−head beadinteractions. In this regard, the tail−head bead interactions,namely Cn−Q0 (choline group), Cn−Qa (phosphate group) andCn−Na (glycerol ester moiety), are considered to be repulsiveaccording to LJ 12−6 potential, where εij varies in the range of2.0−3.5 kJ/mol, and generally increases as C5 goes to C1, whichimplies a more favorable interaction between higher polaritytails and Na, Q0, and Qa beads. This can be inferred from thehigh surface pressure values obtained for C1−DPPC condensedmonolayer compared to higher polarity molecules, whichsuggest that the repulsive interactions between the aforemen-tioned tail−head beads increased with decreasing tail polarity.Consequently, the Cn−DPPC monolayers adopt a moredisordered configuration at higher surface pressure indescending polarity order.This trend is qualitatively consistent with the experimental

results reported by Toimil et al.67 that showed the LE−LCcoexistence region of the π−A isotherms of monofluorinated-DPPC monolayers on the air−water interface were shiftedupward to a higher surface pressure compared to that of thefully hydrogenated counterpart. The formation of the moreexpanded monolayer was attributed to the size of the fluorineatom, which disrupts the surfactant packing and thus weakensthe van der Waals cohesive interactions between chains. It isimportant to emphasize that effects due to the bead size areexcluded in this study because a bond length of 0.47 nm isadopted for the majority of MARTINI beads, which suggestsadditional factors such as the interaction between head and tailsgroups may also play an important role in determining thephase behavior of these monolayer systems.The two-dimensional RDFs of Cn−DPPC monolayers have

been used to identify the onset of the phase transition as themonolayer is expanded. It is calculated from the center of massof each molecule parallel to the lipid−water surface. The RDF,gAB(r), between two molecules of types A and B is defined bythe following equation:

π=

∑ ∑∈ ∈g rV P r

r( )

( )

4iN

jN

ABA B

2

A B

(2)

where V is the volume of the system and P(r) is the probabilityof finding a molecule of type B at distance r from a molecule oftype A. Figure 2 shows the RDFs of Cn−DPPC molecules thathave been calculated at different surface pressures and averagedover 1 μs.

At the highest surface pressure studied (π = 72 mN/m), theRDFs of all the pure single component systems appear similar,with a sharp first peak located at 0.5 nm and broader peaksoscillating out to large distances indicating the presence oflong-range order. This is consistent with the RDF reported forDPPC monolayer using atomistic68 and CG44 models. Whenthe surface pressure is decreased to π = 62 mN/m, the RDF ofthe C5−DPPC film decays rapidly to the ideal gas value within1.5 nm and the intensity of the first peak is reduced. Thissuggests that the C5−DPPC film has become disordered, butthe persistence of the first peak shows that the system retains adegree of short ranged order, which is characteristic of a liquid-like phase. Similar features have been observed in mixedmonolayers comprised of DPPC and palmitoyloleoylphospha-tidylcholine.69 The other systems remain ordered at this surfacepressure. However, a similar peak height reduction and decay isobserved at π = 52 mN/m for the C3− and C4−DPPCmonolayers and at π = 42 mN/m for C2 based lipids. Once thesystems have transformed to their disordered phases, the firstpeak in their RDFs decreases slightly as a function of decreasingsurface pressure, as the systems expand.Increasing the polarity of the tail beads results in decreasing

in the intensity of the RDF as well as reducing the intensity ofthe first peak at higher surface tension in comparison withlower tail polarity molecules. This indicates that the monolayerbecomes more disordered and the Cn−DPPC molecules aredistant and loosely packed as a function of tail bead polarity.These results confirm the onset of the substantial change inmonolayer area observed from the π−A isotherms, where thephase transition take place at lower surface pressure withincreasing tail polarity.The tilt angle adopted by a tail group characterizes the

orientation of the hydrophobic chain with respect to the surfacenormal and results from its interactions with the head groups ofother molecules, its interaction with the subphase, and in thecase of gemini surfactants, interactions between the two head

Figure 2. Radial distribution functions of Cn−DPPC molecules in puremonolayers measured at different surface pressures and averaged over1 μs simulation time.

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groups within the same molecule. Volume exclusion betweenintramolecular chains will tend to tilt the head groups awayfrom each other. Mohwald and co-workers70 suggested that thehydrophilic carbonyl group of C1−DPPC acts as a mediatingforce that pulls the tails toward the water subphase, whichwould also favor large tilt angles. These single molecule effectsare then modified by collective phenomena involving the othermolecules in crowded environments. As a result, thedistribution of tilt angles can provide detailed informationabout film structure in the phase transition region. Unfortu-nately, the orientation of the entire headgroup is not uniquelydefined because each bead along the chain can adopt a differentbond angle. One simple approach is to define a tilt angle as thetilt of the bond connecting two consecutive beads along a chainwith respect to the surface normal. Here, we report on thehead−tail (H−T) and tail−tail (T−T) tilt angles, which aredefined using the bonds formed between the Na−Cn and Cn−Cn beads, respectively (See Figure 3A). The distributions areobtained by measuring the angles from both chains for eachmolecule and are collected over a 1 μs time interval. Figure 3Bshows that the H−T and T−T tilt angle distributions for alldifferent Cn−DPPC systems look similar at π = 72 mN/m, withthe maximum H−T and T−T tilt angles appearing at about 16°and 9° respectively. These are slightly below experimentalmeasurements70−72 that indicate the hydrocarbon chains ofC1−DPPC are tilted from the surface normal by 25° in thecondensed phase. The H−T distribution is wider than the T−Tdistribution. As π is decreased, the C5−DPPC system goesthrough its condensed to expanded phase transition near π = 62mN/m and both tilt angle distributions exhibit significantbroadening and their peaks shift to larger angles of 29° and 24°for the H−T and T−T tilt angles, respectively. In the expandedphase, the distributions continue to exhibit small shifts to larger

tilts with decreasing surface pressure. Similar results areobserved for the C4− and C3−DPPC molecules as they gothrough their respective transitions at lower π. These resultssuggest that the intermolecular chain interactions tend to forcethe chains to stand and that the film structure undergoes asignificant structural change as it enters the compressed phase.

Mixed Monolayers at the Vacuum−Water Interface.π−A expansion−compression isotherms of mixed filmscomprised of 3:1 C1−Cn DPPC are shown in Figure 4. Theincorporation of C2− and C3−DPPC species into a C1−DPPCmonolayer does not result in a significant change in theexpansion−compression isotherms. A further increase in the tailpolarity, i.e., for C4 and C5 beads, shifts the isotherms markedlyupward in comparison with the C1−DPPC monolayer andresults in smaller hysteresis loops. These are accompanied bythe formation of more expanded configurations at lower surfacepressures. The results are in reasonable agreements with theexperimental isotherms reported by Shibata and co-workers59

that indicated the LE−LC transition pressure was increasedupon mixing C1−DPPC with perfluorinated surfactant, whichprovides a correlation between our simulation data and theexperimentally measured isotherms.The nature of the repulsive interactions between the Cn (tail)

and Na (glycerol) beads, which decreases with increasing thetail polarity, help explain the general trends of the simulationisotherms in a way that is consistent with the behavior of thesingle component monolayers shown in Figure 1. According toMarrink’s40 classification, the interactions between the C1, C2,and C3 beads are identical so that the small changes in theisotherms can be attributed to the attractive changes observedin the head−tail interactions causing the C2 and C3 moleculesto become slightly more repulsive, as noted before. However,the upward shift in the isotherms of C1−C4 and C1−C5

Figure 3. (A) Schematic representation of head-to-tail (H−T) and tail-to-tail (T−T) tilt angle. (B) Tilt angle distribution of Cn−DPPC molecules inpure monolayers measured at different surface pressures and averaged over 1 μs simulation time.

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mixtures occurs because the hydrophobic repulsion between Cngroups of the different components increases to level V.Although there are several drawbacks associated with the use

of the LJ 12-6 potential to describe the nonbonded interactionsusing the MARTINI force field, it appears to be suitable for ourstudy because it provides CG beads with wide range of polarcharacter (C1 to C5), with interaction energy values range from

5.6 kJ mol−1 for strongly polar groups to 2.0 kJ mol−1 forinteractions between polar and apolar groups. In this context,the degree of mixing and the spatial distribution of surfactant inthe mixed monolayer systems, RDFs between the center ofmass of the Cn−Cn molecules have been calculated as afunction of time for the C1−Cn mixed monolayers in the highlyordered monolayers and before the occurrence of the phasetransition during expansion (Figure 5). At π = 72 mN/m, theRDFs of C2 and C3 species are typical for the highly orderedmonolayers with the characteristic peaks at 0.5 and 1 nm for theCn−Cn species in the mixed monolayers.69

The intensity of the RDFs for the mixed monolayers do notchange significantly over 1 μs, even when surfactant crowding isreduced by decreasing the surface pressure to 42 mN/m. Thissuggests the system remains well mixed, consistent with anintimate association between the components of the mixedmonolayer. The intensity of the RDFs for the C4 and C5 speciesincrease with time, at π = 72 mN/m, indicating that thedomains of high polarity tail molecules are dynamic on the timescale of the simulation. These intensities become larger whenthe surface pressure was decreased to 62 mN/m, suggestingthat the high polarity molecules become preferentiallysurrounded by molecules of the same kind as the simulationprogresses. This is indicative of domain growth and segregationon the simulation time scale. If the mixture components aredesignated by A and B, then C1−C2 and C1−C3 mixtures canbe considered an ideal mixture, because A−A, B−B, and A−Binteractions are all equally strong. However, the interactionsbetween C1−C4 and C1−C5 mixtures are not the same as theA−A and B−B interactions; consequently, they should beviewed as nonideal mixtures.

Figure 4. (π−A) expansion (dotted)−compression (solid) isothermsof 3:1 C1−Cn mixed monolayers at vacuum-water interface at 25 °C.The error bars are the standard deviation in mean molecular area atthe surface pressure of interest and were obtained from threeindependent simulations.

Figure 5. Radial distribution function of C1−Cn in 3:1 C1−Cn mixed monolayer as a function of simulation time and surface pressure.

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In order to verify the time dependency of the RDFmeasurements, the average number of molecules per cluster(or average cluster sizes of the Cn species) as a function of timeand surface pressure was obtained using a Gromacs utilityprogram, viz. g_clustsize with “-mol” and “-cut =0.35” options.In the routine, a molecule was considered to be a part of acluster if the distance between any CG bead in the moleculeand any CG bead in the cluster is less than a distance of 0.35nm. Data are presented in Figure 6.The measurements for C1−C2 and C1−C3 mixed monolayers

show that Cn species form small clusters (mostly trimers,tetramers and pentamers) for all of the investigated surfacepressures through the expansion−compression cycle. Thisagrees with the previously shown RDF measurements as afunction of time and indicates that C1−C2 and C1−C3 speciesare fully miscible regardless of the surface pressure. Themeasurements of C1−C4 and C1−C5 systems show a significantchange in the average cluster size as a function of surfacepressure with the progress of time. At π = 72 mN/m, thecluster size increases from 5 to 10 Cn molecules during a 1000ns time interval. A further decrease in the surface pressure to 62mN/m increases the cluster size to 15 molecules per cluster forboth mixtures. At π = 52 mN/m, which corresponds to thephase transition in the π−A expansion isotherm of the 3:1 C1−C5 mixed system, the clusters size increases rapidly in the first200 ns, to end with one cluster made of 64 molecules. Similarbehavior occurs for the C1−C4 mixed system at π = 42 mN/m.This agrees with the findings of Laradji et al.,73 who indicatedthat unsaturated phosphatidylcholines with C4 beads under-went phase separation when mixed with C1−DPPC, whilethose with C3 beads type were miscible with C1−DPPC.Top views for the lateral distribution of the Cn molecules in

the mixed monolayer at different surface pressures are shown in

Figure 7. Note, because of periodicity, the size of the clustersshown in the figure below is limited by half of the simulationbox size. In other words, the formation of independent clustersunder PBC requires a simulation box size exceeding thecorrelated length by at least an order of magnitude.Depictions in the first and second columns show snapshots

for the monolayer structure before and after the phasetransition during expansion, respectively and those in thethird column show snapshots for the monolayers aftercompressing back to π = 72 mN/m. The structures of theC1−C2 and C1−C3 mixed monolayers do not change eitherabove or below the phase transition surface pressure, indicatingthat these systems are fully miscible. The monolayerscomprising of C4 and C5 species indicate the formation ofseveral clusters just before the onset of the disorderedconfiguration, confirming the cluster size measurements. Theoccurrence of the phase transition upon monolayer expansioninduces lateral phase separation, ending with the formation ofone cluster composed of 64 molecules (the middle island andthose at the rim due to the PBC in the second column of Figure6, parts C and D, respectively). However, the phase-separatedclusters are stable in the expanded phase and the system doesnot mix on compression, suggesting that the phase-separatedsystems are the thermodynamically stable state. However, itcould be that the solid phase is well-mixed and that kineticeffects prevent the mixing process.At this stage, we are unable to entirely decouple these

thermodynamic effects from kinetics of the phase-separationprocess. While free energy calculations might provide insightinto the importance of separation kinetics on the structures thatare observed here, such calculations are out of scope of thepresent work and will be investigated in detail later.

Figure 6. Average cluster size comprised of Cn molecules as a function of time in 3:1 C1−Cn mixed monolayer at different surface pressures along theexpansion−compression cycle.

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Herein, our results provide a simple approach to predict thephase behavior and the lateral distribution of mixed monolayersmade of amphiphilic molecules with different tail polaritiescompared to the rigorous efforts needed experimentally toexamine phase separation through a variety of microscopicimaging techniques. In this context, a useful comparator systemthat can be described by our model are mixed hydrogenatedand halogenated surfactants monolayers, particularly semi- orperfluorinated surfactants.One of the main findings that highlight the promising

potential of our system to model hydrogenated and fluorinatedsurfactants at air−water interface is the upward shift of thecalculated π−A isotherms of Cn−DPPC monolayers to highersurface pressures when the polarity of the tail beads areincreased. This is consistent with the experimentally reportedisotherms of monofluorinated and fully hydrogenated DPPCmonolayers at air−water interface, which indicated the LE−LCcoexistence region starts at higher pressures for themonofluorinated DPPC in comparison with fully hydrogenatedDPPC. Another important result that obtained from oursimulation is the onset and extent of phase separation in mixedmonolayers. This was accomplished by measuring the averagecluster size and the RDF as a function of time and surfacepressure. Experimentally, phase separation is measured usingsurface microscopy techniques. Our group as other measured

the morphology of mixed Langmuir−Blodgett films of usingatomic force microscopy, confocal fluorescence microscopy andBrewster angle microscopy. Measurements indicate that themixed components tend to form a distinct domain shapes as afunction of surface pressure and composition.One of the main shortcomings of our model is the loss of

many structural details, which limit the usefulness of theMARTINI force field for several phenomena. This inherentdeficiency is explained by the use of four-to-one mappingstrategy to represent a molecule. Another shortcoming is thearbitrary degree of polarity designated by number 1 to 5. Thenonbonded interaction between the interaction sites should beoptimized toward representing carbon−halogen bonds explic-itly, which will make the MARTINI force field a significant toolto explore mixed hydrogenated-fluorinated monolayers. Inaddition to the limited spatial and chemical resolutionassociated with the MARTINI force field, the lack of structuralflexibility of MARTINI proteins, the narrow fluid range and thelow surface tension at the air/water interface can hinderMARTINI calculations from precisely reproducing experimen-tal data.42 There are some efforts to overcome these limitationssuch as using generalized LJ potential and introducingstructural polarization into the GC model.74

The ability to tailor the morphology of surfactant filmscomprised of hydrogenated and perfluorinated or semi-

Figure 7. Top views of the lateral distribution of Cn−DPPC molecules in the mixed monolayer comprised of 3:1 C1−Cn DPPC: (A) C1−C2, (B)C1−C3, (C) C1−C4, and (D) C1−C5 (C1, C2, C3, C4 and C5 molecules are presented in dark gray, blue, green, yellow, and pink, respectively).

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fluorinated surfactants at solid−air and liquid−air interfaces isof considerable technological importance. The extent ofsegregation between the film forming components can betailored by manipulating by the degree of tail polarity to make acompromise between line tension and dipole−dipole inter-action. Our simulation results indicate that the MARTINI forcefield is of potential importance to understand the mixingbetween surfactant molecules of different tail polarity, whichcan be used as a model monolayer film system to providethoughts about mixed perfluorocarbon−hydrocarbon films. Inorder to provide in-depth understanding of mixed monolayersurfactant films, the addressed shortcoming of the MARTNIforce field should be overcome, particularly the implicitexpression of the bead polarity and the effective bead size,which is assumed to be the same for most of the interactionsites.

■ CONCLUSIONS

It has been demonstrated that the lateral organization of Cnbased molecules in mixed C1−Cn monolayers is a function oftail polarity and surface pressure. It has been shown thatincreasing the tail bead polarity shifts the phase transitionregion of mixed lipid monolayers into higher surface pressures.This has been examined by the π−A isotherms, the timedependent RDF measurements and average cluster sizecalculations. Results indicate that the miscibility of the lipidmolecules is decreased as the difference in the bead tail polarityis increased in the expanded monolayers. Although the inherentlimitations associated with the MARTINI force field maynegatively impact the simulation outcome as reportedpreviously, the results obtained here are consistent with thosereported experimentally. Our finding indicates that theMARTINI force field can be used to understand and controlthe phase behavior of mixed apolar surfactant systems at air−water interface with a view toward understanding andcontrolling film morphology and composition.

■ AUTHOR INFORMATION

Corresponding Author*(A.F.E.) E-mail: alaa.eftaiha@hu.edu.jo. Telephone: +962(5)3903333, ext. 4530.

Author ContributionsThe manuscript was written through contributions of allauthors. All authors have given approval to the final version ofthe manuscript.

FundingFunding for this work was provided by the Natural Sciencesand Engineering Research Council of Canada (NSERC), andthe Canada Foundation for Innovation (CFI). All computationswere performed using computing resources provided byWestGrid (www.westgrid.ca) and Compute/Calcul Canada.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

Thanks are paid for Mr. Jason Hlady and Dr. Juan CarlosZuniga at Information and Communications Technology atUniversity of Saskatchewan for providing help in data recoveryas well as for the WestGrid technical support team for their fastresponse to inquiries.

■ ABBREVIATIONSDPPC, dipalmitoylphosphatidylcholine; MD, molecular dy-namics; CG, coarse-grained; P, polar; N, nonpolar; C, apolar;Q, charged; LE, liquid-expanded; LC, liquid-condensed; RDF,radial distribution function; H−T, head-to-tail; T−T, tail-to-tail; PBC, periodic boundary conditions; LJ, Lennard-Jonespotential

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