Molecular Dynamics Simulation of Alkylthiol Self-Assembled

Article pubs.acs.org/Langmuir

Molecular Dynamics Simulation of Alkylthiol Self-Assembled Monolayers on Liquid Mercury Anton Iakovlev,† Dmitry Bedrov,*,‡ and Marcus Müller† †

Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany Department of Materials Science & Engineering, University of Utah, 122 South Central Campus Dr., Salt Lake City, Utah 84112, United States

‡

S Supporting Information *

ABSTRACT: We report computer simulation of the self-assembly of alkylthiols on the surface of liquid mercury. Here we focus mainly on the alkylthiol behavior on mercury as a function of the surfactant surface coverage, which we study by means of large-scale molecular dynamics simulations of the equilibrium structure at room temperature. The majority of the presented results are obtained for octa- and dodecanethiol surfactants. This topic is particularly interesting because the properties of the alkylthiol self-assembled monolayers on liquid mercury are relevant for practical applications (e.g., in organic electronics) and can be controlled by mechanically manipulating the monolayer, i.e., by changing its structure. Our computer simulation results shed additional light on the alkylthiol self-assembly on liquid mercury by revealing the coexistence of a dense agglomerated laying-down alkylthiols with a very dilute 2D vapor on mercury surface rather than a single vapor phase in the low surface coverage regime. In the regimes of the high surface coverage we observe the coexistence of the laying-down liquid phase and crystalline phases with alkylthiols standing tilted at a sharp angle to the surface normal, which agrees with the phase behavior previously seen in X-ray and tensiometry experiments. We also discuss the influence of finite-size effects, which one inevitably encounters in molecular simulations. Our findings agree well with the general predictions of the condensation/evaporation theory for finite systems. The temperature dependence of the stability of the crystalline alkylthiol phases and details of the surfactant chemical binding to the surface are discussed. The equilibrium structure of the crystalline phase is investigated in detail for the alkylthiols of various tail lengths.

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INTRODUCTION A phenomenon of self-assembly is inherent to basically every process in nature and technology. Generally, organic selfassembled monolayers (SAMs) on metal surfaces are used for nanodevice fabrication,1 structure control of a supporting substrate,2 wetting control,3−5 corrosion and wear protection,6 tailoring electric properties of surfaces in organic electronics,7−12 and the creation of biofunctionalized interfaces.13,14 Thiol SAMs on gold surfaces received immense attention from experiments1,15−18 and have been intensively studied by molecular simulations5,19−32 as well. Moreover, other organic and biosurfactants were extensively studied on clay, mica, oxides, and other metal surfaces and nanoparticles13,33−37 Additionaly, the collective behavior and temperature-dependent transitions of the alkyl-based surfactants on crystalline surfaces were previously rationalized as a function of packing density for a wide range of crystalline substrates.34,35 In this paper we expand on our previous letter,38 in which we have presented the first molecular simulations of the selfassembly of normal alkanes (n-alkanes) and alkylthiols (thiols) on the surface of liquid mercury (Hg). A n-alkane molecule consists of a linear chain of alkyl groups (CH2) terminated from both ends by methylene groups (CH3). Unlike n-alkanes, thiols have a sulfur headgroup (S) on one end of the alkyl © 2016 American Chemical Society

chain, which readily creates chemical bonding with mercury once it is on the surface of liquid Hg. It was shown that this difference in the chemical structure between n-alkanes and thiols results in qualitatively different structures that these surfactants form on the surface of liquid mercury at high surface coverage values, i.e., at higher numbers of thiol molecules per unit area (1 nm2). Upon the increase of the thiol surface coverage surfactants undergo a sequence of phase transitions from a partially filled monolayer of laying-down molecules up to highly ordered crystalline-like structures with molecules standing tilted at a sharp angle to the surface normal. n-Alkanes, on the other hand, do not form any standing phases on liquid Hg, rather after the completion of the first layer of the layingdown molecules they start to self-assemble into respective bulk phases. These predictions from our previous molecular simulations were consistent with available X-ray data.39−42 The highly ordered thiol SAMs on liquid Hg were also observed by infrared spectroscopy measurements.43 Finally, optical tensiometry experiments have also indirectly confirmed Received: October 16, 2016 Revised: December 10, 2016 Published: December 30, 2016 744

DOI: 10.1021/acs.langmuir.6b03774 Langmuir 2017, 33, 744−754

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Langmuir complex structural transformations in the thiol SAMs on mercury with the increasing surfactant surface coverage.44 The thiol SAMs on liquid Hg are intensively used in organoelectronics applications for the creation of metal−SAM− semiconductor juctions, the properties of which depend on the shape of the liquid Hg electrode, i.e., on the form and structure of the thiol SAM on it.7 The present knowledge of the latter is limited and mainly originates from several X-ray studies briefly mentioned above.39,40 On the other hand, any system involving mercury is very difficult and hazardous to handle in practice, and the ability to model such systems in a computer simulation is, with no doubt, crucial for the further progress in this area, because simulations allow to probe the validity of various theoretical models or experimental conjectures (e.g., molecular interactions and architecture) directly at the molecular scale. In this paper we focus on the thiol structures as a function of molecular surface coverage. We discuss the emerging thiol phase coexistence regions on the surface of liquid Hg and the equilibrium structure thereof as well as the concomitant finitesize effects. In the next section we will to discuss the molecular model and force fields used in our MD simulations of the thiol self-assembly on liquid mercury. Following, the formation and evolution of thiol SAMs with the increase of the molecular surface coverage as well as the structure of the emerging thiol phases on liquid Hg will be described. To conclude, we draw some final remarks in the last section.

mainly octa- (SC18) and dodecanethiol (SC12) molecules. For the SC18 and SC12 molecules the thiol surface coverage, σ, is varied in the ranges [0.27, 2.11] nm−2 and [0.53, 2.01] nm−2, respectively. The simulations are performed for the system cross section, Acs = Lx × Ly, of 9.936 × 10.104 = 100.4, 14.904 × 15.156 = 225.9, and 29.808 × 30.312 = 903.5 nm2. Periodic boundary conditions are applied in all directions. Empty space is added above and below the film such that molecules on the opposite surfaces do not interact with each other through the periodic boundaries. The width of the mercury film in all the cases is kept approximately the same and equals 8 nm, which is sufficient to avoid the coupling between the two surfaces. Bonded interactions consist of bond, bend, and torsion contributions. The Hg atoms in the film are treated atomistically by using our double-exponent pair force field developed previously.46 The interaction of the surfactants with liquid mercury also follows the double-exponent form.38 The nonbonded pair interactions between the atoms constituting thiol molecules are of the LJ form. The cutoff radii for the double-exponent and LJ potentials are 8 and 15 Å, respectively. No electrostatic interactions are present in the UA-model used in our simulations. Bonded atoms of the same molecule that are separated by three or less bonds do not interact via nonbonded interactions. The functional form and detailed list of all the parameters for the above interactions are given in the Supporting Information. The simulations are performed in the NVT ensemble, in which the temperature is fixed at 293 K by means of the Nosé− Hoover chain thermostat47 of the length of 10 coupled thermostats with a temperature damping parameter of 100 fs. The rRESPA multiple time step method48 as implemented in LAMMPS45 is used with the time step for bonded and nonbonded interactions of 0.5 and 2 fs, respectively. The sampling for analysis is done every 2 ps in the course of at least 80 ns of simulations after equilibrium is reached (or a steady state for oversaturated systems). The system is considered to be in a metastable state or in equilibrium when both the total energy of the system and its surface tension reach a constant level, at which they fluctuate around some mean value. Further information on the system setup and equilibration is given in the Supporting Information. It is useful to define in advance several angles, which we are going to use in the following for the description of the thiol SAM on mercury surface. The tilt angle, θ, is the sharp angle between the molecular axis of a thiol molecule and the direction of the z-axis. The tilt direction angle, ϕ, is the angle between the xy-projection of the thiol molecular axis and the x-axis. In the following treatment of distinct surfactant complexes the direction of the x-axis is chosen to point along the respective S−Hg−S bond. The angles α1, α2, and α3 define the directions from a chosen bound Hg* atom to its first, second, and third nearest neighbors, respectively. All these angles (apart from α3) are schematically depicted in Figure 1b. Finally, the surface tension, γ, is calculated in the course of MD simulations from the asymmetry of the normal and tangential pressure components.46,49

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SIMULATION TECHNIQUES Molecular dynamics (MD) simulations are carried out utilizing the LAMMPS package.45 We use a united-atom (UA) representation for alkyl (CH2) and methyl (CH3) groups in order to simulate the thiols.38 At the surface of liquid Hg two thiol molecules can bind to a single Hg atom in such a way creating a double-tailed surfactant complex consisting of two thiols and a single Hg atom (RS−Hg−SR) as shown in Figure 1a. In the following we will designate as a bound mercury (Hg*) a Hg atom, which is incorporated into such a RS−Hg− SR complex. We use a slab geometry with a Hg film placed in the middle of the simulation cell. As shown in Figure 1b, the film lies in the xy-plane and the z-axis is perpendicular to its surface. An equal number of thiols is preadsorbed on the top and bottom of the Hg film. For the studing of the surface coverage effects we use

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RESULTS Influence of Surface Coverage. Molecular Conformations. Figure 2 and Figure S2 demonstrate the octadecanethiol conformations for the values of the system cross section area Acs = 903.5 and 100.4 nm2, respectively. In the regime of low thiol surface coverage (σ < σl) a monolayer of agglomerated

Figure 1. (a) Schematic view of octadecanethiol molecules on liquid mercury: two thiols molecules are bound to one surface mercury atom thus creating a S−Hg−S bond. (b) Schematic illustration of the angles relevant for the description of the alkylthiol monolayer on mercury surface. Color code: alkyl tails (green); sulfur headgroups (yellow); bound mercury (purple); bulk mercury (red). 745


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Figure 2. Octadecanethiol conformations on liquid mercury for various thiol surface coverage values, σ. Acs = 903.5 nm2. Color code same as for Figure 1.

Figure 3. (a) Alkyl (solid line) and sulfur (dashed line) density profiles perpendicular to the Hg surface for various surface coverages, σ, of octadecanethiols. The center of mass of the system is at z = 0. (b) Probability distributions of finding carbon atoms in a surface element of the cross section of 1 × 1 nm2 for various octadecanethiol surface coverages. Note the peak centered at vanishing surface density for the lowest σ values. Acs = 903.5 nm2.

approaches σ0 and, therefore, the smaller the surface coverage interval (σ0, σ*) (in which the system exists in the oversaturated state) becomes. For example, σ* ≈ 0.8367 and 1.116 nm−2 for Acs = 903.5 and 100.4 nm2, respectively. Only after σ* is reached (not σ0) the formation of the crystalline islands of the standing-up thiols is observed, and the thiol monolayer is phase separated into an inhomogeneous state featuring a coexistence of the laying-down and standingup molecules. The behavior observed in our MD simulations agrees very well with the general predictions of the condensation/evaporation theory of finite systems.50−52 As is clearly seen from the snapshots, the extent and geometry of the crystalline islands of the standing-up thiols depend on the overall thiol surface coverage. With the increase of the thiol surface coverage the number of the SC18 molecules in the crystalline islands grows (Table S3). We consider only those thiols to be in the standing-up conformations that belong to the surfactant complex (RS−Hg−SR), in which both thiol tails have a tilt angle θ < 45°. Additionally, we note that the molecules in the standing-up crystalline islands gradually decrease their tilt angle starting from a particular side of the

SC18 thiols in the laying-down conformations coexist with a very dilute two-dimensional (2D) vapor (bare surface of liquid Hg). Here σl ≈ 0.66 nm−2 is the surface coverage of the liquid laying-down thiols in the coexistence with the vapor phase. This quantity can be determined from the probability distributions of finding a particular number of alkyl groups (surfactants) in a surface element of 1 nm2, which are described below. Between σl and σ0 = 0.8 nm−2 we observe a single compressible monolayer of the laying-down molecules (see e.g. a snapshot for σ = 0.7 nm−2 and Acs = 100.4 nm2 in Figure S2). At σ0 the SC18 monolayer reaches the full coverage in the laying-down conformations (Figure S2). The value of σ0 corresponds to the surface coverage of the SC18 laying-down phase in the coexistence with the standing-up phase. But, unlike a macroscopic system, in simulations the finite-size effects hinder the formation of the standing-up phase after an immediate increase of the surfactant surface coverage above σ0. First, upon the rise of σ above σ0, the monolayer of the laying-down thiols keeps existing in an oversaturated state up to a specific value of the thiol surface coverage, σ*, which is system size dependent. Namely, the larger the system cross-section is, the closer σ* 746


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Figure 4. (a) Surface tension (points) as a function of octadecanethiol surface coverage, σ, for various system cross-sections, Acs. Fit (red solid line) of the MD surface tension by eqs 7 and 8. Dashed lines are the guides for an eye. The fit is done for the points that correspond to the coexistence of the laying-down and standing-up thiols (σ = 1.12, 1.44, and 1.61 nm−2). (b) Finite-size effects for the conformations of octadecanethiols for different system cross sections, Acs, but the same surface coverage σ = 1.12 nm−2. Color code: red (bulk Hg), purple (bound Hg*), yellow (S), green (CH2,3).

island. This is illustrated in Figure S3. In the figure one can see that the first row of thiols on one side of the crystalline island are laying flat on the surface of liquid Hg. The subsequent rows of thiol molecules lay down with their alkyl tails onto the previous rows, in such a way gradually decreasing their the tilt angle. The effect of the nonuniform tilting vanishes as the one goes further away from the side of the island where the thiols are laying flat. The regime of σ < σ* is characterized by the growth of single peaks in the density profiles (perpendicular to the Hg surface) for alkyl and sulfur groups (Figure 3a), indicating the filling up of the first layer of the laying down SC18 thiols. As σ increases above σ*, the density profiles start to develop shoulders away from the Hg film (Figure 3a), which corresponds to the formation and growth of the islands of standing-up surfactants. As it is clear from Figure S3, the sulfur headgroups in the standing-up subphase are adsorbed deeper into the mercury compared to the laying-down one. This corresponds to the increase of the mismatch in the positions of the sulfur and alkyl peaks at low surface coverages as the number of surfactants growth. Another useful characterization of the phase separation of the thiols on liquid Hg is the probability distribution of finding a particular number of the alkyl groups in the surface element with a cross section of 1 nm2. This choice of the surface element is particularly convenient since it is not too big and, thus, resolves the molecular features of the surfactants, and at the same time this surface element is not unphysically small. The limiting size for such a surface element would be πσCH22 = 0.5 nm2, where σCH2 = 3.93 Å is the Lennard-Jones radius of a

CH2 group. We present the surface density distribution of CH2 groups for SC18 thiols in Figure 3b. We see that at the lowcoverage regime (σ < σl) the surface density distributions are characterized by a double-peak pattern. One peak is located at about 10 and the second one at zero CH2 groups per 1 nm2 corroborating the coexistence of the aggregates of the layingdown SC18 thiols with the 2D low-density vapor. The molecular coverages in the interval between σ0 and σ* result in a single-peak pattern, as is seen from the surface density distribution for σ = 0.8367 nm−2 (Figure 3b). For σ > σ* a double-peak pattern re-enters again, but now the second peak emerges at higher surface densities of CH2, namely at about 75 CH2/nm2. This yields the SC18 surface coverage σisl = 4.17 nm−2 in the island of standing-up thiols at the coexistence with the laying-down molecules. The dodecanethiols display similar phase behavior as their longer counterparts as is seen from the MD snapshots of SC12 systems for various values of the SC12 surface coverage (Figure S4). The main difference is that the SC12 thiols reach σ0 and σ* at higher surface coverages compared to the SC18 systems. The full coverage of the monolayer of the laying-down SC12 thiols is attained at σ0 ≈ 1.12 nm−2 as is evident from the respective snapshot (Figure S5). In this case we have been able to resolve the coexistence of the crystalline SC12 islands and the respective laying-down phase starting at σ = 1.44 nm−2. From the comparison of Tables S4 and S3 one can see that the number of the dodecanethiols in the standing-up conformations is notably lower than of the octadecanethiols at the corresponding surface coverages. The SC12 density profiles (Figure S6a) are similar to the ones of the SC18 thiols. The 747


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tension gradually drops down to the value of the second plateau as σ increases toward σ0. One can also rationalize this behavior in the framework of a simple phenomenological model. For this purpose let us think of the mercury substrate as of a reference system (that merely sets the magnitude of the first plateau in the γ−σ isotherm) and consider for a moment the thiol monolayer as a purely 2D system that can have two phases: one compressible phase (laying-down thiols) and another one much denser incompressible phase (standing-up thiols). Then according to the simplest considerations from the condensation/evaporation theory of finite systems,52 if one increases the surface coverage in the compressible state above the full coverage, σ0, of the layingdown thiols, this will compress the system and increase its free energy by

only difference compared to the SC18 systems is that the density profiles of the SC12 molecules feature regions of elevated intensities (for σ > σ*) in the intermediate region between the first peak (due to the laying-down phase) and the extended shoulder (due to the standing-up phase). We attribute such behavior to wider and more fluctuating boundaries of the SC12 crystalline islands (see Figure S4) compared to the SC18 islands. From the respective surface density distributions of the SC12 systems (Figure S6b) one can approximately determine the surface coverage of SC12 molecules within the crystalline islands to be 4.13 nm−2. γ−σ Isotherms. Quite often in experiments the coexistence of various surfactant phases is identified by plateaus in surface tension−surface coverage (γ−σ) isotherms or, equivalently, by plateaus in surface pressure−area per molecule isotherms.39,53 It appears to be a challenge to resolve such plateaus and respective coexistence regions in a computer simulation due to dramatic finite-size effects because of which one has to simulate exceedingly large systems as for an atomistic simulation. Figure 4a shows the surface tension as a function of the SC18 surface coverage for various system cross sections. On the figure one can clearly distinguish two plateau regions separated by a dip in between. The first plateau region corresponds to the coexistence of the laying-down thiols with the 2D vacuum and extends from σ = 0 up to σ < σl, where σl ≈ 0.66 nm−2 is the surface coverage of the 2D liquid phase of SC18 thiols at the coexistence with the corresponding 2D vapor phase of surface coverage of σv, which virtually equals zero in our simulations. In the region between σl and σ0 we have a compressible liquid phase of the laying-down SC18 thiols, which is characterized by a continuos change of the surface tension. As mentioned above, in the region between σ0 and σ* we observe an oversaturated monolayer of the laying-down molecules, which is characterized by surface tension values below the overall level of the second plateau. The second plateau region corresponds to the coexistence of the layingdown and standing-up thiols and starts at σ = σ*. We anticipate that it continues up to the value of σ, at which the first monolayer of the standing-up thiol is completed. The fact that we observe these two plateaus qualitativelya corresponds to the experimental behavior.39 The presence of the dip between two plateaus (for σ between σ0 and σ*) and the departure of the second plateau from a constant level are the finite-size effects, which we are going to discuss in the following. The dip in the γ−σ isotherms corresponds to the region of σ values (between σ0 and σ*), at which oversaturated monolayers of the layingdown thiols exist. As mentioned before, we observe in our simulations that the surface coverage, σ*, at which the phase separation becomes favorable, strongly depends on the system cross section and approaches σ0 for larger Acs in such a way reducing the extent of the oversaturated region. Most prominently this effect is seen for the systems with σ = 1.12 nm−2 and various values of Acs. In Figure 4a we see that for these systems at Acs = 100.4 and 225.9 nm2 the surface tension values are substantially below the second plateau, whereas for Acs = 903.5 nm2 the surface tension virtually lies on the plateau. From the corresponding MD snapshots (Figure 4b) one can see that for smaller system cross sections (Acs = 100.4 and 225.9 nm2) the monolayer resides in the oversaturated state, while for a much larger system (Acs = 903.5 nm2) the number of surfactants suffices in order to phase separate, thus rendering the system inhomogeneous. In the thermodynamic limit oversaturated regions do not exist (σ0 = σ*), and the surface

ΔFhomo =

Acs (σ − σ0)2 2k T

(1)

where kT is the 2D compressibility. On the other hand, if the extra molecules in the system are used to form a crystalline island of the standing-up thiols, the free energy will be incremented by ΔFinhomo = 2πτR

(2)

where τ is the line tension of the boundary between the layingdown phase and the island of the standing-up thiols and R is the radius of the island of the standing-up thiols. Assuming that the shape of the islands is circular and that the boundary between the two phases is sharp, the level rule σ0(Acs − πR2) + σislπR2 = N

(3)

yields R=

(N − σ0Acs)/(π Δσ0)

(4)

where Δσ0 = σisl − σ0. Furthermore, the surface coverage, σ*, at which the formation of a crystalline island becomes more favorable over an oversaturated state, is defined by the condition ΔFhomo(σ *) = ΔFinhomo

(5)

Finally, from eq 5 we obtain ⎛ 16πτ 2k 2σ 4 ⎞1/3 T 0 ⎟ σ * = σ0 + ⎜ A Δ ⎝ ⎠ cs σ0

(6)

The last equation clearly supports our computer simulation observations, namely, that with the increase of the system cross section, Acs, the size of the oversaturated region (i.e., σ*) shrinks closer to the full coverage of the laying-down phase, σ0. From eq 6 we see that σ* = σ0 in the limit Acs → ∞. As mentioned previously, the second plateau in Figure 4a corresponds to the coexistence of the laying-down and standing-up thiols and another effect (that we observe in our simulation but do not expect to have in a macroscopic system) is the slight deviation of the surface tension from a constant level inside the second plateau (σ > σ*) in Figure 4a. In the following, we will designate this macroscopic constant level of the second plateau and the surface coverage-dependent deviation from its value as γpl and Δγτ, respectively. Giving this notation the surface tension of the second coexistence region can be written as 748


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uration) up to 330 K in 4 ns. Afterwards, the system requires another 20 ns in order to reach an equilibrium. A similar procedure for T = 350 K yields partially melted island of SC18 thiols after first 4 ns. After another 24 ns of simulations at T = 350 K the island of the standing-up thiols completely melts away. This basically demonstrates that the crystalline island of the standing-up SC18 thiols remains stable at least up to T = 330 K, as one can see from the MD snapshots in Figures 6a−c. There are 47% of octadecanethiols in the standing-up conformation at T = 330 K compared to 51% at T = 293 K. From the snapshots one can also clearly see that the structure of the island at T = 330 K is much more disturbed than at 293 K. Despite this, the collective tilt angle is preserved even at T = 330 K. The distributions of the tilt angle, θ, and azimuthal tilt direction angle, ϕ, for T = 293, 310, and 330 K are given in Figures 6e and 6f, respectively. The average tilt angle slightly decreases from about 39° to 37° for T = 293 and 330 K, respectively. The distributions themselves become broader with the temperature, which indicates the increase of the rotational disorder with higher temperature. The same holds for the distribution of the azimuthal tilt direction, where the average direction approaches 90° with increasing temperature. The packing of the headgroups in the temperature region from 293 to 330 K remains quite stable because the peak positions in the 2D radial distribution function (RDF) of the bound Hg* atoms (Figure: S8) as well as in the distributions of the first, second, and third nearest neighbors (Figure S9) are almost not influenced in this temperature interval. The loss of the translational order with increasing temperature is seen from the lower peak heights and broader distributions in Figures S8 and S9. Influence of Molecular Architecture. In this subsection we are going to explore the effect of a molecular architecture on the structure of thiols on mercury. An alternative possibility of thiol binding to mercury (compared to the above one) would be a surfactant complex consisting of a single thiol molecule attached to a single Hg atom (single-tailed surfactant) as depicted in Figure 7a on the left side. In other words, we are going to investigate how the absence of the S−Hg−S bond influences the SAM structure and whether the coexistence of the laying-down and standing-up thiols is possible under this condition. As a representative example, we use for this purpose the system of the cross section Acs = 903.5 nm2 and the SC18 surface coverage σ = 1.61 nm−2, which corresponds to 1156 thiol molecules per one side of the mercury film. The total number of the Hg atoms is taken to be the same as in the corresponding system with the S−Hg−S bond. The system is initialized by presetting an island of the standing-up thiols and reaches equilibrium in 4 ns, which is faster compared to the systems with the S−Hg−S bonds. Such short relaxation times are due to the overall shorter length of the surfactants compared to the double-tailed ones. The total simulation time is 107 ns. On the right side of Figure 7a one can see the snapshot of the simulated system without S−Hg−S bonds. Compared to the equivalent system with the S−Hg−S bond, we see that in this case the thiol island is much more extended along the direction of the collective tilt. Figure 7b shows the comparison of tilt angle distributions inside the islands of the standing-up thiols for the single- and double-tailed systems. The average tilt angle in the single-tailed system is about 45.4°, which is larger than that of 39° for the double-tailed surfactants. The distribution of the single-tailed system is broader compared

(7)

Based on the above considerations, the line tension contribution to the surface tension is easily estimated as ⎛ ⎞1/2 ∂ΔFinhomo σ0 2π ⎟ Δγτ = − = τ⎜ ∂Acs ⎝ AcsΔσ0(σ − σ0) ⎠

(8)

We use eqs 7 and 8 in order to fit our MD surface tension values as the function of surface coverage, σ, for Acs = 903.5 nm2 in the second plateau region as indicated in Figure 4a. This yields γpl = 0.2785 ± 0.00012 N/m and τ = (8.4 ± 0.35) × 10−11 N. The experimentally reported values54,55 of the line tension for alkane systems generally fall into the range from 10−12 to 10−9 N. Therefore, our estimate of the line tension seems to be quite reasonable. Moreover, the resulting fit perfectly describes our surface tension obtained from the MD simulations (Figure 4a). The discussed above phase behavior is summarized in a schematic γ−σ diagram presented in Figure 5.

Figure 5. Schematic view of the phase behavior of thiols on liquid mercury as a function of the molecular surface coverage at room temperature. γ0 is the surface tension of the bare surface of liquid Hg. σv (very close to zero) and σl = 0.66 nm−2 (for SC18) are the coexistence surface coverages of the laying-down thiols in the 2D vapor and liquid phases, respectively. σ0 = 0.8 nm−2 and σisl = 4.17 nm−2 are the coexistence surface coverages of SC18 thiols in the laying-down and standing-up phases, respectively. σ* ≈ 0.84 nm−2 (for SC18) is the thiol surface coverage, at which the phase separation into the coexisting phases of laying-down and standing-up phases becomes energetically favorable for Acs = 903.5 nm2. The blue line demonstrates the behavior of a macroscopic system, whereas the red lines illustrate the finite-size effect in molecular simulations.

Finally, one can also characterize various phase coexistence regions of SC12 thiols on liquid mercury (see MD snapshots in Figure S4) by similar γ−σ isotherms, as is shown in the Supporting Information in Figure S7 for Acs = 903.5 nm2. For SC12 surfactants the second plateau starts at slightly higher values of σ because for shorter surfactant the value of σ0 is generally higher. Influence of Temperature. Let us now briefly discuss the thermal stability of the crystalline phase of the standing-up thiols. For this purpose we study the SC18 thiol system for σ = 1.61 nm−2 and Acs = 903.5 nm2 at different temperatures. First, an equilibrated system at T = 310 K is obtained by gradually increasing the temperature from T = 293 to 310 K in the course of 4 ns. The respective equilibrated configuration for T = 293 K is used as the initial one. After this procedure no drift in the system’s energy is observed. In the similar way we increase the temperature starting from T = 310 K (equilibrium config749


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Figure 6. (a−d) Comparison of octadecanethiol conformations on liquid mercury at different temperatures. Color code same as for Figure 1. Temperature dependence of the tilt angle (e) and azimuthal tilt direction angle (f) distributions for the SC18 crystalline islands shown above. Acs = 903.5 nm2 and σ = 1.61 nm−2.

Figure 7. (a) Left: sketch of single-tailed surfactants; Right: molecular conformation of the single tailed surfactants on liquid Hg. Color code same as for Figure 1. Comparison of (b) the tilt angle distributions, 2D radial distribution functions of (c) bound Hg* atoms, and (d) sulfur headgroups for single-tailed (18CS−Hg) and double-tailed (18CS−Hg−S18C) surfactants on the surface of liquid Hg. Acs = 903.5 nm2 and σ = 1.61 nm−2.

to the double-tailed system, indicating a larger degree of disorder in the single-tailed system. This observation is also confirmed by comparing the 2D RDF function of the bound Hg* atoms in the crystalline island of the single-tailed system with the one of the double-tailed system (Figure 7c). The 2D RDF function of the single-tailed system is rather a character-

istic of a liquid-like order. A peculiar feature of the 2D RDF function of the Hg* in the single-tailed surfactants is the presence of the low but very sharp first peak. Such behavior might be an indicator of a short-range ordering like pairing of the Hg* atoms into dimers. This effect is confirmed by directly examining the MD snapshot depicting the Hg* atoms in the 750


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Figure 8. Comparison of (a) alkyl (solid line) and sulfur (dashed line) density profiles perpendicular to the Hg surface, (b) 2D radial distribution functions, (c) distributions of the angle between the base vectors of the lateral unit cell, (d) distributions of tilt angles, and (e) distributions of azimuthal tilt direction angles for pure standing-up phases of thiols of various tail lengths. (f) Distribution of gauche conformations along the backbone of an octadecanethiol molecule.

two thiols and the base vectors of 5.52 and 8.42 Å is used as the initial configuration. The number of thiol molecules (SCn) per one side of the Hg film is 432, which corresponds to the initial cross section of 100.4 nm2. The thiols in the initial configurations are left untilted in order not to bias the system. Each component of the lateral pressure is separately fixed at −273 atm, which corresponds to the coexistence pressure of the laying-down and standing-up SC18 phases in our simulations of the phase coexistence above. Since there is a vacuum above and below the SAM from both sides of the Hg film, the normal component of pressure is left unconstrained, but all off-diagonal pressure components are set to zero. The equilibration and total simulation time are 8.4 and 230 ns, respectively. Additionally, since the fully periodic crystalline thiol phases vary slowly, we increase the sampling interval and use every 20th configuration for the analysis. Figure 8a shows the density profiles perpendicular to the Hg film of the alkyl tails and sulfur headgroups of the SC18 SAM. The density inside the SC18 SAM amounts to about 1000 kg/ m 3, which is higher than the typical density of ∼777 kg/m3 of a bulk of octadecane at room temperature. The 2D RDF functions of the bound mercury and the distributions of the angle between the base vectors of the lateral packing of the Hg* atoms are shown in Figures 8b and 8c, respectively. The distributions of the angle between the base vectors is calculated from the fluctuations of the lateral dimensions of the simulation box. Apart from a slight decrease in the second-nearestneighbor distance as well as in the angle between the base vectors upon the increase of the thiol length the packing of the headgroups is not substantially influenced for the alkyl tail lengths studied herein. These observations amount to a slight increase in the lateral packing from 4.23 to 4.29 nm−2 for the SC12 and SC26, respectively. A similar effect upon increase of the molecular length was seen for SAMs of the partially fluorinated thiols on the surface of gold.56 X-ray experiments39 predicted a rectangular unit cell with two thiols per cell and the

single-tailed system (Figure S10a). A better way to compare single- and double-tailed systems is found by analyzing the RDF functions of the sulfur headgroup because they are present in equal number in both systems. Figure 7d offers a comparison of the 2D RDF functions on the sulfur groups for the surfactant systems with and without S−Hg−S bond. The first very sharp peak in the RDF function of the double-tailed system corresponds to the S−Hg−S bond. One can seen that generally the RDF of the single-tailed system has lower peaks compared to the one of the double-tailed system. It is interestingly to mention that sulfur headgroups in the islands of the singletailed surfactants seem to be more ordered than the respective Hg* atoms, as one can see by comparing the respective MD snapshots in Figure S10. In this case the sulfurs clearly form an oblique lattice with one thiol per unit cell and feature multiple grain boundaries. In order to conclude, we note that the absence of the S−Hg−S generally favors larger degree of the translational and orientational disorder as well as higher tilt angles compared to S−Hg−S surfactants and experimental findings.39 In addition, in the experiments the unit cell with two thiols was proposed, which agrees well with our MD simulations of the surfactants with S−Hg−S bond rather than without it (Figure S11). Therefore, we consider the possibility of the single-tailed surfactants to be rather unrealistic. Structure of Crystalline Phases. In order to investigate the thiol packing in the crystalline islands of the standing-up thiols, we carry out simulations of the surfactants with the S− Hg−S bonds in the ensemble with the constant temperature (T = 293 K) and pressure tensor of a pure standing-up phase. This allows us to eliminate the influence of the finite sizes of the standing-up islands. Additionally, the effect of the chain length is explored in more detail by simulating the SAMs of dodecanethiol (SC12), tetradecanethiol (SC14), octadecanethiol (SC18), and hexacosanethiols (SC26) molecules. In analogy to the initialization of the standing-up phase in the islands, the experimentally proposed39 rectangular unit cell with 751


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Langmuir base vectors of 5.52 and 8.42 Å for octadecanethiols at T = 299 K. Such unit cell dimensions result in the octadecanethiol surface coverage of 4.3 nm−2. In our simulations we obtain also a unit cell having two SC18 molecules and the dimensions of 5.8 and 8.13 Å. The angle between these base vectors is 96.68°. This results in the equilibrium surface coverage of 4.27 nm−2 for SC18 surfactants at T = 293 K, which is very close to the above experimental findings. The average tilt angle, θ, of the thiol SAM increases from 36.5° to 38° upon increasing alkyl tail length from SC12 to SC26, respectively, as determined from the tilt angle distributions (Figure 8d). The distributions grow sharper with the increase of the thiol length, indicating enhanced degree of ordering for longer molecules. For the SC18 monolayer θ = 37.4° (uncertainty in the tilt angle is about 0.25°), which is above 27° found in the X-ray experiments.39 On gold substrates1 the observed tilt angles are about 30°. On one hand, one can naively attribute such values to a specific orientation (with respect to Au substrate) of the Au−S bond. Sharp tilt angles (θ ≤ 29°) in the Langmuir monolayers on water57 are promoted by strong hydrophobic interactions of the surfactants with water. On the other hand, we do not see an obvious reason for the tilt angle of thiols on liquid mercury to have such sharp angles as the just mentioned monolayer on water or gold. One possible explanation in macroscopic systems might be the presence of a long-living spiral structure such as observed in our simulations (Figure S1b). In such structures the molecules in the center are basically untilted, which would effectively decrease the average tilt angle of a whole sample. The average collective tilt direction angle drops from about 75° to 70° as the molecular length increases (Figure 8e). The alkylthiol monolayers on mercury also feature a substantial amount of gauche defects. As an example, the distribution of the gauche defects along the SC18 backbone is shown in Figure 8f. A torsional angle that falls between 30° and 100° was considered to be in gauche conformation for the calculation of the distribution. The largest number of gauche conformations is found in the first torsional angle S−CH2−CH2−CH2. We attribute this to the mismatch between the equilibrium conformations of the CH2−S−S−CH2 and S−CH2−CH2− CH2 torsions. Moving further along the thiol backbone the gauche fraction drops close to zero and then slightly rises again towards the other end (Figure 8f). Such behavior is consistent with the one generally seen in the alkyl-based systems.58 We have also to note that the presence of the gauche defects in the thiol monolayer on mercury was not taken into account for the calculation of the tilt angles in the X-ray experiments.39

coexistence regions, which are in very good agreement with the experimental observations. Our MD simulations have confirmed that at low surface coverage values thiols reside in the laying-down conformations until the first monolayer of the laying-down molecules is completely filled. At surface coverage values lower than that of a completely filled monolayer of the laying-down surfactants thiol agglomerate into 2D clusters that coexist with the 2D very dilute gas on the mercury surface rather than forming a 2D gas phase (that uniformly covers the Hg surface) suggested by experiments.39 Furthermore, as the surface coverage increases above the full coverage of a completely filled monolayer of the laying-down surfactants the monolayer resides up to a given surface coverage in an oversaturated state, following which it phase separates into the coexisting phases of the laying-down and standing-up surfactants. We have shown that in the computer simulations the oversaturated region decreases with the increase of the system cross section, which perfectly agrees with the predictions of the condensation/evaporation theory of finite systems.52 The resolved coexistence of the laying-down and standing tilted at a sharp angle to the surface normal thiols agrees very well with the experimental picture.39 Our simulations also indicate that the studied thiols form a unit cell with two thiols per cell in accord with the X-ray data,39 although the headgroup packing is slightly oblique compared to the experimental predictions.39 Our MD data also confirm the X-ray finding,39 that thiols form a S−Hg−S bond with the Hg atoms, since only in this case we are able to observe in our simulations the (experimentally observed) headgroups packing with two thiol molecules per unit cell.

CONCLUSIONS AND DISCUSSION In this paper we have used the molecular dynamics simulations to carry out large-scale simulations of the alkylthiol selfassembly on the surface of liquid mercury. The main focus of the work was on the self-assembly as a function of the surfactant surface coverage. In order to conduct such simulations, one has to overcome such obstacles as (i) extremely long relaxation times of the thiols on the surface of liquid mercury, (ii) strong finite-size effects, which modify the signature of phase coexistence regions, (iii) insufficient amount of experimental data for the parametrization of the alkylthiol interaction with liquid mercury, (iv) and finally, the liquid mercury has to be treated on an atomistic level to preserve the liquid nature of the substrate and the relevant features of the chemical bonding of thiols to mercury. By overcoming these challenges, we have been able to resolve various phase

Anton Iakovlev: 0000-0003-0856-7071

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b03774. Molecular force fields and the details of setting up and equilibration of the molecular systems; additional data and figures on the structural properties of thiols on liquid mercury (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (D.B.).

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ORCID Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank B. Pokroy for stimulating discussions. A.I. and M.M. acknowledge the financial support from the Volkswagen Foundation within the joint German−Israeli program under Grant VW-ZN2726 and the European Union FP7 under Grant agreement No. 619793 CoLiSA.MMP (Computational Lithography for Directed Self-Assembly: Materials, Models, and Processes) and the GWDG Göttingen, the HLRN Hannover/ Berlin, and the von Neumann Institute for Computing, Jülich, for the computational resources. D.B. acknowledges the financial support from the Alexandr von Humboldt Foudation through an Experienced Research Fellowship and the 752


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University of Utah Center for High Performance Computing for computational resources.

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ADDITIONAL NOTE The surface tension of the bare surface of liquid Hg in our simulations is lower than the experimental value. a

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