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Interfacial Tension Does not Drive Asymmetric Nanoscale Electrowetting on Graphene Fereshte Taherian, Frédéric Leroy, and Nico F. A. van der Vegt Langmuir, Just Accepted Manuscript • Publication Date (Web): 10 Apr 2015 Downloaded from http://pubs.acs.org on April 10, 2015

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Interfacial Tension Does not Drive Asymmetric Nanoscale Electrowetting on Graphene Fereshte Taherian, Frédéric Leroy and Nico F. A. van der Vegt* Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, D-64287, Darmstadt, Germany KEYWORDS: Contact angle, electrocapillarity, graphene, ionic liquid, water

ABSTRACT: We report molecular dynamics simulations of the electrowetting behavior of liquids in confinement between two oppositely charged graphene sheets. We observe that changes in the static contact angles of water, salty (4 M NaCl) water and 1-butyl-3methylimidazolium tetrafluoroborate ([bmim][BF4]) (a room-temperature ionic liquid) exhibit an asymmetric dependence on electric field polarity. The solid-liquid interfacial tension, which is expected to drive these changes, has been calculated independently by integrating the reversible work performed upon introducing positive and negative surface charges. This quantity shows either no dependence on the polarity of the electric field (water), or a dependence exactly opposite to the one obtained by applying the Young-Lippmann equation to the observed contact angles ([bmim][BF4]). Our analysis indicates that the observed contact angle asymmetry finds its

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origin in the liquid structure in the vicinity of the three-phase contact line. In particular, it is suggested that the molecular orientation properties are crucial to determine the asymmetric wetting behavior of pure water, in addition the contrast in the strength of the ion hydration shell has a decisive influence on the NaCl solution behavior.

1. INTRODUCTION Design and optimization of engineering devices and processes such as nano/micro pumps,1 electrospinning2 and electrospray ionization3-4 require a detailed understanding of how nanoconfined polar fluids respond to an external electric field. Such understanding is also essential to clarify the underlying mechanisms of different biological phenomena such as mass transport through charged channels of cell membranes5-7 or membrane electroporation.8-9 On solid surfaces, an important question is if the polarity of the external electric field has any effect on the electrowetting contact angle (CA), and how this effect, if any, can be related to molecular properties of the electrowetting fluid at the solid-liquid (SL) interface. Young’s equation relates the contact angle θ to the solid-liquid (γSL), solid-vapor (γSV) and liquid-vapor (γLV) interfacial tensions

cosθ =

γ SV − γ SL γ LV

(1)

While an electrical field may in principle affect each of these interfacial tensions, the consensus in the literature is that the major contribution to the observed field dependence of cosθ derives from its effect on γSL.10-11 Assuming that the areal capacitance c of the SL interface across which an external voltage V is applied is constant, the change in γSL is obtained from the

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0 0 electrocapillary equation (Lippmann equation): γ SL = γ SL is the value of γSL − 1 2 cV 2 , where γ SL

at zero voltage.10, 12-13 The Young-Lippmann equation which relates the electrowetting CA to the applied voltage is obtained by combining Eq. 1 with the electrocapillary equation above. When electrowetting experiments are carried out on dielectrics, the total areal capacitance ct depends on both the dielectric layer capacitance cP and on the electrical double layer (EDL) capacitance cL, following 1/ct=1/cP+1/cL. Because cL is generally much larger than cP, information about effects arising from microscopic peculiarities of the EDL and possible non-constant values of cL cannot easily be obtained through electrowetting measurements.13 However, Ralston, Sedev and successive coworkers14-16 as well as Nanayakkara et al.17 showed that experiments with electrolytes and room-temperature ionic liquids (RTILs) carried out on fluoropolymer surfaces may reveal the effect of microscopic properties at the SL interface on the electrowetting measurements. Observations like asymmetric variations of the electrowetting CA depending on the polarity of V and non-constant values of the EDL capacitance have been interpreted in terms of adsorption and redistribution of charges (ions)14-16 and in terms of the difference in size between counterions.17 Molecular simulations offer a relatively easier access to interfacial effects under electrowetting conditions because calculations are generally carried out without the dielectric layer. Nanometer sized water droplets on graphite in a uniform electric field (both parallel and perpendicular to the solid surface) characterized through molecular dynamics (MD) simulations exhibit asymmetric CA variations with the polarity of the electric field.18-19 This asymmetric CA behavior was interpreted in terms of asymmetric perturbation of interfacial structural properties such as molecular orientations and hydrogen bonding patterns. These changes are in turn expected to affect the variations of γSL in an asymmetric way.18 A subsequent MD work of Daub et al. showed that solvated salts suppress the electrowetting asymmetry of

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water droplets, presumably due to the fact that ions reduce the orientation bias induced by electric fields on the water molecules close to the surface compared with pure water droplets.20 Kislenko et al. observed asymmetry in the EDL capacitance of a RTIL on charged graphite surfaces in a MD study.21 This result was related to the difference in size of the counterions which influences the interfacial liquid structure in an asymmetric way depending on the surface polarity, as also suggested by the experiments of Nanayakkara et al.17. The studies quoted above show that the polarity of the external electric field indeed has an effect on electrowetting CA variations. Both macroscopic experiments and molecular simulations at the nanometer scale hypothesized that molecular properties at the SL interface are responsible for the observed electrowetting behavior. It remains to explore how the interfacial microscopic changes mentioned above affect γSL depending on the applied electric field. 0 In this article, we describe how Δγ SL = γ SL − γ SL depends on the charge density and polarity of

graphene surfaces that confine aqueous solutions (pure water and a NaCl solution) and a RTIL (1-butyl-3-methylimidazolium terafluoroborate, [bmim][BF4]). Rather than determining the EDL capacitance and its dependence on V, we reformulate the electrocapillary equation by equating ΔγSL with the reversible work of charging the graphene surfaces, calculated by means of a thermodynamic integration approach.22 Wetting CAs are determined independently from MD simulations of liquids forming a bridge between two confining plates. It is found that ΔγSL features symmetric and asymmetric dependencies on the graphene polarity. However, these changes lead to predicted CA values through the corresponding electrowetting equation which are inconsistent with the observed CAs. We resolve this contradiction through the study of the liquid structure in the region of the solid-liquid interface that spans a few nanometers next to the

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three-phase contact line. Although the liquid structure in the vicinity of the contact line plays a key role in determining the contact angles of the aqueous and IL systems, we focus on the aqueous systems in the present article. The contact angle asymmetry concerning the IL is presented here to illustrate that the observations made on the aqueous systems in fact seem to be general. For the sake of clarity, we defer the detailed analysis of the [bmim][BF4] system to a forthcoming paper. 2. METHODOLOGY 2.1. Force Field Models. Three different liquid bridges of pure water, salty (4 M NaCl) water as well as [bmim][BF4] ionic liquid (IL) were modeled between two immobile athermal graphene surfaces. The extended simple point charge (SPC/E) model of water23 was used in this work. The interaction parameters between water and the graphene surfaces were taken from Werder et al.,24 where the Lennard-Jones parameters between the carbon and the oxygen atoms were optimized to reproduce a value of 86° for the contact angle of water on graphite. It should be mentioned that recent experimental works have shown that the contact angle of water on graphite may be strongly influenced by the adsorption of airborne contaminants. It was found that the water contact angle on a freshly cleaved graphite surface is 64.4°,25 i.e. a value smaller than the one employed in the force-field optimization mentioned above. From the simulation work of Kumar and Errington, it can be concluded that the change from 86° to 64.4° would be obtained by increasing the water-carbon interaction from approximately 0.4 kJ/mol to approximately 0.5 kJ/mol.26 Such a relatively small change in the energy value is expected to not significantly affect the orientation properties of the water molecules at the solid-liquid interface, which, as will be shown below, play an important role in determining the aqueous electrowetting behavior. Force field parameters for NaCl were taken from a recent publication by Moucka et al.,27 where the

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ionic chemical potential and the specific volume of the aqueous NaCl solution were reproduced at different salt concentrations. However, we repeated our simulation at one surface charge density with the force-field parameters developed by Netz et al.,28 to ensure that the results are not sensitive to the choice of the force field parameters. To obtain the ion-graphene LennardJones parameters, we applied Lorentz−Berthelot combination rules using the Lennard-Jones parameters of the graphene carbon atom from the work reported by Walther et al.29 The Lorentz−Berthelot combination rules were used to determine the interaction parameters for ionswater and ions-graphene. The pure water system consisted of 26680 water molecules, while the aqueous salt solution with the concentration of 4 M NaCl included 23614 water molecules and 1988 ion pairs. For the simulation of [bmim][BF4] IL, the coarse-grained (CG) model developed by Merlet et al. 30 was refined in this work in order to have a flexible model for [bmim] cation. The anion was considered as a single interaction site (bead) in the CG model (bead A), while the cation was represented with three beads: the alkyl chain (bead T), the imidazolium ring (bead R) and the methyl group connected to the ring (bead H). The graphene surface was mapped to the CG model by considering three carbon atoms as one CG bead denoted by C3. Similarly to the aqueous systems, the coarse-grained graphene surface was considered to be rigid. The interaction parameters for the CG beads are reported in Table 1. The unlike interaction parameters were derived using the Lorentz−Berthelot combination rules. The IL system was composed of 7986 ion pairs. More details on the IL CG model will be presented in the forthcoming paper mentioned above. The liquids were simulated between two graphene surfaces with different surface charge densities reported in Table 2, 3 and 4 for pure water, the NaCl solution and the IL systems,

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respectively. The positive charges were applied on the bottom surface and the corresponding negative charges on the top one. This configuration leads to a neutral system in each case. An uniform fixed distribution of the partial charges on the carbon atoms of the graphene surface was considered here.19, 31 Simulation results of Merlet et al.11 for the ionic liquid [bmim][PF6] have shown that the structure of the liquid at the interface is independent of surface charge fluctuations under constant potential conditions for average surface charges up to 8 µC/cm2, which is much higher than the applied charge densities in this work. The effect of the electrical field generated by the surface charges may lead to water polarization, in which case the use of a polarizable water model is essential. But it has been demonstrated that for the field strengths less than ∼1 V/Å the effect of the water polarization can be neglected.32 Since the electric field strengths corresponding to the surface charges employed in this work are much weaker than this value, the nonpolarizable extended simple point charge (SPC/E) model 23 was used. 2.2. Simulation Details. Although electrowetting experiments are often performed on dielectrics, our simulations were carried out on suspended graphene sheets for simplification to reduce the computation time. The graphene surfaces are separated by a distance of 12 nm for the pure water and NaCl solution liquid bridges and 19.54 nm for the IL bridge and are oriented parallel to the x-y plane. The dimension of the surfaces in x-direction was set to 6.15 nm, for the pure water and the NaCl solution, and 8.118 nm for the IL system. The initial configurations were obtained by equilibrating the liquids before spreading at zero surface change density between the graphene surfaces. In these simulations, no liquid-vapor interface was present (Figure 1.a). The dimensions of the confining surfaces in the y-direction were 10.83, 10.85 and 16.18 nm for the pure water, NaCl solution and the IL systems, respectively. These dimensions

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were chosen in order to approximately match the bulk liquid mass densities. Following the equilibration of the confined liquids, the size of the box in the y-direction was increased, creating a liquid-vapor interface (Figure 1.b) and allowing the liquid to spread on the surfaces. For the pure water and the NaCl solution systems, the final size of the surfaces in y-direction was 35.78 nm, and in the case of the IL it is equal to 56.658 nm. The size of the simulation box in the zdirection for the pure water and for the NaCl solution was equal to 50 nm, and for the IL system is set to 100 nm to exclude the effect of the periodic boundary condition perpendicular to the surfaces. Since the liquid bridges considered in this work have an apparent contact line of infinite length along the x-axis, no curvature effect such as the effect of line tension is expected to play a role in the calculations. Additional calculations on the NaCl solution were performed where the distance between the surfaces was increased to 67.8 nm at the surface charge densities of ±1.15 µC/cm2 to examine the confinement effect on the contact angle calculations. This large system consisted of 283368 water molecules and 23856 ion-pairs. The size of the simulation box in the x, y and z directions was 6.15, 44.73 and 300 nm, respectively.

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Figure 1. Snapshot of the simulation setup (a) in the initial geometry and (b) for the contact angle calculation. The salt solution on the right-hand side is shown at the time zero before spreading of the liquid on the surface took place.

Table  1.  Lennard-­‐Jones  parameters  and  fixed  partial  charges  for  the  CG  model  of  the  ionic   liquid  [bmim][BF4]  and  graphene.     interaction   σ  (nm)   ε  (kJ/mol)   q  (e)   site   A   0.451   3.44   −0.78   H   0.341   0.36   0.1578   R   0.438   2.56   0.4374   T   0.504   2.33   0.1848   C3   0.4788   0.4937   -­‐  

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Table 2. The surface charge densities, magnitude of the electric field in the nanoslit, partial charge of the carbon on the surface, the contact angle for the pure water system. The errors are calculated using blocking average over a time frame of 15 ns with a block size of 3 ns. σ  (µC/cm2)   E=|σ/ε0|  (V/Å)   qC  (e)  (x10-­‐3)   θ  (degree)   1.0   0.113   1.635   75.4  (0.7)   0.75   0.085   1.226   83.9  (0.6)   0.5   0.056   0.818   90.4  (0.6)   0.25   0.028   0.409   93.8  (0.5)   0.0   0.0   0.0   94.8  (0.5)   -­‐0.25   0.028   -­‐0.409   94.7  (0.6)   -­‐0.5   0.056   -­‐0.818   91.5  (0.5)   -­‐0.75   0.085   -­‐1.226   85.7  (0.6)   -­‐1.0   0.113   -­‐1.635   79.1  (0.7)  

Table 3. The surface charge densities (σ), magnitude of the electric field in the nanoslit (E), partial charge of the carbon on the surface (qC), and the contact angle (θ) for the 4 M NaCl system. The errors are calculated using blocking average over a time frame of 15 ns with a block size of 3 ns. σ  (µC/cm2)   E=|σ/ε0|  (V/Å)   qC  (e)  (x10-­‐3)   θ  (degree)   1.75   0.197   2.862   70.3  (0.4)   1.5   0.169   2.453   71.9  (0.3)   1.25   0.141   2.044   71.7  (0.5)   1.15   0.130   1.880   71.3  (0.6)   1.0   0.113   1.635   76.9  (0.3)   0.75   0.085   1.226   85.6  (0.3)   0.5   0.056   0.818   91.4  (0.5)   0.25   0.028   0.409   95.8  (0.5)   0.0   0.0   0.0   96.8  (0.3)   -­‐0.25   0.028   -­‐0.409   96.5  (0.4)   -­‐0.5   0.056   -­‐0.818   95.2  (0.4)   -­‐0.75   0.085   -­‐1.226   91.1  (0.9)   -­‐1.0   0.113   -­‐1.635   84.8  (0.6)   -­‐1.15   0.130   -­‐1.880   81.7  (0.6)   -­‐1.25   0.141   -­‐2.044   80.3  (0.3)   -­‐1.5   0.169   -­‐2.453   80.2  (0.6)   -­‐1.75   0.197   -­‐2.862   80.1  (0.3)  

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Table 4. The surface charge densities (σ), magnitude of the electric field in the nanoslit (E), partial charge of the coarse-grained surface sites (qC) and the contact angle (θ) for the IL system. The errors are calculated using blocking average over a time frame of 15 ns with a block size of 3 ns. σ  (µC/cm2)   E=|σ/ε0|  (V/Å)   qC  (e)  (x10-­‐3)   θ  (degree)   0.6   0.0672   2.943   62.8  (0.7)   0.4   0.0448   1.962   67.5  (0.9)   0.2   0.0224   0.981   72.4  (0.8)   0.0   0.0   0.0   73.6  (0.6)   -­‐0.2   0.0224   -­‐0.981   69.9  (0.8)   -­‐0.4   0.0448   -­‐1.962   60.9  (0.9)   -­‐0.6   0.0672   -­‐2.943   53.7  (0.6)  

The molecular dynamics simulations were performed using the GROMACS package.33 The simulations were carried out at constant volume and temperature (298.15 K) by using the NoséHoover thermostat34 with a coupling time constant of 0.2 ps. The time step was set to 1 fs for pure water and for the salt solution and 2 fs for the IL system. The Coulomb interactions were computed using the particle mesh Ewald (PME) method with the cubic interpolation order.35 The Fourier spacing is set to 0.12 nm. Since the simulation box is not periodic in the z-direction, the Coulomb force and potential are corrected in this direction to have a pseudo-2D Ewald summation.36-37 The cutoff radius for the non-bonded interactions is 1.0 nm for the pure water and the salt solution.27 and 1.6 nm for the IL.30 2.3. Contact Angle Calculations. The liquid bridges were equilibrated for 30 ns, and a production run of 15 ns was performed for the contact angle calculation. Our approach for the contact angle calculation is the following: the simulation box is first divided into slices of 0.15 nm parallel to the surface (z direction). The density distribution for each slice is subsequently calculated along the y direction. Due to the capillary fluctuations of the liquid-vapor interface,

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the density distributions are averaged over 20 ps. The liquid-vapor profile is determined by fitting the density distribution of each slice ( ρ (y) ) to a hyperbolic function:

ρ ( y) =

ρL ρL − tanh[( y − y0 ) / d ] 2 2

(2)

where ρ L , y0 and d are the fitting parameters corresponding to the liquid density, the position of the Gibbs-dividing surface, and the thickness of the vapor-liquid interface, respectively. The value of y0 is taken as the position of the liquid-vapor profile where the mass-density equals half the bulk liquid density value. At the final step, a straight line is fitted to the liquid-vapor profile at distances between 0.9 and 2.4 nm from the surface (inset Figure 3), similarly to other simulations.38-39 Changing the fitting interval, as indicated in Figure 3, does not show any effect on the average value of the contact angle. Figure 3 shows the liquid-vapor profile for the 4 M NaCl solution between two graphene surfaces separated by 67.8 nm and at surface charge densities of +1.15 µC/cm2 (z=0.0 nm) and −1.15 µC/cm2 (z=67.8 nm). For this system, the linear fit was done at distances between 10 and 15 nm from the surface. The contact angle values at different surface charge densities for the pure water, the NaCl solution and the IL are reported in Table 2, 3 and 4, respectively.

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Figure 2. The liquid-vapor profile (y0 red line) at surface charge densities of −1.15 µC/cm2 (z=67.8 nm) and +1.15 µC/cm2 (z=0.0 nm) for the 4 M NaCl system where the distance between the graphene surfaces is set to 67.8 nm. The inset shows the liquid profile for the same system at the 12 nm confinement.

2.4. Electric Potential Calculations. The electrical potential distribution (φ(z)) across the channel is calculated by determining the volume charge density of the solution ( ρe (z) ) as a function of distance to the wall and using the Poisson equation:

ϕ ( z) = −

σ 1 z− ε0 ε0



z

0

z′

dz ′∫ ρ e ( z ′′)dz ′′ 0

(3)

where σ is the charge density of the surface, ε0 is the permittivity of free space and z is the perpendicular distance to the lower surface. The electric potential difference between the

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surfaces (z=0 and 12 nm for the lower and upper surfaces, respectively) and the center of the slit (z=6.0 nm) were determined. For the aqueous slabs, the maximum electric potential difference obtained was always below the oxidation potential of water, which is at 1.24 V.40 The calculations further showed a non-zero value for the potential drop at zero surface charge density (0.36±0.02 V for pure water and 0.41±0.03 V for the 4 M NaCl system). The experimental value for the potential of zero charge for pure water is +0.41 V,41 which is in a very good agreement with our calculations. In the case of [bmim][BF4] IL system, the simulation results of Merlet et al.30, 42 have shown that calculations are performed within the electrochemical stability window of the IL for surface charge densities up to 4.5 µC/cm2.43

3. RESULTS AND DISCUSSION Figure 3 shows the dependence of the CAs on the surface charge density for liquids (pure water, 4 M NaCl in water, and [bmim][BF4]) confined as mentioned above at 298.15 K. The CAs show a clear asymmetric dependence on surface polarity. While for pure water, this observation is in agreement with MD simulations of nanodroplets reported by Daub et al.,18 for the NaCl solution this is not the case.20 While Daub et al.18 attribute the observed asymmetry in electrowetting behavior of pure water to differences in the mean number of hydrogen bonds at the SL interface within the nanodroplets,20 they attribute the absence of electrowetting asymmetry of salty nanodroplets to screening effects of the salt ions.20 For the 4 M NaCl system, CA saturation occurs at surface charge densities |σ|> 1.15 μC/cm2. At these high surface charge densities we observe that hydrated Na+ and Cl− ions are ejected from the bridge, adsorbing on the

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negative and positive surfaces respectively, in agreement with the saturation mechanism previously reported by Liu et al.44 Interestingly, the observed asymmetry in the 12 nm confinement remains present in a liquid bridge (4 M NaCl) of 68 nm thickness in which the relative number of water molecules affected by the external electric field is significantly smaller. It can also be observed that the contact angle asymmetry observed for pure water is found again for the salty solution with larger values of the contact angles. Note that on the negative surfaces, the addition of salt seems to increase the contact angle more than on the positive surfaces at a given σ value.

Figure 3. (a) Contact angles at different surface charge densities σ for 12 nm thick bridges of pure water (red symbols), 4 M NaCl (black symbols) and a 68 nm thick 4 M NaCl bridge (blue symbols) (b) Contact angles at different surface charge densities for 19.5 nm thick bridges of [bmim][BF4].

Figure 4 shows how the SL electrostatic energy, ΔUSL,Coul ⁄A, the SL interfacial free energy, ΔγSL, and the SL interfacial entropy, TΔSSL ⁄A, obtained by taking the difference between the former two quantities, change upon charging the surface. The SL electrostatic energy accounts

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for the Coulomb interactions between the graphene surface charges and all particles in the liquid and was calculated along the cross-sectional area A (base area of 6.15⨯4.0 nm2) at the centerline of the liquid. A spherical cutoff distance was used in these calculations. While the cutoff distance affects the energies, it does not affect their dependence on the electric field polarity as will be discussed later. For pure water (Figure 4a), the SL Coulomb energy is symmetric. The change of the SL interfacial free energy ΔγSL can be readily obtained from the electrostatic energy. This is achieved by calculating the isothermal reversible work of a surface charging process in which the surface charge density is varied between zero (denoted as system A) and σ (denoted as system B). Using   the   thermodynamic   integration   (TI)   method   the   free   energy   change   upon   charging   the   surface   can   be   calculated.   Since   in   our   simulation   the   surface   is   frozen,   only   the   solid-­‐liquid   Coulomb   interaction   potential   (USL,Coul)   is   affected   upon   charging   the   surface,  therefore:  

Δγ SL

λ

1 B ∂U SL, Coul (λ ) = ∫ dλ   A λA ∂λ

 

 

 

 

 

 

 

(4)

Here,   λ   is   a   parameter   which   quantifies   the   transformation   from   the   uncharged   surface   system  to  the  charged  one,  and  ⟨···⟩  denotes  an  ensemble  average  over  the  configurational   distribution   of   the   liquid   molecules   in   contact   with   the   surface.   The   analytical   form   for   USL,Coul(λ)  is:   U SL,Coul (λ ) = ∑∑ iL

iS

qiL qiS (λ ) 4πε 0 riLiS

   

 

 

 

 

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(5)  

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where   q iL  and   qiS  are  the  charges  of  the  liquid  and  the  surface  atoms,  respectively,   riLiS  is   the   distance   between   the   surface   and   the   liquid   atoms   and   ɛ0   is   the   permittivity   of   the   free   space.  The  λ-­‐dependence  of   qiS  can  be  considered  as:    

qiS (λ ) = λ ⋅ qiS ,B + (1 − λ ) ⋅ qiS , A  

 

 

 

 

 

 

 

(6)  

 

 

 

(7)  

 

(8)  

Using  eqs  4  and  5,  the  change  in  γSL  can  be  written  as:   q

Δγ SL

q

1 S , B ∂U SL,Coul (qS ) 1 S ,B = dq = S A qS∫, A ∂qS A qS∫, A

qiL

∑∑ 4πε r iL

iS

dq S  

0 iLiS

With  σ’=nqS,  where  n  is  the  number  of  surface  atoms  per  unit  area,  it  follows:   σ

Δγ SL =

σ ∂U SL,Coul (qS ) 1 B ∂U SL,Coul (qS ) ∂σ ' 1 1 ⋅ d σ ' = dσ '     ∫ ∫ A σA ∂σ ' ∂q n A0 ∂σ '

 

In Eq. 8, ∂U SL,Coul ∂σ ' is the derivative of the SL Coulomb-energy with respect to the surface charge density, averaged over configurations taken out from a MD trajectory with surface charge density σ'. Because the graphene surface atoms are kept frozen in the MD simulations, this calculation does not require additional computational expenditure. All the TI calculations were performed using the setup shown in Figure 1b. The Coulomb interaction potential (USL,Coul/A) between the surface and the liquid is calculated around the centerline within a base area of 6.15⨯4.0 nm2 for the pure water and the salt solution and 8.118⨯4.0 nm2 for the IL. The water molecules are considered to be in the centerline region, if at least a single atom of the molecule resides in the defined volume. In the case of [bmim]+ cation, the geometric center of the molecule is used to assign the ion to the centerline. The error bars reported for the Coulomb interactions were calculated using block averages over a time frame of 15 ns with a

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block size of 3 ns. The integration in eq. 7 was performed by means of the trapezoidal rule, and the error for the ΔγSL calculation is determined using error propagation. Figure 4a (water on graphene) shows that ΔγSL exhibits a symmetric dependence on surface polarity. Therefore, differences in solvent structural organization on oppositely polarized surfaces, including differences in water hydrogen bonding interactions among the interfacial water molecules, do not affect ΔγSL. This conclusion underscores the analysis described in earlier work where it was demonstrated that variations in the liquid-liquid energy are exactly enthalpyentropy compensating in the work of adhesion.45-46 The symmetric nature of ΔγSL is quite remarkable, in particular also in view of the fact that the water CA (Figure 3a) instead exhibits an asymmetric dependence on surface polarity. Hence, the CA asymmetry in nanoscale electrowetting of water on oppositely polarized graphene surfaces cannot be driven by differences in γSL as defined in Eq. 2 for the geometries examined here. Moreover, if the values of ΔγSL as calculated above are inserted in the Lippmann contact angle equation, the predicted change in contact angle between the neutral surface system and a system with a given surface charge σ is far below the observed value. This observation is another evidence that the Lippmann equation has to be cautiously used and that factors other than the changes in γSL may be at the origin of the asymmetric electrowetting behavior. Interestingly, ΔγSL obtained by thermodynamic integration for [bmim][BF4] is instead asymmetric (Figure 4b). This asymmetry can be related to differences in cation and anion sizes leading to differences in structural packing effects at the interface. When these ΔγSL-values are applied in Young’s equation (Eq. 1), we predict an asymmetric CA dependence on surface polarity opposite to what is actually observed (Figure 3b). Hence, the application of Young’s equation with the values of ΔγSL computed at equal field strengths of opposite polarity leads to CA predictions which are in qualitative

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disagreement with the electrowetting CAs of

[bmim][BF4] in the nanoscale confinement

geometry examined here.

Figure 4. (a) The solid-liquid Coulomb energy (black squares, calculated with a spherical cutoff distance of 1.5 nm) and change in the solid-liquid interfacial tension (red circles) for the pure water and (b) [bmim][BF4] RTIL systems (calculated with a spherical cutoff distance of 2.5 nm). The inset shows the change in the solid-liquid interfacial entropy. Lines between data points are included to guide the eye.

Figures 5a and 5b show ΔUSL,Coul/A and ΔγSL for the NaCl solution, respectively, including the ion and water contributions. While the salt more favorably wets the positively polarized surface (Figure 3a), ΔγSL is symmetric. Comparison with the data in Figure 4a (pure water) shows that the contribution of water to the SL electrostatic energy and to ΔγSL is reduced by a factor of 3 in the 4 M salt solution. This may be caused by electrostriction; the water molecules are affected stronger by the electric field emanating from the ions than by the external electric field. In Figure 5 the calculation are extended for the 4 M NaCl system to the surface charge densities where the saturation takes place. In contrast to pure water, both ΔUSL,Coul/A and ΔγSL feature a relatively weak asymmetry in the water contribution. This asymmetry is balanced by an asymmetry of opposite magnitude in the ions contribution, so that the overall behavior appears symmetrical. As

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is shown, the change in the solid-liquid interfacial tension away from the contact line is not consistent with the observed contact angle behavior at high surface charge densities.

Figure 5. The solid-liquid Coulomb energy (a) and change in the solid-liquid interfacial tension (b) for the 4 M NaCl system (calculated with a spherical cutoff distance of 1.5 nm). The contributions of the ions and water molecules are separated. The inset shows the change in the solid-liquid interfacial entropy. Lines between data points are included to guide the eye.

The spherical cutoff used in the calculation of ΔUSL,Coul and ΔγSL was set to 1.5 nm for the pure water and the salt solution, which is the distance where the density of the liquid converges to the corresponding bulk. The overall change in ΔγSL at a given σ is approximately 2.5 times larger with the NaCl solution than with pure water. However, the changes in contact angle measured at the bridge boundaries are of the same order both in the pure water and in the NaCl systems. This again suggests that the origin of the contact angle behavior should be described by another quantity than ΔγSL. The calculation of the change in the solid-liquid interfacial tension along the centerline of the liquid film with different cutoff values are shown in Figures 6 for the 4 M NaCl

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solution system. Although the magnitude of ΔγSL increases with increasing the cutoff, the symmetric behavior of this quantity with respect to σ does not depend on the choice of the cutoff. The calculation of ΔγSL with different cutoffs in the slab geometry (i.e. with no liquid-vapor interface) also leads to the same result.

Figure 6. The change in the solid-liquid interfacial tension for the 4 M NaCl solution at different cutoff values.

The results reported in this paper indicate that the observed asymmetries in the electrowetting CAs of liquids in nanoconfinement cannot be interpreted through the changes in the SL interfacial tension. We suggest that these asymmetries likely originate from molecular properties

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of the fluid in a region close to the three-phase contact line. One may ask how the electrocapillary equation that defines ΔγSL, independently of its formulation, and Young's equation should be used to describe electrowetting at the nanometer scale. This question can be related to what has been learnt about the CA equations derived to understand the wetting properties of rough and chemically heterogeneous surfaces. Marmur and Bittoun concluded that "local conditions at the contact line determine the actual contact angles".47 (Note that Gao and McCarthy have formulated a similar view by noting that Young's equation expresses a force balance at the contact line.48) If one adopts the view according to which the liquid density field can be described as homogenous at each point of the liquid volume close to the solid surface, the statement of Marmur and Bittoun implies that the change in the contact angle upon application of an external electric field can be predicted by ΔγSL as calculated in Eq. 2 under the condition that the other interfacial tensions are insensitive to the applied field. If one now assumes that the proximity of the contact line induces structural constraints that lead to local inhomogenity of the liquid density field which in turn modify the balance of interactions, it is expected according to the statement of Marmur and Bittoun that the actual CA will differ from the value predicted from ΔγSL. The work of Daub et al. on MD simulations of aqueous salty nanodroplets (approximate diameter 6 nm) illustrates the existence of such inhomogeneities close to the contact line (see Figure 4 of ref.20). It should also be noted that Marmur and Bittoun refer to "local conditions at the contact line".47 In a study of nanometer sized water droplets (approximate diameter 6 nm) on rough surfaces, Ritchie et al. concluded that "the contact angle of the nanodrop is exclusively related to the surface interaction energy in the region adjacent to its perimeter."49 The width of the adjacent region mentioned by these authors is of a few molecular diameters. In our calculations, ΔγSL is obtained within a strip of width 4 nm around the center line of the bridges,

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while the contact area spans at least 11 nm in the same direction. In view of the work of Ritchie et al.,49 this distance is large enough such that both the domain used to calculate ΔγSL and the area that defines the contact line are uncorrelated. There is therefore no contradiction between the fact that the variations of ΔγSL and θ upon changes in σ have opposite trends. This is in fact taken as the signature of the influence of σ on the local liquid structure and the resulting balance of interactions in the vicinity of the contact line. Considering the typical length scale at hand in our simulations, we can conclude that the local conditions that determine CAs on charged surfaces act within a range of a few nanometers at most. The large-scale MD simulations of liquids in nanoscopic confinements performed in this work indeed illustrate that the contact line remains important in static wettability upon approaching the mesoscopic length scale of 0.1 μm. To provide a more direct evidence for the influence of the contact line on the observed asymmetry for pure water, the orientation ordering of the water molecules has been calculated. Figure 7 a-c show the orientation ordering of the individual water dipole moment with respect to the normal to the surface through the second Legendre polynomial ( P2 (θ ) =

(

)

1 3 cos2 θ − 1 ) 2

at σ=0 µC/cm2 (Figure 7a), σ=+1.0 µC/cm2 (Figure 7b) and −1.0 µC/cm2 (Figure 7c). At zero charge density and away from the contact line, the dipole moments are oriented parallel to the surface. Additional information indicates that the water molecules are oriented with their plane mainly parallel to the surface with a small tendency of hydrogens to point to the surface.18-19 At heights beyond 0.6 nm, the green color at the liquid-vapor interface in Figure 7a indicates that the water molecules locally tend to orient their dipole moment parallel to the liquid-vapor interface.50 The interference between the orientation of water at the SL and LV interfaces in the vicinity of the contact line leads to a transition area (y between 5-6 nm and z

Interfacial tension does not drive asymmetric nanoscale electrowetting on graphene.

We report molecular dynamics simulations of the electrowetting behavior of liquids in confinement between two oppositely charged graphene sheets. We o...
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