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Mechanism for Asymmetric Nanoscale Electrowetting of an Ionic Liquid on Graphene Fereshte Taherian, Frédéric Leroy, Lars-Oliver Heim, Elmar Bonaccurso, and Nico F. A. van der Vegt Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b04161 • Publication Date (Web): 12 Dec 2015 Downloaded from http://pubs.acs.org on December 14, 2015

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Mechanism for Asymmetric Nanoscale Electrowetting of an Ionic Liquid on Graphene Fereshte Taherian, Frédéric Leroy, Lars-‐Oliver Heim, Elmar Bonaccurso§, 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 § Currently at Airbus Group Innovations, Metallic Technologies and Surface Engineering, 81663 Munich, Germany KEYWORDS: Contact angle, electrowetting, graphene, ionic liquid

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ABSTRACT The electrowetting behavior of 1-‐butyl-‐3-‐methylimidazolium tetrafluoroborate ([bmim][BF4]) confined between two oppositely charged graphene layers is investigated using molecular dynamics simulations. By introducing charges on the surface counterions are attracted to the surface and co-‐ions are repelled from it leading to the reduction of the solid-‐liquid interfacial free energy and consequently the contact angle. Recently, we have shown that changes in the contact angle upon charging the surface are asymmetric with respect to surface polarity, and opposite to the changes in the solid-‐liquid interfacial free energy. In this work, the asymmetry of the solid-‐liquid interfacial free energy is shown to originate from differences in structural organization of the ions at the interface, with positively polarized surfaces inducing a more favorable electrostatic arrangement of the ions. Analysis of the liquid structure in the vicinity of the three phase contact line however shows that the ion size-‐asymmetry, together with differences in orientational ordering of the cations on oppositely polarized surfaces, instead leads to enhanced spreading on the negatively polarized surfaces resulting in a corresponding contact angle asymmetry. 1. INTRODUCTION Due to the application of ionic liquids (ILs) in areas such as fuel cells,1 capacitors,2 catalysis3 or as electrowetting agents,4 the contact between ILs and charged surfaces has been a topic of significant interest during the last years. The wettability of a surface can be modified by applying an external electric field in a process which is known as electrowetting (EW).5-‐6 The consensus in the literature is that the change of the contact angle by the applied field is described by the Young-‐Lippmann (YL) equation. The contact angle reduction in the applied field is caused by a reduced solid-‐liquid interfacial free energy due to adsorption of counterions and desorption of co-‐ions at the interface. According to the YL equation, the change in the contact angle is independent of the applied field polarity, and the solid-‐vapor and the liquid-‐vapor interfacial 2


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free energies are assumed not to be affected by the field. Hence, the change in the solid-‐liquid interfacial free energy is assumed to be the only source of the field-‐induced contact angle reduction. Therefore, understanding the effect of the applied field on the solid-‐liquid interfacial free energy is essential for describing the electrowetting phenomenon. The effect of the surface charges on different structural properties of ILs, such as the layering of ions, the electrical potential at the interface, the volume charge density of the liquid, orientation of cations and anions and the electrical double layer capacitance at the interface has been investigated experimentally7-‐10 and with MD simulations.11-‐19 Experimental results of Mezger et al.,20 where the electron density profile of several ILs at a charged sapphire substrate was determined using high-‐energy x-‐ray reflectivity, have indicated an oscillatory arrangement of ions. Such layering of ILs at charged surfaces has been also observed at the IL-‐Au(111) interface by atomistic force microscopy (AFM) measurements, and was shown to be dependent on ion type.7, 21-‐22 Maolin et al.23 have published the first use of MD simulations to investigate the molecular structure of ILs at a solid surface. Their simulations of [bmim][PF6] at an uncharged graphite surface revealed strong layering of the IL (extending up to 2 nm into the bulk liquid) and flattening of the cations at the interface. Introducing charges on the surface was shown to separate the positive and negative charged layers at the interface, where multiple alternating layers of counter-‐ and co-‐ions have been observed.12, 24-‐25 Experiments and MD simulations have shown that the difference in the size of cations and anions and their affinity to the surface may cause a polarity dependence of the interfacial IL properties such as the volume charge density and the electrical double layer potential. This may further lead to an asymmetric dependence of the electrical double layer capacitance on the surface polarity.11, 14-‐15, 19 Lockett et al.26-‐27 have measured experimentally the double layer capacitance of several ILs with different ion sizes adsorbed at glassy carbon, platinum and gold electrodes using impedance spectroscopy. Results have indicated that the adsorption of cations and anions, due to the asymmetry in their size, is strongly influenced by the electrode polarization. AFM measurements of several ILs at a Au(111) electrode interface have shown that the adsorption of ions is strongly influenced by the polarity 3


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of the applied voltage.28 Simulations of [bmim][PF6] on a charged graphite surface reported by Kislenko et al.14 also revealed a polarity dependence of ion adsorption and, consequently, of the electrical double layer capacitance at the interface. Lynden-‐Bell et al.16 have reported a molecular simulation study of [dmim][Cl] on graphene in which it was found that stronger van der Waals interaction between the cations and the surface leads to the structural changes of the liquid upon charging the surface which are mainly due to the redistribution of the anions at the interface. Paneru et al.29 studied a [bmim][BF4] droplet immersed in hexadecane and electrowetted on a Teflon surface in experiments at different DC voltages. They observed more spreading of the droplet at high negative voltages (above 150 V) than at positive voltages and assigned the asymmetric behavior to the difference in the size of the cation and the anion and their interaction with the surface. Simulation results in the case of nanometer sized water droplets also indicated an asymmetric dependence of contact angle to the polarity of applied electric field.30-‐31 The observed contact angle asymmetry was interpreted through the YL equation and in terms of asymmetry in the bulk solid-‐liquid interfacial free energy due to the polarity dependence of water orientations and hydrogen bonding at the interface. In the above studies, electrowetting asymmetry is interpreted based on the YL equation, assuming that changes in the fluid structure at the bulk solid-‐liquid interface with the external field polarity leads to an asymmetry in the electrical double layer capacitance and therefore the bulk solid-‐liquid interfacial free energy. Recently, we have developed an approach using molecular dynamics (MD) simulations to calculate the change in the solid-‐liquid interfacial free energy by integrating the reversible work performed during the charging process of a surface.32 This approach has been used to calculate the changes in the interfacial free energies of water, aqueous NaCl salt solution and 1-‐butyl-‐3-‐ methylimidazolium tetrafluoroborate ([bmim][BF4]) liquid bridges spanning between two oppositely charged graphene layers. The equilibrium contact angle values showed an asymmetric dependence on the polarity of the surface: water and NaCl salt solution spread more 4


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on the positive surfaces, while [bmim][BF4] shows better wetting on the negative surfaces. However, such a dependency was not found from calculations of the contact angle that use solid-‐ liquid interfacial free energies, obtained from independent calculations, in the YL equation. In the case of water and NaCl solution the solid-‐liquid interfacial free energy was symmetric with the surface polarity, while for [bmim][BF4] the solid-‐liquid interfacial free energy showed an asymmetric behavior however suggesting changes in wetting behavior opposite to the actually observed contact angle variation. Therefore, the YL equation, where the interfacial free energies are taken from the bulk interfaces, fails in describing the observed asymmetries in electrowetting behavior of the liquids at the nanoscale. In the case of water and NaCl solution, field-‐polarity-‐dependent orientation of water dipoles and structural organization of ions at the contact line area leads to the observed contact angle asymmetry.32 In this work, a detailed analysis of the [bmim][BF4] liquid structure at the center and the contact line of the liquid bridge is given to describe, at the molecular level, the main sources of the observed asymmetries in the solid-‐liquid interfacial free energy and the contact angle. We will report different structural properties of [bmim][BF4] such as the density distribution of the ions, the orientational ordering of the cations and the volume charge density of the liquid along the centerline and the contact line of the liquid bridge. This analysis provides a mechanistic explanation for the asymmetric behavior of the contact angle and the solid-‐liquid interfacial free energy. We conclude that the YL equation based on the bulk interfacial free energies describes correctly the nanoscale electrowetting behavior (decrease of contact angle with the surface charge density) but not the observed asymmetry in the contact angle. To explain the asymmetry one needs to take into account the local solid-‐liquid free energy change in the region close to the contact line. A coarse-‐grained (CG) model developed originally by Merlet et al.33 is modified in this work to include the flexibility of the cation. Different bulk properties of the IL such as mass density, diffusion coefficient of the ions and the liquid-‐vapor surface tension are calculated using the refined model, and the comparison with experimental data is provided in Section 2. As it will be 5


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shown in the following, the CG model reproduces very well the experimental wetting behavior of the IL on a graphite surface. The experimental contact angle measurement of the IL on graphite, based on which we parameterized the IL-‐surface interaction potential, is reported in the Supporting Information. The approach to calculate the solid-‐liquid interfacial free energy is shortly described in Section 3, and the contact angle and the solid-‐liquid interfacial free energy calculations are reported. Then, the asymmetry observed in the solid-‐liquid interfacial free energy and the contact angle is discussed based on the packing and distribution of the ions on the positive and the negative surfaces at the centerline and the contact line of the liquid bridge. The main outcomes of the work are summarized in Section 4. 2. METHODOLOGY Molecular Simulation. For the electrowetting simulation of [bmim][BF4] a refined version of the coarse-‐grained (CG) model developed by Merlet et al.33 is used. Figure 1a and b shows a schematic view of the mapping scheme used between the atomistic and the CG models. As it is shown, the [BF4]‒ anion is represented by a single bead A, while three CG beads are used to map the [bmim]+ cation: bead T for the alkyl tail, bead R for the imidazolium ring and bead H for the methyl group of the imidazolium ring.

Figure 1. Schematic CG mapping scheme of (a) [bmim]+ cation, (b) [BF4]− anion and (c) graphene surface. 6


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In the original CG model of Merlet et al.,33 H-‐R and R-‐T bonds are constrained to 0.27 and 0.38 nm, respectively, and the H-‐R-‐T angle is fixed at 116°. However, the atomistic simulation of [bmim][BF4] carried out in this work using the atomistic force field parameters of Chaban et al.34 shows a broad distribution for the intramolecular degrees of freedom of the cation especially for the R-‐T bond and the H-‐R-‐T angle (as it is shown in Figure 2).

Figure 2. Distribution of (a) H-‐R, (b) R-‐T bond lengths and (c) H-‐R-‐T angle obtained from the atomistic and the CG simulations of the bulk IL at 350 K. Therefore, the CG model of Merlet33 is refined here to have a better representation of the IL structure. To do so, the bonds and the angle within the cation are considered to be flexible. The 7


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potential energy functions for the bonds and angles are derived using the iterative Boltzmann inversion method.35 In this method the potential of mean force 𝑈 𝜒 = −𝑘! 𝑇𝑙𝑛 𝑃 𝜒 , where kB is the Boltzmann constant, T is the temperature and 𝑃 𝜒 is the probability distribution of the intramolecular degree of freedom χ (corresponding to R-‐T and H-‐R bonds and H-‐R-‐T angle), is iteratively corrected as following to reproduce the probability distributions extracted from the atomistic simulations (𝑃!"# 𝜒 ):

⎡ P (χ ) ⎤ U i+1 ( χ ) = U i ( χ ) + k BT ln ⎢ i ⎥ ⎢⎣ Patm ( χ ) ⎥⎦

(1)

Here, i is the iteration count, 𝑃! 𝜒 is the calculated distribution at the ith iteration, and 𝑈! 𝜒 and 𝑈!!! 𝜒 are the effective potentials at the ith and (i+1)th iterations, respectively. The iteration procedure is carried out using VOTCA package.36 The comparison of the atomistic and the CG distributions shown in Figure 2 indicates a very good agreement between the atomistic and the CG models. To reproduce correctly the experimental mass density and the IL diffusion coefficients with the CG model the Lennard-‐Jones parameters ε for beads A and T have been manually refined. The interaction parameters are reported in Table 1. Table 1. Lennard-‐Jones parameters and fixed partial charges for the CG model of [bmim][BF4] and the graphene surface. interaction site A H R T C3

σ [nm] 0.451 0.341 0.438 0.504 0.4788

ε [kJ/mol] 3.44 0.36 2.56 2.33 0.4937

q [e] -‐0.78 0.1578 0.4374 0.1848 -‐

Simulations at a constant number of particle, pressure and temperature (NPT) with the number of ions pairs equal to 1331, P=1.0 bar and T=350 K have been performed to determine the mass density and the ionic diffusion coefficients. The equilibration run is set to 30 ns followed by a 20 ns production run. The simulation box has a size of 7.53 nm in x, y and z directions. The 8


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temperature and the pressure are kept constant using the Nose-‐Hoover thermostat37 with a time constant of 10 ps and the Parrinello-‐Rahman barostat38 with a time constant of 20 ps,33 respectively. The timestep is set to 2 fs, and the cutoff radius for the non-‐bonded interaction is equal to 1.6 nm. The particle mesh Ewald (PME) method39 with the cubic interpolation order and Fourier grid spacing of 0.12 nm is used to compute the long-‐range Coulomb interactions. The PME method, used in this work to include the effect of the long-‐range electrostatic interactions, has been applied extensively in the past to study different structural and dynamic properties of ILs at the charged surfaces.25, 40-‐41 The method has been also used to calculate the electrical double layer capacitance of ILs at charged surfaces,11, 14, 19 which requires precise calculation of long range electrostatic interactions. All the simulations are performed using the GROMACS package.42 The comparison of the diffusion coefficients of the cation and the anion and the bulk density of the IL with different simulation models and the corresponding experimental values is shown in Table 2. The results indicate a higher diffusion of the cations in the refined model compared to the original one. We believe that higher diffusion of the cations in the refined model is due to the flattening of the cations by making the T-‐R-‐H angle flexible based on the atomistic simulations. However, the higher diffusion of the cations is not affecting the current discussion, since we are interested in the static contact angle behaviour. Table 2. Atomistic, CG and experimental values of density, diffusion coefficient (cations and anions) and surface tension at T=350K. Model

Density [kg.m−3]

D− D+ Surface tension [×10−11 m2.s−1] [×10−11 m2.s−1] [mN/m]

Atomistic

1158.5 (±0.2)

9.9 (± 0.8)

10.3 (± 0.9)

36.9 (± 1.8)

CG (Merlet et al.)a

1175

10.1

11.3

33.8 (T=400 K)

CG (refined force field)

1174.1 (± 2.9)

10.6 (± 0.2)

13.6 (± 0.1)

40.4 (± 0.7)

Experiment b

1167

9.5

9.2

41.6 (T=341 K)

a T=348 K, Ref.33. b T=348 K, Ref.43.

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Since the wetting properties of the IL are investigated in this work, it is essential to verify if the CG model reproduces the liquid-‐vapor surface tension (γLV). To do so, the box size of the final configuration of the bulk simulation in the z-‐direction is extended to 50 nm. The liquid vapour interfaces are equilibrated for 100 ns under constant temperature and volume of the system. The liquid vapor surface tension is obtained from:44

γ LV =

(

)

Lz ⎡ 2P − Pxx + Pyy ⎤ ⎦ 4 ⎣ zz

(2)

where Pzz, Pxx and Pyy indicate pressure components along z, x and y directions, respectively, and Lz is the size of the box in z direction. The truncation of the Lennard-‐Jones interactions at the cutoff introduces an error in the surface tension calculations which can be corrected as following. In the first step, the density profile of the liquid along the z axis is fitted with a tangent hyperbolic function:

ρ(z) =

ρL ρL − tanh ⎡⎣( z − z0 ) d ⎤⎦ 2 2

(3)

where ρ(z) is the liquid density as a function of z, and ρL, z0 and d are the fitting parameters. In the second step, the fitting parameters are plugged into the following equation to calculate the surface tension tail correction:45 1 ∞ ⎛ 2rs ⎞ ⎛ 3s 2 − s ⎞ γ tail = 12π ε σ 6 ρ L2 ∫ ∫ coth ⎜ dr ds ⎝ d ⎟⎠ ⎜⎝ r 3 ⎟⎠ 0 rC

(4)

Table 2 compares the surface tension of the refined CG model with the atomistic and the original CG model of Merlet et al.33 and with the corresponding experimental value. The simulation results show that the refined CG model closely reproduces the experimental surface tension. The mapping scheme shown in Figure 1c is used for the CG model of the graphene surface. The CG bead of the surface (denoted as C3) is located at the center of the phenyl ring which includes three carbon atoms. The graphene surface is assumed to be rigid in this work. The interaction 10


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parameters between the surface and the liquid are optimized in such a way to reproduce the experimental contact angle of 49° for [bmim][BF4] on the graphite surface. The details of the experimental measurements are provided in the Supporting Information section. The graphite surface consists of six graphene layers, and has a thickness of 1.7 nm. Details of the experimental contact angle measurements are described below. The same approach as used in our recent work46-‐47 on water-‐graphene interfacial systems is applied here to develop the interaction parameters between the surface and the IL. The graphene surfaces in the setup shown in Figure 3b are replaced with graphite (six graphene layers) and the Lennard-‐Jones parameter εC3 is systematically increased from a value of 0.35 kJ/mol to 0.51 kJ/mol in increments of 0.04 kJ/mol. By using a linear interpolation for the contact angle versus εC3, the Lennard-‐Jones parameter which reproduces the experimental contact angle is determined (εC3 = 0.4937 kJ mol-‐ 1). The value of σC3 has been fixed at 0.4788 nm.48 The Lorentz-‐Berthelot mixing rules are used to

generate the interaction parameters between the IL and the surface. For the contact angle calculations, 7986 ion pairs are confined between two graphene surfaces oriented parallel to the x-‐y plane. The dimension of the surface in the x and y directions are set to 8.118 and 16.18 nm, respectively. The distance between the surfaces is set to 19.54 nm to reproduce the bulk mass density of the IL. The size of the simulation box in the z-‐direction is set to 100 nm to exclude the effect of the periodic boundary condition in this direction (Figure 3a). The PME calculations in the z-‐direction are corrected to have a pseudo-‐2D Ewald summation.49 After equilibrating the system in the confined configuration, the graphene surfaces are extended in the y-‐direction to 56.66 nm to create a liquid-‐vapor interface, as it is shown in Figure 3b. Since with this setup the liquid bridge has infinite contact line length, the effect of the line tension is excluded from the calculations. An equilibration run of 30 ns is performed on the liquid bridge, followed by a production run of 15 ns for the contact angle calculations. The same approach described in our recent publication32 is followed here for the contact angle calculations. The final configuration is used for the simulations of the charged surfaces.

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It is worth noting that due to the particular setup of the simulations used in the simulations (Figure 3), the effect of the line tension is excluded from the MD simulation results. With such a setup, it is in fact not possible to calculate the value of the line tension. However, one could use spherical droplets of various sizes to investigate the effect of the line tension on the MD simulation results. This is however out of scope of this work. The contact angle calculations are performed on the charged graphene surfaces with surface charge densities of ±0.2, ±0.4, ±0.6 μC/cm2 and ±0.8 μC/cm2. The corresponding partial charges of the graphene CG bead (C3) are ±0.981×10-‐3, ±1.962×10-‐3, ±2.943×10-‐3 e and ±3.924×10-‐3 e respectively. Such surface charge densities can be introduced experimentally by chemically doping the surface50 or applying external voltage5. The top graphene surface is charged positively, while the corresponding negative charge is applied on the bottom layer to have a neutral system in each case. Simulation results indicate that at surface charge densities ±0.8 μC/cm2 the ions are pulled from the liquid bridge, and the contact angle saturation occurs (Figure 4), in agreement with the simulation results of Liu et al.51

Figure 3. Snapshot of the simulation setup (a) in the initial slab geometry and (b) for the contact angle calculation. The IL on the right-‐hand-‐side is shown in a configuration before spreading of the liquid on the surface has taken place. 12


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3. RESULTS AND DISCUSSION The liquid bridge on an uncharged single graphene layer has a contact angle of 73.6°, which is 24.6° higher than the corresponding value on graphite, due to the weaker van der Waals interaction between the surface and the liquid in the case of graphene. Introducing the positive or the negative charges on the graphene surface leads to the reduction of the contact angle as it is reported in Table 3 and shown in Figure 4 (black squares). On the negatively charged surfaces, the cations are attracted to the surface while the anions are repelled from it. Opposite behavior is observed on the positively charged surfaces where the anions are attracted to the surface and the cations are repelled. Such addition of the counterions and removal of the co-‐ions at the solid-‐ liquid interface leads to the reduction of the solid-‐liquid interfacial free energy and therefore of the contact angle. At surface charge densities above ±0.6 µC/cm2 the cations and the anions are pulled from the bridge on the negative and the positive surfaces, respectively, and leads to the contact angle saturation in agreement with the simulation results of Liu et al.51 The contact angle displayed in Figure 4 at σ ≤ ±0.6 µC/cm2 shows a clear asymmetric dependence on the surface polarity. The liquid spreads more on the negatively charged surfaces. Such asymmetric behavior of the contact angle has been also observed for pure water and aqueous salt solutions.30-‐32 Hanly et al.52 has developed a theoretical approach to calculate the change in the solid-‐liquid interfacial tension of water and salt solutions at a charged surfaces on the basis of the Gouy-‐ Chapman model. The model considers ions as point charges, and it is on the basis of dilute-‐ solution approximation. Such model however was shown to be not applicable for ILs due to the charge delocalization of ions, high concentration of ions, strong correlation between ions and the multilayer structure of ions at the interface.53 Recently, we have proposed a direct method, based on the thermodynamic integration approach,54 to calculate the change in the solid-‐liquid interfacial free energy upon charging the surface.32 The change in the solid-‐liquid interfacial free energy, Δγ SL , between the uncharged surface system (denoted as A) and the system with the 13


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surface charge density σ (denoted as B) is equal to the change in the Gibbs free energy per unit area upon the surface charging process and is calculated using the thermodynamic integration (TI) method54

Δγ SL

λ 1 B ∂H ( λ ) = γ SL,B − γ SL,A = ∫ Aλ ∂λ A

d λ ′

(5)

λ′

In Eq. (5), H is the Hamiltonian of the system, λ is a coupling parameter which quantifies the transformation from the uncharged surface system to the charged one, and ⟨···⟩λ’ denotes an ensemble average over the configurational distribution of the liquid molecules in contact with surface at a surface charge density determined by the set value of the coupling parameter λ. Since only the solid-‐liquid Coulomb interaction potential (USL,Coul) is affected upon charging the surface, the change in the solid-‐liquid interfacial free energy is given by:

Δγ SL =

σ ∂U SL,Coul (σ ′ ) 1 dσ ′ ∫ A0 ∂σ ′

(6)

The change in the solid-‐liquid interfacial free energy is therefore obtained by integrating the average derivative of solid-‐liquid Coulomb interaction at different surface charge densities σ. Using the setup shown in Figure 3, USL,Coul is calculated at the centerline of the liquid bridge with a base area of 8.118 × 4.0 nm2. The cations whose geometric centers are located in the defined centerline region are taken into account in the Coulomb interaction potential calculations. The calculations are done with a spherical cutoff of 2.5 nm corresponding to the distance above the surface where the density of the IL is same as the bulk value. The calculations of ΔγSL at different cutoff distances have shown that even though the magnitude of ΔγSL changes with changing the cutoff, its overall behavior is independent of the choice of it.32 14


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Table 3. Surface charge densities (σ), partial charge of the coarse-‐grained surface sites (qC3), the contact angle (θ) and the change in the solid-‐liquid interfacial free energy at the centerline of the liquid bridge. The errors are calculated using blocking average over a time frame of 15 ns with a block size of 3 ns. σ [µC/cm2] qC3 [e] (x10-‐3) θ [degree] Δ γSL [mJ m-‐2] 0.8 3.924 61.6 (0.9) -‐ 0.6 2.943 62.8 (0.7) -‐3.16 (0.16) 0.4 1.962 67.5 (0.9) -‐1.48 (0.12) 0.2 0.981 72.4 (0.8) -‐0.36 (0.07) 0.0 0.0 73.6 (0.6) 0.0 -‐0.2 -‐0.981 69.9 (0.8) -‐0.33 (0.08) -‐0.4 -‐1.962 60.9 (0.9) -‐1.21 (0.15) -‐0.6 -‐2.943 53.7 (0.6) -‐2.46 (0.20) -‐0.8 -‐3.942 54.3 (0.9) -‐

Figure 4. Contact angles (black squares), solid−liquid Coulomb energy (open red squares) and change in the solid−liquid interfacial free energy (filled red squares) at different surface charge densities. The lines are spline fits to the data points and are included to guide the eye.

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The change in USL,Coul upon charging the surface is displayed in Figure 4 (open red squares). The results show that although the liquid spreads less on the positive surfaces, the solid-‐liquid Coulomb interaction is slightly more attractive on these surfaces than on the negatively charged ones. These results indicate that in addition to the solid-‐liquid Coulomb interaction other parameters such as the change in the solid-‐liquid interfacial entropy and/or structural peculiarities in the three-‐phase contact line region may influence the observed contact angle. The dependence of ΔγSL (obtained from TI calculations) on the surface charge density is shown in Figure 4 by the filled red squares. According to the YL equation, these values of ΔγSL should produce a more favorable wetting on the positive surfaces, which however is opposite to the observed contact angle asymmetry. In the following a detailed analysis of the interfacial structure of the liquid at the centerline and at the contact line of the bridge is given to provide microscopic explanation of the asymmetries observed in the solid-‐liquid interfacial free energy and the contact angle. Solid-‐liquid interfacial free energy asymmetry: Figure 5 shows the number density of the cations and the anions at different surface charge densities calculated around the centerline within a base area of 8.118 × 4.0 nm2. The top panel in Figure 5 shows the density distribution of the ions at the zero surface charge density. Due to the stronger van der Waals interaction between the cations and the surface, there is a higher tendency for the cations compared to anions to be adsorbed on the surface. The specific adsorption of the ions to the surface at zero surface charge density gives rise to an electrical potential distribution drop at the interface which can be quantified using the Poisson equation

ϕ (z) = −

1 ε0

∫

z

0

dz ′ ∫ ρe ( z ′′ ) dz ′′ . A positive value of 0.12±0.03 V is found for the potential z′

0

difference between the graphene surface and the middle of the channel, which confirms the

16


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Langmuir

specific adsorption of cations at zero surface charge density. The specific adsorption of [bmim]+ ions has been also observed previously on graphite surface by MD simulations.11, 19, 23, 55-‐56 The number density profiles of the ions at different surface charge densities shown in Figure 5 indicates a strong layering of the cations and the anions at the interface extending around 2 nm into the bulk liquid. Such strong interfacial layering has been also observed experimentally by x-‐ ray reflectometry20,

57

and atomistic force microscopy (AFM)28,

58

and as well as by MD

simulations11, 19, 25. Due to the difference in the size of the cations and the anions and also the stronger van der Waals interaction between the positive ions and the surface,11, 16 the reorganization of the positive and the negative ions upon charging the surface is different. In Table 4, the number of cations and anions adsorbed or removed from the first (0.59 and 0.69 nm from the surface for cation and anion, respectively) and the second (0.85 and 1.11 nm from the surface for cation and anion, respectively) adsorption layers at different surface charge densities are reported. The position of the layers for cations and anions are determined by the minimum of the corresponding number density. Table 4. Relative cation and anion adsorption (positive numbers) and desorption (negative numbers) from the first (0.59 and 0.69 nm from the surface for cation and anion, respectively) and the second (0.85 and 1.11 nm from the surface for cation and anion, respectively) adsorption layers at different surface charge densities. Surface charge density [μC/cm2] -‐ 0.6 -‐ 0.4 -‐ 0.2 0.0 + 0.2 + 0.4 + 0.6

Relative cation adsorption (+) or desorption (-‐) [%] First layer Second layer 2.50 3.75 1.25 0 -‐1.25 -‐3.75 -‐3.75

Relative anion adsorption (+) or desorption (-‐)[%] First layer Second layer

3.26 0.72 4.87 0 0.92 2.76 2.61

17


-‐5.62 -‐4.61 -‐2.39 0 5.48 7.59 11.09

0.93 0.24 2.16 0 0.56 1.96 0.77

Langmuir

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Figure 5. Number density profiles of the anions and the cations along the centerline of the liquid bridge at different surface charge densities. The simulation results indicate that while the density of the cations close to the surface varies weakly with the charge on the surface, the addition and the removal of the anions on the positive and the negative surfaces, respectively, are shown to be the main structural changes of the liquid at the interface.19 The simulation results however indicate that the addition of the anions to the interface on the positive surfaces is more pronounced than their removal on the negative surfaces. By introducing more positive charges on the surface, removal of a few bulky [bmim]+ ions leads to the adsorption of several smaller [BF4]− ions. However, by increasing the negative charges on the surface on the one hand the adsorption of the [bmim]+ ions is not changing that much due to their high accumulation at the neutral interface, and on the other hand the 18


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Langmuir

attractive interactions between the anions and the high accumulated cations prevent the removal of the anions from the interface. As a result, the accumulation of the negative charges close to the positive surfaces is higher than the positive charges close to the negative surfaces. Similar behavior was found in the atomistic simulation of [bmim][BF4] on graphene by Feng et al.19. As discussed in the introduction, the polarity dependence of the ion adsorption has been also observed experimentally using impedance spectroscopy26-‐27 and AFM measurements.28 Such dependency of ion adsorption leads to an asymmetry in the electrical double layer capacitance at the interface.14 Electrowetting experimental results of Paneru el al.29 for [bmim][BF4] on fluoropolymer surfaces have also shown an asymmetric dependence of the contact angle on the polarity of the applied voltage. The authors have interpreted the results based on the difference in the size of the counter ions and their adsorption to the bulk interface. Hence, the consensus in the literature is that the asymmetry in the electrical double layer capacitance leads to the polarity dependence of the bulk solid-‐liquid interfacial free energy and explains the asymmetric electrowetting based on the YL equation.29-‐31 In the following, we will show that one needs to take into account the local change of the solid-‐liquid interfacial free energy at the vicinity of the contact line to be able to correctly describe the electrowetting asymmetry at the nanoscale. The difference in the charge density distributions close to the surface (away from the contact line, between approx. 6

Mechanism for Asymmetric Nanoscale ... - ACS Publications

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