Toward an Accurate Modeling of Ionic LiquidâTiO2 Interfaces - The

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Towards an Accurate Modeling of Ionic Liquid–TiO Interfaces Henry Weber, Mathieu Salanne, and Barbara Kirchner J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b08538 • Publication Date (Web): 16 Oct 2015 Downloaded from http://pubs.acs.org on October 25, 2015

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The Journal of Physical Chemistry

Towards an accurate modeling of ionic liquid–TiO2 interfaces Henry Weber,† Mathieu Salanne,‡,¶ and Barbara Kirchner∗,† Mulliken Center for Theoretical Chemistry, Universität Bonn, Beringstr. 4+6, D-53115 Bonn, Germany, and Sorbonne Universités, UPMC Univ Paris 06, CNRS, Laboratoire PHENIX, F-75005, Paris, France E-mail: [email protected]

∗ To

whom correspondence should be addressed Center for Theoretical Chemistry, Universität Bonn, Beringstr. 4+6, D-53115 Bonn, Germany ‡ Sorbonne Universités, UPMC Univ Paris 06, CNRS, Laboratoire PHENIX, F-75005, Paris, France ¶ Maison de la Simulation, USR 3441, CEA - CNRS - INRIA - Université Paris-Sud - Université de Versailles, F-91191 Gif-sur-Yvette, France † Mulliken

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Abstract Structural properties of the ionic liquids 1-ethyl-3-methylimidazolium thiocyanate and tetracyanoborate at the anatase (101) surface are of crucial interest for energy harvesting and storage devices, but their investigation via molecular dynamics requires large simulation cells. Thus, two classical interaction potentials with and without polarization effects were parameterized in order to accurately model the interface between the liquid and solid. The parameters were fitted to match ab initio reference interaction energies. Application of the generated force field to model the interface is demonstrated. The adsorption profiles of the ionic liquid’s components reveal a very dense surface layer with an excess of cations, which has some possible implications for the use of the ionic liquids as electrolytes, for example in solar cells.

Keywords: force field, ionic liquids, TiO2 , molecular dynamics


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1 Introduction Ionic liquids (ILs) are a hot topic, even a century after their revival. 1–3 Unique characteristics define this class of liquids, and by the time, different applications emerged. Ionic liquids were successfully applied as electrolytes, 4,5 e.g. in fuel cells, 6–8 batteries, 5,9 supercapacitors 5,10,11 and dye sensitized solar cells (DSCs). 12 For the latter one, ionic liquids (ILs) were investigated to replace volatile organic solvents, 12 as they offer great potential benefits. Beyond being a simple diffusive medium, ILs can affect band edge positions of the employed semiconductor, electron–hole recombination rates in the DSC; and the chemical dye regeneration reaction. 13 Pioneering work by Fredin et al. 13 employing ILs in DSCs pointed out that DSC key parameters as well as overall efficiency are crucially affected by the IL’s nature. In particular, the ILs 1-ethyl-3-methylimidazolium thiocyanate ([C2 C1 Im][SCN]) and 1-ethyl-3-methylimidazolium tetracyanoborate ([C2 C1 Im][B(CN)4 ]) were used as electrolytes in ruthenium-based DSCs, resulting in varying device efficiencies partly attributed to the formation 13 In contrast to this of pseudohalides such as [I2 SCN]− and thus lowering the I− 3 concentration.

study, employing the same ILs in porphyrin-based DSCs has led to an opposing trend concerning device efficiency. 14,15 These findings show that a deeper insight in the specific interactions between all components of a DSC is required to fully understand and predict the device properties. Recent ab initio molecular dynamics (AIMD) studies of the pure IL [C2 C1 Im][SCN] 16,17 and mixtures with SO2 18 demonstrated the excellent solvent properties and the potential for diverse applications of this IL. However, many properties are not accessible via AIMD, because large system sizes or long simulation times are sometimes required. Classical molecular dynamics (MD) is able to fill this gap and give new insights. 19,20 For example, the phenomenon of microheterogeneity in ILs was discovered with the aid of classical MD simulations. 21 Furthermore, interfacial studies often require classical methods because of their size. 22 At interfaces, ILs exhibit a three-dimensional structure which varies markedly from the bulk liquid. 23 The behavior of [C2 C1 Im][SCN] at a graphene interface in the context of supercapacitors was showcased recently by Pensado et al. 24 Strong adsorption of the IL with multiple solvation 3 ACS Paragon Plus Environment


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layers were observed, the cation majorly displayed flat conformations at the surface. Concerning metal oxides, the [C4 C1 Im][NTf2 ]–sapphire interface was studied in a combined classical MD and X-ray reflectivity study. Hydrogen bonding was attributed to induce an ordered adsorption layer with an excess of cations, which in turn caused a multidimensional bilayering profile. 25 Such bilayered morphology was also proven experimentally for a series of pyrrolidinium ILs. 26 The main difficulty for predicting the properties of these interfaces is the lack of accurate force fields. A detailed static quantum chemical study of the ILs [C1 C1 Im][SCN] and [C1 C1 Im][B(CN)4 ] at the anatase (101) surface was previously conducted by us. 27 This interface is of particular interest in DSC research, as detailed knowledge of the electrolyte–semiconductor interactions may shed light onto device differences concerning performance or durability. Attempting to study this interface, computational efficiency limits are reached for a quantum chemical description. Therefore, we developed an efficient classical description which allows us to investigate structural and dynamic properties of the IL–solid interface in detail.

2 Computational Details For the classical description of the ionic liquid, the force field (FF) developed by Pádua et al. was used 28 with the exception of newly derived partial charges, employing the popular OPLS/AA force


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field: 29 bonds

V=

∑ ij

kr,i j (ri j − r0,i j )

angles

∑

+

kθ ,i jk (θi jk − θ0,i jk )

i jk

dihedrals 4

1 − (−1)m cos(mφi jkl )

∑ ∑ Vm,i jkl

+

i jkl

m=1

impropers

∑

+

kχ,i jkl (χi jkl − χ0,i jkl )

i jkl nonbonds

+

∑ i< j

(

4εi j

"

σi j ri j

12

σi j − ri j

6 #

1 qi q j + 4πε0 ri j

)

(1)

with kr, θ , χ being the force constants of the harmonic bond, angle and improper dihedral potential, respectively, r0 , θ0 and χ0 being the equilibrium bond length, bond angle and improper dihedral angle. Vm is the potential of the torsional barrier for the m-th multiplicity. The substrate titanium dioxide was described with the polarizable ion model (PIM) 30 using the latest parameterization of Corradini et al. 31 The PIM is shortly summarized in the following. At first, all point-charge interactions are considered as usual in a Coulomb sum

VCoulomb =

qi q j 1 . ∑ ∑ 4πε0 i j>i ri j

(2)

Formal charges were used as partial charges on the oxygen atoms (qO = −2 e) and the titanium atoms (qTi = +4 e) to ensure transferability. Repulsive and dispersive forces were incorporated with the Born–Mayer–Huggins (BMH) potential, 32,33 which reads as ij

VBMH = ∑ ∑ i j>i

ij C C ij ij Ai j e−ai j ri j − f6 (ri j ) 66 − f8 (ri j ) 88 ri j ri j

!

(3)

with the repulsion parameter Ai j , the ion pair dependent length parameter ai j , the van-der-Waals



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parameters C6 and C8 and the Tang–Toennies 34 type damping functions fn given as ij

ij

ij

fni j

ij

bD ri j

= 1−e

ij

n

(b ri j )k ∑ Dk! k=0

(4)

ij

with the repulsive range parameter bD . In order to accurately describe the many-body electrostatic interactions, the induced dipole moments µi are obtained by minimizing the polarization energy VPol = ∑ i

1 1 ij ij ij ij ji |µi |2 + g (r )q T µ µ µ µ − g (r )q T − T ij i 1 j ij j 1 i i 2 j . ∑ 2αi 4πε0 ∑ i j>i

(5)

The equation contains the atomic polarizabilities αi , the charge-dipole and dipole-dipole interaction tensors T1 and T2 , respectively, and the Tang–Toennies 34 type polarization damping functions gi j (ri j ) = 1 − ci j e−b ji ri j

4

(bi j ri j )k ∑ k! . k=0

(6)

with the additional parameter ci j , which specifies the importance of short-range corrections. Classical Molecular Dynamics Simulation Details. Non-bonded interactions within the IL are described via the Lennard-Jones potential, including potential well depth εi j and the zero energy cross point σi j . A cutoff distance rc of 1.5 nm was used to truncate the Lennard-Jones potential. √ Lorentz–Berthelot mixing rules (εi j = εi ε j and σi j = (σi + σ j )/2) were applied to obtain unlike atom pair parameters for IL–IL interactions. Electrostatic interactions were calculated using a standard Ewald sum technique with an accuracy of 10−6 Hartree beyond a real-space cutoff of rc = 1.5 nm. The new partial charges qi were obtained using a restrained electrostatic potential (RESP) 35 fit of the isolated ions at the HF 6-31++G** level 36,37 with subsequent scaling to ±0.8 e on each individual ion, because it was shown that ±0.8 e is about the amount of the charge transfer

and leads to better description of dynamic properties. 3

256 ion pairs of the IL [C2 C1 Im][SCN] and 200 ion pairs of the IL [C2 C1 Im][B(CN)4 ] were


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simulated between slabs of titanium dioxide in anatase modification with revealed (101) surface. Anatase was described by the force field of Corradini et al. 31 Cell parameters were chosen to match experimental data (a = b = 378.2 pm, c = 950.2 pm). 38 A slab with 10 stoichiometric layers of TiO2 was taken and rotated such that the cell vector a matches the x-axis and the surface normal of the (101) surface matches the z-axis of the system, in order to allow an easier analysis of surface related properties. A 9x6 supercell was then created, leading to an anatase slab of the dimensions a = 3403.8 pm, b = 3271.17 pm, α = β = 90◦ , γ = 110.2947◦ and a thickness of ≈ 1640 pm, containing a total of 540 stoichiometric units of TiO2 . During the simulation, the inner 6 layers were constrained to stay immobile. The outer layers of the anatase slab and the ionic liquid were time–integrated in the N,V, T -ensemble. The CSVR (canonical sampling through velocity rescaling) thermostat 39 with a time constant of τ = 100 fs was utilized to ensure a constant temperature of T = 343.15 K. It was shown by Bussi et al. that the CSVR thermostat yields a canonical distribution, leaves static and dynamic properties largely unaffected by the thermostat parameters and that it is more ergodic than the widely used Nosé–Hoover thermostats. 39 Starting geometries were obtained with the aid of the PACKMOL program package. 40 Densities of the ionic liquids between the slabs was chosen to match the experimental densities, see supporting information. Both systems were equilibrated for at least 50 ps and a subsequent production run to yield 500 ps of simulation time with a time step of ∆t = 0.5 fs was carried out. The relatively short simulation time can be justified by the very low viscosity of the ILs, summarized alongside further details in the supporting information. Radial distribution functions (RDFs), z-density profiles, spatial distribution functions (SDFs) and combined distribution functions (CDFs) are computed with the aid of the T RAVIS program package. 41 Computational details on these analysis are given in the respective reference. 41 The visual molecular dynamics (VMD) program package was used to show molecular structures and SDFs. 42 Graphical representations were produced with the G RACE program package. 43 CDFs were generated using the G NUPLOT software.



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3 Results and Discussion 3.1 Generation of the Force Field We propose the interaction potential Vint between the ionic liquid and TiO2 to be a sum of the nonbonded interaction terms: int int Vint =VLJ +Velectrostatic

with

int int int VLJ =Vrepulsive +Vdispersive " 6 # σi j 12 σi j = ∑ ∑ 4εi j − ri j ri j i∈IL j∈TiO2

and

int int int Velectrostatic =VCoulomb +Vpolarizable

1 = ∑ ∑ 4πε0 i∈IL j∈TiO2

qi q j ri j µ j − gi j (ri j )qi 3 ri j ri j

!

(7)

with the Lennard-Jones parameters σ and ε , partial charges q, induced dipole moments µ , and the Tang–Toennies 34 type polarization damping functions gi j (ri j ) as seen before (Eq. (6)). As the ionic liquid is not polarizable, it follows that their induced dipole moments µi∈IL are zero. To match the ab initio reference, two alternative ways are presented. The first one excluding the polarizability of TiO2 only uses LJ and Coulomb interactions, subsequently called the LJ FF, and the second approach, including the polarizable TiO2 is called the PIM FF in the following. While the simple LJ FF is computationally less expensive, the clear drawbacks are that the TiO2 substrate must be constrained to stay in fixed positions all the time, resulting in a less detailed description of the system. We included this approach, because some applications do not require this level of detail, e.g. large scale simulations or rough sampling, this force field might be sufficient. Utilizing the PIM FF on the other hand, the anatase substrate is able to adapt and respond to its surroundings, resulting in a more sophisticated and detailed description of the interface, though at the price of higher computational demand. In a previous work, the quantum chemical description of this system was investigated. 27 It 8 ACS Paragon Plus Environment

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was found that the PBE-D3 level serves as an efficient tradeoff between computational demand and accurate results. 44,45 Therefore, a total of 631 reference structures were calculated and the QM BSSE-corrected interaction energies Eint were evaluated according to our previous work 27 with

Goedecker–Teter–Hutter pseudopotentials 46,47 and the MOLOPT-DZVP-SR-GTH 48 basis sets. A detailed overview of the composition of the reference structures is given in Table 3. The training set consisted of either small ion pair clusters of [C1 C1 Im][SCN] or [C1 C1 Im][B(CN)4 ] or a condensed bulk phase of [C2 C1 Im][SCN] or [C2 C1 Im][B(CN)4 ]. Clusters of 1, 2 or 3 ion pair size were calculated on a 6 stoichiometric layer anatase slab in a 4x3 supercell, revealing the (101) surface. These reference structures were derived with classical MD utilizing a preliminary force field, 27 and to some extent from ab initio molecular dynamics (AIMD) for the 1 IP systems. The bulk reference structures were obtained from AIMD simulations of the respective IL in a simulation cell including a 6x4, 6 layer anatase slab with exposed (101) surface at the same level of theory. To ensure transferability, i.e. keeping the force fields of Pádua et al. for simulating the IL and of Corradini et al. for the description of TiO2 , only the interaction parameters σi j and εi j from Eq. (7) with i ∈ IL and j ∈ TiO2 were adjusted in the fitting procedure. Parameters of the Tang– Toennies 34 type polarization damping function gi j (Eq. (6)) were set to fixed standard values of bi j = 200 pm−1 and ci j = 1.0 and were not fitted in order to limit the number of fitting parameters. The best set of parameters is determined by minimizing the objective function 2 QM MM − E E ∑N k int int O= , 2 QM N ∑k Eint

(8)

QM targeting the minimal difference in energy over all N reference conformations. Eint is the BSSEMM is the force field interaction energy derived corrected quantum chemical interaction energy, Eint

in a similar fashion: MM Eint = EAB − EA − EB


(9)


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with the energy of the whole system EAB and the energy of the interacting subsystems EA and EB in the adsorption geometry. Quantum chemical interaction energies were chosen as target for the fitting rather than forces in usual force–matching approaches, because the forces on the IL and Ti/O atoms are dominated by the intramolecular IL forces and the interatomic Ti/O forces, respectively. The objective function was minimized with the aid of the M INUIT program package, 49,50 using firstly the downhill–simplex method and subsequently the MIGRAD minimization. Table 1: Derived classical force field parameters εi j and σi j for the PIM FF. For the labeling see Figure 1. i C2 C4/5 C6/8 C7 H2 H4/5 H6/8 H7 N1/3 C ([SCN]− ) N ([SCN]− ) S ([SCN]− ) B ([B(CN)4 ]− ) C ([B(CN)4 ]− ) N ([B(CN)4 ]− ) C2 C4/5 C6/8 C7 H2 H4/5 H6/8 G H7 N1/3 C ([SCN]− ) N ([SCN]− ) S ([SCN]− ) B ([B(CN)4 ]− ) C ([B(CN)4 ]− ) N ([B(CN)4 ]− )

j O O O O O O O O O O O O O O O Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti

εi j / kJ mol−1 0.45903 0.04690 1.25415 0.04185 0.07930 0.23332 0.06714 0.04251 1.25520 0.70668 0.04207 0.15137 0.31804 0.04768 0.90257 1.25499 0.09018 1.25411 0.29064 1.25495 1.25478 0.98123 0.04472 0.36281 0.22721 0.36838 0.09612 1.10119 0.17774 0.48288

σi j / Å 3.082 3.234 3.108 1.645 2.263 2.281 2.480 2.821 2.988 3.119 2.663 3.442 3.053 2.129 3.033 2.673 3.724 2.960 1.568 1.983 1.135 1.848 2.639 3.939 3.574 2.853 3.274 4.637 3.047 2.516

The final fitted parameters for the LJ and PIM FF are listed in Table 1 and Table 2. As can be seen from Table 3, the overall agreement of interaction energies Eint between quantum chemical calculations and force field results is within a standard deviation σ of 6.8 % with minimum 10 ACS Paragon Plus Environment

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Table 2: Derived classical force field parameters εi j and σi j for the LJ FF. For the labeling see Figure 1. i C2 C4/5 C6/8 C7 H2 H4/5 H6/8 H7 N1/3 C ([SCN]− ) N ([SCN]− ) S ([SCN]− ) B ([B(CN)4 ]− ) C ([B(CN)4 ]− ) N ([B(CN)4 ]− ) C2 C4/5 C6/8 C7 H2 H4/5 H6/8 H7 N1/3 C ([SCN]− ) N ([SCN]− ) S ([SCN]− ) B ([B(CN)4 ]− ) C ([B(CN)4 ]− ) N ([B(CN)4 ]− )

j O O O O O O O O O O O O O O O Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti

εi j / kJ mol−1 1.25520 1.25520 1.25520 1.25520 1.05189 1.25520 0.05313 0.04363 1.25518 1.25518 0.40148 1.25477 1.25520 0.12037 1.25520 1.25520 1.25409 1.25493 1.25509 1.25520 1.25520 0.43577 1.25491 1.25519 1.25520 0.82132 0.08240 1.25520 1.25520 1.20871

σi j / Å 2.816 2.883 3.033 3.130 1.740 1.792 1.399 1.667 3.237 2.958 1.861 3.069 2.908 1.259 2.785 3.193 2.939 3.180 2.798 3.000 2.686 2.784 2.500 3.482 3.146 2.507 3.312 4.272 3.026 2.116

Table 3: Overview of training set used to fit the classical force field parameters. Mean BSSEQM corrected reference energies hEint i and mean force field interaction energies for the LJ force LJ PIM i are given as well as the standard deviations field hEint i and the polarizable force field hEint σ in SI units and in percent of the QM reference energy. # System full 1 IP [C1 C1 Im][SCN] 2 IP [C1 C1 Im][SCN] 3 IP [C1 C1 Im][SCN] bulk [C2 C1 Im][SCN] 1 IP [C1 C1 Im][B(CN)4 ] 2 IP [C1 C1 Im][B(CN)4 ] 3 IP [C1 C1 Im][B(CN)4 ] bulk [C2 C1 Im][B(CN)4 ]

631 125 100 100 32 150 50 50 24

QM hEint i/ kJ mol−1 -700.3 -265.3 -409.2 -618.8 -3602.5 -243.4 -624.2 -812.6 -3429.1

LJ i / hEint kJ mol−1 -687.0 -212.8 -397.0 -644.3 -3575.1 -246.6 -564.1 -814.2 -3437.3

PIM i / hEint kJ mol−1 -691.6 -225.1 -408.2 -634.8 -3600.5 -242.2 -579.5 -818.5 -3438.9

σ LJ / kJ mol−1 47.5 58.9 44.6 43.9 70.8 24.5 66.9 28.6 58.8


σ LJ / % -6.8 -22.2 -10.9 -7.1 -2.0 -10.1 -10.7 -3.5 -1.7

σ PIM / kJ mol−1 39.5 47.6 32.3 38.9 50.1 26.4 51.8 28.8 59.1

σ PIM / % -5.6 -17.9 -7.9 -6.3 -1.4 -10.9 -8.3 -3.5 -1.7


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well concerning trends and absolute values (numbers are given in Table 3, supporting information). As we only introduced a very minor change to the original FF, the quality of the IL FF is conserved. As a case study using the derived FFs, the ionic liquids [C2 C1 Im][B(CN)4 ] and [C2 C1 Im] [SCN] were simulated in the confined region between two parallel slabs of anatase with exposed (101) surface, the components are shown in Figure 1. In the following, only results using the more accurate PIM FF are shown, because we aim at high accuracy to gain new insights on the structure of the interface. The feasibility of the LJ FF was tested as well, information on the results are given in the supporting information. The z-dependent density ρz (Figure 2 (a) and (b), note that the surface normal (SN) of the anatase slab coincides with the z-axis of the simulation box) reveals a strong aggregation of both ILs at the surface, because relative density at the surface is observed to be approx. six times the bulk density. This tightly adsorbed layer extends ≈ 400 pm in z direction, followed by ≈ 200 pm of a very low density region for [C2 C1 Im][B(CN)4 ] and ≈ 100 pm for [C2 C1 Im][SCN], where almost no molecules are found throughout the simulation. ρz shows two distinct peaks for the [SCN]− anion and [B(CN)4 ]− anion, which will be discussed later in detail with the aid of combined distance–angle distribution functions. The observed layer thickness correlates well with a computationally and experimentally verified thickness of approx. 450 pm for the IL [C2 C1 Im][NTf2 ]. 25 As we employ a polarizable FF for the substrate TiO2 , the outer layers are flexible and are deflected by the IL, see Figure 2 (c). It can be seen that Ti5c (see Figure 1) atoms are more homogeneously pulled into the direction of the bulk in the [C2 C1 Im][B(CN)4 ] system (blue curve), whereas a distinct shoulder emerges for the [C2 C1 Im][SCN] system (green curve). This is probably due to more distinct and more stable N(SCN)-Ti5c interactions, in contrast to more fluctuating, more homogeneous N(B(CN)4 )-Ti5c interactions. A combined distance-distance distribution function (SI Figure 3) shows clearly that Ti5c is pulled towards the bulk upon coordination of [SCN]− . The O3c oxygen atoms of the first surface layer are consistently moved towards the bulk of the IL. An additional peak arises in the [C2 C1 Im][SCN] system for the surface oxygen atoms at dz ≈ ±720 pm (red curve). This peak is most probably caused by O-C([SCN]− ) interactions, when the thiocyanate 13 ACS Paragon Plus Environment



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aligns flatly in a hollow of the surface, while nitrogen and sulfur can interact simultaneously with two Ti5c titanium atoms. This assumption is supported by a respective distance-distance distribution function, provided in the supporting information (SI Figure 4). It can also be seen that the second stoichiometric layer of TiO2 is significantly less affected by surface phenomena, thus, it is probably reasonable to fix the positions of the substrate atoms for inner layers. Evaluating the integrated z-density, Iz , the surface coverage can be quantified, which is summarized in Table 4. On average, the anatase (101) surface is covered by 1.6 cations and 1.5 anions per nm2 for the [C2 C1 Im][B(CN)4 ] IL, and by 2.3 cations and 1.8 anions for the [C2 C1 Im][SCN] IL, which translates to an excess of cations at the surface. The ratio of cations to anions at the surface is ≈ 1.1 for the [C2 C1 Im][B(CN)4 ] system and ≈ 1.3 for the [C2 C1 Im][SCN] system. Although the [SCN]− anion shows a higher surface number density than the [B(CN)4 ]− anion the smaller sterical demand of the former probably allows for a much higher surface concentration of the cation, leading to a higher cation excess at the surface for the [C2 C1 Im][SCN] IL. A comparable excess of cations was also recently found for the IL [C2 C1 Im][NTf2 ] at a neutral Al2 O3 surface. 25 This finding might be interesting for the use of these ILs as electrolytes, e.g., a positively charged surface might accumulate negatively charged species from the bulk of the liquid or changes the respective Fermi energy EF of the adsorbent material. 54 For the latter, individual contributions of the ILs have to be considered. 27 The excess of cations leads to a multilayered structure, where anion-rich and cation-rich layers alternating. This effect is more pronounced for the [C2 C1 Im][SCN] IL, which is in agreement to the higher cation excess at the surface. The multilayering can be identifed by looking at the long range part of the z-density profile, provided in the supporting information (SI Figure 1). This behavior was also found earlier for the [C2 C1 Im][NTf2 ] IL at the Al2 O3 surface. 25

Considering the molecular structure of the IL’s components, it is apparent that they will have different coordination modes at the surface, 27 which can be distinguished by combined distance– angle distribution functions (CDFs). For the IL [C2 C1 Im][B(CN)4 ], the cation (Figure 3 (a)) features flat (α ≈ 0/180◦ ) and perpendicular (α ≈ 90◦ ) conformations on one side of the surface, 15 ACS Paragon Plus Environment



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and aligns exclusively perpendicular on the other side (Figure 3 (a)). Perpendicular conformations enable favorable interactions between acidic ring hydrogen atoms, especially the most acidic H2 hydrogen atoms, and O2c surface oxygen atoms (See SI Figure 5 for the strong H2-O2c interactions). Favorable hydrogen bond like H2-Osurface interactions were previously identified for the IL [C2 C1 Im][NTf2 ] at the Al2 O3 surface. 25 The CDF in Figure 4 (a) reveals two different [B(CN)4 ]− surface conformations. The close conformation with angles at ≈ 0◦ and ≈ 125◦ indicates a flat conformation with three CN ligands pointing to the surface, and the fourth CN pointing into the bulk. As indicated by the ρz intensities from Figure 2, Table 4 and Figure 4 (a), this is the preferred [B(CN)4 ]− surface conformation, which closely resembles this components minimum energy conformation on that surface. 27 This is probably the preferred conformation, because multiple energetically favorable N–Ti interactions are established at the same time, and van-der-Waals interactions between anion and surface are maximized. A second, less pronounced conformation is identified, with one CN group pointing directly to the surface, and the remaining three pointing to the bulk, which is the vertex conformation. This conformation is more strongly populated on the surface with the flat cations, drawing the whole picture: If the cations align flatly on the surface, there is only enough space for the anion to coordinate with one nitrogen atom. If the cations align perpendicular, the anion can coordinate with three ligands. The components compete for the surface coordination. In the case of [C2 C1 Im][SCN], the cation exclusively aligns in perpendicular, or at least somewhat tilted conformations (α ≈ 45 − 135◦ , Figure 3 (b)). The [SCN]− anion aligns in a close flat conformation, α ≈ 90◦ , or in the majorly populated N atom coordination conformation, α ≈ 180◦ , Figure 4 (b). The S atom coordination conformation is less preferred.

4 Conclusion We presented a parameterization of Lennard-Jones type interaction potentials between the ionic liquids [C2 C1 Im][B(CN)4 ] and [C2 C1 Im][SCN], and the anatase (101) surface, in order to merge


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the existing force fields for the pure compounds. As the TiO2 force field is able to describe all TiO2 modifications, the presented force field should in principle be applicable to study these ILs at other TiO2 surfaces with minor changes, too. The application of the derived polarizable force field was illustrated. For both ILs, a cation excess at the surface was observed, leading to a positively charged surface. The very dense surface layer extends roughly 400 pm into the bulk, followed by an almost unpopulated slab of 100 − 200 pm prior to the bulk phase. The [C2 C1 Im]+ cation aligns preferably perpendicular to the surface, with the acidic H2 hydrogen atom pointing towards the surface. In the IL [C2 C1 Im][B(CN)4 ], flat conformations of the cation are observed as well. The [B(CN)4 ]− anion majorly exhibits the face conformation, where three CN groups interact with the surface. Less populated vertex conformations with one CN–TiO2 interaction are also observed. Favorable N– Ti interactions are also discovered for the [SCN]− anion at the surface, resulting primarily in perpendicular conformations with the nitrogen atom closest to the surface. Less abundant, flat conformations and S atom coordination conformations were found as well. Furthermore, these findings have implications on the use of the ILs as electrolytes, e.g. in DSCs. The strong adsorption of the IL might hinder other components to reach the surface, which can be useful to prevent charge recombination mechanisms, or the positively charged surface might shift the Fermi level of the surface more than can be anticipated from single ion pair calculations.

Acknowledgement This work was financially supported by the DFG project KI-768/12-1 ’Materialsynthese nahe Raumtemperatur’ and the SFB 813 ’Chemie an Spinzentren: Konzepte, Mechanismen, Funktionen’. The support for H.W. by the Fonds der Chemischen Industrie (FCI) is gratefully acknowledged. M.S. is grateful for computing resources on Occigen (CINES), Curie (TGCC) and Turing (IDRIS) obtained through the projects x2014096728 and x2015096728.



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Supporting Information Available The supporting information contains information about the MD runs, z-density profiles for simulations with the PIM and the LJ FF, detailed distance-distance distribution functions and all reference structures used for the fitting procedure. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Hayes, R.; Warr, G. G.; Atkin, R. Structure and Nanostructure in Ionic Liquids. Chem. Rev. 2015, 115, 6357–6426. (2) Plechkova, N. V.; Seddon, K. R. Applications of ionic liquids in the chemical industry. Chem. Soc. Rev. 2008, 37, 123–150. (3) Kirchner, B.; Hollóczki, O.; Canongia Lopes, J. N.; Pádua, A. A. H. Multiresolution calculation of ionic liquids. WIREs Comput. Mol. Sci. 2015, 5, 202–214. (4) Ohno, H., Ed. Electrochemical Aspects of Ionic Liquids, 2nd ed.; John Wiley & Sons, Inc., 2011. (5) MacFarlane, D. R.; Tachikawa, N.; Forsyth, M.; Pringle, J. M.; Howlett, P. C.; Elliott, G. D.; Davis, J. H.; Watanabe, M.; Simon, P.; Angell, C. A. Energy applications of ionic liquids. Energy Environ. Sci. 2014, 7, 232–250. (6) Sun, J.; Jordan, L.; Forsyth, M.; MacFarlane, D. Acid–Organic base swollen polymer membranes. Electrochim. Acta 2001, 46, 1703 – 1708. (7) Rana, U. A.; Forsyth, M.; MacFarlane, D. R.; Pringle, J. M. Toward protic ionic liquid and organic ionic plastic crystal electrolytes for fuel cells. Electrochim. Acta 2012, 84, 213 – 222. (8) Yasuda, T.; Watanabe, M. Protic ionic liquids: Fuel cell applications. MRS Bull. 2013, 38, 560–566. 20 ACS Paragon Plus Environment

Page 20 of 26

Page 21 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(9) Garcia, B.; Lavallée, S.; Perron, G.; Michot, C.; Armand, M. Room temperature molten salts as lithium battery electrolyte. Electrochim. Acta 2004, 49, 4583 – 4588. (10) Balducci, A.; Dugas, R.; Taberna, P.; Simon, P.; Plée, D.; Mastragostino, M.; Passerini, S. High temperature carbon–carbon supercapacitor using ionic liquid as electrolyte. J. Power Sources 2007, 165, 922 – 927. (11) Lin, R.; Taberna, P.; Fantini, S.; Presser, V.; Pérez, C. R.; Malbosc, F.; Rupesinghe, N. L.; Teo, K. B. K.; Gogotsi, Y.; Simon, P. Capacitive Energy Storage from −50 to 100 ◦ C Using an Ionic Liquid Electrolyte. J. Phys. Chem. Lett. 2011, 2, 2396–2401. (12) Gorlov, M.; Kloo, L. Ionic liquid electrolytes for dye-sensitized solar cells. Dalton Trans. 2008, 2655–2666. (13) Fredin, K.; Gorlov, M.; Pettersson, H.; Hagfeldt, A.; Kloo, L.; Boschloo, G. On the influence of anions in binary ionic liquid electrolytes for monolithic dye-sensitized solar cells. J. Phys. Chem. C 2007, 111, 13261–13266. (14) Armel, V.; Pringle, J. M.; Forsyth, M.; MacFarlane, D. R.; Officer, D. L.; Wagner, P. Ionic liquid electrolyte porphyrin dye sensitised solar cells. Chem. Commun. 2010, 46, 3146–3148. (15) Armel, V.; Pringle, J. M.; Wagner, P.; Forsyth, M.; Officer, D.; MacFarlane, D. R. Porphyrin dye-sensitised solar cells utilising a solid-state electrolyte. Chem. Commun. 2011, 47, 9327– 9329. (16) Thar, J.; Brehm, M.; Seitsonen, A. P.; Kirchner, B. Unexpected Hydrogen Bond Dynamics in Imidazolium-Based Ionic Liquids. J. Phys. Chem. B 2009, 113, 15129–15132. (17) Pensado, A. S.; Brehm, M.; Thar, J.; Seitsonen, A. P.; Kirchner, B. Effect of Dispersion on the Structure and Dynamics of the Ionic Liquid 1-Ethyl-3-methylimidazolium Thiocyanate. ChemPhysChem 2012, 13, 1845–1853.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(18) Firaha, D. S.;

Kavalchuk, M.;

Kirchner, B. SO2 Solvation in the 1-Ethyl-3-

Methylimidazolium Thiocyanate Ionic Liquid by Incorporation into the Extended Cation Anion Network. J. Solution Chem. 2015, 44, 838–849. (19) Zhang, Y.; Maginn, E. J. Direct Correlation between Ionic Liquid Transport Properties and Ion Pair Lifetimes: A Molecular Dynamics Study. J. Phys. Chem. Lett. 2015, 6, 700–705. (20) Salanne, M. Simulations of room temperature ionic liquids: from polarizable to coarsegrained force fields. Phys. Chem. Chem. Phys. 2015, 17, 14270–14279. (21) Urahata, S. M.; Ribeiro, M. C. C. Structure of ionic liquids of 1-alkyl-3-methylimidazolium cations: A systematic computer simulation study. J. Chem. Phys. 2004, 120, 1855–1863. (22) Merlet, C.; Rotenberg, B.; Madden, P. A.; Salanne, M. Computer simulations of ionic liquids at electrochemical interfaces. Phys. Chem. Chem. Phys. 2013, 15, 15781–15792. (23) Kornyshev, A. A.; Qiao, R. Three-Dimensional Double Layers. J. Phys. Chem. C 2014, 118, 18285–18290. (24) Pensado, A. S.; Malberg, F.; Costa Gomes, M. F.; Pádua, A. A. H.; Fernández, J.; Kirchner, B. Interactions and structure of ionic liquids on graphene and carbon nanotubes surfaces. RSC Adv. 2014, 4, 18017–18024. (25) Brkljaˇca, Z.; Klimczak, M.; Miliˇcevi´c, Z.; Weisser, M.; Taccardi, N.; Wasserscheid, P.; Smith, D. M.; Magerl, A.; Smith, A.-S. Complementary Molecular Dynamics and X-ray Reflectivity Study of an Imidazolium-Based Ionic Liquid at a Neutral Sapphire Interface. J. Phys. Chem. Lett. 2015, 6, 549–555. (26) Smith, A. M.; Lovelock, K. R. J.; Gosvami, N. N.; Licence, P.; Dolan, A.; Welton, T.; Perkin, S. Monolayer to Bilayer Structural Transition in Confined Pyrrolidinium-Based Ionic Liquids. J. Phys. Chem. Lett. 2013, 4, 378–382.


Page 22 of 26

Page 23 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(27) Weber, H.; Bredow, T.; Kirchner, B. Adsorption Behavior of the 1,3-Dimethylimidazolium Thiocyanate and Tetracyanoborate Ionic Liquid at Anatase (101) Surface. J. Phys. Chem. C 2015, 119, 15137–15149. (28) Canongia Lopes, J. N.; Pádua, A. A. H. Molecular Force Field for Ionic Liquids III: Imidazolium, Pyridinium, and Phosphonium Cations; Chloride, Bromide, and Dicyanamide Anions. J. Phys. Chem. B 2006, 110, 19586–19592. (29) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225–11236. (30) Salanne, M.; Rotenberg, B.; Jahn, S.; Vuilleumier, R.; Simon, C.; Madden, P. Including many-body effects in models for ionic liquids. Theor. Chem. Acc. 2012, 131. (31) Corradini, D.; Dambournet, D.; Salanne, M. Tuning the Electronic Structure of Anatase Through Fluorination. Sci. Rep. 2015, 5, 11553. (32) Fumi, F.; Tosi, M. Ionic sizes and born repulsive parameters in the NaCl-type alkali halides–I: The Huggins-Mayer and Pauling forms. J. Phys. Chem. Solids 1964, 25, 31 – 43. (33) Tosi, M.; Fumi, F. Ionic sizes and born repulsive parameters in the NaCl-type alkali halides– II: The generalized Huggins-Mayer form. J. Phys. Chem. Solids 1964, 25, 45 – 52. (34) Tang, K. T.; Toennies, J. P. An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients. J. Chem. Phys. 1984, 80, 3726–3741. (35) Singh, U. C.; Kollman, P. A. An approach to computing electrostatic charges for molecules. J. Comput. Chem. 1984, 5, 129–145. (36) Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self–Consistent Molecular Orbital Methods. XII.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Further Extensions of Gaussian–Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56, 2257–2261. (37) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. Self–consistent molecular orbital methods. XXIII. A polarization-type basis set for second-row elements. J. Chem. Phys. 1982, 77, 3654–3665. (38) Burdett, J. K.; Hughbanks, T.; Miller, G. J.; Richardson, J. W.; Smith, J. V. Structuralelectronic relationships in inorganic solids: powder neutron diffraction studies of the rutile and anatase polymorphs of titanium dioxide at 15 and 295 K. J. Am. Chem. Soc. 1987, 109, 3639–3646. (39) Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101. (40) Martínez, L.; Andrade, R.; Birgin, E. G.; Martínez, J. M. PACKMOL: A package for building initial configurations for molecular dynamics simulations. J. Comput. Chem. 2009, 30, 2157– 2164. (41) Brehm, M.; Kirchner, B. TRAVIS - A Free Analyzer and Visualizer for Monte Carlo and Molecular Dynamics Trajectories. J. Chem. Inf. Model. 2011, 51, 2007–2023. (42) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14, 33 – 38. (43) Grace development team. http://plasma-gate.weizmann.ac.il/Grace/. (44) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (45) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104. 24 ACS Paragon Plus Environment

Page 24 of 26

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(46) Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 1996, 54, 1703–1710. (47) Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic separable dual-space Gaussian pseudopotentials from H to Rn. Phys. Rev. B 1998, 58, 3641–3662. (48) VandeVondele, J.; Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys. 2007, 127, 114105. (49) CN/ASD Group, MINUIT — Users Guide, nProgram Library D506, CERN, 1993. (50) James, F.; Winkler, M. http://www.cern.ch/minuit, CERN, April 2015. (51) Koßmann, S.; Thar, J.; Kirchner, B.; Hunt, P. A.; Welton, T. Cooperativity in ionic liquids. J. Chem. Phys. 2006, 124, 174506. (52) Kirchner, B. Cooperative versus dispersion effects: what is more important in an associated liquid such as water? J. Chem. Phys. 2005, 123, 204116. (53) Salanne, M.; Madden, P. A. Polarization effects in ionic solids and melts. Mol. Phys. 2011, 109, 2299–2315. (54) Schlichthörl, G.; Huang, S. Y.; Sprague, J.; Frank, A. J. Band Edge Movement and Recombination Kinetics in Dye-Sensitized Nanocrystalline TiO2 Solar Cells: A Study by Intensity Modulated Photovoltage Spectroscopy. J. Phys. Chem. B 1997, 101, 8141–8155.




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