The liquid surface of chiral ionic liquids as seen from molecular dynamics simulations combined with intrinsic analysis Martin Lísal Citation: The Journal of Chemical Physics 139, 214701 (2013); doi: 10.1063/1.4833335 View online: http://dx.doi.org/10.1063/1.4833335 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/21?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Structure, solvation, and dynamics of Mg2+, Ca2+, Sr2+, and Ba2+ complexes with 3-hydroxyflavone and perchlorate anion in acetonitrile medium: A molecular dynamics simulation study J. Chem. Phys. 140, 194501 (2014); 10.1063/1.4875591 Properties of water along the liquid-vapor coexistence curve via molecular dynamics simulations using the polarizable TIP4P-QDP-LJ water model J. Chem. Phys. 131, 084709 (2009); 10.1063/1.3200869 Thermodynamical and structural properties of imidazolium based ionic liquids from molecular simulation J. Chem. Phys. 128, 154509 (2008); 10.1063/1.2907332 Structure, thermodynamics, and liquid-vapor equilibrium of ethanol from molecular-dynamics simulations using nonadditive interactions J. Chem. Phys. 123, 164502 (2005); 10.1063/1.2009730 Ab initio molecular-dynamics study of liquid formamide J. Chem. Phys. 121, 4740 (2004); 10.1063/1.1781612

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

THE JOURNAL OF CHEMICAL PHYSICS 139, 214701 (2013)

The liquid surface of chiral ionic liquids as seen from molecular dynamics simulations combined with intrinsic analysis Martin Lísala) E. Hála Laboratory of Thermodynamics, Institute of Chemical Process Fundamentals of the ASCR, v. v. i., 165 02 Prague 6-Suchdol, Czech Republic and Department of Physics, Faculty of Science, J. E. Purkinje University, 400 96 Ústí n. Lab., Czech Republic

(Received 2 September 2013; accepted 11 November 2013; published online 2 December 2013) We present molecular-level insight into the liquid/gas interface of two chiral room-temperature ionic liquids (RTILs) derived from 1-n-butyl-3-methylimidazolium bromide ([bmim][Br]); namely, (R)1-butyl-3-(3-hydroxy-2-methylpropyl)imidazolium bromide (hydroxypropyl) and 1-butyl-3-[(1R)nopyl]imidazolium bromide (nopyl). We use our currently developed force field which was validated against the experimental bulk density, heat of vaporization, and surface tension of [bmim][Br]. The force field for the RTILs adopts the Chemistry at Harvard Molecular Mechanics (CHARMM) parameters for the intramolecular and repulsion-dispersion interactions along with the reduced partial atomic charges based on ab initio calculations. The net charges of the ions are around ±0.8e, which mimic the anion to cation charge transfer and many-body effects. Molecular dynamics simulations in the slab geometry combined with the intrinsic interface analysis are employed to provide a detailed description of the RTIL/gas interface in terms of the structural and dynamic properties of the interfacial, sub-interfacial, and central layers at a temperature of 300 K. The focus is on the comparison of the liquid/gas interface for the chiral RTILs with the interface for parent [bmim][Br]. The structure of the interface is elucidated by evaluating the surface roughness, intrinsic atomic density profiles, and orientation ordering of the cations. The dynamics of the ions at the interfacial region is characterized by computing the survival probability, and normal and lateral self-diffusion coefficients in the layers. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4833335] I. INTRODUCTION

Room-temperature ionic liquids (RTILs) typically consist of bulky and asymmetric organic cations and inorganic or organic anions. The molecular asymmetry built into the ions opposes the strong charge ordering due to the ionic interactions that normally causes crystallization in simple molten salts. RTILs thus exhibit a wide liquid range. RTILs have a variety of unique properties including negligible vapor pressure at ambient conditions, good thermal stability, favorable solvation behavior, and high reactivity and selectivity. An enormous number of different RTILs can be prepared and their thermophysical properties can be fine-tuned by variations in the molecular structures of cations and anions, and by mixing and matching different ion pairs.1 RTILs find a variety of industrial applications. Examples of these applications include drug delivery as active pharmaceutical ingredients, solvents for green processing, purification processes, supercritical fluid applications, or novel electrolytes in fuel cells, lubricants, heat transfer fluids, and storage media.2 Membranes based on RTILs have also been used for separation of volatile organic compounds from air. Such a separation process is environmentally friendly since contamination of the environment by RTILs is unlikely due to their high chemical stability and negligible vapor pressure. a) Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0021-9606/2013/139(21)/214701/15/$30.00

The relatively high molecular diffusion occurring in RTILs allows high mass fluxes through a membrane and variability of chemical properties of RTILs enables the synthesizing of a convenient RTIL for a particular separation process. The RTILs also exhibit a long life and the possibility to recycle used RTILs.3 A related application involves separation of pharmaceutically relevant enantiomers from racemic mixtures by chiral membranes based on RTILs. Generally, racemic mixtures contain equal amount of two enantiomers (isomers). The enantiomers display identical chemical and physical properties in the non-chiral environment but they should be considered as different chemical species in the chiral environment such as biological systems. From a biochemical and pharmacological point of view, two enantiomers may exhibit completely different biological and pharmacological activities, pharmacokinetic profile and effectiveness, and potency.4, 5 Enantioselective membranes are able to resolve enantiomers due to chiral recognition sites such as chiral side chains, chiral backbones, and chiral selectors. These membranes selectively transport one enantiomer due to the stereospecific interaction between the enantiomer and chiral recognition sites, thereby producing a permeate solution enriched with one enantiomer.6, 7 Recently, we have synthesized two chiral RTILs: (R)1-butyl-3-(3-hydroxy-2-methylpropyl)imidazolium bromide (hydroxypropyl) and 1-butyl-3-[(1R)-nopyl]imidazolium bromide (nopyl), see Figs. S1a and S1b of the supplementary

139, 214701-1

© 2013 AIP Publishing LLC

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-2

Martin Lísal

material,8 respectively. These particular RTILs are derived from 1-n-butyl-3-methylimidazolium bromide ([bmim][Br]) and they are immobilized in dense polymeric membranes by dispersion forces. These unique systems are tested as enantioselective membranes for separation of the (S)-isomer of αpinene from a racemic mixture of (R)/(S) α-pinenes (Fig. S1c of the supplementary material8 ). The α-pinene racemic mixture was selected as a proof-of-concept since it is volatile and very cheap in comparison with other racemic mixtures such as (R)/(S) ibuprofen. The enantioselective membranes based on hydroxypropyl and nopyl contain the (R)-chiral side chain (Fig. S1a of the supplementary material8 ) and (R)-chiral selector (Fig. S1b of the supplementary material8 ), respectively, which work as recognition sites for the (S)-α-pinene. Due to the stereospecific interaction between the (S)-α-pinene and recognition sites of the chiral membranes, a permeate racemic mixture of α-pinenes becomes enriched with the (S)α-pinene.9, 10 The enantiomer-chiral selector binding process is rather complex and still poorly understood at the molecular level. Understanding of the role that molecular interactions such as van der Waals and electrostatic forces, hydrogen bonds, or steric hindrance play in the binding process can guide experimentalists in selection of efficient chiral recognition sites, and it can facilitate the design of chiral RTIL membranes. Atomistic modeling is an ideal tool11 that provides molecular-level insight into the structure and dynamics of chiral RTILs as well as interactions of chiral RTILs with various enantiomers. The literature on molecular-level simulations of RTILs is extensive and providing a comprehensive analysis of all relevant references is beyond the scope of this work. Rather, we review the works most relevant for the present paper, where the reader is referred to several review articles12–14 for a broader understanding. In chiral RTIL membranes, enantiomer molecules pass through liquid/gas interfaces and understanding of the nature and structure of the interface is thus important for the rational design of the membranes. Generally, a set of physical properties such as density, dielectric constant, solubility or diffusion changes abruptly, yet continuously, in the vicinity of a liquid/gas interface from the value characteristic of one phase to that of the other phase. The molecules located at the interface thus experience a markedly different local environment with respect to the bulk phase. Molecular dynamics (MD) simulations based on classical force fields have played an important role in helping to understand how interfacial properties of RTILs are linked to chemical structure and composition. Most simulations have been performed on the [Cn mim][X] (n = {1, 4, 6, 8} and X = {Cl, BF4 , PF6 , Tf2 N}) interfaces and they show very unusual interfacial properties.15–20 At the interface, there is pronounced layering, alternating non-polar with ionic regions. The outermost regions of the interface are populated by alkyl chains, which are followed by a dense and tightly packed layer formed by oppositely charged ionic moieties. Increasing the cation chain length promotes orientations in which the chain is pointing into the gas, thus increasing the coverage of the surface with alkyl groups. Larger anions promote a disruption of the dense ionic layer, increasing the

J. Chem. Phys. 139, 214701 (2013)

orientational freedom of cations and increasing the amount of free space.19, 20 In this work, we present results of MD simulations for the liquid/gas interface of [bmim][Br], hydroxypropyl, and nopyl. We adopt the fully flexible all-atom models that were recently developed by us.21 The force field was validated against the experimental bulk density, heat of vaporization, and surface tension of [bmim][Br]. The force field uses the net charges of the ions around ±0.8e to mimic the anion to cation charge transfer and many-body effects. In contrast to the previous simulations of the RTIL/gas interfaces,15–17 we use the intrinsic interface analysis, proposed by Jedlovszky and his coworkers,22 and identify the molecules corresponding to the interfacial, sub-interfacial, and central (bulk) layers. Then, the layers were characterized in terms of the structural and dynamic properties by computing the surface roughness, intrinsic density profiles, orientation ordering, mobility, and diffusion coefficients. II. MOLECULAR MODELS

Figure 1 shows the chemical structures of the bmim, hydroxypropyl, and nopyl cations together with their atom types. We used a standard functional form for the force field:11 U = Ubonded + Unon-bonded   = kb (b − b0 )2 + kθ (θ − θ0 )2 bonds

+



angles

kφ [1 + cos (nφ − δ)]

dihedrals

+



impropers

+

 i

j >i

kψ (ψ − ψ0 )2 

 4εij

σij rij

12

 −

σij rij

6 

qi qj + 4 0 rij

 ,

(1) where b, θ , φ, and ψ denote the bond length, bond angle, dihedral angle, and improper angle, respectively, a subscript 0 stands for the equilibrium value, kb , kθ , kφ , and kψ are the force constants, n and δ are the dihedral angle parameters, ε and σ correspond to the Lennard-Jones (LJ) energy and size parameters, respectively, qk is the partial charge on atom k, 0 is the permittivity in vacuum, and rij is the distance between atom i and atom j. The intramolecular and LJ force-filed parameters for the RTILs were taken from the generalized Chemistry at Harvard Molecular Mechanics (CHARMM) force field.23, 24 The values of qk were obtained by us21 and they are based on quantum-mechanical calculations performed on the isolated cation-ion pairs with the Charges from Electrostatic Potentials using a Grid based (CHELPG) and Quantum Theory of Atoms in Molecules (QTAIM) methods.25–27 The net charges of the ions are around ±0.8e, which somewhat mimics the anion to cation charge transfer and many-body effects.28, 29 The force field was validated against the experimental properties of [bmim][Br].21 Specifically, the simulation value of bulk density, ρ, underestimated the experimental value by about 2% while the simulation result for the heat of

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-3

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

FIG. 1. Chemical structures of (a) bmim, (b) hydroxypropyl, and (c) nopyl cations along with atom types.

vaporization, hvap , overestimated the experimental result by about 1%. The simulation value of the surface tension, γ , underestimated the experimental value by about 10%, which is quite good result, taking into account the rather large statistical uncertainties associated with the simulation of γ .30 The previous simulations on imidazolium-based RTILs19, 24, 31 and [bmim][Br]21 with force fields based on the CHARMM parameters and scaled partial atomic charge have reproduced experimental values of ρ and hvap within 2% and experimental values of γ within 10%, and we expect similar accuracy for hydroxypropyl and nopyl. III. SIMULATION METHODOLOGY A. Simulation details

MD simulations were performed on the RTILs in contact with gas (vacuum) utilizing 400 ion pairs. A LJ potential was truncated at 15 Å and the Ewald summation technique with the cut-off of 15 Å and precision of 1.0 × 10−5 was employed to treat long-ranged electrostatics. The RTIL/gas interface simulations were performed in the canonical ensemble using the Nos¯e-Hoover thermostat with the thermostat time constant τ T = 0.1 ps at temperature T = 300 K. The interface simulations used an equilibrium bulk configuration from an isobaric-isothermal MD simulation at 1 bar and 300 K.21 We first removed the periodic boundary condition in the z-direction (interface normal direction) and prolonged the simulation box in the z-direction to create two vacuum slabs on both sides of the liquid slab. 49.2 × 49.2 × 150 Å, 53.5 × 53.5 × 170 Å, and 59.7 × 59.7 × 190 Å simulation boxes were created for [bmim][Br], hydroxypropyl, and nopyl, respectively. Schematic of the slab geometry used is shown in Fig. S2 of the supplementary material.8 Then, we performed 5 ns simulations to relax the systems in the slab geometry. Production runs took 20 ns with the time step of 2 fs and a dump of the ions positions was written to file every 1 ps. B. Intrinsic interface analysis

Defining the exact location of the interface in simulations of RTILs is a rather difficult task since density profiles of ions

exhibit a high peak in density at the interface and the density profiles of the ions have an oscillatory character in the bulk region. In most of the previous interface simulations,15–17 the interfacial region of RTILs has been located using the density profiles along the interface normal, typically, as the layer where the density of the ions drops from 90% to 10% of its bulk value. Intrinsic interface analyses,32, 33 on the other hand, allow us to identify the instantaneous location of the interface, at the atomic level, for each molecular configuration and then to determine properties relative to this location. We analyzed the saved ions positions using the intrinsic method of Identification of the Truly Interfacial Molecules (ITIM).22 The ITIM method is based on moving fictitious probe spheres of a given radius along straight lines that are perpendicular to the interface, starting from the gas side. The size of the ions atoms was approximated by their LJ size parameters. Once the fictitious probe sphere touches the first atom it is stopped, and the cation or anion to which the touched atom belongs to is marked as being interfacial. Once the probe sphere is moved along all test lines the full list of the truly interfacial ions is identified. The surface is approximated by the set of the intersection points of the probe spheres with the test lines along which they are moved, at the position where the probe spheres were stopped. Further, repeating the entire procedure for the system, excluding the ions already identified, leads to the identification of consecutive ions layers beneath the interface. The properties of the intrinsic surface depend very weakly on the probe sphere radius if its size is comparable with that of the atoms in molecules. We used a probe radius of 2 Å and the test lines were arranged in 100 × 100, 108 × 108, and 120 × 120 grids along the xy-plane of the interface for [bmim][Br], hydroxypropyl, and nopyl, respectively. Using the ITIM method, we determined the list of the cations and anions that belongs to the interfacial and subinterfacial layers. The rest of the ions were considered to be a part of the central layer. In the ITIM analysis,22 the intersection points of the probe spheres with the test lines define the surface of the individual layers. The surface can be characterized by its roughness which can be conveniently described by dependence of the average normal distance of two surface points, davr , on

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-4

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

their lateral distance, l; l corresponds to the distance of two surface points in the xy-plane and davr represents the distance between these points along the z-axis. The davr (l) curve has typically two distinct parts: it sharply increases at small l, and it becomes flat and approaches a plateau value at large l. Similarly as in our previous work19 and as in Ref. 22, the davr (l) curve was correlated by a function davr =

aξ l b , a + ξ lb

(2)

where a represents the amplitude of the surface roughness and ξ and b are frequency-like parameters of the surface roughness. C. Survival probability

The dynamics of ions exchange between the consecutive layers of the liquid phase was evaluated using the survival probability, L(t), determined for cations and anions in the interfacial and sub-interfacial layers. L(t) is the probability that an ion that is in the given layer at time t0 remains in this layer up to time t0 + t.34 As in our previous work,19 L(t) was wellrepresented by a stretched exponential decay     t β L(t) = exp − , (3) τ where t is time, β is the stretched exponent, and τ is the characteristic residence time. The average residence time τ C is then given by   ∞ 1 τ , (4) L(t)dt =  τC = β β 0 where (x) is the gamma function.35, 36 D. Self-diffusion coefficients

Computed for each layer, the diffusion of the cations and anions was characterized by the time dependence of the center-of-mass (COM) mean-square displacement (MSD) in the normal and lateral directions, MSDz (t) and MSDxy (t), respectively, and are defined as

Ns 1  MSDxy (t) = |xCOM,i (t) − xCOM,i (0)|2 Ns i=1 + |yCOM,i (t) − yCOM,i (0)|2 ,

(5)



Ns 1  2 |zCOM,i (t) − zCOM,i (0)| , MSDz (t) = Ns i=1 where Ns is the number of ions s, xCOM, i , yCOM, i , and zCOM, i are components of the unfolded COM of an ion i, and . is the appropriate ensemble average. The MSDz (t) is well defined up to a time that corresponds to the diffusion of an ion up to a distance comparable with the widths of the layers. In the case of Knudsen diffusion, the values of MSDα (t) increase linearly with time and the slope of the linear increase is related to the COM self-diffusion coefficient Dα via the formula37, 38 MSDα (t) = ADα t + C,

(6)

where A = 2 for normal diffusion (z-direction) and A = 4 for lateral diffusion (xy-direction), and C is an offset constant. The existence of Knudsen diffusion was verified by computing the quantity d ln MSDα (t) , (7) d ln t where Dz and Dxy were evaluated in a region where β z (t)  1 and β xy (t)  1, respectively.39, 40 βα (t) =

IV. RESULTS AND DISCUSSION A. Structure

Traditionally, fluid interfaces are described in terms of the global density profiles and we provide description of the liquid/gas interface of [bmim][Br], hydroxypropyl, and nopyl in terms of the global center-of-mass and charge density profiles in Ref. 8. However, the global density profiles can only detect the interfacial region and, in contrast to ITIM method,22 not the complete list of the cations and anions at the interface. In addition, the global density profiles suffer by broadening of the interface caused by capillary waves. The ITIM analysis, on the other hand, allows identification of the instantaneous location of the interface, at the atomic level, for each molecular configuration which eliminates the broadening of the interface due to capillary waves and enables us to determine various properties relative to this intrinsic surface rather than to the macroscopically planar Gibbs dividing surface. As a result, the ITIM approach provides a detailed picture of the molecular-level structure of RTIL surfaces. This subsection is organized as follows. First, we provide an overall characterization of the interfaces using surface roughness, density, and composition of the interfacial layers. Additionally, we show the occurrence of individual atoms at the surface. Second, the occurrence of individual atoms at the surface is analyzed in detail using intrinsic density profiles. Finally, the orientation behavior of the cations at the interfaces is evaluated using various probability distributions. 1. Surface roughness

Table I summarizes the amplitude of the surface roughness, a, and frequency-like parameters of the surface roughness, ξ and b, of the interfacial and sub-interfacial layers for the RTILs studied. (In Table I, we also provide simulation values of the surface tension γ .21 ) Figure S4 of the supplementary material8 displays for completeness the corresponding davr (l) curves. Two trends are seen from Table I and Fig. S4 of the supplementary material.8 First, the surface of the interfacial layers is smoother both in terms of a and ξ than the surface of the sub-interfacial layers due to a closer packing of cations in the interfacial layers (see the global density profiles in the supplementary material8 for details). Second, the surfaces of the interfacial and sub-interfacial layers of the chiral RTILs are rougher with respect to those of [bmim][Br] due to the presence of chiral chains. In addition, the bulky chiral selector of nopyl leads to the larger surface roughness for the interfacial and sub-interfacial layers of nopyl when compared with hydroxypropyl.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-5

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

TABLE I. The surface tension, γ , and the amplitude of the surface roughness, a, and frequency-like parameters of the surface roughness, ξ and b, of the davr (l) curve, Eq. (2) along with the surface number density of the molecules, ρ t , and cation and anion mole fractions, xc and xa = 1 − xc , respectively, for the interfacial and sub-interfacial layers of [bmim][Br], hydroxypropyl, and nopyl at a temperature of 300 K. RTIL

γ ( mN m )

Layer

a(Å)

ξ

b

ρt ( μmol ) m2

{xc , xa }

[bmim][Br]

39.429 a

Interfacial Sub-interfacial

2.35 2.67

0.43 0.68

1.43 1.40

5.49 6.87

{0.72, 0.28} {0.40, 0.60}

Hydroxypropyl

46.237 a

Interfacial Sub-interfacial

2.44 2.99

0.44 0.78

1.38 1.42

4.73 6.16

{0.72, 0.28} {0.44, 0.56}

Nopyl

32.725 a

Interfacial Sub-interfacial

2.82 3.38

0.45 0.88

1.30 1.32

3.69 5.53

{0.80, 0.20} {0.42, 0.58}

a

Taken from Ref. 21; details regarding simulation of γ and comments on the simulation values of γ are provided in Ref. 8.

The ITIM analysis also provides the list of cations and anions that belongs to the interfacial and sub-interfacial layers and information about the actual atoms that are located at the surface. The surface number density of the molecules, ρ t , and cation and anion mole fractions, xc and xa = 1 − xc , respectively, in the interfacial and sub-interfacial layers and occurrence of individual atoms at the surface are listed in Table I and is shown in Fig. 2, respectively. We see from Table I that the values of ρ t for the interfacial layers are lower compared with those for the subinterfacial layers due to a surplus of cations with respect to anions in the interfacial layers. Actual values of ρ t for the RTILs studied correlate with the values of their bulk density, ρ: ρ[bmim+ ][Br− ] > ρhydroxypropyl > ρnopyl ; see Table 3 in Ref. 21. Table I further confirms substantial surplus of cations with respect to anions in the interfacial layers that is partially balanced by surplus of anions in the sub-interfacial layers (see the global density profiles in the supplementary material8 for details). From Fig. 2, it is clear that most surface atoms belong to the alkyl or chiral chains of the cation, and to the anion. Nevertheless, there is also a non-negligible occurrence of surface atoms belonging to the imidazolium rings. For hydroxypropyl, occurrence of the atoms of alkyl chains dominates over occurrence of the atoms of chiral chains while for nopyl, the trend is opposite. To summarize: (i) Due to a closer packing of cations in the interfacial layer, the surface of the interfacial layer is smoother than that of the sub-interfacial layer for [bmim][Br] and chiral RTILs. (ii) The presence of chiral chains causes an increase in the surface roughness of the interfacial and subinterfacial layers for chiral RTILs with respect to the case of [bmim][Br]. (iii) There is a surplus of cations over Br− in the interfacial layers, while there is a surplus of Br− over cations in the sub-interfacial layers for [bmim][Br] and chiral RTILs, although to a lesser extent. (iv) There is a non-negligible occurrence of the imidazolium rings at the surface despite that the alkyl and chiral chains are mostly exposed to a vacuum for [bmim][Br] and chiral RTILs.

2. Atomic density profiles

To better gauge the structure at the RTIL/gas interface, the intrinsic number density profiles of the individual atoms belonging to the interfacial ions are plotted in Fig. 3. Intrinsic

profiles32, 33 in contrast to global profiles (cf. Ref. 8) are determined relative to the true positions of the interface and they are thus capable to better reveal the underlying structure of a fluid. The global profiles on the other hand artificially smooth fluid structures by the use of rectangular slabs and a fixed reference frame (cf. Fig. 6 of Ref. 21); for differences between the global and intrinsic views of a fluid interface, see Fig. 1 of Ref. 20. To compute the intrinsic profiles we used the width of intrinsic slabs equal to 1 Å and instantaneous positions of the surface were evaluated using the bilinear interpolation.41 [bmim][Br] (Fig. 3(a)). We show the density profiles of ring nitrogens, N1, 4 , carbon between the two nitrogens, C3 , carbon of the methyl group, C8 , the first and terminal carbons of the alkyl chain, C13 and C22 , respectively, and Br− . The pronounced peaks for the terminal C22 of the alkyl chains and Br− suggest that the gas side is mainly populated by the alkyl chains and anions. The density profiles of the nitrogens and C3 on the imidazolium ring have two peaks with a more pronounced peak in the liquid region. There are also two peaks in the C8 density profile: a sharp peak on the gas side and a quite broad peak in the liquid region. In addition, the peak in the C13 density profile is rather broad and located apart the gas phase in the liquid region. These anticipate a dominant orientation with the imidazolium ring perpendicular to the interface, the alkyl chain on the gas side and pointing to the gas phase, and the methyl group orientated to the liquid phase. However, a tail in the C22 density profile positioned in the liquid region and the sharp peak in the C8 density profile together with a less pronounced peak in the nitrogens and C3 density profiles, and the broad peak in the C13 density profile suggest existence of less dominant orientations with the methyl group on the gas side and alkyl chains oriented to the liquid phase. The above findings generally agree with the results of the previous simulations on the RTIL/gas interfaces with the bmim+ and anions of different sizes (Cl, BF4 , PF6 , and Tf2 N).17, 19, 20 Hydroxypropyl (Fig. 3(b)). We present, in addition to the density profiles for the imidazolium ring and alkyl chain atoms (N1, 4 , C3 , C8 , C13 , and C22 ), and for Br− , the density profiles for carbons C9 and C27 , and oxygen O34 of the chiral side chain. The peaks in the density profiles of the imidazolium ring and alkyl chain atoms, and of Br− exhibit a similar pattern as for [bmim][Br]; the outermost peak in the C8 density profile is broader and shifted to the liquid region with respect to the case of [bmim][Br]. The density profiles of

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-6

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

(a)

N1,4 0.010

C13

3

5

0 0

5

10

C3 C8

Density (1/A )

Occurrence at Surface

(a)

Ring Atoms Alkyl Chain Atoms Methyl Substituent Atoms Br-

10

15

20

25

C22 Br0.005

0.000 -15

30

-10

Atoms

-5

0

-5

0

-5

0

z (A) (b)

Ring Atoms Alkyl Chain Atoms Chiral Chain Atoms Br-

N1,4 C3 C8 C13

3

Density (1/A )

Occurrence at Surface

(b)

5

0.005

C22 C9 C27 O34 Br-

0 0

5

10

15

20

25

30

35

40

0.000 -15

Atoms

-10

z (A) (c)

Ring Atoms Alkyl Chain Atoms Chiral Chain Atoms Br-

(c)

N1,4 C3 C8 C13

3

Density (1/A )

Occurrence at Surface

5

C22 0.005

C9 C29,32 Chiral COM Br-

0 0

10

20

30

40

50

60

Atoms FIG. 2. Occurrence of cation atoms and anions at the surface of (a) [bmim][Br], (b) hydroxypropyl, and (c) nopyl at a temperature of 300 K.

carbons C9 and C27 of the chiral side chain exhibit two peaks: a sharp peak in the gas portion of the interfacial region (the C27 peak is shifted more to the gas phase with respect to the C9 peak) and a very broad peak in the liquid region. The density profile for the oxygen on the chiral side chain displays a small peak on the gas side at position corresponding to positions of the C22 , C27 , and Br− peaks and a fat tail which decays slowly towards the liquid region. The oxygen peak copies the Br− peak, reflecting stabilization of the anions by hydrogen bonds of the hydroxyl group on the chiral side chain.21

0.000 -15

-10

z (A) FIG. 3. Intrinsic number density profiles of the individual atoms that belong to the interfacial ions of (a) [bmim][Br], (b) hydroxypropyl, and (c) nopyl at a temperature of 300 K. The scale on the z-axis shows the distances from the true positions of the interface.

These suggest a dominant orientation analogous to that for [bmim][Br]: the imidazolium ring perpendicular to the interface, the alkyl chain on the gas side and pointing to the gas phase, and the chiral side chain mostly orientated to the liquid phase. Similar to [bmim][Br], there are also less dominant orientations with the ring methyl groups on the gas side, alkyl

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-7

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

chains in the liquid region, and chiral side chains pointing to the gas phase. Nopyl (Fig. 3(c)). We display, in addition to the density profiles of N1, 4 , C3 , C8 , C13 , C22 , and Br− , the density profiles of carbons C9 , C29 , and C32 , and COM of the chiral selector. The gas side, similarly as for [bmim][Br] and hydroxypropyl, is still populated by the alkyl chains (cf. a sharp peak in the C22 density profile) along with the anions. However, a tail of the C22 density profile, which is more pronounced with respect to [bmim][Br] and hydroxypropyl, indicates presence of a significant amount of the alkyl chains in the liquid region. In addition, the density profiles of nitrogens, C3 and C8 on the imidazolium ring have only one peak positioned deeply in the liquid region and they show only small amount of the imidazolium ring atoms in the gas portion of the interfacial layer. The peaks of the chiral selector atoms follow a consecutive order of C29, 32 , chiral COM and C9 starting with the methyl groups of the chiral selectors on the gas side and ending with the C9 in the liquid region. The C9 , chiral COM and C29, 32 peaks are more pronounced with respect to the C22 peak and these peaks are sandwiched between the C22 peak and peaks of the imidazolium ring atoms. Moreover, the C9 , chiral COM and C29, 32 density profiles exhibit tails in the liquid region. These anticipate, in contrast to [bmim][Br] and hydroxypropyl, a dominant orientation of nopyl+ where the imidazolium ring is perpendicular to the interface but the chiral selector is on the gas side with its methyl group pointing to the gas phase and alkyl chain is in the liquid region, and pointing to the liquid phase. Analogous to [bmim][Br] and hydroxypropyl, there are less dominant orientations with the imidazolium rings perpendicular to the interface, alkyl chains pointing to the gas phase and chiral selectors oriented to the liquid region. To summarize: (i) For [bmim][Br] and hydroxypropyl, the atomic density profiles predict the following dominant orientation with the imidazolium ring perpendicular to the inter-

face, the alkyl chain on the vacuum side and pointing towards the vacuum, and the methyl group orientated towards the liquid phase; for hydroxypropyl, the chiral side chain is mostly orientated towards the liquid phase. (ii) For nopyl, the atomic density profiles predict that the dominant orientation is that the imidazolium ring is perpendicular to the interface but the chiral selector is on the vacuum side with its methyl group pointing towards the vacuum, and the alkyl chain is in the liquid region and pointing towards the liquid phase. (iii) The atomic density profiles further reveal less dominant orientations as will be shown below. 3. Orientation ordering

Here, we first describe the overall orientation behavior of the cations at the RTIL/gas interface. Since in the interfacial layer there is more than one dominant orientation (see below), we continue with the determination of the prevalence of the different orientations of the cation rings, followed by analysis of the alkyl and chiral side chains. To characterize an orientation of the cation of [bmim][Br] or chiral RTILs at the interface one needs to separately describe the orientation of the imidazolium ring, and alkyl and chiral chains with respect to the interface. First, we defined the θ and  angles for the imidazolium ring as depicted in Fig. 4(a). For the alkyl chain, we then defined the tilt angle of the vector N1 − C22 with respect to the interface normal,18, 20 see Fig. 4(a). In addition, for hydroxypropyl+ we defined tilt angles with respect to the interface normal for the vectors N4 − C9 , N4 − C27 , and N4 − O34 on the chiral side chain. Similarly, for nopyl+ we defined tilt angles with respect to the interface normal for the vectors N4 − C9 and N4 -chiral COM on the chiral selector. Second, each ring orientation, defined by a (cos θ , ) pair, was sorted into a two-dimensional histogram, giving a distribution of ring orientations. Similarly, each alkyl or chiral chain orientation, given by a (cos θ , z)

gas (a)

c

(b)

z

z

liquid a b

Orientation II 90 , alkyl

Orientation I 105 , alkyl

0

25

90

45

Orientation III 105 , alkyl

150

145

FIG. 4. (a) Diagram showing the coordinate axes used for the orientation analysis of imidazolium rings. The vector pointing from N1 to C22 is used to characterize alkyl chain orientations. (b) Diagram showing the three main orientations of the imidazolium ring and alkyl chain in bmim+ , hydroxypropyl+ , and nopyl+ . Nitrogen atoms are represented in dark blue and carbon atoms in cyan. The chiral side chain or chiral selectors of hydroxypropyl+ and nopyl+ , respectively, are not drawn.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-8

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

pair, was sorted into a two-dimensional histogram, giving a distribution of alkyl or chiral chain orientations; θ denotes a tilt angle of a vector with respect to the interface normal. We used bin widths of 0.2, 18◦ , and 1 Å for cos θ ,  and z, respectively. a. Overall cations orientation behavior. The (cos θ , ) and (cos θ , z) distributions for bmim+ , hydroxypropyl+ , and nopyl+ in the interfacial layer are shown in Figs. 5–7, respectively. In the cases of the sub-interfacial and central layers (not shown here), the (cos θ , ) and (cos θ , z) distributions show almost no orientation ordering in comparison with the orientation ordering in the interfacial layer, similarly as in our previous RTIL/gas simulations.19 Bmim+ (Fig. 5). The (cos θ , ) distribution (Fig. 5(a)) is dominated by a large peak around cos θ ≈ −0.3 (θ ≈ 105◦ ) and  ≈ 25◦ which indicates that the imidazolium ring is orientated almost perpendicular to the interface with the alkyl (a) 180

150

(deg)

120

90

60

30

0 -1.0

-0.5

0.0

0.5

1.0

0.5

1.0

cos

(b)

z (A)

0

-10

-20

-1.0

-0.5

0.0

cos

FIG. 5. Orientation of bmim+ in the interfacial layer at a temperature of 300 K (red: high probability, blue: low probability). (a) The (cos θ , ) distribution for the imidazolium ring; θ and  are the angles depicted in Fig. 4(a). (b) The (cos θ , z) distribution for the alkyl chain; θ is the tilt angle of the vector N1 -C22 with respect to the interface normal.

chain pointing to the gas phase (a large peak at cos θ ≈ 1, i.e., θ ≈ 0◦ in Fig. 5(b)) and with the methyl group orientated to the liquid phase. This corresponds to the dominant orientation of bmim+ at the interface as already indicated by the intrinsic atomic density profiles (cf. Fig. 3(a)) and also observed in the previous simulations on [bmim][X]/gas interfaces (X = {Cl, BF4 , PF6 , Tf2 N}).17, 19, 20 Hydroxypropyl+ (Fig. 6). The (cos θ , ) and (cos θ , z) distributions for the imidazolium ring and alkyl chain, respectively, (Figs. 6(a) and 6(b)) display the same pattern as for bmim+ , i.e., the imidazolium ring orientated almost perpendicular to the interface and the alkyl chain pointing to the gas phase. The N4 − C9 vector of the chiral side chain orients preferentially to the liquid phase (a large peak at cos θ ≈ −1, i.e., θ ≈ 180◦ in Fig. 6(c)). Further, the methyl group of the chiral side chain (the vector N4 -C27 ) points preferentially either to the liquid phase (a large peak at cos θ ≈ −1, i.e., θ ≈ 180◦ in Fig. 6(d)) or to the gas phase (a large peak at cos θ ≈ 1, i.e., θ ≈ 0◦ in Fig. 6(d)). The hydroxyl group of the chiral side chain (the vector N4 -O34 ) orients preferentially either to the liquid phase (a large peak at cos θ ≈ −1, i.e., θ ≈ 180◦ in Fig. 6(e)) or somewhat parallel with the interface (a peak at cos θ ≈ 0.2, i.e., θ ≈ 80◦ in Fig. 6(e)); the orientation of the hydroxyl group to the liquid phase has a higher probability with respect to the parallel orientation. This corresponds to the dominant orientation of hydroxypropyl+ at the interface as already indicated by the intrinsic atomic density profiles (cf. Fig. 3(b)). Nopyl+ (Fig. 7). Preferential orientation of the imidazolium ring changed with respect to bmim+ and hydroxypropyl+ . For nopyl+ , the imidazolium ring is also perpendicular to the interface but now with the alkyl chain in the liquid region and chiral selector on the gas side (a major peak at cos θ ≈ −0.3, i.e., θ ≈ 105◦ and  ≈ 150◦ in Fig. 7(a)). However, Fig. 7(a) also indicates a range of imidazolium ring orientations including an orientation with the imidazolium ring almost perpendicular to the interface, alkyl chain on the gas side, and chiral selector in the liquid region (a minor peak at cos θ ≈ −0.3, i.e., θ ≈ 105◦ and  ≈ 25◦ in Fig. 7(a)). The (cos θ , z) distribution for the alkyl chain (Fig. 7(b)) seems to contradict observation in Fig. 7(a) since a major peak at cos θ ≈ 1 (θ ≈ 0◦ ) would anticipate the alkyl chain pointing to the gas phase. However, the peak is related to the orientation of the imidazolium ring corresponding to the minor peak, i.e., the ring perpendicular to the interface, alkyl chain pointing to the gas phase, and chiral selector oriented to the liquid region (cf. also the sharp peak on the gas side in the C22 density profile of Fig. 3(c)). A minor peak seen in Fig. 7(b) at cos θ ≈ −1 (θ ≈ 180◦ ), indicating the alkyl chain oriented to the liquid phase, is thus associated with the dominant orientation of the imidazolium ring observed in Fig. 7(a). Figures 7(c) and 7(d) for the vectors N4 − C9 and N4 -chiral COM, respectively, then clearly show the chiral selector orients preferentially to the gas phase (major peaks at cos θ ≈ 1, i.e., θ ≈ 0◦ in Figs. 7(c) and 7(d)). A minor peak in Fig. 7(c) at cos θ ≈ −1 (θ ≈ 180◦ ) further indicates the presence of a less dominant orientation with the chiral selector pointing to the liquid phase. The above findings agree with what was

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-9

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

(a)

(b)

180

150

0

z (A)

(deg)

120

90

-10

60

-20 30

0 -1.0

-0.5

0.0

0.5

-1.0

1.0

-0.5

cos

(c)

0.5

1.0

0.5

1.0

(d)

0

z (A)

0

z (A)

0.0

cos

-10

-10

-20

-20

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

cos

cos

(e)

z (A)

0

-10

-20

-1.0

-0.5

0.0

0.5

1.0

cos

FIG. 6. Orientation of hydroxypropyl+ in the interfacial layer at a temperature of 300 K (red: high probability, blue: low probability). (a) The (cos θ , ) distribution for the imidazolium ring; θ and  are the angles depicted in Fig. 4(a). (b) The (cos θ , z) distribution for the alkyl chain; θ is the tilt angle of the vector N1 -C22 with respect to the interface normal. (c) The (cos θ , z) distribution for the chiral side chain; θ is the tilt angle of the vector N4 − C9 with respect to the interface normal. (d) The (cos θ , z) distribution for the chiral side chain; θ is the tilt angle of the vector N4 -C27 with respect to the interface normal. (e) The (cos θ , z) distribution for the chiral side chain; θ is the tilt angle of the vector N4 -O34 with respect to the interface normal.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-10

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

(a)

(b) 180

150

0

z (A)

(deg)

120

90

-10

60

-20

30

-30

0 -1.0

-0.5

0.0

0.5

-1.0

1.0

-0.5

(c)

0.5

1.0

0.5

1.0

(d)

0

0

-10

-10

z (A)

z (A)

0.0

cos

cos

-20

-20

-30

-30 -1.0

-0.5

0.0

0.5

1.0

cos

-1.0

-0.5

0.0

cos

FIG. 7. Orientation of nopyl+ in the interfacial layer at a temperature of 300 K (red: high probability, blue: low probability). (a) The (cos θ , ) distribution for the imidazolium ring; θ and  are the angles depicted in Fig. 4(a). (b) The (cos θ , z) distribution for the alkyl chain; θ is the tilt angle of the vector N1 − C22 with respect to the interface normal. (c) The (cos θ , z) distribution for the chiral selector; θ is the tilt angle of the vector N4 − C9 with respect to the interface normal. (d) The (cos θ , z) distribution for the chiral selector; θ is the tilt angle of the vector N4 -chiral COM with respect to the interface normal.

observed for nopyl+ in the intrinsic atomic density profiles (cf. Fig. 3(c)).

b. Prevalence of different orientations of imidazolium rings. The (cos θ , ) distributions in the interfacial layer (Figs. 5(a), 6(a), and 7(a)) typically show one dominant orientation. However, the intrinsic atomic density profiles (Fig. 3) clearly point out a distribution of cation orientations. To identify the full range of preferred cation orientations we followed Hantal et al.18, 20 and decoupled the (cos θ , ) distributions using the intrinsic atomic density profiles. We determined the (cos θ , ) distributions in different intrinsic density profile regions for atoms C3 , C8 , and C22 , and in addition for atoms C9 , C27 , and O34 in the case of hydroxypropyl+ and for atoms C9 , C29 , C32 , and chiral COM in the case of nopyl+ . For example, in the case of the atom C22 on bmim+ , we computed the (cos θ , ) distributions in three regions of the intrinsic density profile (cf. Fig. 3(a)): z < −5.5, −5.5 < z < −4, and −4 < z < 0

which correspond to, respectively, a tail, a small peak, and a pronounced peak in the intrinsic C22 density profile. Figures S5–S7 of the supplementary material8 display, as examples, the (cos θ , ) distributions in different intrinsic density profile regions for selected atoms on bmim+ , hydroxypropyl+ , and nopyl+ , respectively. Figures S5–S7 together with distributions for the angle between the alkyl chain vector N1 -C22 and z (shown below) identify three main orientations of the imidazolium ring and alkyl chain. The three main orientations, denoted as Orientation I, Orientation II, and Orientation III, are depicted in Fig. 4(b). Orientation I with the peak at cos θ  −0.3 (θ  105◦ ) and   25◦ corresponds to the dominant orientation already seen in Figs. 5(a) and 6(a) for bmim+ and hydroxypropyl+ , and to the less dominant orientation seen in Fig. 7(a) for nopyl+ . Specifically for Orientation I, the imidazolium ring is perpendicular to the interface and the alkyl chain is on the gas side, but the imidazolium ring is slightly tilted in such a way that the vector C5 -C2 is almost perpendicular to the

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-11

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

interface normal. Orientation II with the peak at cos θ  0 (θ  90◦ ) and   90◦ , which is absent for nopyl+ , corresponds to an orientation with the imidazolium ring parallel to the interface and the alkyl chain pointing to the gas phase. The imidazolium ring exhibits a large freedom to nod along the N1 -N4 axis, with the N1 -N4 axis remaining perpendicular to z, as indicated by large broadness along cos θ , which extends between values of around −0.6 and 0.6. Orientation III with the peak at cos θ  −0.3 (θ  105◦ ) and   150◦ , which is the dominant orientation seen in Fig. 7(a) for nopyl+ , has the imidazolium ring once again perpendicular to the interface but now with the methyl group on the gas side and the alkyl chain on the liquid side. To determine the prevalence of different imidazolium ring orientations we first defined, similarly as Hantal et al.,18, 20 the following zones for the three main orientations; Orientation I: −0.75 < cos θ < −0.1, 0◦ <  < 50◦ , Orientation II: −0.6 < cos θ < 0.6, 60◦ <  < 120◦ , and Orientation III: −0.6 < cos θ < 0, 130◦ <  < 170◦ . The zones are marked as dark red rectangles in Figs. S5–S7 of the supplementary material.8 We then computed the percentage of the three main orientations corresponding to these zones in the interfacial layer. For bmim+ , hydroxypropyl+ , and nopyl+ , it

8 7

c. Orientation analysis of alkyl and chiral side chains. We complete analysis of the orientation ordering at the interface by computing orientational distributions for the angle between the alkyl chain vector N1 -C22 and interface normal, angles between the chiral side chain vectors N4 − C9 , N4 C27 , and N4 -O34 and interface normal, and angles between the chiral selector vectors N4 − C9 and N4 -chiral COM and interface normal. The orientational distributions for bmim+ , hydroxypropyl+ , and nopyl+ are displayed in Fig. 8. Overall, the orientational distribution for the alkyl chain confirmed our previous findings regarding the preferred orientations of the (f )

8

Orientation I (27%) Orientation II (21%) Orientation III (4%) Reminder Orientations (48%)

7 6

Orientation I (20%) Orientation II (24%) Orientation III (5%) Reminder Orientations (51%)

7

Orientation I (10%) Orientation III (13%) Reminder Orientations (77%)

6

5

6 5 4

4

5 4

3 3

3 2

2

2 1

1 0 -1.0

9 8

P(cos )

9

P(cos )

(b)

10

P(cos )

(a)

yields, respectively, 27%, 21% and 4%, 20%, 24% and 5%, and 10%, 0%, and 13% for Orientations I, II, and III, respectively. Note that this analysis allows us to classify about half of the interfacial number of cations for [bmim][Br] and hydroxypropyl, and only about a quarter of the interfacial number of cations for nopyl. In the case of nopyl, it is not very surprising since Fig. 7(a) already indicated a wide range of imidazolium ring orientations. The remainder orientations either deviate slightly from the three main orientations or adopt other less prevalent orientations.

-0.5

0.0

0.5

0 -1.0

1.0

1

-0.5

cos

0.0

0.5

0 -1.0

1.0

-0.5

cos

(c)

10

Orientation I (20%) Orientation II (24%) Orientation III (5%) Reminder Orientations (51%)

4

0.5

1.0

0.5

1.0

11

(g)

5

0.0

cos

9

Orientation I (10%) Orientation III (13%) Reminder Orientations (77%)

8

P(cos )

P(cos )

7

3

6 5 4

2

3 2

1

1

0 -1.0

-0.5

0.0

0.5

0 -1.0

1.0

-0.5

(d)

(e) Orientation I (20%) Orientation II (24%) Orientation III (5%) Reminder Orientations (51%)

4

Orientation I (20%) Orientation II (24%) Orientation III (5%) Reminder Orientations (51%)

2

P(cos )

4

P(cos )

P(cos )

3

(h)

6

5

3

2 1 1

0 -1.0

-0.5

0.0

cos

0.5

1.0

0 -1.0

-0.5

0.0

cos

0.0

cos

cos

0.5

1.0

17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1.0

Orientation I (10%) Orientation III (13%) Reminder Orientations (77%)

-0.5

0.0

0.5

1.0

cos

FIG. 8. Orientational probabilities of the angle between (a) the alkyl chain vector N1 -C22 and interface normal for bmim+ , (b) alkyl chain vector N1 − C22 and interface normal, (c) chiral side-chain vector N4 − C9 and interface normal, (d) the chiral side-chain vector N4 − C27 and interface normal, (e) chiral side-chain vector N4 − O34 and interface normal for hydroxypropyl+ , (f) alkyl chain vector N1 − C22 and interface normal, (g) chiral selector vector N4 − C9 and interface normal, and (h) chiral selector vector N4 -chiral COM and interface normal for nopyl+ at a temperature of 300 K. Each curve corresponds to a region dominated by one of the main imidazolium ring orientations (as defined by the dark red rectangles in Figs. S5–S7 of the supplementary material8 ) along with the reminder of orientations.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-12

Martin Lísal

alkyl chains (cf. Fig. 4), while the orientational distributions for the chiral side chain or chiral selector provide further insight into their preferred orientations with respect to the three main orientations of the imidazolium ring. Bmim+ (Fig. 8(a)). Figure 8(a) confirms that the alkyl chains of Orientation I orient perpendicular to the interface (the maximum at cos θ  −1, i.e., θ  0◦ ), the alkyl chains of Orientation II also orient to the gas phase with the maximum at cos θ  0.7 (θ  45◦ ) while the alkyl chains of Orientation III preferentially point to the liquid phase with a broad maximum at cos θ  −0.8 (θ  145◦ ). The remainder orientations of the alkyl chains mostly adopt perpendicular alignment with respect to the interface as indicated by a pronounced maximum at cos θ  1 (θ  0◦ ). Hydroxypropyl+ (Figs. 8(b)–8(e)). Orientation behavior of the alkyl chains is quite similar to that of bmim+ (cf. Figs. 8(a) and 8(b)) except the maximum in the orientational distribution of Orientation II is at cos θ  1 (θ  0◦ ). From Figs. 8(c)–8(e), we further see that the chiral side chains of Orientation I point to the liquid phase with the peaks at cos θ  −0.6 (θ  130◦ ). The chiral side chains of Orientation II adopt two roughly equally probable orientations; the chiral side chains either preferentially point to the liquid phase (the maxima at cos θ ≈ −1, i.e., θ ≈ 180◦ ) or preferentially orient somewhat parallel with the interface (the maxima at cos θ ≈ 0.2, i.e., θ ≈ 75◦ for the N4 − C9 vector, cos θ ≈ 0.6, i.e., θ ≈ 55◦ for the N4 -C27 vector, and cos θ ≈ 0.1, i.e., θ ≈ 85◦ for the N4 -O34 vector). The chiral side chains of Orientation III point to the gas phase with the maxima at cos θ  1 (θ  0◦ ) for the vectors N4 − C9 and N4 -C27 and the maximum at cos θ ≈ 0.7 (θ ≈ 45◦ ) for the vector N4 O34 . The chiral side chains of the reminder orientations orient either to the liquid phase (the maxima at cos θ ≈ −1, i.e., θ ≈ 180◦ ) or to the gas phase. In the latter case, the methyl groups of the chiral side chains align preferentially perpendicularly with respect to the interface (the maxima at cos θ  1, i.e., θ  0◦ for the vectors N4 − C9 and N4 -C27 ) while the hydroxyl groups of the chiral side chains orient somewhat parallel with the interface (the maximum at cos θ  0.35, i.e., θ  70◦ for the N4 -O34 vector). Both orientations are roughly equally probable. Nopyl+ (Figs. 8(f)–8(h)). There are only two main orientations: Orientation I and Orientation III. Figure 8(f) shows that the alkyl chains of Orientation I preferentially orient perpendicular to the interface (the maximum at cos θ  1, i.e., θ  0◦ ) while the alkyl chains of Orientation III preferentially point to the liquid phase (the maximum at cos θ  −0.65, i.e., θ  130◦ ). The alkyl chains of the reminder orientations adopt two preferential orientations with the alkyl chains pointing either to the gas phase (the maxima at cos θ  1, i.e., θ  0◦ ) or to the liquid phase (the maximum at cos θ  −1, i.e., θ  180◦ ). As seen in Figs. 8(g) and 8(h), the chiral selectors of Orientation I mostly point to the liquid phase while the chiral selectors of Orientation III and the reminder orientations preferentially orient perpendicular to the interface. The probability of the chiral selectors of the reminder orientations pointing to the gas phase is higher with respect to that of the alkyl chains of the reminder orientations (cf. Figs. 8(f)–8(h)).

J. Chem. Phys. 139, 214701 (2013)

To summarize, the detailed orientation analysis suggests a distribution of cation orientations rather than a single preferred arrangement in the interfacial layer of [bmim][Br] and chiral RTILs. Specifically, less than half of the cation orientations corresponds to the three preferred orientations: Orientation I with the imidazolium ring perpendicular to the interface and the alkyl chain on the gas side, Orientation II with the imidazolium ring parallel to the interface and the alkyl chain pointing towards the gas phase, and Orientation III with the imidazolium ring perpendicular to the interface but with the methyl group on the gas side and the alkyl chain on the liquid side; Orientation II is absent in the case of nopyl+ . Due to steric reasons, the chiral chains of hydroxypropyl+ and nopyl+ then orient mostly in the opposite direction with respect to the alkyl chains. The remainder orientations show either slight deviation from the three preferred orientations or adopt other less prevalent orientations. There is no strong orientation ordering beneath the interfacial layer.

B. Dynamics

1. Mobility

The survival probabilities of cations and anions were determined in the interfacial and sub-interfacial layers to evaluate the dynamics of ions exchange between the consecutive layers and they are shown in Fig. S8 of the supplementary material.8 The values of β, characteristic residence time τ and average residence time τ C , Eqs. (3) and (4), are listed in Table II for the RTILs studied. Generally as evident from Table II and Fig. S8 of the supplementary material,8 the cations stay considerably longer in the interfacial layer than in the sub-interfacial layer while the anions exhibit the opposite trend. In the interfacial layer, mobility of the cations is one to two order slower than mobility of the anions. In the sub-interfacial layer, mobility of the cations and anions is rather similar. The slower mobility of the cations in the interfacial layer with respect to cations mobility in the sub-interfacial layer is associated with the “dead-end-street” effect: cations in the interfacial layer can leave the layer in one way, i.e., to the sub-interfacial layer while the cations in the sub-interfacial layer can leave the layer in two ways, i.e., either to the interfacial layer or to the central layer. However, the mobility behavior of the anions is rather surprising and contrary to the mobility of bulky anions such as Tf2 N− which exhibit slower mobility in the interfacial layer than in the subinterfacial layer. For example in the case of [bmim][Tf2 N] interface, the anions reside in the interfacial layer about 50% longer than the cations19 and the ratio of Tf2 N− τ C in the interfacial layer to Tf2 N− τ C in the sub-interfacial layer is about four. The faster mobility of the anions in the interfacial layer with respect to the anions mobility in the sub-interfacial layer can be explained by the lower anion density in the interfacial layer when compared with the anion density in the sub-interfacial layer (cf. the anion COM density profiles of the interfacial and sub-interfacial layers in the left column of Fig. S3 in the supplementary material8 ). Comparing the [bmim][Br] interface with [bmim][Tf2 N] interface, mobility of bmim+ is about 50% faster in the

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-13

Martin Lísal

J. Chem. Phys. 139, 214701 (2013)

TABLE II. The stretched exponent β, characteristic residence time τ , and average residence time τ C of the stretched exponential decay (3) that was used to fit the survival probability for the cation and anion in the interfacial and sub-interfacial layers of [bmim][Br], hydroxypropyl and nopyl at a temperature of 300 K. Cation RTIL

Anion

Layer

β

τ (ns)

τ C (ns)

β

τ (ns)

τ C (ns)

[bmim][Br]

Interfacial Sub-interfacial

0.73 0.52

0.57 0.02

0.70 0.04

0.50 0.51

0.01 0.03

0.02 0.05

Hydroxypropyl

Interfacial Sub-interfacial

0.77 0.44

3.09 0.12

3.61 0.30

0.43 0.40

0.01 0.07

0.04 0.25

Nopyl

Interfacial Sub-interfacial

0.72 0.46

3.07 0.12

3.80 0.29

0.44 0.46

0.01 0.11

0.03 0.25

interfacial layer and about three times faster in the subinterfacial layer. In the case of the chiral RTILs studied, mobility of both the cations and anions in the interfacial and subinterfacial layers is substantially slower when compared with [bmim][Br] due to the chiral side chain of hydroxypropyl+ and chiral selector of nopyl+ along with cation-anion association. (Mobility of the cations and anions in the interfacial and sub-interfacial layers of hydroxypropyl and nopyl is rather similar.) Specifically, the ratio of τ C for the cations of the chiral RTILs to τ C for bmim+ is about five in both the interfacial and sub-interfacial layers while the ratio of τ C for Br− of hydroxypropyl and nopyl to τ C for Br− of [bmim][Br] is about two for the interfacial layer and five for the sub-interfacial layer.

From Table III, we generally see a marked difference between the normal and lateral diffusions of ions in the interfacial layer and, to a lesser extent, also in the sub-interfacial layer; the difference almost disappears in the central layer where Dz and Dxy of the ions are expected to be close to a bulk self-diffusion coefficient. Within accuracy of our simulations, self-diffusion coefficients of the cations and anions of the particular RTILs are almost the same in the central layers, suggesting a small difference in self-diffusion of cations and Br− in the bulk [bmim][Br], hydroxypropyl, and nopyl. The self-diffusion of the ions of [bmim][Br] is considerably faster in the central layer (about five times in terms of the selfdiffusion coefficients) compared to the both chiral RTILs. In addition, the self-diffusion coefficients of the cation and Br− of hydroxypropyl and nopyl are roughly the same in the central layers. In the case of [bmim][Br], the normal diffusion in the interfacial and sub-interfacial layers is slower than that in the central layer by a factor about two while the lateral diffusion in the interfacial layer is faster than that in the sub-interfacial and central layers by a factor about three. Somewhat similar self-diffusion behavior was observed for the [bmim][Tf2 N] interface but Dz and Dxy were smaller due to bulky Tf2 N− .19 The rather fast lateral diffusion in combination with slow normal diffusion in the interfacial layer with respect to the layers beneath the interface is associated with the orientation ordering of bmim+ at the interface. Here, the bmim+ alkyl tails

2. Diffusion

The values of normal and lateral self-diffusion coefficients, Dz and Dxy , respectively, for the interfacial, subinterfacial, and central layers are listed in Table III. Due to the relatively small size of the interfacial and sub-interfacial layers with respect to a size of the central layer values of Dz and Dxy in these layers are subject to large statistical uncertainties. We estimate that the statistical uncertainties of Dz and Dxy are up to 20% in the interfacial and sub-interfacial layers, and are up to 10% in the central layer.

TABLE III. The normal and lateral self-diffusion coefficients, Dz and Dxy , respectively, of the cation and anion in the interfacial, sub-interfacial, and central layers of [bmim][Br], hydroxypropyl, and nopyl at a temperature of 300 K. Cation 2

RTIL

Anion 2

2

2

Dz ( nm ns )

Dxy ( nm ns )

Dz ( nm ns )

Dxy ( nm ns )

[bmim] [Br]

Interfacial layer Sub-interfacial layer Central layer

2.2 × 10−2 2.2 × 10−2 3.0 × 10−2

8.8 × 10−2 3.8 × 10−2 3.2 × 10−2

1.3 × 10−2 1.2 × 10−2 3.0 × 10−2

10.5 × 10−2 3.3 × 10−2 3.3 × 10−2

Hydroxypropyl

Interfacial layer Sub-interfacial layer Central layer

1.0 × 10−2 0.5 × 10−2 0.4 × 10−2

1.2 × 10−2 0.6 × 10−2 0.4 × 10−2

0.9 × 10−2 0.5 × 10−2 0.4 × 10−2

1.2 × 10−2 0.9 × 10−2 0.5 × 10−2

Nopyl

Interfacial layer Sub-interfacial layer Central layer

0.6 × 10−2 0.6 × 10−2 0.4 × 10−2

1.7 × 10−2 0.8 × 10−2 0.6 × 10−2

0.8 × 10−2 0.5 × 10−2 0.6 × 10−2

3.2 × 10−2 1.1 × 10−2 0.6 × 10−2

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-14

Martin Lísal

preferentially point to the gas phase, the alkyl tails preferentially orient parallel with respect to the interface normal and the bmim+ rings preferentially tilt perpendicularly to the interface. This prefers a displacement of bmim+ without reorientation in the lateral direction by exchange of neighboring cations over the displacement in the normal direction by sliding in the direction of the alkyl tail orientations. This, together with the presence of the free boundary at the interface enhances the lateral diffusion of both the cations and anions with respect to the diffusion in layers beneath the interface. The interfacial layer is also more compact than the sub-interfacial and central layers which may further contribute to lowering the normal diffusion in the interfacial layer in comparison with the layers beneath the interface. The orientation ordering of the cations diminish in the layers beneath the interface, and as a consequence, the difference between the normal and lateral diffusions disappears and Dz and Dxy become close to the self-diffusion coefficient in the central layer. In the case of hydroxypropyl, difference between the normal and lateral diffusions in the interfacial layer is less pronounced in comparison with [bmim][Br] and nopyl. In addition, the normal and lateral diffusions within each layer are within statistical uncertainties almost identical. This can be attributed to strong cation-anion association mainly due to hydrogen bonds between Br− and the hydroxyl group on the cation chiral side chain.21 Quite surprisingly, self-diffusion of the ions in the interfacial layer is faster than that in the sub-interfacial and central layers by a factor about two. This suggests that due to interfacial orientation ordering, displacements of cations without re-orientation by sliding in the direction of the alkyl tail orientations (normal diffusion) and exchange of neighboring cations (lateral diffusion) are faster than the displacements in the sub-interfacial and central layers where the orientation ordering disappears. The interface with nopyl exhibits similar self-diffusion behavior as the hydroxypropyl interface but the difference between the normal and lateral diffusions in the interfacial layer is significant. In addition, we analyzed re-orientation dynamics of the cations in the interfacial, sub-interfacial, and central layers using the re-orientation correlation functions.19 The analysis is provided in Ref. 8. V. CONCLUSIONS

An all-atom non-polarizable force field based on the CHARMM parameters for the intramolecular and van der Waals interactions, and ab initio reduced partial atomic charges was employed to study the liquid/gas interfaces of two chiral RTILs and [bmim][Br]. The two chiral RTILs: (R)1-butyl-3-(3-hydroxy-2-methylpropyl)imidazolium bromide (hydroxypropyl) and 1-butyl-3-[(1R)-nopyl]imidazolium bromide (nopyl) were derived from the [bmim][Br], modifying the imidazolium ring by the chiral side chain for hydroxypropyl and chiral selector for nopyl. MD simulations along with the intrinsic analysis based on method of ITIM were performed to compare the liquid/gas interface of the chiral RTILs with the interface of [bmim][Br] at a temperature of 300 K, focusing on the structural and dynamic properties of the interfaces. The ITIM analysis determined the ions belonging to

J. Chem. Phys. 139, 214701 (2013)

the interfacial, sub-interfacial, and central layers together with surface of these layers. MD simulations predicted a significant enhancement of the cation and anion numbers and charge densities at the interface in comparison with the liquid phase. Due to the closer packing of cations in the interfacial layer, the interfacial surface was smoother than the sub-interfacial surface. The presence of the chiral chains caused that the interfacial and subinterfacial surfaces of the chiral RTILs were rougher with respect to those of [bmim][Br], with a larger roughness of the interfacial and sub-interfacial surfaces for nopyl than for hydroxypropyl due to the bulky nopyl chiral selector. The ITIM analysis also determined the surplus of the cations with respect to the anions at the interfacial region which was balanced by surplus of the anions in comparison with the cations in the sub-interfacial layer. The atomic density profiles suggested that the gas side of the interface was primarily populated by the alkyl chains of cations in the cases of [bmim][Br] and hydroxypropyl, and by the chiral selectors of cations in the case of nopyl and imidazolium rings were located away the gas side. However, the atomic density profiles also revealed less dominant orientations of cations at the interface with the methyl group of the imidazolium rings on the gas side and alkyl chains in the liquid region. The prevalence of different orientations of imidazolium rings, alkyl, and chiral chains at the interface was then provided in details by the orientation-ordering analysis. Below the interface, the orientation ordering of the cations became rather weak with respect to the interface. The mobility of the ions, which was characterized by the survival probability, indicated the cations stayed considerably longer in the interfacial layer than in the sub-interfacial layer while the anions exhibited the opposite trend. Mobility of both the cations and anions of the chiral RTILs in the interfacial and sub-interfacial layers was substantially slower when compared with [bmim][Br] due to the chiral side chain of hydroxypropyl+ and chiral selector of nopyl+ along with cation-anion association. Mobility of the cations and anions in the interfacial and sub-interfacial layers of hydroxypropyl and nopyl was rather similar. Diffusion of the ions, which was described by the normal and lateral self-diffusion coefficients, exhibited a marked difference between the normal and lateral diffusions in the interfacial and sub-interfacial layers. The difference almost disappeared in the central layer where the both self-diffusion coefficients of the ions are expected to approach a bulk selfdiffusion coefficient. The self-diffusion coefficients of the ions in the central layer suggested a small difference in selfdiffusion of cations and Br− in the bulk RTILs studied. As expected, the self-diffusion of the ions in the central layers of hydroxypropyl and nopyl was considerably slower with respect to that in the central layer of [bmim][Br].

ACKNOWLEDGMENTS

This research was supported by Grant Programme of the Ministry of Education, Youth and Sports (Project No. LH12020) and Internal Grant Agency of J. E. Purkinje

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

214701-15

Martin Lísal

University (Grant No. 53222 15 0008 01). The author wishes to thank Pavel Izák for a fruitful discussion. 1 P.

Wasserscheid and T. Welton, Ionic Liquids in Synthesis (Wiley-VCH, Verlag, Weinheim, 2008). 2 N. V. Plechkova and K. R. Seddon, Chem. Soc. Rev. 37, 123 (2008). 3 P. Izák, K. Friess, and M. Šípek, in Handbook of Membrane Research: Properties, Performance and Applications, edited by S. V. Gorley (Nova Science Publishers, New York, 2010), pp. 387–402. 4 S. W. Smith, Toxicol. Sci. 110, 4 (2009). 5 M. R. Islam, J. G. Mahdi, and I. D. Bowen, Drug Saf. 17, 149 (1997). 6 A. Berhod, Chiral Recognition in Separation Methods: Mechanisms and Applications (Springer, Berlin, Heidelberg, 2010). 7 R. Xie, L. Chu, and J. Deng, Chem. Soc. Rev. 37, 1243 (2008). 8 See supplementary material at http://dx.doi.org/10.1063/1.4833335 for the global center-of-mass and charge density profiles, surface tension calculation, re-orientation dynamics, and additional figures. 9 K. Tang, J. Cai, C. Yang, Y. Liub, P. Zhanga, and Y. Liua, Sep. Purif. Technol. 92, 30 (2012). 10 P. D˙ zygiel, P. Wieczorek, and P. Kafarski, J. Sep. Sci. 26, 1050 (2003). 11 A. R. Leach, Molecular Modelling: Principles and Applications (Pearson, Harlow, 2001). 12 E. J. Maginn, Acc. Chem. Res. 40, 1200 (2007). 13 B. L. Bhargava, S. Balasubramanian, and M. L. Klein, Chem. Commun. 2008, 3339. 14 E. J. Maginn, J. Phys.: Condens. Matter 21, 373101 (2009). 15 R. M. Lynden-Bell, Mol. Phys. 101, 2625 (2003). 16 R. M. Lynden-Bell and M. Del Pópolo, Phys. Chem. Chem. Phys. 8, 949 (2006). 17 M. E. Perez-Blanco and E. J. Maginn, J. Phys. Chem. B 114, 11827 (2010). 18 G. Hantal, M. N. D. S. Cordeiro, and M. Jorge, Phys. Chem. Chem. Phys. 13, 21230 (2011). 19 M. Lísal, Z. Posel, and P. Izák, Phys. Chem. Chem. Phys. 14, 5164 (2012). 20 G. Hantal, I. Voroshylova, M. N. D. S. Cordeiro, and M. Jorge, Phys. Chem. Chem. Phys. 14, 5200 (2012).

J. Chem. Phys. 139, 214701 (2013) 21 M.

Lísal, Z. Chval, J. Storch, and P. Izák, “Towards molecular dynamics simulations of chiral room-temperature ionic liquids,” J. Mol. Liq. (in press). 22 L. B. Pártay, G. Hantal, P. Jedlovszky, Á. Vincze, and G. Horvai, J. Comput. Chem. 29, 945 (2008). 23 W. Shi and E. J. Maginn, J. Phys. Chem. B 112, 2045 (2008). 24 G.-E. Logotheti, J. Ramos, and I. G. Economou, J. Phys. Chem. B 113, 7211 (2009). 25 C. M. Breneman and K. B. Wiberg, J. Comput. Chem. 11, 361 (1990). 26 R. Bader, Atoms in Molecules: A Quantum Theory (Oxford University Press, USA, 1994). 27 R. Bader, Chem. Rev. 91, 893 (1991). 28 C. Schröder, Phys. Chem. Chem. Phys. 14, 3089 (2012). 29 J. Rigby and E. I. Izgorodina, Phys. Chem. Chem. Phys. 15, 1632 (2013). 30 A. S. Pensado, P. Malfreyt, and A. A. H. Pádua, J. Phys. Chem. B 113, 14708 (2009). 31 H. Liu and E. Maginn, J. Chem. Phys. 135, 124507 (2011). 32 M. Jorge, P. Jedlovszky, and M. N. D. S. Cordeiro, J. Phys. Chem. C 114, 11169 (2010). 33 M. Jorge, G. Hantal, P. Jedlovszky, and M. N. D. S. Cordeiro, J. Phys. Chem. C 114, 18656 (2010). 34 E. Lloyd, Handbook of Applicable Mathematics. Volume II: Probability (Wiley, New York, 1980). 35 M. N. Berberan-Santos, E. N. Bodunov, and B. Valeur, Chem. Phys. 315, 171 (2005). 36 C. P. Lindsey and G. D. Patterson, J. Chem. Phys. 73, 3348 (1980). 37 M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1987). 38 D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Academic Press, London, 2002). 39 C. Cadena, Q. Zhao, R. Q. Snurr, and E. J. Maginn, J. Phys. Chem. B 110, 2821 (2006). 40 M. Lísal, M. Pˇredota, and J. K. Brennan, Mol. Simul. 39, 1103 (2013). 41 K.-T. Chang, Computation for Bilinear Interpolation. Introduction to Geographic Information Systems (McGraw-Hill, New York, 2009).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.0.65.67 On: Fri, 06 Feb 2015 08:47:13

The liquid surface of chiral ionic liquids as seen from molecular dynamics simulations combined with intrinsic analysis.

We present molecular-level insight into the liquid/gas interface of two chiral room-temperature ionic liquids (RTILs) derived from 1-n-butyl-3-methyli...
1MB Sizes 0 Downloads 0 Views