Fully Atomistic Simulations of the Ionic Liquid Crystal [C16mim][NO3

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Article 16

Fully-atomistic Simulations of the Ionic Liquid Crystal [C MIm] [NO]: Orientational Order Parameters and Voids Distribution 3

Giacomo Saielli J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b12469 • Publication Date (Web): 05 Feb 2016 Downloaded from http://pubs.acs.org on February 14, 2016

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The Journal of Physical Chemistry

Fully-Atomistic Simulations of the Ionic Liquid Crystal

[C16mim][NO3]:

Orientational

Order

Parameters and Voids Distribution Giacomo Saielli,a,b* aCNR

Institute on Membrane Technology, Unit of Padova, Via Marzolo, 1 – 35131, Italy

bDepartment

of Chemical Sciences, University of Padova, Via Marzolo, 1 – 35131 Padova, Italy

KEYWORDS Ionic Liquids, Liquid Crystals, Voids, Order Parameters, Molecular Dynamics.

ABSTRACT We present a Fully Atomistic Molecular Dynamics simulation of the smectic phase of the ionic liquid crystal (ILC) 1-hexadecyl-3-methylimidazolium nitrate, [C16MIm][NO3]. We have characterized the structure of the phase by means of a set of radial distribution functions resolved along the director and in the plane of the smectic layers. The results obtained allow us to discuss the similarities in the microscopic structure of Ionic Liquids (ILs) and ILCs. In addition to this we have calculated the orientational order parameters, S, of the methylene groups of the alkyl chain and compared them with the results obtained for phospholipidic membranes from 2H-NMR experiments. We also discuss the orientational order parameters of the imidazolium ring. Finally we analyze the distribution of voids in the ILC phase. We have found that voids of considerable

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volume to host a non-polar gas, e.g. xenon, are localized in the hydrophobic layers and almost absent in the ionic layers.

1. Introduction Ionic liquid crystals (ILCs) have attracted the attention of the chemistry and materials science communities because they have the potential to combine the features of liquid crystals (LCs), that is long-range order and macroscopic anisotropy, with those of ionic liquids (ILs), like exceptional solvent properties and low-volatility.1-3 Typical thermotropic ILCs are composed of quaternized nitrogen salts, such as imidazolium,4-8 pyridinium,9, 10 bipyridinium,11-14 pyrrolidinium,15 and guanidinium16-18 paired with common inorganic anions, such as halides, bistriflimide, tetrafluoroborate, hexafluorophospate. This kind of salts form ILs when the alkyl chains are shorter than about 10-12 carbon atoms. Instead, for longer chains, they exhibit mesomorphism, very often of smectic type because the driving force is micro-segregation between the hydrophobic chains and the ionic layers. From the application point of view, ILCs have been studied as electrolytes in solar cells19 and batteries,20 membranes for water desalination,21 electrochemical sensors22, 23 and electrofluorescence switches.24, 25 The microscopically ordered structure of the ILC molecules have been found to have a significant impact on the performance of the ILC based devices. Moreover, the dynamic and structural properties of ILCs have been found to depend on the confining effect of porous membranes because of the presence of long-range order.26


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Understanding the relationship between the molecular structure and the type and stability of the mesophases formed by ILCs is a formidable challenge considering that even the “simpler” task of predicting the melting point of ILs has not been fulfilled yet.27 Therefore, viewing at ILCs as “complex” ILs does not pave the way for an easy understanding. On the other hand, the large amount of literature concerning the structure-properties relationships of non ionic LCs, though essential for a comparison, cannot be easily applied to ionic mesophases because here the electrostatic interaction is a dominant factor, contrary to what observed in LC science. Classical Molecular Dynamics (MD) simulation based on Fully Atomistic (FA) Force Fields (FF) is a very effective tool to study the structural and dynamic properties of both ionic liquids2834

and liquid crystals.35-37 On the one hand, in the isotropic phase of ILs the nano-segregation between charged and

hydrophobic domains has been first predicted by computer simulations38-40 then confirmed experimentally.41 The role of electrostatic interaction in creating a continuum polar network that favours the nanosegregation of the hydrophobic chains has also been clearly highlighted.42 Moreover, by increasing the temperature, an additional liquid-liquid phase transition, from the nano-segregated structure to a uniform structure was observed by computer simulations. 43 Concerning LCs, accurate prediction of transition temperatures from FA simulation is still a challenging task since the phase structure and transition points strongly depend on minor details of the intra- and inter-molecular potential.35, 44 To this end, a general FF for the simulation of liquid crystals has been recently proposed.45 However, ILCs combine together the long range order of LCs with the strong electrostatic interactions of ILs; this renders them extremely viscous fluids (both the real ones and the



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classical MD models) and their simulation requires long equilibration and production times, especially if the phase diagram has to be explored. Some insights on their structural and dynamic properties have been recently obtained using a Coarse-Grained Force Field (CG FF) of 1hexadecyl-3-methylimidazolium nitrate as an example.46, 47 We have also investigated the effect of varying the alkyl chain length in the homologous series of [Cnmim][NO3]46 and what are the microscopic structural changes that accompany the transition from the locally nano-segregated isotropic phase into the layered smectic phase.48 The use of a CGFF allowed to explore the whole phase diagram of the model compound at a reduced computational cost. In this work, starting from a configuration obtained from the previous CG FF simulations, we reconstruct a FA system by adding all missing hydrogens to the CG sites and rebuilding the FA imidazolium and anion site. The use of a FA FF is important, not only to test the FF itself, but also when atomistic resolution is needed, e.g. in calculating the orientational order parameters from the MD simulations. These properties are usually obtained from experiments on deuterated samples and their investigation requires the knowledge of the position of the hydrogens (deuteriums) in the molecule. Here the starting configuration is in the bilayered smectic A phase (SmA) and we will analyse in detail its structure, orientational order parameters and voids distribution. 2. Computational Details FA MD simulations of 1-hexadecyl-3-methylimidazolium nitrate, [C16MIm][NO3], see Figure 1, were run with the DL_POLY Classic software.49 The initial box was built starting from an equilibrium structure of a SmA phase obtained at 505 K using a CG version of [C16MIm][NO3].46, 47 All CG sites of the alkyl chains and the methyl group on N3 were replaced


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by CH2 and CH3 groups following simple geometrical rules for the hydrogen positions. The CG site of the imidazolium ring was replaced by a FA version in the plane defined by the CG site itself, the methyl on N3 and the CH2 on N1. Ne anion CG site was replaced by a NO3 group with random orientation. The configuration so obtained (512 ion pairs, 33280 atom) first was relaxed by energy minimization and then two simulations in the NPT ensemble were started at 500 K and 550 K, respectively. The temperature is higher than the temperature where the real system exhibit a SmA phase (up to 455 K) however the CG model exhibited a SmA phase in the range 500-550 K and keeping a higher temperature allows a faster dynamics therefore a better equilibration of the system. In fact, it is known that non-polarizable FA FF, such as this one, overestimate the electrostatic interaction, therefore slowing down the dynamics.50 To partially overcome such limitation, which would hamper a proper exploration of the thermodynamic ensemble at room temperature, it is convenient to set a higher temperature for the simulation. For both temperatures the simulation length was 15 ns. We have discarded the first 5 ns as equilibration and used the last 10 ns for production saving a configuration every 1 ps. The integration time-step was set to 0.5 fs, the cut-off for the Lennard-Jones interaction was set to 14 Å and the electrostatic interactions were treated using the Ewald sum with automatic parameter optimization to have a precision of 10-6. This resulted in a Ewald convergence parameter α of of 0.0225 Å-1 and indexes of the k vector between 16 and 18 depending on the temperature (box size). Temperature and pressure were controlled with the Hoover thermostat and barostat51, 52 and the equation of motion integrated using the leapfrog algorithm53 with a shake algorithm to constrain C-H bonds (tolerance 10-8).54, 55 The 10 ns trajectory file was used for the calculation of the average properties. Structures and configurations are visualized with VMD software.56



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We have used the CL&AP FA Force Field. Details of the parameterization can be found in the original papers. 33, 57, 58

Figure 1. Structural formula of 1-hexadecyl-3-methylimidazolium nitrate, [C16MIm][NO3].

3. Results and Discussion 3.1 Structure. In Figure 2 we show a snapshot of the system at T = 500 K. There are two layers in the simulation box and the planes are oriented perpendicularly to the z axis of the box. The phase is a bilayered smectic phase with an alternation of head-to-tail and tail-to-head orientation of the cations within the same smectic layer. The hydrophobic chains, therefore, are highly interdigitated, see Ref. 46, 47 Only a discrete number of plane orientations (including that one in Figure 2) are compatible with the periodic boundary conditions in order to avoid defects at the box edges. This arrangement is clearly a result of the way in which the box was initially constructed, starting from the results of previous coarse-grained simulations.46-48, 59 Some average properties are reported in Table 1. Because of the relatively high temperature of the simulations the density is lower than what found experimentally for similar salts at room temperature.


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Figure 2. Snapshot of the equilibrium box at 500 K. As it will be discussed in detail in the following, and as it appears from the snapshot, there is a clear micro-segregation of the ionic parts from the alkyl chains. It is also evident that, apart from a density modulation along the z axis, there is no or little order in the layer plane. Table 1. Average box volume,V, box axes, bx, by, bz and density, d. V (Å3)

bx, by (Å)

bz (Å)

d (g/mL)

500 K 365930 ± 35 70.025 ± 1 74.025 ± 1 0.859 550 K 381000 ± 50 70.975 ± 1 75.637 ± 1 0.825



Cat-Cat Cat-An An-An

8

g(r)

6 4 2 0 4

C16-C16 C13-C13 C10-C10 C7-C7 C4-C4

3 g(r)

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

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2 1 0

0

5

10

15

20

r/Å

Figure 3. Radial Distribution Functions, g(r), at T = 500 K. “Cat” is the centre of mass of the imidazolium ring, “An” is the centre of mass of the anion. The dot line represents the bulk limiting value of 1. Radial distribution functions (RDF) at 500 K are shown in Figure 3. The typical alternation of the maxima of the cation-cation (cat-cat) and anion-anion (an-an) g(r) with respect to the mixed cat-an g(r) is clearly evident and indicates that the local structure of the ionic layer is similar to the structure of similar imidazolium-based ILs (the cation here is defined by the geometric centre of the imidazolium ring). It is noteworthy that the values of g(r) at short distances are generally relatively high, even the minima between peaks are above or close to 1. This is a result of the normalization of the RDF at long distances together with the micro-segregated structure of the ILC. This means that the probability to find a particle, e.g. a cation head, or an anion, at a large distance (in the bulk) is relatively low because of the relatively large volume of hydrophobic chains where there are no such particles. Thus, the normalization by a low probability increases the overall height of the RDF at short distances. Keeping this in mind, and considering also that it is not


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recommended to directly compare the height of RDFs corresponding to systems with different densities, we can nevertheless draw some conclusion by comparing the RDF of Figure 3 with the analogous of other ILs. Such inspection reveals that the ionic layer of the ILC appears more ordered than the liquid phase of ILs. For example, the maximum of the cat-an g(r) for [bmim][Cl] and [bmim][PF6] investigated in Refs.

60, 61

at the same temperature, is lower (ca. 3.5-4.5, see

Figure 2 in Ref. 61) than the peak value found here (ca. 7.5). Therefore, the segregation of the alkyl chains out of the ionic layer allows for a closer packing of the ions in ILCs compared to ILs. Although ILs with short alkyl chain are well-known to exhibit a complex structure with nanosegregation of ionic and alkylic moieties, such segregation does not extend over a macroscopic scale, as in thermotropic ILCs, but it is limited to few correlation lengths. In contrast ILCs can be viewed as ILs where the nano-segregation has extended to the point to become macroscopic. As we have shown in Refs.

48, 59

there is an increased degree of heterogeneity in a SmA phase

compared to the isotropic phase of the same imidazolium salt for chains longer than about C12. The change in the heterogeneity order parameter (introduced by Voth and Wang in Refs. 43, 62 to describe the degree of nano-segregation in ILs) has been monitored by MD simulations both as the chain length increases59 as well as during the Iso-to-SmA transition.48 In both cases, the role of alkyl segregation from a nano-scale to a macroscopic scale was highlighted as responsible for the occurrence of a LC phase in ILs. In Figure 3 we also show the g(r) of several pairs of C atoms of the chain. They show a relatively poor structure consistent with a liquid-like phase of the alkyl layer. The correlation, however, appears relatively high for the C16 terminal methyl group. This can be explained considering that the terminal methyl groups of the alkyl chains are, on average, distributed in a relatively narrow range of positions along the director, that is roughly in the middle of the hydrophobic layer; as a



consequence the pair correlation is increased compared to an isotropic liquid. Also, the contact distance for the C16-C16 RDF is shorter than in the case of the other carbons of the chain: the three hydrogens of the methyl group, in fact, allow a closer approach, compared to the carbon of a methylene group bearing an additional bulky substituents. RDF at 550 K are rather similar and are not discussed here.

0.004

ρ(z)

0.003 0.002 0.001 0.000 -30

-20

-10

0

10

20

30

-30

-20

-10

0

10

20

30

0.004 0.003

ρ(z)

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0.002 0.001 0.000

z/Å

Figure 4. Probability distribution along the director (z axis) of the anion, blue line; C2 carbon of the imidazolium ring, red line; C16 carbon (terminal methyl) of the alkyl chain, black line. Top: 550 K; bottom 500 K.

The RDF contains important information on the local structure of the fluid; however it is spherically averaged while a SmA mesophase has a cylindrical symmetry whose axis is defined by the director of the phase, that is the direction normal to the layers and, in our case, coincident


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with the z axis of the box. Therefore for a more appropriate description of local structure of the phase it is convenient to use distribution functions resolved along the director (z axis) or perpendicular to it (xy plane). In Figure 4 we show the density profile along the director, ρ(z), of three representative atoms: the nitrogen of the anion, the C2 carbon of the imidazolium ring and the terminal methyl carbon of the alkyl chain. It is clear that there is a well defined micro-segregation between the ionic parts and the alkyl chains with little overlap between the two sub-layers, the ionic one and hydrophobic one. Together with that, we also note a modulation typical of smectic phases. This result is not fully in agreement, at a quantitative level, with the distribution found for the smectic phase of the same system in the same range of temperature and described by a CG FF.46 In that case the density profile along the director of the single sites representing the cation head, the anion and the terminal methyl were less modulated and weaker, though still typical of SmA phases. A thorough comparison of the two force fields is outside the scope of the present study; we note, however, that the CG FF was initially developed for the isotropic phase of imidazolium ILs, therefore we can expect that the description of the ordered mesophases might not be quantitatively comparable with the results of FA simulations. It has been shown, in fact, that the result of a coarse-graining procedure depends on the phase structure where it is conducted so a full transferability of the CGFF is not guaranteed.63



2.0

Cat-Cat Cat-An An-An

1.5

g⊥(r⊥)

1.0 0.5

0.0 2.0

C16-C16 C13-C13 C10-C10 C7-C7 C4-C4

1.5 1.0

g⊥(r⊥)

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

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0.5 0.0

0

5

r⊥ / Å

10

15

20

Figure 5. Radial distribution functions, g⊥(r⊥), resolved perpendicular to the director (in the xy plane of the layers).

To complement the description of the phase structure as viewed along the director, in Figure 5 we show the perpendicular radial distribution functions, g⊥(r⊥), where r⊥ = Sqrt(rx2 + ry2), that is the radial distribution in the plane defined by the layers and perpendicular to the director. We note a weak in-plane structure of the ionic layer not different from what usually observed in the isotropic phase of ILs, with a cation-anion alternation. In contrast, the in-plane ordering of the alkyl chains is very limited, thus consistent with a liquid-like structure of the hydrophobic layer. To summarise, the insights obtained from the analysis of the distribution functions allow to draw a comparison between the structure of the isotropic phase of imidazolium ILs and the structure of the smectic ionic mesophase of imidazolium-based ILCs. In the first kind of systems the local structure is highly ordered, compared to simple molecular, non-ionic liquids. The pattern found


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with MD simulations consists in alternating cations and anions, as expected from the strong electrostatic interaction. This is manifested also in the high viscosity of ILs, compared to molecular non-ionic liquids.64 A nanoscale segregation is also present between the ionic moieties and the relatively short alkyl chains, as mentioned in the Introduction. However, the isotropic distribution of ILs does not allow a complete segregation of the two moieties on a macroscopic scale, which necessarily results in a perturbation of the cation-anion interaction by the relatively short alkyl chains and in a perturbation of the hydrophobic domains by the ions. In contrast, in ILCs the segregation is complete: as a consequence there is a much stronger cation-anion interaction, and a correspondingly stronger modulation in the g(r), since now the ionic layer is not perturbed by the presence of alkyl chains. Nevertheless, in both systems the structure of the radial g(r) and perpendicular g⊥(r⊥), do not extend beyond few ionic radii, indicating the lack of long-range tridimensional order as would be expected in a crystalline phase. This is also the reason why the system remains in a liquid state. Similarly, the hydrophobic layer is almost free of ions as a result of the hydrophobic interactions. Although the alkyl chains have a significant degree of orientational order (see below) they are translationally disordered within the hydrophobic layer. These results indicate a relatively high degree of similarity between the isotropic phase of shortchain ILs and the smectic phase of analogous long-chain ILCs. The main difference is in the larger degree of nano-segregation which, in ILCs, extends to macroscopic scale on the layer planes, while in ILs it remains uncorrelated in the long-range in all dimensions. This results in quantitative differences in the structure and in the corresponding radial distribution functions, while most qualitative features remain similar. This view is supported by recent experimental findings: X-ray scattering and thermal analysis of a series of imidazolium salts of varying chain length revealed a metastable ILC phase also for the short-chain homologues.65 This observation allowed the Authors



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of Ref.

65

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to relate the nano-segregation of ILs to the macroscopic layering of the homologous

long-chain ILCs.

3.2 Orientational order parameters. The NMR technique plays a major role in the experimental determination of the orientational order parameters of LC phases.66 Dipolar and/or quadrupolar orientation-dependent interactions are not averaged to zero in ordered phases and the observed splittings in the NMR spectra are related to the order parameters. Of particular relevance is the use of 2H NMR to obtain information on the orientational order of alkyl chains in LC66 as well as acyl chains in phospholipid membranes.67 Recently, the amount of information that can be extracted from NMR in LC has been extended also to translational smectic order parameters 68


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500 K 550 K

SCn-2 - Cn

0.4

0.3

0.2

0.1

0.30 0.25

500 K 550 K

0.20

−SCH

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


0.15 0.10 0.05 0.00 0

2

4

6

8

n

10 12 14 16

Figure 6. Orientational Order Parameters.

In Figure 6 we report the orientational order parameters, S, of the chain segment connecting carbons Cn and Cn-2, and of the C-H bond segment for each methylene unit of the alkyl chain; such vectors are schematically represented in Figure 7. S is defined as the ensemble average of the second order Legendre polynomial, , where β is the angle between the selected vector and the director and therefore here it is calculated with respect to the layer normal. As we see in Figure 6, chain segments close to the imidazolium head have a relatively high order parameter, around 0.4. This decreases as we move down the alkyl chains and the last segment, connecting carbon C16, the terminal methyl, with carbon C14, has a rather low order parameter,



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just above 0.1. Similarly, C-H order parameters (to be compared with experimental SC-D data since these are obtained after deuteration of the methyl groups) have a relatively high values for methylene groups close to the imidazolium and decrease as we step down the chains. The S value of the terminal methyl group is particularly low. Values obtained for C-H bonds of the same carbon are identical, after ensemble average, up to the third digit.

Figure 7. Left: schematic representation of the vectors used for the calculation of the order parameters S. Right: numbering of the sites of the imidazolium ring.

We note that the values of the order parameter for C-H bonds is negative because of the average orientation of the C-H bond vector is close to the smectic layer plane, that is perpendicular to the director. To the best of our knowledge there are no experimental data concerning this kind of imidazolium salts. However the trend is quite similar to what observed in Lα phase of membranes. For example, −SCD values of the methylene groups of sn2 chain of DMPC membrane obtained from MD simulations at 303 K were between ca. 0.20 down to 0.10 for C13 with a jump to ca. 0.02 for the terminal C14 methyl.67 It is also of interest to calculate the orientational order parameter of the aromatic C-H bonds, that is C2-H2, C4-H4 and C5-H5 of the imidazolium ring, see Figure 7. These are reported in Table 2.


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Table 2. Orientational order parameters S for the C-H vectors of the imidazolium ring at the two temperatures investigated. SC2-H2 SC4-H4 SC5-H5 500 K −0.17 0.09

−0.12

550 K −0.17 0.08

−0.11

The fact that SC2-H2 and SC5-H5 have a negative sign, while SC4-H4 has a positive sign (although the magnitude is very small), can be qualitatively explained considering an imidazolium cation with the alkyl chain in the all-trans conformation and aligned with the layer normal. This is indeed a very crude approximation of the average orientation of the cation in the smectic phase, but, as we will see, it captures some essential features of the orientational order of the phase. As we can see in Figure 8, with such orientation the C4-H4 bond vector is more likely to be aligned along the layer normal (the director) while the two bond vectors, C2-H2 and C5-H5, are more likely to be oriented close to the layer plane, thus perpendicular to the director. In fact the calculated values of P2(cosβ ) for the angles β between the three bond vectors and the vector defined by the alkyl chain carbons in Figure 8 are –0.47, 0.12 and −0.23, in fair qualitative agreement (at least as far as the signs are concerned) with the order parameters obtained from the simulations.



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Figure 8. Partial snapshot of a minimized structure (B3LYP/6-31G**) of a long-chain imidazolium cation. The chain of alkyl carbons is aligned along the director, z axis.

3.3 Voids distribution. Another important issue that we have investigated in this work is the distribution of voids in the smectic phase of the [C16MIm][NO3]. Recently the voids distribution in ILs has been discussed in the literature since it appears to be related with the ability of ILs to adsorb gases. 69-73 Voids in ILs have been also probed experimentally using the positron annihilation lifetime spectroscopy (PALS) technique.

74-76

On the other hand it is now accepted that ILs are constituted, at the

nanoscopic level, by a continuous network of ionic and hydrophobic regions nano-segregated, although they are perfectly isotropic on a macroscopic scale. Therefore, one of the important questions concerning voids in ILs, is whether they form preferentially in the ionic regions or in the hydrophobic regions of ILs. ILCs offer an invaluable opportunity to shed light on this issue since the hydrophobic region of ILCs is completely segregated from the ionic polar network on a macroscopic scale.


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Figure 9. Snapshot of the simulation box at (top) 550 K; (bottom) 500 K. On the left the full box showing also the voids in yellow. On the right the same box after removing all molecules to highlight the voids.

The distribution of voids has been calculated as follows: the box has been divided in 200x200x200 volume elements and for each element we have tested whether or not the distance from the closest atom was below the Lennard-Jones parameter for the contact between that particular atom and a probe atom, xenon in this case. Such contact distances varied from 3.224 Å for the contact with H to 3.749 for a contact with the imidazolium carbons. If a volume element was not in contact with any atom it was taken as a free volume element. In Figure 9 we show two snapshots taken at the end of the production run at both temperatures investigated. The striking feature is that voids are concentrated in the hydrophobic layer and completely absent in the ionic layer. In Figure 10 we show the distribution of voids, calculated over the 10 ns of production run,



as a function of the position along the director. It is clear that the occurrence of voids is limited to the hydrophobic layers and the probability to find voids in the ionic layer is close to zero. The sum of all the free volume elements, calculated as outlined above, amounts to 0.06% and 0.17% at 500 and 550 K, respectively. A word of caution is necessary since the volume so calculated is not the total free volume but only the total of volumes that can host a probe of the size of xenon. This result can be qualitatively explained with the strong electrostatic interaction between the charged moieties in the ionic layer (imidazolium head and anion) which leave no space in between to host non-polar gases. The analysis of the in-plane radial distribution function, g⊥(r⊥) in Figure 5, clearly shows that the ionic layer is significantly more ordered than the hydrophobic layer, with a well-defined charge alternation, that means close packing of cations and anions. In contrast, the flexibility and, most important, the weak van der Waals interactions present in the hydrophobic layer allow for the formation of voids of considerable size. Moreover, the trend in the voids distribution in Figure 10 somehow follows the inverse trend in the order parameters S shown in Figure 6: the largest fraction of voids (the lower order parameters) are observed in the middle of the hydrophobic layers. Therefore the formation of voids is favored within the liquid-like, disordered and weakly interacting alkyl chains.

50 40

Vvoids(z)

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-60

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-20

0

20

40

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Figure 10. Distribution of voids, along the director, in the ionic smectic phase of the [C16MIm][NO3]. Black bars: T = 550 K; red bars: T = 500 K.

We can extrapolate our results to the case of the isotropic phase of ILs and state that voids in ILs are more likely formed within the hydrophobic domains rather than within the polar network of ions. Interestingly, voids in n-alkanes have been measured by means of PALS technique by Goworek et al.

77.

The Authors found that for long-chain alkanes in the liquid phase the life-time of the

positronium is almost independent on the chain length and the corresponding “bubble” representing the void has an average radius of 3.8 Å, in very good agreement with the result of our simulations showing several voids larger than a xenon atom.

4. Conclusions We have presented a detailed investigation of the structural properties of the ionic liquid crystals [C16MIm][NO3] in the smectic phase at two different temperatures. While ionic liquids and liquid crystals are widely studied by molecular dynamics simulations, fully atomistic simulations of ionic liquid crystals are rarer. This is indeed due to the difficulty of simulating fluid phases in the bulk which are at the same time highly viscous and complex from the point of view of the symmetry and structure. In this case, we have started from the results previously obtained using a coarsegrained force field. Of particular relevance, are the results concerning the order parameters, both for the alkyl chains’ methylenes groups as well as for the C-H bonds of the imidazolium ring. In fact, ring protons can be exchanged with deuterium in a relatively easy way.78 Therefore the prediction of these



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simulation concerning the expected order parameters of the imidazolium ring are valuable for the experimentalist and we hope they will stimulate a 2H-NMR experimental investigation of imidazolium-based ionic liquid crystals. We also believe that the result concerning the distribution of voids is very important because of the extensive discussion in the literature concerning voids in ionic liquids. These have been investigated by MD simulations and experimental techniques. Despite the structure of ILs is nanosegregated, with a continuum polar network of ions separated by the clusters of alkyl chains, it is not clear where the voids are mostly located. ILs have relatively short alkyl chains, a relatively small size of the hydrophobic domains and an isotropic distribution of molecules. All this factors hampers a clear detection the distribution of voids, either by MD simulations as well as by experiments. In contrast ILCs are ordered on a macroscopic scale, alkyl chains are longer and the size of the hydrophobic domains is relatively large and well localized. It is therefore possible, at least by MD simulations, to determine where voids are preferentially formed. Our results indicate that voids of significant volume cannot be formed within the ionic layer but only within the hydrophobic one. This suggest that also in the isotropic phase of ILs the voids are preferentially formed in the hydrophobic nano-domains rather than in the continuum polar network of ions. Indeed an open question remains: which is the solubility and the dynamics of a non-polar solute, such as xenon, in the ILC matrix. This cannot be derived simply from the knowledge of the voids distribution. Voids are expected to play a role since the energy cost of creating a cavity, when considering the free energy of transfer of a solute from the gas phase into a solvent, is an important contribution. It is not the only one, though: solute-solvent interactions also contribute to the free energy variation and, just from a purely speculative point of view, one might expect strong interactions of the polarizable xenon with the polarizable π-systems of the imidazolium ring, or


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the anion, rather than with the alkyl chains. To address this issue a set of simulations of Xe dissolved in the same ILC matrix will be presented in a forthcoming paper.79 We can anticipate that Xe is observed to be distributed mostly within the hydrophobic layers, as expected based on the voids distribution. However, while we found no voids in the ionic layers we do find a nonnegligible population of Xe in the ionic layers of the ILC. This will allow the parameterization of a theoretical model to describe the structural and dynamic properties of Xe (namely the local and the long-range diffusion coefficients) in the ILC matrix.

AUTHOR INFORMATION Corresponding Author *Email: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT I thank the Supercomputing Centre CINECA (Italy) for granting cpu time through the ISCRA projects HP10BDI66L and HP10C1V9ME. I also thank the Laboratorio Interdipartimentale di Chimica Computazionale (LICC) of the University of Padova for cpu time. Financial support from MIUR (PRIN 2010N3T9M4, FIRB RBAP11C58Y) is gratefully acknowledged. I thank the CNRCAS bilateral agreement 2014-2016 for support. Finally, I wish to thank dr. Diego Frezzato (University of Padova) for useful discussions.



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ABBREVIATIONS IL: Ionic Liquid; ILC: Ionic Liquid Crystal; LC: Liquid Crystal; VDW: van der Waals REFERENCES

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(77) Goworek, T.; Pietrow, M.; Wawryszczuk, J.; Zaleski, R.; Zgardzi, B. Intermolecular Free Volumes and Intramolecular Defects in n -Alkanes. J. Phys.: Conf. Series 2011, 265, 012023-9 (78) Giernoth, R.; Bankmann, D. Transition-Metal Free Ring Deuteration of Imidazolium Ionic Liquid Cations. Tetrahedron Lett. 2006, 47, 4293-4296. (79) Frezzato, D.; Saielli, G. J. Phys. Chem. B 2016, accepted.

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Ionic Liquid Crystals exhibit a strong localization of voids in the hydrophobic layers and no voids in the ionic layers.


Fully Atomistic Simulations of the Ionic Liquid Crystal [C16mim][NO3

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