Dynamic Heterogeneity and Flexibility of the Alkyl Chain in Pyridinium

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Dynamic Heterogeneity and Flexibility of the Alkyl Chain in Pyridinium-Based Ionic Liquids Tatsiana Burankova, Giovanna G. Simeoni, Rolf Hempelmann, Juan F. Mora Cardozo, and Jan Peter Embs J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b10235 • Publication Date (Web): 05 Dec 2016 Downloaded from http://pubs.acs.org on December 13, 2016

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The Journal of Physical Chemistry

Dynamic Heterogeneity and Flexibility of the Alkyl Chain in Pyridinium-Based Ionic Liquids Tatsiana Burankova,†,‡ Giovanna Simeoni,¶ Rolf Hempelmann,† Juan F. Mora Cardozo,‡ and Jan P. Embs∗,‡ †Department of Physical Chemistry, Saarland University, Saarbr¨ ucken, Germany ‡Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, Villigen PSI, Switzerland ¶Heinz Maier-Leibnitz Zentrum and Physics Department, Technical University of Munich, Garching, Germany E-mail: [email protected]

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Abstract Changing the number of carbon atoms in the substituents of ionic liquids (ILs) is a way to shift the balance between Coulomb and van der Waals forces and, thus, to tune physicochemical properties. Here we address this topic on the microscopic level by employing quasielastic neutron scattering (QENS) and provide information about the stochastic ionic motions in the N-alkylpyridinium based ILs in a relatively expanded time range, from short time (sub-picosecond) particle rattling to long time diffusive regime (hundreds of picoseconds). We have systematically investigated the effect of the alkyl chain length on the picosecond dynamics by employing partial deuteration of the samples and varying the number of carbon atoms in the alkyl substituent. The localized dynamics of the side groups have appeared to be enhanced for bulkier cations, which is opposite to the trend observed for the translational motion. This result highlights the role of the conformational flexibility of the alkyl group on the dynamical properties of ILs.

Introduction The application fields of ionic liquids (ILs) 1 have undergone a tremendous expansion in the last decades. Electrochemistry, 2,3 organic synthesis and catalysis, 4 electrocatalysis 5 have profited from the usage of ILs. A prerequisite for the further progress in the field is a rational molecular design of ILs, which would allow one to control the physicochemical properties of ILs in the way that their values meet specific technological requirements. The application oriented strategy to synthesize new effective materials should be obviously based on the knowledge about the dynamical and structural properties of ILs not only on the macroscopic scale, but also on the microscopic scale. One way to modify the chemical structure of ILs and, thus, to design new compounds with targeted functionality is to change the number of carbon atoms in alkyl moieties of an organic cation. The interest to this approach has been driven by the observations that alkyl 2


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chains lead to the formation of polar and non-polar domains on the mesoscopic scale. 6,7 This structural heterogeneity inevitably influences physicochemical properties of ILs. 8–10 However, even if only one parameter is varied, for instance the number of carbon atoms in the side groups, sometimes it is not easy to predict how the system characteristics would change. This is a result of the complex interplay of different interactions between ions in ILs. Owing to the bulky size of cations, the Coulomb forces are softened, on the other hand, large hydrocarbon groups strengthen the van der Waals interaction. The most prominent example is the dependence of the melting temperature on the alkyl chain length: 7,11 The melting point can be either lowered or raised by introducing a longer alkyl substituent. The balance between the two interactions is also reflected in the nonlinear sensitivity of thermodynamic parameters to additional methylene groups in the structure of the alkyl substituent. 11,12 It is believed that this behavior is related to the structural organization of the ILs with longer side groups (n > 6), which aggregate together into spatially heterogeneous domains. To highlight the change of the dominant interaction in the system, which leads to the observed trend shifts, the so called Crytical Alkyl Size (CAS) was introduced. 10–12 The self-diffusion coefficients of both cations and anions usually decrease with increase in the number of carbon atoms in the alkyl chain of imidazolium-based ILs, 13,14 nonetheless, the trend can be opposite for n < 4. 13,15 It is not a universal rule that larger cations lead to slower dynamics. 16 Higher viscosity and lower conductivity of ILs with bulky cations are in general unfavorable for electrochemical applications. Nevertheless, compounds with longer alkyl moieties can demonstrate better electrochemical stability. 17 Further, enhanced van der Waals interactions and increased molar volume are beneficial for such processes as CO2 capturing. 18,19 The rates of chemical reactions can sometimes show no apparent correlation with the viscosity of ILs, because the involved processes are determined by microviscosity and microheterogeneity of the solvent. 20 Hence, internal friction induced by side chain motions warrants further thorough microscopic investigation. The influence of the alkyl chain groups on the dynamics of ILs has been investigated

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by various methods on molecular level including the analysis of the vibrational and spectral diffusion dynamics of a vibrational probe, 21 the study of fluorescence decay anisotropy, 22 different types of NMR spectroscopy, 23–25 MD simulations. 15,26–28 The study by Urahata et al. 15 clearly showed the dynamical hierarchy of motions in imidazolium-based ILs. The fast relaxation processes (subpicoseconds) of the alkyl groups can be observed before the longtime translational and reorientational diffusive dynamics set in as a result of the sample melting. Despite the bulkier size, the cations can be more mobile than the smaller anions, since the cation displacements are less hindered in the plane of the imidazolium ring and perperdicular to the alkyl group. The focus of the works by Tsuzuki et al. 26,27 was the factors controlling ion diffusion in ILs. Among such parameters as the size and shape of the ions, magnitude of the interaction between the species, the conformational flexibility of the alkyl chain was considered in detail. The authors showed, that internal torsional rotations enhance the microscopic dynamics and lead to larger values of the self-diffusion coefficient as compared to the ions with a stiff backbone. 26 NMR methods disclosed the hierarchy of relaxation times (from 15 to 230 ps) along the 1-alkyl-3-methylimidazolium cation. 23 As the number of carbon atoms in the molecular structure increases, the dynamics of all atoms becomes slower except for the terminal section of the alkyl group. Quasielastic neutron scattering (QENS) 29,30 provides tools to investigate the internal flexibility of side groups, but the method has been applied only for individual ILs so far, consequently, the information is fragmentary. There have been few QENS reports on comparison of two compounds from homologous series of ILs , 31–33 the most extensive study on 1-methyl-3-imidazolium based ILs with different alkyl substituents (n = 2, 4, 8) having been presented only recently. 34 The time range of the probed stochastic processes (unrestricted diffusion, spatially constrained diffusion, reorientations of the terminal groups etc.) varies depending on the technique and the instrument resolution. Time-of-flight (TOF) experiments are conducted for a broad time range and used to characterize single-particle processes in the liquid phase, 33,35–38 whereas dynamics of ILs in the solid phase are best resolved by backscat-

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tering instruments. 35,39 Collective dynamics in ILs have primarily been investigated by means of neutron spin echo (NSE) on the time scale of 10 ps–10 ns, 40 time-of-flight measurements with polarization analysis being an alternative for a shorter time scale (0.1 ps–10 ps). 41 In comparison to the other above mentioned methods, an unbeatable advantage of QENS is that this experimental technique has a simultaneous access to the spatial characteristics of processes in addition to the relaxation times. The main idea of this work was to provide a systematic QENS study on the transport properties and internal dynamics of a series of N-alkylpyridinium-based ILs with the bis(trifluoromethylsulfonyl)imide anion ([Cn Py][Tf2 N]). Pyridinium-based ILs are considered to be a cost effective alternative to their imidazolium-based counterparts for the separation of CO2 from natural gas. 18 They are promising for usage as electrolytes in electrochemical doublelayer capacitors, 17 as extractants for desulfurization with high extractive performance. 42 As many other ILs, owing to the hydrogen containing cation, the N-aklylpyridinium-based ILs are well suited for characterization by means of QENS . Additionally, partial deuteration of these compounds is feasible and allows disentangling the motions of different parts of the cation. This is not the first time we address the subject of proton dynamics in these materials. 31,33,38,41 Our previous measurements on individual samples (n = 4, 12) showed the existence of two processes on the picosecond time scale. The slower one is the long-range diffusion of the cations as a whole. This processes turned out to be partially of collective nature. The faster motions were characterized as single-particle and localized dynamics. These results provide a solid basis for the further investigation focused on the alkyl chain length dependence. Thus, here we report on the QENS measurements performed on five Nalkylpyridinium-based ILs (n = 4, 5, 6, 7, 12). Taking into account decidedly heterogeneous dynamics of ILs, we expanded the time window of the studied molecular motions (0.1 ps – 100 ps) by employing either different instruments or by varying the resolution function of the instrument. Deuterium labeling aimed to help us to distinguish the contributions of the

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pyridinium ring and of the alkyl side chain.

Experimental Details Samples The N-alkylpyridinium-based ILs [Cn Py][Tf2 N] (Figure 1) with different number of carbon atoms in the alkyl substituent (n = 4, 5, 6, 7, 12) were synthesized and characterized at the Chemistry Department, Saarland University, as described in our previous publications. 33 In addition to the totally protiated IL [C4 Py][Tf2 N], we had two partially deuterated samples at our disposal. In the first case the pyridinium ring was deuterated, whereas the butyl chain remained protiated. The second sample, conversely, had the deuterated side chain. The partially deuterated ILs were prepared by the same procedure as the protiated ILs, but with deuterated educts. The physicochemical properties of these ILs related to our study (density, viscosity, self-diffusion coefficients) can be found in the literature. 43–48

Figure 1: Structure of the N-alkylpyridinium-based ionic bis(trifluoromethylsulfonyl)imide anion investigated in this study. 5, 6, 7, 12

liquids with the R=Cn H2n+1 , n=4,

Table 1 summarizes the neutron scattering (coherent and incoherent) and absorption cross sections for the cations and for the anion. We see that the incoherent cross section of the [Tf2 N] anion can be neglected. In the case of the totally protiated samples, the incoherent contribution from the cation makes up more than 90% of the total scattering cross section. This allowed us to focus on the single particle dynamics of the N-alkylpyridinium cations. Although deuterium labeling increases the influence of the coherent scattering, the number of hydrogen atoms in the partially deuterated species, [C4 PyD ] and [(C4 )D Py] was still sufficient 6


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to apply the same assumption as for the protiated samples. Table 1: Summary of the Neutron Cross Sections of the Studied Speciesa species Tf2 N C4 Py (C4 )D Py C4 PyD C5 Py C6 Py C7 Py C12 Py a

σscat [b] 65.70 1209.87 540.33 837.85 1379.34 1548.93 1718.52 2566.48

σabs [b] 9.68 21.07 11.51 15.76 23.21 25.35 27.48 38.18

σinc [b] 0.52 1124.29 420.26 733.10 1284.67 1445.19 1605.71 2408.32

σcoh [b] 65.18 85.58 120.07 104.75 94.67 103.74 112.81 158.16

σinc /σscat [%] 0.80 92.93 77.78 87.50 93.14 93.30 93.44 93.84

σabs is given for neutrons with the wavelength of 5.75 ˚ A. 1 b = 10−28 m2

QENS Experiment QENS measurements were conducted both on FOCUS at the Swiss spallation source (SINQ) and TOFTOF at Research Neutron Source Heinz Maier-Leibnitz (FRMII). All of the instruments have direct geometry and high flexibility in changing the wavelength of incident neutrons and hence the width of the resolution function (ǫres ). In order to expand the time range of the probed motions we performed experiments with different instrument settings; the experimental conditions are summarized in Table 2. Table 2: Applied settings of the TOF-spectrometers parameter instrument elastic energy resolution ǫres , FWHM [µeV] accessible Q-range [˚ A-1 ] energy transfer range ∆E [meV]

λ=12.0 ˚ A TOFTOF

λ=6.00 ˚ A TOFTOF

λ=5.75 ˚ A FOCUS

λ=3.20 ˚ A TOFTOF

7.5

50

60

370

0.10–0.85

0.3–1.80

0.40–1.70

0.70–2.80

[-0.4;0.4]

[-1.3;1.3]

[-1.4;1.4]

[-6.0;6.0]

The detector efficiency was calibrated by measuring a vanadium standard. The vanadium spectra were also used as the resolution functions R(Q, E) of the instruments. For the further background subtraction empty sample holder runs were performed at different temperatures 7



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accordingly. The thickness of the samples in a hollow cylindrical sample holder was equal to 0.2 mm, which guaranteed that neutron beam transmission through the sample exceeded 90%. Thus, the effects of multiple scattering are negligible and unwanted absorption can be considered to be suppressed. The self-shielding correction was made at the step of data reduction.

Data Analysis The standard data reduction of the TOFTOF was performed using the LAMP 49 software package.

The DAVE 50 program was used for both the data reduction of the FOCUS

spectra and the further examination of all the data sets S(Q, E) at separate Q-groups. Where it was necessary to stabilize fitting results, the simultaneous analysis of the 2Dscattering maps was carried out directly in the IDL-environment (http://www.exelisvis. com/ProductsServices/IDL/Language.aspx) using the MPfit procedure. 51 The analytical models applicable to the analysis of ILs on picosecond time scale 33,52 include the jump-diffusion model, 53 the rotational diffusion, 30 the diffusion in a sphere model, 54 and the Gaussian model for localized translational motion. 55 In the liquid phase one normally observes a superposition of long-range diffusion and localized motions such as out-of-plane libration of the aromatic ring, conformational changes of the butyl-chain, and chain librations. The characteristic line widths of the corresponding confined and unrestricted processes, however, differ by a factor of 10. This fact simplifies the analysis greatly, since the incoherent dynamic structure factor can then be given as a convolution of the independent global and localized dynamic structure factors, multiplied by a Debye-Waller factor, exp(−2W ).

S(Q, E) = exp(−2W )Sglob (Q, E) ⊗ Sloc (Q, E)

(1)

The line shape of Sglob (Q, E) is given by a single Lorenzian L(E, Γglob ). According to the jump-diffusion model 53 its half width can be expressed as follows:

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Γglob (Q) =

~Dtr Q2 1 + Dtr Q2 τ0

(2)

where Dtr is the self-diffusion coefficient and τ0 is the residence time. Because QENS probes stochastic motions on the picosecond time scale, Dtr has the meaning of a short-time diffusion constant, if compared, for example, to the NMR spectroscopy. As in our previous works 41,52 we used the Gaussian model 55 to describe the localized dynamics of the particles in the confinement within a “soft” boundary:

SG (Q, E) = e

−Q2 σ 2

"

δ(E) +

∞ X (Q2 σ 2 )n 1 n=1

n!

~nDloc /σ 2 π (~nDloc /σ 2 )2 + E 2

#

(3)

where Dloc stands for the diffusion coefficient of the localized motion and σ characterizes the size of the domain, in which the particles are diffusing. Mathematically, σ 2 is the variance of a centered Gaussian variable, which characterizes the displacement of a particle. The subscript G is used to distinguish the model function proposed in the original work by Volino et al. 55 from the modifications of this expression employed in the present work to describe the localized dynamics of the pyridinium-based ILs. The main difficulty in constructing the model function S(Q, E) is the necessity to take into account possibly different dynamics of the pyridinium ring and of the alkyl substituent and to describe the flexibility of the side chain. The part of the cation close to the aromatic ring is more ”rigid”, 23 so that a certain fraction of the hydrogen atoms can appear as totally immobile species on the time-scale of a QENS-experiment. The latter problem can be solved by introducing a new parameter pmob , the fraction of mobile particles, into the dynamic structure factor.

Sloc (Q, E) = (1 − pmob ) + pmob SG (Q, E)

(4)

The issue concerning the flexibility of side chains is more complicated. MD simulation can give a hint about the characteristic radii of confinement or the geometry of jump motions 9



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(occupancy and position of sites), which can be used for fitting QENS spectra. 32,36 Without this complementary information, physically reasonable distribution functions of radii f (σ) can be introduced and the corresponding average dynamic structure factor can be presented as follows:

SG (Q, E) =

Z

∞

f (σ) SG (Q, E; σ)dσ

(5)

0

The simplest distribution law used to describe the localized dynamics of the alkyl groups is a linear variation of the radii of the spherical volumes as a function of the number of the carbon atom, to which the hydrogen atoms are bound. 56 There are some advanced distribution functions for rigidly fixed molecules, which take into account chain rotation about its own axis or in a cone with or without additional body fluctuations, 57 yet this approach requires additional information about the molecular structure (bond length and angles). We found that the linear distribution can serve as a satisfactory description of the side group flexibility for the partially deuterated sample, whereas the lognormal distribution was applied in a more general case of the protiated samples. " # 2 2 (ln(r/a) − σlgn ) 1 √ exp − f (r; a, σlgn ) = 2 2σlgn σlgn r 2π

(6)

where a corresponds to the maximum of the distribution, σlgn stands for the standard deviation of the variable’s natural logarithm. At this point a technical digression is in order. The number of free parameters in the fit model can not be unlimited even in the case of the simultaneous fit with both E and Q being independent variables. There is a risk to obtain an overparametrized function if the complexity of the fit function is increased. The two new parameters of the distribution function (σlgn , a) already cause this problem. For this reason we used a two-step fit procedure. On the first step we obtained the best fit parameter values assuming no distribution of radii (σlgn = 0), on the second step we refined the results by allowing σlgn to increase and fixing

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Results and Discussion Dynamics of the Partially Deuterated Samples in the Liquid Phase The description of the unrestricted diffusion of ILs in terms of the jump-diffusion model has been relatively established, 34–36 whereas the interpretation of the localized processes varies greatly. The main difficulty is the necessity to assign the observed relaxation times either to the aromatic ring, or to the alkyl group, or to the whole cation. The direct approach to distinguish restricted motions of the individual parts of the cation is to employ partial deuteration. For this reason we analyzed QENS spectra of the two samples [C4 PyD ][Tf2 N] and [(C4 )D Py][Tf2 N], in which the contribution either of the pyridinium ring or the butyl substituent, respectively, was suppressed by means of deuterium labeling. It is necessary to keep in mind that the coherent contribution becomes more significant with increasing the number of deuterium atoms incorporated in the cation structure. However, in our recent investigation 41 we showed that, although collective effects can influence unrestricted jumpdiffusion, the localized dynamics remain unaffected. The experiments on [C4 PyD ] and [(C4 )D Py] were conducted on FOCUS and TOFTOF with different wavelengths of incident neutrons (Table 2). On the intermediate time scale of 1 ps–20 ps covered on FOCUS, the spectra of both the samples feature two quasielastic components. The narrow one is common for [C4 PyD ] and [(C4 )D Py] and related to the translational jump diffusion of the cation as a whole. The broader contribution of the localized dynamics 31,38 shows up for [(C4 )D Py] as well as for [C4 PyD ], although a preliminary inspection of the spectra prove that their line widths are different for the partially deuterated samples. As previously discussed, we applied the scattering law based on the Gaussian model with a linear distribution function to fit the [C4 PyD ] spectra. The linear dependence of the radii of confinement was necessary to capture the possible diversity of the motions of the butyl chain (chain librations, torsional rotations of the chain backbone). Thus, the dynamic structure

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factors for the global and localized motions in eq 1, Sglob (Q, E) and Sloc (Q, E) read:

Sglob (Q, E) = Sloc (Q, E) =

1 Γglob π Γ2glob + E 2 3 X i=0

(8)

pi · SG (Q, E; σi )

where SG (Q, E; σi ) is expressed by eq 3, Γglob is described by the jump-diffusion model (eq 2), pi = {2/9, 2/9, 2/9, 3/9} is the vector of the fractions of the hydrogen atoms in the chain moving in a confinement with the characteristic size of σi = σmin + (σmax − σmin ) · i/3, i = {0, 1, 2, 3}. The minimal confinement radius, σmin , is attributed to the hydrogen atoms of the butyl substituent closest to the pyridnium ring, whereas σmax characterizes the localized dynamics of the terminal CH3 -group. The spectra of the sample with the deuterated butyl chain were fitted under the assumption that the contribution of the localized motion is determined by eq 4. One radius of confinement was enough to characterize the shape of the quasielastic broadening in this case. On the other hand, the fraction of mobile particles was not equal to unity. This may happen, because various out-of-plane motions of the pyridinium ring do not lead to large displacements of the hydrogen atoms close to the libration axes. The intensity factor I0 (Q) ˚−1 (Figure 3). This of [(C4 )D Py] had a pronounced broad correlation peak around Q=1.3 A is an indication of a substantial coherent contribution in this Q-range, which has a strong impact on the narrower component Γglob of the diffusional process. For this reason, Γglob was included in eq 1 without implying any explicit analytical dependence on the wavevector transfer Q. Figure 3 demonstrates that the slow component of [(C4 )D Py] is visibly modulated at the above mentioned Q-value at all the temperatures. It is obvious that these dependencies cannot be used for the evaluation of the parameters of the jump-diffusion model, Dtr and τ0 . Nevertheless, the linewidths of the diffusional components of both samples are indeed consistent with each other at all the temperatures.

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data. The diffusion in a sphere model 54 describes restricted diffusion in a volume with impermeable boundaries and, hence, better suited to be compared with the geometry of the aromatic ring. The sphere radius is equal to 2.2 ˚ A at T =350 K, which is in agreement with the distance between the center of the pyridinium ring and the outer hydrogen atoms (lcentre–C +lC–H = 1.400+1.084 ≈ 2.5 ˚ A). This supports the view that the considered localized dynamics do not correspond to the movement of the cation as a whole in the cage formed by its neighbors, but to chain conformations and ring librations, in other words, the dynamics are geometrically restricted. Expanding the Relaxation Time Landscape The previously discussed spectra of the N-alkylpyridinium-based ILs were measured using only one setting of FOCUS with the wavelength of incident neutrons λ=5.75 ˚ A (Table 2), which provided a resolution function with FWHM=60 µeV (tobs ∼ 22 ps). Although valuable information can be obtained from the quasielastic broadening observed under these experimental conditions, some details remain undisclosed. First, all the applied fit models include a flat contribution, which accounts for faster unresolved processes. If to expand the dynamic range form the neutron energy gain side to −4.0 – −3.0 meV, it becomes visible that the background component can only roughly be presented as a linear function and only for a limited energy window (∼ [−1.0, 1.0] meV), its linewidth being close to the value of 1.2–1.5 meV. Second, the single Lorentzian describing the global diffusion is an acceptable approximation only for a coarser resolution function. This description is not valid any more for a backscattering spectrometer with finer resolution. 58 Therefore, we expanded the observation time scale by performing QENS-experiments on the two partially deuterated samples [C4 PyD ][Tf2 N] and [(C4 )D Py][Tf2 N] on TOFTOF at FRM II with two complementary wavelengths of incident neutrons λ=3.00 ˚ A (tobs ∼ 3 ps) and λ=12.0 ˚ A (tobs ∼ 150 ps) at the temperature of T =310 K. Neutrons with λ=3.00 ˚ A were intended to probe relaxation processes faster than 1 ps.

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The global diffusion and localized dynamics observed in the FOCUS spectra (λ=5.75 ˚ A) can not be resolved in this case and were modeled by a single Lorentzian contribution without applying any explicit analytical expression for its analysis. To prove the validity of this approach, the best fit parameters (Table S1) and the corresponding fit model for λ=5.75 ˚ A were used to generate an artificial spectrum of [C4 PyD ] for the coarser resolution function ˚−1 the line widths of the narrow Lorentzian at λ=3.00 ˚ A. At the Q-values of 1.4 and 1.5 A component in the simulated spectrum equal 55 and 60 µeV; whereas these quantities amount to 41 and 53 µeV for the experimental data, respectively. This demonstrates that the longrange as well as the localized components, seen with λ=5.75 ˚ A, are merged into a single Lorentzian Γeff (Q) contribution for the coarser instrumental resolution. At the same time the broader contribution is, indeed, characterized by the linewidth of 1.1 meV, close to the estimation in the case of λ=5.75 ˚ A. Therefore, the dynamic structure factor (eq 1) for the data collected at λ=3.00 ˚ A included an effective global component, Sglob (Q, E); the faster process with the linewidth of ∼ 1 meV, Sloc (Q, E), was modeled by the Gaussian model (eq 3) with the parameters Dfast and σfast :

Sglob (Q, E) =

1 Γeff (Q) π Γeff (Q)2 + E 2

(9)

Sloc (Q, E) = (1 − pmob )δ(E) + pmob SG (Q, E; σfast , Dfast ) where pmob is the fraction of mobile particles. Surprisingly, no distinct difference between the fit parameters of the ring and chain was detected on the time scale faster than 1 ps (Table S4 of the Supporting Information). This fact points out to the common character of this rattling motion. On the other hand, the linewidths Γeff (Q) of the ring are definitely narrower at every accessible Q-group than those of the chain due to the differences in the second fast processes as observed on FOCUS with λ=5.75 ˚ A. In contrast to λ=5.75 ˚ A, the wavelength λ=12.0 ˚ A provides quite a narrow resolution function (FWHM = 7–8 µeV), which allowed us to investigate the slowest detected diffusional 17



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process in more detail. As it turned out, the slow translational motion cannot be described by a single relaxation time or one Lorentzian, as in the case of the FOCUS data. In the time domain, this means that the intermediate scattering function I(Q, t), which is a Fourier transform of the dynamic structure factor:

I(Q, t) =

Z∞

−∞

S(Q, E) exp i E~ t dE

(10)

deviates from the single-exponential behavior at larger times, when the so-called α process occurs. This is quite a common situation for polymers and glass forming materials; the intermediate scattering function I(Q, t) is often approximated by the so-called stretched exponential function (also known as Kohlrausch-Williams-Watts law). 59 The QENS data were transformed from the (Q, E)- into (Q, t)-space by performing a Fourier transform. The results for different sets of the data (wavelengths of incident neutrons ˚−1 for both partially deuterated samples are presented in λ=3.00; 5.75; 12.0 ˚ A) at Q=0.8 A Figure 5. The difference in the decay rates for both the chain and the ring is almost negligible for t < 1 ps even at higher Q-values, which is in agreement with the results of the analysis in the (Q, E)-domain. The decrease in the intermediate scattering function of the chain is more rapid than that of the ring at the intermediate time (1 ps < t < 50 ps), the gap between the two branches of I(Q, t) for each part of the cation being Q-dependent. At longer times (t > 50 ps) the difference between the decay rates of the two curves disappears again, because this time range corresponds to the motion of the cation as a whole. This result can be considered as a physical justification for including two components (long-range and restricted diffusion) in the analysis of QENS spectra on the intermediate time scale.

Chain Length Dependence The systematic QENS measurements on the N-alkylpyridinium-based ILs with different length of the alkyl substituent were conducted with the intermediate resolution function

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Figure 5: Intermediate scattering function of the partially deuterated pyridinium-based ILs obtained within different observation time ranges at Q=0.8 ˚ A−1 on TOFTOF (λ=3.0, 12.0 ˚ A) ˚ and FOCUS (λ=5.75 A). The filled and open symbols represent the correlation functions of the ring-deuterated and chain-deuterated samples, respectively. The data sets measured with a certain wavelength of incident neutrons are marked with the same color. (50–60 µeV) on FOCUS and TOFTOF. We studied five protiated samples (n=4, 5, 6, 7, 12) in the temperature range from 300 to 400 K in terms of the proposed description including the translational jump-diffusion (eq 2) and localized diffusion in a confinement with ”soft” boundaries (eq 3). The lognormal distribution (eq 6) was chosen to solve the problem of possibly different hydrogen mobility in the terminal groups and those located closer to the pyridinium ring. From the experiments on the partially deuterated ILs we could see that the displacements of the protons nearest to the aromatic group were negligible. In addition, the analysis of the ring dynamics also implied the existence of a certain fraction of immobile species. For this reason, the fit model also contained pmob as a free parameter.

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The temperature dependence of the diffusion coefficients of the long-range motion is consistent with the Arrhenius law (Figure 6). There is a clear correlation between the size of the alkyl chain and Dtr : The bulkier cations move slower. This trend is common for other homologous series of ILs, observed not only by QENS, 34 NMR, 13 but also by the other methods, which work on a similar time scale. 21 The faster localized quasielastic contribution provided an experimental indication of the enhancing effect of the alkyl chain flexibility on the microscopic dynamics, theoretically studied by Tsuzuki et al. 26 First, although there is a little difference between the temperature dependencies of the average confinement size of mobile particles for n = 4, 5, 6, 7, the results for the sample with the dodecyl chain show that the internal motions of the group occur in significantly larger volumes (Figure 7, lower panel). Despite the evident decrease of pmob for larger n (Figure 7, upper panel), the total number of hydrogen atoms in the cation increases faster, so that more and more particles contribute to the internal dynamics on the picosecond timescale. However, pmob never reaches unity, which is in agreement with the observations for the partially deuterated samples. Finally, opposite to the slower global diffusion the localized motions become faster as n increases, while the activation energies remain unaffected (Figure 6, Table 3). This, at first sight, counterintuitive result can arise from a more loose packing of the bulk ILs with longer side groups and is in line with the density dependence of these pyridinium-based ILs on the number of carbon atoms in the alkyl chain. 47,48 Further, the observed dependencies of Dloc and hσi correlate with an additional increase of the absolute entropy in the liquid phase, when the alkyl chain length is longer than the CAS and the motions of the alkyl moieties are intensified in the nonpolar domains. 12 We would also like to stress that the discussed details could be overlooked if the linewidths or the relaxation times of the quasielastic contributions were separately analyzed in terms of the model-independent approach. The reason lies in the concurrent dependence of the quasielastic lines and correspondingly of the relaxation times on both the diffusion coefficient and the characteristic size of the confinement: HWHM ∼ ~/τ ∼ ~Dloc /σ 2 (eq 3). 21




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Table 3: Activation energies of the long-range and localized diffusion of the studied N-alkylpyridinium-based ILs sample [C4 Py][Tf2 N]a [C4 PyD ][Tf2 N]a [(C4 )D Py][Tf2 N]a [C5 Py][Tf2 N]b [C6 Py][Tf2 N]b [C7 Py][Tf2 N]b [C12 Py][Tf2 N]a

unrestricted EA [kJ/mol] 13.6(0.2) 13.5(0.7) – 14.9(0.8) 14.9(0.4) 15.4(0.4) 13.9(0.4)

localized EA [kJ/mol] 8.7(0.8) 7.4(0.4) 5.5(0.2) 9.0(0.4) 8.4(0.2) 9.0(0.4) 7.6(0.5)

The EA -value characterizing the unrestricted diffusion of [(C4 )D Py] remains undetermined due to the coherent scattering leading to the strong modulation of the corresponding linewidths. a FOCUS, ǫres =60 µeV; b TOFTOF, ǫres =50 µeV

Conclusions The central subject of this study is the alkyl chain dependence on the different aspects of the cation dynamics of ILs seen by QENS in the picosecond time regime. In particular, we have studied a series of N-alkylpyridinium ILs with different number of carbon atoms in the alkyl substituent (n=4, 5, 6, 7, 12), so that clear trends and dependencies can be established for both the motion of the cation as a whole and the internal dynamics. Since QENS is sensitive to all the protons in the structure of the organic cation, it was necessary to dissect the contributions of its different parts. Therefore, we used the large difference of the incoherent cross section of H and D and included partially deuterated samples in our study. In the time range of interest we detected that the flexible alkyl chain, as well as the pyridinium ring give rise to the broadening of the elastic line, observed from the totally protiated sample. We managed to characterize the internal motion of the butyl substituent assuming that the radii of confinement increase linearly with the ordinal number of the carbon atom in the chain. The evaluated numerical values of the spatial characteristics pointed to the motions restricted by the cation geometry. Additionally, the diffusion coefficients of the long-range and localized diffusion of the ring and the chain were calculated. Thus, deuterium labeling offered instructive clues to the description of the protiated samples. 23



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The partially deuterated samples were also used to trace, in which time window the internal alkyl chain motions enhance the microscopic dynamics of the cation. By tuning the linewidth of the resolution function we considered the broad dynamical range from 0.1 ps to 100 ps and could focus either on the long-range translation motion or on the very fast localized processes in the range of subpicosecons and, hence, to obtain a more coherent picture of molecular motions. As a result, the most pronounced difference in the relaxation behaviour of the butyl chain and the pyridinium ring was observed in the intermediate time range of several picoseconds. Moreover, the comparison of the intermediate scattering functions of the partially deuterated ILs justified the usual consideration of two processes (unrestricted diffusion and localized dynamics) in the commonly studied dynamical range. Finally, we provided the spatial and time characteristics of the above mentioned processes for the protiated compounds with different length of the alkyl substituent. The most interesting finding in this context was the opposite dependencies of the diffusion coefficients of the unrestricted and localized diffusion on the length of the side group. While the global diffusion slows down, if the size of the cation increases, the localized motions of the bulkier alkyl groups become faster.

Acknowledgement Financial support by the German Research Foundation (DFG) within the Scientific Priority Program SPP 1191 Ionic Liquids, is gratefully acknowledged (project no. HE2403/8-3). This work is based on the experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland. We thank the Heinz Maier-Leibnitz Zentrum (FRM II) for the beam time on TOFTOF and Tobias Unruh for the help with the measurements. We are also immensely grateful to Verlaine Fossog und Elena Reichert for synthesizing the samples.

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Supporting Information Available Four tables with the best fit parameters of the models applied to fit the QENS spectra of all the samples.

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This material is available free of charge via the Internet at http://pubs.acs.org/.

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Dynamic Heterogeneity and Flexibility of the Alkyl Chain in Pyridinium

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