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Localized Relaxational Dynamics of Succinonitrile L. van Eijck,*,†,‡ A. S. Best,§,| S. Long,⊥ F. Fernandez-Alonso,# D. MacFarlane,∇ M. Forsyth,O and G. J. Kearley‡,[ Institut Laue-LangeVin, BP 156, 6 rue Jules Horowitz, F-38042 Cedex 9, Grenoble, France; Department of Radiation, Radionuclides and Reactors, Delft UniVersity of Technology, Mekelweg 15, 2629 JB Delft, Netherlands; NoVel Battery Technologies, CSIRO Energy Technology Minerals Building, BayView AVenue, Clayton VIC 3168, Australia, Box 312 Clayton South VIC 3169, Australia; Department of Chemical Technology, Delft UniVersity of Technology, P.O. Box 5045, 2600 GA Delft, The Netherlands; GHD, LeVel 7, 180 Lonsdale Street, Melbourne 3000, Australia; Rutherford Appleton Laboratory, ISIS Facility, Didcot OX11 0QX, United Kingdom; School of Chemistry and Department of Materials Engineering, Faculty of Science, Monash UniVersity, Clayton, Victoria 3800, Australia; and Bragg Institute, Building 87, Australian Nuclear Science and Technology Organisation PMB 1, Menai NSW 2234, Australia ReceiVed: January 5, 2009; ReVised Manuscript ReceiVed: July 3, 2009
Succinonitrile (NtCsCH2sCH2sCtN) is a good ionic conductor, when doped with an ionic compound, at room temperature, where it is in its plastic crystalline phase (Long et al. Solid State Ionics 2003, 161, 105; Alarco et al. Nat. Mater. 2004, 3, 476). We report on the relaxational dynamics of the plastic phase near the two first-order phase transitions and on the effect of dissolving a salt in the plastic matrix by quasi-elastic neutron scattering. At 240 K, the three observed relaxations are localized and we can describe their dynamics (τ ≈ 1.7, 17, and 140 ps) to a certain extent from a model using a single molecule that was proposed by Be´e et al. allowing for all conformations in its unit cell (space group IM3M). The extent of the localized motion as observed is however larger than that predicted by the model and suggests that the isomerization of succinonitrile is correlated with a jump to the nearest neighbor site in the unit cell. The salt containing system is known to be a good ionic conductor, and our results show that the effect of the ions on the succinonitrile matrix is homogeneous. Because the isomerizations and rotations are governed by intermolecular interactions, the dissolved ions have an effect over an extended range. Due to the addition of the salt, the dynamics of one of the components (τ ≈ 17 ps) shows more diffusive character at 300 K. The calculated upper limit of the corresponding diffusion constant of succinonitrile in the electrolyte is a factor 30 higher than what is reported for the ions. Our results suggest that the succinonitrile diffusion is caused by nearest neighbor jumps that are localized on the observed length and time scales. 1. Introduction To achieve high ionic conductivity for applications like batteries, the electrolyte often is chosen to be a liquid or a gel. A large effort has been devoted to a search for other materials with comparable ionic conductivity that would better suite the technical and mechanical demands that these applications require.3,4 One such material is succinonitrile (NtCsCH2s CH2sCtN, abbreviated SuCN). It is a plastic crystalline material in which the molecules undergo rotational diffusion within their cubic unit cell and is a good solvent for electrolyte salts which render it ionically conductive. Such materials have been studied in a number of contexts including electrolytes for lithium batteries2,5 and also photoelectrochemical solar cells6 and fuel cells.5 While a number of molecular plastic crystalline compounds are known, the dinitrile compounds appear to be * To whom correspondence should be addressed. E-mail:
[email protected]. † Institut Laue-Langevin. ‡ Department of Radiation, Radionuclides and Reactors, Delft University of Technology. § Novel Battery Technologies. | Department of Chemical Technology, Delft University of Technology. ⊥ GHD. # Rutherford Appleton Laboratory. ∇ School of Chemistry, Monash University. O Department of Materials Engineering, Monash University. [ Bragg Institute.
some of the most interesting; succinonitrile is one of the simplest members of this family. Among other useful properties, these compounds appear to form stable interfaces on electrode materials within electrochemical devices. Such interfaces are the key to safe operation of lithium batteries.5 In all cases, transport of an active ion (Li+ in the battery case, I3-/I- in the solar cell case, and protons in the fuel cell) is required and the role of the plastic crystalline matrix in this process is of fundamental importance in understanding these materials. These active ions are typically added to the SuCN “solvent” by dissolving (in some papers, this is described as doping) an appropriate dissociable salt into the SuCN. This produces a highly conductive solid state electrolyte with conductivity as high as 10-3 S/cm at room temperature.1 The driving force behind the cation dynamics in this plastic crystal are thought to be either the rotational diffusion of the SuCN matrix “propelling the cation through the matrix” or a high diffusion rate of the crystal (void) defects (which are supposedly occupied by the cation). To further investigate these questions, previous work has applied NMR techniques7-9 to an example of a plastic crystalline salt where the crystal structure of the salt was known. In this work, we have performed quasi-elastic neutron scattering (QENS) to investigate the relaxational dynamics of the matrix, the spatial extent of these dynamics, and the effect of the dissolved salt on these dynamics.
10.1021/jp9000847 CCC: $40.75 2009 American Chemical Society Published on Web 07/22/2009
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van Eijck et al. applied the one-molecule model proposed by Be´e et al.10 to find the isomerization and rotation rates of the molecule that describe the set of quasi-elastic signals over 3 orders of magnitude. The spatial extent of the observed dynamics is however larger than that of a fixed molecule, and only upon solvating the salt, the SuCN matrix dynamics turns diffusive. 2. Experimental Section
Figure 1. Typical orientation of the SuCN molecule in its cell. This approximate trans orientation can be transformed into a gauche conformation by rotating one-half of the molecule 120° over the cube diagonal, which is approximately the central C-C bond.
The dynamics and the structure of this plastic crystal have been studied in the past by X-ray and neutron scattering and dielectric spectroscopy,10-15 optical methods,16,17 and computer simulations.18-20 From early work on SuCN,11,12 it is known that the two molecules of a unit cell are at (0 0 0) and (0.5 0.5 0.5) in the unit cell and we can expect only localized dynamics when the plastic crystal is perfect. Be´e et al.10 have reported on the QENS of the pure SuCN, and we proceed to investigate the spatial extent of the dynamics at a time scale of 10-12-10-9 s. From the diffraction experiments of Derollez et al.,11 one can make the simplified structural picture of the matrix in which the nitrogen atoms have a position centered on one of the faces of the cubic unit cell and where the two central carbon atoms lie approximately on one of the four diagonals inside the cell (see Figure 1). With its two nitrogens at the opposite faces in a unit cell cube, the molecule is in its trans orientation, with a 4-fold rotation around its long axis. With its two nitrogens at neighboring faces of the cube, the molecule is in a gauche conformation, with the dihedral angle of the four carbon atoms being 120°. The gauche conformation is generated from the trans conformation by a rotation of one-half of the molecule over a 3-fold axis that is the unit cell cube diagonal. The internal barrier of rotation directly from one to another gauche conformation is high due to steric hindrance; hence, the transition will rather occur via the trans conformation. Derollez et al. have found that only 23% of the molecules is in the trans conformation in the plastic phase,11 and Be´e et al.10 have distinguished two types of rotational/reorientational motions, one being the rotation of the trans molecule over its 4-fold long axis (t T t) and the other being a trans T gauche conformational change (t T g). If the matrix and/or cation diffusion is driven by defect dynamics or defect hopping, we can expect a signature of the diffusion in the QENS signal. Besides the relaxational dynamics of the matrix, the effect of the dissolved salt on the matrix dynamics is also reported together with the temperature dependence of the lattice parameter that was obtained from simultaneous neutron diffraction data. To our surprise, the data extracted from our QENS experiments show dynamics that are localized up to the nanosecond time scale, but the maxima in the dynamic structure factors are found to be at rather lower Q values than what can be expected for the hydrogen jump distances when assuming only molecular isomerizations and rotations around the equilibrium positions. However, we have
The materials were obtained from Aldrich and were not further purified: succinonitrile (99%) and LiBF4 (99%). The salt was dissolved (molar concentration 5%) in the molten SuCN and dried thereafter for more than 24 h in a vacuum at 65 °C. The QENS experiments were performed on the OSIRIS spectrometer21 at the ISIS spallation source of the Rutherford Appleton Laboratory, United Kingdom, and at the highresolution backscattering spectrometer IN1622 at the Institut Laue-Langevin, Grenoble, France. The samples were loaded into instrument standard airtight aluminum cans in an inert environment. We have taken spectra at three different temperatures: one in the solid phase (210 K) and two in the plastic crystal phase. The phase transition temperatures vary depending on the sample composition, and thus, we chose different temperatures in the plastic phase: 240 and 320 K for the pure SuCN and 255 and 300 K for the SuCN-salt mixtures. One may expect for each system a change in the relaxation and/or jump rate with temperature when the potential energy landscape changes but also the redistribution of the kinetic energy over the different types of motion in the plastic crystal phase. When the grouping of relaxation processes is sufficiently pronounced, we can discriminate the corresponding time constants from the QENS signal, and retrieve the relative contribution of the groups to the QENS signal. Given the accessible neutron momentum transfer range (Q) of the instrument, we may then derive the spatial extent of the components and separate local dynamics from translational diffusion. On IN16, we have measured the quasi-elastic broadening to probe the diffusion of the pure SuCN at 240 K. 2.1. OSIRIS. The quasi-elastic broadening from the samples was measured with a 25 µeV energy resolution, using the PG(002) setting (0.3 Å-1 < Q < 1.8 Å-1). Data reduction and correction were done using the software MODES23 provided at ISIS. A diffraction bank is available at this spectrometer (0.8 Å < d < 20 Å) which allowed us to track structural changes in situ at the same temperatures as the QENS measurements. 2.2. IN16. Using the Si(111) setup of the backscattering spectrometer IN16,22 one probes the nanosecond molecular dynamics spanning the same Q-range as the OSIRIS spectrometer but within an energy window of (14 µeV (resolution of 0.9 µeV). 3. Model The data obtained on these instruments is first fitted with Lorentzians, and the extracted parameters are then compared with those from a one-molecule mathematical model. This mathematical model for the rotational relaxation of a single molecule is introduced by Be´e and Amoureux,10 and we calculate its S(Q,ω) that we then parametrize using the same fitting routine as that used for the data. We use this one-molecule model merely to demonstrate that it can be applied to describe localized dynamics over 3 orders of magnitude in the dynamic range that is covered by the two instruments. Only two types of relaxations are allowed by this model, but they couple the 72 molecular orientations in the unit cell and the
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Figure 2. Conditional probabilities P(rx,t|r(g|t),t)0) against time starting from a gauche conformation rg (top) or from a trans conformation rt (bottom) with x ) 1-72. The two rates here are arbitrarily chosen for demonstration. Since the rate ktft for this example is higher than ktfg or kgft, the probabilities develop differently depending on whether an rt or rg conformation is “selected” at t ) 0. The probability of the selected conformation thus decays from 1 at t ) 0, while all other conformations start with their respective probability P(t)0) ) 0.
corresponding S(Q,ω) therefore extends over such a large dynamic range. For the OSIRIS data, a fitting model of two Lorentzians (representing the exponentially decaying process groups) and a delta function are convoluted with the instrumental resolution function and fitted to the data to yield a width and intensity per Lorentzian. The IN16 data was fitted using only one Lorentzian, and the one-molecule model S(Q,ω) was fitted using three Lorentzians. The model as proposed by Be´e10 describes one molecule in the center of its unit cell and allows for t T g, t T gj, and t T t motions but not for direct g T gj. Because of the symmetry of the molecule, we assume that the rates to and from g are identical to those to and from gj. We generate the S(Q,ω) from the conditional and equilibrium probabilities (respectively {P(t),P(tf∞)}) of the molecule being in one of its 72 possible conformations in its unit cell (the vector P(t) thus consists of 72 elements). For this, the rate equation dP(t)/dt ) KP(t) is solved numerically starting with a P(t)0) that selects one of the 72 possible molecular conformations (P(rx,t)0) ) 1) with the probability of all other conformations P(ry*x,t)0) ) 0, where r represents one of the 72 conformations. The rate equation is solved until dP/dt ≈ 0 for each of the 72 conformations. The 72 × 72 matrix K is built using only the rate constants as defined by Be´e,10 being ktft, ktfg, and kgft. The latter two are coupled by the experimentally determined trans-gauche ratio in the plastic phase Rt/g, which is set to 0.282 throughout this article.11 All inter- and intramolecular interactions are therefore replaced by only these two rate parameters, which is a very coarse approximation. We note that the trans conformation of the isolated molecule is lower in potential energy than the gauche conformation according to DFT calculations (see, e.g., ref 19), so that the experimentally determined Rt/g must be governed by intermolecular interaction. Following the hypothesis that the probability rate of a whole molecule rotation ktft is higher than that of an isomerization t T g due to steric hindrance, we show in Figure 2 the development with time of the probabilities (according to this model) of each of the conformations, starting from a gauche or trans conformation. The S(Q,ω) for a set {ktft,ktfg} (calculated as described in ref 24) is then fitted with three Lorentzians. Unlike the fitting
Figure 3. (a) Typical QENS spectrum on a picosecond time scale (matrix dynamics 240 K) from OSIRIS with the components fitting to it: the two Lorentzians lor1 and lor2 are convoluted with the resolution function resol and fitted to the data obs. The total of the fitted components is plotted as fit. The two Lorentzian components can be well separated in the fit. (b) The IN16 data can be fitted using one Lorentzian.
procedure for the observed spectra, we do not use an experimental resolution function to convolute the calculated S(Q,ω). By comparing the fits of the data with those of the model, we aim to find a set {ktfg,ktft} of the model with which we can reasonably describe the data. Obviously, this model does not allow the effect of the dissolved salt to be incorporated other than via these two input parameters (the isomerization and rotation rates). From Figure 2, it is clear that the many ways of relaxation of the molecule in the unit cell can be grouped according to the time development of their probabilities. Each of these curves will contribute different frequency components to the final S(Q,ω) which complicates the assignment of the extracted fitting parameters to specific geometrical relaxations. 4. Results and Discussion For all samples, the quasi-elastic broadening is absent on the time scale of both instruments when below the plastic crystal phase temperature (210 K). A typical QENS spectrum of the plastic phase on both instruments is shown in Figure 3. It demonstrates that the two relaxational components are clearly distinguishable on the OSIRIS spectrometer. The results of fitting the data are expressed in the intensity and the width of the Lorentzians of the fit, and the Q
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Figure 4. Temperature dependence of the fitting results for the pure SuCN matrix. (a and b) The width of all components is constant with Q for Q > 1 Å-1. (c and d) The intensity of the fast component increases with temperature, while that of the slow component is nearly constant. The curves show the structure factors fitted on the data points 1 Å-1 < Q < 2 Å-1 with the function I(Q) ) A(1 - j0(QR)), where j0 is the Bessel function of the first kind (0th order), A is a scaling factor, and R is the jump distance.
Figure 5. Fitting results for both Lorentzians (fast, slow) for the electrolyte. (a and b) The width of all components increases with temperature. Above 1 Å-1, the width is constant with Q, except for the electrolyte at 300 K. (c and d) The intensity of the fast component increases with temperature, while that of the slow component is nearly constant. The curves show the structure factors fitted for 1 Å-1 < Q < 2 Å-1.
dependences of these are shown in Figures 4 and 5 for two temperatures in the plastic phase, respectively, for the pure SuCN matrix and the electrolyte. Except for the electrolyte at 300 K, the broadening for Q > 1 Å-1 is constant with Q (see Figures 4a,b and 5a,b), so we are not measuring translational diffusion but a localized motion, like rotational diffusion. The curves for the dynamic structure factors in Figures 4 and 5 are fitted only using the data above Q ) 1 Å-1. As the fit results above 1 Å-1 clearly demonstrate the localized character of the dynamics we are observing, we may expect little or no in-
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Figure 6. The model is correctly fitted using three Lorentzians with model parameters kgt ) 0.002 ps-1 and ktt ) 0.2 ps-1.
coherent quasi-elastic scattering for small Q values (the scattering cross section of our samples is mostly incoherent). Indeed, the fitted intensities below 1 Å-1 are small and even a small multiple scattering contribution would have a significant effect in this Q-range. In this work, we concentrate on the Q > 1 Å-1 region. Similarly, Figure 10 shows the fit results for IN16. The full width at half-maximum of the Lorentzian broadening of the three components corresponds roughly to relaxation time constants of 1.7, 17, and 140 ps. In early dielectric work,14 one relaxation component was found of several tens of picoseconds at 240 K, but the authors were not able to assign the relaxation particularly to the isomerization or molecular rotation. Later, Golemme et al.13 extracted relaxational constants from NMR via T1 between 10 and 300 ps in the plastic phase and selfdiffusion constants of the order of milliseconds by pulse train NMR. These T1 NMR and dielectric data compare with the 17 ps components of our fits, but as we will show later, this component is intimately correlated with the other two components of 1.7 and 140 ps if we apply our one-molecule model. From the Q dependence of the width of these three Lorentzians, we know that the observed dynamics is localized, which is in accordance with the observation that the time scale for selfdiffusion as found by pulse train NMR is milliseconds. 4.1. Succinonitrile. The data of the pure SuCN is compared to the one-molecule model, which can be applied to describe these dynamics which extend over 3 orders of magnitude, and we discuss where this model fails to describe the data. To compare the data with the model, we first fit the model with three Lorentzians and compare these fit results with those of the observed data. Figure 6 shows that the model system can be reasonably well described by three Lorentzians, and we found that a reasonable comparison of these fits with those of the data on both OSIRIS and IN16 is obtained using the model parameters kgt ) 0.002 ps-1 and ktt ) 0.2 ps-1. The comparison of the fits from the data and the fits from the model is shown in Figure 7, and we obtain reasonable correspondence for over three decades of dynamics range. No further optimization of the model is done. For Q > 1 Å-1, the observed data indicates that these dynamics are of localized character (Figure 7), similar to the model which is by definition localized. The comparison demonstrates that the isomerization and rotation dynamics of a single molecule with only two
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Figure 7. Comparison of the model with the data set IN16/OSIRIS: the quasi-elastic broadening. At Q < 1 Å-1, the fitting procedure is less accurate, since the S(Q,ω) has little quasi-elastic intensity in this region. This hold for the observed and model S(Q,ω).
Figure 8. Comparison of the model with the data set IN16/OSIRIS: the quasi elastic intensity in arbitrary units. The intensities of the different instruments are scaled with respect to each other, but there is only one scaling factor for the two fastest components (OSIRIS) with respect to the model fits.
relaxation rates (i.e., one isomerization and one rotation) extend over 3 orders of magnitude in relaxation time constants. On the other hand, it shows that the structure factors of the model do not compare well with the data. Considering the region Q > 1 Å-1, we see that the model predicts the maxima at higher Q values than our observations. For the pure SuCN matrix, the structure factors therefore suggest longer jump distances than what the model describes, but an extended instrumental Q range is required to firmly claim so (see Figure 4c,d). Also, the S(Q,ω) of the model is lacking a Debye-Waller factor which would shift the maxima in the structure factors downward. It is therefore not possible to make a quantitative comparison of the structure factor maxima of the model and the data. Nevertheless, a comparison of the experimental structure factors (Figure 4c,d) shows no clear shift of the maxima to lower Q with temperature for either component for the pure SuCN. Figure 4 shows opposite trends for the two components on OSIRIS with respect to the width and intensity: the number of fast relaxations increases with temperature but not their relaxation time constant, while the number of slow relaxations stays constant and the potential energy landscape seems to change its relaxation time constant. Considering the molecular conformations that are involved, it is likely that the fast relaxation is mostly correlated to the t T t rotation and the slowest to the isomerization t T g, but as shown in Figure 2, the time dependence of each of the relaxation pathways will contain different frequency components in the Fourier transform to S(Q,ω). On IN16 (Figure 10), we observe that the relaxation (τ ≈ 140 ps) is correlated with a larger jump distance (about 3.2 Å) than any distance in the one-molecule model. Since the SuCN matrix stays crystalline, the closest jump distance for the molecule as a whole would be 5.5 Å, for which the nearest neighbor site at (0.5, 0.5, 0.5) would have to be free. In the
plastic phase (space group IM3M), the hydrogens on either a trans or gauche molecule form (time-averaged) a quasi-shell due to the continuous rotation of the molecule. This quasi-shell has a radius 1.3 (trans) and 1.5 Å (gauche) centered on the unit cell site, and it is therefore possible that a whole-molecule jump of 5.5 Å corresponds to a hydrogen jump distance of 3.2 Å (averaged over all four hydrogens involved). A more quantitative analysis would require a correction for the Debye-Waller factor which is omitted by comparing the pure SuCN to the SuCN with the dissolved salt. 4.2. Electrolyte. For the electrolyte, we observe similar trends in relaxation time constants as for the pure SuCN matrix on the OSIRIS spectrometer, except at 300 K where the isomerization is correlated with a translation (Figure 5b), but since the broadening does not increase quadratically with Q, it is not liquid-like translational diffusion. Although the salt has a notable effect on the dynamics of the SuCN matrix, the data is well described by two Lorentzians rather similar to the pure SuCN and no extra relaxations appear, which suggests that the salt is homogeneously dissolved and there is no significant separation of salt-rich and salt-poor regions in the electrolyte. It is the slowest component measured on OSIRIS (Figure 4b,d vs Figure 5b,d) that shows the effect of the salt. For both the pure matrix and the electrolyte, the intensity of this relaxation does not increase with temperature. If this means that all molecules in the plastic crystalline phase of pure SuCN contribute this observed signal, then we may conclude that the salt has a homogeneous effect on all SuCN molecules. Figure 5d suggests that the maximum of the structure factor shifts downward (Q ≈ 1.6 Å-1) with temperature. The corresponding length scale of relaxation thus changes from 2.0 to 2.4 Å. As shown in Figure 9, this can still be explained as a fixed molecule jump, but considering the Q dependence of the width, a site jump might be correlated to the isomerization. Like
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Figure 9. Distribution of jump distances (grouped into 0.1 Å bins).
Figure 11. Evolution of the (200) diffraction peak with temperature for the electrolyte (a) and pure SuCN (b). The spectra are offset along the y axis for visibility. (b) From 240 to 320 K, the temperature step is 5 K.
Figure 10. IN16 fitting results for 240 K. (top) The curve shows the structure factor fitted on the data points 1 Å-1 < Q < 2 Å-1 with the function I(Q) ) A(1 - j0(QR)), where j0 is the Bessel function of the first kind (0th order), A is a scaling factor, and R is the jump distance. (bottom) The fwhm of the fitted Lorentzian. The curve through the data shows the average Lorentzian width.
with the pure SuCN matrix, the closest molecular jump distance is over the unit cell diagonal (5.5 Å) but the jump distance observed here is considerably smaller than that or the 3.2 Å of the 0.14 ns relaxation. As stated before, more than 70% of the molecules are in the gauche conformation and a molecular jump of 5.5 Å could correspond to a hydrogen jump (averaged over four hydrogens) of 2.4 Å if the molecule would “roll over” to the neighboring site that is closest to the “hydrogen side” of the gauche molecule (i.e., opposite the “nitrogen side”). Like how the molecular jump distance of 5.5 Å could be accompanied with a hydrogen jump distance of only 2.4 Å, indeed larger hydrogen jump distances would be seen if this molecule would jump to a nearest neighbor void that is not closest to the “hydrogen side” of the molecule. This is a possible explanation for the difference in the position of the structure factor maximum of Figure 5d compared to the 0.14 ns relaxation of Figure 10. Assuming diffusion based on this type of jumps, one can estimate the upper limit of the diffusion coefficient Dmax ) l2/ (6τ) using a jump distance of 5.5 Å and a relaxation time of 17 ps. This yields Dmax ) 2.9 × 10-9 m2/s for the SuCN molecule in the electrolyte which is a factor of 30 higher than what is observed by Long et al.1 for both the cation and the ion at 300 K. In the analysis of the structure factors in this article, we have not corrected for the Debye-Waller factor, which will influence the maxima of the structure factors. We note that these maxima
Figure 12. Temperature dependence of the fit parameters of the (200) diffraction peak. A Gaussian on a flat background was fitted to each of the peaks of Figure 11. The dissolved salt does not enhance the temperature dependence of any of these parameters.
do not significantly shift with temperature for the pure SuCN, but nevertheless, the corresponding jump distances should be considered as qualitative. The comparison of the electrolyte with the pure SuCN matrix should however not be too much affected by this failure. An analysis in terms of the elastic incoherent scattering function would not allow us to study the individual structure factors of the two relaxational components. 4.3. Diffraction. The comparison of the Q dependence of the one-molecule model and the data supports our suggestion that the jump distances are significantly larger than those merely based on a molecule fixed on its crystal site. The temperature dependence of the (2 0 0) reflection (Figures 11 and 12) shows how the average free volume in the unit cell increases for pure SuCN and very similarly for the electrolyte. At the same time, the intensity diminishes and the peak slightly broadens with temperature for SuCN, while both are less temperature dependent for the electrolyte. Because of the increase in free volume and disorder with temperature, the probability of a whole-molecule site jump from
Localized Relaxational Dynamics of Succinonitrile (000) to (0.5,0.5,0.5) is increasing with temperature. The onset of the diffusion of the SuCN molecules in the electrolyte at 300 K as shown in Figure 5b can however not be explained from the analysis of the diffraction peak. The d-spacing of SuCN + salt is very similar to the pure SuCN, and the disorder is even slightly smaller. From positron annihilation studies,25 it is known that most crystal defects in the plastic phase are vacancies, but the concentration is reported by Baughman et al. to be only 0.1%.26 The vacancy density is not probed by diffraction, but other crystal defects could change the average lattice parameter and we observe no such effect when the salt is dissolved. 5. Conclusions We have found three localized relaxational components in the dynamics of the succinonitrile plastic crystal with the relaxation time constants 1.7, 17, and 140 ps. Using the model by Be´e10 of one molecule with 72 conformations in its unit cell, we can reproduce these observed S(Q,ω)’s to a certain extent, except that the data shows larger hydrogen jump distances than those predicted by this model. The observed dynamics are thus localized but in a volume larger than what one would expect for the SuCN molecule fixed on its lattice site. We associate the relaxation τ ) 140 ps with a whole-molecule jump to the neighboring unit cell site, and likely the relaxation of τ ) 17 ps also involves a site jump when the salt is dissolved. The effect of addition of the salt is studied for the two fastest components, and the (200) diffraction peak is studied. The suggested equilibrium of a disordered electrolyte phase nanodispersed in a mostly plastic crystalline matrix phase, as stated in ref 2 is not supported by our findings. Although the salt has a noticeable effect on the dynamics of the SuCN matrix, the same fitting model (two Lorentzians) describing the pure SuCN can be applied to the electrolyte which indicates that the salt is homogeneously dissolved and there is no significant separation of salt-rich and salt-poor regions in the electrolyte. The rotational diffusion of the matrix molecules is somewhat slowed down upon addition of the LiBF4, and at a molar salt concentration of 5%, this effect would not be visible if the fraction of a pure plastic crystalline matrix phase would be abundant compared to a hypothetical salt-rich region. The gauche conformation is the most abundant in the plastic phase, even though the trans conformation is of lower potential energy for an isolated molecule. This means that the intermolecular interactions govern the conformation distribution and via this intermolecular interaction of the SuCN matrix the ions indirectly affect the matrix over a larger range than just a few neighboring SuCN molecules. At 300 K, we find that the addition of the salt disturbs the localized character of the dynamics and the maximum in the structure factor (Figure 5d) corresponds to a larger average hydrogen jump diffusion distance. We propose that the assigned isomerization is correlated with a jump of the whole molecule to its nearest neighbor site in the unit cell, since most defects in this plastic crystal are known to be vacancies.25 The temperature dependence of the unit cell parameter, as observed by diffraction, is rather similar for the electrolyte and
J. Phys. Chem. C, Vol. 113, No. 33, 2009 15013 the pure SuCN matrix, so there is not much more play on average in the electrolyte than in the pure SuCN matrix. From the lack of signature of the salt on the averaged cell parameters, one could conclude that the ions occupy the already available voids in the matrix although the reported vacancy density in the pure SuCN is only 0.1%.26 An enhanced vacancy density would not be observed by diffraction at these concentrations. Via the intermolecular interactions of the highly polar SuCN molecules, the effect of an ion would extend well beyond its nearest neighbor SuCN molecules. This in turn would mean that the onset of diffusion as observed at 300 K with the salt dissolved would also be a collective phenomenon. The dynamics of the SuCN molecule are localized but in a volume larger than what is calculated from isomerizations and rotations of a translationally fixed molecule. The corresponding upper limit of the diffusion constant is a factor of 30 higher than NMR determined ionic diffusion constants.1 References and Notes (1) Long, S.; MacFarlane, D. R.; Forsyth, M. Solid State Ionics 2003, 161, 105. (2) Alarco, P.-J.; Abu-Lebdeh, Y.; Abouimrane, A.; Armand, M. Nat. Mater. 2004, 3, 476. (3) Abouimrane, A.; Whitfield, P. S.; Niketic, S.; Davidson, I. J. J. Power Sources 2007, 174, 883. (4) Li-Zhen, F.; Xiao-Liang, W.; Fei, L.; Xun, W. Solid State Ionics 2008, 179, 1772. (5) Long, S.; Howlett, P. C.; MacFarlane, D. R.; Forsyth, M. Solid State Ionics 2006, 177, 647. (6) Wang, P.; Dai, Q.; Zakeeruddin, S. M.; Forsyth, M.; MacFarlane, D. R.; Gra¨tzel, M. J. Am. Chem. Soc. 2004, 126 (42), 13590. (7) Seeber, A. J.; Forsyth, M.; Forsyth, C. M.; Forsyth, S. A.; Annat, G.; MacFarlane, D. R. Phys. Chem. Chem. Phys. 2003, 5 (12), 2692. (8) Adebahr, J.; Seeber, A. J.; MacFarlane, D. R.; Forsyth, M. J. Phys. Chem. B 2005, 109 (43), 20087. (9) Adebahr, J.; Seeber, A. J.; MacFarlane, D. R.; Forsyth, M. J. Appl. Phys. 2005, 97 (5), 093904. (10) Be´e, M.; Amoureux, J. P.; Lechner, R. E. Mol. Phys. 1980, 39, 945. (11) Derollez, P.; Lefebvre, J.; Descamps, M.; Press, W.; Fontaine, H. J. Phys.: Condens. Matter 1990, 2, 6893. (12) Derollez, P.; Lefebvre, J.; Descamps, M.; Press, W.; Grimm, H. J. Phys.: Condens. Matter 1990, 2, 9975. (13) Golemme, A.; Zamir, S.; Poupko, R.; Zimmermann, H.; Luz, Z. Mol. Phys. 1994, 81, 569. (14) Longueville, W.; Fontaine, H.; Chapoton, A. J. Chim. Phys. 1971, 68, 436. (15) Fontaine, H.; Fouret, R. AdV. Mol. Relax. Processes 1973, 5, 391. (16) Wro`z¨, T.; Kubicki, J.; Naskrecki, R.; Bancewicz, T. J. Chem. Phys. 1995, 103, 9212. (17) Foggi, P.; Righini, R.; Torre, R.; Angeloni, L.; Califano, S. J. Chem. Phys. 1992, 96, 110. (18) Cardini, G.; Righini, R.; Califano, S. J. Chem. Phys. 1991, 95, 679. (19) Umar, Y.; Morsy, M. A. Spectrochim. Acta, Part A 2007, 66, 1133. (20) Feng, X.; Laird, B. B. J. Chem. Phys. 2006, 124, 044707-1. (21) Telling, M. T. F.; Andersen, K. H. Phys. Chem. Chem. Phys. 2005, 7, 1255. (22) Frick, B.; Magerl, A.; Blanc, Y.; Rebesco, R. Physica B 1997, 1177, 234–236. (23) Howells, W. S. MODES Manual; ISIS Facility: Chilton, U.K., 2003. (24) Be´e, M. Quasi Elastic Neutron Scattering; Adam Hilger/IOP Publishing Ltd: Bristol, England, 1988. (25) Eldrup, M.; Pedersen, M. J. Phys. ReV. Lett. 1979, 43, 1407. (26) Baughman, R. H.; Turnbull, D. J. Phys. Chem. Solids 1970, 32, 1375.
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