Dynamics in the Plastic Crystalline Phases of ... - ACS Publications

Article Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Dynamics in the Plastic Crystalline Phases of Cyclohexanol and Cyclooctanol Studied by Quasielastic Neutron Scattering E. Novak,†,‡,§ N. Jalarvo,*,‡,§ S. Gupta,∥ K. Hong,⊥,# S. Förster,§ T. Egami,†,¶,◇ and M. Ohl§ †

Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States Neutron Sciences Directorate, Oak Ridge National Laboratory (ORNL), Oak Ridge, Tennessee 37831, United States § Jülich Centre for Neutron Science (JCNS), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany ∥ Department of Chemistry and Macromolecular Studies Group, Louisiana State University, Baton Rouge, Louisiana 70803, United States ⊥ Center for Nanophase Materials Sciences, Oak Ridge National Laboratory (ORNL), Oak Ridge, Tennessee 37831, United States # Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States ¶ Materials Science and Technology Division, Oak Ridge National Laboratory (ORNL), Oak Ridge, Tennessee 37831, United States ◇ Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States ‡

S Supporting Information *

ABSTRACT: Plastic crystals are a promising candidate for solid state ionic conductors. In this work, quasielastic neutron scattering is employed to investigate the center of mass diffusive motions in two types of plastic crystalline cyclic alcohols: cyclohexanol and cyclooctanol. Two separate motions are observed which are attributed to long-range translational diffusion (α-process) and cage rattling (fast β-process). Residence times and diffusion coefficients are calculated for both processes, along with the confinement distances for the cage rattling. In addition, a binary mixture of these two materials is measured to understand how the dynamics change when a second type of molecule is added to the matrix. It is observed that, upon the addition of the larger cyclooctanol molecules into the cyclohexanol solution, the cage size decreases, which causes a decrease in the observed diffusion rates for both the α- and fast β-processes.

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INTRODUCTION In today’s highly mobile, information-based society, the demand for portable electronic devices powered by long lasting batteries is ever increasing. Currently, the energy market is dominated by rechargeable lithium-based liquid electrolyte batteries due to their high energy density, design flexibility, and high ionic conductivity.1 However, these batteries have major safety concerns due to their dangerous liquid electrolyte, which can be flammable, and they are prone to leakage.2 This concern has prompted significant research in the field of energy science recently, largely due to the emergence of electric vehicles. A safer alternative would be to use a solid state ionic conductor, such as a glass or polymer, which would not leak if the battery is damaged. A promising candidate for solid state ionic conductors is plastic crystals (PCs), which are orientationally disordered crystals, also known as orientational glasses.3 PCs are a type of molecular glass former that possesses properties of both liquids and solids. The centers of mass of the molecules are positioned on lattice sites, while the orientations of the molecules are dynamically disordered. Translational motion is largely confined, but rotational degrees of freedom are available for motion. Ions diffuse through this system by the “revolving © XXXX American Chemical Society

door” mechanism, where the molecules rotate to increase the free volume, creating space for the ions to diffuse efficiently through the opening of these doors.4−7 Some PCs have been reported with technologically relevant ionic conductivities around ambient temperatures upon the addition of ions.4,5,8,9 PC systems tend to have complex phase diagrams with metastable phases and multiple phase transitions and are highly dependent on cooling and heating rates. Investigations have shown that the PC phase can be stabilized and extended throughout a larger temperature range through the formation of a binary PC mixture.6,10 This also allows for the tuning of the ionic conductivity by altering the concentration of the constituents. However, the ionic conductivities of two different binary PC mixtures have been investigated recently with conflicting results.4,6 In one system, the addition of larger molecules to a solution of smaller molecules increased the ionic conductivity, while in the second system the opposite occurred. In this paper, we investigate one of these systems, i.e., cyclooctanol (OCT) and cyclohexanol (HEX) and their Received: April 11, 2018 Revised: May 14, 2018 Published: May 18, 2018 A

DOI: 10.1021/acs.jpcb.8b03448 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

choppers were set at 60 Hz, and the wavelength was centered at 6.4 Å. Samples were cooled slowly from ambient temperature to 20 K over the course of approximately 3 h using a closed cycle refrigerator. The resolution function was measured at 20 K for each sample, and measurements at higher temperatures were performed for approximately 3 h/temperature. The data was normalized using an annular vanadium standard and reduced using Mantid, and model fits were performed with the DAVE software package.15 Data Analysis. The QENS intensity is proportional to the dynamic incoherent structure factor Sinc(Q, E). This contains information about the correlation of the same scatterer at different times, allowing for accurate measurements of diffusive motions. Due to the large incoherent cross section of hydrogen and the high amounts of hydrogen contained in each molecule, the measured intensity will yield information about the motion of the hydrogen in the system. The data was binned to 18 averaged Q values, and each of them was fit using the expression16−19

mixture, using backscattering neutron spectroscopy to better understand the dynamics of their PC phases. The materials are measured in their pure forms and in a binary mixture to shed light on how the motion of the molecules changes when the binary mixture is created. Ions are not added to the solutions to ensure that the measured signal only reflects the motion of the PC matrix. For the revolving door mechanism, the rotation of the molecules is the most important motion that determines the success of the ionic diffusion in PCs. However, translation of the center of mass of the molecules is also important and can influence the amount of free volume created. Within the context of Götze’s mode coupling theory (MCT), there exists two motions above the crossover temperature: a slower longrange translational diffusion (α-process) and a faster cage rattling (fast β-process) motion.11,12 A cage is formed by the nearest neighbors (and to a lesser extent second nearest neighbors) when their positions are fixed in space. When this occurs, a particle inside the cage can only undergo small amplitude, subdiffusive motions that are less than the diameter of the molecule, known as cage rattling. This is representative of the local environment in PCs where the molecules are largely fixed in space on lattice sites. For a particle to move over longer distances, a “door” needs to be opened in the cage. This increase in free volume will allow the particle to break free from the cage and contribute to the structural relaxation (α-process). In the case of ionic diffusion, an ion that is stuck inside the cage will now be able to escape out through the door. However, the cage can only open when many particles in the system are able to cooperatively rearrange. This framework has been confirmed by molecular dynamics simulations.13 The free volume created by the α- and fast β-process thereby directly influences the success of the revolving door mechanism and the ionic diffusion. Quasielastic neutron scattering (QENS) can access the dynamics associated with these two processes and probe the changes in a binary mixture. This knowledge leads to a better understanding of how to tune the local environment so that the ionic conductivity can be optimized.

I(Q , E) = [X(Q )δ(E) + (1 − X(Q ))Sqe(Q , E)] ⊗ R (Q , E ) + B (Q , E )

(1)

Here, δ(E) is a delta function representing the elastic signal and Sqe(Q, E) is the model representing the quasielastic scattering. R(Q, E) is the resolution function. X(Q) represents the fraction of elastic scattering in the signal, also known as the elastic incoherent structure factor (EISF). The symbol ⊗ represents the numerical convolution, and B(Q, E) is the linear background term arising from the sample, sample environment, and spectrometer. Two motions are clearly observable at the measured time scale, corresponding to a slower (narrower Lorentzian component) and a faster (broader Lorentzian component) dynamic process. We associate the narrower Lorentzian to the long-range translational diffusion and the broader Lorentzian to cage rattling. Evidence supporting this reasoning will be presented in detail later in the Discussion section. Therefore, a single Lorentzian model was insufficient and a two-Lorentzian model was needed for Sqe(Q, E) of the form

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MATERIALS AND METHODS Three samples were investigated in this experiment: cyclooctanol (C8H16O), cyclohexanol (C6H12O), and 80% cyclohexanol−20% deuterated cyclooctanol (C8D16O) in terms of mol % concentration. Protonated OCT was purchased from Tokyo Chemical Industry Co. (TCI) with a reported purity of >98.0%. Protonated HEX was purchased from Sigma-Aldrich with a purity of 99%. The fully deuterated OCT was synthesized at the Center for Nanophase Materials Sciences (CNMS) at Oak Ridge National Laboratory (ORNL). QENS measurements were performed using the backscattering spectrometer BASIS at the Spallation Neutron Source (SNS) at ORNL.14 Annular aluminum sample cans were used with a thickness of 0.05 mm to minimize multiple scattering effects by ensuring the sample transmission was ≥95%. All samples were mixed in the appropriate amounts and loaded into the sample holders inside a glovebox under an inert controlled atmosphere to reduce exposure to moisture. The standard instrumental setup was used with an energy resolution of fwhm = 3.5 μeV, yielding an accessible energy range of ±120 μeV and Q range from 0.2 to 2.0 Å−1. Note that plastic crystals are known to have coherent structural peaks at this Q-range, usually above 1 Å−1. For this reason, a range of Q values had to be removed from the data analysis to avoid the effects of the coherent signal. The

Sqe(Q , E) = (1 − P(Q )) + P(Q )

Γ1(Q ) 1 2 π E + Γ12(Q )

Γ2(Q ) 1 2 π E + Γ2 2(Q )

(2)

where (1 − P(Q)) and P(Q) represent the spectral weights of the narrow and broad Lorentzian terms of width Γ1 and Γ2, respectively. The first term (1 − P(Q)) is a measurable quantity called the elastic incoherent structure factor (EISF), that is the fraction of elastic intensity in the total scattering signal20 EISF =

IE IE + IQE

(3)

where IE and IQE are the respective integrated elastic and quasielastic intensities. The total EISF contains the quasielastic intensity integrated from both Lorentzian functions. However, for the calculations in this paper, only the EISF with respect to the broad component intensity is investigated so that the length scales for the fast β-process can be calculated. Physically, the EISF is directly related to the region of space accessible to the scatterers and yields information about the geometry of the B


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Figure 1. (a) QENS data for OCT at Q = 1.0 Å−1 and temperatures of 230, 240, 270, and 280 K. The solid lines are a fit of eq 1, and the dotted− dashed line is the resolution function. The inset displays all of the fit components for T = 280 K, with the narrow and broad Lorentzians shown in green and blue, respectively. (b) EISF for the broad Lorentzian where the solid lines are a fit of eq 5. Γ vs Q2 for the (c) narrow Lorentzian and (d) broad Lorentzian where the solid lines are fits using eq 6.

⎡ ⎛ 3j (QrCage) ⎞2 ⎤ ⎢ ⎟⎟ ⎥ EISF = p1 + (1 − p1 )⎜⎜ 1 ⎢ Qr ⎝ ⎠ ⎥⎦ Cage ⎣

motion.21 Diffusive motion inside the cage can be modeled using the diffusion within a sphere model16,19,20,22 ⎛ 3j (QrCage) ⎞2 ⎟⎟ EISF = p1 + (1 − p1 )⎜⎜ 1 ⎝ QrCage ⎠

× [p2 + (1 − p2 )j0 2 (QrIntra)]

(4)

(5)

Here, p2 again represents the fraction of hydrogen that is immobile to the motion, j0 is the zero-order Bessel function, and rIntra is the sphere radius. This additional term has been previously used to account for the skeletal motion of CH2 groups about the C−C bonds.22 Let it be noted that the two models described here, i.e., diffusion “within” and “on” a sphere, are indeed distinct processes. The diffusion within a sphere model describes a diffusive motion that is free to move inside the confinement radius of a sphere. On the other hand, the diffusion on a sphere model describes a motion that is confined to move only along the surface of a sphere. This describes bonded atoms or side groups whose motion is confined to a distinct length scale associated with the bond length. The EISF is supposed to approach a value of 1 as Q approaches zero. However, the low Q values were too small, which is most likely the result of multiple scattering. These effects were minimized by using a thin sample with high transmission. Multiple scattering corrections are not necessary for the interpretation of

where rCage is the confinement radius of the sphere, j1 is the first-order Bessel function, and p1 represents the fraction of hydrogen in the system that is “immobile” and does not contribute to the diffusive motion. A relatively good fit is achieved using eq 4 for the higher temperature measurements, but this approach can be improved as follows. Since the molecules in PCs are positioned on lattice sites, they are expected to have small translational diffusion components compared to rotational motion. As the temperature is decreased, the molecules will also experience smaller amplitudes of cage rattling. This means that rotation of the molecule and segmental motion not associated with center of mass motion will have a larger effect on the EISF. This is worsened by the fact that there is a limiting momentum transfer value at higher Q-values that denotes the crossover from center of mass motion to intramolecular motion. Therefore, a second component has been added to eq 4 to account for this motion, known as the diffusion on a sphere model,16,19,20,22 to give the full expression: C


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The Journal of Physical Chemistry B Table 1. Diffusion Coefficients and Residence Times sample OCT (PC II) OCT (PC I) HEX (PC II) HEX (PC I) 80−20 mix (PC I)

T (K) 230 240 270 280 260 280 260 280

Dα (10−11 m2/s) 0.54 0.70 4.52 6.87 6.17 6.12

± ± ± ± ± ±

Dβ (10−10 m2/s)

0.09 0.08 0.44 0.94 0.72 0.56

1.44 1.97 4.21 6.19 7.08 5.03 2.06 2.08

3.27 ± 0.49

± ± ± ± ± ± ± ±

0.17 0.21 0.45 0.81 0.52 0.89 0.39 0.34

τα (ns) 2.02 1.62 1.43 1.32 0.94 1.28

± ± ± ± ± ±

τβ (ns)

0.19 0.13 0.03 0.03 0.04 0.04

1.49 ± 0.06

0.152 0.152 0.144 0.139 0.139 0.124 0.126 0.114

± ± ± ± ± ± ± ±

0.007 0.006 0.003 0.003 0.001 0.003 0.004 0.005

Figure 2. (a) QENS data for HEX at Q = 1.0 Å−1 and temperatures 260 and 280 K. The solid lines are a fit of eq 1, and the dotted−dashed line is the resolution function. The inset displays all of the fit components for T = 280 K, with the narrow and broad Lorentzians shown in green and blue, respectively. (b) EISF for the broad Lorentzian where the solid lines are a fit of eq 5. Γ vs Q2 for the (c) narrow Lorentzian and (d) broad Lorentzian where the solid lines are fits using eq 6.

the expression D = ⟨L2⟩/6τ. The broader component shows broadening less than Q2 at higher momentum transfers, indicating localized jump at the corresponding length scale. At the low Q regime, the HWHM does not approach zero at Q = 0 Å−1 and plateaus at a constant value instead. This shows evidence of the diffusion taking place in a restricted space, since the widths do not continue to decay at longer length scales. For diffusion in a sphere, the confinement radius, RΓ, can be calculated using25

our data, and this rather complex procedure was therefore omitted. The Q dependency of the HWHM of the narrower Lorentzian exhibits the typical features associated with longrange translational diffusion. This can be modeled using a jump diffusion model with a random distribution of jump lengths16,18,20,23,24 Γ(Q ) =

⎞ ℏ⎛ 1 ⎜1 − 2⎟ τ⎝ 1 + τDQ ⎠

(6)

where D is the diffusion coefficient and τ is the residence time between successive jumps of the molecule. The mean square jump length ⟨L2⟩ is related to the diffusion coefficient through

Γ= D

4.33296D RΓ 2

(7) DOI: 10.1021/acs.jpcb.8b03448 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 3. (a) QENS data for the 80−20 mixture at Q = 1.0 Å−1 and temperatures of 190, 230, 260, and 280 K. The solid lines are a fit of eq 1, and the dotted−dashed line is the resolution function. The inset displays all of the fit components for T = 280 K, with the narrow and broad Lorentzians shown in green and blue, respectively. (b) EISF for the broad Lorentzian where the solid lines are a fit of eq 5. Γ vs Q2 for the (c) narrow Lorentzian and (d) broad Lorentzian where the solid lines are fits using eq 6.

and 1.3 Å−1 includes coherent structural features and was thus eliminated from the HWHM and EISF fits. An X-ray diffraction pattern for OCT at 280 K has been included as Supporting Information to display this feature. The EISFs for PC phases I and II look essentially very different, which indicates that a major change in the dynamics occurs upon the transition. PC phase I was satisfactorily fit with the model described in eq 5, whereas this model could not reproduce the EISF for PC phase II. The HWHM for the narrow component and broad component are displayed in Figure 1c and d, respectively, and have been fit with eq 6. The fits for the narrow component are in rather good agreement with the experimental data. On the other hand, the broader component has some systematic deviation from the fits at the low Q regime, as discussed above. However, the diffusion coefficients and the residence times can be reliably extracted, and the values are listed in Table 1. Cyclohexanol (HEX). The phases of HEX have also been thoroughly investigated.6,29,30 The calorimetric study by Adachi et al.30 highlights the complexity of PC phase diagrams and how temperature ramp rates affect phase formation. In general, HEX has a transition from ordered crystal III to PC II at 244 K, followed by PC II to PC I transition at 265 K and PC I fusion at 299 K. The sample was measured at 20 K for the resolution function and then heated to 260 and 280 K to measure the dynamics of PC II and PC I phases, respectively. The spectra

where Γ is the HWHM plateau value at low Q and D is the diffusion coefficient extracted from eq 6.

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RESULTS Cyclooctanol (OCT). The phases of OCT have been thoroughly investigated.6,10,26−28 There are four main phases reported for OCT that are of interest: the liquid phase, PCs I and II, and the low temperature ordered crystal III. The phase transitions are reported as crystal III to PC II at 221 K (achieved by extrapolation), PC II-I at 261.7 K, and crystal I fusion at 295.3 K. For our experiment, a quasielastic signal was first observed at 190 K with very low intensity after slowly heating the sample from 20 K. Upon additional heating, it transitioned into the PC II phase for the measurements at 230 and 240 K and subsequently the PC I phase at 270 and 280 K. We report incoherent QENS data for protonated OCT in Figure 1a for an average momentum transfer of Q = 1.0 Å−1 and for temperatures of 230, 240, 270, and 280 K. The solid black lines are the resulting fit of eq 1 with two Lorentzian functions. The dotted−dashed line is the resolution function that was measured at 20 K. The resolution function is strongly asymmetric as a result of the instrument design and the moderator emission spectrum.14 The EISF with respect to the broad component is displayed in Figure 1b. The solid lines are the fit given by eq 5. Data in the intermediate Q range of 1.2 E


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The Journal of Physical Chemistry B Table 2. EISF Fit Parameters and Calculated Cage Sizes sample OCT (PC I) HEX (PC II) HEX (PC I) 80−20 mix (PC I)

T (K) 270 280 260 280 260 280

RCage (Å) 4.52 3.67 5.11 3.99 2.77 2.85

± ± ± ± ± ±

0.35 0.57 0.40 0.90 0.44 1.23

RIntra (Å) 0.85 0.90 1.17 1.13 0.70 1.05

and the fits of eq 4 are shown in Figure 2a. The same process that was applied to treat the data for OCT was used for the HEX analysis, and the HWHM and EISF are shown Figure 2b− d. Again, Q values from 1.2 to 1.5 Å−1 were excluded due to coherent scattering effects. The calculated line shape given by eq 1 deviated from the experimental results in the high Q range for HEX. The error was due in part to the narrow Lorentzian attempting to fit the elastic intensity. Other sources for this error are presented in the Discussion section. As a result, the jump diffusion model was only fit for Q ≤ 1.1 Å−1 for the narrow Lorentzian and we had to exclude the additional points of Q = 1.8 and 1.9 Å−1 from the EISF fitting procedure. 80% Cyclohexanol−20% Deuterated Cyclooctanol (80−20 Mixture). A calorimetric study on a wide range of concentrations of a binary mixture of OCT and HEX with 1 mol % lithium salt added has recently been reported by Reuter et al.6 While the phase diagrams for the pure components are rather complex, the opposite was seen for the various mixtures. There was only one PC phase that was observed before melting. The authors comment that the salt seems to stabilize the PC phase. However, another investigation10 of OCT and cycloheptanol (HEPT) binary mixtures without salt also exhibited this increase in phase stability. Creating a binary mixture appears like a promising way to stabilize the PC phases. In our experiment, the sample transitioned into a PC state around 190 K and remained for the measurements at 230, 260, and 280 K. The same process that was applied to treat the data for OCT was used for the 80% protonated HEX−20% deuterated OCT mixture, which will be referred to as the 80−20 mixture for the extent of this paper. The use of selective deuteration enables us to highlight the signal of the protonated molecules, since the incoherent neutron scattering cross section of hydrogen is about 40 times that of deuterium. In the mixture, we will observe the motion of the protonated HEX molecules and will neglect the signal from the deuterated OCT molecules. This allows us to focus on how the motion of the HEX molecules is affected by the addition of OCT to the system. The results of these measurements on the 80−20 mixture can be observed in Figure 3. Note that the HWHM for 190 K was not added to Figure 3c and d because the error bars were rather large and cluttered the figure. Diffusion coefficients were unable to be extracted from this data set so only the EISF will be displayed for 190 K. Extracted Values. Table 1 displays the diffusion coefficients and residence times extracted from applying eq 5 to the HWHM for both the fast and slow components. The diffusion coefficients are in units of 10−11 m2/s for the αprocess and 10−10 m2/s for the fast β-process. The characteristic radii for diffusion in a sphere, RCage, and diffusion on a sphere, RIntra, were extracted from fitting the EISF with eq 5 and are listed in Table 2. These are also compared to the cage sizes, RΓ, extracted from HWHM fits. The meaning of the weight parameters, P1 and P2, has been explained in the text earlier.

± ± ± ± ± ±

0.06 0.10 0.02 0.07 0.36 0.21

P1 0.88 0.85 0.95 0.93 0.78 0.76

± ± ± ± ± ±

P2 0.02 0.05 0.01 0.04 0.13 0.25

0.22 0.13 0.35 0.17 0 0

± ± ± ± ± ±

RΓ (Å) 0.05 0.08 0.01 0.03 0.61 0.11

6.44 7.81 7.53 5.95 3.93 4.37

Note that a value of 0.25 for a weight parameter means that 75% of the hydrogen is participating in that motion and that 25% is essentially “immobile” on the measured time scale.

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DISCUSSION QENS investigations on PC materials typically focus on the rotation of the whole molecule or side groups, such as threefold jumps observed in methyl groups.31 We initially considered rotational motion in this study, but it became clear that we see center of mass diffusion instead. The DQ2 dependence of Γ(Q) is the characteristic feature of unconstrained long-range translational diffusion, rather than the Q-independent relationship typically seen with localized motion. While the slower motion is rather straightforward to analyze in terms of the jump diffusion model, the faster motion is more challenging. The plateau at low Q suggests that the motion becomes restricted at long length scales. Above the plateau, the broadening is described by the jump diffusion model, which suggests that this motion is a fast diffusion process within a confined geometry. A common relaxational process observed in glass formers is the fast β-process, which is often attributed to fast, subdiffusive motions inside a cage formed by a particle’s nearest neighbors, also known as cage rattling.11,12 This type of motion can be measured using dielectric spectroscopy at a frequency in the GHz to THz range, which appears as an excess in the minima between the main structural peaks (α and β) and the boson peak.32,33 The frequency of this motion is perfectly aligned with the accessible energy range at BASIS, as illustrated by Figure 1 in the paper by Gupta et al.17 Spherical symmetry can be used to model the cage in our system, where the nearest neighbors compose the cage boundaries. Therefore, the diffusion inside a sphere model developed by Volino and Dianoux25 was chosen. This type of motion has been observed in a wide range of systems using QENS.16,22,23,34 Comparing the diffusion coefficients displayed in Table 1, OCT is observed to diffuse much more efficiently in the PC I phase rather than the low temperature PC II phase. For the PC I phase, Dα is approximately an order of magnitude larger, while Dβ is 3 times larger than in the PC II phase. In contrast, the lower temperature PC II phase in HEX has higher diffusion coefficients than the PC I phase for both processes. At first glance, this may seem surprising, since diffusion rates typically increase with temperature. However, this is due to a change in the local environment between the two phases which enables the molecules to diffuse more efficiently in the PC II phase. This may be attributed to the larger cage size in the PC II phase, as seen in Table 2. The diffusion coefficients for OCT and HEX have very similar values for both processes in their respective PC I phases. To our knowledge, diffusion coefficients for the temperatures measured in this paper have not been reported for either molecule. However, self-diffusion coefficients have been reported for HEX using the pulse field gradient nuclear magnetic resonance (PFG-NMR) technique F


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The Journal of Physical Chemistry B for the temperature range 350−440 K.35 Diffusivities measured by QENS are usually larger than those measured by PFGNMR, since these techniques measure different length scales.36,37 Neutrons probe length scales from a few Å to a few dozen Å, while PFG-NMR probes much longer length scales up to μm order. Extrapolating this data to lower temperatures gives an estimated value of Dα = 2.85 × 10−11 m2/ s for 280 K. We report a diffusion coefficient of (6.12 ± 0.56) × 10−11 m2/s at this temperature. Upon addition of OCT molecules into the HEX solution (80−20 mixture), both diffusion rates decreased by about half for 280 K. Dα for the mixture is now in close agreement with the extrapolated value for pure HEX from ref 17. At the temperatures below 280 K for the 80−20 mixture, the broadening for the α-process deviates from the DQ2 behavior and becomes Q-independent, which prevents diffusion coefficients from being calculated. As the temperature is decreased, it becomes increasingly more difficult for the molecule to overcome the jump barriers and the longrange diffusion becomes restricted. The molecule is confined to a lattice site where it can only participate in small scale motions, such as rotations. This feature can also be observed in the widths for the fast β-process in Figure 3d. For the highest temperature, 280 K, Γ(Q) covers a range from approximately 19 to 35 μeV with a clear diffusive relationship. However, this range becomes increasingly smaller as the temperature decreases and approaches a constant value at 230 K. At this temperature, Γ(Q) only varies from 25 to 29.5 μeV and is considered constant. We would like to briefly address the poor fitting results at the high Q-values for the slow process in HEX, as seen in Figure 2c. The jump diffusion model has a DQ2 dependence at low Q and plateaus to a value at high Q, as seen in OCT and the 80−20 mixture. However, the experimental observed Γ(Q) values decrease below the theoretical value given by the jump diffusion model at large momentum transfers for HEX. One cause for this is that the narrow Lorentzian was attempting to fit the elastic signal. The theoretical fit achieved using eq 1 was not perfect for these Q-values, and it is possible that the experimental line shape is not sufficiently described by Lorentzian functions. Another reason is due to the limitations of the jump diffusion model, which in many liquid and glass forming systems can only accurately describe data up to Q ≈ 1 Å−1.22,34 Above this point, measurements transition from observing the center of mass motion and focus on intramolecular motion instead. The assumption that the diffusive jumps are infinitesimally small becomes invalid. A more sophisticated model that includes the precise jump distances of the hydrogen atoms is necessary to model the diffusion in this momentum range. However, we are successful in explaining the low Q-values by the jump diffusion model. This enables us to accurately calculate diffusion coefficients by only using the low Q-values in the fitting procedure. The EISF for the lower temperatures, i.e., T < 240 K, was modeled using eq 4 for both OCT and the 80−20 mixture. The overall quality of the fit was relatively good, but the extracted length scales of RCage and RIntra were very small. This suggests that the motion is not diffusive and rather localized, since the molecule is confined to a lattice site. Attempts were made to fit this data with other models, such as rotational jumps on a circle, all of which proved to be unsuccessful in describing the data. We believe that one of these models should adequately explain the data and that the failure is due to the very low

quasielastic intensity measured at the low temperatures, which made the fitting procedure difficult. The values of RIntra displayed in Table 2 were extracted from eq 4. The values range from 0.7 to 1.17 Å, which is close to the C−H bond distance of 1.09 Å. The value for 0.7 Å is small but acceptable once the error of 0.356 Å is considered. This type of motion is attributed to the various small-scale motions of the hydrogen atoms about the carbon atoms. The effect of this motion in the data becomes more prominent at high Q, which is why we needed the extra correctional term in eq 4. Analyzing the weight parameters P1 and P2, there is the general trend that the parameter increases as the temperature is decreased. This is exactly what we would expect to see, since the weight parameter represents the fraction of hydrogen in the system that is considered immobile in the energy window of the observed relaxational process. As the temperature is lowered, the motion becomes frozen in and more hydrogen become immobile. The small values for P2 suggest that a large majority of the hydrogen is participating in the motion, which supports the idea that these are just small amplitude motions of the hydrogens around the carbon atom. The fast β-process has been thought to be a prerequisite for the α-process, since these small length scale relaxations can increase the free volume and open the cage. Confining the diffusive motion inside the cage will hinder the ability of the local environment to properly rearrange and cages will not sufficiently open to allow for long-range translational diffusion. As seen in Table 2, the average cage sizes, RCage, for HEX and OCT are determined to be 4.5 and 4.1 Å, respectively. The diameters of the molecules are approximately 4.96 and 5.9 Å for HEX and OCT, respectively. Considering the sizes of the OCT molecule and the cage, the molecule is free to move about its center of mass in any direction with an amplitude around 1 Å inside the cage. The HEX molecule has even more freedom than OCT to move around the cage, approximately 2 Å, which explains the observed faster dynamics. These distances seem reasonable in comparison to the mean-squared displacements derived from neutron scattering experiments on various glass formers.22,38,39 In one of these studies, Mamontov measured the glass former glycerol at BASIS to investigate the diffusive dynamics in the liquid state at 360 K.22 Identical to our investigation, two distinct motions were observed and attributed to a slower, long-range diffusion and a faster, cage rattling process. Using the diffusion within a sphere model, the calculated cage size, RCage, was determined to be 8.0 Å, which was close to the estimated cage size of 5.7−7.8 Å. As expected, this value is much larger than the values we report for HEX and OCT, since glycerol was measured in the liquid state. The main goal of this investigation is to determine how the dynamics change when a binary PC mixture is created. We have already reported the average cage sizes for the pure samples of HEX and OCT to be 4.5 and 4.1 Å, respectively. Upon addition of OCT into the HEX solution, the average cage size was reduced to only 2.8 Å. The HEX molecules are now largely confined to their lattice positions, with freedom to move approximately 0.3 Å in any direction. This increased confinement is most likely the reason why there is such a drastic decrease seen in the self-diffusion coefficients for the 80−20 mixture. The larger OCT molecules reduce the amount of free volume available for HEX movement inside the cage. This reduces the diffusion inside the cage and results in the less efficient formation of open cage doors for the particle to break free from the cage and contribute to the α-process. In this G



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framework, the fast β-process has a large effect on the success of the main structural relaxation in glass formers. This result supports the conclusion by Reuter et al. on the ionic conductivity in HEX−OCT binary PC mixtures.6 They observed a decrease in the ionic conductivity of Li ions in the system with increasing concentrations of the larger OCT molecules in the solution. They argued that this is due to a decrease in the reorientational relaxation times of the PC matrix. In the current investigation, we observed a decrease in two different translational diffusion processes, which, in addition to the slower rotation of the molecules, shows that the larger OCT molecules reduce the free volume and decrease the overall mobility of the smaller HEX molecules. This makes the PC matrix less efficient at conducting the Li ions. In addition, the features of increased phase stability and an extension of the temperature range for the PC phase, as observed in the HEX−OCT6 and HEPT−OCT10 systems, is probably a result of this increased confinement. While fitting the EISF with eq 5 is one way to estimate the cage size, there is a second method available that involves fitting Γ(Q) for the broad Lorentzian with eq 6 instead. Once Dβ is obtained, it can be inserted into eq 7 along with the plateau value of Γ(Q) at low Q. This will yield the confinement radius for the fast diffusion process. The values extracted from both methods are compared in Table 2. It is interesting that the distances from fitting Γ(Q), RΓ, are larger than those from fitting the EISF, RCage. However, both methods produce the same general result where the cage size for the 80−20 mixture is smaller than the pure samples. We believe that the RCage values are more realistic, since the amplitude of cage rattling should be less than the diameter of the particle in accordance with MCT.11,12 For PC materials, the ionic conductivity is dominated by the revolving door mechanism, especially at lower temperatures where translational movement is confined. Götz et al. argues that there should be no significant translational diffusion in PC systems, since the centers of mass are completely fixed on lattice sites with strict symmetry.40 This statement is true for low enough temperatures, such as the measurements at T < 240 K in this investigation. However, we have observed that there is significant translational movement in the PC phases at temperatures just below the liquid phase, i.e., T ≈ Tm − 40 K. The average position of the molecules is still considered to be positioned on lattice sites, but they can now make small amplitude motions inside the cage, as we have shown. The results in this paper show that the cage size influences both the fast, short-range diffusion inside the cage and the slower, longrange translational diffusion between cages. Manipulating the cage size, which is possible through the formation of a binary mixture of varying concentration, can be a useful tool for controlling the local environment in PC systems. This can be used to tune the ionic conductivity for PC-based, solid state ionic conductors. It should be noted that rotation of the molecules is still very important here, but we have demonstrated that manipulating the cage size can be an additional way to control the diffusion of ions in a PC system. Our findings confirm a clear change in the observed dynamics when the mixture is formed, and a more in-depth QENS investigation of this concentration dependent behavior is needed over a wide range of binary mixtures to obtain a generalized behavior in such PCs.

CONCLUSION In the present work, we have investigated the well-known PC systems of HEX and OCT in their pure forms and in an 80% HEX−20% OCT mixture using QENS. Two distinct center of mass motions were observed, i.e., long-range translational diffusion (α-process) and cage rattling (fast β-process). A jump diffusion model was employed to determine diffusion coefficients and residence times for each sample. It was found that the diffusion coefficients for both processes decreased upon the formation of the 80−20 mixture. The diffusion within a sphere model was applied to the EISF to determine the cage sizes for the fast β-process. The cage sizes were determined to be an average of 4.1, 4.5, and 2.8 Å for the OCT, HEX, and 80−20 mixture, respectively. The reduced diffusion coefficients for the 80−20 mixture are attributed to the increased confinement of the particle inside the cage, as observed by a reduction in cage size. A reduction in the rotational and translational mobility of the molecule hinders the ability of the PC matrix to efficiently conduct ions in this type of system. Therefore, manipulation of the cage size is possible by forming a binary PC mixture, which, by altering the concentration of the constituents, can be a useful tool to control the ionic conductivity in PC-based, solid state ionic conductors.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.8b03448.

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X-ray diffraction spectra for cyclooctanol to demonstrate the large coherent signal in the intermediate Q-range (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

E. Novak: 0000-0001-7813-1180 N. Jalarvo: 0000-0003-0644-6866 S. Gupta: 0000-0001-6642-3776 K. Hong: 0000-0002-2852-5111 S. Förster: 0000-0002-7323-2449 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

Research conducted at ORNL’s SNS and CNMS was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Financial support was provided by Jülich Center for Neutron Sciences (JCNS). S.G. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under EPSCoR Grant No. DE-SC0012432 with additional support from the Louisiana Board of Regents. T.E. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. We would like to thank Dr. Peter Lunkenheimer and Dr. Alois Loidl for their valuable discussions and Dana Vieweg for the X-ray diffraction measurements. H


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