Impedance spectroscopy studies of proton conductivity in imidazolium malonate

SOSI-14217; No of Pages 6 Solid State Ionics xxx (2017) xxx–xxx

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Impedance spectroscopy studies of proton conductivity in imidazolium malonate Paweł Ławniczak a,⁎, Katarzyna Pogorzelec-Glaser a, Adam Pietraszko b, Bożena Hilczer a a b

Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Okólna 2, 50-422 Wrocław, Poland

a r t i c l e

i n f o

Article history: Received 15 December 2016 Received in revised form 14 February 2017 Accepted 15 February 2017 Available online xxxx Keywords: Imidazolium malonate Proton conductivity Impedance spectroscopy Single crystal X-ray diffraction

a b s t r a c t Imidazolium malonate ɱstands out from other proton conducting compounds of nitrogen containing heterocyclic bases with dicarboxylic acids due to a presence of both ordered and disordered imidazolium in the crystal lattice. Our impedance spectroscopy studies of electric conductivity revealed that in the range 273 K ≤ T ≤ 318 K the dc conductivity is characterized by an activation energy of Ea1 = 0.50 eV and the activation energy decreases to Ea2 = 0.17 eV at temperatures 318 K ≤ T ≤ 358 K. Single crystal X-ray diffraction studies showed that imidazolium malonate has the same triclinic structure with P-1 space group and rather high thermal displacements factors at 280 K as well as at 340 K. The results suggest that the low-temperature activation energy can be ascribed to phonon assisted 180° flipping of ordered imidazolium cations, observed earlier in NMR experiments. The ‘fast-like diffusion’ of protons in the high temperature range we consider to be due to the presence of disordered imidazolium cations enhanced by high thermal displacements. © 2017 Elsevier B.V. All rights reserved.

1. Introduction A search for materials with fast proton transport in anhydrous conditions focused the attention on nitrogen containing heterocycles and proton conducting ionic liquids [1–5]. As hydrogen bonding is the most important interaction controlling the crystal structure of organic molecules we have synthesized compounds of imidazolium and benzimidazolium with various dicarboxylic acids HOOC\\(CH2)n\\COOH (n = 0, 1, 2, 3, 4, 5, 7 and 8).The two carboxyl groups of the alkanediacids facilitated formation of crystals with various base-to-acid ratio and we have studied hydrogen bond network, crystal structure and ac electric conductivity of the compounds [6–12]. Rich architecture of the imidazolium (Im) salts with dicarboxylic acids has been earlier studied by MacDonald et al. and classified into four types of layer-structure with different N\\H⋯O and O\\H⋯O bond network and chain orientation [13]. The imidazolium, as well as the benzimidazolium cations, in all the compounds studied were found to be well ordered in the crystal lattice with only one exception of Im salt with malonic acid (n = 1) [6–13]. Two kinds of Im cations ordered and disordered were found in imidazole malonate (Im-MAL) at room temperature [6] and the exceptional structure of the salt has been confirmed later at 120 K [14]. The disordered imidazolium species have been also observed in 13C{1H}CP/MAS NMR spectrum of Im-MAL [15]. Moreover, the NMR studies of molecular motions revealed that above 263 K the ordered Im cations undergo an ⁎ Corresponding author. E-mail address: [email protected] (P. Ławniczak).

180o flip around the pseudo 2-fold axis with an activation energy of 58 ± 6 kJ/mol. The activation energy obtained from the Arrhenius plot of Im flipping rate in the temperature range 263–318 K was lower than that of 72 kJ/mol reported by us from electric conductivity measurements in the range 230 K–303 K [6]. To get more information on the relationship between structure, molecular dynamics and proton diffusion in the Imcations compound, containing only three carbon atoms in the diacid chain and well defined ordered and disordered Im-cations, we measured electric conductivity in the frequency range 1 Hz–10 MHz at temperatures from 273 K to 358 K. Single crystal X-ray diffraction studies of ImMA were performed at 280 K and 340 K. 2. Experimental Imidazolium malonate salt was obtained by dissolving imidazole (Fluka, 98%) and malonic acid (Aldrich 98%) in distilled water at room temperature. The crystallization of the salt was carried out by slow evaporation of the solvent at room temperature and plate-like ImMAL crystallites of ~5 mm in length and ~0.3 mm thick were obtained. For electric measurements the crystallites were pressed (P = 30 MPa at T = 293 K) into the form of pellets and the surfaces of the samples were covered with a silver paste (Hans Wolbring). Electric conductivity measurements of polycrystalline Im-MAL samples were performed by means of impedance spectroscopy. Complex impedance of the samples was measured using an Alpha-A High Performance Analyzer (Novocontrol GmbH) within frequency range 1 Hz– 10 MHz and temperature range from 273 K to 358 K with voltage

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oscillations of ± 1 V. The temperature was controlled using a Quatro Cryosytem with an accuracy better than ±0.1 K. Single crystal X-ray diffraction studies of Im-MAL were performed on an X'calibur diffractometer (Rigaku - Oxford Diffraction Company) with MoKα radiation at 280 K and 340 K. Integration, scaling and absorption corrections were made with CrysAlis program 171.38.141 version, corrected for Lorentz polarization. The crystal shape was optimized by using an X-Shape program. The structure was solved with SHELXS97 program and refined using full-matrix least-squares methods. Subsequent structure refinements were carried out using JANA2006 program with all measured reflections included up to 0.75 Å. 3. Results and discussion 3.1. Temperature variation of electric conductivity Electric properties of Im-MAL compound were studied by impedance spectroscopy method and due to rather low dimensions of the crystals grown we performed the measurements on polycrystalline samples. Fig. 1 shows Z″ (Z′) dependences for Im-MAL at 293.2 K and 353.2 K (Z″ denotes the imaginary part and Z’ the real part of complex impedance Z*). In the frequency window from 1 Hz to 10 MHz the complex impedance plots consist of two semicircles. The high frequency semicircle is correlated with the interior of grains/crystallites (gi), whereas the low frequency semicircle is related to the grain boundaries (gb). The measured complex impedance Z* can be described by connected in series two double RC parallel circuits: Z
ðωÞ ¼

R1 1 þ ðiωR1 C 1 Þ1−α 1

þ

R2 −R1 1 þ ðiωðR2 −R1 ÞC 2 Þ1−α2

ð1Þ

where R1 denotes the resistance of the first contribution, R2 is the resistance of the sum of both contributions (the grain interiors gi and the grain boundaries gb), C1 and C2 denote electric capacities of the two circuits, α1 and α2 are the parameters, ω = 2πf is angular frequency of the

measuring field. The parameters obtained from fitting the experimental data can be used also to resolve the two contributions in the frequency dependences of the real Z′ and the imaginary Z″ part of complex impedance Z*. Fig. 2 shows an example of frequency dependences of Z′ and Z″ with the contributions of the grain interiors (gi) and the grain boundaries (gb) at the temperature of 293.2 K. The both contributions (gi and gb) were found to vary with temperature. Temperature variation of effective dc conductivity of the polycrystalline sample as well as those of the grain interior and the grain boundary contributions resolved by fitting the experimental data are shown in Arrhenius plot in Fig. 3. Two activation energies can be distinguish in the Arrhenius plot: Ea1 = 0.50 eV in the temperature range from 273 K to 318 K and Ea2 = 0.17 eV at higher temperatures, between 318 K and 358 K. The low temperature activation energy Ea1 obtained here by us is lower than that reported earlier (0.75 eV) but for temperatures 230 K ≤ T ≤ 303 K covering also the range without imidazolium ion flipping [6]. It should be however observed that Ea1 = 0.50 eV is also lower than the activation energy Eflip = (58 ± 6) kJ/mol = (0.60 ± 0.06) eV reported by Mizuno et al. for 180o flipping motion of ordered imidazolium ions in the temperature range 263 K ≤ T ≤ 318 K [15]. On heating the samples above 318 K one observe a considerable decrease in the activation energy, which up to 358 K attains the value of Ea2 = 0.17 eV. The low activation energy is considered as characteristic of the fast ion transport, which should be conditioned by a change in molecular or lattice dynamics or structure. In inorganic acid salt, for instance in AHXO4 and A3H(XO4)2 families (A = Rb, Cs, NH4 and X = S, Se) fast proton transport in the superionic phase is related not only to proton disorder in the O\\H ⋯ O bonds but also to high thermal displacement of the atoms [16,17]. To yield information on thermal displacement in the two temperature ranges characterized by different activation energies Ea1 and Ea2 we performed single crystal X-ray diffraction studies of Im-MAL at 280 K and 340 K and determined thermal displacements factors of the atoms. More detailed studies of the crystal structure are already finished and will be published in near future. The fitting procedure enabled us to resolve the contributions from grain interiors (gi) and from grain boundaries (gb) to total dc conductivity of the polycrystalline sample. In Fig. 3 one can observe that in the low temperature range the conductivity related to the interior of the grains σ'gi (bulk conductivity) is higher than that of the grain boundaries σ'gb. Above ~ 318 K the situation becomes reversed and the differences between σgi and σgb are rather small. It is worth to mention that the polycrystalline sample should be considered as a composite the properties of which are determined not only by the properties and volumetric ratio of constituent phases but also by their connectivity as well as by interfaces, grain sizes and shapes. Though the way in which different phases are interconnected is the most important the mixing rule of a given property is highly complicated [18,19]. 3.2. Frequency dependence of electric conductivity To obtain more information on the proton dynamics in Im-MAL, we have focused our attention on the electric conductivity dispersion. Frequency dependences of measured conductivity at selected temperatures are shown in Fig. 4. As suggested by Almond and West [20,21] the frequency dependence of electric conductivity in ion-conducting materials can be nicely fitted with experimental equation suggested by Jonscher [22,23]:   n  f σ0ac ¼ σ dc 1 þ f0

Fig. 1. Nyquist plots of polycrystalline Im-MAL sample at various temperatures; the points represent the measured data, whereas the red line shows calculated total impedance of the sample, the magenta line presents fitted data for the grain interiors and blue line – fitted data for grain boundaries. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

ð2Þ

where σdc denotes the dc conductivity, f is the frequency of measuring field and n is frequency exponent, typically in the range 0.6 b n b 1 [24]. The frequency-dependent conductivity σ'ac is a sum of frequency independent σdc conductivity and a part the frequency dependence of

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Fig. 2. Frequency dependences of the real part of impedance Z′ and the imaginary part Z″ for polycrystalline Im-MAL salt at 293.2 K; circles are the results of the measurements, the curves are obtained from fitting with the same parameters as in Fig. 1.

which is described by fractional power law. The frequency f0 marks an onset of the dispersion and corresponds to the time interval at which the correlated backwards hopping ends and random macroscopic diffusion sets in [25]. At sufficiently low frequencies (below f0) the conductivity is almost frequency independent, whereas at higher frequencies the frequency dependence of electric conductivity is described by the fractional power law. The frequency f0, at which the conductivity rapidly increases, is temperature dependent and moves toward higher frequencies with increasing temperature. The ac conductivity at various temperatures T can be scaled into a ‘master curve’. We have used so-called Summerfield scaling method [26] with relation   σ 0ac f ¼F σ dc T σ dc

ð3Þ

The scaled experimental conductivity spectra are shown in Fig. 5. The canonical scaling takes a shape of the master curve presented and the vertical and horizontal scales are related by σdcT ∝ f0 [27]. In contrast to previously presented results for benzimidazolium azelate (BIm-AZE) [10] the scaled data do not superimpose into a single master curve in the high-frequency range at temperatures below 318 K. At temperatures T N 318 K the scaled ac conductivities perfectly overlap

each other into a single master curve, and the only visible effect of the temperature is to speed up or slow down the hopping motion of the ions on heating or cooling the sample. The deviation in the lowtemperature region from the behavior reported for BIm-AZE we would like ascribe to the difference in the structure. BIm-AZE, with 2:1 base:acid stoichiometry, has all benzimidazolium cations ordered and involved in N\\H ⋯ N and N\\H ⋯ O bonds, which with O\\H ⋯ O bonds between the anions form a layer-type structure. However, in the layer-type architecture of Im-MAL two imidazolium cation are well ordered and involved in N\\H ⋯O hydrogen bonds, whereas the third Im cation is disordered also at low temperatures [6,14]. It seems that at temperatures above ~318 K another factor than the cation disorder becomes more important in proton diffusion. As the electric conductivity was measured for polycrystalline samples we tried to characterize the conductivity related to the grain interiors σgi and that due to the grain boundaries σgb. Scaling of the both contributions was made similarly to the procedure used for σ'ac and the real part of the both contributions σ'gi and σ'gb can be calculated using following equations:

σ0gi ¼

σ0gb ¼

Fig. 3. Arrhenius plot of dc conductivity for Im-MAL. Circles denote total dc conductivity of the polycrystalline sample, magenta line – conductivity of the grain interiors and blue line – conductivity of grain boundaries. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

1

d 2

Z01 ð f Þ þ Z″1 ð f Þ =Z01 ð f Þ S 1

d 2

Z02 ð f Þ þ Z″2 ð f Þ =Z02 ð f Þ S

ð4Þ

ð5Þ

Fig. 4. Frequency dependences of electric conductivity of Im-MAL polycrystalline sample at various temperatures measured on heating.

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the dispersive region reveal that the ion hopping in highly disordered grain boundary phase is temperature dependent.

3.3. Crystal structure at 280 K and 340 K

Fig. 5. Master plot for Im-MAL sample obtained using ‘Summerfield scaling method’.

where Z′1 and Z″1 are the values of real and imaginary part of the impedance in the high frequency range, Z′2 and Z″2 – impedances in the low frequency range, d – thickness and S – surface area of the sample. Master plots of the σ'gi and σ'gb conductivities, obtained from fitting, are presented in Fig. 6. The ac conductivity axis is scaled by respective dc conductivities, whereas the frequency axes is scaled by temperature and dc conductivity of the grain interior or the grain boundaries. One can observe a difference in the shape of master curves of the both contributions. Scaled ac conductivity of the grain interior phase σ'gi was found to obey the time-temperature superposition, which points to the same mechanism of proton hopping [25], whereas the master curve for σ'gb shows visible temperature dependence. Changes in the slope of the master curve in

Fig. 6. Master plots of fitted σ'gi and σ'gb conductivity contributions of Im-MAL at selected temperatures.

As it has been reported earlier the structure of Im-MAL is of layertype and belongs to triclinic system with P-1 space group and Z = 2 at room temperature and at 120 K [6,14]. Our electric conductivity studies of the compound have shown that in the temperature range from 273 K to 358 K the electrical transport is characterized by two different activation energies (Fig. 3) but differential thermal calorimetry studies did not reveal any endothermic anomaly related to a phase transition. Since phonon assisted fast proton diffusion has been observed by us in several acid salts [16,17] we performed single crystal X-ray diffraction studies at 280 K and 340 K to yield information on thermal displacement factors in Im-MAL crystals. The architecture of Im-MAL crystals at 280 K and 340 K was found to be the same as at lower temperatures. The unit cell contains: two acid molecules linked with O(4)\\H⋯O(4) bond, two ordered imidazolium ions and one disordered imidazole ring occupying two symmetrically equivalent positions with the probability of 0.5. The layers, parallel to (− 2 − 11) plane, contain imidazolium cations and oxygen atoms O(1) and O(2) of carboxyl group of the malonic acid. The disordered Im ring is attached to the carboxyl group by N(1B1)\\H ⋯ O(1) and N(1B2)\\H⋯O(2) hydrogen bonds and linked with two ordered Im cations with O(1)⋯H\\N(1A1) and O(2)⋯H\\N(1A2) bonds. The three-

Fig. 7. Fragments of layers in Im-MAL crystal with O4\ \H4… O4 bond in projection onto the (−3 2 1) and onto the (−3 7 −4) plane at 340 K.

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approximation (ellipsoid) was used for imaging thermal vibrations of other atoms. The N\\H⋯O and O\\H ⋯O hydrogen bonds are marked by red dotted lines and the pictures were obtained with “Diamond 3.2” program. Fig. 8 shows the space filling representation of the projection of the Im-MAL structure on the plane normal to the triclinic a axis at 280 K and 340 K. One can observe an increase in the thermal vibrations of all atoms on rising the temperature from 280 K to 340 K (Table 1). The refinement of the Im-MAL crystal structure at 8 temperatures has been already finished and the results will be published in near future together with joint probability density functions and one particle potential. 4. Summary and concluding remarks

Fig. 8. Projection of Im-MAL structure on the plane normal to the triclinic a axis at 280 K and 340 K in the space filling representation.

dimensional structure of Im-MAL crystal consists of sandwiches composed of two layers rotated by 180° around the triclinic a axis. Fig. 7 shows graphic representation in space filling model of a fragment of a single layer in projection onto the (− 3 2 1) plane and a fragment of the arrangement of neighboring layers in the 3D structure of Im-MAL crystal. The atoms are in form of spheres with diameter proportional to that of real atoms. Thermal vibrations of hydrogen atoms are given in an isotropic approximation (spheres), whereas anisotropic

Imidazolium malonate appears as an exception among proton conducting salts of heterocyclic basis with dicarboxylic acids due to the presence of both ordered and disordered cations in the crystal lattice. We performed electric conductivity studies of polycrystalline Im-MAL pellets by means of impedance spectroscopy in the temperature range 273 K–358 K and analyzed the contributions of grain/crystallite interiors and grain boundaries to the total conductivity of the sample. Dc conductivity of Im-MAL was found to be characterized by two different activation energies: Ea1 = 0.50 eV at low temperatures, from 273 K to 318 K, and Ea2 = 0.17 eV at temperatures in the range 318 K ≤ T ≤ 358 K. From NMR studies [15] it is apparent that the ordered imidazolium cations undergo 180o flipping around the pseudo 2-fold axis in the low temperature range (staring from 263 K) however, the activation energy of the motion was assessed as Eflip = (0.60 ± 0.06) eV i.e. higher than the Ea1 value from our impedance studies. Moreover, calculated conductivity value (1·104 S/m) due to imidazolium flipping at 303 K was ~3.5 times lower than that measured by us by means of impedance spectroscopy (Fig. 4). The difference may suggest another factor to be involved and to facilitate the proton diffusion, particularly because at higher temperatures we observed even a decrease in the activation energy to Ea2 = 0.17 eV. Following our experiences with fast proton transport in acid salts [16,17] we have looked for the effect of anisotropic thermal displacement (especially in the case of atoms involved in hydrogen bonding) and performed single crystal diffraction studies of Im-MAL at 280 K and 340 K. As shown in Table 1 thermal displacement factors at 280 K are rather high and in this respect they can explain higher conductivity value and Ea1 b Eflip. We consider however, that by no means the 20–30% increase in displacement factors on heating to 340 K could be taken as a reason of the observed ‘fast-like proton diffusion’ above 318 K. As so low activation energy (Ea2 = 0.17 eV) we have not found in other compounds of nitrogen containing heterocyclic bases with dicarboxylic acids [7–12] we propose that the ‘fast proton diffusion’ in Im-MAL is facilitated by the disordered imidazolium cations. Acknowledgements One of us (P.Ł.) acknowledges the financial support from the National Science Centre in Poland (grant no. 2014/15D/ST3/03433).

Table 1 Anisotropic thermal displacement parameters Uij of atoms (Å2 × 103) in Bi-MAL crystals at 280 K and 340 K. 280 K

O(1) O(2) N(1A1) N(1A2) N(1B1) N(1B2)

340 K

U11

U22

U33

U23

U13

U12

U11

U22

U33

U23

U13

U12

67.6(3) 70.4(4) 47.7(3) 48.6(3) 54.3(8) 55.4(8)

34.1(2) 40.4(2) 37.3(3) 33.6(3) 27.0(5) 29.5(5)

28.6(2) 24.6(2) 25.0(2) 27.9(2) 31.5(5) 26.9(5)

11.08(2) 11.08(2) 09.2(2) 08.6(2) 12.7(4) 13.8(4)

8.0(2) 7.4(2) 6.0(2) 7.7(2) 3.6(5) 4.0(5)

15.7(2) 18.2(2) 06.9(3) 08.1(3) 08.1(5) 06.8(5)

84.0(0) 89.5(5) 60.9(5) 63.3(5) 67.8(11) 70.7(11)

44.4(3) 51.9(3) 47.7(4) 41.7(4) 33.7(7) 35.0(7)

34.5(3) 30.4(3) 30.7(3) 35.6(3) 35.8(7) 32.1(6)

14.2(2) 14.0(2) 11.0(3) 10.6(3) 12.8(5) 15.1(5)

08.8(3) 09.9(3) 12.2(3) 11.0(3) 02.8(7) 04.6(7)

20.1(3) 24.9(3) 25.5(4) 12.9(4) 08.9(7) 08.9(8)

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Please cite this article as: P. Ławniczak, et al., Impedance spectroscopy studies of proton conductivity in imidazolium malonate, Solid State Ionics (2017), http://dx.doi.org/10.1016/j.ssi.2017.02.013