Time–Temperature Scaling of Conductivity Spectra ... - ACS Publications

Letter pubs.acs.org/JPCL

Time−Temperature Scaling of Conductivity Spectra of Organic Plastic Crystalline Conductors Supti Das and Aninda J. Bhattacharyya* Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India ABSTRACT: Organic plastic crystalline soft matter ion conductors are interesting alternatives to liquid electrolytes in electrochemical storage devices such as lithium-ion batteries. The solvent dynamics plays a major role in determining the ion transport in plastic crystalline ion conductors. We present here an analysis of the frequency-dependent ionic conductivity of succinonitrile-based plastic crystalline ion conductors at varying salt composition (0.005 to 1 M) and temperature (−20 to 60 °C) using time−temperature superposition principle (TTSP). The main motivation of the work has been to establish comprehensive insight into the ion transport mechanism from a single method viz. impedance spectroscopy rather than employing cluster of different characterization methods probing various length and time scales. The TTSP remarkably aids in explicit identification of the extent of the roles of solvent dynamics and ion−ion interactions on the effective conductivity of the orientationally disordered plastic crystalline ion conductors. SECTION: Liquids; Chemical and Dynamical Processes in Solution

O

and polymer ion conductors.10,11 However, compared with polymer ion conductors the plastic crystalline electrolytes are spatially homogeneous (absence of simultaneous presence of amorphous and crystalline domains in the same sample), thus providing a more accurate evaluation of contribution of solvent dynamics and ion−ion/solvent interactions as a function of temperature and composition. Prior to sample preparation, lithium perchlorate (LiClO4, lithium battery grade, Chemetall) was heated to 110 °C under vacuum for the removal of physisorped water and succinonitrile (SN, Aldrich) was sublimated twice to remove impurities. Requisite amount of LiClO4 (x = (0.005−1) M or (0−7) mol %) was added to molten SN (Tm ≈ 60 °C) and stirred at 60 °C under a dry N2 atmosphere until a homogeneous transparent mixture was obtained. All samples (LiClO4−SN) were stored in glass vials under vacuum at room temperature until further usage. For conductivity measurements as a function of temperature (range: −20 to 60 °C; liquid circulator thermostat−Julabo FP50MC), molten LiClO4−SN samples were poured in between two stainless-steel electrodes of an airtight home-built conductivity cell (cell const ≈ 0.05 cm−1). The conductivity cell was assembled inside an argon-filled glovebox (MBraun MB 20G LMF; water: < 0.1 ppm) and was inserted into a glass jacket having provisions for measuring under static vacuum (1 mbar). Ionic conductivity versus temperature was estimated using ac-impedance spectroscopy (Novocontrol

rganic plastic crystalline ion conductors,1−3 which also include the ionic liquids,4,5 have been the subject of intensive investigations due to their tremendous potential in electrochemical energy storage systems such as rechargeable batteries.6 Several organic plastic crystalline materials have excellent solvating properties, giving rise to high ionic conductivities in the solid state at ambient temperature. In this light, an important example is succinonitrile (C2H4(CN)2, abbreviated as SN).1,7,8 Versatile physical properties of SN make it a suitable organic solid solvent for dissolution of a wide range of monovalent and higher valent salts. Ion transport in SN-based ion conductors is not clearly understood. General understanding is based on the fact that ion transport in the conducting plastic phase is intrinsically related to the isomer (trans ↔ gauche) dynamics. It is proposed that the presence of SN in the trans isomer conformation in the plastic phase leads to the creation of defects (or spaces),9 which provide highmobility pathways to the free charge carriers. (Below the plastic-to-normal crystalline transition temperature, Tnp (≈ −30 °C), SN is bereft of dynamics and exists in the gauche conformation and conductivity is low). However, this is not conclusive because at the length and time scale of the mobile ions the orientationally disordered host resembles conventional liquids and factors such as ion−ion/solvent interactions play an important role in determining the overall effective conductivity. We demonstrate here that influence of solvent dynamics and ion−ion interactions on ion transport in SN-based ion conductors can be explicitly obtained from appropriate scaling of the frequency-dependent ionic conductivity, σ(ν). In the realm of ionics, a similar approach has been adopted previously to account the role of host dynamics in ion transport in glass © 2012 American Chemical Society

Received: October 28, 2012 Accepted: November 16, 2012 Published: November 16, 2012 3550

dx.doi.org/10.1021/jz301742z | J. Phys. Chem. Lett. 2012, 3, 3550−3554

The Journal of Physical Chemistry Letters

Letter

Alpha−A) over the frequency range ((1 to 3) × 106) Hz (signal amplitude = 0.05 V). Figure 1A is a log−log plot of the real part of the complex conductivity (σ′(ν)) as a function of frequency (ν) at various

cases, the spectra can be shifted on both the conductivity and frequency scales to superimpose all σ′(ν) versus ν curves at different temperature spectra to a single curve, the so-called “master curve”. This is usually referred to as the time− temperature superposition principle (abbreviated as TTSP). Application of TTSP implies that at different temperatures frequency-dependent conductivities display identical profiles. Different approaches have been proposed to superimpose the individual temperature−conductivity spectrum. Superposition of the real part of the complex conductivity σ′(ν) can be achieved via a suitable scaling procedure, which can be expressed as: σ ′(ν)/σ dc=F(ν /ν0)

(1)

Here σdc denotes the dc conductivity, F is a scaling function that is independent of temperature, and ν0 is an individual scaling parameter for each conductivity isotherm. An important point for concern is the suitable choice of ν0 for each σ′(ν) versus ν curve required to superimpose the spectra measured at different temperature for generation of a “master curve”. Among various approaches, the most effective approach is to address the frequency scaling parameter, ν0, according to the definition proposed by Kahnt.15 ν0 is assigned as the onset frequency of the conductivity dispersion, ν*, such that

σ ′(ν*) = 2σdc

(2)

In the widely used “Summerfield scaling”,16,17 the frequency scaling parameter, ν0, is chosen as σdcT for a given composition at different temperature. Therefore, σdcT and ν* are proportional to each other in the Summerfield scaling, implying that the transport mechanism does not change with temperature. Thus, in this case, the scaling function in eq 1 can be expressed by

σ ′(ν)/σ dc=F(ν /σdcT )

Figure 1. (A) Frequency-dependent ionic conductivity of 0.005 M LiClO4−SN at various temperatures. The black round symbols mark the onset frequencies of dispersion (ν*), defined via σ′(ν*) = 2σdc. (B) Time−temperature superposition principle (TTSP) of ionic conductivity spectra using Summerfield scaling obtained from the corresponding spectrum at a particular temperature (T) of panel A.

(3)

On the other hand, according to the more general “Baranovskii and Cordes scaling”, ν0 is equal to (σdcTT−α) for a given composition at different temperatures, where α symbolizes the Coulomb interaction between mobile ions.18−21 Therefore, the “Summerfield scaling” is a special case of “Baranovskii and Cordes scaling” with α = 020 in

temperatures for 0.005 M LiClO4−SN (0.035 mol % or 0.05 wt %). Very low-frequency (ν ≤ (1 to 10−2) Hz) conductivity values show deviations from the expected low-frequency plateau. Lower conductivity is attributed to the prominent polarization effect typically observed in ion-conducting materials. However, the deviations are significantly less at lower temperature (T ≈ −20 °C) because these are much closer to the plastic-to-normal crystalline transition temperature, Tnp (≈ −30 °C). Following this regime, the conductivity is observed to be frequency-independent and assumes a constant value, known as the dc value, σ′ = σdc. The frequency range of the plateau that implies macroscopic long-range transport is observed to depend very much on temperature. The dc conductivity, σdc, is obtained by fitting the data to an appropriate model equivalent circuit consisting of a parallel combination of a constant phase element (Q) and an ohmic resistance (R), as discussed ref 12. With further increase in ν, σ′(ν) displays strong frequency dispersion above a characteristic frequency. The onset of conductivity dispersion shifts to higher frequency with increasing temperature. Many materials exhibit a temperature independent profile of the conductivity spectra13,14 at frequencies less than a few megahertz. In such

ν0 = ν* ∝ σdcTT −α

(4)

Roling et al. have also shown ν0 to be proportional to (σdcT/x) at an arbitrary temperature with different composition, where (x) is mole fraction of mobile ions.10 Several studies have reported the application of this “Summerfield scaling” procedure to the conductivity spectra of ion-conducting glasses.10,22−24 The advantage of this scaling law is that σdc and temperature are directly obtained from experiments and not determined arbitrarily. We concentrate now on the applicability of the scaling concept to LiClO4−SN plastic crystalline ion conductors, as discussed above. A linear behavior between log(σdc) and log(ν*) is observed and shown in Figure 1A. The slope of the straight line connecting the onset frequencies (ν*) with σdcT is estimated to be equal to one in dilute salt concentration sample (i.e., 0.005 M LiClO4−SN). This shows the direct proportionality between σdcT and ν*. A “master curve” was generated from the spectra by shifting them along both the axes (i.e., dividing the experimental σ′(ν) by σdc and ν by σdcT). Figure 1B displays the “master curve” (superimposition of σ′(ν) data), 3551

dx.doi.org/10.1021/jz301742z | J. Phys. Chem. Lett. 2012, 3, 3550−3554

The Journal of Physical Chemistry Letters

Letter

Figure 2. Frequency-dependent ionic conductivity of (A) 0.04 M LiClO4−SN and (B) 1 M LiClO4−SN at different temperatures. The black round symbols mark the onset frequencies of dispersion (ν*), defined via σ′(ν*) = 2σdc. (C,D) TTSP of ionic conductivity spectra using Summerfield scaling obtained from the corresponding spectrum at a particular temperature (T) of panels A and B, respectively.

increase in conductivity with temperature for the electrolyte with dilute (0.005 M LiClO4−SN) salt concentration is due only to the increase in mobility of ions. The increase in temperature results in an increase in trans ↔ gauche isomer dynamics, leading to increase in ionic mobility and hence conductivity.25 Now let us turn to the samples with higher salt concentrations such as (0.04 to 1) M LiClO4−SN. We observe that σdc is no longer directly proportional to the onset frequency and increases more strongly than ν*(T), as depicted in Figures 2A,B. The slope of the straight lines connecting the onset frequencies of dispersion (ν*) with σdcT is observed to exceed one, being in the range 1.10 to 1.32. At higher concentrations the spectra at different temperatures cannot be superimposed to a master curve using the Summerfield scaling principle (Figure 2C,D). Rather, the high salt concentration is analyzed using a scaling principle suggested by Baranovskii and Cordes (abbreviated as BC; eq 4).20 The difference between Summerfield and BC is that the BC procedure introduces an additional factor Tα to generate the master curve. As a result, Summerfield follows as a special case with α = 0 as previously mentioned. The deviation from Summerfield scaling was reported for the first time by Murugavel and Roling19,21 for single ion-conducting glasses. Roling in ref 18 elaborated the BC scaling approach using the random barrier model with and without Coulomb interactions between the particles. The value of α has been accounted to be closely related to the strength of Coulomb interactions between

resulting from the usage of the Summerfield scaling formulation to 0.005 M LiClO4−SN sample. Scaling is observed to work well for all frequencies except at low frequencies, where electrode polarization effects dominate. The scaling, in particular, is observed to be not very effective in the lowtemperature regime of (−20 to 0) °C because this is in the close proximity of the transition from plastic (trans ↔ gauche) to normal (gauche) crystalline phase.25 However, this inability does not affect the key investigation issues of the present work. So, in the dilute salt concentration regime, the Summerfield scaling is satisfied, implying that the increase in temperature does not have any affect in the ion conduction mechanism. The temperature dependence of the ionic conductivity can be written as the product of the number density of the mobile ions (N), their mobility (μ), and their charge (q) according to σ(μ , T ) = N (T )μ(ν , T )q

(5)

The increase in ionic conductivity with temperature can have different implications: it may be due to an increase in the number density of mobile ions (N) or the mobility of the charge carriers (μ). As previously discussed in the case of Summerfield scaling, σdcT is proportional to ν* at constant number density (N). The condition for constant number density exists only when the degree of dissociation → 1; that is, all salt has dissociated into free cations and anions in the plastic crystalline matrix and temperature does not have any additional effect. Such a situation will prevail at low salt content as in 0.005 M LiClO4−SN. Therefore, it is highly likely that the 3552

dx.doi.org/10.1021/jz301742z | J. Phys. Chem. Lett. 2012, 3, 3550−3554

The Journal of Physical Chemistry Letters

Letter

ions.18,26 According to the theoretical model suggested by Roling et al., the negative exponent (α) value implies the absence of Coulomb interactions between mobile ions, whereas with increasing Coulomb interactions the exponent value increases and tends to zero (Summerfield scaling). They also showed (experimentally) that α can take the positive values in the case of ion-conducting inorganic glasses exhibiting high electronic polarizabilities.26 Figure 3A,B shows the conductivity

implies the increase in characteristic mean-square displacement (with time) of the mobile ions, ⟨r2(t*)⟩ (where t* = 1/2πν*) with temperature. The mean-square displacement gives an important basis for understanding of the physical meaning of different scaling approaches. The increase in ⟨r2(t*)⟩ with temperature means that either there is an increase in the number density of mobile ions or there is a decrease in the number of accessible paths for percolation of the ions with increasing temperature.26 In case the number density of mobile ions gets thermally activated, more number of ions would become mobile with increasing temperature and therefore contribute to the dc conductivity or long-range transport. Conversely, the number of accessible paths for the ion transport can decrease due to the structural rearrangements or an increased local mobility of chain segments with increase in temperature. This could block some pathways of ions, aiding an increase in the characteristic mean-square displacement. The second type is observed in polymer ion conductors or polyelectrolytes, where the segmental motions of the chains alter with the increase in temperature. In the case of plastic crystalline ion conductors, which are composed of small molecules, blocking effects of chain segments with temperature are absent. This implies that the increase in conductivity with temperature can be attributed to the increase in the number density of mobile ions (arising from dissociation of ion-pairs) in the case of electrolytes with 0.04 to 1 M salt content. This implies that in the high salt concentration regime temperature dependence of ion−ion interaction plays a dominant role in determining the overall effective conductivity of plastic ion conductors. In conclusion, the TTSP suggests that the increase in temperature does not affect the isomer dynamics-mediated ion transport in dilute salt concentration (≤0.005 M) regime. Because of negligible ion association, temperature increases ionic mobility, that is, ion dynamics on all time and length scales. However, at high salt concentrations (0.04 to 1 M) where the ion association is substantial, the increase in temperature leads to splitting of ion pairs and thus an increase in mobile ions. This factor predominates isomer dynamics and is the main contributor to ionic conductivity. We have convincingly established here that scaling analysis of the frequency-dependent ionic conductivity provides a suitable alternative to probe the ion transport mechanism in soft matter ion conductors, especially the orientationally disordered plastic crystalline conductors. The analysis provides explicit insight (compared with other involved methods such as X-ray diffraction and Brillouin scattering25,28) on the various factors and their relative importance (as a function of composition and temperature) on ion transport in disordered soft matter ion conductors. In the future, it would be greatly beneficial to estimate the transition from one ion transport mechanism to another in terms of a concentration threshold from the scaling formalism. This can be achieved only if the scaling procedure involves a mechanism for tackling the salt concentration in the electrolyte.

Figure 3. Scaling of conductivity spectra using Baranovskii and Cordes procedure: (A) 0.04 M LiClO4−SN and (B) 1 M LiClO4−SN electrolytes.

spectra of 0.04 M LiClO4−SN and 1 M LiClO4−SN, respectively, scaled using the BC procedure. The spectra at different temperature could be conveniently superimposed to a master curve, and the time−temperature superposition principle is very well-fulfilled. Slight deviations at low-frequency regime are due to polarization effect, as previously discussed in the case of 0.005 M electrolyte. However, the deviations are observed to be much less at higher salt concentration samples. This is attributed to further lowering of the plastic-to-normal crystalline transition temperature,27 thus ensuring a monophasic sample in the temperature and composition regime for the conductivity measurements. The positive value of the α exponent (∼0.01 to 0.15, depending on temperature and salt concentration) implies an increase in Coulomb interaction with increasing salt concentration.18 Additionally, a positive value of α exponent in high salt concentration electrolytes indicates that the temperature dependence of ν* is not much more pronounced than that of σdcT. On a microscopic scale, α > 0

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +91 80 22932616. Fax: +91 80 23601310. Notes

The authors declare no competing financial interest. 3553

dx.doi.org/10.1021/jz301742z | J. Phys. Chem. Lett. 2012, 3, 3550−3554

The Journal of Physical Chemistry Letters

■

Letter

(20) Baranovskii, S. D.; Cordes, H. On the Conduction Mechanism in Ionic Glasses. J. Chem. Phys. 1999, 111, 7546−7557. (21) Murugavel, S.; Roling, B. Ac Conductivity Spectra of Alkali Tellurite Glasses: Composition-Dependent Deviations from the Summerfield Scaling. Phys. Rev. Lett. 2002, 89, 195902−4. (22) Roling, B.; Martiny, C.; Brückner, S. Ion Transport in Glass:Influence of Glassy Structure on Spatial Extent of Nonrandom Ion Hopping. Phys. Rev. B 2001, 63, 214203−9. (23) Sidebottom, D. L. Universal Approach for Scaling the Ac Conductivity in Ionic Glasses. Phys. Rev. Lett. 1999, 82, 3653−3656. (24) Funke, K.; Banhatti, R. D. Ionic Motion in Materials with Disordered Structures. Solid State Ionics 2006, 177, 1551−1557. (25) Das, S.; Prathapa, S. J.; Menezes, P. V.; Row, T. N. G.; Bhattacharyya, A. J. Study of Ion Transport in Lithium PerchlorateSuccinonitrile Plastic Crystalline Electrolyte Via Ionic Conductivity and in Situ Cryo-Crystallography. J. Phys. Chem. B 2009, 113, 5025− 5031. (26) Murugavel, S.; Roling, B. Ionic Transport in Glassy Networks with High Electronic Polarizabilities: Conductivity Spectroscopic Results Indicating a Vacancy-Type Transport Mechanism. J. Phys. Chem. B 2004, 108, 2564−2567. (27) DSC (scan rate = 5 °C/min, temperature range: −80 to 80 °C) shows shift in Tnp from −32 °C for Pure Sn to −37 °C due to the addition of salt (0.04 to 1 M). (28) Das, S.; Bhadram, V. S.; Narayana, C.; Bhattacharyya, A. J. Brillouin Scattering Investigation of Solvation Dynamics in Succinonitrile-Lithium Salt Plastic Crystalline Electrolytes. J. Phys. Chem. B 2011, 115, 12356−12361.

ACKNOWLEDGMENTS S.D. acknowledges IISc for SRF and A.J.B. thanks IISc and DST, Govt. of India for financial support.

■

REFERENCES

(1) Sherwood, J. N. The Plastically Crystalline State: Orientationally Disordered Crystals; John Wiley & Sons: New York, 1979. (2) Wang, P.; Dai, Q.; Zakeeruddin, S. M.; Forsyth, M.; MacFarlane, D. R.; Grätzel, M. Ambient Temperature Plastic Crystal Electrolyte for Efficient, All-Solid-State Dye-Sensitized Solar Cell. J. Am. Chem. Soc. 2004, 126, 13590−13591. (3) Jin, L.; Nairn, K. M.; Forsyth, C. M.; Seeber, A. J.; MacFarlane, D. R.; Howlett, P. C.; Forsyth, M.; Pringle, J. M. Structure and Transport Properties of a Plastic Crystal Ion Conductor: Diethyl(methyl)(isobutyl)phosphonium Hexafluorophosphate. J. Am. Chem. Soc. 2012, 134, 9688−9697. (4) Armand, M.; Endres, F.; MacFarlane, D. R.; Ohno, H.; Scrosati, B. Ionic-Liquid Materials for the Electrochemical Challenges of the Future. Nat. Mater. 2009, 8, 621−629. (5) Peñalber, C. Y.; Baldelli, S. Observation of Charge Inversion of an Ionic Liquid at the Solid Salt−Liquid Interface by Sum Frequency Generation Spectroscopy. J. Phys. Chem. Lett 2012, 3, 844−847. (6) Armand, M.; Tarascon, J. M. Building Better Batteries. Nature 2008, 451, 652−657. (7) Alarco, P. J.; Abu-Lebdeh, Y.; Abouimrane, A.; Armand, M. The Plastic-Crystalline Phase of Succinonitrile As a Universal Matrix for Solid-State Ionic Conductors. Nat. Mater. 2004, 3, 476. (8) Eldrup, M.; Pedersen, N. J.; Sherwood, J. N. Positron Annihilation Study of Defects in Succinonitrile. Phys. Rev. Lett. 1979, 43, 1407−1410. (9) Hawthorne, H. M.; Sherwood, J. N. Lattice Defects in Plastic Organic Crystals. Part 3.-Plastic Deformation in Pure and Impure Camphene. Trans. Faraday Soc. 1970, 66, 1799−1801. (10) Roling, B.; Happe, A.; Funke, K.; Ingram, M. D. Carrier Concentrations and Relaxation Spectroscopy: New Information from Scaling Properties of Conductivity Spectra in Ionically Conducting Glasses. Phys. Rev. Lett. 1997, 78, 2160−2163. (11) Sidebottom, D. L.; Green, P. F.; Brow, R. K. Scaling Behavior in the Conductivity of Alkali Oxide Glasses, Polymers, and Doped Crystals. J. Non-Cryst. Solids 1996, 203, 300−305. (12) In the plastic-phase temperature range, the impedance spectra for the bulk were fitted by a resistance, R, and constant phase element, CPE (Q1), in parallel. capacitance, C = (R1−N·CPE)1/N, and Er = (Ck)/ E0, where K is the cell constant. The electrode−electrolyte interface (Spike) was fitted with another CPE (Q2) element. The values obtained for Q2 (10−6 F) reflected blocking character of the stainless steel electrode. (13) Dyre, J. C.; Schrøder, T. B. Universality of Ac Conduction in Disordered Solids. Rev. Mod. Phys. 2000, 72, 873−892. (14) Dyre, J. C.; Maass, P.; Roling, B.; Sidebottom, D. L. Fundamental Questions Relating to Ion Conduction in Disordered Solids. Rep. Prog. Phys. 2009, 72, 046501−16. (15) Kahnt, H. Ionic Transport in Oxide Glasses and Frequency Dependence of Conductivity. Ber. Bunsenges. Phys. Chem. 1991, 95, 1021−1025. (16) Summerfield, S. Universal Low-Frequency Behaviour in the A.C. Hopping Conductivity of Disordered Systems. Philos. Mag. B 1985, 52, 9−22. (17) Summerfield, S.; Butcher, P. N. Universal Behaviour of Ac Hopping Conductivity in Disordered Systems. J. Non-Cryst. Solids 1985, 77, 135−138. (18) Roling, B. Modeling of Ion Transport Processes in Disordered Solids: Monte Carlo Simulations of the Low-Temperature Particle Dynamics in the Random Barrier Model. Phys. Chem. Chem. Phys. 2001, 3, 5093−5098. (19) Murugavel, S.; Roling, B. Murugavel and Roling Reply. Phys. Rev. Lett. 2003, 91, 049602−1. 3554

dx.doi.org/10.1021/jz301742z | J. Phys. Chem. Lett. 2012, 3, 3550−3554