Ion dynamics behavior in solid polymer electrolyte

SOSI-13109; No of Pages 5 Solid State Ionics xxx (2013) xxx–xxx Contents lists available at ScienceDirect Solid State Ionics journal homepage: www.elsevier.com/locate/ssi Ion dynamics behavior in solid polymer electrolyte Neelam Srivastava ⁎, Manindra Kumar Department of Physics (MMV), Banaras Hindu University, Varanasi, 221005, India a r t i c l e i n f o Article history: Received 17 May 2013 Received in revised form 1 October 2013 Accepted 5 October 2013 Available online xxxx Keywords: Polymer electrolyte Power law scaling UPL/SLPL Conductivity a b s t r a c t A conducting polymer system, having room temperature conductivity ~1.26 × 10−4 S/cm (for 50% NaI concentration) and ionic transference number ~0.80, has been prepared by mixing NaI in a novel polymer host (synthesized polymer + poly (ethylene oxide)). Mobility (μ) and total number of charge carriers (N), estimated from dielectric parameters, have a value of ~1.65 × 10−2 cm2 V−1 s−1 and 4.70 × 1016 cm−3 respectively. Inverse relationship between conductivity power law exponent n and N/N0 (fractional number of dissociated charge carriers) is explained in terms of statistical nature of ion dynamics. The temperature dependence of “n” studied separately in universal power law (UPL) and super linear power law (SLPL) region revealed that exponent n responds differently to temperature in these two different regions. Ion hopping frequency (ωp), obtained from universal power law (UPL) region, is used for scaling of conductivity and permittivity curves. Conductivity scaling followed a master curve Y = 1 + Xn, having n = 0.85 ± 0.07, covering both UPL as well as SLPL region which confirms that both phenomena have the same origin. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Conducting (ionic, electronic or ionic–electronic mixed conducting) materials are technologically important; hence considerable importance is being given to understand ion dynamics in these conductors [1–4]. AC conductivity data, presented as logσ vs. logω curves (where σ is real part of conductivity and ω is frequency), shows a remarkable universal nature [5], exhibited by all thermally activated hopping conductivity (ionic/electronic conduction in crystalline/amorphous materials); hence is extensively used to understand the charge carrier dynamics of disordered materials [6]. The conductivity power law σ (ω) = σ0 + Aωn proposed by Jonscher [7] is followed by a wide variety of materials. Here σ0 is the frequency independent dc conductivity and n is the power law exponent restricted to be 0 b n b 1 and this behavior is correlated with hopping of ions. Almond and West [8–10] represented the same conductivity law in terms of ion hopping frequency (ωp) as σ (ω) = σ0 [1 + (ω/ωp)n]. These are known as universal/sublinear power law (UPL). They deal with correlated ion hopping at a large time scale. UPL explains only a small portion of conductivity dispersion. Extension of conductivity dispersion study covering wider variety of materials in broader frequency and temperature range, has indicated that “n” does not limit to b 1 [11,12]. “n” ≥ 1 is related with movement of caged/localized ions. Nowick et al. [13–15] have proposed a new power law to explain NCL, which was superposition of UPL and a nearly constant loss term, represented as σ(ω) = σ0 [1 + (ω/ωp)n] + Aωm, where m = 1, and generally ⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (N. Srivastava). known as augmented power law. Lunkenheimer and Loidl [16] claimed that UPL is followed by a super linear power law (SLPL) with an exponent (m) b 2, which is also valid for many disordered materials and are gaining universal status. Recently many theoretical models are proposed to explain n N 1 and going beyond 2 also. These models are applicable to variety of material and new universality is recognized and designated as Second Universality [5] where as First Universality is Jonscher's power law universality. First and second universality and its transition from one to other have been summarized by Funke and his group in their recent review article [5]. NCL/SLPL is supposed to have their origin in coulombic cage. In polymer electrolyte two different possibilities arises, i) caging due to matrix molecules [17] or ii) due to neighboring mobile charge carriers [18]. These two caging effects manifest themselves in different ways in exponent “n” vs. temperature data. In case (i) exponent n will increase with decrease in temperature [19], whereas for case (ii) n will increase with increasing temperature [20]. Typical value of n in UPL region should lie ~0.5–0.65 whereas for other phenomenon it will have higher value. Hence the study of n vs. different parameters (salt concentration and temperature) has plenty of hidden information. Here onwards n b 1 will be represented by nUPL and n N 1 by nSLPL. Controlling factors (matrix or neighboring ions) of ion dynamics can be understood by scaling behavior of logσ vs. logω curve [21]. If the effect, of controlling factors, on conductivity is restricted to control number of charge carriers and mobility only and not the underlying mechanism then scaling will result in single master curve i.e. if NCL/ SLPL is due to coulombic cage caused by mobile charge carrier, scaling could be observed in frequency range including UPL and NCL/SLPL both whereas matrix controlled NCL/SLPL will result in poor scaling beyond UPL region. 0167-2738/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ssi.2013.10.026 Please cite this article as: N. Srivastava, M. Kumar, Solid State Ionics (2013), http://dx.doi.org/10.1016/j.ssi.2013.10.026 2 N. Srivastava, M. Kumar / Solid State Ionics xxx (2013) xxx–xxx 2. Experimental 3. Results and discussion 2.1. Materials used Series of prepared material was characterized to optimize the salt concentration and to understand ionic conduction in it. Fig. 2 shows that 50% salt containing material is maximum conducting (~ 1.26 × 10− 4S/cm) with mobility (μ) ~ 1.65 × 10− 2 cm2 V− 1 s− 1 and total number of charge carriers (N) ~ 4.70 × 1016 cm− 3 respectively. Because of limitation of pages, the present paper aims to discuss only ion dynamics in the system and hence the details of procedure related to other characterization (such as structure, ionic transference number, mobility and number of charge carriers etc.) are communicated somewhere else, but authors would like to mention here that mobility calculated using Klein et al. approach [22] is only an approximate value. This is because the formula derived in their paper is achieved after approximations and is derived for single ion conductor and hence when used for real systems having multiple ions, it results in average value [23]. The material has total ionic transference number ~ 0.80. Material has multiple charge carriers, besides presence of electronic conduction possible charge carriers in the system are Na+, I−, H+ and OH−. Possibility of H+ and OH− arises from hygroscopic nature of material. Polyethylene oxide (PEO, Sigma-Aldrich, mol wt = 6 × 105), triethylenetetramine (Loba Chem), 1-3 propane sultone (Sigma-Aldrich), sodium iodide (NaI, Fisher Scientific), glutaraldehyde (Loba Chem), and methanol (Fisher Scientific) were used for preparing the materials. 2.2. Preparation of polymer electrolyte films Polymer electrolytes films were prepared by solution cast technique. Appropriate amount of triethylenetetramine and methanol were stirred at room temperature. In the resultant solution 1-3 propane sultone was added drop wise for 10 minutes and stirred at room temperature. This was an exothermic reaction and the temperature of the solution was 70 °C. The solution was left for cooling at room temperature; after that, the solution was stirred at 50 °C. After getting homogeneous and viscous solution, NaI (in different wt%: 0, 10, 20, 30, 40, 50) is added and solution is stirred for one hour. After that 2 mL of glutaraldehyde is added into the solution and stirred at 50 °C. Material was liquidus and “free standing films” could not be obtained. Hence 10 wt% PEO was added in prepared material to get free standing films. PEO was mixed with anhydrous methanol and stirred vigorously at 40 °C until a homogeneous solution was formed and then prepared material was poured in it and stirred. The resultant homogeneous solution was poured in a polypropylene Petri dish and solvent was allowed to evaporate slowly in ambient condition. After complete evaporation of solvent, free standing films of different compositions were obtained. So obtained material showed a highest conductivity of the order of 10−4S/cm. The estimated ionic transference number is ~0.80, which indicates a mixed conducting nature of prepared material. The proposed structure of the prepared material is given in Fig. 1. The prepared material has been characterized using computer controlled HIOKI LCR meter 3532-50 in the frequency range 42 Hz to 5 MHz. The obtained real and imaginary impedances have been further used for calculating the conductivity (σ) and dielectric properties (ε′ and ε″) by following relations: ′ σ ¼ l=Z A ð1Þ  2   2  ′ ″ ′ ″2 ″ ′ ′ ″2 ε ¼ Z = Z þ Z ωC and ε ¼ Z = Z þ Z ωC ð2Þ where ε′ and ε″ are real and imaginary part of permittivity, Z′ and Z″are real and imaginary part of impedance, ω is angular frequency and C is capacitance of empty measuring cell of electrode area A and sample dimension Į. 3.1. Variation of exponent “n” with temperature AC conductivity vs. frequency plot with different salt concentration is shown in Fig. 3. The dc conductivity regions are well separated depending upon the salt concentration. Towards higher frequency side, curves tend to collapse in a single curve, which indicates the possible presence of NCL/SLPL region in the present system [24]. The derivative study ∂(logσ)/∂(logω) of the curve indicated varying value of exponent n from 0 to N 2, confirming existence of NCL/SLPL region. Fig. 4 shows the deviation from power law fitting and confirms different values of n existing in different regions. Hence Fig. 4 was divided into two regions marked by arrow and separate fitting was done. Fig. (a) and (b) (shown in inset of Fig. 4) are fittings i) in the frequency region above the arrow where derivative showed n N 1 indicating SLPL region and ii) in the rest of the frequency region i.e. below the arrow where derivative showed n b 1 representing ion hopping (UPL) region. PEO was used for sample preparation whose melting point (Tm) is 68 °C. In the present study, nSLPL and nUPL are drastically affected near Tm and they follow different trend as shown in Fig. 5a and b. The number of charge carriers as well as their kinetic energy both will increase with temperature. Hence a statistical dominance of “long range hopping charge carriers' over “caged mobile charge carriers” is expected. Chandra and Chandra [25] discussed that melting of PEO has pronounced effect on number of charge carriers than on mobility. Both these factors will increase random hopping of charge carriers hence after Tm the long range hopping will be replaced by dc conduction process as shown in Fig. 5a. Variation of nSLPL showed a jump at Tm i.e. from b2 to N2. ADWP model [26] given for glasses correlates the glass Fig. 1. The proposed structure of the prepared material. Please cite this article as: N. Srivastava, M. Kumar, Solid State Ionics (2013), http://dx.doi.org/10.1016/j.ssi.2013.10.026 N. Srivastava, M. Kumar / Solid State Ionics xxx (2013) xxx–xxx Fig. 2. Variation of conductivity, mobility and number of charge carriers with salt concentration at 34 °C. transition temperature with b 2 and N2 values by the following equation: nSLPL   ¼ 1 þ T=T g ≥1 3 Fig. 4. Frequency-dependent conductivity after removing electrode polarization portion and in inset (a) shows SLPL region and (b) shows UPL region at room temperature i.e. 34 °C. dissociated mobile charge carriers (N/N0). N/N0 can be calculated using following formula [27] ð3Þ which predicts a very slow increase in nSLPL with temperature and permits nSLPL to have value b2 and N 2 before and after glass transition temperature respectively. In the present case also nSLPL has a constant value (b2 and N2 before and after phase transition respectively) within experimental limits but a sudden jump is observed at phase transition temperature. Peculiar point is that the phase transition is related with Tm not with Tg. Authors could not find any theory in literature, correlating Tm and nSLPL and hence this experimental finding is open for theoreticians to explain. Here attention is required towards the fact that in PEO based polymer electrolyte a sudden jump in conductivity at Tm is explained in terms of release of charge carriers along with increased flexibility of polymer chains [25]. Hence the increased caging of ions (indicated by jump in nSLPL) may be either due to increased number of charge carriers or increased flexibility of host matrix. Correlating it with scaling phenomenon (discussed later) observed in complete frequency region, caging due to mobile charge carrier seems to be more appropriate explanation, but in absence of theoretical model a definite conclusive statement is not possible. 3.2. Variation of N/N0 and n with salt concentrationSince NCL/SLPL is explained in terms of localized or caged movement of ions, it is anticipated to have a relation with fractional number of N=N0 ¼ exp½−U=2εkB T Š ð4Þ where N is dissociated number of charge carrier and N0 is total number of charge carrier, U is the dissociation energy of the salt and ε is the dielectric constant of the matrix at temperature T and kB is Boltzmann constant. Variation of N/N0, nUPL and nSLPL with salt concentration is shown in Fig. 6. nUPL curve exactly follows a mirror image of N/N0 curve. nSLPL also shows an inverse trend but not as exactly as shown by nUPL. Origin of this inverse relation lies in the fact that ion dynamics (UPL or SLPL) is a statistical phenomenon. Before discussing this inverse relation in detail, attention is required towards the trend of N/N0 with salt concentration. At low salt concentration higher value of N/N0 is expected in comparison to that at higher salt concentration. At higher salt concentration increasing coulombic interaction between dissociated ions may decrease N/N0, whereas at low salt concentration ions will be comparatively apart from each other resulting in less coulombic interaction allowing them to remain dissociated. In the present study, low value of N/N0 is found at low salt concentration. This smaller value of N/N0, at low salt concentration, indicates that some of the ions are not available as mobile charge carriers. Low potential cages/adducts exists in polymer matrix [17]. Ions will be trapped in these adducts and will move around adduct forming charge species, so the long range hopping is restricted. Once the host matrix is fixed, the number of low potential adducts in the system will remain approximately the same. Hence with increase in salt concentration mobile charge carriers will dominate over the number of caged charges indicated by increased value of N/N0. In polymer based electrolyte systems ion association or formation of ionpairs with increasing salt concentration is a known fact [28]. Such ion association or ion-pair formation will again contribute to dominance of caging effect (not allowing the ions to hop). This seems to be the reason of almost constant value of N/N0 at higher salt concentration. The dominance of mobile charge carriers over caged ions can be interpreted as statistical dominance of ion hopping over caged ion motion (or NCL/SLPL phenomenon) i.e. exponent n will tend towards its ideal value 0.5–0.65. Same is indicated by inverse relation between N/N0 and n. 3.3. Scaling of ac conductivity and dielectric permittivity- Fig. 3. Frequency-dependent conductivity at various salt concentrations at 34 °C temperature. NCL/SLPL is localized motion of ions or we can say movement of caged ions. The reasons of caging can be different; it may be due to Please cite this article as: N. Srivastava, M. Kumar, Solid State Ionics (2013), http://dx.doi.org/10.1016/j.ssi.2013.10.026 4 N. Srivastava, M. Kumar / Solid State Ionics xxx (2013) xxx–xxx to mention that σ0 and ωp have to be estimated from fitting of ion hopping region. In the present case, these values are estimated from the region where logσ vs. logω curve derivative showed n b 1. Scaling parameters have been estimated carefully after neglecting polarization region. Since n is strictly not independent of frequency hence for comparison of data a fixed frequency range has been selected for all curves. The scaling of the conductivity follows the following law:   σ=σ 0 ¼ F ω=ωp where F ðxÞ ¼ 1 þ x n ð5Þ where F is the scaling factor and ω is the frequency. Fig. 7 shows the scaled conductivity curve with exponent n = 0.85 ± 0.07. The scaled conductivity spectra, with respect to salt concentration, collapsed into a single master curve including UPL as well as SLPL region. This can be interpreted as existence of a single phenomenon for all curves in complete experimental frequency range [29] indicating composition independent charge transport mechanism i.e. doping concentration is only affecting the charge concentration and/or mobility without influencing conduction mechanism. Single master curve obtained covering both UPL as well as SLPL region confirms that the ion hopping and SLPL have the same origin. The same scaling was tried with respect to temperature also but since ωp goes beyond the experimental frequency limit, it could be done only for two temperatures as shown in Fig. 6 inset. Scaling has been successfully obtained for dielectric permittivity also. After the removal of contribution from electrode polarization, permittivity value εs′ contributed by mobile ions was obtained at low frequency [30,31]. Then the permittivity change Δε = ε∞′ −εs′ is a direct consequence of relaxation of hopping ions where ε∞′ is is high frequency dielectric constant. Sidebottom [32] suggests that the scaling of the real part of the permittivity can be done as: Fig. 5. (a). Variation of nUPL as a function of temperature. (b). Variation of nSLPL as a function of temperature. coulombic potential of neighboring ions or due to host matrix. Scaling of impedance data is a simple technique, to differentiate between two because if the underlying mechanism is the same then master curve is achieved else scaling fails. For scaling, values of σ0 and ωp are required. ωp denotes the transition from dc conductivity to dispersive conductivity and it is the value of ω at which σ(ω) = 2σ0(ω) where σ0 can be found from fitting the σ=σ0 +Aωn equation. Here it is important Fig. 6. Variation of nUPL, N/N0 and nSLPL as a function of salt concentration at 34 °C of temperature.     ′ ε −ε∞ =Δε ¼ F ω=ωp where ωp ¼ σ 0 =ε0 Δε: ð6Þ Fig. 8 shows the scaling of the permittivity curve with salt concentration and temperature. Both the curves are fitted into a single master curve. It indicates a single mechanism applicable to all the curves in complete frequency range. Fig. 7. Scaling behavior of conductivity curve for varying salt concentration and in inset for varying temperature (for interpretation of the references to color in this figure legend, the reader is referred to the web version of the article). Please cite this article as: N. Srivastava, M. Kumar, Solid State Ionics (2013), http://dx.doi.org/10.1016/j.ssi.2013.10.026 N. Srivastava, M. Kumar / Solid State Ionics xxx (2013) xxx–xxx 5 from universal power law (UPL)/sublinear power law region. Conductivity scaling followed a single master curve Y = 1 + Xn, having n = 0.85 ± 0.07 covering both UPL as well as SLPL region. The scaled master curve confirmed that single phenomenon is governing all possible charge motion in system. References [1] [2] [3] [4] [5] Fig. 8. Scaling behavior of permittivity spectra for varying salt concentration and temperature respectively. 4. Conclusions The present study confirms that power law universality is applicable to conducting polymer materials having multiple charge carriers. Ion hopping as well as localized ion movement was observed at room temperature in limited frequency range (42 Hz to 5 MHz). Fractional number of dissociated mobile charge carrier (N/N0) and power law exponent (n) has inverse relation which is correlated with statistical nature of ion dynamics and caging of ions. Temperature dependent behavior of exponent n, in ion hopping and localized ion movement range, has shown totally different trend. nUPL follows an expected decreasing trend with increasing temperature whereas a sudden jump observed in nSLPL at melting temperature phase transition. Scaling of conductivity and permittivity curves has been done using ωp obtained [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] D.L. Sidebottom, B. Roling, K. Funke, Phys. 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