Impact of I2 Additions on Iodide Transport in ... - ACS Publications

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Impact of I2 Additions on Iodide Transport in Polymer Electrolytes for Dye-Sensitized Solar Cells: Reduced Pair Formation versus a Grotthuss-Like Mechanism Friedemann Call‡,§ and Nicolaas A. Stolwijk* Institut f€ ur Materialphysik and Sonderforschungsbereich 458, University of M€ unster, D-48149 M€ unster, Germany

ABSTRACT We find evidence that the enhancement of charge transfer with increasing additions of I2 to poly(ethylene oxide) with dissolved NaI may be due to reduced cation-anion pair formation rather than the operation of a Grotthusslike transport mechanism. This conclusion can be drawn from a combination of conductivity measurements with 125I and 22Na radiotracer diffusion experiments over a wide temperature range and their simultaneous evaluation within a comprehensive ion-transport model. The results are relevant to the understanding and optimization of charge transport in dye-sensitized solar cells based on the I-/I3 redox couple. SECTION Energy Conversion and Storage ye-sensitized solar cells (DSSCs) constitute a promising alternative to conventional semiconductor-based photovoltaic systems because they combine an appreciable conversion efficiency with a simple, low-cost production process.1,2 DSSCs rely on the light-induced excitation of dye molecules and the subsequent electron transfer across the conduction band of TiO2 nanoparticles toward the transparent working electrode. The circuit is closed by a counter electrode and an electrolyte layer which commonly consists of an organic liquid dissolving an alkali metal iodide and a small amount of pure iodine (I2). In this electrolyte, the iodine almost completely reacts with the plentiful I- ions according to

D

I - þ I2 f I3I3

In this mechanism, I2 interchanges between the mono- and triiodide ions, which in an electrochemical or solar cell, effectively leads to the vehicle-free transfer of two electronic charges and thus adds to the long-distance migration/diffusion of I- and I3 between the electrodes. A crucial argument for invoking the Grotthuss mechanism was given by the notion that the current increase cannot be explained by the occurrence of cation-anion pairs since it was presumed on intuitive grounds that the formation of (electrically neutral) ion pairs should increase with increasing ion density and hence lead to a decrease of the charge-transport capacity. However, recent work shows that pair formation in ionic liquids may behave differently from that in aqueous or organic electrolyte solutions as it was found to increase with increasing temperature.12 Similar counterintuitive ion pair behavior has long been recognized for polymer electrolytes based on inorganic salts in general13 and has been evidenced by recent experiments on complexes of polyethers with alkali metal iodides in particular.14,15 Moreover, very recent work on the system poly(ethylene oxide)-sodium iodide (PEO-NaI) strongly indicates that the formation of NaI0 pairs decreases with increasing salt concentration. The present Letter reports a basic study of ionic transport in amorphous PEO30 NaI/I2 with a fixed EO/Na ratio of 30 over a wide temperature range above the PEO melting point. In particular, we investigated the change of the total ionic conductivity (σdc) and the individual cationic and anionic tracer diffusivity (DNa * , DI*) as a function of the iodine concentration by choosing three different I2/NaI molar ratios z (0, 1/10, and 1/4).

ð1Þ 3-5

thus forming as oxidized iodide species. The suitable redox couple and the effective charge energy level of the I-/I3 transfer via the two iodide species involved allow for the regeneration of the dye. However, to avoid problems related to leakage and limited durability, efforts have been undertaken to replace the liquid electrolytes by polymer electrolytes5-7 or systems containing ionic liquids.8,9 The solar-cell efficiency crucially depends on the diffusivity of the iodide species, that is, D1- and D3-, in the electrolyte. Usually, an effective diffusion coefficient, often attributed to I3 , is deduced from measurements of the limiting current in an electrochemical cell.3,4 In such experiments, it was observed that the saturation current increases with increasing total iodide concentration in the electrolyte.3,10 In addition, an increase of the saturation current or conductivity with increasing weight-in fraction of I2 at constant iodide concentration was found.4,5 Both phenomena were interpreted in terms of a Grotthuss-like exchange mechanism characterized by the following reaction sequence3,10,11 I3- þ I - f I - - I2 ... I - f I - ... I2 - I - f I - þ I3r 2010 American Chemical Society

Received Date: May 17, 2010 Accepted Date: June 17, 2010 Published on Web Date: June 22, 2010

ð2Þ 2088

DOI: 10.1021/jz100644z |J. Phys. Chem. Lett. 2010, 1, 2088–2093

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Figure 2. Tracer self-diffusion coefficients of cations (22Na) and anions (125I) in PEO30NaI/I2 (1:z) electrolytes with different I2 mole fractions z, as indicated. The solid and dashed lines result from simultaneous fitting of all transport data within a comprehensive model (see text).

Figure 1. Depth profiles of 125I and 22Na in PEO30NaI/I2 (1:1/4) resulting from simultaneous diffusion at 160 °C for 40.5 min. The solid lines are best fits of a mixed Gaussian/erfc function (see text).

Our choice of a prototype electrolyte with a relatively low molar salt concentration of Na/EO = 1/30 (coresponding to ∼5.2 1020 cm-3 or 0.9 M) avoids complications due to the precipitation of a crystalline PEO3NaI, which, according to the PEO-NaI phase diagram, should occur at the lower end of the temperature range of interest (65-200 °C).16 Moreover, the PEO30NaI reference system without I2 has been extensively investigated in a previous study,14,17 so that the pertaining set of data was available yet. The experiments on PEO30NaI/I2 (1:1/10) and PEO30NaI/I2 (1:1/4) with z = 1/10 and 1/4, respectively, were performed with the same procedures and equipment as those used before.14,17 Figure 1 shows typical depth profiles of 22Na and 125I in PEO30NaI/I2 (1:1/4) that arise from simultaneous diffusion at 160 °C for 40.5 min. The deeper penetration of 125I reflects the higher diffusivity of the anion. The solid lines are solutions of the diffusion equation based on a thin-film diffusion source of finite thickness generating profile shapes varying between the Gaussian and the complementary error function.18 The good fits of the experimental profiles allow for a reliable determination of the ionic self-diffusion coefficients, which are displayed in Figure 2 for the three complexes investigated. * at any temperature in all three Obviously, DI* exceeds DNa * does not significantly vary cases. It is remarkable that DNa with the I2 concentration, whereas a monotonic increase of DI* with increasing value of z becomes manifest in Figure 2. A similar increase with an enhanced I2 admixture is found for the charge diffusivity Dσ plotted in Figure 3. These data were obtained from the measured conductivity σdc by using the Nernst-Einstein equation Dσ

σdc kB T Cs e2

Figure 3. Charge diffusivity Dσ in PEO30NaI/I2 (1:z) electrolytes with different I2 mole fractions z, as deduced from dc conductivity data. The solid lines result from simultaneous fitting of all transport data within a comprehensive model (see text).

few as possible, as many as necessary. In particular, the model must be able to explain the increase of both DI* and Dσ with the increasing amount of added I2, namely, with increasing I3 concentration (cf. eq 1). Previous studies of the PEO-NaI system14,19 and related ones20,21 have shown that the disparities among the individual ionic diffusivities and the total charge diffusivity can be rationalized within a model that allows for cation-anion pairing. On the basis of this finding, it has to be expected that the formation of NaI0 pairs according to the reaction Naþ þ I - hNaI0

ð3Þ

will play a prominent role. Initially, we assumed a similar association behavior of I3 , thus leading to the occurrence of NaI03 pairs. However, no consistent results were obtained, which may be related to the fact that I3 contributes to both mass (DI*) and charge (Dσ) transport, whereas NaI30 only contributes to mass transport. This led us to the idea that the virtual absence of NaI30 pair formation may be a crucial feature since it can be understood from the bulky character of the I3 ion and the concomitant delocalization of the electric charge. This concept was implemented in a general

where kB denotes the Boltzmann constant, T is temperature, Cs is salt concentration (i.e., number density), and e is elementary charge. We note that the solid curves in Figures 2 and 3 result from a simultaneous fit of all experimental data within a comprehensive ion-transport model to be presented next. In theoretically describing the observed ion-transport behavior, we are guided by the principle of simplicity, which implies that only crucial factors are elaborated on, that is, as

r 2010 American Chemical Society

ð4Þ

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tions C1p and C3p, respectively, and assuming that C3p ≈ 0 holds to a good approximation leads to the mass balance relations C1 = C1- þ C1p and C3 = C3-, while the total iodide and Na concentrations are equal to the salt concentration according to C1 þ C3 = CNa = Cs. The virtually full transformation of I2 to I3 (C2 ≈ 0) implies that C1/C3 = 1-z/1, which translates to the identity relations

Table 1. Symbols Used for Physical Quantities and Model Parameters symbol

description

B-

common VTF parameter for I- and I3

Bþ

VTF parameter for Naþ

B1p = Bþ

VTF parameter for NaI0 pairs

C1-

concentration of unpaired I- anions

C1p

concentration of NaI0 pairs

C1 = C1- þ C1p

concentration of species containing I-

C2 = 0 C3-

concentration of unreacted I2 concentration of unpaired I3 anions

C3p = 0

concentration of NaI30 pairs

C3 = C3- þ C3P

concentration of species containing I3

C- = C1- þ C3-

concentration of unpaired anions

Cþ = C-

concentration of Naþ

Cs

salt concentration (number density)

CNa = Cs

total concentration of sodium

CI = C1 þ 3C3 D1-

total concentration of iodine diffusivity of I-

D1p

diffusivity of NaI0 pairs

D01p = D0þ

prefactor of NaI0 pair diffusivity

D3-

diffusivity of I3

D- = D1- = D3D0-

=

D01-

=

D03-

-

common prefactor of I and diffusivity of Naþ

D0þ D* Na

prefactor of Naþ diffusivity radiotracer diffusivity of Na

I3

k1p ¼ k01p expð- ΔH1p =kB TÞ

radiotracer diffusivity of I

Dσ

charge diffusivity deduced from DC conductivity

I = r1pD1p/(1 þ 2z)D* f1p I

fractional pair component of iodine transport

f3- = C3-D3-/C-D-

fractional I3- component of negative-charge transport

ΔH1p kB

enthalpy of NaI0 pair formation Boltzmann constant

r1p ðz, TÞ ¼ 1 - z=2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ ½1 - 1 þ 4k1p ð1 - z=2Þ þ ðk1p zÞ2 =2k1p

k1p =

Dσ ¼ ð1 - r1p ÞðD þ þ D - Þ

prefactor of reduced pairing reaction constant

r1p = C1p/Cs ΔS1p = kB ln(k01p)

fraction of NaI0 pairs entropy of NaI0 pair formation

σdc

DC conductivity

t- = D-/(D- þ Dþ)

anion transference number (including both I- and I3)

T0

common VTF parameter (zero-mobility temperature)

z

weight-in I2-to-NaI ratio

DNa ¼ ð1 - r1p ÞD þ þ r1p D1p

ð8Þ

ð9Þ

In the case of iodine, the transport balance CIDI* = C1-D1- þ 3C3-D3-þ C1pD1p includes the I3 contribution. Realizing that the total iodine concentration is enhanced by the I2 addition, that is, CI = (1 þ 2z)Cs, the (tracer) diffusivity results as

DI ¼ ð1þ2zÞ - 1 ½ð1 - r1p þ 2zÞD - þ r1p D1p

ð10Þ

We note that for z = 0, the above equations reduce to their forms reported previously.14,21,22 Like in the original version of the model, the “true” 0 diffusivity of each mobile species, Naþ, I-, I3 , and NaI , obeys a Vogel-Tammann-Fulcher(VTF)-like temperature dependence DX ¼ D0X exp½- BX =ðT - T0 Þ

theoretical framework published earlier,14,21,22 leading to an extended formalism that will be outlined in the following. The presence of I3 in the electrolyte causes the negative charge to be divided among two iodide species. Using the symbols compiled in Table 1, this may be expressed as C- = C1- þ C3- = Cþ, which also includes the charge-neutrality requirement. Introducing the NaI0 and NaI30 pair concentra-


ð7Þ

where 1 - r1p denotes the ionic fraction Cþ/Cs = C-/Cs. Similarly, summing up all Na transport terms according to CNaD* Na = CþDþ þ C1pD1p provides an expression for the Na (tracer) diffusivity of the form

reduced reaction constant for NaI pairing

k01p

ð6Þ

thus providing r1p as a function of the I2 fraction z and temperature T. The diffusivity D- (=D1- = D3-) is introduced as the common diffusivity of I- and I3 . Then, the charge diffusivity arises from the corresponding transport equation CsDσ = CþDþ þ C1-D1- þ C3-D3- as

reaction constant for NaI pair formation k01pCs

ð5Þ

In this Boltzmann expression, ΔH1p denotes the pair formation enthalpy while k01p = exp(ΔS1p/kB) contains the corresponding entropy (cf. Table 1). The mass action relationship is solved in a straightforward manner as

diffusivity

D* I

C3 ¼ C3 - ¼ zCs

Applying the law of mass action to the pairing reaction in eq 1 yields the equation r1p = k1p(1 - r1p)(1 - r1p - z) with the pair fraction r1p = C1p/Cs and the dimensionless reaction constant k1p given by

common diffusivity of I- and I3

Dþ

k01p

C1 ¼ ð1 - zÞCs

ð11Þ

Here, the index X stands for þ, -, and 1p, which accounts for the approximation that the parameters for I- and I3 coincide (e.g., D- = D1- = D3-). The parameter T0 characterizes the chain segment flexibility of a particular complex (indicated by z) and is taken to be common for all mobile species. A further reduction of the number of independent parameters

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Table 2. Parameter Values and Their Statistical Error within the Ion-Transport Model Obtained from Simultaneous Fitting of the Experimental Data for z = 0, 1/10, and 1/4 T0 (K)

D0þ (cm2 s-1)

Bþ (K)

D0(cm2 s-1)

B(K)

ΔS1p (kB)

ΔH1p (eV)

216

4.4 10-5

927

8.5 10-5

735

8.49

0.223

fixed

1%

0.5%

3%

1%

5%

7%

Figure 5. Anion transference number t- and fractional triiodide component of negative-charge transport f3- in PEO30NaI/I2 (1:z) electrolytes with different I2 mole fractions z, as indicated. The solid and dashed lines result from simultaneous fitting of all transport data within a comprehensive model (see text).

assumptions. In Figure 4, the pair impact is also reflected by the fractional pair component of iodine transport defined as I I = r1pD1p/(1 þ 2z)D*. f1p I Indeed, it is seen that f1p decreases with increasing z and with decreasing T. Two other relevant quantities are plotted in Figure 5. The anion transference number t- = D-/(D- þ Dþ) is obviously not influenced by the added I2 fraction, which agrees with the model assumption that Dþ and D- are independent of z. By contrast, the fractional I3 component of negative-charge transport f3- = C3-D3-/C-D- = z/(1 - r1p) strongly increases with an increasing amount of I2 as a result of the reaction given in eq 1. Furthermore, the increase of f3- with increasing T is caused by the T-enhanced pair formation (cf. Figure 4). This effect diminishes the concentration of I- and thus strengthens the relative importance of I3 as a carrier of negative charge. It should be emphasized that our attempts to take into account the Grotthuss mechanism (cf. eq 2) were not successful. In principle, this mechanism provides an additional con* and tribution to DI* in eq 10, but it has no influence on DNa Dσ.26 The implementation of a Grotthuss term in fitting operations without the NaI30 pair formation yields negligibly low values for the Grotthuss diffusivity and not significantly better error statistics. By contrast, in fitting runs with assumed equal pairing behavior of I3 and I , no satisfactory adjustments were obtained by including the Grotthuss term. In summary, we have shown that the effect of I2 addition on ionic transport in PEO30NaI electrolytes can be consistently explained by the strongly reduced association tendency of I3 as compared to that of I with the constituent cation species. This phenomenon can be rationalized by characteristic features of the triiodide anion, that is, the bulky dimensions and the concomitant charge delocalization. For applications in solar cells, the high values of t- determined by this study (0.6-0.9) and their increase both with increasing I2 fraction and decreasing temperature seem beneficial. Also, the low contribution of ion pairs to iodine transport (f I1p) and the decrease of the pair fraction (r1p) both with increasing z and decreasing T are favorable from a practical viewpoint. On the other hand, there is no need to invoke a Grotthuss-like

Figure 4. Pair fraction r1p and fractional pair component of iodine transport fI1p in PEO30NaI/I2 (1:z) electrolytes with different I2 mole fractions z, as indicated. The solid and dashed lines result from simultaneous fitting of all transport data within a comprehensive model (see text).

is based on the results of molecular dynamics calculations for PEO-LiX systems, which demonstrate that B1p = Bþ and D01p = D0þ hold to a good approximation.21,23,24 Altogether, this leaves seven independent parameters for each PEO30NaI/ I2 (1:z) complex, ΔH1p, ΔS1p, D0þ, D0-, Bþ, B-, and T0. In separate preliminary analysis of each complex, the experimental Dσ, D* Na, and D* I data were simultaneously fitted by least-squares minimization, which then involved 3 7= 21 free parameters in total.25 Here, most of the adjusted parameters of each kind appeared to be of similar magnitude among the three pertinent complexes, but they exhibited a considerable statistical uncertainty. This inspired us to devise a single fitting procedure including all three complexes with their specific z values but in which all other parameters were chosen to be independent of z. This complies with the expectation that small fractions of I2 have only minor effects on the physical properties of the electrolytes. In addition, the T0 value was fixed at 216 K, which was taken from unpublished data of the PEO-NaI system comprising the dependence of the glass transition temperature (Tg) and ionic transport properties on the salt concentration (T0 = Tg 44 K). The results of this unified fitting procedure with only six free parameters are displayed by the solid curves in Figures 1 and 2 and by the numerical values compiled in Table 2. The good quality of the model fit as revealed by the plots shows that the differences in Dσ and D* I among the complexes can be largely attributed to variations in the pair fraction induced by changes in the I2 fraction z. Figure 4 shows that r1p increases with increasing temperature for all complexes, in agreement with previous studies.13,19,21 Moreover, r1p appears to be lower the higher the I2 fraction z is chosen, which complies with the model


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Present Addresses:

mechanism to account for the observed transport behavior in PEO30NaI/I2 (1:z) electrolytes with z e1/4. Similar investigations on PEO30NaI/I2 (1:z) for z = 0 and 1/4 (not shown here) pointed in the same direction. The present findings raise the question whether in more concentrated systems, for example, based on ionic liquids,3,4 the role of the Grotthuss mechanism may have been overestimated by virtually neglecting the possible impact of ion association.

‡ Institut f€ ur Technische Thermodynamik, Deutsches Zentrum f€ ur Luft- und Raumfahrt, 51147 K€ oln, Germany.

Notes §

E-mail: [email protected].

ACKNOWLEDGMENT The authors thank J. F€ogeling, S. Obeidi,

EXPERIMENTAL PROCEDURES

and M. Wiencierz for help in experiment and data analysis. Financial support by the Deutsche Forschungsgemeinschaft within the collaborative research centre SFB 458 is gratefully acknowledged.

Only brief descriptions of sample preparation and the employed experimental methods are given here. To avoid contact with ambient moisture and air, all critical preparation steps and experimental procedures were carried out in closed containers or in a nitrogen-flushed glovebox. The inclusion of small amounts of I2 in the base polymer-salt complex led to production batches with a uniform red-brown color but proved to be without difficulty otherwise. For more details, the reader is referred to our earlier publications.17,27 Appropriate amounts of PEO with a molecular weight of 8 106 and NaI were dried under dynamic vacuum at elevated temperature and subsequently homogeneously dissolved with or without I2 in water-free acetonitrile. After evaporation of the solvent under dynamic vacuum, the newly synthesized PEO30NaI/I2 complexes were characterized by Archimedes-type mass density measurements and differential scanning calorimetry (DSC). The density of PEO30NaI/I2 (1:z) slightly increased from 1.31 (z = 1/10) to 1.33 g/cm3 (z = 1/4), which is in line with the value of 1.26 g/cm3 for the I2-free complex (z = 0) synthesized previously.17 In DSC analysis, the only feature in the second and multiple heating/cooling cycles was the endothermic peak near 67 °C due to the melting of PEO. No indications for precipitation were observed. The ionic conductivity (σdc) was investigated by impedance spectroscopy using a HP Agilent 4192A LF impedance analyzer covering the ac frequency (ν) range from 5 Hz to 13 MHz. The electrolyte was enclosed in a cylindrical cavity between two coplanar stainless steel electrodes. The measuring cell was operated under a continuous flow of pure N2 gas. The dc conductivity was obtained from the plateau region of the |σdc| versus ν plot, where the phase angle approaches 0.17 The reproducibility of the data was verified by repeated heating and cooling cycles on two different samples. In the radiotracer diffusion experiments, the isotopes 22Na and 125I were added in trace amounts to thin PEO30NaI layers acting as a diffusion source on top of cylindrical PEO30NaI/I2 samples. Using suitable encapsulants, the isothermal diffusion treatment was carried out in a preheated oil bath and terminated by quenching in water. Radiotracer depth profiling was done in a serial manner using microtome sectioning at -50 °C and subsequent detection of the γ- or β-radiation.17,21

REFERENCES (1)

(2) (3)

(4)

(5)

(6)

(7)

(8) (9)

(10)

(11)

(12)

(13)

AUTHOR INFORMATION Corresponding Author:

(14)

*To whom correspondence should be addressed. E-mail: stolwij@ uni-muenster.de. Phone: þ49 (0)251 8339013. Fax: þ49 (0)251 8338346.


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O'Regan, B.; Gr€ atzel, M. A Low-Cost, High-Efficiency Solar Cell Based on Dye-Sensitized Colloidal TiO2 Films. Nature 1991, 353, 737–740. Gr€ atzel, M. Solar Energy Conversion By Dye-Sensitized Photovoltaic Cells. Inorg. Chem. 2005, 44, 6841–6851. Papageorgiou, N.; Athanassov, Y.; Armand, M.; Bonhote, P.; Pettersson, H.; Azam, A.; Gr€ atzel, M. The Performance and Stability of Ambient Temperature Molten Salts for Solar Cell Applications. J. Electrochem. Soc. 1996, 143, 3099– 3108. Kawano, R.; Watanabe, M. Equilibrium Potentials and Charge Transport of an I-/I3 Redox Couple in an Ionic Liquid. Chem. Commun. 2003, 330–331. Kalaignan, G. P.; Kang, M.-S.; Kang, Y. S. Effects of Composition on Properties of PEO-KI-I2 Salts Polymer Electrolytes for DSSC. Solid State Ionics 2006, 177, 1091–1097. Nogueira, A. F.; Longo, C.; De Paoli, M.-A. Polymers in Dye Sensitized Solar Cells: Overview and Perspectives. Coord. Chem. Rev. 2004, 248, 1455–1468. Li, B.; Wang, L.; Kang, B.; Wang, P.; Qiu, Y. Review of Recent Progress in Solid-State Dye-Sensitized Solar Cells. Sol. Energy Mater. Sol. Cells 2006, 90, 549–573. Gorlov, M.; Kloo, L. Ionic Liquid Electrolytes for DyeSensitized Solar Cells. Dalton Trans. 2008, 2655–2666. Nazmutdinova, G.; Sensfuss, S.; Schr€ odner, M.; Hinsch, A.; Sastrawan, R.; Gerhard, D.; Himmler, S.; Wasserscheid, P. Quasi-Solid State Polymer Electrolytes for Dye-Sensitized Solar Cells: Effect of the Electrolyte Components Variation on the Triiodide Ion Diffusion Properties and Charge-Transfer Resistance at Platinum Electrode. Solid State Ionics 2006, 177, 3141–3146. Kawano, R.; Watanabe, M. Anomaly of Charge Transport of an Iodide/Tri-Iodide Redox Couple in an Ionic Liquid and Its Importance in Dye-Sensitized Solar Cells. Chem. Commun. 2005, 2107–2109. Ruff, I.; Friedrich, V. J.; Csillag, K. Transfer Diffusion. III. Kinetics and Mechanism of the Triiodide-Iodide Exchange Reaction. J. Phys. Chem. 1972, 76, 162–165. Stolwijk, N. A.; Obeidi, Sh. Combined Analysis of SelfDiffusion, Conductivity, and Viscosity Data on Room Temperature Ionic Liquids. Electrochim. Acta 2009, 54, 1645– 1653. Ratner, M. A.; Nitzan, A. Conductivity in Polymer Ionics: Dynamic Disorder and Correlation. Faraday Discuss. Chem. Soc. 1989, 88, 19–42. Stolwijk, N. A.; Obeidi, Sh. Radiotracer Diffusion and Ionic Conduction in a PEO-NaI Polymer Electrolyte. Phys. Rev. Lett. 2004, 93, 125901–125904.


pubs.acs.org/JPCL

(15)

(16)

(17)

(18) (19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

Obeidi, Sh.; Stolwijk, N. A.; Pas, S. J. Mass and Charge Transport in a Cross-Linked Polyether-Based Electrolyte. The Role of Ion Pairs. Macromolecules 2005, 38, 10750– 10756. Fauteux, D.; Lupien, M. D.; Robitaille, C. D. Phase Diagram, Conductivity, and Transference Number of PEO-NaI Electrolytes. J. Electrochem. Soc. 1987, 134, 2761–2766. Obeidi, Sh.; Zazoum, B.; Stolwijk, N. A. Ionic Tracer Diffusion and DC Conductivity in the Polymer Electrolyte PEO30NaI. Solid State Ionics 2004, 173, 77–82. Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, U.K., 1995. Stolwijk, N. A.; Wiencierz, M.; Obeidi, Sh. Mass and Charge Transport in the PEO-NaI Polymer Electrolyte System: Effects of Temperature and Salt Concentration. Faraday Discuss. 2007, 134, 157–169. Bastek, J.; Stolwijk, N. A.; K€ oster, Th.; van W€ ullen, L. Systematics of Salt Precipitation in Complexes of Polyethylene Oxide and Alkali Metal Iodides. Electrochim. Acta 2010, 55, 1289–1297. F€ ogeling, J.; Kunze, M.; Sch€ onhoff, M.; Stolwijk, N. A. ForeignIon and Self-Ion Diffusion in a Crosslinked Salt-in-Polymer Electrolyte. Phys. Chem. Chem. Phys. doi: 10.1039/b923894h. Stolwijk, N. A.; Obeidi, Sh. A Model for Diffusion and Ionic Conduction in Polymer Electrolytes. Diffus. Defect Data, Pt. A: Defect Diffus. Forum 2005, 237-240, 1004–1015. Maitra, A.; Heuer, H. Understanding Correlation Effects for Ion Conduction in Polymer Electrolytes. J. Phys. Chem B 2008, 112, 9641–9651. In most previous evaluations of the model with z = 0, we additionally assumed B- = Bþ to hold but allowed D01p to be independent of D0þ. However, this approach is not supported by MD calculations. It is noteworthy that individual model-free fits to all sets of data (3 3 = 9), for example, by a three-parameter VTF-type function, would require 93=27 parameters to be adjusted in total. The present experiments under equilibrium conditions should be distinguished from limiting-current measurements across an electrochemical cell, which involve field-driven migration effects. In the later case, the Grotthuss mechanism may, in principle, enhance the charge-transfer efficiency. Stolwijk, N. A.; Obeidi, Sh. Rubidium Impurity Diffusion in a Poly(Ethylene Oxide)-Sodium Iodide Polymer Electrolyte. J. Phys. Chem B 2006, 110, 22496–22502.


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