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Effect of the Morphological Features of the Poly(vinylidene difluoride)-Based Gel Electrolytes on the Ionic Mobility for Lithium Secondary Batteries Yuria Saito,*,† Sahori Takeda,† Shigemasa Yamagami,† Toshiki Yagi,‡ Keisuke Watanabe,‡ and Shota Kobayashi‡ †

National Institute of Advanced Industrial Science and Technology, 1-8-31, Midorigaoka, Ikeda, Osaka 563-8577, Japan Kureha Corporation, 16, Ochiai, Nishiki-Machi, Iwaki, Fukushima 974-8686, Japan

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ABSTRACT: Highly conductive solid electrolytes used in energy storage systems could be developed by the systematic control of the ion conduction mechanism in the solid medium. In this study, we evaluated the ion migration mechanism of poly(vinylidene difluoride) (PVDF) gel electrolytes in relation to the structural/morphological features of the physically cross-linked PVDF gels. By measuring the spin−spin relaxation times (T2) of the cation/anion species of the quenched gel electrolytes, we found that anions with short T2 were located close to the crystalline phase forming the cross-links, while cations with long T2 were located in the solution-rich amorphous phase. The discrete locations of the cations and anions are suitable for preferential cation transport because the anions are restricted in the crystalline phase by the anion/crystallite interactions, as confirmed by the estimation of the microviscosity (βan). Enhancing the cation mobility by controlling the two-phase condition of the PVDF gel is a new and promising approach for obtaining electrolytes that can be applied in high-power batteries.



concentration.8 It was also verified that the introduction of Lewis acid ionic groups in the PVB reduced the anion mobility, resulting in increased cation transport number.9 In other words, the ion conduction properties of the chemically crosslinked gel electrolytes have been elucidated considerably in terms of the effects of the polar groups in the polymer chains. In contrast, poly(vinylidene difluoride) (PVDF) polymer gels without any specific polar groups on the chains are composed of a network of physically cross-linked PVDF crystallites.10 The solution phase and/or the amorphous phase, which captures the solution, is maintained inside the crystalline network, leading to a swollen gel.11,12 Because the cross-links composed of the aggregated crystallites are weaker than the covalent cross-links, resulting in lower elasticity of the polymer network,13 the swollen structure of the PVDF gel is not stable enough to adequately retain the solution within its network. Therefore, phase separation of the polymer and solution occurs easily, depending on the polymer fraction and the gel preparation conditions. Despite the difficulty in controlling the homogeneous morphology and the subsequent unexplained conductivity features of the PVDF gel electrolytes, PVDF materials have been widely used as electrolytes and binders in lithium secondary batteries.14,15 This is probably

INTRODUCTION Polymer gel electrolytes are promising materials for lithium secondary batteries because of their high conductivities, equal to those of electrolyte solutions, and their self-supporting property suitable for their safe operation during the charge− discharge cycles.1,2 In addition, the flexible gel structure decreases the structural restriction of the battery (e.g., filmtype batteries), which is in turn highly advantageous for battery mounting system design. In practice, however, the ion conduction mechanism in the gel materials, which directly determines the performance of the devices using the gel, has not been systematically investigated. Polymer gel electrolytes are composites of solid polymers and electrolyte solutions, in which the solution is held within a cross-linked polymer network, leading to a swollen structure. In gel electrolytes based on poly(ethylene oxide) (PEO) and poly(vinyl butyral) (PVB), covalent cross-links are formed by the respective Lewis base polar groups, i.e., ether oxygen (−O−) and hydroxyl group (−OH).3−5 The resulting swollen gels are stable in that the solution is retained inside the network because of the strong elasticity of the polymer chains.6 Furthermore, the polar sites on the PEO and PVB chains promote salt dissociation of the electrolyte solution and consequently attract the dissociated cationic species via Coulombic interactions in the gel.7,8 Previously, we have confirmed that the cation mobility in the PVB-type polymer gel electrolytes selectively decreased upon increasing the −OH © XXXX American Chemical Society

Received: November 22, 2018 Revised: February 12, 2019

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respectively, were measured at 25 °C using the pulsed gradient spinecho (PGSE) NMR technique with a JNM-ECP300W wide-bore spectrometer (JEOL, Ltd., Akishima, Japan).25 A Hahn-echo pulse sequence was used for the measurements. A half-sine-shaped gradient pulse was applied twice in succession after the 90° and 180° pulses to determine the attenuation of the echo intensity with diffusion of the probed species.26,27 The typical pulse width (δ) and diffusion time (Δ) for the pulse sequence were 0−7 and 20 ms, respectively. The ionic conductivity of the gel was measured by the impedance method using a frequency analyzer (Model 1250, Solartron Analytical, Wokingham, UK) combined with a potentiostat (Model 1287, Solartron Analytical, Wokingham, UK) and an impedance analyzer (HZ-Pro S4, Hokuto Denko Corp. Tokyo, Japan). An alternating current (ac) voltage of 100 mV was applied in the frequency range of 1 mHz to 65 kHz or 1 MHz.

because PVDF is chemically inert to ions in the gel containing the lithium salt, in contrast to the PEO and PVB, which attract the cations, leading to a reduction in the cation mobility. Thus, we believe that the correlation between the gel morphology and dynamic properties of PVDF gel electrolytes should be systematically evaluated to design gels suitable for use as ion transport media. Two key points should be considered for this study. First, appropriate indexes of physical properties that represent the gel morphology must be chosen. In this case, we used the relaxation features of the coherent spins of the probed nuclear species in NMR measurements because the relaxation behaviors directly reflect the conditions surrounding the target ionic species.16,17 Second, we must construct a suitable model to explain the ion transport mechanism in light of the gel morphology. In the field of polymer materials, several models of mass transfer in gel and polymer solutions have been developed, such as the obstacle model,18 hydrodynamics model,19 and free volume model.20 These could explain the changes in the dynamic values as a function of the macroscopic parameters of the gel such as the polymer concentration. However, the ionic mobility is essentially determined by the frictional resistance arising from the microscopic interactions between the ions and the surrounding species and medium.21 We have already developed a unique analytical approach for determining factors governing the ionic mobilities of the electrolytes under the influence of van der Waals and Coulombic interactions between the ion/surrounding species and the medium.8,22 Essentially, the structural/morphological differences of gels, for example, the sizes of the crystalline and amorphous phases in the gel and their mixing ratios, are expected to be reflected in the estimated ionic mobilities and microviscosities, which provide information about ion dynamics over a few micrometer scale. In this study, we applied this approach to investigate the ion migration features of PVDF-type polymer gel electrolytes depending on the morphological properties of the gel. We believe that this research could lead to a more rational and effective application of PVDF materials in high-power battery systems.





OUTLINE OF THEORETICAL DERIVATIONS The diffusion coefficients of the cation, anion, and ion pair species, i.e., Dca, Dan, and Dpair, respectively, and the microviscosities η, α, and β responsible for the diffusion coefficient values were estimated as follows: Under the equilibrium state of the lithium salt dissociation in the lithium electrolyte solution, dissociated cations and anions as well as the associated ion pairs exist. However, these are not detected individually on the NMR experimental time scale, wherein the average environment is probed because of rapid exchange between the entities. As a result, the measured diffusion coefficients DLi, DF, and DH, which were probed by the 7Li, 19F, and 1H nuclear species, respectively, could be defined by the inherent diffusion coefficients of the entities Dca, Dan, and Dpair, as shown in eq 1.28 DLi = xDca + (1 − x)Dpair DF = xDan + (1 − x)Dpair DH = DPC = Dsolv

(1)

where x is the degree of the dissociation of the lithium salt in the solution. As Dca and Dan represent the diffusion coefficients of the single entities, i.e., the cation and anion, respectively, they are directly related to the cation and anion mobilities, respectively, according to the Einstein relation.29 In addition, Dpair represents the diffusion coefficient of the associated ion pair, LiTFSI. As the solvent species are neutral and do not dissociate, DH, which was directly estimated from the peak of PC species (DPC), corresponds to the diffusion coefficient of the solvent species, Dsolv. Furthermore, the ionic conductivity is the sum of the cation and anion conductivities, which are functions of the carrier concentration (xN) and the ionic diffusion coefficient, as shown in eq 2.30

EXPERIMENTAL SECTION

PVDF-type polymer gel electrolytes were prepared as follows: The starting material, PVDF−HFP copolymer powder (number-average molecular weight = 280000 and melting temperature = 155 °C), was obtained from the Kureha Corporation (Iwaki, Japan). The prescribed weight of the polymer powder, electrolyte solution (1 M lithium bis(trifluoromethanesulfonyl)imide (LiTFSI)/propylene carbonate (PC)), and solvent (dimethyl carbonate (DMC), Kishida Chemicals, Osaka, Japan) were mixed and stirred at room temperature. The mixture was then heated to 90 °C to ensure that the polymer dissolved completely to obtain a homogeneous sol. After that, the solution was placed in a dish for cooling to remove DMC and obtain the precursor material. The polymer fraction of the gel was varied from 5 to 10 and 15 wt %. For the measurement of the ionic conductivity and diffusion coefficient, the precursor was cut according to the cell size and placed into each cell. After the cell was heated at 150 °C to obtain a homogeneous sol again, the samples were annealed (cooled from 150 to 30 °C for 24 h) or quenched (cooled from 150 to 30 °C for 30 min) to form a gel with different thermal hysteresis. The spin−spin relaxation time, T2, was measured using the Carr− Purcell−Meiboom−Gill (CPMG) method of the NMR technique,23,24 and the T2 values were estimated from the slope of the log plots of the echo signal intensity against time. The diffusion coefficients DLi, DF, and DH of the probed nuclear species, 7Li (116.8 MHz), 19F (292.7 MHz), and 1H (300.5 MHz),

σ=

e2 xN (Dca + Dan) kT

(2)

where e, k, T, and N represent the electric charge, Boltzmann constant, absolute temperature, and salt concentration in the solution, respectively. As DH directly reflects the diffusion coefficient of the neutral PC species of the solvent (Dsolv), the diffusion coefficient of the ion pair (Dpair) was estimated using the sizes of ion pairs (rpair) and PC (rPC), based on the relationship Dsolv/Dpair = rpair/rPC, according to the van der Waals size and Stokes−Einstein equation.31,32 As a result, Dca, Dan, and x can be determined by simultaneously solving eqs 1 and 2. B

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Figure 1. Observed diffusion coefficient ratios, DLi/DH and DF/DH, of the gel electrolytes composed of (a) PEO and 1 M LiBF4/EC + EMC, (b) PVB and 1 M LiTFSI/EC + DMC, and (c) PVDF and 1 M LiTFSI/PC as a function of the polymer fraction of the gel.

Figure 2. Peak intensity ratios, i.e., the peak after the Hahn-echo pulse sequence without the field gradient pulse to the initial coherent peak after 90° pulse (I(90° + 180° pulses, δ = 0)/I(90° pulse)) of the PVDF gel prepared by (a) annealing and (b) quenching, while changing the polymer fraction of the gel. (c) Typical pulse sequence for the diffusion coefficient measurement. In the evaluation of the T2 behavior, we used an echo signal with δ = 0 (without the application of the gradient pulse).

Each of the inherent diffusion coefficients, Dca, Dan, and Dsolv, is a function of the size and microviscosity of the corresponding species, which can be presented according to the Stokes−Einstein relation, as follows:29 Dsolv = Dan = Dca =



η′ = η + α

η″ = η +

ranion α + βca rcation

RESULTS AND DISCUSSION

Comparison of the Diffusive Features of the PVDF Gel and Chemically Cross-Linked Gels. The diffusion behaviors of the gel electrolytes containing varying polymer fractions show the characteristic features of ion transport associated with the chemical structure and morphology of the gel. Figure 1 shows the observed diffusion coefficients, DLi and DF, normalized by that of the neutral solvent species, DH, as a function of the polymer fraction of the three types of gel electrolytes.7,8 DLi and DF can be assumed to roughly represent the diffusion characteristics of the cation and anion species, respectively, according to eq 1. This normalized plot represents the features of the changes in the cation and anion mobility, except for the effect of the change in the gel viscosity, which is simply reflected by the change in DH. The DLi/DH of PEO and PVB gels decreased steeply compared with DF/DH upon increasing the polymer fraction of the gel. This is because the Lewis basic polar sites of the ether oxygen, −O− of PEO, or the −OH group of PVB would interact with the cations, thus selectively reducing the cation mobility. On the contrary, the attenuation rates of DLi/DH and DF/DH of the PVDF gel are smaller than those of the PEO and PVB gels, showing a

kT 6πrPCη

kT , 6πranionη′

kT , 6πrcationη″

difference between them could be estimated as a net effect if both terms are present simultaneously in a sample.

(3)

where η, α, and βca are the microviscosities attributed to the van der Waals interactions with the surrounding species, Coulombic interactions between the cation and anion species, and Coulombic interactions between the cation and attractive sites on the membrane, respectively. Notably, when examining the interaction between attractive sites and the anion, βan had to be included in the equation for Dan, whereas βca had to be removed from the equation for Dca (eq 3). This is because our model of solving three simultaneous equations (eq 3) could independently estimate only three parameters (η, α, and βca or βan). However, as βca and βan compete with each other, the C

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Figure 3. NMR echo decay as a function of time for T2 measurements of the 7Li and 19F species of gels with 10 wt % PVDF prepared by (a) annealing and (b) quenching.

Figure 4. T2 estimated from the slope of decay determined in Figure 3 for (a) annealed and (b) quenched gels. T2(F) of the annealed and quenched gels at 15 wt % of PVDF were estimated by two component fitting: T2(F1) is the major component (≥80%), while T2(F2) is the minor component (80%, and a minor component, T2(F2), with the fraction of T2(F).

obtained, which was similar to the correlation of T02(Li) and T02(F) of the solution without the polymer, as shown in Figure 4. However, upon decreasing the temperature below 80 °C, T2(Li) and T2(F) became separated. Considering that for preparing the gel heating the mixture of the polymer and solution at >90 °C is required to form a homogeneous sol, the correlation T2(Li) ≫ T2(F) below 80 °C can be attributed to gel formation, thereby implying that the solid phase composed of the crystalline network and solution-rich phase is the cause of T2(Li) ≫ T2(F). E

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Figure 6. (a) Ionic conductivities, (b) inherent diffusion coefficients of the cations (Dca) and anions (Dan), (c) cation transport numbers (tLi), (d) microviscosities due to cation/anion interactions (α), and (e) ion/PVDF interaction (βan, βca) of the gel as a function of the PVDF polymer fraction in the gel. The values at p = 0 are for the electrolyte solution without PVDF.

phase, as confirmed by the T2 results. In practice, the α values of the quenched gels were lower than those of the annealed gel and decreased with increasing polymer fraction, as can be seen in Figure 6c. This indicates the presence of a high barrier for the approach of the cations and anions toward each other caused by the fact that they are located in different phases of the quenched gel. For the annealed gel, in which cations and anions predominantly coexisted in the solution-dominant region inside the polymer network, βca > 0 was obtained, which indicates that the cation species experienced a relatively strongly restricted motion compared to the anion species. This might be because the positively charged cations were easily attracted to the F-rich PVDF structure. In practice, for gels with a smaller PVDF amount than 5 wt %, the polymer network would not be enough to form a stable and homogeneous swollen gel. As a result, the morphological difference between the annealed and quenched gels would be small, thereby explaining the result that Dan of the quenched gel is fairly large compared to Dan of the annealed gel with 5 wt % PVDF.

During the gelation process, it is probable that the lithium salt acts as the nucleation agent for crystal deposition because the PVDF sol is easily gelated with the salt, rather than without it. In fact, during the process of crystal deposition and growth, it seems that the anion species were selectively bound to the crystallites away from the cation species. Estimation of the Inherent Diffusion Values (Dca, Dan) and Microviscosities (η, α, βan). Figure 6 shows the measured ionic conductivities and the inherent diffusion coefficients (Dca, Dan, and Dpair) and microviscosities (η, α, and βan or βca) responsible for the magnitudes of the diffusion coefficients estimated according to the theoretical model. The changing trends of Dca and Dan with the polymer fraction showed characteristic features, depending on the cooling process used for the gelation. For the quenched gel, Dan decreased monotonously and Dca remained constant with the increasing polymer fraction. On the contrary, Dca decreased and Dan remained constant with the polymer fraction for the annealed gel. These anomalous features of the ionic mobilities depending on the gel preparation conditions reflect the interactions, characterized by α (cation/anion interaction) and βca or βan (cation or anion/polymer interaction), of the ionic species from the surroundings in the phase where ions are present. The decrease in Dan with the polymer fraction is associated with the increase in βan in the quenched gel, while the decrease in Dca is caused by the increase in βca in the annealed gel. The fact that βan > 0 in the quenched gel indicates that the anion mobility in the gel is relatively restricted compared to the cation mobility. This could be recognized from the fact that the anions were present separately in the vicinity of the crystalline phase, which was highly viscous and imposes a larger resistance to motion, as opposed to the cations, which were present in the solution-rich



CONCLUSIONS In this study, we evaluated the ion migration mechanism of PVDF gel electrolytes associated with the morphological features of physically cross-linked PVDF gels. As a result, we found that the location of the cation and anion species in the gel depended on the gel morphology, which depends on the preparation conditions. In the case of quenched gels, cations were located in the solution-rich phase inside the polymer network, while anion species were dominantly located close to the crystalline phase comprising the cross-linked network, which was confirmed by the result of T2(Li) ≫ T2(F). In an F

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(6) Koga, T.; Tanaka, F. Elastic Properties of Polymer Networks with Sliding Junctions. Eur. Phys. J. E: Soft Matter Biol. Phys. 2005, 17, 225−229. (7) Kataoka, H.; Saito, Y.; Uetani, Y.; Murata, S.; Kii, K. Interactive Effect of the Polymer on Carrier Migration Nature in the Chemically Cross-Linked Polymer Gel Electrolyte Composed of Poly(ethylene glycol)dimethacrylate. J. Phys. Chem. B 2002, 106, 12084−12087. (8) Saito, Y.; Okano, M.; Kubota, K.; Sakai, T.; Fujioka, J.; Kawakami, T. Evaluation of Interactive Effects on the Ionic Conduction Properties of Polymer Gel Electrolytes. J. Phys. Chem. B 2012, 116, 10089−10097. (9) Saito, Y.; Okano, M.; Sakai, T.; Kamada, T. Lithium Polymer Gel Electrolytes Designed to Control Ionic Mobility. J. Phys. Chem. C 2014, 118, 6064−6068. (10) Tazaki, M.; Onodera, A.; Homma, T. Morphological Study of Gels Prepared from Poly(vinylidene fluoride) in Organic Solvents. Kobunshi Ronbunshu 1993, 50, 533−536. (11) Voice, A. M.; Davies, G. R.; Ward, I. M. Structure of Poly(vinylidene fluoride) Gel Electrolytes. Polym. Gels Networks 1997, 5, 123−144. (12) Liu, F.; Hashim, N. A.; Liu, Y.; Abed, M. R. M.; Li, K. Progress in the Production and Modification of PVDF Membranes. J. Membr. Sci. 2011, 375, 1−27. (13) Song, M.-K.; Kim, Y.-T.; Kim, Y. T.; Cho, B. W.; Popov, B. N.; Rhee, H.-W. Thermally Stable Gel Polymer Electrolytes. J. Electrochem. Soc. 2003, 150, A439−A444. (14) Nagai, A. Applications of Polyvinylidene Fluoride-Related Materials for Lithium-Ion Batteries. In Lithium-Ion Batteries; Springer: New York, 2009; pp 155−161. (15) Voice, A. M.; Southall, J. P.; Rogers, V.; Matthews, K. H.; Davies, G. R.; McIntyre, J. E.; Ward, I. M. Thermoreversible Polymer Gel Electrolytes. Polymer 1994, 35, 3363−3372. (16) Richardson, P. M.; Voice, A. M.; Ward, I. M. Two Distinct Lithium Diffusive Species for Polymer Gel Electrolytes Containing LiBF4, Propylene Carbonate (PC) and PVDF. Int. J. Hydrogen Energy 2014, 39, 2904−2908. (17) Richardson, P. M.; Voice, A. M.; Ward, I. M. NMR SelfDiffusion and Relaxation Time Measurements for Poly(vinylidene fluoride) (PVDF) Based Polymer Gel Electrolytes Containing LiBF4 and Propylene Carbonate. Polymer 2016, 97, 69−79. (18) Ogston, A. G. The Spaces in a Uniform Random Suspension of Fibres. Trans. Faraday Soc. 1958, 54, 1754. (19) Cukier, R. I. Diffusion of Brownian Spheres in Semidilute Polymer Solutions. Macromolecules 1984, 17, 252−255. (20) Amsden, B. Solute Diffusion within Hydrogels, Mechanisms and Models. Macromolecules 1998, 31, 8382−8395. (21) Bockris, J. O’M.; Reddy, A. K. N. In Modern Electrochemistry; Plenum Press: New York, 1998; p 453. (22) Saito, Y.; Morimura, W.; Kuse, S.; Kuratani, R.; Nishikawa, S. Influence of the Morphological Characteristics of Separator Membranes on Ionic Mobility in Lithium Secondary Batteries. J. Phys. Chem. C 2017, 121, 2512−2520. (23) Carr, H. Y.; Purcell, E. M. Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments. Phys. Rev. 1954, 94, 630−638. (24) Meiboom, S.; Gill, D. Modified Spin-Echo Method for Measuring Nuclear Relaxation Times. Rev. Sci. Instrum. 1958, 29, 688−691. (25) Saito, Y.; Kataoka, H.; Capiglia, C.; Yamamoto, H. Ionic Conduction Properties of PVDF-HFP Type Gel Polymer Electrolytes with Lithium Imide Salts. J. Phys. Chem. B 2000, 104, 2189−2192. (26) Tanner, J. E. Use of the Stimulated Echo in NMR Diffusion Studies. J. Chem. Phys. 1970, 52, 2523−2526. (27) Price, W. S.; Kuchel, P. K. Effect of Nonrectangular Field Gradient Pulses in the Stejskal and Tanner (Diffusion) Pulse Sequence. J. Magn. Reson. 1991, 94, 133−139. (28) Kataoka, H.; Saito, Y.; Sakai, T.; Deki, S.; Ikeda, T. Ionic Mobility of Cation and Anion of Lithium Gel Electrolytes Measured

environment with a shorter relaxation time for anions, Dan was reduced due to the increase in βan, which is attributed to the enhanced anion/crystalline polymer interaction with increasing polymer fraction. In the case of annealed gels, cations and anions predominantly coexisted in the solution-rich phase, as can be concluded from the result of T2(Li) ≳ T2(F) and the analogy of the correlation of T2(Li) ≅ T2(F) of the electrolyte solution and homogeneous sol. This difference between the two types of gels is due to the initial process of gelation. More specifically, the deposition of a large number of crystallites involves the utilization of the lithium salt as the nucleusforming species upon quenching the sol. During this process, it is likely that the anions were selectively bound to the crystallites. In contrast, a relatively small number of crystallites would deposit and gradually grow to form large crystals that cross-link during the annealing process of gelation. Therefore, in the annealed gel, both the cations and anions would remain in the solution-rich phase inside the network because of the low amount of the initially deposited crystalline phase, which could only capture a few anions. On the basis of the results from this study, we can conclude that to design effective gel electrolytes for lithium secondary batteries, PVDF gel electrolytes prepared by quenching would be beneficial because of the reduced anion mobility caused by the selective uptake of anion species close to the crystalline phase. Furthermore, gels with enhanced cation mobilities and cation transport numbers would be promising as electrolytes in highpower battery systems that are indispensable for electric vehicles and other similar devices. In summary, the significant finding of this study is that PVDF gel electrolytes could have discrete phases that capture the cations and anions separately, thus enabling the selective control of the cation and anion mobilities by controlling the gel morphology. .



AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel +81-72-851-4527. ORCID

Yuria Saito: 0000-0002-9616-6309 Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS The authors thank the Kureha Corporation for financially supporting this research.



REFERENCES

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