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Electronic and Ionic Dynamics Coupled at Solid-Liquid Electrolyte Interfaces in Porous Nanocomposites of Carbon Black, Poly(vinylidene Fluoride) and # Alumina Eddie Panabière, Jean-Claude Badot, Olivier Dubrunfaut, Aurelien Etiemble, and Bernard Lestriez J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12204 • Publication Date (Web): 27 Mar 2017 Downloaded from http://pubs.acs.org on March 29, 2017

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The Journal of Physical Chemistry

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Electronic and Ionic Dynamics Coupled at Solid-Liquid Electrolyte Interfaces in Porous Nanocomposites of Carbon Black, Poly(vinylidene fluoride) and  Alumina Eddie Panabière,1,2,4 Jean-Claude Badot,1*, Olivier Dubrunfaut,2 Aurélien Etiemble,3 and Bernard Lestriez 4 1

Chimie ParisTech, PSL Research University, CNRS, Institut de Recherche de Chimie Paris, 75005 Paris, France 2 GeePs | Group of Electrical Engineering - Paris, UMR CNRS 8507, CentraleSupélec, Sorbonne Universités, UPMC Univ Paris 06, Univ Paris-Sud, Université Paris-Saclay, 3 & 11 rue Joliot-Curie, 91192 Gif-sur-Yvette, France 3 Univ Lyon, INSA Lyon, CNRS, MATEIS, UMR 5510, F-69621 Villeurbanne, France 4 Institut des Matériaux Jean Rouxel, UMR CNRS 6502, Université de Nantes, 2 rue de la Houssinière, BP32229, 44322 Nantes, France

*Address correspondence to [email protected]

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Abstract Better fundamental understanding of the transport properties within nanocomposite materials consisting of interpenetrated percolating networks and used as electrodes is needed to improve their performance for a variety of devices. The simultaneous measurement of their effective ionic and electronic conductivities requires sophisticated experimental set up. Here, the reciprocal influence of ionic and electronic transfers at different scales of model porous nanocomposites made of carbon black-poly(vinylidene fluoride)- alumina wetted by a nonaqueous electrolyte is investigated by Broadband Dielectric Spectroscopy (BDS) from 40 to 1010 Hz, between 223 and 293 K. Experimental results show that the coupling of electronic and ionic dynamics at interfaces in the nanostructured composite material results in significant decrease of the electronic conductivity compared to the dry state and increase of the ionic conductivity compared to the bulk electrolyte.


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Nanocomposite materials consisting of several interpenetrated and percolating phases are widely used as electrodes, not only for a variety of electrochemical cells such as fuel cells (1), electrolyzers (2), supercapacitors (3,4) and batteries (5), but also for composite actuators (6), chemical sensors (7), dye-sensitized solar cells (8) and more generally devices with reactions at the liquid–solid interface (9). Such electrodes are generally mixed ionic-electronic conductors, in which ions and electrons are confined to transport within the specific conducting network (10). Particularly true for electrochemical storage and energy transformation devices, the transport properties play critical roles in determining their performance, which is pivotal to improve for serving as power sources to shift from using fossil fuels to cleaner renewable energy sources (11). To reach this goal, an increased fundamental understanding of the factors that play on the transport properties within such nanocomposite materials is still required (12,13,14,15). All studies devoted to electronic conductivity are locked to macroscopic or longrange values (i.e. dc-conductivity), which give limited information on the electrical transport in nanocomposite electrodes (16). For lithium-ion batteries, these materials are hierarchical architectures since they contain agglomerates of active material nanoparticles (AM) and of conductive additive (carbon black in the form of nanoparticles, CB) separated by insulating nano-gaps or nano- barriers that limit the electronic transfer. The ionic conductivity is generally extrapolated from the bulk properties of the liquid electrolyte (LE) by introducing the porosity and the pores tortuosity, and by using the Bruggeman law (17). Such an approach is very far from directly measuring the true mass transport parameters of electrolyte species when they are confined within the electrode’s porosity and in a battery under load (with an applied current/difference of potential between the two current collectors) (18). Indeed, the geometry of the electrode architecture is not the only one parameter that plays on the electrolyte species diffusion. We must also consider the role of interfaces (adsorption of ions to the surface of active material and carbon nanoparticles), and interactions at such interfaces (19). An



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interesting interfacial effect is observed in the so-called soggy-sand electrolytes, in which the addition of oxide nanoparticles results in an increased ionic conductivity of one type of ion and decreased conductivity of the counter ion, with respect to the bulk liquid electrolyte, as a consequence of specific adsorption (20,21). However, simultaneous measurement of the effective ionic and electronic conductivities is very rare because it requires sophisticated experimental set up (10,12,22). In this way, ex-situ broadband dielectric spectroscopy (BDS from 40 to 1010 Hz) has provided information on the electronic conductivity and electric polarizations induced by electronic transfers at the different scales of various electrode materials (16,23,24,25,26) from interatomic to macroscopic scale via intermediate sizes, such as nano- and micrometric. The BDS allows to measure simultaneously complex conductivity () and permittivity () related by 𝜎(𝜔) = 𝑖𝜔𝜀0 𝜀(𝜔)

(1)

where  = 2 is the angular frequency in rad.s-1 ( being the frequency in Hz) and 0 = 8.8410-12 F.m-1 the vacuum permittivity. According to the selected representation, real and imaginary parts of () and () are directly plotted as functions of the frequency or in the form of Nyquist plots (i.e. imaginary vs. real part). These have the advantage of facilitating the decomposition of the spectra in several relaxations resulting of the different polarization reversals. More the objects are small and conducting, more the relaxations frequencies are higher thereby justifying a wide frequency range from few Hz to few GHz. For example, the nanoparticles will give rise to relaxations at higher frequencies than their agglomerates with sub-micrometric sizes. Moreover, ions will give responses at lower frequencies than the electrons. Furthermore, in-situ BDS device was recently developed to study the evolution of the electronic conduction when the electrode comes in contact with the electrolyte and during electrochemical cycling (27). The existence of strong interactions between the liquid electrolyte


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and the active material (LiNi1/3Mn1/3Co1/3O2) has been shown. The interactions at CB/electrolyte interface were unfortunately masked because the CB content was low in these electrodes. The active material is here substituted by an insulating compound, -Al2O3 to detect and evidence possible interactions between the carbon black and the electrolyte. In the present paper, we report the BDS study of a nanocomposite material made of -Al2O3, carbon black (nanoparticles) and poly(vinylidene fluoride) (PVdF), soaked by a lithium battery organic electrolyte.

RESULTS AND DISCUSSION Materials and architectures of the composites. Compositions of the samples are given in Table 1. SEM observations (presented in Supporting Information S1) reveal the -Al2O3 particles are thin micrometric flakes (50-100 nm thick) with granular texture made of sintered spherical particles (mean diameter 10-20 nm). CB has a complex structure of primary particles (mean diameter 37 nm) (28) forming chemically bound agglomerates (average size 150 nm) (28) that tend to further agglomerate, resulting in void volumes in the interstices of the CB agglomerates (28), as well as in the interstices between CB agglomerates and -Al2O3 particles. PVdF preferentially bound to CB and forms CB+PVdF clusters (29) because it has weak interactions with alumina as a consequence of electrostatic repulsion between fluorine and oxygen atoms (30). The total porosity of the samples, which is determined from their mass composition, their dimensions and the density of each compound, increases from 47 to 58%. (Table 1). Such an increase of the porosity with the increase of the CB content is generally reported (28,31). Existence of mesopores is demonstrated by the BJH method (Supporting Information S2). Whatever the sample, the nitrogen adsorption-desorption isotherms are characteristic of solids with wide distributions of mesopores from 2 to 40 nm. The mesoporosity slightly decreases from 32 to 28% with the increase of the CB content (Table 1). Comparison



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of the total porosity to the mesoporosity shows that the macroporosity of the samples (Figure 1a), which gathers pores of dimension larger than 40 nm, increases linearly with increasing the amount of CB from 15 to 30% (Table 1). No variation in the BET surface area was found depending on the sample composition, with a mean value of 42.4 ( 2) m² g-1. Such a result is likely due to the similar BET surface area of -Al2O3 and CB, respectively 60 and 62 m² g-1. Let’s note that for CB, it is mainly the geometrical surface area of these nanoparticles that contributes to the surface area. For micrometric -Al2O3 flakes the surface area is rather due to the mesopores inside the sintered -Al2O3 agglomerates (32). FIB-SEM 3D reconstructions of S4 and S7 (Figure 1b-e and Supporting Information S3) illustrate the larger amount of CB+PVdF and the higher porosity of S7 compared to S4. Density profiles of -Al2O3, CB+PVdF and porosity were determined to characterize the volumetric spatial distribution inside the composites (Supporting Information S3). These profiles reveal a fairly homogeneous composition in the investigated volumes for both samples. Comparison to mean values calculated from the samples composition shows that FIB-SEM does not see the mesopores distributed at the surface and within the -Al2O3 flakes. Indeed, the volume fraction of the -Al2O3 phase after image analysis is found equal to the sum of the mean volume fractions of -Al2O3 and the mesoporosity (see values in Table 1 and Figure S6). However, the volume fraction of the CB+PVdF mixture is well quantified by FIB-SEM as it is found equal to the sum of the mean volume fraction of CB and PVdF. Finally, the porosity quantified by FIB-SEM is equal to the macroporosity of the samples. Several quantitative parameters about the nanocomposites architecture were calculated from FIB-SEM reconstructions (Supporting Information S3). The median macropores size was found equal to 60 and 90 nm in S4 and S7, respectively. These macropores were found to be fully intra-connected in both samples. The CB+PVdF agglomerates are nearly 100% intraconnected in S7, which means that in the  600µm3 volume studied of S7, nearly 100 %v of the


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CB/PVdF mixture belongs to a unique ramified cluster. The intra-connectivity of S4 is only 46%, which means that from the geometrical point of view, the network of CB+PVdF agglomerates is in the percolation threshold range slightly above its composition.

Percolations of electronic and ionic conductivities in Al2O3/CB/PVDF composites. Complex permittivity () and conductivity () of the dry and the wet samples are determined with ex-situ and in-situ devices respectively. Hereafter, dried and wet samples are labeled with respective “d” and “w” index (see experimental part), and “e” and “i” indices mean electronic and ionic, respectively. In Figure 2, the electric spectra of the different samples are plotted vs. the frequency ( = /2). The real part of the conductivity is shown in Fig. 2a and 2b for dry and wet samples, respectively. The frequency dependent permittivity (real part ’) is also reported in Fig. 2c and 2d for dry and wet samples, respectively. Note that the dielectric spectra of the wet samples are reliable up to 1×109 - 2×109 Hz because of the occurrence of unwanted resonance (see Supporting Information S4) probably due to electromagnetic perturbations in the coupling of the sample with the in-situ device. Fig. 2a shows two sets of plots depending on the CB content. A first set of samples (in red) corresponds to dry materials S5d, S6d, S7d and S8d with CB contents CB above 0.05 (%v) and conductivities ranging from 0.5 to 12 S.m-1, independent of the temperature (Supporting Information 5). Such characteristics are typical of CB-based composites above the percolation threshold (16). The second set of dry samples (in black) corresponds to S1d, S2d, S3d and S4d with lower CB contents (0 < CB < 0.05) and lowfrequency conductivities ranging from 10-7 to 3×10-4 Sm-1 at room temperature. For this later set of samples, the conductivities depend strongly on the temperature with activation energies of about 0.5-0.6 eV (Supporting Information S5). As -alumina has a proton affinity, it gives rise to a dominant protonic conductivity in these samples in which the CB percolation is not achieved. These electrical behaviors are in agreement with FIB-SEM analysis, according to



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which S4 is slightly below the geometrical percolation of the CB+PVdF agglomerates, while these ones are largely intra-connected in S7. Fig. 2b shows the frequency dependent conductivity (real part) for the wet samples with pores filled by the liquid electrolyte. When comparing with Fig. 2a, the two sets of samples show narrowed range of low-frequency conductivities values between 5×10-2 and 1 S.m-1 at room temperature. The low-frequency conductivities of S1 to S4 are naturally increased since they are now mainly due to ionic transfers within the pores filled with the electrolyte that shows a bulk conductivity of about 0.9 S.m-1 at room temperature. However, S5w to S8w samples with percolated CB have conductivities that have surprisingly decreased by at most one order of magnitude. This is due to a decrease of the CB electronic conductivity owing to a strong interaction with the solvent dipoles and ions of the electrolyte, as we will later detail. The permittivity plots (Fig. 2c and d) are discussed in section 3.2. Nyquist plots of complex resistivity (” vs. ’) and conductivity (” vs. ’) at room temperature for dry S4d S5d, S8d and wet S1w, S6w and S8w samples are shown in Figure 3. They evidence resistances and capacitances due to sample/current collector and/or electrolyte/CB interfaces, which allow to obtain the true dc-conductivities of the different samples. Nyquist plots for the other samples are shown in Supporting Information S6. Resistivity plots of S5d (Fig. 3a) and S8d (Fig. 3b), in which CB is percolated, are single circular arcs which tend to cross ’ axis at the origin. Experimental data are similar for the other CB-percolated samples S6d and S7d. Dc-conductivities ed of these percolated samples, which are extracted from the low frequency intercept of the ’ axis, are temperature independent between 223 and 293K (Supporting Information 5). The conductivity plot of S4d (Fig. 3c) shows two contributions: a low-frequency part below 103 Hz (zoom in Fig. 3c) and a high-frequency part above 3×109 Hz both described by a skewed straight line (Fig. 3c). Extrapolated low- and high-frequency parts cross the ' axis at 𝜎 ′ = 𝜎𝐻 + = 1.1×10-4 S.m-1 and 𝜎 ′ = 𝜎𝑒𝑑 = 0.15 S.m-1,


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respectively. The dc-conductivity 𝜎𝐻 + of S4d is due to the proton diffusion within the sample pores, while ed corresponds to the electronic part of the sample conductivity since 𝜎𝑒𝑑 >> 𝜎𝐻 + . Consequently, the electrical equivalent circuit of the sample can be schematized by a resistance RH  H-1 in parallel with a capacitor Ced and a resistance Red  ed-1 in series (insets of Fig. 3e and 3f). In this case Ced symbolizes the PVdF nano-gap between the gold electrode and the CB agglomerates of the sample. The conductivity plot of S1w (Figure 3d) shows two significant contributions: a circular arc and a straight line at low and high frequency, respectively. The circular arc, which crosses the ’ and ” axes at zero, is typical of a blocking junction between an ionic conductor (ions in sample pores) and a metal (gold collector), whose electrical equivalent circuit is an ionic double-layer capacitance in series with an ionic resistance (of the electrolyte within the pores). The straight line, which corresponds to a (iω)0.17 frequency response of the complex conductivity, is due to the ionic diffusion of electrolyte species (i.e. Li+ and PF6− ) in the porous network. The ionic conductivity, i, of S1w is thus given by the intersection of the circular arc and the straight line on the ’ axis. It follows Arrhenius laws with activation energies of 0.21 eV and 0.50 eV above and below 250 K, the melting point of the electrolyte (Figure 4a). The freezing of the electrolyte below 250 K is responsible for the large increase of activation energy. The results are similar for the other wet samples S2w, S3w and S4w which are also only ionic conductors with similar activation energies (Table 1). The Nyquist plots of S6w and S8w (Fig. 3e and 3f) show also two contributions: a circular arc and a high frequency tail. The lowfrequency part of the circular arc crosses the ' axis at ' = ew, unlike the case of only ionic conductors where ew = 0. In this case, a parallel resistance R ew  ew-1 is added into the electrical equivalent circuit (insets of Fig. 3e and 3f). Figure 4a shows that ew does not undergo any discontinuity through the freezing temperature of the electrolyte and follows an Arrhenius law with an activation of about 0.06 eV over the whole temperature range. Hence, this



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demonstrates the conductivity ew is the electronic conductivity of the CB network in the wet sample. The results are similar for S5w, S7w and S8w for which the mean activation energies are between 0.01 and 0.08 eV over the whole temperature range (Table 1). The width of the circular arc gives the ionic conductivity i as it undergoes a discontinuity at 250 K. The ionic conductivity i of S6w follows Arrhenius laws with activation energies of about 0.14 eV and 0.40 eV above and below 250 K respectively (Fig. 4a). The results are similar for S5w, S7w and S8w (Table 1). Fig. 4a also shows a higher ionic conductivity for S6w compared to S1w, which is discussed later. Such temperature dependence of electronic and ionic conductivity is in good agreement with the result of previous measurements by electrochemical impedance spectroscopy on LiNiO2-based positive electrode (33). An advantage of BDS over EIS is that the former technique gives access to both conductivities through a single one measurement while the later technique requires two separate measurements on two different samples. The electronic conductivity ed of the dry samples as a function of the CB content CB is fitted by the percolation law expression given by 𝜎𝑒𝑑 ∝ (𝜙𝐶𝐵 − 𝜙0𝑒 )𝑡

(2)

with the percolation threshold 0e ≈ 0.050 and the percolation exponent t ≈ 1.8 (Fig. 4b). This result is consistent with a 3D percolation of the CB network in the dry S5d to S8d samples, as shown by FIB-SEM analysis for S7. The electronic conductivity occurs only through the CB/PVdF agglomerates. The results show also that dc-conductivities of percolated dry samples are mainly due to electron tunneling between the CB agglomerates (see Supporting Information S7). Indeed, tunneling electronic conduction can occur through gaps of insulating polymer separating two conducting agglomerates of CB particles and depends of the gap thickness (16,34,35). The electronic conductivity of the wet samples ew is lower than that of the dry samples ed whatever CB (Figure 4b) and is thermally activated (Table 1). Such drop in


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conductivity has already been reported by Peterson et al. who observed that the introduction of similar kind of electrolyte mixture to LiCoO2/CB/PVdF lithium battery composite electrodes reduced electronic conductivity by around 60% (36). This result was claimed to be due to the swelling of the PVdF polymer by the liquid electrolyte, leading to larger gaps and hence resistance between CB agglomerates. However, ew has the same percolation threshold (0e ≈ 0.050) than ed, since no electronic conduction was detected in the wet samples below 0e. The swelling of the PVdF by the electrolyte has thus a negligible effect on the electronic conductivity and thus on the CB network. Otherwise, a different percolation threshold would have been observed for wet materials. The presence of attractive van der Waals forces between CB particles and agglomerates in contact should compensate the effect of the swelling (37,38). Contrary to the electronic conductivity of the dry samples, the wet samples electronic conductivity ew is thermally activated and is given by Arrhenius law (Figure 4a and Table 1): 𝐸

𝜎𝑒𝑤= 𝜎0𝑒𝑤 𝑒𝑥𝑝 (− 𝑘 𝑎𝑇) 𝐵

(3)

with Ea the activation energy (in eV), kB (= 1,381.10−23 J.K−1) the Boltzmann constant, T (K) the temperature, and 0ew the prefactor attributable to the conductivity of CB agglomerates. The activation energy corresponds to the barrier created by electron-ion interactions at the CB surface. Adsorbed solvent molecules and ions increase the dielectric strength of the medium around CB particles. Thus, a higher potential barrier is required to transport electrons across the nano-gaps between CB particles. It is then suitable to compare the conductivity 0ew of CB agglomerates wetted by the electrolyte (given by Eq. 3) with the conductivity ed of the network of dry CB agglomerates in order to analyze the interactions at the CB/electrolyte interface when the CB is percolated. The plot of Figure 4c shows that the ratio 0ew/ed is a decreasing function of the carbon content CB with the following characteristics: a) 0ew/ed > 1 if CB = 0.053 and 0.069; b) 0ew/ed < 1 if CB = 0.078 and 0.092; c) 0ew/ed = 1 for CB ≈ 0.075. The meaning



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of 0ew/ed > 1 is that the number of mobile electrons and their mobility are higher in wet samples compared to dry samples. This effect results of coulombic repulsive interaction between the electrons and anions PF6− , which likely predominate over the cations Li+ at the CB surface for CB < 0.075 (see below). For 0ew/ed < 1, the number of mobile electrons as well as their mobility is lower than in dry samples. In this case, the majority of the electrons is trapped and also slowed by their attractive interaction with the adsorbed cations Li + which predominate over the anions PF6− at the CB surface for CB > 0.075. For 0ew/ed = 1 at CB ≈ 0.075, a zero charge interface (zci) occurs because the number of adsorbed Li + is equal to the number of adsorbed PF6− at the CB surface (39). The origin of the charge inversion of the interface CB/electrolyte interface is the result of specific interactions between the electrolyte, the -alumina and CB surfaces. Indeed, it is well known that Li+ ions are attracted to the surface of -alumina where they strongly bind with the electron donating oxygen basic surface sites 20,21, 40. Clear

evidence was also given for the preferential adsorption of Li+ (compared to PF6− )

ions at the surface of CB (37,38). There is thus a competitive adsorption and a partition of Li+ ions between the -alumina and the CB surfaces. At low CB concentration, we speculate that Li+ ions are preferentially captured by -alumina, while at higher CB concentration more Li+ are left to interact and adsorb at CB surface. This would be due to the increase in the samples macroporosity with increasing CB content, favoring the supply of electrolyte species from the reservoir situated in the separator above the sample in the cell. The occurrence of the reversal of the CB surface charge and of a zci state when the CB content increases in the composite is thus a plausible hypothesis to explain the variations in the number of electrons and their mobility within CB agglomerates. Let’s remind however that in all cases the electronic conductivity in the wet state is reduced compared to the dry state as a consequence of the raising of an energy barrier for electrons hopping at the nano-gaps between CB agglomerates (Fig. 4b).


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When the ionic conductivity is plotted against the macroporosity M, a percolation transition is evidenced at approximately M = 0M  0.20-0.22 corresponding to the CB content CB between 0.023 (S2w) and 0.039 (S3w) which lies before the CB percolation threshold CB ≈ 0.050 (Figure 5a). This representation is justified by the existence of a macropore space bond percolation as observed by FIB-SEM in S4 and S7 (Fig. 1). The ionic conductivity is therefore mainly due to ion diffusion in the electrolyte filling the macropores above their percolation threshold 0M. Below 0M, the conductivity is due to ion diffusion in filled mesopores and is nearly constant and lower than the “free” electrolyte conductivity with a similar activation energy Ea = 0.21-0.22 eV (Table 1). Above 0M and outside the critical region (i.e. S2w to S4w), the experimental data for S5w to S8w (Fig. 5a) are fitted by a straight line which is described by the expression of the effective medium theory (41,42) given by 𝑧

2

σi = 𝜎0𝑖 [𝑧−2 𝜙𝑀 − 𝑧−2]

(4)

with i = 7 S.m-1 the maximum conductivity that the liquid would have if its volume fraction was M = 1. However it does not correspond to the conductivity of the liquid in the free state because the transport mechanism is different in the wet composite, as demonstrated by the decrease of the activation energy (see below). The mean number of macropore throats that meet at a given point in their network (or pore coordination number) z is found equal to 9.4. This result is close to the 3D bond percolation model of BCC lattices for which z = 8 and 0M  0.18 and also with the experimental value of pore space percolation threshold in cements (0M ≈ 0.20) 43. Here, by analyzing the FIB/SEM images, it is possible to determine the distribution of macropores coordination number in the composites (see Supporting Information S3). For both samples, the value z = 9.4 appears to correspond to the upper limit of the distribution. The ionic conductivity of lithium-ion and composite electrodes and separators is generally well represented by the Bruggeman law, which is given by



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σi = σ0 γ Φm

(5)

where 0 is the free electrolyte conductivity, Φ the volume fraction of electrolyte (or the total porosity of the sample),  a numerical coefficient and m the Bruggeman exponent (Supporting Information S8). The equation (5) fits the ionic conductivity values of the samples S1w to S4w below the CB percolation threshold, by using the intervals 2.4 ≤  ≤ 2.5 and 1.5 ≤ m ≤ 3.2 of the literature (18,44) (Fig. 5a). But for the samples with CB contents above the CB percolation threshold (i.e. S5w to S8w), the ionic conductivity is about 4 times higher than predicted by Equation (5). This remarkable result agrees with the study made by Orikasa et al. (12) on a composite electrode LiFePO4/CB/PVdF. In their study as in this one, the ionic conductivity is measured simultaneously to the electronic conductivity, while in general the ionic conductivity is measured for non-electronically conducting separators, or extrapolated from numerical simulations which consider only the ionic flux, or measured on electronically conducting electrode but when no electrons flux goes through the film simultaneously to the ionic flux (18,44). In fact, the ionic conductivities of the samples S5w to S8w are higher than expected by

equation (5) because their activation energy Ea ≈ 0.14 eV is lower than that of the pure LP40 electrolyte (Ea ≈ 0.21 eV, see Figure S18). The decrease of Ea is then observed when an electron flux occurs simultaneously with the ionic flux through the sample. The existence of an electron flux through the sample would lower the ionic diffusion energy barriers. Considering the margin of experimental error on Ea, its decrease justifies the conductivity value 0i = 7 S.m-1 obtained from the fit of Eq. 4. Furthermore, it is remarkable that no modification of the ionic conductivity was observed in the case of a CB+PVdF/ LiNi1/3Mn1/3Co1/3O2 electrode wetted by a similar type of electrolyte (27). In the latter study, the CB content was low, i.e. slightly above the percolation threshold, and the pores were larger, i.e. in the micrometric range. Thus the surface area at the solid-liquid interface was likely too small to significantly play on the ionic conductivity within these samples. Consequently, the modification of the ionic diffusion under


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electronic flux through the sample would only take place if the ratio surface/volume of the pores is sufficiently high. This assumption should be verified on other types of composite materials.

Conductivity relaxation and double-layer capacitance. Conductivity relaxations (see Fig. 3 d to f) are due to space-charge polarizations induced by ionic double-layer fluctuations at the solid-liquid interface. The results are consistent with the following response

𝜎(𝜔) = 𝜎𝑇 −

𝜎𝑖

(6)

1+(𝑖𝜔𝜏𝑖𝑛𝑡 )1−𝛼

where int is the mean relaxation time,  (0 < < 1) an empirical parameter, andT = i + ew the total conductivity with i the ionic conductivity and ew the electronic one. The  parameter means the existence of a distribution of relaxation times that is all the wider as  is greater. The corresponding relaxation frequencies reported in Table 1 are given by

𝜈𝑖𝑛𝑡 =

1 2𝜋𝜏𝑖𝑛𝑡

=

1 2𝜋𝑅𝑖 𝐶𝑖𝑛𝑡

=

𝜎𝑖 2𝜋𝜀0 Δ𝜀𝑖𝑛𝑡

(7)

where int is the effective permittivity of the double-layer proportional to its capacitance Cint. From the knowledge of int and i (Table 1), int is determined by the expression (7) and thus plotted vs. the macroporosity and the CB volume fraction CB in Fig. 5b. The evolution of int vs. M, CB is rugged and shows two main regions (I and II) bounded by the percolation threshold (CB = 0e = 5%) of the CB network: the region I corresponds to an electronic insulator and the region II to an electronic conductor. This boundary is characterized by a strong decrease of int of about three order of magnitude when CB ≥ 0e. This reveals a drastic change in the nature of the solid-liquid interface when going from Region I (CB ≤ 0e) to Region II (CB ≥ 0e). In the region I, frequency int (Table 1) and dielectric relaxation strength int (Fig. 5b) are respectively minimal and maximal at the percolation threshold of the macropores (M ≈ 0.21) in agreement with the percolation theory (30,45,46). In this region I, the double-layer capacitance is mainly due to Al2O3- electrolyte interface, and thus to the preferential



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adsorption of Li+ at Al2O3 surface, as already mentioned (38,39). In the region II, the lower value of int results from the preferential adsorption of ions (Li+ and PF6-) at the surface of the carbon black. The order of magnitude of int drop is probably be due to the decrease of surface potential between ions and CB which would be lower than the potential at alumina surface. The total interfacial potential T is generally given by Δ𝜓𝑇 = Δ𝜓𝑑𝑖𝑝 + Δ𝜓𝑖𝑜𝑛

(8)

where dip is the potential generated by interfacial dipoles (i.e. solvent molecules) and ion the potential generated by ions (Li+ or PF6-). As ion = 0 at the zci, the potential is only generated by the interfacial dipoles, i.e. T = dip. This explains the minimum value of the double-layer capacitance in the region II for a CB volume fraction (CB ≈ 7.5%) corresponding to the zci. Dielectric relaxations: electron local motions in Al2O3/CB/PVDF composites. We have previously seen that the conductivity Nyquist plots allow to understand the conduction mechanisms at the macroscopic scale by taking account of the relaxation behaviors at lower frequencies. At higher frequency, complex permittivity plots are preferred in order to detect relaxations due to polarization reversals due to local motions of charge carriers (electrons in electrode materials) and to dipole rotations. In the considered frequency range, the dielectric spectra of composite electrodes are generally described by the frequency dependent complex permittivity

𝜀(𝜔) = 𝜀ℎ𝑓 + [∑𝑞

∆𝜀𝑞

𝜎

1−𝛼𝑞 𝛽𝑞

[1+(𝑖𝜔𝜏𝑞 )

]

𝑑𝑐 ] + 𝐴(𝑖𝜔)𝑠−1 + 𝑖𝜔𝜀

0

(10)

where hf the residual (or higher frequency) permittivity of the sample, dc the dc-conductivity of the sample, which has been studied exhaustively in the above sections, and s an empirical parameter (0≤ s ≤ 1). The term in brackets is the sum of the Havriliak-Negami (HN) relaxation functions for which 0 ≤ q ≤ 1 and 0 ≤ q ≤ 1 (q and q: fitting parameters). The power-law


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17

term A(i)s-1 is observed for disordered conducting networks. q is the dielectric strength of the relaxation q and q the mean relaxation time. The multiscale electric polarizations induce dielectric relaxations due to electron motions from the agglomerate to the sample scales. These polarizations are essentially due to the existence of interfaces at the different levels of the samples, i.e. macroscopic and CB agglomerates scales. The lengths of the agglomerates vary from the nano- to the sample size when the CB content gets closer to the percolation threshold. The dielectric relaxations thus generated are of the type Maxwell-Wagner-Sillars (MWS)

47

which are here typical space-charge relaxations from nano- to macroscopic sizes. There is a hierarchy of MWS relaxations whose frequencies take place in any frequency from few Hz up to microwave frequencies. The permittivity of S5d to S8d is on average somewhat higher than that of S1d to S4d (Fig. 2c). The difference is mainly due to the existence of more intensive polarizations of CB agglomerates with higher CB content and thus to forward-backward electron motions within them, as we will later detail. Fig. 2d shows that the permittivity of the wet samples is globally higher than the dry samples because of the existence of additional polarizations below 107 Hz due to ion motions within the pore network. In order to evidence the contributions of the different polarization and relaxation, the decomposition procedure of the dielectric spectra is obtained from the Nyquist plots of the complex permittivity , i.e. imaginary part ” vs. real part ’. Nyquist plots of complex permittivity for some of the dry (S4d, S5d) and wet (S2w, S8w) samples at room temperature are shown in Fig. 6 as matter of examples. Nyquist plots for the other samples are shown in Supporting Information S9. The permittivity Nyquist plot of S4d (Fig. 6a), which is near to the CB percolation threshold 0e is decomposed into three contributions including two dielectric relaxations. The lower frequency contribution 1, represented by an inclined straight line corresponding to the power-law term A(i)-0.85 is due



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to proton diffusion in the disordered mesopores network of alumina with activation energy of about 0.68 eV. After subtracting the contribution 1, two relaxations, 2 (large skewed arc) and 3 (small skewed arc) are found with relaxation frequencies of 2×102 and 6×106 Hz, respectively. The relaxation frequencies of the two contributions are not temperature dependent indicating they are due to electron motions. The first one (contribution 2) can be attributed to the Au/sample interface giving rise to a space-charge polarization at the sample scale, which is thus observed at lower frequency. This contribution 2 is well fitted by HN function with 2 ≈ 0.11 and 2 ≈ 0.64 with a temperature dependent dielectric increment 2 ≈ 3000 at 293 K and 2 ≈ 800 at 253 K. As CB is not percolated, the space-charge results from the presence of PVdF nano-gaps between the CB agglomerates and the current collector. The second one (contribution 3) is fitted by a Cole-Davidson (CD) function with 3 = 0 and 3 ≈ 0.32 with the increment 3 ≈ 26 whatever the temperature that allows its attribution to the polarization of CB agglomerates, in agreement with previous work (16). The permittivity Nyquist plot of S5d (Fig. 6b) with CB percolation is decomposed into only two contributions including one dielectric relaxation. The first one (contribution 1), represented by a vertical straight line, is due to the power-law frequency dependent permittivity (-1) and thus corresponds the dcconductivity (d) contribution of the sample (Eq. 10). The dielectric relaxation (contribution 2) can be fitted by Cole-Davidson function ( = 0 in Eq. 10) with the characteristic frequency  = 2×107 Hz (i.e.  ≈ 8 ns),  = 0.32,  = 63, and  ≈ 3.6 whatever the temperature. In the higher frequency part of the relaxation, the CD function gives rise to the following conductivity:  ≈  with  = 1- = 0.68. The latter behavior describes the ac-conductivity in the random conducting carbon black network that has a disordered structure. The sample S6d with CB percolation has a similar behavior than the sample S5d as its complex permittivity is fitted by the sum of a dc-conductivity contribution and a CD relaxation with  = 8×107 Hz (i.e.  ≈ 2ns),  = 0.35,  = 40, and  ≈ 3.6 whatever the temperature. Insulating samples S2d and S3d, which


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19

are far from the percolation threshold, have behaviors different from that of S4d. Dielectric relaxations corresponding to CB agglomerate polarizations are fitted by CC symmetric functions with  = 2×1010 Hz and 6×109 Hz (i.e.  = 8ps and 26ps),  = 0.39 and 0.60,  = 4 and 8 whatever the temperature for S2d and S3d, respectively. Moreover, there is no detected dielectric relaxation in the scanned frequency range for S8d which is the better electronic conductor. Relaxation frequencies r and dielectric relaxation strengths  of CB agglomerate polarization (contributions 2 in the Nyquist plots of S5d, S6d and S7d, and contributions 3 for S4d, S3d and S2d) are plotted in Figures 7a and 7b, respectively, as a function of CB. Frequency r and dielectric relaxation strength  are respectively minimal and maximal at the percolation threshold in agreement with the percolation theory (30) (see Supporting Information S10). The permittivity Nyquist plots of S2w (Fig. 6c) were obtained after subtracting the contribution of the Ag/sample blocking junction to the total complex conductivity of the sample (see Fig. 3d). The obtained dielectric spectrum is decomposed into two contributions including one dielectric relaxation. Contribution 1, represented by a vertical straight line shows powerlaw frequency dependent permittivity (-1) corresponding to the dc-conductivity contribution of the sample (Eq. 10). Contribution 2, represented by a skewed arc well fitted by the HN function has relaxation frequency  that follows Arrhenius law with activation energies of about 0.23 eV and 0.40 eV above and below 250 K respectively. This relaxation results of polarization fluctuations mainly due to ion motions along the mesopores of the -alumina because its activation energy is similar to that of the ionic conductivity (Table 1). The results are similar for S3w and S4w with no CB percolation, and naturally for S1w without CB. The dielectric behavior of the samples with CB percolation (S5w, S6w, S7w and S8w) is significantly different. Figure 5d shows the permittivity Nyquist plot of S8w that can be decomposed into two contributions. The first one is a straight line above 4×106 Hz due to a power-law frequency dependent complex permittivity () α (i)-0.95. The contribution 2 is a dielectric relaxation



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well fitted by a CC function ( = 0 in Eq. 8) with 2 = 0.21, 2 = 72 and 2 = 3.5×107 Hz at room temperature. The relaxation frequency is independent of the temperature with mean values of about 3.5×107 Hz and 5.5×107 Hz, respectively above and below the freezing temperature of the electrolyte (Fig. 7c). This thermal behavior is thus the response of electron motions within CB clusters as there is no activation energy. The slight increase of 2 at the freezing temperature demonstrates that interactions between ions and electrons decrease when the electrolyte changes from liquid to solid state. Figure 7a compares the electron relaxation frequency r in CB clusters for dry and wet samples. For CB ≤ 0.07, r is slightly higher for wet compared to dry samples, whereas for CB ≥ 0.07 it is the opposite. Both relaxation frequencies become equal for CB ≈ 0.07 corresponding to the zci for which the CB/electrolyte interface has similar number of adsorbed anions (PF6-) and cations (Li+). The dielectric strength jumps from a constant value = 30 for CB ≤ 0.07 up to higher value between = 60 to 70 for CB > 0.07 (Figure 7b). This behavior would be explained by the inversion of the electric field at the CB/electrolyte interface. Since the majority of adsorbed ions are Li+ for CB > 0.07, there is an excess of electrons trapped at the CB surface. The interfacial electric field thus created between lithium ions and electrons tends to pull the electrons toward the electrolyte and increases the surface dipole (i.e. space-charge length) in the CB side, which explains the increase of  for CB > 0.07. For CB < 0.07 (i.e. samples S5w and S6w),  is lower than the corresponding dielectric strength of the dry samples. In this case, since the net surface charge is negative (electrolyte side), as discussed above, there is a deficit of electrons at the CB surface. The interfacial electric field tends to pull the electrons toward the core of the CB clusters and thus decreases the volume of the polarization associated to electron motions, which explain the decrease of . Moreover, the relaxation frequency r is therefore proportional to both the electronic mobility in the CB agglomerates and inversely proportional to their size. The latter is a decreasing function of CB content when it is percolated


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21

according to the percolation theory. Above the zci, the influence of the electronic mobility on r is even more significant as the number of adsorbed Li+ is larger. In this latter case, electron trapping and slowing are therefore more intensive. Below the zci, the behavior of r is more influenced by the cluster size as for dry samples owing to a larger number of adsorbed anions. Relevance of the results for practical lithium battery performance. The energy density of these devices is limited because the volume occupied by the inactive components (current collectors, separator, conductive carbon, binder, and electrolyte) is important. This is because the electrodes are limited in thickness for kinetic reasons. Indeed, at the scale of the active material grains, the oxidation-reduction reactions can be ultra-fast. However, there are significant limitations to the charge transport kinetics (ions and electrons) through the electrode. Although critical toward performance, the transport properties are still poorly understood due to a lack of experimental characterizations, and they are generally extrapolated from bulk properties of the conductors (carbon additive and electrolyte) (48,49). We see here that the transport mechanisms are changed from bulk materials in composites. In particular, the diffusion of ions in the electrolyte is accelerated by the simultaneous transport of electrons in the carbon black network. The fingerprint that ionic diffusion is assisted through a coupling with the electrons of higher mobility could be observed in some experimental works. For example in Liu et al. (50) and Fongy et al. (51), the rate performance of LiFePO4-based electrodes in the diffusion limited regime is improved when the CB+binder network is made less tortuous. As a consequence, and as shown recently by Besnard, N. et al. (15), battery models must be revisited for more accurate predictions. It is needed to implement in situ measured transport properties in these models.



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CONCLUSIONS Broadband dielectric spectroscopy allowed to measure both the ionic and electronic transport properties in the -Al2O3/CB/PVdF nanocomposite materials studied here. There are two electrical percolation behaviors when the carbon black (CB) content is increased in these nanocomposites wetted by an electrolyte. The first one results from the building of interconnectivity within the CB network, in which the electronic conductivity is achieved by electron tunneling in dry samples. The second one results from the creation by the CB agglomerates of macroporous interstices between the -alumina particles. Interconnectivity of these macropores results in a sudden rise of the ionic conductivity, which is also shown to follow a percolation law. The ionic percolation threshold occurs at a lower CB content than the electronic one. In the wetted samples, there is about one order of magnitude decrease of the electronic conductivity owing to adsorption of electrolyte ions at CB surface creating energy barriers opposing the electronic transfer between CB agglomerates. Furthermore, a charge inversion of the CB/electrolyte interface is identified. When PF6− predominate over Li+ ions at the CB surface, the number of mobile electrons and their mobility are higher than in the dry sample, due to coulombic repulsive interaction between the electrons and anions. When Li+ predominate over the PF6− ions, at higher CB contents, the number of mobile electrons as well as their mobility is lower than in the dry composite. In this case, the majority of the electrons are trapped and also slowed by their attractive interaction with the adsorbed cations. Above the two percolation thresholds, the ionic conductivity is higher up to five times the expected value from the well-known Bruggeman equation. This is because the activation energy for ionic transport is decreased compared to the bulk electrolyte, likely because the simultaneous electron flux through the sample accelerates the ionic diffusion.


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In summary, we showed that in a nanocomposite composed of a solid electronic conductor and a liquid ionic conductor, there exists a coupling of the dynamics of ionic and electronic species at the solid-liquid electrolyte interface. Due to the large interfacial surface area, this coupling induces significant modifications of the transport properties across the nanocomposite film thickness compared to the bulk materials. This work opens thus new prospects for optimization of devices made of mixed ionic-electronic conductors by the nanostructuration of the two percolating networks.

METHODS Composite materials preparation. Nanocomposites were prepared according to the following procedure: (i) a copolymer of poly(vinylidene fluoride) (PVDF, kynarflex 2751-00 from Arkema) was dissolved in acetone during 4 hours; (ii) carbon black, which is a batterygrade fine highly synthetic graphite nanopowders with high degree of crystallinity (CB, CNERGY Super C65 from Emerys, Brunauer-Emmett-Teller (BET) surface area of 62 m² g-1 [28]) and gamma-alumina (-Al2O3 from Alfa Aesar, 99.997% metal basis, 60 m² g-1) were mixed and grinded manually with a mortar and then added to the solution, which was stirred for 12 h; (iii) the solvent was evaporated by heating at 50 °C; (iv) the solid was collected; and (v) about 20 mg of it was cold pressed at 260 MPa to get cylindrical pellets with a diameter of 7 mm and thickness between 400 and 500 m. The volumetric composition of the nanocomposites, including the total porosity, was calculated from their mass composition, their dimensions and the density of each material (1.78 for PVdF-HFP, 2.27 for CB and 3.66 for Al2O3), and is given in Table 1. As electrolyte, we used 1M LiPF6 electrolyte solution in EC/DEC (1:1) from Merck (LP40). 3D morphological quantification. FIB/SEM tomography was performed for two of the samples: S4 and S7. All experimental details are given in Supporting Information S3.



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Broadband dielectric spectroscopy (BDS). Broadband dielectric measurements were made from 40 Hz to 10 GHz with two impedance analyzers (Agilent 4294 from 40 Hz to 110 MHz and Agilent 4291 from 1MHz to 1.8 GHz) and one vector network analyzer (Agilent E8364B from 10 MHz to 10 GHz). The experimental devices consists of a cell in which the cylindrically shaped sample fills the gap between a coaxial waveguide (APC7mm standard) and a short circuit (27,52,53). Metallic contacts were made by sputtering gold directly on both opposite faces of the dry sample in order to provide good contacts. One face of the sample (face 1) is partially covered by the gold film in its center with a same diameter (3 mm) than the inner conductor of the coaxial waveguide. On the opposite face (face 2), the gold film covers all its surface area in contact with the short-circuit (diameter = 7 mm). The “ex-situ” device is used to measure the permittivity and conductivity of the porous dry sample: the face 1 being directly in contact with the inner conductor. A waterproof “in-situ” device is used to measure permittivity and conductivity of the same metallized sample which has been filled with the electrolyte. After drying at 50 °C for 1 h, the sample was filled by the electrolyte and assembled inside the in-situ cell in an argon-filled glove box (H2O, 1ppm). A coaxial window between the coaxial waveguide and the sample protects it from the humidity and protects the coaxial waveguide from the electrolyte. After a relevant calibration of the analyzers, the sample admittance is computed from measurements of the complex reflection coefficient of the device. The knowledge of the admittance allows determining the complex (relative) permittivity of the sample. Complete dielectric spectra are made from about 600 measurements in the whole frequency range. The knowledge of the complex permittivity allows the calculation of complex resistivity and conductivity. All the measurements are recorded in the range 200 to 300 K under dry N2 flux whatever the used device.

Conflict of interest. The authors declare no competing financial interest.


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25

Acknowledgments. Financial funding from the ANR program no. ANR-15-CE05-0001-01 (PEPITE)

is

acknowledged.

We

also

thank

the

CLYM

(Centre

Lyonnais

de

Microscopie:www.clym.fr) supported by the CNRS, the “Grand Lyon” and the Rhône-Alpes Region for use of the Zeiss NVision40 FIB/SEM. T. Douillard is acknowledged for having performed the FIB/SEM images. Supporting Information available. 1/ Scanning electron microscopy (SEM) observations of Al2O3/CB/PVDF nanocomposites; 2/ BET-BJH measurements; 3/ Focused Ion Beam with Scanning Electron Microscopy (FIB-SEM) tomography; 4/ High frequency resonances; 5/ Temperature dependence of the low-frequency conductivity in dry Al2O3/CB/PVDF composites; 6/ Nyquist plots of complex conductivity and resistivity with respect to the carbon black volume fraction CB; 7/ Tunneling conduction in dry Al2O3/CB/PVDF composites; 8/ Application of the Bruggeman law for Al2O3/CB/PVDF porous nanocomposites; 9/ Nyquist plots of complex permittivity with respect to the carbon black (CB) volume fraction CB: dry samples; 10/ Permittivity and percolation theory.

References (1) Jiang, S. P. Nanoscale and Nano-Structured Electrodes of Solid Oxide Fuel Cells by Infiltration: Advances and Challenges. Int. J. Hydrogen Energy 2012, 37, 449-470. (2) Ni, M.; Leung, M. K. H.; Leung, D. Y. C. Technological development of Hydrogen Production by Solid Oxide Electrolyzer Cell (SOEC). Int. J. Hydrogen Energy 2008, 33, 2337– 2354. (3) Gogotsi, Y.; Simon P. True Performance Metrics in Electrochemical Energy Storage. Science 2013, 334, 917-918.



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(4) Higgins, T. M.; McAteer, D.; Mesquita Coelho, J. C.; Mendoza Sanchez, B.; Gholamvand, Z.; Moriarty, G.; McEvoy, N.; Berner, N. C.; Duesberg, G. S.; Nicolosi, V.; Coleman, J. N. Effect of Percolation on the Capacitance of Supercapacitor Electrodes Prepared from Composites of Manganese Dioxide Nanoplatelets and Carbon Nanotubes. ACS Nano. 2014, 8, 9567-9579. (5) Armand, M.; Tarascon, J. M. Building Better Batteries. Nature 2008, 451, 652–657. (6) Ken, M.; Kinji, A.; Takushi, S.; Kenji, K.; Ichiroh T.; Naohiro, T.; Don, N. F.; Kenji, H.; Takanori, F.; Takuzo, A. Highly Conductive Sheets from Millimeter-Long Single-Walled Carbon Nanotubes and Ionic Liquids: Application to Fast-Moving, Low-Voltage Electromechanical Actuators Operable in Air. Adv. Mater. 2009, 21, 1582-1585. (7) Zhao, Y.; Liu, H.; Kou, Y.; Li, M.; Zhu Z.; Zhuang, Q. Structural and Characteristic Analysis of Carbon Nanotubes-Ionic Liquid Gel Biosensor. Electrochem. Commun. 2007, 9, 2457-2462. (8) Wang, A.; Chung, D. D. L. Dielectric and Electrical Conduction Behavior of Carbon Paste Electrochemical Electrodes, with Decoupling of Carbon, Electrolyte and Interface Contributions. Carbon 2014, 72, 135-151. (9) Eder, D. Carbon Nanotube-Inorganic Hybrids. Chem. Rev. 2010, 110, 1348-1385. (10) Shetzline, J. A.; Creager S. E. Quantifying Electronic and Ionic Conductivity Contributions in Carbon/Polyelectrolyte Composite Thin Films. J. Electrochem. Soc., 2014, 161, H917-H923. (11) Winter M.; Brodd R. J., What Are Batteries, Fuel Cells, and Supercapacitors? Chem. Rev. 2004 104, 4245-4269. (12) Robert, D.; Douillard, T ; Boulineau, A.; Brunetti, G.; Nowakowski, P.; Venet, D.; BayleGuillemaud, P.; Cayron, C. Multiscale Phase Mapping of LiFePO4‑Based Electrodes by Transmission Electron Microscopy and Electron Forward Scattering Diffraction. ACS Nano 2013, 7, 10887-10894.


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DOI:

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32 Table 1. Volume fractions (in %) of the different components of carbon black (CB)-poly(vinylidene fluoride) (PVdF)-alumina (Al2O3) nanocomposites with both types of porosity (in %). Dried and wet samples are labeled with respective index “d” (S1d to S8d) and “w” (S1w to S8w). Electronic conductivities (ed) of the dry samples Electronic (ew) and ionic(i) conductivities of the wet samples with their activation energies: HT and LT means the temperatures above and below the freezing temperature of the electrolyte, respectively. Conductivity relaxation frequencies (int) due to polarizations at solid-liquid interfaces.

Samples

S1 S2 S3 S4 S5 S6 S7 S8 Dry samples (d-index): compositions in %vol and conductivities 46.6 40.0 37.6 35.2 33,1 30.0 28.6 27.3 Al2O3 PVdF 7.4 6.7 6.5 6.2 5.9 6.1 5.6 5.5 0.0 2.3 3.9 4.6 5.3 6.9 7.8 9.2 CB CB *Total porosity 46 51 52 54 56 57 58 58 Mesoporosity 31 31 29 30 31 30 29 28 15 20 23 24 25 27 29 30 Macroporosity M 0.8 1.0 6.0 11.6 ed (S.m-1) 0 0 0 0 Ea (eV) Wet samples (w-index): conductivities and conductivity relaxation frequencies 0.16 0.31 0.71 1.24 ew (S.m-1) 0.08 0.06 0.04 0.01 Ea (eV) 0.06 0.08 0.08 0.18 0.43 0.60 0.63 0.71 i (S.m-1) 0.20 0.21 0.20 0.23 0.14 0.14 0.14 0.14 Ea (eV) (HT) 0.50 0.50 0.45 0.45 0.50 0.40 0.40 0.40 Ea (eV) (LT) 60 4 12 67 6.0×104 1.6×105 1.5×105 6.5×104 int (Hz) *Total porosity = Macroporosity + Mesoporosity: the porosity determined by FIB/SEM FIB/SEM was found

equal to the macroporosity M, which is determined as the difference between the total porosity T and the BJH mesoporosity m,BJH (FIB/SEM = M = T - m,BJH).


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Figure captions Figure 1. Architectures of nano composites of carbon black (CB)-poly(vinylidene fluoride) (PVdF)-alumina (Al2O3). a) Macroporosity (the difference between the total porosity and the mesoporosity accessed by BET-BJH measurements) as a function of the CB volume content; b) to e) FIB-SEM reconstructions of samples S4 and S7: -alumina in grey, CB+PVdF in blue on b) and c), respectively S4 and S7, and detected macroporosity in grey b) and c), respectively S4 and S7. Figure 2. Real parts of conductivity ’ and permittivity ’ vs. frequency of dry (a and c) and wet (b and d) samples at 293 K. The insets in b and d show the resonance due to the coupling between samples and the in-situ device above 2×109 Hz. Figure 3. Nyquist plots at 293K of: a) complex resistivity (” vs. ’) for dry sample S5d; b) complex resistivity (” vs. ’) for dry sample S8d; c) complex conductivity (” vs. ’) for dry S4d sample with the zoom of its low-frequency part (figure on the right) and the inset showing the electrical equivalent circuit in the low and middle frequency ranges (Ce = capacitance of PVdF gap between metallization and carbon black; RH+ = resistance due to proton diffusion; Re = resistance of the carbon black); d) complex conductivity (” vs. ’) for wet sample S1w; e) complex conductivity (” vs. ’) for wet sample S6w; f) complex conductivity (” vs. ’) for wet sample S8w. Insets in (e) and (f) show the electrical equivalent circuit of samples S6w and S8w in the low frequency range (Cint = ionic double-layer capacitance; Ri = resistance of the electrolyte within the pores; Re = resistance of the CB network). Figure 4. a) Electronic and ionic conductivities vs. inverse temperature 1/T for the wet samples S1w and S6w (■: total conductivity (i+ew), ■: ionic conductivity (i) and ■: electronic conductivity (ew)); b) Electronic conductivity vs. CB volume content CB for dry (□) and wet



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(■) samples: black dotted curve (---) fit Eq. 4 with t = 1.8 and 𝜙0 ≈ 0.046 at 293 K; c) Ratio (0ew/ed) vs. CB volume content CB. (0ew = conductivity prefactor in Eq. 6). Figure 5. (a) Experimental ionic conductivity i vs. macroporosity M and total porosity  at room temperature: straight line (solid line) is determined with effective medium theory (Eq. 4) vs. M; Bruggeman expression (Eq. 5) is fitted by  = 2.4 and m = 1.5 (chain-dotted line) and by  = 2.4 and m = 3.2 vs. ). b) Effective permittivity int proportional to double-layer capacitance as function of macroporosity and carbon black volume fraction. Figure 6. Nyquist plots (” vs. ’) at 293 K of: a) S4d with two dielectric relaxation domains 2 and 3 upon subtracting the low-frequency contribution 1 (straight line) and the domain 2 respectively; b) S5d with one dielectric relaxation domain 2 upon subtracting the low-frequency contribution 1 (straight line); c) S2w: with one dielectric relaxation domain 2 upon subtracting the low-frequency contribution 1 (straight line); d) S8w: with one dielectric relaxation domain 2 upon subtracting the low-frequency contribution 1 (giant circular arc). Figure 7. Parameters of the dielectric relaxation due to electron motions within CB agglomerates or clusters. a) Relaxation frequency  vs. CB volume content CB for dry (■ at 293 K) and wet (■ above percolation threshold at 293K) samples; b) dielectric relaxation strength  vs. CB volume content CB for dry (■ at 293 K) and wet (■ above percolation threshold at 293K) samples; c) relaxation frequency 2 (for wet sample) of electron motion in CB cluster vs. inverse temperature 1/T for the wet sample S8w.


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35

a)

b)

c)

y

S4

z x

-alumina CB+PVdF

d)

S7

e)

Macropores

Figure 1.



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a)

b)

c)

d)

Figure 2


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a)

b)

-1

ed = ed

-1

ed = ed

c)

d)

e)

f)

Figure 3.



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(a)

(b)

(c)

Figure 4


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(a)

(b)

Figure 5



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(a)

(b)

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Figure 6


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(a)

(b)

(c)

Figure 7



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Electronic and Ionic Dynamics Coupled at Solid ... - ACS Publications

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