# Operando Gravimetric and Energy Loss Analysis of Na
3 V 2 (PO 4 ) 2 F 3 composite films by EQCM-D

Jeronimo Miranda Castro, Pierre-Louis Taberna, Patrice Simon

► To cite this version:

Jeronimo Miranda Castro, Pierre-Louis Taberna, Patrice Simon. Operando Gravimetric and Energy Loss Analysis of Na 3 V 2 (PO 4 ) 2 F 3 composite films by EQCM-D. ACS Nano, 2025, 19 (2), pp.2419-2426. 10.1021/acsnano.4c13052 . hal-04915739

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Submitted on 28 Jan 2025

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# Operando Gravimetric and Energy Loss Analysis of Na₃V₂(PO₄)₂F₃ composite films by EQCM-D

Jeronimo Miranda<sup>a,b</sup>, Pierre-Louis Taberna<sup>a,b,*</sup>, Patrice Simon<sup>a,b,*</sup>

<sup>a</sup> Université Toulouse III Paul Sabatier, CIRIMAT, UMR-CNRS 5085, 31062 Toulouse Cedex 9, France.

<sup>b</sup> Réseau sur le Stockage Electrochimique de l'Energie (RS2E), Fédération de Recherche, CNRS 3459, Amiens 80039, France.

## KEYWORDS

Electrochemical Energy Storage, NVPF, EQCM-D, EQCM,

## ABSTRACT

The ever-growing need for energy storage requires new technologies to meet the increasing demands. In this context, Sodium-ion (Na-ion) batteries have emerged as a potential complementary technology to Lithium-ion batteries. Among other materials, Na₃V₂(PO₄)₂F₃ (NVPF) is a promising cathode for Na-ion batteries due to its high operating voltage and good energy density. In order to further characterize the (dis)charge behavior of NVPF, the electrochemical quartz microbalance with dissipation monitoring (EQCM-D) was employed to track both the frequency changes and dissipative losses at electrode/electrolyte interface. The
electrode composite preparation proved to be crucial for extending the potential window to both Na₃V₂(PO₄)₂F₃/Na₂V₂(PO₄)₂F₃ and Na₂V₂(PO₄)₂F₃/Na₁V₂(PO₄)₂F₃ domains. Composites prepared with raw NVPF powder (1-20 µm particles) and PVDF binder exhibited large dissipative changes during (dis)charging, attributed to the soft visco-elastic nature of the binder and substantial hydrodynamic interaction of the large particles. On the other hand, composites prepared by sieved NVPF particles (< 1 µm particles) with NaCMC binder showed rigid properties, enabling an extended and more accurate gravimetric analysis. This allowed for the determination of a linear charge-to-mass relationship for the full potential window of NVPF, reflecting the potential independent (de)insertion of bare Na-ions (23 g mol⁻¹). Additionally, reversible dissipative changes were observed for the Na₃V₂(PO₄)₂F₃/Na₂V₂(PO₄)₂F₃ transition, with no further dissipative changes observed during the Na₂V₂(PO₄)₂F₃/Na₁V₂(PO₄)₂F₃ process.

## TEXT

Although regarded as a promising alternative to the well-established Lithium ion (Li-ion) technology,¹,² Sodium ion (Na-ion) batteries remain at an early stage of development for which further work is required to grant their full potential.³,⁴ With this aim, increased efforts have been devoted to the development of high-voltage cathode materials, showing not only high energy densities, but also considerable power capabilities.³ On this front, the fast ionic conductor Na₃V₂(PO₄)₂F₃ (NVPF) appears as an attractive candidate, due to its high potential of operation, as well as a fairly large capacity of 128 mAh g⁻¹ for the reversible exchange of two Na-ions.⁵ Considering an average potential of 3.95V vs Na/Na⁺, this results in an energy density of about 510 Wh Kg⁻¹,⁶ which is comparable to the values of conventional positive electrodes for Li-ion batteries. On the other hand, the reported phase transitions occurring during the charge/discharge
of NVPF,⁷ as well as its low electronic conductivity,⁵ limit the high-power performance of this material compared to other NaSICON Na-ion cathode materials such as Na₃V₂(PO₄)₃. In order to better understand the performance of NVPF, different operating techniques have been employed to track structural changes under operating conditions, allowing to identify the underlying mechanisms of charge storage in this material.⁷,⁸ Among several factors impacting the performance of a battery, a significant role is played by the insertion and diffusion of ions into the structure of the active material. In this regard, the electrochemical quartz microbalance (EQCM) appears as a relevant technique to monitor the mass changes of the electrode under polarization,⁹,¹⁰ making it an efficient technique to understand ionic flow during operation.¹¹,¹² In general terms, the frequency change of the EQCM sensor is associated to a change in mass by the Sauerbrey equation:¹³

$$ \Delta m_n = - \sqrt{\frac{\mu_q \rho_q \Delta f_n}{2 f_1^2 n}} \qquad (\text{Equation 1}) $$

where $\mu_q$ is the elastic shear modulus of the quartz (g cm⁻¹ s⁻²), $\rho_q$ (g cm⁻³) the crystal density, $f_1$ the fundamental frequency (Hz) and $f_n$ (Hz) the frequency of the n-th overtone (n). Additionally, integration of the charge accompanied by the EQCM mass allows to calculate the effective molecular weight of the species inserted at the active material by means of the Faraday's law.¹⁴

Although broadly employed to track interface phenomena, such as the (de)insertion of ions into battery materials¹¹, or desolvation phenomena upon (dis)charging,¹⁵ the frequency variations of the EQCM sensor are not solely dependent on gravimetric changes, but also on the visco-elastic and hydrodynamic properties of the composite electrode attached to it (i.e., active material, conductive additive and binder). Generally, a method to validate the gravimetric mode of the EQCM relies on tracking the motional resistance (R) of the sensor during polarization (EQCM-
R).¹⁶ However, although widely employed to check for Sauerbrey conditions, the specific oscillating circuit used to measure R is prone to disturbances from stray capacitance and requires electrical compensation.¹⁷ Hence, R remains only a qualitative indicator of the energy losses. On the other hand, a more robust method to track the hydrodynamic/visco-elastic changes involves the measurement of the dissipation factor D (ppm) of the EQCM sensor (Equation 2):¹⁸

$$D = \frac{W_n}{f_n} 10^6 \qquad (\text{Equation 2})$$

where $W_n$ is the full-width-half-maximum (FWHM) of the resonant peak for the n-th overtone.

The dissipation factor D given by Equation 2 is a measure of the energy losses at the interface of the resonator and its surrounding media. Although D can be obtained by EQCM with admittance analysis (EQCM-A, Figure S1a), a more efficient way to do so is achieved by measuring the damping factor of the frequency oscillation decay (Figure S1b).¹⁹,²⁰ This alternative technique is known as EQCM-D (i.e., EQCM with dissipation monitoring). Initially, a driving signal is used to set the sensor to resonance for a short period and, after the signal is turned off, the amplitude of the decaying oscillation is monitored. This alternative method allows the extraction of D by fitting the exponentially decaying sinusoidal function, which can be achieved in an order of milliseconds, allowing both a high sampling rate and better accuracy than the EQCM-A method. In addition, the short circuit mode utilized by the EQCM-D signal reduces the capacitive interference and improves the measurement stability as compared to EQCM-A.²¹

Apart from the changes related to mass, the resonance frequency of the sensor is affected by changes to the mechanical properties of the film (visco-elastic), as well as the interaction
between its surface morphology and the surrounding media (hydrodynamic).²² The overall frequency response of the quartz is then given by Equation 3.

$$ \Delta f_{total} = \Delta f_{mass} + \Delta f_{hydrodynamic} + \Delta f_{viscoelastic} \quad (Equation 3) $$

Hence, the hydrodynamic and viscoelastic properties of the film should be carefully considered before performing a gravimetric analysis by Equation 1. In this regard, Dargel et al. (2017)²³ reported the influence of binder and particle size on the EQCM-D frequency and dissipation response of a LiFePO₄ composite electrode, in both aqueous and organic media. The study described how the frequency response of the EQCM sensor is mainly ascribed to the whole composite electrode (e.g. material, additives and binder), rather than the intrinsic properties of the intercalation material.

The aforementioned results are the baseline of the present work. Herein, we investigate the (de)insertion of Na-ions from/into the NaSICON NVPF structure using EQCM-D, by comparing two different electrode compositions: an electrode obtained from a mixture of NVPF powder with large particle size distribution mixed with PVDF binder (raw-NVPF/PVDF), and a second composite electrode resulting from small NVPF particles mixed with NaCMC binder (sieved-NVPF/NaCMC).

In this work, an initial EQCM-R test performed using the raw-NVPF/PVDF sample suggested that the frequency response was partially influenced by the film composition (i.e., softness, rugosity), which lowered the accuracy of the gravimetric approach. These results were confirmed by EQCM-D performed at several overtones, which evidenced that the visco-elastic changes of the composite film cause dissipative loss changes, which in turn affect the resonance frequency response, making the gravimetric analysis less accurate. In order to minimize the impact of
visco-elasticity, two modifications were simultaneously made by preparing electrodes with smaller NVPF particles, while simultaneously using a rigid NaCMC binder. As expected from Dargel et al, these changes allowed to minimize the contribution of visco-elasticity to Equation 3 and permitted an accurate gravimetric analysis over and extended potential window. Interestingly, dissipative changes were observed even under these conditions caused by small hydrodynamic interactions, but do not appreciably impact the accuracy of the gravimetric approach. Hence, this study highlights the importance of electrode formulation in detecting dissipative and gravimetric changes inherent to insertion materials rather than composite films, allowing to perform accurate EQCM analysis of high-voltage cathode materials.

## RESULTS AND DISCUSSION

From a general view, the charging of NVPF results in two distinct voltage plateaus observed at 3.7 and 4.2 V vs Na/Na⁺, assigned to the reversible processes Na₃V₂(PO₄)₂F₃/Na₂V₂(PO₄)₂F₃ (Na₃-VPF/Na₂-VPF) and Na₂V₂(PO₄)₂F₃/Na₁V₂(PO₄)₂F₃ (Na₂-VPF/Na₁-VPF), respectively. The full oxidation to Na₀VPF is possible, but requires a large polarization, for which it was excluded from the scope of this study.²⁴,²⁵ Although EQCM characterizations has already been reported for the Na₃-VPF/Na₂-VPF region,⁸ to the best of our knowledge, no EQCM report has addressed the full operating range of Na₃-VPF/Na₁-VPF using a conventional EQCM set-up. A first attempt to collect a full EQCM signal is shown in Figure 1.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** EQCM-A (9MHz) of the raw-NVPF:PVDF coating in 1M NaPF6 EC:DMC (1:1, vol.%) + 2 wt.% FEC, showing a) the cyclic voltammogram, b) simultaneous frequency change and, c) charge vs frequency change.</figcaption></figure>

Figure 1a and Figure 1b respectively depict the cyclic voltammogram and simultaneous frequency variation of the raw-NVPF:PVDF coated quartz for the Na₃-VPF/Na₁-VPF (dis)charge. Note that because of the background current coming from reactions on the Au/Ti sensor (Figure S2), the potential window in the EQCM set-up remains limited to 4.2V vs Na/Na⁺, meaning that the full charge to Na₁-VPF is not achieved. Nevertheless, for simplicity, we refer to the two distinct regions in the voltammogram as the zones corresponding to Na₃-VPF/Na₂-VPF (low potential peak) and Na₂-VPF/Na₁-VPF (high potential peak) processes. Figure 1c present a charge vs frequency plot, whose slope can be associated with the weight of the inserting ion (under a purely gravimetric regime). It is to note that the partial irreversibility of the charge indicated by the red bar in Figure 1c is largely caused by the undesired electrochemical activity of the Au/Ti sensor surface at high potentials (Figure S2).

Figure 1c shows that the frequency varies linearly with the charge for Zones I and IV (low potential Na-ion insertion/de-insertion), but a non-linear variation and hysteresis is observed for
Zones II and III (high potential Na-ion insertion/de-insertion). Quantitatively, the linear change observed for Zones I and IV change results in a value of 32 ± 1 g mol⁻¹ (cycles 2 to 9, in 2.9 to 3.9 V vs Na/Na⁺ window), which is somehow higher than the expected 23 g mol⁻¹ corresponding to the removal/insertion of bare Na-ions from the NVPF structure. On the other hand, Figure 1c shows a clear nonlinear region for the Na₂-VPF/Na₁-VPF oxidation (Zones II and III), which is unexpected for the de-insertion/ insertion of Na-ions into the material. Hence, although the gravimetric analysis yields reasonable results within a limited potential window, it was suspected that the undesired behavior at high potentials could be indicative of non-fully gravimetric conditions, lowering the accuracy of this approach. Hence, to understand this non-linear behavior, the changes in the hydrodynamic/visco-elastic properties of the electrode should be considered

To further elucidate the behavior observed in Figure 1, the tracking of several frequency overtones by EQCM-D is required, to better assess the dissipative losses occurring during Na-ion (de)insertion into the raw-NVPF:PVDF sample. In this regard, not only EQCM-D allows for the simultaneous acquisition of a set of frequencies and dissipation factors, but also opens the possibility to probe the material at different decay lengths. The decay length of the shear wave of the EQCM-D sensor is given by Equation 4:

$$ \delta_n = \sqrt{\frac{\nu_L}{\pi n f_1}} \qquad (\text{Equation 4}) $$

where $\nu_L$ is the kinematic viscosity (cm² s⁻¹) of the liquid in contact with the sensor, $f_1$ the fundamental frequency and n the value of the overtone.²⁶
The decay length represents the distance of the shear wave decaying from the crystal/liquid interface into the bulk of the medium.²⁷ For a linear system, the higher the overtone, the lower the decay length. Accordingly, a multiple overtone analysis increases the probing resolution from the electrode surface.²⁸ In this way, the mechanical properties of the composite film (e.g. swelling, cracking, particle size evolution, roughness, pore-size distribution) can be analyzed at different scales, revealing a more intricate picture of the composite electrode surface structure.³¹

Several previous works have presented EQMC-D models to describe the resonance characteristics of the coated quartz as a function of the overtone.¹⁸ In largely general terms, three main scenarios can be depicted corresponding to (a) purely elastic, (b) hydrodynamic and (c) visco-elastic regimes. The elastic situation (a) occurs for a non-slipping, rigid and smooth active layer which undergoes a mass change without changing its rigid properties. In this case, $\Delta f_n/n$ is independent of the overtone and the dissipation changes are close to zero. In the case of battery materials, this is hardly ever the case, due to particle volume changes and the formation of a solid electrolyte interface (SEI, or CEI), which resulting in changing hydrodynamic interaction at the electrode/electrolyte interface, resulting in non-constant hydrodynamic losses (b). In this second hydrodynamic case, $\Delta f_n/n$ tends to decrease linearly with the overtone number, while $\Delta D_n$ increases. Lastly, a visco-elastic regime (c) is characterized by a non-rigid active layer composite, showing frequency dependent mechanical properties. In that case, both $\Delta f_n/n$ and $\Delta D_n$ are not monotonically related to the overtone.

Hence, considering the more comprehensive picture offered by this technique, EQCM-D measurements of the raw-NVPF:PVDF electrode composite were collected and are shown in Figure 2.
<figure><img src="image_3.png" /></figure>

**Figure 2.** EQCM-D (5MHz) of the raw-NVPF:PVDF coating in 1M NaPF₆ EC:DMC (1:1, vol.%) + 2 wt.% FEC, showing a) the cyclic voltammogram and b) simultaneous changes of (i) frequency and (ii) dissipation.

Figure 2a shows the EQCM-D results obtained during cyclic voltammetry of the raw-NVPF:PVDF sample. For sake of clarity, the simultaneous frequency variations for several overtone are shown in Figure 2b(i) as a function of time (corresponding potentials are shown in the top x-axis). The fundamental frequency was excluded from EQCM-D analysis as mounting stress, swelling of the O-ring and bubble formation largely affect this particular mode, resulting in unreliable $f_1$ data and so, often excluded in literature<sup>23,26,29,30</sup>. Evidently, Figure 2b(i) shows a significant mismatch in the $\Delta f_n/n$ response during the (de)insertion of Na-ions for different overtones. Although the general trend is similar with that observed in Figure 1, the frequency profiles show non-monotonic changes (i.e., non-directional with $n$), suggesting that the visco-elastic properties of the composite film vary substantially upon cycling. This is more clearly observed in Figure 2b(ii), where substantial dissipative changes are observed during (de)sodiation. In this experiment, all overtones show dissipation changes over the analyzed range
related to the visco-elastic properties of the sample. Indeed, the EC:DCM solvent mixture is known to swell PVDF because of the poor affinity of EC with other carbonates, causing a preference for the solvent molecules to enter the PVDF polymer matrix,³¹,³² giving rise to a more pronounced visco-elastic behavior of the composite electrode.

Additionally, results obtained cycling the sample in a limited potential window for Na₃-VPF/Na₂-VPF are shown in Figure S3a and Figure S3b. In this case, dissipative loss changes of several tens of ppm happen even when cycled in this reduced potential range. The observed variation are not monotonic with the overtone, indicating that viscoelasticity changes occur even in this limited domain. Indeed, Reviakine et al. (2011) suggested that for gravimetric conditions to be established, ΔDₙ/(Δfₙ/n) << 4 x10⁻⁷ Hz⁻¹ for a 5 MHz crystal ³³. In the case of the raw-NVPF:PVDF sample, a maximum ΔD₃/(Δf₃/3) = 3 x10⁻⁷ Hz⁻¹ is observed, which suggests that gravimetric conditions are not fully established even for the largest penetration depths for n = 3. All together, these results evidence that the raw-NVPF:PVDF sample behaves as a visco-elastic film during the (de)insertion of Na-ions, which likely reduced the quality of the gravimetric analysis shown in Figure 1c.

Insights into the origin of these dissipative loss changes can be obtained from the work of Dargel et al. (2017),²³ which discussed the influence of electrode composition on EQCM-D analysis for LiFePO₄ composite electrodes. Notably, large particles covered with PVDF binder generate agglomerates, which in turn cause deviations from the Sauerbrey relation, particularly at high overtone orders, where the penetration distance becomes considerably smaller than the particle size. ²³,³⁴ Hence, both the inhomogeneity of the coating, as well as the visco-elastic nature of the PVDF binder in the selected electrolyte limit the gravimetric window.
Considering these findings, a second electrode was prepared by spray coating sieved-NVPF particles and replacing the PVDF binding with NaCMC. Figure S4 shows that while the raw-NVPF powder consists of particles of a largely distributed size (1-20 µm), the sieved-NVPF powder is solely composed of particles smaller than 1 µm, ensuring a more homogenous active layer, and minimizing the hydrodynamic losses related to the heterogeneity of the film. Additionally, contrary to PVDF, NaCMC acts as a rigid polymer structure in organic mixtures.³⁴ Hence, it is expected to observe a much lower contribution of the binder to the overall dissipative losses of the composite electrode in the organic media used in the present study.

As a first indicator of the rigidity of the coatings, Figure S5 shows that, when measured in air, the sieved-NVPF:NaCMC coating exhibits five times lower $\Delta D_n$ than the raw-NVPF:PVDF coating of similar mass loading ($\Delta f_n/n$).²⁸ This simple measurement of the coating in air clearly evidences the more rigid and homogenous properties of the sieved-NVPF:NaCMC film, even prior to contact with the electrolyte. The overall effect of the simultaneous change of binder and particle size on the EQCM-D signal of NVPF is shown in Figure 3.

<figure><img src="image_4.png" /></figure>
**Figure 3.** EQCM-D (5MHz) of the sieved-NVPF:NaCMC coating in 1M NaPF₆ EC:DMC (1:1, vol.%) + 2 wt.% FEC, showing a) the cyclic voltammogram and b) simultaneous changes in (i) frequency, (ii) dissipation and (iii) derivative of the dissipation with respect to time.

Figure 3b(i) and 3b(ii) evidence a perfectly overlapping of the Δf<sub>n</sub>/n with small variations in the dissipation values, characteristic of purely gravimetric frequency changes with minor hydrodynamic losses. This result indicates a mass change independent of the overtone for both the Na<sub>3</sub>-VPF/Na<sub>2</sub>-VPF and Na<sub>2</sub>-VPF/Na<sub>1</sub>-VPF regimes. Interestingly, it seems that the simultaneous substitution of particle size and binder allows extending the gravimetric mode of EQCM to the potential of Na<sub>2</sub>-VPF/Na<sub>1</sub>-VPF, which permits the use of the Sauerbrey model for the whole operational potential window. To demonstrate the combined effect of reducing the size of the particles and using a stiff binder, Figure S6 shows the EQCM-D results obtained for two additional samples, namely, sieved-NVPF/PVDF and raw-NVPF/NaCMC, confirming that the sieved-NVPF/NaCMC formulation remains the best choice for gravimetric analysis at several overtones. In both cases, the samples show non-superimposed frequency profiles during polarization. In the case of the sieved-NVPF/PVDF sample, while dissipative losses are smaller for the low overtone orders compared to raw-NVPF/PVDF, the effect of viscoelasticity is still considerable at higher overtones, indicating a breach of the Sauerbrey conditions. This is further evidenced by the mixing (non-monotonic ordering) of the dissipation values during polarization. On the other hand, the dissipation values for the raw-NVPF/NaCMC increase monotonically, as expected for hydrodynamic behavior, denoting the importance of switching to a stiff binder to suppress visco-elastic effects. Nevertheless, the hydrodynamic losses are large as compared to those observed for the sieved-NVPF/NaCMC, resulting in non-strictly superimposed frequency profiles compared to Figure 3b(i).
<figure><img src="image_5.png" /></figure>

**Figure 4.** Gravimetric EQCM-D (5MHz) analysis of the sieved-NVPF:NaCMC coating in 1M NaPF₆ EC:DMC (1:1, vol.%) + 2 wt.% FEC.

Contrary to Figure 1c, Figure 4 shows that although an irreversible charge (red bar in Figure 4) still exists due to the undesired activity of the Au/Ti substrate, the frequency change varies linearly with the charge, regardless of the overtones. Moreover, no hysteresis of the frequency exists at high potentials for the sieved-NVPF:NaCMC sample. Consequently, the absence of visco-elastic changes in this sample allow the calculation of an effective molar weight of 23.0 ± 0.5 g mol⁻¹ (cycles 2 to 9, in 2.9 to 4.2 V vs Na/Na⁺ window), confirming the insertion of bare Na-ions along the whole Na₃-VPF/Na₁-VPF process.

On the counter side, Figure 3b(i) shows that regardless of the perfectly superimposed frequencies, there still exists a reversible/non-zero behavior of the ΔDₙ, showing greater dissipative values for the higher overtone orders. Note that the values of ΔDₙ remain considerably small, with maximum values slightly superior to 5 ppm for the highest overtone n = 11, compared to the values observed in Figure 2b(ii) for the raw-NVPF:PVDF sample ( > 25 ppm for n = 11). Accordingly, this denotes a maximum range from ΔD₃/(Δf₃/3) = 3 x 10⁻⁹ Hz⁻¹ to ΔD₁₁/(Δf₁₁/11) = 5 x 10⁻⁸ Hz⁻¹, which largely attest for gravimetric conditions ( << 4 x 10⁻⁷ Hz⁻¹)
even considering the relatively minor dissipative changes. Additionally, Figure 3b(ii) shows that $\Delta D_n$ increases in line with the overtone number, as it is expected for changing hydrodynamic losses occurring at the active layer/electrolyte interface, which contrasts with large and non-monotonic $\Delta D_n$ changes observed for the soft visco-elastic changes of the raw-NVPF:PVDF sample.

In order to take this analysis further, the derivative of $\Delta D_n$ with respect to time is shown in Figure 3b(iii), clearly showing two distinct dissipative domains; while large dissipation changes exist for the Na₃-VPF/Na₂-VPF transition (Zones I and IV), the dissipative changes are close to zero for the Na₂-VPF/Na₁-VPF domain (Zones II and III). To explain the substantial difference between the two domains, it is suggested that the evolution of the dissipative losses happening during the low potential Na₃-VPF/Na₂-VPF zone are associated to the specific phase changes undergone by NVPF in this potential region.⁷ The structural changes caused by such process result in important differences at the electrode/electrolyte interface (i.e., changing volume of the particles, roughness, cracking), resulting in larger dissipative loss changes. Indeed, while the low potential Na₃-VPF/Na₂-VPF domain is driven by a two-phase reaction mechanism, the high potential plateau Na₂-VPF/Na₁-VPF is largely dominated by the existence of a solid solution (in the Na₁.₈-VPF - Na₁.₃-VPF region), which might be responsible for the absence of change in dissipative losses in this region where the particles experience low and gradual volumetric evolution. In order to explain this observation, the unit cell volume of NVPF was tracked by in situ XRD. Results shown on Figure S7 are in accordance with previously reported data in literature⁷, in which volume change is observed for both Na₃-VPF/Na₂-VPF and Na₁.₈-VPF - Na₁.₃-VPF regions. Then, the absence of dissipative losses for the Na₁.₈-VPF - Na₁.₃-VPF cannot
be correlated solely to the of unit cell volume change, but are related to potential dependent macroscopic changes in the morphology of the surface.

Alternatively, the voltammogram shown in Figure S8, obtained using a cavity micro-electrode (CME) was used to better emphasize the intrinsic kinetic behavior of the active NVPF material.<sup>35,36</sup> Figure S8 reveals a peak separation of about 125 mV for the low potential peak, while the value is only 40 mV for the high potential region. Moreover, the low potential regions shows a broader current profile (120 mV FWHM), while the high potential region shows a sharper current (50 mV at FWHM). These results are consistent with relatively sluggish electrochemical process of the Na<sub>3</sub>-VPF/Na<sub>2</sub>-VPF, associated with a distribution of activation energy for the active sites in the particles.<sup>37</sup> Note that the broadness of the peaks is emphasized by the low mass loading characteristic of CME and EQCM-D experiments, but these results can be similarly observed in Swagelok cells with low mass loadings (Figure S8). The sluggish reaction kinetics observed in the Na<sub>3</sub>-VPF/Na<sub>2</sub>-VPF biphasic first order transition could then be at the origin of the dissipative changes observed in this work. Differently, the fast Na<sub>2</sub>-VPF/Na<sub>1</sub><sup>-</sup> VPF solid solution redox process at high potential have a lower impact on the external surface of the electrode, and are associated with minor dissipative loss changes.

## CONCLUSIONS

An EQCM-D study of Na-ion (de)insertion in NVPF was reported in 1M NaPF<sub>6</sub> EC:DMC (1:1, vol.%) + 2 wt.% FEC electrolyte. Two different samples were used, namely raw-NVPF:PVDF (1-20 µm) and sieved-NVPF:NaCMC (<1 µm). The two samples showed a remarkably different EQCM-D signal. While the EQCM-D profile of the raw-NVPF:PVDF coating was dominated by dissipative losses arising from the volume change of the particles and the soft visco-elastic nature of the PVDF binder, a limited impact in the dissipation changes was observed for the sieved-
NVPF:NaCMC composite film. The clear difference was explained by the rigid nature of the NaCMC binder in the selected electrolyte, as well as the more homogenous and rigid deposited layer formed by the small NVPF particles. These differences allowed to extend of the gravimetric analysis to both Na₃-VPF/Na₁-VPF and Na₂-VPF/Na₁-VPF potentials, confirming a constant (de)insertion of de-solvated Na-ions (23 g mol⁻¹) into the material. These results do not suggest that a rigid binder necessarily has a positive impact on NVPF based Na-ion batteries, as the rigid nature of the film might limit its cycling stability. On the other hand, this electrode preparation approach allowed for the study of intrinsic properties of the NVPF material, otherwise hidden behind the visco-elastic behavior of the *raw*-NVPF:PVDF film. As a result, two distinct zones of dissipation change were observed. While the EQCM-D signal of Na₃-VPF/Na₂-VPF shows reversible dissipative losses, Na₂-VPF/Na₁-VPF occurs at a constant value of energy loss. The monotonically increasing profile of ΔDₙ observed during low potential (de)sodiation of the *sieved*-NVPF:NaCMC sample is characteristic of hydrodynamic changes, which likely arise from the changing morphology of the film in this low potential region. Alternatively, the high potential (de)sodiation Na₂-VPF/Na₁-VPF shows no considerable changes in energy loss, indicating a constant morphology of the film in this regime. The underlaying nature of these two zones is likely associated with the previously reported phase transitions and solid solution undergone by NVPF. It is suspected that while the phase transition occurring in the Na₃-VPF/Na₂-VPF domain cause changes in the dissipative losses of the electrode, no major variations are detected for the Na₂-VPF/Na₁-VPF range, as this transition is dominated by a long solid solution. The cyclic voltammetry at low mass loadings characteristic of EQCM emphasize broader current peaks, and a larger potential distance between the back-and-forth peaks, for the low potential Na₃-VPF/Na₂-VPF region, indicating sluggish kinetics concomitant with the
dissipative changes observed by EQCM-D. This result in well aligned with the slower biphasic
first order transition of NVPF. In contrast, the sharp current peak in the Na₂-VPF/Na₁-VPF
region, mostly occurs during a solid solution region, where only gradual evolution of the unit cell
parameters is expected, resulting in a nearly constant value of energy loss of the EQCM-D
signal.

METHODS

Carbon coated NVPF EQCM samples were prepared following the protocol reported by Dargel *et al.* (2017).<sup>23</sup> Briefly, two samples of different particle size were used; *raw*-NVPF samples refer to the powder used as received (ranging from 1 to 20 µm), and *sieved*-NVPF samples denote the samples prepared using only the smaller particles of the same powder (1 µm maximum size). This was achieved by thoroughly sonicating the *raw*-NVPF powder in ethanol, followed by retrieval of the particles still in suspension after 20 min. All tests were carried out in 1M NaPF<sub>6</sub> EC:DMC (1:1, vol.%) + 2 wt.% FEC (E-Lyte) at room temperature.<sup>38</sup> In all cases, sodium metal worked as both counter and reference electrodes.

EQCM-A (EQCM with series motional resistance monitoring) was performed using a
QCM922A instrument (SEIKO EG&G Co.). EQCM-D experiments (EQCM with dissipation
monitoring at several overtone) was performed using a QSense Explorer (Biolin Scientific).

Experiments were carried out using either a 9 or 5 MHz Au/Ti sensor of 1.28 cm² contact area (AWSensors). Electrode coatings were prepared by spraying a suspension of carbon coated NVPF, carbon black (Ketjenblack EC-300J) and binder in an 8:1:2 weight ratio (binder in solvent: 0.4 mg/mL PVDF in N-Methyl-2-pyrrolidone or 0.4 mg/mL NaCMC in water). 100 to 200 mL of the solutions were spray coated onto the quartz sensor over a heating plate at 120 °C,
followed by vacuum drying overnight at 120 °C. Mass loadings ranged between 20 to 40 mg cm⁻².

## ASSOCIATED CONTENT

The following files are available free of charge.

Fundamentals of EQCM-A and EQCM-D techniques, blank experiments, EQCM-D analysis of all samples in a limited potential window, SEM images *raw* and *sieved* NVPF samples, EQCM-D mass loading analysis, Swagelok tests at different NVPF mass loading (PDF).

## AUTHOR INFORMATION

### Corresponding Author

* Patrice Simon – Université Toulouse III Paul Sabatier, CIRIMAT, UMR-CNRS 5085, 31062 Toulouse Cedex 9, France; Réseau sur le Stockage Electrochimique de l’Energie (RS2E), Fédération de Recherche, CNRS 3459, Amiens 80039, France; orcid.org/0000-0002-0461-8268; E-mail: patrice.simon@univ-tlse3.fr

* Pierre-Louis Taberna – Université Toulouse III Paul Sabatier, CIRIMAT, UMR-CNRS 5085, 31062 Toulouse Cedex 9, France; Réseau sur le Stockage Electrochimique de l’Energie (RS2E), Fédération de Recherche, CNRS 3459, Amiens 80039, France; orcid.org/0000-0002-5310-048; E-mail: pierre-louis.taberna@univ-tlse3.fr

### Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.
ACKNOWLEDGMENT

P.S acknowledges the support of the ERC (MoMa-STOR Synergy grant #951513) and the
LABEX STORE-EX. P.L.T thanks the support of the Agence Nationale de la Recherche. J.M
was supported by the ERC (MoMa-STOR Synergy grant #951513). P.S. and P.L.T thank the
support of the PEPR Batteries ANR-22-PEBA-0003. This paper is published under a CC-YB
license agreement.

ABBREVIATIONS

EQMC-D, Electrochemical Quartz Microbalance with Dissipation Monitoring; NVPF,
Na₃V₂(PO₄)₂F₃; Na₁-VPF, Na₁V₂(PO₄)₂F₃; Na₂-VPF, Na₂V₂(PO₄)₂F₃.

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