### 1. Introduction

### 2. Principle of voltammetry

### 2.1 Linear sweep and cyclic voltammetry

^{−1}). LSV shows various results depending on the following factors: 1) the rate of electron transfer process, 2) the electrochemical reactivity of the materials, and 3) the scan rate for measurement. The results of LSV are presented as one of anodic or cathodic peak as described in Fig. 1a. Although CV is very similar to LSV, it does not finish with a single sweep within a fixed voltage range. For example, assuming the voltage range from E

_{1}to E

_{2}, when E

_{2}is reached at the end, it reverses to E

_{1}again. Because of this feature, it is called ‘cyclic’ current

*versus*voltage plot is termed a ‘cyclic voltammogram’, as shown in Fig. 1b. In the CV measurements, the most important parameter is the scan rate (

*v*). The voltage is swept from E

_{1}to E

_{2}and it represents the slope for a linear voltage change during the measurement. By repeating several cycles with the same conditions, additional information on the voltage, reversibility, and cyclability of redox reactions can be obtained. Also, it can be used to investigate the kinetics of electrochemical redox reaction by changing the scan rate.

### 2.2 Comparison of cyclic voltammogram and *dQ/ dV* plot

*dQ/dV*) plot, it can be recorded based on a similar principle with cyclic voltammogram. Although it provides useful information on the redox reaction of electrochemical systems the difference between cyclic voltammogram and

*dQ/dV*plot should be recognized as cyclic voltammogram contains the rate information. In general, the current (I) is plotted on the y-axis versus the voltage (V) on the x-axis in the cyclic voltammogram and it can be transformed into to

*dQ/dV*plot. For transformation of cyclic voltammogram to

*dQ/dV*, the I and V can be expressed as

*v*is scan rate (V s

^{−1}),

*V*is the voltage (or potential, V),

*I*is the current (A),

*Q*is charge stored (Ah), and t is time (s). And the formula (4) which indicate the y-axis of

*dQ/dV*plot was obtained by combining the equation (2) and (3)

*dQ/dV*plot, it is necessary to understand the commonalities and differences between CV and

*dQ/dV*.

### 2.3 Equations of voltammetry for intercalation system

*E*

_{p}is independent on the variation of scan rate

*v*, and anodic (

*E*

*) and cathodic (*

_{p,a}*E*

*) peak potential separation, is 59.0/*

_{p,c}*n*mV,

*i*

*/*

_{p,a}*i*

*=1, in addition, the following equation is satisfied.*

_{p,c}^{+}intercalation reactions tend to follow a quasi-reversible process since cathodic and anodic peaks are dependent on the scan rate [15]. The cyclic voltammogram of quasireversible process shows gradual peak shifts to higher potential value with an increase of scan rate than one of reversible process due to the overpotential.

*n*is the total number of electrons reacted per mole in the electrochemical process, A is the electrode area (cm

^{2}), C is the concentration of the electrode material at surface, and D is the diffusion coefficient.

^{+}ion diffusivity, two boundary conditions should be considered according to the scan rate; i) a semi-infinite diffusion process (a fast scan rate) and ii) a finite diffusion process (a slow scan rate). In the case of the semi-infinite diffusion process, the peak current is proportional to the square root of scan rate. In contrast, the peak current is proportional to scan rate in the finite diffusion process, in which the anodic/cathodic reaction can be characterized by the following equation;

*β*(=

*nFv*(

*l*

^{2}/

*D*)/

*RT*) is a dimensionless characteristic time parameter,

*l*means distance of electrode and

*F*(=9.65 × 10

^{4}C/mol) refer to Faraday constant.

### 2.4 Sweep rate voltammetry technique

*i*is current (A),

*v*is scan rate (mV s

^{−1}), and

*a*,

*b*are adjustable values. Then

*b*value can be obtained by using simultaneous equations.

*b*value can be explained by the sum of the faradaic (diffusion-controlled) and non-faradaic (capacitive) currents. If only diffusion-controlled reaction occurs without any faradaic reaction, the observed current would be proportional to the square root of the scan rate,

*v*

^{1/2}, according to Randles-Sevcik equation, equation (6). On the other hand, the capacitive current (also called “non-faradaic” or “double-layer” current.) follows linearly to the scan rate;

*i*

*is the current for electric double-layer charging,*

_{c}*A*is surface area of electrode and

*C*

*is the capacitance of electric double-layer. As can be seen from the above equation (10), the capacitive current is proportional to scan rate,*

_{d}*v*, therefore, the capacitive current is dominantly measured at a fast scan rate. On the contrary, the recorded current will be mainly associated with a diffusion-controlled reaction at a slow scan rate.

*b*value of total electrochemical reactions composed of diffusion-controlled and capacitive reactions will have values between 0.5 (diffusion-controlled) and 1.0 (capacitive). Set a log on both side of equation (9), then it can be plotted like Fig. 4a.

*k*

_{1}

*v*and

*k*

_{2}

*v*

^{1/2}correspond to the current attributed to capacitive reaction and diffusion-controlled reaction, respectively. Then,

*k*

_{1}and

*k*

_{2}can be obtained through the linear fit of

*v*

^{1/2}plot from the equation (17) as shown in Fig. 4b.

*k*

_{1}represents the slope and

*k*

_{2}is the y intercept value. Thus, by determining

*k*

_{1}and

*k*

_{2}, the fraction of the current can be obtained at fixed potential.

### 2.5 Estimation of diffusion coefficient through voltammetry

*v*

^{1/2}. Like calculating

*b*value, from the relationship of i

_{p}vs.

*v*

^{1/2}, the apparent diffusion coefficient of Li

^{+}(D

_{Li+}) can be obtained. If the Randles-Sevcik equation is considered as a linear equation, the plot for current i

_{p}as a function of the square root of the scan rate,

*v*

^{1/2}, shows a linear correlation, and all variables can be found as constants. Like sweep rate CV technique, the diffusion coefficient can be obtained by linear fitting of the slope from the plot i

_{p}vs.

*v*

^{1/2};

### 2.6 Determination of specific capacity by voltammetry

^{−1}. is the voltage window and

*i*(

*E*) is the current.

*m*is the mass of active material, and

*v*is the scan rate.

**Δ**

*Q*is the capacity (C or mAh) and

**Δ**

*U*is the voltage window (V). Further specific capacity (Q) in mAh g

^{−1}was evaluated from the cyclic voltammograms using the following equation[18],

### 3. Factors affecting the shape of voltammetric curves

### 3.1 Particle size

^{+}. As a result of enhancement in kinetics of redox reaction, the overall peak current increases at the same scan rate in the cyclic voltammograms. For these reasons, the same active material exhibits different electrochemical performance depending on its particle size. In practice, Yang et al, reported the different electrochemical behaviors in the cyclic voltammograms obtained from LFP nanoplates and microplates having different particle sizes at various scan rates (Fig. 5a) [19]. Wang et al, also showed the particle size effect of TiO

_{2}on the cyclic voltammograms, in which the contribution of Li

^{+}intercalation become smaller but that of capacitance increases by decreasing the particle size [21].

^{+}intercalation reaction changed to surface reaction, the overall reaction shows faster kinetic reaction. Therefore, the electrochemical reaction mechanism could be tuned by control the particle size, showing different cyclic voltammograms. Liu et al. also mentioned some electrodes which is composed of various particle sizes of Si exhibit significant differences in cyclic voltammograms [22]. The characteristic alloying reaction peak of Si with Li

^{+}is not clearly detected due to sluggish alloying kinetics of large-particle Si. However, a characteristic alloying reaction peak is more clearly observed in the small-particle Si, which means that the kinetics of the alloying reaction of Si can be effectively enhanced by the particle size reduction.

### 3.2 Electrolyte concentration

^{+}in electrolytes fundamentally, and also the peak split between cathodic and anodic peak has nothing to do with the concentration of electrolytes. However, Fig. 5b shows some extent of peak shift with electrolyte concentration. The reaction voltage of the Li intercalation reaction is related to kinetics of ions in the electrolyte. Basically, electrolytes serve as H

^{+}, Na

^{+}, and Li

^{+}carriers and do not have a significant effect on the Li

^{+}ion diffusion process within the electrode because the charge transfer reactions in the electrode is much slower than those in electrolyte. In the case of aqueous Na ion battery (SIB), however, the redox peaks corresponding to Na

^{+}insertion and extraction are becoming sharper and closer, which indicates faster kinetics at high electrolyte concentrations [23]. As expected by Nernst equation, it is because the equilibrium potential shifts toward more positive direction as the electrolyte concentration increases. Some authors mentioned that the characteristic shifted potential with different electrolyte concentration depends on specific ions, such as H

^{+}, Na

^{+}, and Li

^{+}[24,25].

### 3.3 Scan rate

^{15}. In principle, the currents induced by the capacitive reaction and the diffusion-controlled reaction are proportional to

*v*and

*v*

^{1/2}, respectively (equation 6, 10). This is because the peak current becomes a semi-infinite diffusion process at a high scan rate, and in slow rate condition the peak current is proportional to the square root of the scan rate. Therefore, the general formula including the all of scan rate describe by Aoki et al as mentioned in equation (8). This is the basic principle of the sweep rate CV technique, which can analyze what reaction contributes to charge storage at fixed potential.

### 3.4 Electrode thickness

^{+}ion diffusion from surface to bulk becomes more difficult [33]. The bulk potential of the electrode depends on distance from surface, which causes potential drop [20].

### 3.5 Temperature

^{+}diffusion in the lattice of the active materials, and this diffusion process is temperature-sensitive. When potential is applied, the capacitive currents occur and the Helmholtz layer is continually reconfigured on the surface of electrode. The temperature dependence is significantly different between the capacitance of non-faradaic process and the diffusion-controlled reaction of faradaic process. When the peak split decreases at high temperatures, it indicates that the rate of electrochemical reaction becomes faster and the corresponding redox peaks can appear earlier [20] as shown in Fig. 5d.

### 4. Applications of voltammetry to the study of Li battery

### 4.1 Sweep rate voltammetry technique

^{+}intercalating cathode materials, approximately 94% of the total capacity is derived from a surface-controlled reaction. As a result, they show excellent power capability maintaining a high discharge capacity of 110 mAh g

^{−1}even at a high current density of 5000 mA g

^{−1}. The sweep rate CV technique provides an analysis of the pseudocapacitve electrochemical behavior of the surface-controlled reaction in LiF-MnO nanaocomposite.

^{+}intercalating anode materials such as Nb

_{2}O

_{5}[28,29], TiO

_{2}[20,21,36] using the sweep rate CV. Based on equation (17), each contribution of capacitive and intercalation reactions to the total capacity of the anode materials was calculated at a specific voltage, as shown in Fig. 6c.

_{2}O

_{5}, the

*b*value is estimated to be almost 1.0 at a slow sweep rate (< 20 mV s

^{−1}), indicating a surface-controlled reaction. On the other hand, the

*b*value decreases to 0.7 at a faster sweep rate (> 20 mV s

^{−1}). These differences with scan rate can come from ohmic contribution, including active material, SEI resistance, and/or diffusion limitations [37,38]. Since these results depend on the sort and the reaction mechanism of the electrode materials, it is necessary to closely examine the experimental conditions. According to the above paper, the capacitance effect of Nb

_{2}O

_{5}, TiO

_{2}, which is known that Li insertion reaction is the main mechanism, increases greatly depending on various conditions such as electrode thickness, particle size and sweep rate.

### 4.2 Estimation of diffusion coefficients

^{+}diffusivity of various anode materials also can be estimated. To clarify the reaction mechanism, it needs to analyze Li

^{+}diffusivity when each phase transition occurs in the active materials. For example, spinel LiMn

_{2}O

_{4}exhibits multiple phase transitions, LiMn

_{2}O

_{4}→ Li

_{0.5}Mn

_{2}O

_{4}and Li

_{0.5}Mn

_{2}O

_{4}→ λ-MnO

_{2}, during the charge process. The corresponding Li

^{+}diffusivities are calculated to be MnO

_{2}are 4.63 × 10

^{−12}and 1.04 × 10

^{−11}cm

^{2}s

^{−1}, respectively, and in the discharge process are 2.88 × 10

^{−12}and 1.68 × 10

^{−12}cm

^{2}s

^{−1}, respectively. The Li

^{+}diffusivity values obtained by the sweep rate CV are comparable to the diffusion coefficient calculated from PITT (1.9 × 10

^{−12}to 8 × 10

^{−11}cm

^{2}s

^{−1}). Note that the sweep rate CV can be used for estimation of the diffusion coefficients in the single-phase reaction. However, the values of the diffusion coefficients obtained from the materials which undergo phase transition need to be carefully approached for their reliability.

^{−12}cm

^{2}s

^{−1}and 10

^{−12}cm

^{2}s

^{−1}by CV and EIS measurements, respectively. The diffusion coefficient measured by EIS is about 5 times lower than one calculated from GITT. A significant difference of diffusion coefficients of WO

_{3}were also obtained by CV and GITT. The difference is even more pronounced at high scan rates (above 2 mV s

^{−1}), because the Randles-Sevcik method tends to generate large potential gradients in the active material, which greatly overestimates the diffusion coefficient. In addition, the characteristic is attributed to different equilibrium conditions between analytical methods. In practice, the EIS measurement is conducted under more equilibrium conditions (more relaxation time) compared with GITT. However, both methods show similar variation of Li

^{+}diffusivity in silicon. The diffusion coefficient for single-phase reaction is more reliable when the slope of log (peak current) vs. log (scan rate) is 0.5 (i.e. diffusion-controlled). When Li

^{+}transport is governed by the cell resistance, such relationship will be invalidated which is called as “cell-impedance-controlled” situation [43].

### 4.3 Stepwise voltage window technique

_{1.2}Ni

_{0.13}Mn

_{0.54}Co

_{0.13}O

_{2}) [44]. To clarify the reaction mechanism of Li-rich cathode materials, a lot of research has been carried out on anionic redox as well as cationic redox reactions in these days. The measurement proceeds with an increase of potential cut-off starting from a small value, gradually increasing to the existing voltage window after a few formation cycles. For example, in a voltage window from 2.0 to 4.8 V, the potential cut-off gradually increases from 2.0 to 3.5, to 3.7, to 3.9, and finally reaches 2.0 to 4.8 V. As shown in Fig. 7a, the voltage hysteresis appears noticeably beyond 4.1 V (red curves) when the charge voltage window starts to increase gradually from 2.0 V. In the corresponding

*dQ*/

*dV*curve, it was observed that the charge capacity beyond 4.1 V is only partially recovered on reduction at a high voltage and the remaining reduction took place at a low voltage (below 3.6 V). The charge compensation above 4.1 V (red curves) can be assumed to be the contribution of anionic oxidation, since the cationic oxidation is nearly finished at about 4.1 V. Similarly, in Fig. 7c and 7d, anionic redox reaction is clearly visible at reductions of less than 3.4 V. It shows that the voltage hysteresis due to anionic redox reaction appears asymmetrically during the charge-discharge process.

### 5. Conclusions

^{+}diffusivity of each reaction by varying the scan rate. Furthermore, anionic redox, which is mainly studied in Li-rich cathode materials, can also be analyzed through a stepwise voltage window technique.