2. Understanding electrochemical kinetics of charge transfer process by analyzing the electrochemical data during the cyclic voltammetry measurements

Redox reactions involve both surface adsorption/desorption and intercalation/deintercalation of electrolyte cations as shown in Eq. (1):

$$\rm{MO}\_{\rm{X}}\rm{C} \leftrightarrow \rm{MO}\_{\rm{X}} + \rm{C}^{+} + e^{-} \tag{1}$$

where MO is the transition metal oxide and C<sup>+</sup> is the charge carrier (e.g., Li<sup>+</sup> , Na+ , or K<sup>+</sup> ). Upon the incorporation (via intercalation or adsorption) of C<sup>+</sup> , M cations will be reduced to balance the charges, and vice versa. Moreover, due to the dispersive nature of the electrode composites, separate percolation paths for ion and charge transport may be present, resulting in different paths for long range electronic and ionic conduction. Therefore, influences of the kinetic parameters (e.g., scan rate, potential window) and the structural parameters (e.g., size, morphology, and crystalline structures) on the redox reactions are crucial to understand the charge-storage mechanism in electrode materials. All the kinetic and structural parameters need to be optimized in order to design cost-effective electrode materials that can store more energy while maintaining a stable electrode/electrolyte interface.

The understanding of the electrokinetics of charge storage inside the metal oxide nanomaterials can be obtained through analyzing the current-voltage curves at various scan rates obtained from CV measurements in the half-cell. The total charge stored in the electrode during SC operation is dependent on a relatively fast surface-controlled capacitive charge storage process and a relatively slow diffusion-controlled redox charge storage process. The latter is promoted by the battery-like intercalation/de-intercalation redox processes of the charge carriers (e.g., Li+ , Na+ ), while the former is attributed to the electrical double layer (i.e. EDL capacitance) and pseudocapacitance formed via the separation or adsorption and desorption of charge carriers at the near surface of the electrode.

For a strictly diffusion-limited redox reaction, the rate of charge transfer reactions, namely the current (id), is proportional to the square root of the scan rate (ν) according to Eq. (2) [11].

$$i\_d = 0.495 FCA \left(\frac{DanFv}{RT}\right)^{\frac{1}{2}} \tag{2}$$

$$i\_d = k\_d v^{0.5} \tag{3}$$

where C is the concentration of charge carriers in the accumulation layer, α is the charge transfer coefficient, D is the diffusion coefficient of the charge carrier inside the electrode materials, n is the number of electrons involved in the Faradaic reaction, A is the surface area of the electrode materials, F is Faraday's constant, R is the molar gas constant, and T is the temperature. Eq. (2) can be further simplified to a form shown in Eq. (3) when all the reaction conditions are fixed except the scan rate.

diffusion-limited redox process. Therefore, the analysis of different charge storage mechanisms also becomes important. The goal of this chapter is thus to examine the parameters (e.g., size, morphology and structure) that will affect the evolution from battery-like behavior to pseudocapacitor behavior and to explore the interplay of these parameters to control redox

2. Understanding electrochemical kinetics of charge transfer process by

Redox reactions involve both surface adsorption/desorption and intercalation/deintercalation

the charges, and vice versa. Moreover, due to the dispersive nature of the electrode composites, separate percolation paths for ion and charge transport may be present, resulting in different paths for long range electronic and ionic conduction. Therefore, influences of the kinetic parameters (e.g., scan rate, potential window) and the structural parameters (e.g., size,

MOXC \$ MO<sup>X</sup> þ C<sup>þ</sup> þ e� (1)

, Na+

) large-sized battery-materials; (b, b<sup>0</sup>

)

, M cations will be reduced to balance

, or K<sup>+</sup>

). Upon

analyzing the electrochemical data during the cyclic voltammetry

) nano-sized battery-materials.

Figure 2. Schematics of charge transfer and storage processes observed in (a, a<sup>0</sup>

where MO is the transition metal oxide and C<sup>+</sup> is the charge carrier (e.g., Li<sup>+</sup>

the incorporation (via intercalation or adsorption) of C<sup>+</sup>

kinetics.

measurements

pseudocapacitive materials, and (c, c<sup>0</sup>

90 Supercapacitors - Theoretical and Practical Solutions

of electrolyte cations as shown in Eq. (1):

On the other hand, the capacitive current (ic) from EDL capacitance and pseudocapacitance has a linear dependence on the scan rate according to Eq. (4):

$$
\dot{\mathbf{u}}\_c = A \mathbf{C}\_c \mathbf{v} \tag{4}
$$

$$
\dot{a}\_c = k\_c \upsilon \tag{5}
$$

where Cc is the capacitance from capacitive process and A is a constant. Eq. (4) can be further simplified to a form shown in Eq. (5) when all the reaction conditions are fixed except the scan rate.

Accordingly, the overall current at a given potential can be express as the sum of two separate charge storage mechanisms, that is capacitive current and kinetic current as shown in Eq. (6). Therefore, at higher scan rates, the overall current is dominated by capacitive current (ic), due to its stronger linear dependence on scan rates shown in Eq. (6), whereas the overall current is dominated by diffusion-limited kinetic current (id) at lower scan rates. In this context, the overall current (itotal) is usually described by a simple power law as shown in Eq. (7).

$$\dot{\mathbf{i}}\_{\text{total}} = \dot{\mathbf{i}}\_c + \dot{\mathbf{i}}\_d = k\_c \boldsymbol{\upsilon} + k\_d \boldsymbol{\upsilon}^{0.5} \tag{6}$$

$$\dot{a}\_{\text{total}} = a\upsilon^b \tag{7}$$

various scan rates at a given potential. Therefore, the current attributed to diffusion-limited redox process (id <sup>¼</sup> kdv<sup>0</sup>:<sup>5</sup><sup>Þ</sup> and capacitive process (ic <sup>¼</sup> kcv<sup>Þ</sup> at each scan rate can be obtained. And thus the potential- and scan rate-dependent charge storage mechanisms (e.g., capacitive

Figure 4. Electrokinetics analysis (kc and kd values) of Na-ion storage within the manganese oxide materials. CV current responses of the manganese oxide material are shown at the scan rates of (a) 5 mV s�<sup>1</sup> and (b) 200 mV s�<sup>1</sup>

Enhancing Pseudocapacitive Process for Energy Storage Devices: Analyzing the Charge Transport…

http://dx.doi.org/10.5772/intechopen.73680

current (black line) is obtained experimentally and the diffusion-limited redox current (blue dot line with shadow) is calculated; (c) a stacked bar graph showing diffusion-limited redox capacity and capacitive capacity contribution of the manganese oxide material as a function of scan rate from 5 to 200 mV s�<sup>1</sup> (diffusion-limited redox capacity contributions

Figure 4a and b show the typical CV curves of the manganese oxide material at scan rates of

capacitive current are calculated and plotted. The complete results of diffusion-limited redox and capacitive contributions of manganese oxide from 5 to 200 mV s�<sup>1</sup> can be found in Figure 4c. It is clear that diffusion-limited redox contributions to the overall charge storage

process contributed nearly 69% of the overall current, while it only remained 25% at high scan

manganese oxide material can be attributed to its layered MnO2 component, where the large interlayer distance (~0.7 nm) facilitates the transport of Na-ion during charge and discharge

3. Understanding electrochemical kinetics of charge transfer process using

Modeling electrodes or full-cells of batteries or supercapacitors has been extensively studied [12–15]. For example, Popov and coworkers have developed a one-dimensional model to analyze the performance of a hybrid system comprised of battery and supercapacitor (based on a Sony 18650 battery and a Maxwell's 10F supercapacitor) under pulse discharge currents

itotal=v<sup>0</sup>:<sup>5</sup> <sup>¼</sup> kcv<sup>0</sup>:<sup>5</sup> <sup>þ</sup> kd (8)

, diffusion-limited redox

. The total

93

, where the distributions of diffusion-limited redox current and

. The enhanced capacitive contribution for Na-ion storage found in the

or diffusion-controlled redox) during the CV scans can be revealed.

decreased with the increasing scan rate: at low scan rate of 5 mV s�<sup>1</sup>

5 mV s�<sup>1</sup> and 200 mV s�<sup>1</sup>

rate of 200 mV s�<sup>1</sup>

numerical analysis

processes.

are indexed).

where a is an adjustable parameter and b is a variable heavily dependent on the relative contribution from ic or id. It is apparent that the value of b is equal to either 0.5 or 1 when the overall currents are strictly dominated by capacitive (ic) or kinetic (id) current, respectively.

Figure 3 shows the electrokinetic analysis of aqueous K-ion storage within vanadium oxide nanostructures using cyclic voltammetry (CV) measurements in a three-electrode half-cell with a 1 M KCl electrolyte, where the b-values of the peaks in all three of the color shadowed sections of the anodic and cathodic scans are plotted. In the potential range from �0.1 to 0.3 V (gray region in Figure 3a) the K-ion storage in the vanadium oxide is dominated by a diffusion-limited redox process as the b-values for the anodic and cathodic scans are close to 0.5 (banodic = 0.44, bcathodic = 0.69). In the potential range from 0.7 to 0.9 V (red region in Figure 3a) the charge storage process is controlled by surface-related capacitive process because the b-values for the anodic and cathodic scans are very close to 1.0 (banodic = 0.95, bcathodic = 0.99). While in the potential range from 0.3 to 0.7 V (blue region in Figure 3a) both the surface-controlled capacitive and diffusion-limited redox processes contribute to the charge storage as the b-values for the anodic and cathodic scans are between 0.5 and 1.0 (banodic = 0.81, bcathodic = 0.87). The electrokinetic analysis suggests that charge storage of the vanadium oxide nanostructures benefits from both capacitive and diffusion-limited redox processes. The former process allows the high rate performance and the latter allows the high capacity performance of K-ion storage in the vanadium oxide nanostructures. The contribution of capacitive process (double-layer capacitance and/or pseudo-capacitance) and diffusionlimited redox process to the overall capacity can be quantified with the infinite sweep rate extrapolation, as shown in Figure 3c. For example, at a scan rate of 5 mV s�<sup>1</sup> , 46% of the total capacity is attributed to capacitive process, whereas 93% of the total capacity is attributed to capacitive process at 200 mV s�<sup>1</sup> .

Moreover, after rearranging Eq. (7) into Eq. (8), the values of kc and kd can be determined by the slope and intercepts of the resulting linear function via plotting i=v<sup>0</sup>:<sup>5</sup> as a function of v<sup>0</sup>:<sup>5</sup> at

Figure 3. Electrokinetics analysis (b-values) of K-ion storage within the vanadium oxide nanostructures. (a) Cyclic voltammetric curves at various scan rates. (b) The calculated b values during the anodic and cathodic scans. (c) A stacked bar graph showing the percent of total capacitance coming from the diffusion limited and capacitive contributions.

Enhancing Pseudocapacitive Process for Energy Storage Devices: Analyzing the Charge Transport… http://dx.doi.org/10.5772/intechopen.73680 93

itotal <sup>¼</sup> ic <sup>þ</sup> id <sup>¼</sup> kcv <sup>þ</sup> kdv<sup>0</sup>:<sup>5</sup> (6)

where a is an adjustable parameter and b is a variable heavily dependent on the relative contribution from ic or id. It is apparent that the value of b is equal to either 0.5 or 1 when the overall currents are strictly dominated by capacitive (ic) or kinetic (id) current, respectively.

Figure 3 shows the electrokinetic analysis of aqueous K-ion storage within vanadium oxide nanostructures using cyclic voltammetry (CV) measurements in a three-electrode half-cell with a 1 M KCl electrolyte, where the b-values of the peaks in all three of the color shadowed sections of the anodic and cathodic scans are plotted. In the potential range from �0.1 to 0.3 V (gray region in Figure 3a) the K-ion storage in the vanadium oxide is dominated by a diffusion-limited redox process as the b-values for the anodic and cathodic scans are close to 0.5 (banodic = 0.44, bcathodic = 0.69). In the potential range from 0.7 to 0.9 V (red region in Figure 3a) the charge storage process is controlled by surface-related capacitive process because the b-values for the anodic and cathodic scans are very close to 1.0 (banodic = 0.95, bcathodic = 0.99). While in the potential range from 0.3 to 0.7 V (blue region in Figure 3a) both the surface-controlled capacitive and diffusion-limited redox processes contribute to the charge storage as the b-values for the anodic and cathodic scans are between 0.5 and 1.0 (banodic = 0.81, bcathodic = 0.87). The electrokinetic analysis suggests that charge storage of the vanadium oxide nanostructures benefits from both capacitive and diffusion-limited redox processes. The former process allows the high rate performance and the latter allows the high capacity performance of K-ion storage in the vanadium oxide nanostructures. The contribution of capacitive process (double-layer capacitance and/or pseudo-capacitance) and diffusionlimited redox process to the overall capacity can be quantified with the infinite sweep rate

extrapolation, as shown in Figure 3c. For example, at a scan rate of 5 mV s�<sup>1</sup>

.

capacitive process at 200 mV s�<sup>1</sup>

92 Supercapacitors - Theoretical and Practical Solutions

capacity is attributed to capacitive process, whereas 93% of the total capacity is attributed to

Moreover, after rearranging Eq. (7) into Eq. (8), the values of kc and kd can be determined by the slope and intercepts of the resulting linear function via plotting i=v<sup>0</sup>:<sup>5</sup> as a function of v<sup>0</sup>:<sup>5</sup> at

Figure 3. Electrokinetics analysis (b-values) of K-ion storage within the vanadium oxide nanostructures. (a) Cyclic voltammetric curves at various scan rates. (b) The calculated b values during the anodic and cathodic scans. (c) A stacked bar graph showing the percent of total capacitance coming from the diffusion limited and capacitive contributions.

itotal <sup>¼</sup> avb (7)

, 46% of the total

Figure 4. Electrokinetics analysis (kc and kd values) of Na-ion storage within the manganese oxide materials. CV current responses of the manganese oxide material are shown at the scan rates of (a) 5 mV s�<sup>1</sup> and (b) 200 mV s�<sup>1</sup> . The total current (black line) is obtained experimentally and the diffusion-limited redox current (blue dot line with shadow) is calculated; (c) a stacked bar graph showing diffusion-limited redox capacity and capacitive capacity contribution of the manganese oxide material as a function of scan rate from 5 to 200 mV s�<sup>1</sup> (diffusion-limited redox capacity contributions are indexed).

various scan rates at a given potential. Therefore, the current attributed to diffusion-limited redox process (id <sup>¼</sup> kdv<sup>0</sup>:<sup>5</sup><sup>Þ</sup> and capacitive process (ic <sup>¼</sup> kcv<sup>Þ</sup> at each scan rate can be obtained. And thus the potential- and scan rate-dependent charge storage mechanisms (e.g., capacitive or diffusion-controlled redox) during the CV scans can be revealed.

$$i\_{\text{total}}/v^{0.5} = k\_c \upsilon^{0.5} + k\_d \tag{8}$$

Figure 4a and b show the typical CV curves of the manganese oxide material at scan rates of 5 mV s�<sup>1</sup> and 200 mV s�<sup>1</sup> , where the distributions of diffusion-limited redox current and capacitive current are calculated and plotted. The complete results of diffusion-limited redox and capacitive contributions of manganese oxide from 5 to 200 mV s�<sup>1</sup> can be found in Figure 4c. It is clear that diffusion-limited redox contributions to the overall charge storage decreased with the increasing scan rate: at low scan rate of 5 mV s�<sup>1</sup> , diffusion-limited redox process contributed nearly 69% of the overall current, while it only remained 25% at high scan rate of 200 mV s�<sup>1</sup> . The enhanced capacitive contribution for Na-ion storage found in the manganese oxide material can be attributed to its layered MnO2 component, where the large interlayer distance (~0.7 nm) facilitates the transport of Na-ion during charge and discharge processes.
