**5. Conclusions**

This study establishes, empirically, that T-SDM capacitors, based on dielectrics created by filling micron scale titania tubes that form during titanium ionization with aqueous salt solutions, are superior to all other energy storage capacitors, relative to standard metrics. Using a recently developed constant current protocol, it was demonstrated that the capacitance, dielectric constant, and energy and power density as a function of discharge time follow power law relationships. Plotted on a Ragone chart, the power vs. energy density data is linear. All data lie above the values recorded for supercapacitors, ultra capacitors, and electrolytic capacitors on standard Ragone charts. Furthermore, the consistency of the data, that it resulted in power law relationships for capacitors derived from nine different salt solutions, indicates that the data and the fitted power laws are precise and are probably accurate. Notably, dielectric constants of more than 10<sup>8</sup> were recorded, and even for very short discharges for all capacitors, the dielectric constant was >10<sup>5</sup> , establishing that the dielectrics are SDM over a broad range of discharge times (ca. 10−3–>10 s). Finally, it should be noted that the measured power delivery increases as the discharge time decreases. For three of the capacitors, the measured power delivery was greater than 70 W/cm<sup>3</sup> for a 10 ms discharge, a time frame and a power delivery value consistent with the needs of pulsed power systems.

### **Author details**

Steven M. Lombardo and Jonathan Phillips\* \*Address all correspondence to: jphillip@nps.edu Naval Postgraduate School, Monterey, CA, USA

#### **References**

[1] Christen T, Carlen W. Theory of Ragone plots. Journal of Power Sources. 2000;**91**:210

[2] Ragone D. Review of battery systems for electrically powered vehicles. SAE Technical Paper 680453. 1968. DOI: 10.4271/680453

data suggest that effective dipole length follows a very simple pattern as a function of

It is notable that this is only the second time [13] the constant current charge/discharge method has been employed to determine the power law relationship for 'supercapacitor' parameters, specifically capacitance, dielectric constant, and energy and power density, over orders of magnitude of discharge times. This method arguably provides higher fidelity, more reliable, insight into 'frequency' dependence of this type of capacitor than other measurement

This study establishes, empirically, that T-SDM capacitors, based on dielectrics created by filling micron scale titania tubes that form during titanium ionization with aqueous salt solutions, are superior to all other energy storage capacitors, relative to standard metrics. Using a recently developed constant current protocol, it was demonstrated that the capacitance, dielectric constant, and energy and power density as a function of discharge time follow power law relationships. Plotted on a Ragone chart, the power vs. energy density data is linear. All data lie above the values recorded for supercapacitors, ultra capacitors, and electrolytic capacitors on standard Ragone charts. Furthermore, the consistency of the data, that it resulted in power law relationships for capacitors derived from nine different salt solutions, indicates that the data and the fitted power laws are precise and are probably accurate. Notably, dielectric con-

discharge times (ca. 10−3–>10 s). Finally, it should be noted that the measured power delivery increases as the discharge time decreases. For three of the capacitors, the measured power

[1] Christen T, Carlen W. Theory of Ragone plots. Journal of Power Sources. 2000;**91**:210

were recorded, and even for very short discharges for all capacitors,

, establishing that the dielectrics are SDM over a broad range of

for a 10 ms discharge, a time frame and a power delivery

discharge time.

84 Supercapacitors - Theoretical and Practical Solutions

protocols.

**5. Conclusions**

stants of more than 10<sup>8</sup>

**Author details**

**References**

the dielectric constant was >10<sup>5</sup>

delivery was greater than 70 W/cm<sup>3</sup>

Steven M. Lombardo and Jonathan Phillips\*

\*Address all correspondence to: jphillip@nps.edu Naval Postgraduate School, Monterey, CA, USA

value consistent with the needs of pulsed power systems.


[19] Xu Y, Lin Z, Zhong X, Huang X, Weiss NO, Huang Y, Duan X. Holey graphene frameworks for highly efficient capacitive energy storage. Nature Communications. 2014;**5**:4554. DOI: 10.1038/ncomms 5554

**Chapter 5**

Provisional chapter

**Enhancing Pseudocapacitive Process for Energy**

**Electro-kinetic Study and Numerical Modeling**

Electro-kinetic Study and Numerical Modeling

Devices: Analyzing the Charge Transport Using

Fenghua Guo, Nivedita Gupta and Xiaowei Teng

Fenghua Guo, Nivedita Gupta and Xiaowei Teng

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

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

Abstract

supercapacitors.

interface, electrokinetics

**Storage Devices: Analyzing the Charge Transport Using**

Supercapacitors are a class of energy storage devices that store energy by either ionic adsorption via an electrochemical double layer capacitive process or fast surface redox reaction via a pseudocapacitive process. Supercapacitors display fast charging and discharging performance and excellent chemical stability, which fill the gap between high energy density batteries and high-power-density electrostatic capacitors. In this book chapter, the authors have presented the current studies on improving the capacitive storage capacity of various electrode materials for supercapacitors, mainly focusing on the metal oxide electrode materials. In particular, the approaches that mathematically simulate the behavior of interaction between electrode materials and charge carriers subject to potentiodynamic conditions (e.g., cyclic voltammetry) have been described. These include a general relationship between current and voltage to describe overall electrokinetics during the charge transfer process and a more comprehensive numerical modeling that studies ionic transport and electrokinetics within a spherical solid particle. The two aforementioned types of mathematical analyses can provide fundamental understanding of the parameters governing the electrode reaction and mass transfer in the electrode material, and thus shed light on how to improve the storage capacity of

Keywords: pseudocapacitance, diffusion-limited redox process, electrode/electrolyte

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Enhancing Pseudocapacitive Process for Energy Storage

DOI: 10.5772/intechopen.73680


#### **Enhancing Pseudocapacitive Process for Energy Storage Devices: Analyzing the Charge Transport Using Electro-kinetic Study and Numerical Modeling** Enhancing Pseudocapacitive Process for Energy Storage Devices: Analyzing the Charge Transport Using Electro-kinetic Study and Numerical Modeling

DOI: 10.5772/intechopen.73680

Fenghua Guo, Nivedita Gupta and Xiaowei Teng Fenghua Guo, Nivedita Gupta and Xiaowei Teng

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

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

#### Abstract

[19] Xu Y, Lin Z, Zhong X, Huang X, Weiss NO, Huang Y, Duan X. Holey graphene frameworks for highly efficient capacitive energy storage. Nature Communications.

[20] Sahu V et al. Ultrahigh performance supercapacitor from lacey reduced graphene oxide

[21] Zwilling V, Darque-Ceretti E, Boutry-Forveille A, David D, Perrin MY, Aucouturier M'. Structure and physicochemistry of anodic oxide films on titanium and TA6V alloy.

[23] Cortes FJQ, Arias-Monje PJ, Phillips J, Zea H. Empirical kinetics for the growth of titania nanotube arrays by potentiostatic anodization in ethylene glycol. Materials & Design.

[24] Lombardo SM. Characterization of Anodized Titanium-Based Novel Paradigm Supercapacitors: Impact of Salt Identity and Frequency on Dielectric Values, Power and

[25] Phillips J, Clausen B, Dumesic JA. Iron pentacarbonyl decomposition over grafoil. Production of small metallic iron particles. The Journal of Physical Chemistry.

[26] Phillips J, Dumesic JA. Iron pentacarbonyl decomposition over grafoil: II. Effect of sample outgassing on decomposition kinetics. Applied Surface Science. 1981;**7**:215-230 [27] Barsoukov E, MacDonald JR. Impedance Spectroscopy: Theory, Experimental and

[28] MacDonald JR, Kenan WR. Impedance Spectroscopy. Emphasizing Solid Materials and

[29] Kim Y, Kathaperumal M, Chen VW, Park Y, Fuentes-Hernandez C, Pan MJ, Kippelen B, Perry JW. Bilayer structure with ultrahigh energy/power density using hybrid sol–gel dielectric and charge-blocking monolayer. Advanced Energy Materials. 2015;**5**:1500767.

[30] Gogotski Y, Simon P. True performance metrics in electrochemical energy storage.

[31] Conway BE.Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications. Springer Science and Business Media; New York, NY USA. 1999

[32] Simon P, Burke AF. Nanostructured carbons: Double-layer capacitance and more.

[33] Ji H et al. Capacitance of carbon-based electrical double-layer capacitors. Nature

[34] Reynolds GJ, Krutzer M, Dubs M, Felzer H, Mamazza R'. Electrical properties of thinfilm capacitors fabricated using high temperature sputtered modified barium titanate.

Energy Densities. M.S. Thesis, Naval Postgraduate School; 2016

Applications. 2nd ed. New York, NY, USA: John Wiley & Sons; 2005

Systems. New York, NY, USA: John Wiley & Sons; 1987

nanotubes: Synthesis and applications. Angewandte

nanoribbons. ACS Applied Materials and Interfaces. 2015;**3110**(2015):7

2014;**5**:4554. DOI: 10.1038/ncomms 5554

Surface and Interface Analysis. 1999;**27**:629

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[22] Roy P, Berger S, Schmuki P'. TiO<sup>2</sup>

86 Supercapacitors - Theoretical and Practical Solutions

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1980;**84**:1814

Supercapacitors are a class of energy storage devices that store energy by either ionic adsorption via an electrochemical double layer capacitive process or fast surface redox reaction via a pseudocapacitive process. Supercapacitors display fast charging and discharging performance and excellent chemical stability, which fill the gap between high energy density batteries and high-power-density electrostatic capacitors. In this book chapter, the authors have presented the current studies on improving the capacitive storage capacity of various electrode materials for supercapacitors, mainly focusing on the metal oxide electrode materials. In particular, the approaches that mathematically simulate the behavior of interaction between electrode materials and charge carriers subject to potentiodynamic conditions (e.g., cyclic voltammetry) have been described. These include a general relationship between current and voltage to describe overall electrokinetics during the charge transfer process and a more comprehensive numerical modeling that studies ionic transport and electrokinetics within a spherical solid particle. The two aforementioned types of mathematical analyses can provide fundamental understanding of the parameters governing the electrode reaction and mass transfer in the electrode material, and thus shed light on how to improve the storage capacity of supercapacitors.

Keywords: pseudocapacitance, diffusion-limited redox process, electrode/electrolyte interface, electrokinetics

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 1. Introduction

Supercapacitors (SCs), also called electrochemical capacitors, are a class of energy storage devices that store electrical energy by either ionic adsorption via an electrochemical double layer capacitive process or fast surface redox reaction via a pseudocapacitive process. As shown in Figure 1, SCs bridge the performance gap between high energy density batteries and high-power-density capacitors (referring to electrostatic capacitors), the two leading electrical energy storage technologies [1]. Batteries technology, especially non-aqueous lithium-ion batteries (LIBs), has been successfully used in various applications in the past two decades especially in consumer electronics and electrical vehicles. On the other hand, capacitive storage technology offers a number of desirable properties hardly found in batteries, including fast charging and discharging process (usually achieved within seconds), long-term cycling life (>10<sup>6</sup> cycles), and high power performance (able to deliver at least 10 times more power than batteries). As a result, capacitive storage technology is very important for applications where a large amount of energy needs to be either stored or delivered quickly, including repetitive conversions between kinetic energy and electric energy (e.g., regenerative braking and forklifting), pulse power applications for laser or radar, power conditioning in the electrical grid to smooth the output of a full or half wave rectifier [2]. It is notable that both capacitive and battery storage technologies have promising applications in stationary storage. Renewable sun and wind energy sources generally have on-peak and off-peak load variations. To accelerate the adoption of renewable energy generation sources, chemical energy storage (e.g., batteries) and capacitive energy storage (e.g., capacitors) are required. Thus, electricity generated during off-peak hours can be stored efficiently and economically for use during peak demand [3].

Although SCs offer complementary energy storage solution for many applications that are not suitable for batteries, the relatively low storage capacity and energy density limit SCs in more widespread usage. SCs usually contain three general classes of charge storage mechanisms:

• Electrical double-layer (EDL) capacitive process relies on the charge separation in a Helmholtz double layer at electrode/electrolyte interface by means of static charge (non-faradaic). The storage capacity of an EDL capacitor can be improved by a large surface area of the electrode/electrolyte interface (most EDL capacitors have a capacitance in a range from 10

energy storage. Carbons are ideal EDL electrode materials for its high electrical conductivity, large surface area, and low density, delivering a storage capacity of up to 150 F g<sup>1</sup>

• Pseudocapacitive process relies on the charge transfer process primarily happening at the interface between the electrode and the electrolyte. Three faradaic mechanisms have been identified to account for the capacitive electrochemical features that appear in pseudocapacitors, namely, underpotential deposition, redox pseudocapacitance, and intercalation pseudocapacitance [5]. Underpotential deposition typically involves hydrogen atom on the near surface on noble metal oxides (e.g., IrO2 or RuO2) [6]. Redox pseudocapacitance occurs at or near the surface of a material, accompanied by adsorption of ions [7]. Intercalation pseudocapacitance occurs when ions intercalate into the channels or layers of a redox-active material accompanied by a faradaic charge-transfer with no crystallographic phase change [8]. Metal oxides, metal carbides or nitrides are ideal pseudocapacitive electrode materials for their reversible redox activity, wide electrochemical potential and high chemical stability [9]. The storage capacity of a pseudocapacitive material is much higher than an EDL capacitive material (the former has a capacitance larger than 100 μF/cm2

• Diffusion-limited redox process relies on the kinetically limited intercalation reactions as found in most standard battery materials, where ion intercalation and de-intercalation are intrinsically tied to the slow kinetics of solid phase transition between the intercalated and non-intercalated phases. It is notable that the difference between pseudocapacitive charge storage and battery-like diffusion-limited intercalation is rather vague, especially when the dimensions of an electrode material decreases from the micron-scale down to the nanoscale [10]. At the nanoscale, the specific surface area of a material (overall surface area per unit volume) increases inversely with the size, which results in a significant enhancement of redox pseudocapacitance and intercalation pseudocapacitance. Such enhancement of surface redox (pseudocapacitive) process may become the more dominant charge storage process traditional battery-like intercalation process as the sizes of materials progress from micro-scale to nanoscale. Thus, the materials may evolve from being a typical battery material to a pseudocapacitor material based on their size and/or nanoscale architecture, where phase transition is no longer a distinct structural feature of the electrode materials between the intercalated and non-intercalated states (Figure 2). As discussed above, improving the storage capacity of SCs requires the enhancement of redox processes, such as redox pseudocapacitance, intercalation pseudocapacitance, as well as

). EDL capacitors serve as the basis for the current technology in capacitive

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

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

,

89

to 20 μF/cm<sup>2</sup>

in ionic liquid electrolytes [4].

nearly one magnitude higher than the latter).

Figure 1. Ragone plot showing supercapacitors are intermediate energy storage devices filling the gap between batteries and conventional capacitors.

Although SCs offer complementary energy storage solution for many applications that are not suitable for batteries, the relatively low storage capacity and energy density limit SCs in more widespread usage. SCs usually contain three general classes of charge storage mechanisms:

1. Introduction

88 Supercapacitors - Theoretical and Practical Solutions

economically for use during peak demand [3].

and conventional capacitors.

Supercapacitors (SCs), also called electrochemical capacitors, are a class of energy storage devices that store electrical energy by either ionic adsorption via an electrochemical double layer capacitive process or fast surface redox reaction via a pseudocapacitive process. As shown in Figure 1, SCs bridge the performance gap between high energy density batteries and high-power-density capacitors (referring to electrostatic capacitors), the two leading electrical energy storage technologies [1]. Batteries technology, especially non-aqueous lithium-ion batteries (LIBs), has been successfully used in various applications in the past two decades especially in consumer electronics and electrical vehicles. On the other hand, capacitive storage technology offers a number of desirable properties hardly found in batteries, including fast charging and discharging process (usually achieved within seconds), long-term cycling life (>10<sup>6</sup> cycles), and high power performance (able to deliver at least 10 times more power than batteries). As a result, capacitive storage technology is very important for applications where a large amount of energy needs to be either stored or delivered quickly, including repetitive conversions between kinetic energy and electric energy (e.g., regenerative braking and forklifting), pulse power applications for laser or radar, power conditioning in the electrical grid to smooth the output of a full or half wave rectifier [2]. It is notable that both capacitive and battery storage technologies have promising applications in stationary storage. Renewable sun and wind energy sources generally have on-peak and off-peak load variations. To accelerate the adoption of renewable energy generation sources, chemical energy storage (e.g., batteries) and capacitive energy storage (e.g., capacitors) are required. Thus, electricity generated during off-peak hours can be stored efficiently and

Figure 1. Ragone plot showing supercapacitors are intermediate energy storage devices filling the gap between batteries


As discussed above, improving the storage capacity of SCs requires the enhancement of redox processes, such as redox pseudocapacitance, intercalation pseudocapacitance, as well as

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

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

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+

), 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

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].

id <sup>¼</sup> <sup>0</sup>:495FCA <sup>D</sup>αnFv

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

On the other hand, the capacitive current (ic) from EDL capacitance and pseudocapacitance has

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

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).

RT <sup>1</sup>

2

id <sup>¼</sup> kdv<sup>0</sup>:<sup>5</sup> (3)

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

ic ¼ ACcv (4)

ic ¼ kcv (5)

,

91

(2)

energy while maintaining a stable electrode/electrolyte interface.

Na+

rate.

the near surface of the electrode.

conditions are fixed except the scan rate.

a linear dependence on the scan rate according to Eq. (4):

Figure 2. Schematics of charge transfer and storage processes observed in (a, a<sup>0</sup> ) large-sized battery-materials; (b, b<sup>0</sup> ) pseudocapacitive materials, and (c, c<sup>0</sup> ) nano-sized battery-materials.

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 kinetics.
