Faculty of Chemical Technology

Poznań, 2018 r.

Institute of Chemistry and Technical Electrochemistry

Field of study: Chemical Technology

Adam Ślesiński

Modification of electrochemical capacitor components and a proper assessment of the final system

Modyfikacja komponentów kondensatora elektrochemicznego oraz prawidłowa ocena parametrów układu

DOCTORAL THESIS

Promoter:

Prof. dr hab. Elżbieta Frąckowiak

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I would like to thank my promoter prof. dr hab. Elżbieta Frąckowiak and prof. François Béguin and dr Krzysztof Fic for supporting supervision.

Special thanks to dr John R. Miller (USA) for common research and scientific advice.

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Table of contents

1 FOREWORD TO ENERGY STORAGE, MANAGEMENT AND TRANSFER ... 5

1.1 G ENERAL OUTLOOK OF ENERGY STORAGE DEVICE TYPES AND THE POSITION OF ELECTROCHEMICAL CAPACITOR ... 9

2 ELECTROCHEMICAL CAPACITORS... 15

2.1 S CIENTIFIC PRINCIPLES OF OPERATION ... 15

2.2 E LECTRICAL DOUBLE - LAYER ... 16

2.2.1 Faradaic and non-faradaic charge storage ... 18

2.3 C ELL CONSTRUCTIONS AND BASIC CELL COMPONENTS ... 19

2.3.1 Electrodes ... 20

2.3.2 Electrolyte ... 24

2.3.3 Separator ... 26

2.3.4 Current collectors ... 27

3 PHYSICOCHEMICAL INVESTIGATION METHODS OF ELECTROCHEMICAL CAPACITOR MATERIALS ... 29

3.1 TPD-MS ... 29

3.2 B OEHM METHOD ... 30

4 ACCURATE CAPACITOR STORAGE SYSTEM DESIGN BASED ON SINGLE-CELL TEST DATA ... 31

5 THE AIM OF THE WORK ... 32

6 EXPERIMENTAL ... 33

7 ELECTROCHEMICAL INVESTIGATION METHODS OF ELECTROCHEMICAL CAPACITOR CELLS ... 34

7.1 DC TECHNIQUES ... 34

7.1.1 Constant current ... 34

7.1.2 Constant potential sweep ... 36

7.1.3 Constant power ... 37

7.2 AC TECHNIQUES ... 38

7.2.1 Impedance measurements ... 38

7.3 C ELL AGEING ... 40

7.3.1 Voltage hold test ... 41

7.3.2 Cycling test ... 41

8 PROPER ASSESSMENT OF CELL CHARACTERISTICS ... 43

8.1 M ETHOD FOR CALCULATION OF ELECTRODE CONTRIBUTION TO THE CELL ... 43

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9 PROPER EVALUATION OF SELECTED CELL PARAMETERS ... 51

9.1 C HARGE REDISTRIBUTION EFFECT ... 51

9.2 R AGONE PLOTS ... 53

9.3 F LOATING AND CYCLING ... 55

10 MODIFICATION ROUTES AIMING AT INCREASING THE VOLTAGE WINDOW OF ELECTROCHEMICAL CAPACITORS ... 57

10.1 M ODIFICATION OF ELECTRODE MATERIAL ... 58

10.2 M ODIFICATION OF ELECTROLYTE FORMULATION ... 69

11 CELL MODELLING FOR GIVEN APPLICATION ... 74

12 CONCLUSIONS ... 85

REFERENCES ... 88

13 SCIENTIFIC ACHIEVEMENTS ... 94

13.1 P UBLICATIONS AND CHAPTERS ... 94

13.2 S CIENTIFIC CONFERENCES ... 95

13.3 P ATENT APPLICATIONS ... 96

14 ABSTRACT ... 97

15 STRESZCZENIE ... 99

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1 Foreword to energy storage, management and transfer

The flow of energy is an inevitable feature of our universe. Each physical phenomenon is related to the energy transfer which has been defined by physicists as the ability to perform the work.

Every time, when the energy is transferred, it must be stored somewhere, it cannot be created nor destroyed according to the energy preservation law. Although many energy forms can be listed, humanity is still not able to gather whatever form of energy and transform it to another, usable and easily available source. The concept of energy has always been known for people.

They have used it in many different means during the ages in their everyday life.

Generally, energy storage systems could be classified into a couple of main storage technologies: electrical, mechanical, thermal and chemical. This work will focus on the electrochemical energy storage technology: as electrical and chemical phenomena could be used together. The first information on the electricity use in humankind can be found among ancient Egyptian priests. They were most probably using some kind of electricity, as it was found on certain drawings which were preserved until XX century. There were also discoveries in Ancient Far East on a clay jar which had separated terminals that could serve as an electric charge storage system when it was filled with a natural organic acid. However, we know nothing about the utilization of these devices. In ancient Greece, Tales noticed and described the ability of an amber to be electrified, without giving a strict name for this phenomenon. Many years later, in XVI century William Gilber gave the definition of electricity and proved that there are many more materials than can be electrified. He has also described the effect of magnetic field. Energy storage, transfer and management was coming to be reality.

After many more discoveries related to the electricity, in XVIII century Benjamin Franklin during his experiments with a kite proved that electric charges coming from storm skies can charge Leyden jar. It was a first prototype of a capacitor, which was developed in Netherlands in 1746. Later his discovery was used as a lightning rod or grounding, which is successfully used even now. Later, Charles Coulomb gave a theory in which he described that the objects electrified in single sign were repulsing and those electrified opposite sign were attracting with a force proportional to the distance between them. In 1771 Galvani discovered the flow of electric current by touching a frog leg with two different metals. The leg spontaneously moved.

Later, Alessandro Volta described that two different metals in contact with a wet body causes

a chemical reaction. He was a constructor of a first galvanic cell. In XIX century, Ampere has

extended the knowledge by introduction of electrodynamics. In 1830, Michael Faraday

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discovered that the movement of a magnet close to the spiral-shaped conductor invokes the current flow. Based on the discovery, Lenz introduced first electric motor. After that, Maxwell has combined the knowledge on electricity with magnetism giving a rise to electromagnetism.

Since then, a lot of useful devices which utilize these phenomena were introduced. There were for example a telegraph by Morse, telephone by Bell, bulb by Edison, generator by Tesla and many more. Today, electricity is a convenient mean to store, manage and transfer the energy.

Currently, the world relies on the electric energy. There are no global market shares which can withstand power interruptions. The electric devices become more and more complex, which brings about constantly increasing demand for electricity. Therefore, many research units around the world are involved in the development of energy storage, management and transfer devices that would meet the energy requirements of the modern world. ¹

Energy storage devices play an important role in the field as it is not always satisfactory to use the energy directly as it is produced from primary sources (as coal, petrol, wind, solar, potential energy, etc.). Very often this way seems to be feasible, mainly in stationary energy suppliers, such as in electric plants. However, it is not always possible to accommodate this big facility, as for example in mobile devices and others. This would require installation of reactors (ovens, internal combustion engines, nuclear reactors, etc.) in addition to the devices of interest, which is usually not justified according to their additional mass, volume and system complexity.

Therefore, storage of the energy is an excellent way to supply power to the devices in which their on-site production is not feasible or not available.

As already mentioned, this work will focus on electrochemical energy storage systems.

Electrochemical energy storage systems can be essentially divided into two main categories:

batteries and electrochemical capacitors. This division is based upon their operation principle.

Batteries rely on redox reactions only, where a change in oxidation state of reactants occurs

while their chemical potential is essentially fixed. Electrochemical capacitors, on the other

hand, rely on electrostatic interactions where only the electric potential is changed during which

oxidation state remain unchanged. In real world these two limiting conditions can interfere, so

a battery contribution can be found in electrochemical capacitors and vice-versa. Accordingly,

their performance parameters are influenced by their nature. Therefore, both kinds of devices

find their native applications adequate to specific technology. In the design of the

electrochemical energy storage their purpose must be strictly defined in order to create an

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efficient and cost-effective system. Often, the design includes the minimum weight and minimum volume storage system which meet the requirement of certain applications.

The batteries could be divided into two main groups - primary and secondary cells. The first kind can be in principle discharged only once, while the second can be charged and discharged many times. The applications area of batteries is already mature, since the oldest, commercially produced rechargeable cell, lead-acid battery was introduced in 1859 (France), when it received a lot of attention. Since then, other types appeared, from which the most important are nickel- cadmium, nickel-metal hydrides and finally lithium-ion. ² Electrochemical capacitors were first produced in 1960’s by SOHIO (Ohio, Cleveland), thus ca. 100 years after the batteries appeared. This relatively new technology, in order to exist, needs to find the market niches, those already dominated by batteries or even better, the entirely new ones.

It means that electrochemical capacitors have been developed for tenths of years. They already exist on the market, to serve in various applications. The state-of-the-art devices provide high performance, however they are not free of drawbacks. Shortly, it operates using expensive and not environmental friendly components. Moreover, in order to build the capacitors, the costly manufacturing process must be adapted. Therefore, a cheap and eco-friendly alternative has been proposed in the literature. Although a lot of research has been devoted to this technology, it still cannot compete with the devices already established, as a reason of limited performance.

A couple of companies have already tried to sell their eco-friendly product, however, their success is still far away. Fortunately, the technology still looks promising.

This work aims for the successful competition to the state-of-the-art. First part is devoted to the

literature review, which attempt to gain the knowledge in the field of electrochemical

capacitors, where all the most essential information available in the literature, and related to the

topic of the dissertation may be found. To maintain the high value of the part, most of the

bibliography originates from the last decade. It starts with the general introduction to the

electrochemical capacitors, following a brief outlook on the background of capacitors. The

special emphasis is put on the activated carbon electrodes and their modification, redox

electrolytes, electrochemical measurements and performance simulations of the capacitors

operating in aqueous medium. Additionally, other cell components as current collectors,

separator and housing will be described, as all these elements are responsible to reliable

operation of the cell. Then, the investigation methods for the materials used in the capacitors

are presented and critically evaluated. It is necessary to assess which identification techniques

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of the materials are important and used in the field of electrochemical capacitors (ECs). There

is an attempt of finding a link between the physical structure of the material and its

electrochemical performance. The electrochemical performance of the devices presented in the

experimental part is validated by the means of various electrochemical techniques, which are

described and shown in an informative manner. The novel approach for electrochemical

description of the system developed in the work is also thoroughly described in the experimental

section. Furthermore, two main strategies aiming at extending the operational voltage of the EC

are shown. The last but not least part puts the electrochemical capacitors operating in aqueous

medium forward to widespread use by the means of the modelling of final capacitor. Along

with that, the commercialization of these devices should become closer. It is of vital importance

to link the basic science into the capacitor engineering and finally, their production.

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1.1 General outlook of energy storage device types and the position of electrochemical capacitor

Batteries and electrochemical capacitors mentioned in the previous chapter are only the examples of electrochemical energy storage technologies. ^3,4 In general, all EC technologies, may be classified in various ways. One of the classifications is to divide them depending on the form of energy stored: mechanical, thermal, electrical and chemical as listed in Figure 1. All other types of classifications result from their performance properties, such as application, localization of energy reservoir or charging/discharging time. However, they are all closely related.

Figure 1: Different types of energy storage systems (ESS) with the examples

The scheme contains only examples. Usually, the use of certain type of energy storage system is nonexchangeable, which means there are certain conditions in which any storage device is used that determines the proper type. From the application point of view the most important is to consider the space and infrastructure available. Second, it is necessary to account for investments, operation and possible revenue costs. Finally, the serviceability must be considered. If all these aspects are simultaneously taken into account, the fruitful outcomes could be generated. For example, in stationary applications the energy and power densities are of little importance, while in mobile devices they matter. The same applies to the volume, it has much more meaning if it comes to mobile devices. Generally, the stationary application can accommodate bigger devices.

Pumped hydro engages the water reservoirs situated at various ground levels. As a result of water flow induced by gravity, its potential energy can be converted to the kinetic one using various generators. The advantage is that with big reservoirs, the energy might be relatively cheap. Flywheels, is an example of mechanical energy storage in which the kinetic energy is directly available from a rotating wheel. It offers therefore high efficiencies, however, due to the mechanical frictions, an important self-discharge occurs, therefore the energy cannot be stored for long time. A compressed air is often used in hydraulic-driven devices, this type of

Mechanical

•flywheel

•pumped hydro

•compressed air

Thermal

•thermoeletric storage

Electrical

•capacitor

•coil

Chemical

•battery

•fuel cell

•electrochemical

capacitor

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energy storage offers high torque at all times. Generally, no self-discharge occurs here, therefore it may be stored longer. In thermoelectric storage, the electricity results from two reservoirs of different temperatures. To charge it, it is necessary to heat up one reservoir. The self-discharge occurs as a result of thermal dissipation. Very popular, also in stationary, but especially in mobile devices are chemical and electrical energy storage devices. There are several kinds of them available nowadays, each having its own characteristic performance.

The most energetic one is fuel cell, where the energy comes from the burning of hydrogen stored, for example, in pressurized tanks. The energy depends on the molecular mass of fuel.

Then, less energetic are Li-ion cells which operate thanks to the reversible intercalation of Li

ions within a graphite electrode. They are most often used as power supplies in modern mobile

devices. Another type is a nickel-cadmium battery which are nowadays less and less used due

to the content of toxic metals. They have been pushed out by Li-ion technology. However, they

are still often used in military. Lead-acid batteries are still very popular energy storage devices,

especially in automotive or UPS applications. Furthermore, their recycling is efficient. The

most famous tool for comparison of different technologies is so called Ragone plot, named after

the inventor David V. Ragone. It is a simple diagram which shows the energy output of the

energy storing devices at various discharge power levels. For the most adequate comparison

between various devices, it is usually made on the mass or volume basis. Figure 2 shows the

localization of the energy storage devices. The diagonal lines indicate the characteristic time-

constant, which can be attributed to each technology. It says how fast the energy storage system

is able to charge or discharge. Therefore, it is easily noticeable that the systems such as fuel

cells offer high energy output, however, only at low power, so that the average discharge time

is equal to as long as 10 hours. ⁵

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Figure 2: A comparison of electric, chemical and mechanical energy storage systems in a Ragone plot

On the other hand, the fastest traditional electronic capacitors can discharge within milliseconds. However, they store 10 000 less energy per unit mass. In general, chemical energy storage systems offer long time-constants, while the physical ones short time-constants.

Ultracapacitors are special kind of devices in which physical and chemical interactions co-exist.

Depending on the specific cell construction they may act only as ordinary capacitors and show also a traces of battery-like behaviour. They receive a lot of attention thanks to the high power, which they achieve, releasing only moderate amounts of energy. However, it is known that each energy storage technology suits its most adapted applications, therefore they are especially handy in applications where batteries are no longer fast enough. Moreover, ultracapacitors include many more features which make them attractive. ^6,7

Their ability to deliver or gather energy at high power is currently often used by the industry.

First of all, electrochemical capacitors could be found in stationary applications where they

serve as grid energy storage. Nowadays, many renewable power sources can be found

worldwide, such as wind farms or solar power plants. However, the problem related to these

sources is that occasionally they may produce more energy than the local demand is. In such

cases, it is better to shut down the wind farm in order not to overcharge the grid. This may result

in increased amortization costs. It would be more cost-effective to store this energy for further

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use (for example at high energy demand period). This is where the supercapacitors come to be useful. (Figure 3)

Figure 3: Various energy storage technologies and their applications

Another important and capacitor-oriented application is the regenerative energy capture. It may be stationary as well as mobile. The first case often includes the capturing of potential energy of lowered object. The example might be a crane which recovers the energy during load lowering and within short time uses this energy to boost the lifting. The mobile application found in transport industry is mainly to use regenerative braking energy. After capacitor charging, the energy is used for vehicle acceleration. Electrochemical capacitors are also used where current peaks occur, this includes uninterruptible power systems. For all these applications, the high reliability is expected, which capacitors can offer. There are also another minor applications of ECs.

Not only are the exceptional properties of the capacitors which make them valuable, but also it

is their price. There are several main types of ECs proposed in the literature. They can be

divided based on the solvent for the electrolyte in which they operate, because basically, it is

factor that determines the cell voltage. The most widely used and commercialized is the organic

solvent as it can offer maximum voltage of ca. 2.7 V (acetonitrile) or 2.5 V (propylene

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carbonate). Very promising technology engages water-based medium, however, maximum achievable voltage is still ca. 1.5 V. The highest voltage windows are found in ionic liquid capacitors (up to 4 V). Table 1 compares these three capacitor types. It can be noticed that the medium is directly related to the energy density of each capacitor type. It is well seen in the formula for energy stored in capacitors, E, where the voltage, U, is found to be squared. ⁸

𝐸 = 1

2 ∙ 𝐶 ∙ 𝑈 ² [𝑊ℎ]

𝐶 = 𝜀 𝑆 𝑑 [𝐹]

C is called the capacitance and it is equal to the multiplication of permittivity of the medium and surface area of electrode divided by the thickness of dielectric layer (in capacitors thickness of electrode/electrolyte interface). ⁹

Table 1: The properties specific to the concrete capacitor technology based on its electrolyte medium

water-based organic-based ionic liquid

voltage 0.8 – 1.5 V 2.5 - 2.7 V 3.5 V

energy density 10 Wh kg ^-1 15 Wh kg ^-1 20 Wh kg ^-1

conductivity 100 mS cm ^-1 10 mS cm ^-1 8 mS cm ^-1

power density 10 kW kg ^-1 5 kW kg ^-1 1 kW kg ^-1

safety high low medium

price low high extremely high

Another important feature of each electrolyte solution type is its conductivity, which results from ions mobility in the medium. The most conductive are water-based media, which can achieve even up to few hundred of mS cm ^-1 . Then, it is substantially less for organic-based electrolyte, and even less for ionic liquids. The property which evolves from conductivity, σ, is a power, P, of the device. The empirical formula is:

𝑃 = 𝑈 ² 𝜎 4 [𝑊]

Again, it is directly proportional to the voltage squared, but also to the conductivity. Therefore, its high value ensures high power of the device. More often the power is expressed simply as:

𝑃 = 𝐸

t = 𝐶 ∙ 𝑈 ²

2 ∙ 𝑡 [𝑊]

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The highest safety is attributed to water-based electrolytes as they are devoid of toxic and environmental unfriendly components. Moreover, they are inflammable, what cannot be said about organic electrolyte. Additionally, the organic solvent is flammable, volatile and toxic.

Ionic liquids are generally considered as safe and inflammable electrolytes, however, they carry another important drawbacks.

Apart from the physical properties, the end user is especially interested in the pricing. Currently

it is relatively high for organic-based capacitor. The price is even higher for capacitors operating

in ionic liquids, but they exist only in the investigation stage. The cheapest are capacitors which

use water-based medium. Due to their low voltage abilities, they are not widespread. However,

owing to their low price and high safety in accompaniment to their performance properties they

remain perfect candidates for the development.

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This section aims at introduction to the construction, components and working principles of electrochemical capacitors. For the full understanding of the technology and implementation of innovative solutions, it is necessary to familiarize with the basic scientific and engineering aspects of the devices. Generally, scientists use two (or more precisely three) types of electrochemical setups to investigate electrochemical capacitors. First, is the typical three- electrode electrochemical setup in which a working, auxiliary and reference electrode may be found. Working electrode is a capacitive one, on which capacitor-related phenomena are aimed to be observed, auxiliary electrode is usually an oversized platinum mesh for charge balancing and reference is a typical reference electrode for potential control. Second example is where both, working and counter electrodes are made of capacitive materials and reference is added.

Third setup is where only two capacitive electrodes are present in electrolyte solution. The selection of the setup depends on the purpose of an experiment.

2.1 Scientific principles of operation

The operation of electrochemical capacitors is based on the same principle as observed in traditional capacitors found in electronics together with additional phenomena specific to the technology. The operation of capacitor is based on attraction and repulsion of charges by the oppositely polarized electrodes. During the charge accumulation process, the electrodes increase their absolute potential values (in an electrode called positive one, the potential value increases, while on a second one, called negative, the potential value decreases). The voltage of such capacitor is proportional to the amount of charge stored on the electrodes or the potential difference of two electrodes. During charging and discharging, the capacitors operate in variable voltage range. Theoretically, the voltage during charging could rise to infinite, however, in the reality limitations are encountered. Capacitance, i.e., the ability to store the charge, as shown in the formula, is a measure of the charge (q) accumulated in the voltage range (U).

𝐶 = 𝑑𝑞 𝑑𝑈 [𝐹]

For an ideal capacitor it is a constant value, often related to the characteristics of an electrode

double layer. The schematic representation of a capacitor is found in Figure 4.

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Figure 4: Scheme of a capacitor

In traditional electronics we find, among others, ceramic, air, foil or electrolytic capacitors. In construction way, they generally differ by the dielectric used. First three types are dry, while the last one use liquid electrolyte. It is the phenomenon called dielectric breakdown which mostly determines their upper voltage limit. For dry capacitors it can be even a couple of hundreds of volts, while for electrolytic capacitors, usually not more than 50 V. However, in both cases, the specific capacitance is extremely low due to use of low surface area materials, which make them low specific energy devices.

Electrochemical capacitor electrodes are made of high surface area material, usually activated carbon, which make them high-capacitance devices. However, their maximum voltage, on the other hand, is dictated by the dielectric strength of insulator (electrical double-layer, EDL), which differs depending on the solvent used, but in general does not exceed few volts. However, the energy values are much higher than in traditional capacitors. Electrochemical capacitors can be ideally represented by two capacitors (two electrode/electrolyte interfaces) connected in series by electrolyte solution (Figure 5).

Figure 5: Electrocal equivalent circuit of electrochemical capacitor

2.2 Electrical double-layer

The term electrochemical capacitor (EC) is often abbreviated as EDLC, which stands for

Electrochemical Double Layer Capacitor. Electrical double layer is a phenomenon formed at

electrode/electrolyte interface, which is the working element of the capacitor. ^10,11 As the name

depicts, it is basically composed of two layers of opposite charged species. There have been

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several descriptions proposed in the history: the first model was proposed by Helmholtz (Figure 6a). He concluded that upon immersing a conductive electrode in the solution, its charge is neutralized by the responsive orientation of the charges in the solution (as ions). 60 years later Gouy and Chapman enhanced the theory by accounting for a diffuse model of EDL (Figure 6b).

The diffuse model included the charge distribution being the function of a distance from the interface according to Maxwell-Boltzman statistics. The electric potential decreases in the exponential fashion as the function of a distance from the interface. The theory holds true only at low concentrations of electrolyte. In 1924 it was modified by Stern, where he proposed to combine Helmholtz and Gouy-Chapman theories, where part of the ions are adsorbed on the surface and part is distributed in the solution (Figure 6c). The theory was still not perfect, therefore, two decades later Grahame proposed an extension, in which he stated that some species are able to penetrate to the surface losing their solvation shell (specifically adsorbed ions) which was called Inner Helmholtz Plane (IHP). The outer Helmholtz plane (OHP) contains solvated ions at the further distance from an electrode. Beyond the outer Helmholtz layer is the diffuse layer. In 1963 Bockris et al. accounted for solvent molecules adsorbed directly at the electrode/electrolyte interface, which electric permittivity is related to electric field strength. This last theory is usually satisfactory for the description of the most phenomena.

Figure 6: Electrical double-layer representations ¹² : a) Helmholtz model, b) Gouy-Chapman model, c) Stern model

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From the electrical point of view the double layer can be treated as a dielectric. Dielectric is a material which possesses intermolecular forces that are strong enough to resist against external electric field (it possesses electrical permittivity). The intermolecular bonds are not being broken, instead the conformation changes. The electrical permittivity is often expressed in terms of relative permittivity (also known as dielectric constant). It is a factor of how much the electric field between the charges is smoothed by the material in relation to vacuum.

𝜀 _𝑟 = 𝜀 𝜀 ₀

However, when the electric field becomes stronger and stronger, the intermolecular bonds begin to break. In that case, the avalanche breakdown of dielectric occurs at the voltage specified by the material property - its dielectric strength. Then, the flow of current appears. In case of aqueous solvent the value is in the region of 1.23 V and strongly depends on the electrode texture. The texture of electrode influences the electric field intensity in electric double layer.

In case of smooth planar electrodes the electric field intensity is equal in all points, whereas in case of porous carbon electrodes, the electric field at the edges is more intense and therefore the breakdown of electric double layer takes place. The concept of dielectric constant, although it offers significant performance increase of electrochemical capacitor, is very scarce in the literature. ¹³

2.2.1 Faradaic and non-faradaic charge storage

In electrochemical capacitors field the charge can be stored in two ways: faradaic and non-

faradaic. The term non-faradaic charge storage relates to pure physical double layer electrostatic

interactions. In this mode, all the charge delivered to or drawn from the cell is consumed for

electric potential increase or decrease, respectively. It is related only to non-specific adsorption

of ions within the double layer. In addition to electrostatic interactions, also faradaic charge

storage may occur at the same time. Here, the charge is devoted to fast and reversible redox

reactions of the species adsorbed on the electrode surface. In that case it is the chemical potential

which undergo changes. It may be conveniently shown during constant current charging as in

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Figure 7: Current components during electrochemical capacitor constant current charging. I dl - double layer current I f - faradaic current. Reproduced from ¹⁴ .

2.3 Cell constructions and basic cell components

For the proper and reliable operation of electrochemical capacitor it is necessary to account for all components of the device simultaneously, as its weakest part ultimately determines the cell performance. Each device constitutes of electrodes, electrolyte, separator and current collectors.

These components are enclosed in the casing, from which the current collectors are extended and connected with external circuit. The final device may be of different constructions. The most widely used type in the industry is a cylindrical cell, in which the electrode assembly is rolled inside. There are also prismatic cells, known as pouch cells, which very often contain several layers of electrodes sandwiched one on another. These two types are usually stacked in various configurations to increase the voltage output. There may be found also coin-cell types, which contain very little amount of electrode material, but owing to their compact and suitable size often used on printed circuit boards (Figure 8).

Figure 8: Various capacitor designs

onset of non-ideal polarizability

I dl

I f I dl

I = I dl + I f onset of non-ideal

polarizability

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There is also other type of cell used at the R&D stage called Swagelok® cell. It is a PTFE vessel into which current collectors are introduced. (Figure 9) The vessel is equipped with third, small hole for reference electrode introduction for the monitoring of single electrode responses. It allows for quick and reliable assembly of the cell from which the basic electrochemical data might be acquired.

Figure 9: Cross-section of a Swagelok® cell design

2.3.1 Electrodes

The electrodes of electrochemical capacitor can be made from different active materials. First of all we should make a distinction based on the capacitor nature - whether it is an electric double layer capacitor or pseudocapacitor, because depending on the type, different materials are usually used. In case of the electric double layer capacitor, the active material should possess high surface area and high conductivity. It is satisfied by activated carbon which is the most popular electrode material used. Besides, carbon nanotubes and graphene are attractive materials. Various different kinds of other carbonaceous materials could be enumerated, such as carbon nanoonions, carbide-derived carbon (CDC), carbon fibres, carbon quantum dots. A relatively new material, not carbonaceous are MXenes. ^15,16

The nanomaterials used in electrode manufacturing possess porous structure. There is an official position by IUPAC to discriminate pores of different dimensions: pores of diameter <

2 nm are called micropores, between 2 nm and 50 nm are mesopores, while the pores larger than 50 nm are macropores. They were divided based on the role they play in the nanomaterial.

Micropores are responsible for ions adsorption, mesopores for their effective transport, while macropores create the channel entrances on the surface. ^17,18

Activated carbon is the most often used microporous material in the field of electric double

layer capacitors. The reason is its extremely high surface area which can reach up to about

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2000 m ² g ^-1 . ¹⁹ Moreover, it is cheap, its production is easy, which makes it attractive for the industry. Activated carbons are produced from various organic precursors of high elemental carbon content. The most often used carbons are produced from coconut shells, however, other precursors such as algae, wood, pestles and others are available. The requirement for precursor is that it originates from a waste material, which reduces the price even more and retain sustainable production. It does not also create the ethics problem related to the food processing.

The typical production line of activated carbon includes carbonisation of precursor followed by activation. Carbonisation means the conversion of a precursor into rich carbon-containing product through pyrolysis. It results in moderate surface area material. In order to increase the surface area even more, it is necessary to activate the material by introduction of microporosity.

In general there are two activation pathways: physical and chemical. The first case involves the use of water steam or carbon dioxide. ²⁰ During physical activation works according to pressure and temperature induces porosity development. Chemical activation, on the other hand, involves the prior impregnation of carbonised material with chemicals such as: KOH, ZnCl 2 or H 3 PO 4 . ^21–25 These aggressive chemicals at high temperature cause the partial burn-off of the initial material by releasing reactive by-products.

Graphene is another material found in the area of energy storage electrodes, which received a lot of attention after its discovery in 2004. There are claims that this material provides high energy and high power densities. ²⁶ It is a two-dimensional material made from single layer of graphite. ²⁷ Theoretically, according to calculations, it can reach 2600 m ² g ^-1 . However, there is an issue with this material. Namely, the graphene layers tend to stack due to strong van der Waals forces related with electron cloud on benzene rings of graphite. Second, what implies from this fact is that is extremely difficult to obtain pure graphitized graphene devoid of oxygen.

Sometimes, the oxygen content can reach about 10-20%, which cause the material to reach lower heat and electric conductivities than expected. Irrespective, the research on graphene is currently very intense. It is necessary to mention that the price of graphene is very high. There are several ways for graphene production, from which exfoliation seems to be most adaptive since it produces the graphene with relatively low number of defects. Graphene is also often obtained via chemical vapour-deposition. ^28,29

Carbon nanotubes received an alias of one-dimensional materials owing to their shape. They

are single or multi walled graphene tubes of nanometer diameter. Always their length is much

higher than the diameter. Owing to their nature, they possess high conductivity, while having

ca. 500 m ² g ^-1 . Therefore they found interest to study as electrochemical capacitor electrode

~ 22 ~

materials. Having high conductivity, they ensure high power of the device, however, in typical EDLC they allow to obtain only moderate capacitance values, ca. 40 F g ^-1 . On the other hand, carbon nanotubes are successfully used as a support for pseudocapacitive materials (MnO 2 , RuO 2 , etc.), where their mesoporosity is preferred. ^30–33 What is important about these materials is their complicated processability during electrode formation process. Carbon nanotubes are obtained via catalytic decomposition of hydrocarbons, during chemical vapour deposition process. Recently, there is an interest of growing aligned nanotubes directly on current collector substrate. ³⁴ It allows reaching extremely high power of the devices.

Carbon nanoonions, although manufactured long time ago, have been used as material for electrochemical capacitors just in the last decade. From a material science point of view they are spherical multi walled fullerene particles. They share only their external surface area, therefore they allow for reaching high power as similar surface area as CNTs. The microcapacitors with carbon nanoonion electrodes are able to retain their capacitance even at 15 A g ^-1 or 100 V s ^-1 . ^35,36 Carbon nanoonions can be produced by several methods, however, they are often obtained as a by-product coexisting with other form of carbon. One of the most pure synthesis comes from the thermal annealing of carbon nanodiamonds at 2000°C.

Carbide derived carbon (CDC), as its name depicts is a type of carbonaceous material derived from carbides, such as TiC, SiC or others. ^37–39 They are also known as tunable nanoporous carbons, which means that by proper selection of the preparation conditions it is possible to influence their porosity. The pore size distribution may be then adapted to the pore size of specific ions, which will lead to efficient utilization of microporosity and finally high capacitance values may be obtained.

Very often, the as-received carbon material is subjected to a modification for the adjustment of its properties. ^40–44 As the textural properties are usually tuned during activated carbon preparation (by selection of precursor type, carbonization or activation step conditions), their chemistry is most conveniently adapted just on the final product as a post-treatment. Depending on the post-treatment type and associated level of generated energy, new surface groups or doping of the atoms in crystal lattice (heteroatoms) may occur. The modification of carbons includes the variety of treatments, in which the primary goal is to introduce the heteroatoms or new surface groups. ^45,46 The most often studied modification is the introduction of oxygen.

Different methods and oxidants are used to introduce surface oxygen groups. In general, there

are wet and dry methods. Wet methods include the dispersion of activated carbon in oxidizing

~ 23 ~

agent solution, while the dry one the purging in oxidant atmosphere. As solutions, the most often used are hydrogen peroxide, nitric acid, persulfates, perchlorates, permanganates, etc. Dry method usually involves oxygen or ozone gas. Wet methods offer wider selection of possible oxidants, while dry method usually requires less effort related to the purification after the process. The additional intensive parameters of the treatments, temperature and pressure, generally influence the chemistry of newly formed product. Gas treatment is often carried out at hundreds of Celsius degrees, while wet methods, which use water as a medium is usually limited to water boiling point. As a rule of thumb, higher temperatures and pressures cause the deeper modification inside the carbon structure. The amount of new groups is controlled rather by the time of modification. The role of oxidation is to adjust the carbon properties to its designated application, to enhance adsorption, selectivity, activity (e.g. towards oxygen reduction reaction) in catalysis.

Other popular type of modification is the nitrogen doping. There has been done a lot of work done on modifying carbons for supercapacitors by nitrogen rich substances, such as ammonia, melamine, urea, etc. ^47,48 The nitrogen, by having five valence electrons, increases the electron cloud density in the crystal lattice if present as a heteroatom. It has been noticed that nitrogen doping increases carbon capacitance and conductivity, especially in acidic medium. While present on the surface, the donor properties of activated carbon are enhanced and the carbon increases its basicity. The introduction of nitrogen and oxygen has also been studied in one process, called ammoxidation.

There are also other elements which are often used as a dopants, such as boron, phosphorus or sulphur, however, less studied. ⁴⁹ Sulfur-doped carbon materials exhibit wide band gap as a result of electron-withdrawing properties of sulphur. The carbons enriched with sulphur characterize by higher electrical conductivity and surface wettability, although sulphur alone is a hydrophobic insulator. ^50,51 Boron contains three valence electrons, so doping of boron decreases the electron density in crystal lattice of graphene, therefore it can be used for tuning the electronic properties of carbon. Very attractive approach is a co-doping, where two or more elements are used to dope carbonaceous material. Usually, phosphorus is introduced together with sulphur or nitrogen. ^50,52–54

Different groups of electrode materials are non-carbonaceous conducting polymers. ^55–57 They possess good electrical conductivity, while giving rise to extremely high conductivity.

Moreover, they are relatively cheap. The most often used polymers are polyaniline (PANI),

~ 24 ~

polypyrrole (PPy) and poly[3,4-ethylenedioxythiophene] (PEDOT). However, as a result of swelling they have a limited mechanical stability which imposes worse cyclability. Second, the potential window oscillates in the region of 1 V, which is not very attractive from the point of view of application.

Another materials used in the supercapacitor area are transition metal oxides, such as MnO 2 or RuO 2 . They exhibit activity at positive potentials (positive electrode) giving to rise to extremely high pseudocapacitance contribution. Pseudocapacitance is a type of charge storage mechanism, where a consecutive redox reactions occur within a certain and broad potential range. As a result, the final capacitance looks like a double layer capacitance by showing its constant value.

2.3.2 Electrolyte

It is very important to use the term electrolyte carefully in the area of electrochemical devices.

It is useful to discriminate between electrolyte and solvent. Generally solvent is a substance that dissolves a solute. Solvent has zero conductivity, as there are no free charge carrier species.

The electrolyte is formulated once a substance (usually salt) which ionizes in the presence of a polar solvent is added. The term electrolyte is also used to express this solution as a whole, keeping in mind that it is ionized form of solvent. Therefore, the solvent becomes a charge carrier reservoir, while the salt is dissolved in it. The three common types of electrolytes are available: water-based, organic-based and a special one called ionic liquids. ⁵⁸ , ⁵⁹

Organic based electrolytes are for the moment most commonly used in industry. These symmetric capacitors work reversibly using the 1 mol L ^-1 tetraethylammonium tetrafluoroborate dissolved in acetonitrile or propylene carbonate solvent even up to 2.7 V or 2.5 V, respectively. ^60–62 Owing to high voltage, the capacitors attain relatively high energy density. However, due to low conductivity of the electrolyte, the cells suffer from low power.

The most important drawback in using this electrolyte is its toxicity and high price ⁶³ . To be able to use organic-based electrolyte it is necessary to dry the carbon prior to electrolyte introduction on cell assembly line, because the organic electrolyte loses its abilities even in the presence of water traces.

Water-based electrolytes are not as widely used due to certain complications related to the cell

operation, however, they also carry a number of advantages. Aqueous electrolytes may be acids,

bases or neutral salt solutions. Acids and bases, usually sulphuric acid and potassium hydroxide

are often used to describe newly discovered electrode materials. They are characterized by high

~ 25 ~

conductivity (almost 1 S cm ^-1 ) and are stable up to about 1.2 V. Recently, the use of neutral salt solutions, such as Na 2 SO 4 , Li 2 SO 4 , etc. has been shown to reach even 2.2 V. ^64–66 In order to understand the differences in the operation of the cells in aqueous electrolytes, a chart called Pourbaix diagram is introduced (Figure 10) ^67,68 .

Figure 10: Water stability limits. The dashed lines indicate the theoretical oxidation and reduction potentials.

The dashed lines indicate the equilibrium potentials of half-reactions related to water decomposition. The general equations are:

[+] 2H 2 O ↔ O 2 + 4e ^- + 4H ⁺ E ox = 1.23 - 0.059pH (1)

[-] 2H ⁺ + 2e ^- ↔ H 2 E red = -0.059pH (2)

As there is a proton present in the reactions, the equilibrium potentials depend on pH, which is equal to -log[H ⁺ ]. The electrodes of electrochemical capacitor operate in various potentials but the maximum theoretical voltage of aqueous supercapacitor is 1.23 V.

It has been presented that using neutral salt solution (such as sulfates, Li 2 SO 4 , Na 2 SO 4 , …) the safe voltage can be extended ⁶⁵ , ⁶⁶ , ⁶⁹ . The main reason for that is a phenomenon called hydrogen storage, sometimes described as hydrogen evolution overpotential. During deep negative polarization of carbon, the reduction of hydronium cations lead to formation of nascent hydrogen which is further stored in the porosity, according to the reaction:

C + H 2 O + e ^-  <C-H> + OH ^-

Furthermore, another product is a hydroxyl anion, which imposes the alkaline character in the porosity. Along with the pH increase, the equilibrium reaction (E red ) shifts towards more negative values. This may be observed on the cyclic voltammetry curves, where progressively,

E _red E _ox

-1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6

0 2 4 6 8 10 12 14

E / V vs. S HE

pH

~ 26 ~

negative potential cut-off is extended. At the reversal of potential sweep, we may observe the increase in anodic current responsible for desorption of previously stored hydrogen (Figure 11).

Figure 11: Demonstration of hydrogen storage phenomenon at electrolyte pH of 7 (2 mV s ^-1 )

The electrolyte might be also a source of additional redox reactions which boost the capacitance of electrochemical capacitors. Very promising example in the field is related to the inorganic iodides. ⁷⁰ By their progressive addition to the supporting electrolyte (for example Li 2 SO 4 ). ⁷¹ . It has been proved that the careful selection of carbons for proper electrodes is beneficial in terms of reached capacitance values and stabilities in long term operation at high voltage. ⁷² However, the literature gives also the examples of many other inorganic and organic compounds. ^73,74

2.3.3 Separator

The primary role of separator is to provide the physical separation of capacitor electrodes that prevents internal short circuiting. The important parameters applicable to separators are material (chemical resistance), porosity and thickness. When selecting a separator, one must consider the resistance of the electrolyte soaked within. The more tortuous and longer ion pathway, the higher is the resistance. The most often used separator is made of an inert material, such as glass fibre mat. It is possible to obtain the porosity as high as 90%, however, in order to preserve integrity, it must be sufficiently thick, such as 250 μm, as in the case of Whatman GF/A. Usually, the higher is the thickness, the separator absorbs more electrolyte. This has an effect on the system weight and volume, which generally tend to be reduced in order to provide high energy and power densities of the device. Recently, the research focused on the use of

-700 -500 -300 -100 100 300 500

-1.2 -0.8 -0.4 0 0.4

i / mA g -1

E vs. SHE (V)

~ 27 ~

polymeric membranes, such as PVDF, PA or PP membranes. ⁷⁵ They allow obtaining even 20 μm thickness. However, along with the thickness reduction, the porosity decreases. Therefore, a compromise must be held. Another reason of using polymeric membranes is to provide immiscible regions within a cell around both electrodes. It allows using two different electrolytes which introduces asymmetry or hybridization. Asymmetry, in the following case, means that the electrodes operate in two different electrolytes, but the mechanism of charge storage for both remains the same. ⁷⁶ There can be for example two electrolytes of different pH values. Hybridization, on the other hand, means to introduce two electrolytes which provide different charge storage mechanism. Redox reaction providing electrolyte on one electrode, and typical capacitive charge storage on the second one. In both cases as well as in symmetric systems, when there is only one electrolyte giving one charge storage mechanism on both electrodes, it is necessary to consider proper current collector material, which is stable in the used environment.

2.3.4 Current collectors

The role of current collector, as it name depicts, is the collection of charges from high surface area, capacitive electrode. It provides the integrity of the laminate structure and enables reliable connection to the external circuit. ^77,78 A good current collector should be:

- highly conductive,

- stable in the environment, - thin,

- light.

The selection of current collector material depends on the environment in the capacitor.

Whether it is the capacitor operating in organic solution or ionic liquids, aluminium current collectors are of good choice, because aluminium is stable in this electrolyte at working potentials of electrodes when polarizing up to 2.7 V. The advantage of aluminium is its high electric and heat conductivity, easy processability, low price and low density.

In order to select the possible current collectors for aqueous capacitor the corrosive diagrams

of Pourbaix give a good indication. The most stable materials for this purpose are noble metals,

such as gold or platinum. However, due to high price and low abundance in earth’s crust the

use of these metals is limited to R&D stage. It gives the possibility to eliminate the influence

of current collector and focus the investigation on carbon electrode. Aluminium, contrary to

organic solution, is found to be unstable in aqueous one. Therefore, other materials, such as

~ 28 ~

stainless steel or nickel are considered to use. Stainless steel is the most often used material for current collector during investigations. There are plenty of stainless steel types available, from which type AISI 316L is the most popular owing to its composition. This austenitic nickel- chromium steel contains molybdenum in composition, therefore, it has superior acid-resistant properties comparing to other types of steel (as for example AISI 301). Steel has low resistance, however, it is ca. 3 times denser than aluminium. Usually, it is possible to obtain thicknesses as low as 10 μm, when the typical thickness of the aluminium current collector is 30 μm. Taking into account the thicknesses and densities of both materials the final weight per surface area is comparable.

Recently, there is a research devoted to production of current collector free electrodes for electrochemical capacitors. ^79–82 This usually goes together with developing flexible systems.

These electrodes are often produced using carbon nanotubes and reduced graphene oxide,

which are characterized by high conductivity. Although there are many reports on graphene

excellent electrical conductivity, this property is still hardly achievable and metal current

collectors still pursue.

~ 29 ~

3 Physicochemical investigation methods of electrochemical capacitor materials

In the field of electrochemical capacitors the proper material characterization gives the possibility to gain broader knowledge of exact chemical and physical phenomena during operation of the cells. The deep understanding of it allows for more reliable and controlled optimization of electrochemical cell parameters. A number of non-electrochemical methods for material characterization could be listed. Usually, these techniques require separate sample of electrode, active or electrode material powder to be prepared, which is destructed after the experiment. This includes: Thermoprogrammed desorption coupled with Mass Spectrometry (TPD-MS), Boehm titration. Another techniques which are not destructive: ASAP, XPS or Raman spectroscopy. Depending on the environment in which the sample is investigated, it may be divided into: in-situ, ex-situ, operando or post mortem analyses. The ex-situ or post mortem techniques are TPD-MS, ASAP, Boehm titration, XPS. Raman spectroscopy, being non-destructive technique may be in-situ, operando or post mortem (if special transparent electrochemical vessel is used). Depending on the purpose of the experiment, the proper decision on the timing of characterization must be taken. Very often, the images using SEM (Scanning Electron Microscopy) or TEM (Transmission Electrode Microscopy) are shown.

This part reviews on these techniques often applied in the area of supercapacitors which contain their description for proper understanding during experimental part of the thesis.

3.1 TPD-MS

Thermoprogrammed desorption coupled with Mass Spectrometry is a technique in which

desorption of volatile species takes place during programmable thermal ramp and the

corresponding mass loss of the sample is recorded. The difference to TGA (Thermogravimetry

Analysis) is that the sample during heating does not react with surroundings. The sample is

placed in the chamber and heated to high temperatures (usually 900°C). Additionally, the

attached mass spectrometer returns the mass-to-charge ratios (m/z) of detected species. Finally,

it is possible to determine amount and nature of gases evolved. Based on this, the thermograms

provide information on the chemical groups present on the carbon surface.

~ 30 ~ 3.2 Boehm method

The Boehm titration, is used to quantify surface oxygen functional groups of activated carbons in discrete pK ranges. ^83,84 The method uses NaOH, Na 2 CO 3 , NaHCO 3 and HCl and its main assumption is that the amount of acidic sites is determined under the principles that:

- NaOH neutralizes carboxylic, lactonic and phenolic groups on the carbon surface;

- Na 2 CO 3 neutralizes carboxylic and lactonic groups;

- NaHCO 3 neutralizes only carboxylic groups.

The total amount of basic sites can be calculated from the amount of HCl required during the

titration.

~ 31 ~

4 Accurate capacitor storage system design based on single-cell test data

The above part of the work focuses mostly on the review of electrode materials, electrolytes and other cell components, as well as thorough description of scientific principles of operation.

The aim is usually the improvement of energy storage abilities. This is an important approach, however, the technical point of view regarding the application of these capacitors cannot be skipped. The development stage of electrochemical capacitors includes their testing in small electrochemical vessels. This usually comprises only small amounts and thus small electrode areas. It does not comply with the commercial capacitor sizes which are able to store useful amounts of energy. Therefore, the approach in which the electrical equivalent circuit model of a capacitor is build is acquired. ^85–90 The model is further simulated in order to assess and obtain the information on the requirements for a cell stack in real application. Measurements on electrochemical capacitors usually provides the basic data on capacitance, series resistance, leakage current, and open-circuit voltage decay. These parameters are important, however, they do not express the dynamic performance of an active material, which is especially important when tasked with creating a minimum-size storage system for a given power profile. ⁹¹ Typical examination approaches are not sufficient therefore for engineering of electrochemical capacitors. Ragone plots are shown to face the energy vs. power of the device, however, they also do not provide dynamic data. Modelling and simulations are necessary steps for obtaining this information.

Modelling of a laboratory capacitor allows sizing the industrial-type device by upscaling its dynamic response. The typical procedure involves stipulating a circuit model which represents the electrical response of the laboratory capacitor. ^92–95 Then, modification of the initial model is applied to reach the maximum correlation between experimental and simulated results.

Finally, it is possible to design the full-size storage system which is able to precisely meet the

power profile of a specific application.

~ 32 ~ 5 The aim of the work

The aim of the work is a modification of electrochemical capacitor components such as electrode material or electrolyte in order to improve its properties. The improvement of maximum cell voltage, capacitance of the device and finally the energy density of a device will be considered. All these parameters will positively impact the future application of an electrochemical capacitor operating in aqueous medium making the competition to the state-of- the-art.

Initially in the experimental part of the work certain issues are raised which aim at indicating the proper measurement approach of the cell. First, the technique which allows accurate determination of electrode contributions to the electrochemical capacitor during voltammetry scan of two-electrode cell is proposed. The plausible errors which may occur during measurements of each electrode separately are eliminated while the precision and time of measurement is improved.

Second, a comment is made on the proper evaluation of the cell testing techniques and their parameters determination. Very often, based on the experiments the efficiencies are determined.

However, in most cases more care should be taken.

Then, two strategies of energy density improvements are proposed. Both aim primarily at increasing the operational voltage, rather than capacitance. There are two, independent methods of modification of electrochemical capacitor working components, i.e. electrodes and electrolyte. Modification of electrodes is done in order to impose the electrode/electrolyte interfaces, by changing their donor/acceptor nature to ensure more favourable operational conditions. Modification of electrolyte aims at shifting the electrode terminal potentials to extend the thermodynamic stability of electrode/electrolyte interfaces by activation of certain redox reactions, which occur in competition to electrolyte decomposition.

Finally, an electrical model of the electrochemical cell is proposed, which is further simulated

to assess the cell performance in real application. This approach allows for modelling of

capacitor stack performance based on single laboratory-scale cell measurements. Based on the

simulations, the minimum-sized energy storage device can be designed for a specific

requirements of power and energy ratings.

~ 33 ~ 6 Experimental

The electrodes of the capacitors are prepared accordingly to the device they are intended to be used in. In the present work, two capacitor vessels are used: Swagelok® cells and pouch cells.

Irrespectively of the device, the active material is produced via the same procedure: 97% of activated carbon material (indicated where appropriate) is mixed with 3% of polymeric binder (polytetrafluoroethylene, PTFE). The suspension is prepared in a beaker and mixed with isopropanol or ethanol. Further, Ultraturrax is used in order to homogenize the sample. Finally, the dispersion is subjected to evaporation in rotary evaporator. The resulting dough is then rolled to form a thin (250 μm) film. In case, when Swagelok cells are going to be used, the circular discs, playing a role of electrodes are punched. In case of pouch cells, the film electrodes are deposited on the current collector foil made of stainless steel AISI 316L. The separator used is Whatman GF/A 250 μm. The important modifications to the given conditions are depicted in the appropriate chapters.

Prototype capacitor measurements part includes the test cell where the two leads of the prototype capacitor were attached to a potentiostat/galvanostat (Bio-logic, France) using a true four-lead connection. Electrical measurements were performed using three voltage windows:

0.8 to 0.4 V, 1.2 to 0.6 V, and 1.6 to 0.8 V. The sequence began with 30 galvanostatic

charge/discharge cycles at 0.4 A g ⁻¹ to condition the capacitor. This was followed by

electrochemical impedance measurements (EIS, 8 points per decade at a bias voltage of ¾ times

the upper voltage value, over the frequency range 1 mHz to 1 kHz) and then galvanostatic

charge/discharge cycles at 0.16, 0.4, 0.8, 1.6, and 4.0 A g ⁻¹ . Final measurements were constant-

power charge/discharge cycles over each voltage window at 0.16, 0.4, 0.8, 1.6, and 4.0 kW kg ⁻¹ .

Prototype modelling is done by impedance circuit-model fitting tool embedded in the EIS

software to derive initial two- and three-time-constant equivalent circuit models for the three

voltage windows. SPICE (Simulation Program with Integrated Circuits Emphasis) circuit

simulation software “MicroCap” 11 was then used to predict model performance. Comparisons

were then made with constant-current charge/discharge measurements. Finally, circuit

parameters were adjusted in an iterative fashion to improve model accuracy. This continued

until no further model improvements could be realized. The circuit models were devised to

accurately represent the two-terminal electrical response of the test cell - circuit elements in the

models do not in any way represent actual physical process that are occurring within the cell.