Energy Density Of A Supercapacitor Biology Essay

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Super capacitors that have higher energy density than a normal capacitor have been developed. Though the energy density of a supercapacitor is less than that of a battery, its power density is higher which makes it suitable for applications that require a sudden initial amount of current due to its ability to discharge immediately. Supercapacitors are used in conjunction with batteries to boost its power supply capability. In some cases, batteries have now been replaced by supercapacitors.

A super capacitor differs from a normal capacitor because it is made up of two electrodes, a separator and an ion carrier (electrolyte). Another distinct feature that differentiates super capacitor from a normal capacitor is high values in capacitances which could be up to hundreds or even some few thousands of farads while it is very hard to find a normal capacitor with a value up to one farad [1], [2].

Researches have shown that such capacitance values could be achieved by using porous carbon as the electrode material which provides a larger surface area and thus boost the capacitance value. Carbon is one of the cheapest available resources on earth which can be from different sources, implying that the porosity differs from one source to another [1], [2] and [3]. To improve the performance of supercapacitor, research has been carried out by investigating different materials that could be applied in this aspect. Besides, the electrolyte, the separator as well as the packaging have effects on the overall performance of the supercapacitor [4], [5]. Similar to battery performance measurements, there are different types of measurements applicable to supercapacitors as well. Such measurements include charge/discharge tests, cyclic Voltammetry and impedance spectroscopy. The study will be focused on impedance spectroscopy measurements and cyclic Voltammetry analysis.

1.1 Supercapacitor electrode materials

There are three classes of supercapacitor electrode materials. The first one is based on carbon which offers a surface area as large as 3000m2/g that can yield a capacitance of 145F/g. The carbon used could be in the form of carbon cloth, activated carbons, carbon aerogel, and carbon black, carbon derived from silicon carbide or titanium carbide precursors. Supercapacitors formed with carbon are known as electrochemical double layer capacitors (EDLC).

The second class is for supercapacitors based on redox reactions (pseudocapacitors) in which electrodes are made up of electronically conductive polymers. Their capacitance values usually yields 300-400F/g but they have a problem of long term stability giving only thousands of cycles over a wide voltage range. Examples include polyaniline (pani), poly (3 - methylthiopene) (PMet), poly (dithieno [3, 4 -b: 3,'4'-d] thiopene) (PDTT1), poly (3-p-fluorophenylthipene) (PFPT) etc.

The third class is for materials with high redox capacitance. Examples include mesoporous metals, their oxides, hydroxides, oxyhydroxides, a combination of any two of them, and metal nitrides with very good electronic conductivity. The metal could be nickel, cobalt, titanium, tin, palladium, lead and ruthenium, in their pure form or as part of an alloy. Examples are nickel oxide (NiO), nickel hydroxide (Ni(OH)2), nickel oxyhydroxide (NiOOH), lead dioxide (PbO2), cobalt oxide (CoO2), titanium dioxide, palladium oxide, ruthenium dioxide (Ruo2), molybdenum nitride (Mo2N) and Iridium oxide (IrO2) [3], [6], [7] and [8]. Its technology is similar to that of a battery.

The method of preparation of a supercapacitor electrode material determines its capacitance. For example, a capacitance of about 720F/g is obtained from a RuO2 prepared at low temperatures by sol-gel process. The resulting material obtained is in amorphous form. Other methods of preparation give a typical value of 50F/g. Mo2N with specific capacitance up to 40F/g is an alternative to RuO2 [6].

Manganese oxide is also a low cost electrode material due to its multiple oxidation states and the structural ability to incorporate cations [9]. A lot of techniques have been employed in its preparation such as nanocasting, sonochemical method, thermal decomposition method, hydrothermal synthesis method, sol-gel route, the coprecipitation method and electrochemical deposition method. Each of the method gave a certain structure which resulted in several forms of manganese oxides such as hierarchically porous MnO2, mesoporous MnO3 with crystalline pore walls, discrete nanoporous MnO2 and Mn2O3 particles, layered MnO2 nanobelt etc. The maximum obtained specific capacitance from manganese oxide electrode was 350F/g [10].

Asymmetric hybrid capacitors have been developed by a combination of a double layer electrode and a pseudocapacitance electrode. The combination produces capacitances 3 to 10 times that of an EDLC. The thickness of the double layer electrode and that of the redox electrode ranges from 9:1 to 100:1, with the thickness of the redox electrode ranging from 10µm to 70µm. This gives an optimal energy density. In some cases the physical sizes of the electrodes is made to be the same in order to improve on the number of cycles. In essence the problem of sharper reductions in available capacity suffered by the conventional redox electrodes at high discharge rates is being tackled by reducing the extent to which it is discharged there by increasing its lifetime [9].

Based on the above discussion, the supercapacitor is categorized as shown in the block diagram below showing the different classes of supercapacitors down to their electrode sources.

Figure 1.1 Block diagram of supercapacitor types and sources.

1.2 Impedance Spectroscopy and equivalent circuit modeling

Impedance spectroscopy involves taking measurements of impedance over a wide range of frequencies. The impedance considered in the case of the supercapacitor is complex due to its reactive nature. The range of frequencies is divided into two. There is the lumped constant range below 100mHz and distributed constant range above 100mHz. Data obtained from impedance spectroscopy is presented in form of plots such as the Nyquist plot, Bode plots and Lissajous figures or sometimes modeled in the form of equivalent circuits [3], [11], [12].

1.2.1 Modeling supercapacitors without redox reactions

In [12], the supercapacitor considered is the one without Faradaic reactions (no pseudocapacitance); refer to section 1.1 in which the electrode is made up of porous carbon. The carbon pore is assumed to be cylindrical. Based on this, the following equivalent circuits were developed.

Figure 1.2 " Schemes of electrochemical impedance of EDLC (a) Lumped constants type equivalent circuit (b) Distributed constants equivalent circuit" [12].

Figure 1.3 Distributed constant-type equivalent circuit of a single pore [12].

The lumped constant-type equivalent circuit was expressed as a series combination of a solution resistance and capacitance. It was obtained by taking measurements within the lumped constant range of frequencies showing a straight vertical line in which the solution resistance is constant while the capacitance value changes. Such type of model is mathematically represented by:

(1.1)

Where: c is capacitance.

Now comparing with

, (1.2)

(1.3)

But

(1.4)

Substituting (1.4) into (1.3) yields

(1.5)

Equation (1.5) is an indicator that the imaginary part of the impedance in the lumped constant range of frequencies diminishes with frequency.

The distributed constant type was modeled as having a solution resistance and impedance per segment of the electrode pore. Their impedance spectrum is similar to that of the lumped constant type at low frequencies and showed a locus with an angle of 450 in the high frequency range. This is because the current distribution on the electrode is non-uniform in the high frequency range as shown in figure 1.3, indicating loop currents I1, I2,

…, IN-1, IN.

Now assuming the AC voltage source in Fig.1.3 is E, the total impedance for the circuit can be obtained as. The imaginary part impedance is due to the presence of Zseg which is considered to be a capacitor [3], [12].

1.2.2 Modeling supercapacitors with redox reactions

Redox reaction in supercapacitor involves charge transfer by diffusion, convection and migration. In modeling supercapacitors with redox reactions (pseudocapacitance), any of the following circuit elements may be introduced:

1.2.2.1 Constant phase element.

The CPE is a circuit element having impedance expressed by:

(1.6)

Where: 𝛚 - Radial frequency.

Where Qo has the same value as the admittance at 𝛚=1rad/s with a unit of S.sn. the phase angle of the impedance is independent of frequency and has an angle of (-90*⍺) degrees.

At ⍺= 1, the impedance is the same with that of a capacitor. When n is close to 1, its response resembles that of a capacitor with a constant phase angle less than 90o. The CPE behavior is usually caused by electrode roughness, surface disorder, slow adsorption or diffusion reactions, non-uniformity of current and voltage, electrode geometry and porosity. Fractal electrodes normally exhibit this behavior [3], [13], [14], [15].

1.2.2.2 Warburg Impedance.

The Warburg impedance occurs as a result of diffusion transport to electrodes. It is dependant on the frequency of the perturbation. At high frequencies, its value is small since the distance moved by diffusing reactants is small. At lower frequencies the reactants have to move a greater distance there by increasing the Warburg impedance. It is mathematically represented by the equation

(1.7)

This forms a line with an angle of 45o to the real axis on the Nyquist plot.

The variable σ, in equation (1.7) is the Warburg coefficient expressed as:

(1.8)

Where: R - Ideal gas constant (8.314472 (15) JK-1mol-1).

T - Thermodynamic temperature.

n - Number of electrons involved.

F - Faraday constant.

A - Surface area of the electrode.

C*o - Bulk concentration of the oxidant.

Do - Diffusion coefficient of the oxidant.

C*R - Bulk concentration of the reactant.

DR - Diffusion coefficient of the reactant.

The unit of σ is Ω.s-0.5. It could either be determined using equivalent circuit fitting using a circuit that has a Warburg element in it or by finding the slope under its plot. Equivalent circuit fitting softwares mostly return an admittance value for the Warburg element from which the Warburg coefficient can be computed using the relationship [16]:

(1.9)

When σ is known, the magnitude of the Warburg impedance could be determined using:

(1.10)

Equation (1.7) only applies when the diffusion layer has an infinite thickness. In the case where the diffusion layer is bounded, the impedance is given by:

(1.11)

Where 𝛿 is the Nernst diffusion layer thickness and D is the diffusion coefficient of the electro active species [11].

More over in the case in which the diffusion layer is finite, the Tangent (T) circuit element and Open Finite-Length Diffusion (OFLD, sometimes shortened 'O') circuit element can be used to model the behavior of the supercapacitor or any electrochemical device [17].

1.2.2.3 T circuit element (Tanhyperbol)

The impedance behavior of the T circuit element is similar to that of the Warburg impedance at high frequencies. However, at lower frequencies, its behavior resembles that of a series combination of a resistor and a capacitor with

(1.12)

(1.13)

Where: R is resistance.

B is time constant which has a unit of sec0.5.

Yo is an admittance parameter.

is the thickness of the thin layer.

D is the diffusion coefficient.

Figure 1.4 Impedance behavior of a T circuit element [17].

Its impedance is given by:

(1.14)

Y0 is an admittance parameter expressed as:

(1.15)

The T element derives its name from the tan hyperbolic function in its admittance when equation (1.12) is inverted. This is the reason why sometimes it is described as a "Tanhyperbole" circuit element.

1.2.2.4 O circuit element (Cothyperbol)

The behavior of the O circuit element shown in figure 1.5 is as a result of the use of a rotating electrode (RDE) in impedance studies. In this type of system, there exists a region near the electrode in which mass transport happens by diffusion alone due to the presence of a thin layer of unstirred solution (Nernst diffuse layer (NDL)) and a large source of material outside that layer. Sandwiched in between these regions is a porous membrane in which molecules can diffuse. At high frequencies its behavior is similar to the Warburg impedance while at low frequencies it shows the behavior of a Randles cell [18], [19].

Figure 1.5 Impedance behavior of an O circuit element [18].

Its impedance is given by:

(1.16)

B depends on the NDL which also depends on the speed of rotation of the electrodes [19]. It is called a "Cothyperbole" because its admittance has a Cothyperbole when equation (1.14) is inverted.

Another circuit element used in impedance spectroscopy is the Gerischer (G) which also has the behavior of Warburg impedance at high frequencies sharing some resemblance with the O circuit element at low frequencies as shown in figure 1.6.

Figure 1.6 Impedance behavior of a G circuit element [20].

It results from a chemical reaction happening in the bulk solution called the common electrode (CE) mechanism. Its impedance is given by:

(1.17)

Where: k is a rate constant parameter having a unit per second (s-1) [14].

Table 1.1 Circuit elements used for modeling impedance spectroscopy data.

Description

Symbol

Parameter

Resistance

R

R

Capacitance

C

C

Inductance

L

L

Warburg

W

Yo

CPE

Q

Yo, ⍺

Tanhyperbole

T

Yo, B

Cothyperbole

O

Yo, B

Gerischer

G

Yo, B

A combination of the above circuit elements is used in modeling the behavior of different types of processes occurring in an electrochemical device such as a supercapacitor. For example the Randles cell is a combination of a double layer capacitor (Cdl), an equivalent series resistance (Rs), an equivalent parallel resistance or charge transfer resistance (Rct) and Warburg impedance as shown in the figure below:

Figure 1.7 Randles cell [21].

Sometimes the double layer capacitance is replaced by a constant phase element [20]. A simulated EIS Nyquist plot for the Randles cell is shown below:

Figure 1.8 Simulated EIS of a Randles cell [21].

1.3 Cyclic Voltammetry

Cyclic Voltammetry involves applying a preset increasing voltage to the working electrode until it reaches a set value. Upon reaching the set value, the voltage is being decreased down to its initial value. During the process, the current at the working electrodes is recorded and plotted against the applied voltage. The resulting plot obtained is called a voltammogram. The applied voltage waveform is triangular since it is ramped linearly and then decreased as shown in figure 1.9. The rate at which it is ramped is called the scan rate. Figure 2.0 is an example of a voltammogram for a reversible reaction. The measurement taken is for a single cycle. In some instances, measurements are taken for a multiple number of cycles [22] [23].

Figure 1.9 Input voltage waveform used in cyclic Voltammetry [23].

Figure 1.10 an example of a voltammogram [23].

Cyclic Voltammetry is used in studying the quantification of concentrations, diffusion effects, irreversibility, reaction intermediates and in identification of electron transfer steps. It is sometimes used in determining voltage levels for stable operations, which is carried out because instability can lead to gas evolution and metal electroplating [24], [25].

Figure 2.0 above showed four parameters Epc, Ipc, Epa and Ipa which represent the cathodic peak potential, cathodic peak current, anodic peak potential and anodic peak current respectively. Sometimes the terms cathodic and anodic are replaced by the terms reduction and oxidation when describing cyclic Voltammetry parameters. If the rate of electron transfer is very high, the value of the peak potentials becomes independent of scan rate. This phenomenon is an indicator for a reversible electrode reaction and following relationship then holds [26], [27]:

(1.18)

Where n is the number of electrons involved in the process. Since Epc and Epa are determined experimentally, n could be determined from equation below:

(1.19)

Another important parameter that could also be observed from the voltammogram is the thermodynamic reversible potential denoted Eo. It is a parameter that is independent of scan rate which takes a value 85% that of the peak potential [27]. Cyclic Voltammetry is also used in capacitance computation by dividing the anodic current at a particular point by the scan rate [28].

CHAPTER 2

Literature Review

2.0 Introduction

The discovery of the electrochemical double layer supercapacitor was done by General Electric engineers in 1957 while performing experiments with devices based on porous carbon electrodes. Then it was realized that energy is stored within the carbon pores. Though they did not make much effort towards its development, Standard Oil of Ohio made their own discovery accidentally while working on fuel cells in 1961. They designed it using activated charcoal as the electrode material in which the electrodes were separated by a thin insulator. This serves as the basis for the design of supercapacitors to date. Standard oil did not commercialize their invention rather the technology was sold to NEC which was then commercialized in 1978.

In 1971 Tassati and Buzanca discovered that ruthenium dioxide films have almost the same electrochemical charging behavior with a capacitor. Continental Group Inc. contracted the author and his workers to carry out more researches on the use of ruthenium oxide type of supercapacitor. The research was carried in between 1975 and 1980 [29], [3].

During the earlier days of its discovery, it was used as a memory backup in computers. Production increased slowly and supercapacitors with improved performances and reduced cost were developed due to advances in materials science from the mid 90s to date [29].

Market analysis made by Lux research showed that the supercapacitor market is expected to rise from last year's $208 million to $877 million by 2014 with a 27% compound annual growth. The forecast stated further that application in cell phones and digital camera will make up $550 million while large scale applications will make $320 million [30], [31]. Another research by Nano Markets revealed that the demand of supercapacitors from the smart grid will reach $1.1 billion by 2016.Thus in order to boost the supercapacitor production to meet up with its future demand, several R & D's on various materials that will enhance its performance and lower its cost are in progress. Moreover the technology of the ultra battery expected to be released within the next few years that integrate the lead acid battery and supercapacitor technology necessitates R & D's in this field [32].

Supercapacitor as one of the components in power electronics for renewable energy devices aids in the usage of cheap sources of energy such as solar energy which reduces carbon emission. Another area which employs supercapacitors is in hybrid electric vehicles (HEV). Such vehicles make use of gasoline and power electronics devices in conjunction. By so means, fuel economy is enhanced there by releasing lesser carbon into the atmosphere than in conventional vehicles. This together with many other advantages of the usage of supercapacitors necessitates its enhancement through R & D's.

2.1 Activated Carbon

Amongst all the supercapacitor electrodes materials, activated carbon is the most commonly used due to its cheapness, high surface area, good electrical conductivity and thermal stability [10]. In the design of a supercapacitor using activated carbon, the issue of pore size is taken into consideration. This is because the pores in activated carbon have complex structure consisting of macro pores, meso pore, and micro pore. The importance of knowing the pore size is in order to select the electrolyte that will give a larger capacitive value. To obtain a large capacitance, the electrolyte's ions most penetrate and cover the surface of the electrode. This is only possible if the ion radius is less than the pore radius. It is known that micro pores have the least diameter. As such the ion radius must be smaller than the radius of the micro pores [12].

Figure 2.1 Sample of activated carbon [33]

Figure 2.2" Conceptual scheme of pore activated of carbon "[12]

The size of a macro pore is larger than 50nm, that of a micro pore less than 2nm and meso pores have sizes in between 2nm and 50 nm [34]. The pore is cylindrical. For the carbon scheme showed in figure 2.2, different sizes of cylindrical pores exist. It is called a branch pore electrode structure. In an instance where a single pore exists, the carbon electrode is called a single pore electrode [12].

The number of branches in the branch pore electrode structure is based on the number of a micro pores against a meso pore and meso pore against a micro pore. For example if there are 3 micro pores against a meso pore and 3 meso pores against a macro pore, the branch structure then resembles figure below:

Figure 2.3 Branch pore Structure with 3 micro pores against a meso pore and 3 meso pores against a micro pore" [12].

2.2.1 Equivalent Circuit Model of a Branch pore carbon.

Analysis made in [12] based on theoretical formula of transmission line model impedance solved by Levie resulted in the following for the electrode model with repeated pore structure.

Figure 2.4 "(a) Conceptual model of pore electrode with repeated structure, (b) equivalent circuit for pore electrode with repeated structure, and (c) simplified equivalent circuit of pore electrode with repeated structure "[12].

Zm is the impedance of mth pore. The solution resistance of the mth pore designated Rsol,m is given by:

(2.1)

The total impedance is then

(2.2)

(2.3)

(2.4)

(2.5)

Where Zma, Zme and Zmi represent the impedance for the macro pore, meso pore and micro pore respectively.

In an instance where the carbon structure is composed of b1 meso pores against a macro pore and b2 micro pores against a meso pore, the total impedance is expressed as

(2.6)

In this case

(2.7)

(2.8)

(2.9)

Figure 2.5 (a) Conceptual model of pore electrode with b1 = 3 and b2 = 3. (b) Equivalent circuit of the model (c) Simplified equivalent circuit of the model [12].

2.2.2 TYPES OF ACTIVATED CARBON

Activated carbon is categorized based on source, physical form, the type of activation process and post treatment.

Classification Based On Source

Activated carbon can be from various sources such as bituminous coal, anthracite, coconut shells, wood, peat, lignite and a lot of other carbon containing materials. Activated carbon is sometimes designated or labeled with its source [35].

Classification Based On Activation Process

There are two types of activation processes

Physical reactivation.

Chemical activation.

Physical reactivation is done in two stages. In the first stage, the material containing carbon is subjected to a temperature between the range of 600-900oC and then pyrolyzed under this condition. The word pyrolyzed is derived from pyrolysis meaning decomposition of organic material under heat in the absence of oxygen. This process is called carbonization. In the second stage the carbonized material is subjected to a temperature above 250oC which usually ranges from 600-1200oC in an oxidizing atmosphere e.g. carbon dioxide, steam and oxygen. The second stage is called activation or oxidation. Activated carbon produced in this way has a fine pore structure which makes it suitable for the adsorption of liquids and vapor.

In chemical activation, the material is first influenced by a chemical which could be an acid, base or salt before being carbonized under lower ranges of temperatures typically 450-900oC. Examples of chemicals used include phosphoric acid (P2O5), potassium hydroxide (KOH), sodium hydroxide (NaOH) and zinc chloride (ZnCl2). Activated carbon produced using chemical activation have larger pore structure and is more likely to adsorb large molecules. Chemical activation is mostly preferred because it involves the use of lower temperatures and is also not time consuming [33], [36].

The type of activated carbon suitable for EDLC is the one obtained by the pyrolysis of coconut shells, coal and wood in a nonoxidizing atmosphere or by pyrolysis of organic polymers [3]. KOH activated carbon nanotubes (CNTs) are also used for EDLC. It has been reported that supercapacitors produced using KOH activated CNTs produced a capacitance of 300Fg-1 with a specific capacitance of 9.9µF/cm-2. The activation was carried out on a highly volatile bituminous coal which resulted in a specific area of 3150m2/g and a pore volume of 1.612cm2/g. Depending on the type of activation method used, the surface area of carbon can be increased by a factor up to 15 or more times its original surface area and since capacitance is proportional to the surface area of the electrode material used, activated carbon electrode is considered to be the best among the carbon based supercapacitors. The only thing that then matters is the carbon source and activation process [37].

Classification based on physical form

Based on physical form and particle size, activated carbon is classified as:

Powdered Activated Carbon (PAC): This type of carbon has a very small particle size. The particles are so small such that 95-100% of it will pass through a mesh sieve. It can be in the form of powder or fine granules with an average diameter ranging from 0.15 -0.25mm.

Granular Activated Carbon (GAC): This has a larger particle size when compared with PAC. Diameter ranges from 0.297-0.8mm.

Classification based on post treatment

In this context activated carbon is classified as:

Extruded Activated carbon (EAC): This is a mixture of PAC and a binder which forms a cylindrical shaped activated carbon block with diameters ranging from 0.8-130mm.

Polymer Coated Carbon: This is obtained by coating a porous carbon with a biocompatible polymer without blocking its pores.

Impregnated Activated carbon: This is a type of porous carbon impregnated with an inorganic compound such as iodine, silver or cations of some selected metals such as Aluminum (Al), Manganese (Mn), Zinc (Zn), Iron (Fe), Lithium (Li) and Calcium (Ca) [33], [38].

2.3 Separator Materials

The separator could either be cellulose based (special paper) or polypropylene in the form of self stranding films. The paper separator has the advantage of high porosity resulting in low equivalent series resistance. It has a disadvantage of poor mechanical properties resulting from low tensile and puncture strength. As a result the polypropylene film separator is commonly used due to its good mechanical properties, resistance against solvents and chemistry and low cost of production by means of biaxial stretching [5], [39]. Other separator materials include polyethylene membrane, porous glass fiber tissue or a combination of polypropylene and polyethylene [8].

2.4 Electrolyte materials

Electrolyte could either be organic or aqueous.

2.5 Packaging supercapacitors

When packaging a supercapacitor one has to take its size, type and use into consideration. Thin prismatic supercapacitors are used in mobile electronics such as phones cameras etc. coin-type cans are used for PC-board and so on. However, when packaging a supercapacitor the end plates must have good contact with the electrodes in order to minimize ESR. The packaging should be able to protect the electrochemical system against oxygen and water vapor in order to prevent oxidation transformations that can lead to the evolution of gas. The container used should be able to tolerate pressure generated by the electrochemical decomposition. In some cases a weak point is provided in the container for safety when there is hazard such as overcharge. This will enable the cell to open softly. The weight of the container is preferably taken to be one tenth the total weight of the supercapacitor cell.

There are mainly two types of supercapacitor packages:

Prismatic package.

Cylindrical package.

The cylindrical package comprises the coin type cell and the winded type. In the coin type cell an electrode is placed in the cell, a separator in between followed by the second electrode all of which most have been soaked in an electrolyte solution. The cell is then assembled with its cover and crimped [3], [40].

Figure 2.6 a coin type cell supercapacitor [41].

The winded type is as shown below:

Figure 2.7 a wounded cylindrical cell supercapacitor [40].

Figure above showed the winded type with aluminum tabs inserted in between active layers. The active layers comprises of the electrodes and the separator. A good connection has to be established in between the aluminum and the protruding current collectors to minimize ESR as discussed earlier.

Figure 2.8 below shows a sample of a prismatic packaged supercapacitor internally composed of rectangular electrodes separated by a separator, an electrolyte and current collectors attached to each electrode which are further extended to form the external leads.

Figure 2.8 a prismatic supercapacitor [42].

Prismatic packaged supercapacitors have an advantage of low ESR when compared with the cylindrical type [41]. It is sometimes called the stacked type because several cells can be stacked together to form a single supercapacitor. The connection between the cells is dependent on which parameter is needed to be high. If capacitance is to be high, parallel connection is used. Series connection is used in a case where the voltage is needed to be higher. The increment in each parameter is at the expense of the other [43]. Thus several arrangements could be made to achieve a specific capacitance and voltage based on series and parallel connections which includes the use of several cells and may add to cost and size. This is an area that needs to be developed so that materials with high capacitance values could be achieved. By so doing the size of the supercapacitor will be reduced because a few numbers of cells would be required to compensate for an increased voltage rating, at the same time taking the material cost into consideration.

For testing applications in laboratories, cylindrical supercapacitors are packaged in a test cell as shown below:

Figure 2.9 Sample of a supercapacitor test cell [43].

The method of assembly is the same with that of the coin cell type. The only difference is in the mechanical structure and how to assemble together. The test cell can take several other forms but still satisfying the same reason. There is also a plastic cell with metallic current collectors. It doesn't matter which type is used so far it satisfies the criteria needed in a supercapacitor cell.

CHAPTER 3

SURFACE AREA MEASUREMENTS

3.0 Introduction

The surface area of most solids is determined by a principle known as adsorption. A gas that comes in contact with any solid surface is being attracted, resulting in the formation of an adsorbed layer of molecules of the gas that came in contact with the solid. The adsorption process may involve a chemical interaction or not. In the instance where there is chemical attraction the process is called chemical adsorption or shortened chemisorption. Adsorption involving a physical interaction only is termed physical adsorption. The terms adsorbate and adsorbent are used for the gas and solid respectively. It is a spontaneous process leading to a change in free energy, ∆G, which is negative. This is usually accompanied by a decrease in entropy, ∆S as a result of loses in degrees of by the gas. The free energy change is given by:

(4.1)

Thus for ∆G to be negative, the enthalpy change, ∆H, has to be negative with a magnitude large enough to cancel the entropy term.

An example of a physical adsorption is the change in phase from gaseous to liquid form in which only forces of molecular attraction are involved. Chemisorption involves the formation of a bond. This makes the enthalpies much higher than that in physical adsorption. The enthalpy in a physical adsorption takes a value less than 20KJmol-1 while that of chemisorptions usually exceeds 80KJmol-1.

A physical adsorption occurs between any adsorbate and adsorbent while chemisorption is specific in the sense that a chemical reaction can occur in between certain gases and a particular solid surface. The desorption process (reverse of adsorption) for the physical adsorbed gas in very easy and takes place under a reduced pressure without any rise in temperature. Desorption of a chemisorbed gas involves breaking of the chemical bonds, a process done under a low pressure and high temperature which is difficult compared to physical desorption.

3.1 Applications of Adsorption

Heterogeneous catalysis.

Measurement of surface area.

This chapter will focus on measurement of surface area.

3.2 Methods of surface area measurement by adsorption

3.2.1 Volumetric method

A simple volumetric apparatus for the measurement of adsorption is shown below:

Figure 3.1 Volumetric apparatus for gas on solid adsorption measurement [44].

The apparatus consists of a manometer, a burette and a sample bulb. Reservoirs attached to the manometer and burette is for controlling the level of mercury.

The first step in starting an experiment involves measuring the volumes of the gas path and the empty space in the sample bulb. In order to keep the volume of the gas path constant, measurements are carried out by setting the right arm of the manometer to a fixed zero point. This is known as the calibration process. As the calibration process continues, the sample may be heated to remove any gas present. Helium gas is used in this stage because it is a poor adsorbate. With the helium in the apparatus, volume is altered by a known amount using the burette and an equivalent drop in pressure is measured.

Surface area is measured by using nitrogen as adsorbate, in which the sample bulb is dipped into liquid nitrogen for both calibration and measurement. The amount of nitrogen is supposedly known. The sample bulb is then opened, leading to a decrease in pressure as a result of increased volume and adsorption. Measurements over a range of gas pressures are taken and analysis is done using the BET equation as shown below:

(4.2)

And

(4.3)

Where:

P - Actual gas pressure.

po - Saturation pressure (pressure at which saturation occurs).

nσ - Amount adsorbed.

nmσ - Amount required for complete monolayer coverage of the surface (monolayer capacity)

E1 - Activation energy (enthalpy of desorption).

Ev - Enthalpy of vaporization of the adsorbate.

The equation resembles that of a straight line implying that plot of the left hand side of the equation against the relative pressure () should result in a straight line. nmσ and Z are determined from the line from which surface area is calculated from nmσ, considering the area of nitrogen molecule to be 0.162nm2.

In present generation apparatus, improvements have been made in such a way that mercury is no longer used in altering the volume of the setup. Mean while calibrated flasks each having an individual tap is used. Electronic pressure transducers are used as the pressure sensing devices.

3.2.2 Flow methods

This makes use of a flow system. The adsorbate is mixed with a diluting agent, leading to a change in the concentration of the gas mixture as it is being adsorbed by the surface. A mixture is helium and nitrogen is commonly used. As the sample cools to a temperature near 77K adsorption takes place leading to a reduction in nitrogen from the gas mixture flowing over the sample, there by changing the concentration of the mixture after passing the sample. This change in concentration is measured using matched thermal conductivity detectors located before and after the sample as shown in figure 3.3. Multipoint analysis (taking several measurements) using different amount of the adsorbate in the mixture gives accurate results. Data obtained is fitted to either the Langmuir adsorption equation or the BET equation.

The Langmuir adsorption equation is shown below:

(4.3)

Where:

(4.4)

a1 is an adsorption factor and b1 is a desorption factor.

The term is referred to as the relative adsorption.

So with the value of the surface area can be determined.

Figure 3.2 a modern gas adsorption measuring instrument by flow method [44].

An example is the micromeritics product, ASAP 2020 in which experimental settings are done using software which later on returns the results with some analyzed data. Thus one only has to measure weight of the sample before starting the experiment, input into software, attach the sample to the apparatus and then give a command via software for the experiment to begin.

Figure 3.3 micromeritics ASAP 2020 surface area and porosity analyzer.

3.2.3 Gravimetric methods

This involves the use of a microbalance. An adsorbent is bombarded with an adsorbate gas under a certain pressure. Sufficient time is given for the mixture to reach equilibrium before determining the mass change. The process is repeated at different pressures, each time determining the number of moles adsorbed, which is then plotted against pressure to obtain an adsorption isotherm. A micro balance can handle a pressure of 120Mpa [44].

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