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Aim of the Homogenisation Process

Introduction: Eukaryotic cells such as liver cells enclose a variety of different types of membrane bound structures called organelles (nuclei, mitochondria) as well as macromolecules (ribosomes) (Padh, 1992).
Subcellular fractionation is an invaluable technique allowing scientists and researchers alike to successfully isolate and separate specific subcellular components within the cell (Becker et al, 2009). This allows researchers to study the different organelles (using biochemical techniques) in a greater degree of detail therefore increasing our knowledge about the many different types of organelles and macromolecules, thus leading to new scientific advances in this ever advancing era of science and technology (Bonney, 1982; Berns, 1986).
It is this very method which in the past allowed Christian de Duve to discover the lysosomes and peroxisomes for which he shared a Nobel Prize with Albert Claude and George Palade in 1974 (Becker et al, 2009).
Subcellular fractionation can be safely divided under 3 major headings: Homogenisation proceeded by fractionation and finally purification.
Homogenisation: The aim of the homogenisation process is to effectively and efficiently disrupt and break the cells outer membrane thereby releasing their subcellular components (nuclei, mitochondria). This disruption and breaking of the cells must be achieved in a manner that will leave the delicate organelles of interest undamaged and morphologically intact (Loewen, 2003).
The cells to be homogenised are kept in an isotonic buffer (0.25M sucrose, 1mM EDTA and 1mM of Tris at pH 7.0). This is to protect the fragile organelles from osmotic damage due to osmotic unbalance as well as environmental instability such as pH interference (Guteriezze, 2010).
Many different homogenisation techniques exist and are available, some such include mechanical grinding using Potter-Elvehjen glass homogeniser, cutting methods using warren blender, ultrasonic vibrations in a process called sonication and utilising high pressure such as in the French Press (Loewen, 2003).
The Potter-Elvehjen glass homogenizer was used in this experiment. The Potter-Elvehjen glass homogeniser consists of a Teflon pestle which is closely fitted into a glass homogeniser. The homogenising machine moves the Teflon pestle in a verticle up-down motion while simultaneously rotating within the glass homogeniser containing the cells to be homogenised (Mangiapane, 2010).
The space between the Teflon pestle and glass homogeniser is incredibly small (0.004?-0.006?). Therefore as the Teflon pestle moves throught the glass homogeniser a shear force is generated which causes disruption of the cells. The organelles which are released by this process pass undamaged, safetly through the gap between the pestle and glass homogeniser (Loewn, 2003; Mangipane, 2010).
The shear forces produced can sometime be destructive to the organelles causing irreversible damage and therefore shear forces need to be controlled. This can be controlled by adjusting the gap width between the pestle and glass homogeniser. A bigger width can protect organelles from damage but the negative side effect of this is that the generated shear forces will not be strong enough to disrupt the cells and therefore few or none organelles will be present in the homogenate. Therefore a careful balance between cell disruption and organelle damage must be maintained.
Chemical, physical and structural damage can be caused to organelles due to shear forces which can cause errors when purifying the organelle using biochemical techniques due to enzymes specific to the particular organelle being damage or rendered inactive and these problems must therefore be overcome. Some such precautions which when utilised can overcome or minimise unnecessary damage includes the use of different homogenisation techniques which are more suitable for the cells being homogenised (osmotic disruption, chemical disruption may be considered). Carefull usage of the homogenising equipment (Lowen, 2003).
Fractionation: Once the homogenate has been formed, it is ready to be placed in a centrifuge and undergo centrifugation which will separate the different fractions/organelles. Centrifugation generates a centrifugal force which separates the different types of organelles based on their size and density as well as the density and viscousity of the solution the homogenate is in. Therefore the the higher the molecular weight of the organelle the greater the distance I will travel down the centrifuge tubes or the higher its sedimentation rate and consequently the smaller the molecular weight of the organelle the smaller the distance it will travel down the centrifuge tube or the lower its sedimentation rate (Becker et al,2008; Mangipane, 2010). The greater an organelles sedimentation rate is the greater the organelles sedimentation coefficient (in Svedberg units, named after Theodor Sveber who developed the ultracentrifuge) will also increase (Becker et al, 2009).
Centrifugal forces can be calculated using
For example, if a homogenate containing nuclei, mitochondria and ribosomes is subjected to a centrifugal force, logically the nuclei will be near the bottom of the tube, the ribosomes at the top part of the tube and the mitochondria somewhere in between the nuclei and ribosomes.
There are 2 main type of centrifugation methods: Differential centrifugation and density gradient centrifugation.
Differential centrifugation
This type of centrifugation works on the principles that large dense molecules (nucei) will have a higher sedimentation rate compared to small and less dense molecules (ribosomes) (Becker et al, 2009). During low centrifuge speeds and short times the heavy and dense organelles sediment and can be collected, while as high centrifuge speeds and longer timer the lighter and less dense molecules will sediment and can also be collected (manipulative techniques).
Therefore in the homogenate used in the experiment, by using appropriate centrifuge speeds and times the nuclei and mitochondria can be separated using 1500g for 10min and 20000g for 10min respectively.
Density gradient centrifugation
The method used in density gradient centrifugation, also known as rate-zonal centrifugation works on the principle of separating molecules based on their densities and is achieved by using a density gradient in the centrifuge tube (manipulative techniques; Becker et al, 2009). The density gradient is normally provided by a concentrated sucrose solution which increases in density towards the bottom of the centrifuge tube. The sample requiring fractionation is placed in a layer over the density gradient sucrose solution (Becker et al, 2009). As the centrigugation process proceeds, the different molecules or organelled of different densities are separated based on their densities and that of the increasing sucrose density. When the fractionation bands have been formed are are distinctive the fraction may be remover via a syringe or separation methods. This type of centrifugation can be used to further separate mitochondria from lysosomes and peroxisomes since each of them has a different density.
Measurements of enzyme activity and macromolecular composition of fractions. “purity” of fractions.
During the centrifugation processes, such as in the differential centrifugation the various types of organelles and macromolecules form gelatinous pellets at the end of each consecutive centrifuge (Dyson, 1979). The different pellets produced contain a variety of different fractions of subcellular organelles and macromolecules and is not specific for just a single type of organelle or macromolecule. As an example in the first centrifugation process to form the nuclei fraction at 1500g for 10mins, the nuclei is pelleted along with other molecules of similar size and molecular weight such as unbroken cells, cell debris and pieces of the cell membranes (Bonney, 1982). In the second centrifugation to form the mitochondrial fraction at 20000g for 10min the pellet contains mitochondria, lysosomes and peroxisomes due to their similar sizes and molecular weight. In the final centrifugation process at 20000g for 10min a supernatant fraction was formed containing many small and low molecular weight molecules such as the endoplasmic reticulum, microsomes and ribosomes (Minorsky, 2009; Berns, 1986).
As stated before fractions will not only require the organelles of interest but also other organelles and macromolecules. It is therefore necessary to be able to assess the purity of the fractions. This can be done in a variety of ways.
Microscopic analysis via the light microscope or even electron microscope can be used to identify the different macromolecules present within the fraction, therefore giving an indication whether or not the fractionation procedure has been successful. A mitochondrian therefore can be differentiated from a peroxisome or lysosome basen on its structure (Bonney, 1982). Microscopic anaylsis can also be used in assessing the biochemistry of the fraction by using various cytochemical techniques.
Biochemical techniques are a very good way of assessing the type of organelle present as well as the purity of a fraction. Measuring enzyme activity is an excellet method sine some enzymes are very specific and found in one particular organelle.
Marker enzymes present in fractions and importance of the techniques involoved in the advancement of biochemistry and cell biology.
Marker enzyems are routinely used in subcellular fractionation to differentiate between the many different types of organelles and macromolecules present within the cell. Mitochondria for example can be detected indirectly by the presence of succinate dehydrogenase while lysosomes can be detected by Acid Phosphatase (Bonner, 2007).
The function of the mitochondria for example is to generate adenosine triphosphate (ATP) by a process called oxidative phosphorylation and an enzyme specific to the mitochondrion called succinate dehydrogenase can be used as a marker enzyme to differentiate between the presence of mitochondria and other organelles and macromolecules present in the fraction (Padh, 1992). Succinate dehydrogenase (SDH) is specific to the inner mitochondria membrane and is responsible for catalysing the oxidation reaction of Succinate, which is a component of the citric acid cycle, into fumarate which is another component of the citric acid cycle. Since flavin adenine dinucleotide (FAD) is reduced producing FADH2 (Guterize, 2010; Padh, 1992;Girolamo, 2010).
Succinate is the electron doner while FAD is the electron acceptor. The products of the above reaction are then reacted with an artificial electron acceptor called INT(a tetrazolium salt) to form a red coloured compound called formazan.
This reaction is required because both the fumarate and FADH2 produced in reaction are colourless and therefore there is no certain way of determining succinate dehydrogenase activity, therefore the intensity of the red coloured formazan produced during a specific timeframe in the second reaction can be measured using a spectrophotometer gives an indirect indication of succinate dehydrogenase activity and therefore an indication of the presence of mitochondria as well as its purity within the fraction (guterize, 2010; padh, 1992).
Electron microscopy of the isolated organelles is generally the final step in assessing the purity of the fractions as well as studying their morphology (padh, 1992).
It is these methods and techniques used in subcellular fractionation which has allowed researchers such as George Palade and Christian de Duve studying to understand and discover the structures, biochemistry and roles played by the various organelles.
Results: Table 1 shows the volumes of the homogenate, nuclei fraction, mitochondrial fraction and supernatant fraction. The Homogenate volume was obtained after rat liver homogenisation; NF volume was obtained after 2 consecutive centrifugations at 1500g for 10min; MF volume was also obtained by 2 consecutive centrifugations at 20000g for 10min; SF volume was obtained from the supernatant of the MF centrifugation.
Table 2 shows known amounts of bovine serum albumin (BSA) which underwent the biuret reaction; the absorbance’s were measure using a spectrophotometer at 550nm. As protein amount increases so do the absorbance’s. This data was used to plot a BSA standard curve.
Figure 1 illustrates the BSA standard curve which is a line of best fit. From this graph, the protein amount is determined by using the absorbance values for the different fraction shown in table 3 below. H, NF, MF and SF correspond to homogenate, nuclei fraction, mitochondrial fraction and supernatant fraction respectively. The vertical and horizontal red, blue, green and black coloured lines represent H, NF, MF and SF respectively.
From the above graphical data Protein concentration (mg/ml), total protein amount (mg) and protein recovery for each fraction relative to the homogenate can be calculated.
Homogenate:
Nuclei Fraction:
Mitochondrial Fraction:
Supernatant Fraction:
From the above results the total percentage of protein recovery relative to the homogenate can be determined:
The above calculated results are show together in table 3.
Table 3 shows the absorbance values obtained from the spectrophotometer. Row B shows the amount of protein that was determined from the BSA standard curve. Row C showed the amount of protein present in 1ml of each fraction; the homogenate had the highest protein concentration, followed by the SF and MF and finally by the NF containing the lowest amount of protein concentration. Row D shows the total amount of protein in each of the fraction and therefore follows the same pattern as the values for Row C. Row E shows the amount of protein recovered relative to the homogenate; The percentage of protein recovery was as follows: SF>MF>NF.
Table 4 shows the actual fraction concentrations used, obtained by diluting the original fractions (table 3) with phosphate buffer. The supernatant fraction was left undiluted.
Table 5 shows absorbance of each of the fractions (0.2ml) which were diluted by the addition of 4ml of ethyl acetate within formazan. The average absorbance minus the control gives the corrected mean absorbance for each of the fractions. The control values for all 4 fractions were 0 because they were given as negative values by the spectrophotometer. The highest absorbance was recorded for the SF followed by the homogenate, MF and NF.
By obtaining the data collected from the previously calculations in tables 1, 3 and 5 it is possible to calculate; the total activity of Succinate Dehydrogenase (SDH), the percentage recovery of SDH relative to the homogenate, the specific activity of SDH and the relative specific activity of SDH relative to the homogenate in all 4 fractions (H, NF, MF and SF).
Below are the equations which will be used in the calculations:
Beer-Lamberts Law: The calculations below will make (concentration) the subject of the formula as well as prove that the units for = or .
∴ this can be rearranged to form,
, since always equals to , the equation can now be represented as,
, the units of this new formula can be calculated as follows,
the in the bottom fraction can be cancelled out with the at the top giving,
Which ∴ gives which is Molarity or concentration.
The equation will be used throughout the rest of the calculations. The Formazan molar extinction coefficient= and the assay volume used will be 0.004L (4ml).
Homogenate: The absorbance for the homogenate in table 5 was 1.1385 therefore,
∴ since this can be arranged to give,
The volume used was which gives therefore,
Activity ∴
∴ total activity of in -1
The answer is required in ∴ since
Therefore total activity for Homogenate =
∴
Therefore specific activity for Homogenate
Nuclei Fraction (NF):
The absorbance for the nuclei fraction in table 5 was 0.117 therefore,
∴ since this can be arranged to give,
This gives,
Activity ∴
∴ total activity of in
The answer is required in ∴ since
Therefore total activity for Nuclei Fraction =
∴
Therefore specific activity for Nuclei Fraction
Mitochondrial Fraction (MF):
The absorbance for the mitochondrial fraction in table 5 was 0.398 therefore,
∴ since this can be arranged to give,
This gives,
Activity ∴
∴ total activity in in –
The answer is required in ∴ since
Therefore total activity for Mitochondrial Fraction =
∴
Therefore specific activity for Mitochondrial Fraction
Supernatant Fraction (SF):
The absorbance for the supernatant fraction in table 5 was 1.485 therefore,
∴ since this can be arranged to give,
This gives,
Activity ∴
∴ total activity in in
The answer is required in ∴ since
Therefore total activity for Supernatant Fraction =
∴
Therefore specific activity Supernatant Fraction
Calculations for the % SDH recovery and specific SDH activity relative to the homogenate;
Since the % SDH recovery and specific SDH activity is to be calculated relative to the homogenate, therefore the homogenate percentage for them both will be 100%
Nuclei Fraction:
Mitochondrial Fraction:
Supernatant Fraction:
The main findings of these calculations can be summarized in the table below:
Table 6 shows that SDH activity is highest in the SF, followed by the homogenate, MF and finally by NF. The %of SDH recovery (relative to the homogenate) was greatest in the SF, followed by the MF and the NF. The specific SDH activity was greatest in the SF followed by the MF, NF and lastly by the homogenate. The % of specific SDH activity (relative to the homogenate) was greatest in the SF, followed by the MF and NF.
Figure 2 illustrates the main findings from table 6. It can be seen that % SDH recovery increases from the Nuclei fraction to the supernatant fraction. The % of specific SDH activity steadily falls from the supernatant fraction to the nuclei fraction.
Discussion: According to the results obtained in table 3, it was seen that 99.25% of the protein relative to the homogenate was still present within all the fractions. This high percentage recovery indicates that very little protein was lost during the formations of the nuclei, mitochondrial and supernatant fractions by centrifugation. The 0.75% of protein that was lost is most likely to have been lost while homogenizing the pellets formed during each consecutive centrifugation process. During the usage of hand homogenizers small quantities of the pellet containing the proteins are stuck to the homogenizing vessel or the pestle. These small quantities of proteins being lost during each hand homogenizing process therefore contributes to the loss of proteins recovery. From this high protein recovery it can be said that the overall homogenisation process was very efficient.
During each successive centrifugation at different speeds a distinct pellet was formed, thus indicating the separation of organelles. In table 3, different amounts of proteins were present within the pellets. Since these proteins are associated with the different organelles present, this indicates that since different amounts of proteins were found in the fractions therefore various different types of organelles must also be present. But this is not always the case since proteins from other fractions could have been damaged due to the homogenization and centrifugation processes. Therefore the calculations performed on Succinate Dehydrogenase activity, recovery and specificity (table 6, figure 2) showed that that the total SDH activity was highest in the supernatant fraction. Since SDH is a specific marker enzyme to the mitochondrion organelle as explained earlier, the data suggests that the separation of mitochondria during centrifugation to be present within the suspected mitochondrial dfraction was not optimal. The supernatant also had a very high protein content of 885mg (table3) which indicated therefore that most of the organelles have separated into this freaction, thus indicating the hight amount of SDH activity within the supernatant fraction.
In a differential centrifugation process the successive increases in the centrifugal forces applied should create a gradient of the presence of different organelles, with the heaviest molecules in the centrifuge tubes with lowed centrifugal forces, the mediam molecular weighted organelles such as mitochondria in a centriguge in the centrifuge with a medium centrifugal force is applied and small molecular weight organelles such as ribosomes in the centrigue tubes where the highest centrifugal forces are applies.
Therefore the separation of organelles has occurred but not to a great extent as seen by the reults in table 3 and table 6. Seperation of organelles could have been greatly improved by possibly refining the lab protocol. To ahieve better mitochondrial separation and therefore more accurate SDH activity measurments the centrifugation process should be done at 20000g but for 20min and not 10min as stated by Loewen (2003) and Becker et al (2009). This will help separate the mitochondria out better.
Different centrifugation methods such as density gradient centrifugation can be utilized after the intital differential centrifugation to better separate organelles of similar sizes such as mitochondria, lysosomes and peroxisomes. The new fractions produced can by the densiy gradient centrifugation can be recovered with the use of a syringe. Many other techniques such as the initail homogenisation stage could also have been changed and other techniques could have been used as described earlier.
Conclusion: It was found by this experiment that subcellular fractionation is not a perfect method and therefore inaccuracies must be expected. But it is a process that has revolutionaised our understanding of cell structure and function.
It was found in the experiment that differential centrifugation can separate organelles to an extent to form a nucleic fraction, mitochondrial fraction and supernatant fraction. Marker enzymes which are present in specific organelles can be used to help distinguish between different organelles as well as the fractions relative purity. SDH was used in this experiment and was found to be present higher in the supernatant, possibly due to experimental error. SDH was specific to the supernatant fraction therore again indicating the presence of mitochondria in the supernatant.
The usage of such techniques in this ever advancing era of science and technology has set the stage for future studies and techniques involved in further studying the cells and increasing our knowledge of life as each day passes.

Cyclic Voltammetry Principle

Cyclic voltammetry is the most widely used technique for acquiring qualitative information about electrochemical reactions [34, 35]. The power of cyclic voltammetry results from its ability to provide considerable information on the thermodynamics and kinetics of heterogeneous electron transfer reactions [47, 48], and coupled chemical reactions [36, 37]. It also provides mathematical analysis of an electron transfer process at an electrode [41, 49, 50].
Basic Principle of Cyclic voltammetry An electron transfer process with a single step may be represented as;
O ne ⇋ R (2.1)
where O and R are oxidized and reduced form of electoractive species respectively, which either is soluble in solution or absorbed on the electrode surface and are transported by diffusion alone.
Cyclic voltammetry consists of scanning linearly the potential of a stationary working electrode (in an unstirred solution), using a triangular potential waveform. Depending on the information sought, single or multiple cycles can be used. During the potential sweep, the potentiostat measures the current resulting from the applied potential. The resulting plot of current vs. potential is termed as cyclic voltammogram.
The excitation signal in cyclic voltammetry is given in Fig. 2.1a. Initially the potential of the electrode is Ei. Then the potential is swept linearly at the rate of ν volts per second. In cyclic voltammetry reversal technique is carried out by reversing direction of scan after a certain time t =λ .The potential at any time E (t) is given by
E (t) = Ei – νt t<λ (2.2a)
E (t) = Ei – 2νλ νt t≥λ (2.2b)
Here”ν” is scan rate in V/s.
The shape of the resulting cyclic voltammogram can be qualitatively explained as follows:
When potential is increased from the region where oxidized form “O” is stable, cathodic current starts to flow as potential approaches E0 for R/O couple until a cathodic peak is reached. After traversing the potential region in which the reduction process takes place, the direction of potential sweep is reversed.
The reaction-taking place in the forward scan can be expressed as
O e- → R
During the reverse scan, R molecule (generated in the forward half cycle, and accumulated near the surface) is reoxidized back to O and anodic peak results.
R  O e-
In the forward scan as potential moves past Eo, the near-electrode concentration of O falls to zero, the mass transfer of O reaches a maximum rate, in unstirred solution, this rate then declines as the depletion of O further and further from electrode takes place. Before dropping again current passes through a maximum. Reversal of scan repeats the above sequence of events for the oxidation of electrochemically generated R that now predominates in near-electrode region.
The continuous change in the surface concentration is coupled with an expansion of the diffusion layer thickness (as expected in the quiescent solutions). The resulting current peaks thus reflect the continuous change of the concentration gradient with time, hence, the increase to the peak current corresponds to the achievement of diffusion control, while the current drop (beyond the peak) exhibits a t-1/2 dependence (independent of the applied potential). For the above reasons, the reversal current has the same shape as the forward one.
Electrochemical Cell
Electrochemical cell is a sealed vessel which is designed to prevent the entry of air. It has an inlet and outlet to allow the saturation of solution with an inert gas, N2 or Ar. Removal of O2 is usually necessary to prevent currents due to the reduction of O2 interfering with response from system under study. The standard electrochemical cell consists of three electrodes immersed in an electrolyte;
Working electrode (WE)
Reference electrode (RE)
Counter electrode (CE)
Working Electrode (WE)
The performance of the voltammetric procedure is strongly influenced by the working electrode material. Since the reaction of interest (reduction or oxidation) takes place on working electrode, it should provide high signal to noise characteristics, as well as a reproducible response. Thus, its selection depends primarily on two factors: the redox behaviour of the target analyte and the background current over the potential region required for the measurement. Other considerations include the potential window, electrical conductivity, surface reproducibility, mechanical properties, cost, availability and toxicity. A range of materials have found application as working electrodes for electroanalysis, the most popular are those involving mercury, carbon or noble metals (particularly platinum and gold).
Reference Electrode (RE)
This functional electrode has a constant potential so it can be used as reference standard against which potential of other electrode present in the cell can be measured. Commonly used reference electrodes are silver-silver chloride or the calomel electrode.
Counter of Auxiliary Electrode (CE)
It is also termed as auxiliary electrode and serves as source or sink for electrons so that current can be passed from external circuit through the cell.
The potential at WE is monitored and controlled very precisely with respect to RE via potentiostat. This may be controlled in turn via interfacing with a computer. The desired waveform is imposed on the potential at the WE by a waveform generator. The potential drop V is usually measured by the current flowing between the WE and CE across a resistor R (from which (I=V/R), the latter connected in series with the two electrodes. The resulting I/V trace, termed as a voltammogram is then either plotted out via an XY chart recorder or, where possible, retained in a computer to allow any desired data manipulation prior to hard copy being taken.
Single Electron Transfer Process Three types of single electron transfer process can be studied.
Reversible process
Irreversible process
Quasi-reversible process
Based on values of electrochemical parameters, i.e. peak potential Ep, half peak potential (Ep/2), half wave potential (E1/2), peak current (ip), anodic peak potential Epa, cathodic peak potential Epc etc, it can be ascertained whether a reaction is reversible, irreversible or quasi-reversible. Ep is the potential corresponding to peak current ip, Ep/2 is the potential corresponding to 0.5 ip, E1/2 is the potential corresponding to 0.85 ip. These electrochemical parameters can be graphically obtained from the voltammogram as shown in the Fig. 2.2.
Reversible Process
The heterogeneous transfer of electron from an electrode to a reducible species and vice versa
O ne ⇋ R
is a form of Nernstian electrode reaction with assumption that at the surface of electrode, rate of electron transfer is so rapid that a dynamic equilibrium is established and Nernstian condition holds i.e.
CO(0,t) ∕ CR(0,t) = Exp[(nF∕RT)(Ei-νt-Eo)] (2.3)
In equation (2.3), Co and CR are concentration of oxidized and reduced species at the surface of electrode as a function of time, Eo is the standard electrode potential, Ei is the initial potential and ν is the scan rate in volts per second. Under these conditions, the oxidized and reduced species involved in an electrode reaction are in equilibrium at the electrode surface and such an electrode reaction is termed as a “reversible reaction”.
Current Expression
Due to difference in concentration of electroactive species at the surface of electrode and the concentration in the bulk, diffusion controlled mass transport takes place. Fick’s second law can be applied to obtain time dependent concentration distribution in one dimension of expanding diffusion layer.
∂Ci(x, t) ∕∂t = Di∂2Ci(x, t) ∕∂x2 (2.4)
Peak current is a characteristic quantity in reversible cyclic voltammetric process. The current expression is obtained by solving Fick’s law [51].
i = nFACo*(πDoa)1/2 χ(at) (2.5)
where i = current, n = number of electrons transferred, A is the area of electrode, Co* is the bulk concentration of oxidized species, Do is the diffusion coefficient, χ (at) is the current function and a = nFν/RT
At 298K, function χ(at) and the current potential curve reaches their maximum for the reduction process at a potential which is 28.5/n mV more negative than the half wave potential i.e. at n(Ep-E1/2) = – 28.50 mV, Ï€1/2χ(at) = 0.4463 ( Table 2.1). Then the current expression for the forward potential scan becomes
(2.6)
where ip is the peak current or maximum current.
Using T=298K, Area (A) in cm2, Diffusion coefficient (Do) in cm2/s, concentration of species O (Co*) in moles dm-3 and Scan rate (ν) in volts sec-1, equation (2.6) takes the following form,
(2.7)
Equation (2.7) is called Randle’s Sevick equation [39, 40].
Diagnostic Criteria of Reversibility
Certain well-defined characteristic values can be obtained from the voltammogram, for a reversible electrochemical reaction.
Relationship between peak potential (Ep) and half wave potential (E1/2) for a reversible reaction is given by,
(2.8a)
(2.8b)
Where E1/2 is potential corresponding to i = 0.8817ip [41].
At 298 K
(2.8c)
From equations (2.8a) and (2.8b) one obtains,
(2.9a)
At 298K
(2.9b)
The peak voltage position does not alter as scan rate varies. In some cases, the precise determination of peak potential Ep is not easy because the observed CV peak is somewhat broader. So it is sometimes more convenient to report the potential at i = 0.5ip called half peak potential, which can be used for E1/2 determination [52].
(2.10a)
At 298 K
(2.10b)
(2.10c)
From equations (2.8a) and (2.10a) we obtain,
(2.11a)
At 298K
(2.11b)
The diagnostic criterion of single electron transfer reversible reaction is often sufficient to get qualitative as well as quantitative information about the thermodynamic and kinetic parameters of the system.

For a reversible system, should be independent of the scan rate, however, it is found that generally increases with . This is due to presence of finite solution resistance between the reference and the working electrode.
Irreversible Process
For a totally irreversible process, reverse reaction of the electrode process does not occur. Actually for this type of reaction the charge transfer rate constant is quite small, i.e. ksh ï‚£ 10-5cm sec-1, hence charge transfer is extremely low and current is mainly controlled by the rate of charge transfer reaction. Nernst equation is not applicable for such type of reaction.
The process can be best described by the following reaction
O ne  R
Delahay [51] and later on Mastuda, Ayabe [48], and Reinmuth [53] described the stationary electrode voltammetric curves of the irreversible process.
Irreversibility can be diagnosed by three major criteria.
A shift in peak potential occurs as the scan rate varies.
Half peak width for an irreversible process is given by
(2.12)
Here α is transfer coefficient and na is the number of electrons involved in rate determining step of charge transfer process.
At 298K
(2.13)
Current expression is given as,
i = nFACo*(πDob)1/2 χ(bt) (2.14)
The function χ(bt) goes through a maximum at π1/2χ(bt) = 0.4958.(Table 2.2).
Introduction of this value in equation (2.14) yields the expression (2.15) for the peak current.

A plot of ln ip vs. (Ep-Eo) for different scan rates would be a straight line with a slope proportional to -naF and an intercept proportional to ks,h.
Quasi-reversible Process
Quasi-reversible process is termed as a process which shows intermediate behaviour between reversible and irreversible processes. Both charge transfer and mass transfer control current of the reaction. For quasi-reversible process value of standard heterogeneous electron transfer rate constant, ks,h lies between 10-1 to 10-5 cm sec-1[42]. Cyclic voltammogram for quasi-reversible process is shown in Fig. 2.3.
An expression relating the current to potential dependent charge transfer rate was first provided by Matsuda and Ayabe [48].
(2.17)
where, ksh is the heterogeneous electron transfer rate constant at standard potential Eo of redox system,is the transfer coefficient and  = 1- .
In this case, the shape of the peak and the various peak parameters are functions of  and the dimensionless parameter , defined as [54]
(2.18)
For quasi-reversible process current value is expressed as a function of.
(2.19)
where is expressed as
(2.20)
is shown in Fig. 2.4. It is observed that when  > 10, the behavior approaches that of a reversible system.
It is observed that for a quasi-reversible reaction, ip is not proportional to 1/2. For half peak potential we have
at 298K (2.21)
This implies,
These parameters attain limiting values characteristic of reversible or totally irreversible processes as  varies. For  >10, (,) = 2.2 which gives Ep-Ep/2 = 56.5mV (value characteristic of a reversible wave). For < 10-2,  = 0.5, (,) =3.7, which yields totally irreversible characteristics. Thus a system may show Nernstian, quasi-reversible, or totally irreversible behaviour depending on , or experimentally on the scan rate employed. At small υ (or long times), systems may yield reversible waves, while at large (or short times), irreversible behaviour is observed [54].
Variation of Δ with Λ and α is shown in Fig. 2.5.
For three types of electrode processes Matsuda and Ayabe [48] suggested following zone boundaries.
a) Reversible (Nernstian)
Λ15; ksh  0.3 υ1/2cm s-1
b) Quasi-Reversible
15 Λ  10-2 (1 α); 0.3 υ1/2  ksh  2 10-5 υ1/2 cm s-1
c) Totally Irreversible
Λ < 10-2 (1 α); ksh < 2 10-5 υ1/2 cm s-1
Source: Bard, A.J.; Faulkner, L.R. Electrochemical Methods, Fundamentals and Applications, John Wiley, New York, 1980, pp 225.
Source: Bard, A.J.; Faulkner, L.R. Electrochemical Methods, Fundamentals and Applications, John Wiley, New York, 1980, pp 227.
Multi Electron Transfer Process
Multi-electron transfer process usually takes place in two separate steps. Two-steps mechanism, each step characterized by its own electrochemical parameters is called “EE mechanism”.
Stepwise reversible “EE mechanism” is given by following reaction,
A n1e ⇋ B (E10) (2.22a)
B n2e ⇋ C (E20) (2.22b)
where, A and B are electroactive species and n1 and n2 are the number of electrons involved in successive steps. If A and B react at sufficiently separated potentials with A more easily reducible than B, the voltammogram for overall reduction of A to C consists of two separated waves. The first wave corresponds to the reduction of A to B with n1 electrons and in this potential range the substance B diffuses into the solution. As potential is scanned towards more cathodic values, a second wave appears which is made up of two superimposed parts. The current related to substance A, which is still diffusing toward electrode increases since this species now is reduced directly to substance C by (n1 n2) electrons. In addition, substance B, which was the product of the first wave, can be reduced in this potential region and a portion of this material diffuses back towards the electrode and reacts.
Each heterogeneous electron transfer step is associated with its own electrochemical parameters i.e. ks,hi and αi, where i =1, 2 for the 1st and 2nd electron transfer respectively.
Based on the value of Eo, we come across three different types of cases [50] as shown in the Fig. 2.6.
Types of Two Electron Transfer Reactions [50] Case 1: Separate Peaks
When Eo  -150mV the EE mechanism is termed as “disproportionate mechanism [55]. Cyclic voltammogram consists of two typical one-electron reduction waves. The heterogeneous electron transfer reaction may simultaneously be accompanied by homogenous electron transfer reactions, which in multi-electron system leads to
disproportionation. Each disproportionation reaction can be described as,
2R1 ⇋ O R2 (2.23)
The equilibrium constant K (disproportionation constant) is given by
(2.24)
It can be derived from the difference between the standard potentials using (2.25)
Case 2: < 100mV —-Peaks Overlapped
In this case, the individual waves merge into one broad distorted wave whose peak height and shape are no longer characteristics of a reversible wave. The wave is broadened similar to an irreversible wave, but can be distinguished from the irreversible voltammogram, in that the distorted wave does not shift on the potential axis as a function of the scan rate.
Case 3: = 0mV Single peak
In this case, in cyclic voltammogram, only a single wave would appear with peak current intermediate between those of a single step one electron and two electron transfer reactions and Ep-Ep/2 = 21 mV.
Case 4: E1o < E2o—-2nd Reduction is Easy than 1st one
If the energy required for the first second electron transfer is less than that for the first, one wave is observed having peak height equal to 23/2 times that of a single electron transfer process. In this case, Ep – E1/2 = 14.25 mV. The effective E0 for the composite two electron wave is given by [50].
Source: Polcyn, D.S.; Shain, I. J. Anal. Chem. 1966, 38, 370.
Cyclic Voltammetric Methods for the Determination of Heterogeneous Electron Transfer Rate Constant Cyclic voltammetry provides a systematic approach to solution of diffusion problems and determination of different kinetic parameters including ks,h. Various methods are reported in literature to determine heterogeneous rate constants. Nicholson [41, 42], Gileadi [56] and Kochi [37] developed different equations to calculate heterogeneous electron transfer rate constants.
Nicholson’s Method [41, 42]
Nicholson derived an expression for determination of heterogeneous electron transfer rate constant ksh. This method is based on correlation between and ks,h through a dimensionless parameter by following equation,
(2.26)
where is scan rate.
for different values of ΔEp can be obtained from the Table 2.3. Hence, if ΔEp (Epa-Epc) is determined from the voltammogram, can be known from Table 2.3. From the knowledge of, , ksh can be calculated using equation (2.27).
If D o= DR then γ=1
(2.27)
This method is applied for voltammograms having peak separation in the range of 57mV to 250mV, and between this range, the electrode process progresses from reversible to irreversible. With increasing scan rate, the peak separation and hence ψ decreases.
It can be seen from the Table 2.3, that for reversible reactions i.e. for the current voltage curves and is independent of . For totally irreversible reaction i.e. for the back reaction becomes unimportant, anodic peak and is not observed. For quasi-reaction i.e. for 0. 001<<7, the form of current curves and depends upon .
Separation of cathodic and anodic peak potential as a function of the kinetic parameter  in the cyclic voltammogram at room temperature.
Kochi’s Method
Kochi and Klinger [37] formulated another correlation between the rate constant for heterogeneous electron transfer and peak separation.
The expression for ksh given by Kochi was
(2.28)
The standard rate constant ksh can be calculated from the difference of peak potentials and the sweep rates directly. This equation applies only to sweep rates which are large enough to induce electrode irreversibility. The relation derived by Kochi is based on following expressions derived by Nicholson and Shain [41].
(2.29a)
(2.29b)
where β = 1-α , and υ is the scan rate.
Equations (2.29a) and (2.29b) yield
(2.30)
This expression is used for the determination of the transfer coefficient. Assuming that (for reversible reaction).
We have,
(2.31)
Gileadi’s Method
Gileadi [56] formulated a more sophisticated method for the determination of heterogeneous electron transfer rate constant, ks,h, using the idea of critical scan rate, c. This method can be used in the case where anodic peak is not observed.
When reversible heterogeneous electron transfer process is studied at increasing scan rates, peak potential values also vary and process progresses towards irreversible. If are plotted against the logarithm of scan rates, a straight line at low scan rates and ascending curve at higher scan rate is obtained. Extrapolation of both curves intersects them at a point known as “toe”. This “toe” corresponds to the logarithm of critical scan rate, c. as shown in Fig. 2.7. Hence critical scan rate can be calculated experimentally.
ks,h can be calculated as,
(2.32)
where υc is the critical scan rate, α is a dimensionless parameter, called transfer coefficient and Do is the diffusion coefficient.
Coupled Chemical Reactions Although charge transfer processes are an important part of entire spectrum of chemical reactions, they seldom occur as isolated elementary steps. Electron transfer reactions coupled with new bond formation or bond breaking steps are very frequent. The occurrence of such chemical reactions, which directly affect the available surface concentration of the electroactive species, is common to redox processes of many important organic and inorganic compounds. Changes in the shape of the cyclic voltammogram resulting from the chemical competition for the electrochemical reactant or product, can be extremely useful for elucidating the reaction pathways and for providing reliable chemical information about reactive intermediates [35].
It is convenient to classify the different possible reaction schemes in which homogeneous reactions are associated with the heterogeneous electrons transfer steps by using letters to signify the nature of the step. E represents an electron transfer at the electrode surface, and C represents a homogenous chemical reaction. While O and R indicate oxidized and reduced forms of the electroactive species, other non electroactive species which result from the coupled chemical complication are indicated by W, Y, Z, etc [57]. The order of C with respect to E then follows the chronological order in which the two events occur [58]. So according to sequence of step, the systems are classified as EC, ECE, CE etc. These reactions are further classified on basis of reversibility. For example, subclasses of EC reactions can be distinguished depending on whether the reactions are reversible (r), quasi-reversible (q), or irreversible (i), for example Er Cr, ErCi, EqCi, etc.
Two Steps Coupled Chemical Reactions
In two steps reactions, a variety of possibilities exist, which include chemical reactions following or preceding a reversible or an irreversible electron transfer [59, 60, 61, 62]. The chemical reactions themselves may be reversible or irreversible.
a) Preceding Chemical Reactions (CE)
In a preceding chemical reaction, the species O is the product resulting from a chemical reaction. Such a reaction influences the amount of O to be reduced so forward peak is perturbed. For a preceding chemical reaction, two mechanisms are possible, depending on whether the electron transfer is reversible CrEr or irreversible CrEi [58].
Reversible Electrode Process Preceded by a Reversible Chemical Reaction (CrEr Reaction)
The process in which a homogeneous chemical reaction precedes a reversible electron transfer is schematized as follows:
(2.33)
where Y represents the non electroactive species and O and R are the electroactive congeners.
Since the supply of electroactive species O results from the chemical reaction, it is important to know that how much of O is formed during the time scale of cyclic voltammogram. In this connection, it must be noted that the time scale of voltammetry is measured by the parameter
a = nFÏ…/RT for a reversible process
and b = αnaFυ/RT for a quasi reversible or an irreversible process
It means that the time scale of cyclic voltammetry is a function of the scan rate, in the sense that higher the scan rate, the higher is the competition of the voltammetric intervention with respect to the rate of chemical complication.
The limit at which the chemical complication can proceed is governed either by the equilibrium constant K or the kinetics of the homogeneous reaction (l = kf kr). In this regard, it is convenient to distinguish three limiting cases depending on the rate of chemical complication [41].
Slow preceding chemical reaction (kf kr < 20) most of O will already be present in solution, the response is apparently not disturbed by the latter, i.e. it appears as a simple reversible electron transfer.
When K is small, the small electron transfer again appears as a simple reversible process except that the peak current will be smaller than is expected on the basis of quantity of Y in the solution. This results because the concentration of the electroactive species CO, being determined by the equilibrium of the preceding reaction is equal to a fraction of species Y placed in the solution.
where C* = CO (x,0) CY(x,0)
Fast preceding chemical reaction (kf kr >> nFÏ…/RT) When K is large, once again the response appears as a simple reversible electron transfer, but the measured standard potential Eo/* is shifted toward more negative values compared to the standard potential Eo/ of the couple O/ R by a factor of .
When K is small, because of the fast continuous maintaining of the small equilibrium amount of O, the complete depletion of O at the electrode surface will never be reached, so that the forward profile no longer maintains the peak shape form, rather assumes a sigmoidal S-shaped curve, the height of which remains constant at all scan rates.
Intermediate preceding chemical reaction (kf kr = nFÏ…/RT) In this case, the kinetics can be studied using the ratio between the kinetic and the diffusive currents according to the relationship
(2.34)

Irreversible Electrode Process Preceded by a Reversible Chemical Reaction (CrEi Reaction)
This process is schematizes as.
(2.35)
In this case, not only the thermodynamic K (kf / kr) and kinetic (kf kr) parameters of preceding chemical reaction but also the kinetic parameters of the electron transfer (α, k0) play a role. Obviously the lack of reverse peak is immediately apparent, due to the irreversibility of the charge transfer. The curves are also more drawn out because of the electron transfer coefficient, α.
Slow preceding chemical reaction (kf kr << nFÏ…/RT)
In this case, the process appears as a simple irreversible electron transfer. The peak height of the process depends on the equilibrium constant because, as mentioned in the previous case, the concentration of the active species CO is a fraction of the amount C* put in the solution:
Fast preceding chemical reaction (kf kr >> nFÏ…/RT)
If instead the reaction kinetics is fast, there are two possibilities:
If K is large, again the response appears as if the preceding chemical reaction would be absent. However, the peak potential is shifted towards more negative values than those that would be recorded in the absence of the chemical complication by a factor equal to .
If K is small, as in the preceding case, an easily recognizable S-like curve voltammogram is obtained having a limiting current independent from the scan rate
(2.36)
Intermediate preceding chemical reaction (kf kr = nFÏ…/RT)
Here again, the kinetics can be studied using the ratio between the kinetic and diffusive currents according to the relationship
(2.37)

b) Following Chemical Reactions (EC) The process in which the primary product of an electron transfer becomes involved in a chemical reaction is indicated by EC mechanism. It can be represented by
O ne ⇋ R
R ⇋ Z (2.38)
where O and R are the electroactive congeners and Z represents the non electroactive species.
Several situations are possible depending on the extent of electrochemical reversibility of the electron transfer and on the reversibility or irreversibility of the chemical reaction following the electron transfer.
As a general criterion, in cyclic voltammetry, the presence of a following reaction has little influence on the forward peak, whereas it has a considerable effect on the reverse peak.
Reversible Electrode Process Followed by a Reversible Chemical Reaction (ErCr Reaction) ErCr mechanism can be written as
(2.39)
Once again the voltammetric response will differ to a greater or lesser extent with respect to a simple electron transfer depending on the values of either the equilibrium constant, K, or the kinetics of the chemical complication (kf kr) [58].
Analogously to that discussed for preceding equilibrium reactions, three limiting cases can be distinguished.
Slow following chemical reaction (kf kr << nFÏ…/RT)
If the rate of chemical reaction is low, it has a little effect on the process, thus reducing it a simple reversible electron transfer.
Fast following chemical reaction (kf kr >> nFÏ…/RT)
If the rate of the chemical complication is high, the system will always be in equilibrium and the voltammogram will apparently look like a non complicated reversible electron transfer. However, as a consequence of the continual partial removal of the species R from the electrode surface, the reduction occurs at potential values less negative than that of a simple electron transfer by an amount of .
Due to the fast kinetics of the chemical complication, the potential will remain at this value regardless of the scan rate.
Intermediate following chemical reaction (kf kr=nFÏ…/RT)
If the kinetics of the chemical reaction are intermediate with the scan rate the response gradually shifts from previous value for a fast chemical reaction [which was more anodic by w.r.t. to value of the couple O/R] towards the Eo/ value assuming more and more the values predicted by the relationship
(2.40)
In other words, the response (which for the fast kinetics is more anodic compared to E0/) due to the competitive effects of the potential scan rate moves towards more cathodic values by 30/n (mV) for every ten fold increase in the scan rate. However, it is noted that at the same time, the reversible peak tends to disappear, in that on increasing the scan rate, the species Z does not have time to restore R. This is demonstrated by the current ratio which is about one at low scan rates, but it tends to zero at high scan rates.

Reversible Electrode Process Followed by an Irreversible Chemical R

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