Analytical method development for electrocatalysis
By: Ziwei ZHANG Z5014489
Supervisor: Kuang-Hsu Wu
SCHOOL OF CHEMICAL ENGINEERING
Certificate of Originality
I declare that this assessment item is my own work, except where acknowledged, and has not been submitted for academic credit elsewhere, and acknowledge that the assessor of this item may, for the purpose of assessing this item: Reproduce this assessment item and provide a copy to another member of the University; and/or, Communicate a copy of this assessment item to a plagiarism checking service (which may then retain a copy of the assessment item on its database for the purpose of future plagiarism checking). I certify that I have read and understood the University Rules in respect of Student Academic Misconduct.
Signature ________________ Date _______________
The electrochemical process are made up by a variety of heterogeneous chemical reactions which usually involve the electron transfer occurs between the solid surface and an adjacent solution phase. Apparently, during the continuous reaction, it requires the supply of reactant to the surface of the electrode and the removal of product. The rotating disk electrode and rotating ring-disk electrode techniques are widely used in investigating reaction mechanisms related to the redox chemistry. The equation derived from those techniques having some limitation and only applicable under the assumptions, which is not benefit to analyse the nature of the electrochemical reactions and the process of electrode transfer. As the fact that the existing theory and calculation is not considered the electron layer structures. This report provide an overview of RDE and RRDE techniques, and discuss the equations governing from the techniques. Following by the discuss of the limitation of the equations. Finally the electron double layer will be introduced, which include the develop of the double layer model . Here the report is aim to find the problem for existing theories and prove there is inner-sphere reaction happened on he IHP, then find the best performance electrocatalyst. The detailed explanation will given in the research plan.
TOC o “1-3” h z u 1.Introduction PAGEREF _Toc514902338 h 42. Rotating disk electrode method: PAGEREF _Toc514902339 h 53. Rotating ring-disk electrode method PAGEREF _Toc514902340 h 66.Electrical double layer development: PAGEREF _Toc514902341 h 74.Analyzation of oxygen reduction reaction electrokinetic PAGEREF _Toc514902342 h 105. Equations for RDE and RRDE technique PAGEREF _Toc514902343 h 127. Potentialities for equation improvement: PAGEREF _Toc514902344 h 178. Equipement preparation : PAGEREF _Toc514902345 h 176. Research Plan PAGEREF _Toc514902346 h 187. Conclusion PAGEREF _Toc514902347 h 208. Reference PAGEREF _Toc514902348 h 20
It has been fifty years since the rotating ring-disk electrode developed in Russia during the cold war. The system became a widely used electroanalytical tool for electrochemistry reaction. The rotating disk electrodes first developed by Alexander Naumovich Frumkin who was a leading electrochemist at Moscow State University. After that, one of Frumkin’s colleagues called Benjamin Levich began to explore the role of the solution convection on the rate of chemical reaction, and ten years later, he published the book called “Physicochemical Hydrodynamics” in 1952. Since in the age of technology underdevelopment, the commercial RDE equipment is unavailable, scientist made the electrode rotators using motors and a fishing line connected pully to control the rotation rate.Due to the absence of the metal, they used the red powder which may contain iron oxide particles to be the rotating disk electrode. By the excellent mass transport control provided by RDE more scientist applied this method to make advance electrochemical measurement. In 1957, Levich and Koutecký developed the equation which considered both mass transport to the surface and the rate of the electrochemical half-reaction. CITATION Fra18 l 3081 (Dalton, 2018) The equation is known as Koutecký levich equation.
We Will Write a Custom Essay Specifically
For You For Only $13.90/page!
Frumkin found that the rotating electrode still have more research value, and he was interested in observing the generation of short-lived intermediator during the reaction for electrochemistry. In 1958 Frumkin improved the RDE system, to rotating ring-disk electrode. The separate concentric ring electrode is added around the rotating disk electrode to allow the ring to collect any electrochemical intermediates generated from the disk. The first investigation is used the aqueous oxygen reduction reaction (ORR). Frumkin and Levich get the approximate equation of Nmax under several simplifying assumption. The research team admitted the error for result from the collection efficiency approximation equation would be at least five percentage, but the error was later shown to be significantly larger than expected.
Nowadays the Koutecký levich analysis is an effective method by modifying mass transport effects to extract the electrokinetic information. However, during the K-L analysis derivation there are several assumption made, which resulted the inaccuracy in calculation.
2. Rotating disk electrode method:For analysing the electrochemical reaction, the separation for electrochemical processes occurring on the electrode surface from the processes that affect the transport of the reactant and the reaction products are necessary. The quantitative description of mass transfer stage is allowed by electrochemical measurement in agitated solutions and provide correction for analysing of the kinetic of the heterogeneous convection reaction. However in the experiment it only possible to accurate describe the influence of mass transfer and the movement of the solution near the electrode in some particular cases CITATION DuC l 3081 (Du, 2014).
The convective-diffusion equation is solved under the steady state condition. The major advantage of the RDE system is the construction of the system is simple and the operation is simplicity.
The main structure of RDE is shown in Fig.1. The conductive disk electrode is imbedded in a non-conductive polymer material, and the polymer rod is directly attached by a flexible rotating shaft to an electric motor which is designed to rotate at a certain angular velocity. The brush contact created the electric connection to the electrode, and it decided the noise level observed in the current at the rotating disk electrode. In practical, the carbon-silver materials are normally used to reduce the noise of the current. The methodological feature and the simplicity operation made the RDE system become one of the main techniques applied in the experiment of electrochemistry. The high accuracy and its possibility of conducting the experiment under steady state condition make the RDE system one of the most feasible method for investigating the kinetics and mechanisms of electrode processes. CITATION Lee08 l 3081 (Lee, 2008)3. Rotating ring-disk electrode methodDue to the electrode reaction products are continuously swept away from the surface of the disk, the RDE technique is not applicable to the reversal technique. The rotating ring- disk electrode is designed to obtain more information related to the reversal technique. The reaction happened on the disk electrode can be obtained by measuring the current at ring electrode. Theoretically, in the RRDE system, the current-potential characteristics of the disc are independent of the performance of the ring. Once the disc current is found to change with the current or the potential of the ring, the system may be defective or the ring and disk are coupled undesirably. Comparing to the single working electrode, the experiment result obtained by RRDE system will be more reliable. CITATION Lee08 l 3081 (Lee, 2008)The typical structure of the RRDE is shown in the Fig.2, the RRDE system is made up by three main element, which are the central disk electrode with inner radius r1, a ring electrode with inner radius r2 and outer radius of r3 and a thin insulating gap of thickness (r2-r1) to separate the ring and disk electrode. The working electrode and spacer surface are lie on one plane, and forming a planner surface. The whole system is in rotating motion about the axis, and each electrode is an independent unit, so that there are two morintor record the potetial and current sepearatlyCITATION Jia l 3081 (Jia, 2014).
295885410978Figure 2 Rotating ring-disk electrode
Figure 2 Rotating ring-disk electrode
Figure 1 Rotating disk electrode
6.Electrical double layer development:Helmholtz
The theory of the existence of the double layer at the surface of the metal which in contact with the electrolyte is first come up with Helmholtz in 1879. Helmholtz was first to realized that charged electrodes immersed in electrolytic solutions repel the co-ions of the charge while attracting counterions to their surfaces CITATION Kim l 3081 (Kim, n.d.).This concept is a simplest approximation that the surface charge is neutralized by opposite sign counterions placed at an increment of d away from the surface. CITATION Nen13 l 3081 (Markovic, 2013)The structure of the Helmholtz double layer is present in Fig.3(a). The double layer model usually contain two plane: the inner Helmholtz plane(IHP) and outer Helmholtz plane(OHP) the two layer has opposite charge and form at the interface between the electrode and electrolyte. CITATION che l 3081 (chemlabinkaist, n.d.)The electric potential is also illustrated in the figure, under this theory the surface charge potential is constant throughout the metallic phase, and linearly dissipated from the surface to the contortions satisfying the charge.
This earliest model described the interface of the electrode layer but it doesn’t consider diffusion of the ions in the solution, the possibility of adsorption onto the surface and the interaction between solvent dipole moments and the electrode.
In 1910 and 1913, Gouy and Chapman both observed that capacitance was not a constant and it depended on the applied potential. Gouy suggested that the counter ions are not rigidly held, but tend to diffuse into the liquid phase until the counter potential set up by this departure restricts this tendency. CITATION Luc95 l 3081 (LucaRighetto, 1995)The kinetic energy of the counter ions will, in part, affect the thickness of the resulting diffuse double layer. Gouy and Chapman developed the theories by adding the diffuse layer, the detail structure is shown in Fig 3(b). The change in concentration of the counter ions near a charge surface follows the Boltzman distribution CITATION Sto02 l 3081 (Stojek, 2002).
The concentration of the oppositely charged ions decreasing with distance from the surface, this is called the diffuse double layer.
Although this theory considered the ion diffusion, it is still not entirely accurate. In the experiment, the double layer thickness is generally found to be greater than calculated valve. This may result by the Boltzman distribution cause this equation made an assumption on the molar concentration, the approximation is applicable for bulk solution but not to be true near a charge surface.
The Gouy-Chapman model is found to failed for highly charged double layers. The reason for the failure is that it assume the ions behaves as point charges, which it not true in reality, and it assumes that there is no physical limits for the ions in their approach to the surface. In 1924, Stern suggested to combine the Helmholtz model with the Gouy-Chapman model, and given an internal Stern layer in this layer he assumed that it is possible that some of the ions are specifically absorbed by the surface in the plane, the detailed structure is shown in Fig.3(c). In his theory, the ions has finite size, so that cannot approach to the surface closer than few nmCITATION Sab l 3081 (SabineGoldberg, 2005).
Thus, the double layer is formed in order to neutralize the charged surface and, in turn, causes an electrokinetic potential between the surface and any point in the mass of the suspending liquid. This voltage difference is on the order of millivolts and is referred to as the surface potential. The magnitude of the surface potential is related to the surface charge and the thickness of the double layer. the potential drops off roughly linearly in the Stern layer and then exponentially through the diffuse layer, approaching zero at the imaginary boundary of the double layer. The potential curve is useful because it indicates the strength of the electrical force between particles and the distance at which this force comes into play.
Figure 3 (a)Structure of Helmholtz model (b) Structure of Gouy-chapman model (c) Structure of Stern model of the electrical double-layer
More recently in 1940, Grahame modified Stern model, cause he realised that the full interpretation of the thermodynamic data required two planes of closest approach. one for specifically adsorbed ions and one for non-specifically adsorbed ions, and a diffuse layer region extending to the bulk electrolyte phase.
The model proposed that some ionic or uncharged species can penetrate the Stern layer, although the closest approach to the electrode is normally occupied by solvent molecules. This could occur if ions lose their solvation shell as they approach the electrode. This model proposed the existence of three regions CITATION Dim01 l 3081 (A.Sverjensky, 2001). The inner Helmholtz plane (IHP) passes through the centres of the specifically adsorbed ions. The outer Helmholtz plane (OHP) passes through the centres of solvated ions at the distance of their closest approach to the electrode. Finally the diffuse layer is the region beyond the OHP. The detail of the model is shown in Fig.4 CITATION Ple01 l 3081 (Pletcher, 2001).
Figure 4 Grahame’s model
4.Analyzation of oxygen reduction reaction electrokinetic
The rotating disk electrode and rotating ring-disk electrode are convective electrode system which widely used in investigating reaction mechanisms related to the redox chemistry. One of the application of RDE, and RRDE system is used to study the kinetics of catalytic oxygen reduction reaction which is the most complex and important process for electrochemical energy device.
The main process happened on the RRDE electrode is shown in Fig.5. The reduced species Rd left form the disk electrode will undergo one of two passes which include (1) electrochemical reaction to produce oxidized species. (2) escape from the electrode surface through desorption to form RaqCITATION Kua15 l 3081 (Kuang-Hsu Wu, 2015). Under the situation of first pass, the reduced species is first arrive at the outer Helmholtz plane and then transfer to the inner Helmholtz plane for the reaction to form the oxidized species adsorb on the surface of ring electrode. And finially the absorbed oxidized species will desorpted and diffused in solution. There is also has the potential for the reduced speices which arrived on OHP directly oxidized to the oxidized species.
Figure 5 Oxygen reduction reaction processes happens at the disk and ring electrodes of the RRDE.
Inner-and outer-sphere electron transfer reaction
The electrode reaction is differentiate into inner-sphere reaction and outer-sphere electron transfer reactions. For the outer-sphere reaction, the electrons transfer between the electrode and the ORR reaction takes place at the plane separated by at least a solvent layer from the electrode which is outer Helmholtz plane, the reaction between two species in which the original coordination spheres are maintained in the activated complex. The inner-sphere reaction, a coordinated ligand of electroactive metal complexes is bound to the electrode surface and electron transfer may take place through the ligand adsorbed on the electrode. it occur in an activated complex where the ions share a ligand CITATION Bar10 l 3081 (Bard, 2010).
The Fig.6 shows the mechanism of outer- and inner-sphere electrode reactions.
The rate constant if an inner-sphere electrode reaction is highly dependent on the electrode material, but the outer-sphere electrode reaction should be less dependent CITATION Ich13 l 3081 (Ichimura, 2013).
Figure 6 Mechanism of electrode reactions: (left) outer-sphere mechanism and (right) inner-sphere mechanism.
By using the Koutecky- Levich plot, the kinetic rate constant is easily obtained. The RDE and RRDE methods have been recognized as the commonly used techniques to analyses the catalyst’s stability and the nature of the electrochemical reactions. The methods used for studying the electrocatalysis and electrokinetic are Levich equation and Koutecky-Levich equations.
Electrocatalyst for ORR
The reason for catalytic oxygen reduction reaction is due to the slow kinetics, the electrocatalyst can improve the transmit rate of reduced space transfer from OHP to IHP.
5. Equations for RDE and RRDE techniqueDiffusion-convection layer (RDE and RRDE)
The current density of the electrode electron-transfer reaction and the reactant diffusion contribute to the current density which measured from the rotating electrode.
The simple model of the reaction is shown in the following for analyse the electron-transfer kinetics of electrochemical system CITATION Ort86 l 3081 (Orth, 1986):
O+n??-?ktkb?RWhere the O and R are stand for the oxidant and reductant, the n? represent the electron transfer number, kf and kb stand for the forward and backward reaction rates, respectively. For analysing the electrode kinetics, it will focus on such an elementary reaction so that the n? is normally 1.
During the oxidant reduction process, the relationship between the flow rate and the flow of electrolyte solution from the bottom of the electrode edge upward with a direction parallel to the electrode surface is shown in the Fig.7.
Figure 7 (A) electrolyte solution flow along the electrode surface (B) the flow rate distribution near the electrode surface along the direction parallel to the electrode surface.
The Uy present the solution flow rate in cm/s. It shows that the flow rate is not uniform along the axis, the closer to the electrode surface led to the smaller flow rate. However for the y-axis, at the distance ?0 the flow rate reaches constant. The distance of ?0 is defined as the thickness of diffusion conversion. Within this diffusion-convection layer, both diffusion and convection are exist. The diffusion-convection layer thickness can be approximately calculated by the equation:
The D0 stands for the diffusion coefficient of oxidant, v means the kinetic viscosity, y is the distance at the vertical direction. From the equation it can conclude that there are linear relationship between y, Uy and the ?0.
Since the diffusion-convection current density is express in:
Coo: reactant concentration
Cos:reactant concentration at electrode surface
when the Cos reaches to zero the iDC?0will get the maximum value, and it is defined to be the diffusion-limiting current density:
By substituting the equation (3) into (1) and (2):
IDC?0=nFD023?-16y-12Uy12 Coo (5)
From the above equation, it suggested that the current density distribution at different location of the electrode surface is not constant, which is not desired for the study of reaction kinetic mechanism. However the rotating electrode can make a uniform thickness of the diffusion- convection layer over the surface of the electrode which can producing a uniform distribution of the current density CITATION Lee08 l 3081 (Lee, 2008).
Levich equation (RDE and RRDE)
The limiting current density can be express as:
Where the ? stand foe the electrode rotating rate. The equation is knowns as Levich equation.
The thickness of the diffusion-convection layer for rotating electrode will be expressed as equation:
This equation proves that for RDE the thickness of the diffusion-convection layer is not a function related to the electrode surface location, and the current density over the whole RDE surface is uniformly distributionCITATION JNi l 3081 (Nikolic, 2000).
When the electrochemical reaction is a reversible reaction, at the beginning of the reaction, the reductant is not exist in the solution where the CRo=0, the Nernst electrode potential is expressed in :
When the iDC?0=0.5 IDC?0 and substitute into the equation (8) the electrode potential will become half-wave potential and the equation(8) can be rewrite into:
By using the RDE technique, based on the current-potential curves it measured, the half-wave potential is very useful in evaluating the electrochemical reactions. However, when using the half-wave potential to evaluation the irreversible electrochemical reaction, it need to be careful CITATION Lee08 l 3081 (Lee, 2008).
Koutecky-Levich Equation( RDE and RRDE)
Normally the diffusion-convection process could not catch up the electron transfer process if the speed of the electron transfer kinetic of ORR is very fast. The oxidant’s surface concentration will soon exhausted to zero. Under this situation, by using the levich equation, the plot for IDC.0 VS ?-12 will be a straight line CITATION Lee08 l 3081 (Lee, 2008).
However, when the speed of electron transfer kinetics of ORR is much slower than the diffusion-convection process. The oxidant’s surface will only exhausted to zero when a much larger overpotential is controlled. In this case, the plot will be not be straight line, with the increasing of the ?-12 , the line will gradually fall off. The effect of a slow electron-transfer kinetic can be express as:
By substituting the equation (11) and (12) to equation (10):
This equation is named Koutecky-Levich equation.
By using this equation, the intercepts at different electrode potentials can be used to get the exchanger current density and the electron transfer coefficient. CITATION Mas14 l 3081 (Masa, 2014)Collection efficiency (RRDE)
An important parameter to indicate the amount of the disk reaction products or intermediates reaching the ring electrode is known as collection efficiency.
The reaction happened on RRDE is shown in Fig.8:
Figure 8 Reaction on RRDE
The potential controlled the disk electrode make the reaction occur on the disk electrode to produce R, a part of R which is XR will be transferred to the ring electrode. If the ring electrode is controlled at a sufficiently positive potential, the reverse reaction can happened at a limiting mass transport rate, that any R reaching the ring electrode is oxidized immediately. Sine the area of the ring electrode surface is limited, it is impossible to detect all the R coming from the disk electrode reaction. In practical, the collection efficiency for the commercially RRDE is around 20~40%, depending on the relative geometric sizes of the ring and disk electrode. Moreover the collection efficiency is strongly depend on the rotating rate of the electrode, also the thickness of the isolator ring between the ring and disk electrode will influence it.
The equation for calculating the collection efficiency is summarized by Brad and Faulkner as follow CITATION WJA65 l 3081 (ALBER, 1965):
Excepting using the above equation, the collection efficiency can also be experimentally measured using the ORR (Jia, 2014).
Limitation of the equation
The above equation are only based on the first order reaction, which is not applicable for the higher order reaction CITATION WJA651 l 3081 (ALBERY, 1965). Furthermore the reaction didn’t considered the structure of the electrode layer, due to the structure of electrical double layer, the inner layer reaction is ignored when analysing the electrokinetic. For the theoretical convenience the model neglects specific adsorption effects and assumed when the charge transfer occurs, the electroactive species is only exist in the outer Helmholtz plane CITATION Rui16 l 3081 (Zhou, 2016).
7. Potentialities for equation improvement:
As mentioned above the derivation of the equation didn’t include the inner-sphere reaction happened on the IHP. For the improvement for the equation it need to consider the kinetics for reduced species transfer from OHP to IHP, which could also prove there is inner-sphere reaction happened in the electrochemical reactions. The possibility of reduced species at OHP directly doxidized to the oxidized species.
8. Equipement preparation :Electrode material choosing:
The most important criteria for choosing electrocatalysis of ORR are activity and stability of catalyst. The activity could indicate how fast the electrochemical reaction can be speeded up by the catalyst, and the stability stand for how long the catalyst can last for catalysed the reaction before it activity decrease to a lower level for the requirement CITATION Fen14 l 3081 (Feng, 2014).
The most common metals used for the disk electrode is noble metals Pt and Au, and the glassy carbon is commonly used non-metal. The glassy carbon or the metal electrode is normally used as current collector which is coated by the catalyst layer. The Au is the best choice for RDE electrode due to the stable properties, the glassy carbon could be oxidized at high potential with a long period test. For the electrode the Pt is most common used electrode.
Working electrode preparation:
the surface of the electrode need to be smooth, before using the system, the electrode surface need to be washed by using pure acetone and DI water under the ultrasonication for at least three times. After that the electrode is ready for catalyst coating, the catalyst metal required to mixed ultrasonically with deionized water and then add some alcohol to form a well-mixed mixture. The mixture will then coated on the electrode surface, and finally left in air for dry. Normally, a small drop of diluted ionomer solution such as Nafion is pipetted on the coated layer before is use, which could avoid the falling of catalyst from the electrode surface CITATION Lee08 l 3081 (Lee, 2008)..
For the RRDE system, one thing need to pay attention is that it is very important to keep the electrode rotating in a stable speed during the measurement.
6. Research PlanAim
This project is aim to analyse the electrokinetic for the oxidant reduction reactions by using rotating disk electrode method and rotating ring-disk electrode method. Interesting the electrochemical reaction and prove that there inner-sphere reaction happened on inner Helmholtz plane. And finally upgrading the KL equation to a more comprehensive equation which can applied to the higher order reaction. The performance of catalyst with different material will also be test.
The electrochemistry is a subject that concern the interrelation of electrical and chemical effect. A large part of this field is the study of chemical reaction caused by the electric current and the production of energy by chemical reaction.
In the existing theory and calculation for electrokinetic, the model neglects specific adsorption effects, and for the theoretical convenience the model neglects specific adsorption effects and assumed when the charge transfer occurs, the electroactive species is only exist in the outer Helmholtz plane. Under those assumption, the governed equation will have limit application and errors in calculation which is adverse to the study of electron transfer for electrochemical reactions, and the electrokinetic analyses.
RDE, KL method:
The glassy carbon material of rotating disk electrode are used for the experiment. The electrode will coated by the catalyst material and immersed in 0.1 M NHPI solution. The plot of current density as a function of ?12 with the change of rotating rate at 400rpm, 900rpm, 1600rpm, 2500rpm and 3600rpm. The potential of the electrode is charged between 0 and 0.4 V, with the scanning rate of 5mV/s. The different catalysts material will be test.
The Pt-Pt material of rotating ring-disk electrode are used in this research. The inner radius of the central disk electrode, the inner and outer radius of ring electrode need to be measured before the experiment. The theoretical collection efficiency can be calculated from the equations in section 5. The carbon based catalyst is coating on the surface of the electrode. After set up the system the nitrogen is passing into the system to get rid of the oxygen. The 0.1 M NHPI is chosen as the electrolyte, the linear scanning voltammetry (LSV) is used to plot the ORR curve. The voltage is changed from 1 V to 0 V with the scanning rate of 10 mV/s the current will be record CITATION Rui161 l 3081 (Ruifeng Zhou, 2016). The different catalysts material will be test. The kinetics for kcp should be found out, and kr related parameters need to analyses. Finally, check if results follow the expectation of the analytical equations.
The result for using those two method will compared.
Since the inner-sphere reaction has never been considered in the exiting calculating theory, due to it properties. The application for RDE and RRDE for analyse the electrocatalyst and the inner-sphere reaction will become a new theory. Since the fact that the existing KL theory has limit application, the governing of new equation is necessary for more accurate calculation. The result of this research is likely to indicate the essence of electrochemical reaction and the effects of electrocatalysts.
BIBLIOGRAPHY A.Sverjensky, D., 2001. Interpretation and prediction of triple-layer model capacitances and the structure of the oxide-electrolyte-water interface, s.l.: s.n.
ALBER, W. J., 1965. Ring-Disc Electrodes Part 2.-Theoretical and Experimental Collection Efficiencies, s.l.: s.n.
ALBERY, W. J., 1965. Ring-Disc Electrodes Part 5.-First-Order Kinetic Collection Efficiencies at the Ring Electrode , s.l.: s.n.
Bard, A. J., 2010. Inner-Sphere Heterogeneous Electrode Reactions. Electrocatalysis and Photocatalysis: The Challenge, s.l.: s.n.
chemlabinkaist, n.d. Discrimination of Inner- and Outer-sphere Electrode Reactions by Cyclic Voltammetry Experiments , s.l.: s.n.
Dalton, F., 2018. Historical Origins of the Rotating Ring-Disk Electrode , s.l.: s.n.
Du, C., 2014. Rotating Disk Electrode Method, s.l.: s.n.
Feng, L., 2014. s.l.: s.n.
Ichimura, S. T. a. A., 2013. Discrimination of Inner- and Outer-Sphere Electrode Reactions by Cyclic Voltammetry Experiments, s.l.: s.n.
Jiang, R., 2000. Steady-State Potential Scan at Rotating Disk Electrode and Applications, s.l.: s.n.
Jia, Z., 2014. Rotating Ring-Disk Electrode Method, s.l.: s.n.
Kim, J. U., n.d. Electrical double layer: revisit based on boundary conditions, s.l.: s.n.
Lee, S.-J., 2008. Fundamentals of Rotating Disc and Ring–Disc Electrode Techniques and their Applications to Study of the Oxygen Reduction Mechanism at Pt/C Electrode for Fuel Cells, s.l.: s.n.
LucaRighetto, 1995. The triple layer model revised, s.l.: s.n.
Markovic, N. M., 2013. Interfacing electrochemistry , s.l.: s.n.
Masa, J., 2014. Koutecky–Levich analysis applied to nanoparticle modified rotating disk electrodes: Electrocatalysis or misinterpretation?, s.l.: s.n.
Nikolic, J., 2000. Theoretical Concepts and Applications of a Rotating Disk Electrode, s.l.: s.n.
Orth, R. J., 1986. Application of the Rotating Ring-Disk Electrode in Determining the Second-Order Rate Constant for the Reaction Between Cu(I) and Fe(lll) in 1.0 mol/dm 3 HCI, s.l.: s.n.
Pletcher, D., 2001. Instrumental Methods in Electrochemistry, s.l.: s.n.
SabineGoldberg, 2005. Inconsistency in the triple layer model description of ionic strength dependent boron adsorption, s.l.: s.n.
Stojek, Z., 2002. The Electrical Double Layer and Its Structure, s.l.: s.n.
Wu, K.-H., 2015. An Extension to the Analytical Evaluation of the Oxygen Reduction Reaction Based On the Electrokinetics On aRotating Ring–Disk Electrode , s.l.: s.n.
Zhou, R., 2016. Determination of the Electron Transfer Number for the Oxygen Reduction Reaction: From Theory to Experiment, s.l.: s.n.