Advanced Research Methods in Materials Engineering (PDF)

„ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Advanced research methods in the engineering of materials Lecture 7 Basic polarization techniques for testing the corrosion resistance of materials....

„ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Advanced research methods in the engineering of materials Lecture 7 Basic polarization techniques for testing the corrosion resistance of materials. 1 Wrocław University of Science and Technology, Wrocław, 2020  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Corrosion of metals and alloys in aqueous solution or in any other ionically conducting medium takes place by an electrochemical mechanism. The electrochemical corrosion reaction requires four elements: 1. anode, 2. cathode, 3. metallic conductor, 4. electrolytic conductor. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 2 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 2  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Oxidation reaction. The metal is oxidized (loss of electrons) at the anode. This process is called corrosion. The anodic (corrosion) reaction can be written as: The metallic ions, or other reactive species or ions are carried from the anode to the cathode by the ionically-conducting electrolyte. Electrolytes are mostly liquids, but they may also be solids. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 3 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 3  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Reduction reaction. There are two types of ions: anions and cations. Anions are negatively charged and they move towards the anode. Cations are positively charged and they move towards the cathode. The electrolyte may contain several species that could undergo reduction. The most commonly occurring reduction reactions at the cathode are: hydrogen ion reduction: oxygen reduction: The electrons left by the metal ions at the anode site are carried to the cathodic site by the metallic conductor. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 4 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 4  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. In order for electrochemical corrosion to take place all four processes should occur simultaneously. Absence of any one of the four elements prevents corrosion from taking place. In the presence of all four elements a balance is established, so that the rate of anodic reaction (oxidation) is equal to that of cathodic reaction (reduction). Electrochemical polarization measurements are used to determine the rate of anodic or cathodic reactions individually or collectively. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 5 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 5  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Gibb’s free energy change (ΔG). If ΔG (Gibb’s free energy change) is negative as a result of a process or reaction then the result of the process or product of the reaction is one of lower energy than the starting material. Therefore the product is more stable and, hence, the process is energetically possible. If the free-energy change is positive then the reaction does not take place spontaneously. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 6 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 6  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. From ΔG to potential. The free energy change related to the potential is shown in equation: where: E is the potential, n is the number of electrons transferred and F is the Faraday constant. Therefore the potential is a measure of the reaction (corrosion) tendency. Positive potential (E) corresponds to negative ΔG and hence to spontaneous reaction. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 7 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 7  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Potential. The arrangement of metals based on standard potentials is known as the: 1. Standard Oxidation-Reduction (redox) Potential or 2. Standard Equilibrium Reduction Potential or 3. Standard Potential or 4. Electro-Motive Force (EMF) Series or 5. Standard Reversible Potential. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 8 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 8  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Standard potential. The standard potential is the potential of a metal in contact with its own ions at a concentration equal to unit activity. In this series the potential is presented as reduction reaction. The same series can be developed based on oxidation reaction, in which case the values will be the same but the ‘signs’ will be reversed. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 9 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 9  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Potential vs. corrosion tendency. Let us consider: What happens when copper and zinc pieces each immersed separately into their own ions are electrically connected (commonly called short- circuited)? The standard redox potentials can be used to understand the corrosion tendency of metals. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 10 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 10  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Nernst equation. To determine the potential of a metal in which the reactants are not at unit activity, Nernst derived an equation : where: E is the potential, Eo is the standard redox potential, R is the gas constant, T is the absolute temperature, n is the number of electrons transferred, F is the Faraday constant and aoxid and ared are the activities (concentrations) of oxidized and reduced species. Potential becomes more and more positive as the amount of oxidized species increases. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 11 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 11  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Mixed potential. In order for corrosion to occur no metals need to be in contact with their own ions. In practice both anode and cathode can exist on the same metal sample, which can also act as metallic conductor. When a piece of metal is immersed into an electrolyte and all four elements are established, a potential is developed and corrosion starts to occur. This potential is called corrosion potential or mixed potential (different from ‘standard equilibrium potential’). Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 12 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 12  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Mixed potential. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 13 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 13  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Potential and reference electrode. The measurement of the corrosion potential is the fundamental primary step for understanding the corrosion tendency of metals or alloys in an electrolyte. However, the potential of a single electrode cannot be directly measured; only the difference between potentials of two electrodes can be measured. For this reason the corrosion potential of an electrode is measured using another electrode called a ‘reference electrode’. Therefore the corrosion potential should always be reported with respect to a particular reference electrode. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 14 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 14  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Potential and reference electrode. Some commonly used standard reference electrodes are: 1. the saturated calomel electrode (SCE); 2. the silver/silver chloride (Ag|AgCl) electrode and 3. the copper/copper sulphate (CCS) electrode. The corrosion potential measured against one reference electrode can be converted against another reference electrode. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 15 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 15  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Potential and reference electrode. With most modern potentiostats, all potentials are specified or reported as the potential of the working electrode with respect to either the reference electrode or the open-circuit potential. The former is always labeled as “vs. Eref” and the latter as “vs. Eoc”. The equations to convert from one form of potential to the other are: One sign convention is used. The more positive a potential, the more anodic it is. More anodic potentials accelerate oxidation at the Working Electrode. Conversely, a negative potential accelerates reduction at the Working Electrode. 16 https://www.gamry.com/ 16  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Potential and reference electrode. IMPORTANT NOTE! There has been some confusion in the corrosion literature on the use of term ‘open-circuit potential’. Some references use the term ‘open-circuit potential’ to represent ‘corrosion potential’ or others to represent ‘equilibrium potential’. For discussion... Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 17 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 17  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Potential and reference electrode. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 18 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 18  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Potential and current. If a metal (e.g., zinc) is in equilibrium with its ions at unity it would be at the standard redox potential, and the redox potential of the zinc (EZnn+|Zn) at other concentrations of its ions can be calculated from Nernst Equation. The rate of exchange of electrons under this condition is known as exchange current density (iZnn+|Zn). Similarly if we consider the hydrogen electrode in equilibrium with H+ ions, it would be at the redox potential (EH+|H) and a corresponding exchange current density (iH+|H). ??? What will happen if we combine these two systems ??? Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 19 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 19  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Mixed potential. The system moves If the zinc is immersed from reversible into a solution containing potentials of zinc and hydrogen H+ ions (e.g., hydrochloric towards the acid), the potential of the corrosion potential. metal will not be at the redox potential of either the zinc or the hydrogen. The potential will stabilize at the mixed or corrosion potential (Ecorr). Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 20 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 20  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Mixed potential. At Ecorr the rate of zinc The system moves dissolution is equal to the from reversible potentials of zinc rate of hydrogen and hydrogen evolution and charge towards the corrosion potential. conservation is maintained. The current at Ecorr is known as Icorr, which is the rate at which the zinc will corrode when it is immersed in hydrochloric acid. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 21 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 21  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical nature of corrosion. Corrosion current and potential. The relationship between potential for activation controlled processes and current is given by equation: where: E is the potential, η is commonly known as the overpotential, β is a constant known as the Tafel constant, I is the rate of oxidation or reduction in terms of current. Determination of Icorr, Ecorr, and I–E relationship is the underlying fundamental principle in calculating the corrosion rate by electrochemical polarization techniques. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 22 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 22  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” The basics of polarization techniques. Tafel equation. The model we use for the corrosion process assumes that the rates of both the anodic and cathodic processes are controlled by the kinetics of the electron-transfer reaction at the metal surface. This is generally the case for corrosion reactions. An electrochemical reaction under kinetic control obeys the Tafel equation: 23 https://www.gamry.com/ 23  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” The basics of polarization techniques. Tafel equation. where: I is the current resulting from the reaction I0 is a reaction-dependent constant called the exchange current E is the electrode potential E0 is the equilibrium potential (constant for a given reaction) β is the reaction’s Tafel constant (constant for a given reaction, with units of V/decade). The Tafel equation describes the behavior of one isolated reaction. In a corrosion system, we have two opposing reactions: anodic and cathodic. 24 https://www.gamry.com/ 24  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” The basics of polarization techniques. Types of polarization control. If the potential of an electrode is controlled and the response of current is monitored then the method is called potentiostatic. If the potential of the electrode is varied at a constant rate and the response of the current is continuously monitored then the method is called potentiodynamic. On the other hand, if the current of an electrode is controlled and the response of the potential is monitored then the method is called galvanostatic. If the current of the electrode is varied at a constant rate and the response of the potential is continuously recorded then the method is called galvanodynamic. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 25 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 25  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” The basics of polarization techniques. Types of polarization control. Most electrochemical measurements are conducted by controlling the potential (potentiostatic or potentiodynamic) rather than by controlling the current (galvanostatic or galvanodynamic), because of the theoretical relationship between potential and energy. The most common electrochemical methods for determining general corrosion rates are linear polarization resistance (LPR) and Tafel extrapolation (potentiodynamic polarization curves). In some studies very high values of potentials are applied and also the direction of the potential is reversed to study localized corrosion (cyclic potentiodynamic polarization). Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 26 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 26  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Linear Polarization Resistance technique. From Rp to Icorr. Rp is defined mathematically as in equation : Rp is related to corrosion current (Icorr) as in: The constant B is defined in equation: where βa and βc are anodic and cathodic Tafel constants. By combining the above equations we obtain: If βa and βc values are known the corrosion rate can be calculated from Rp. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 27 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 27  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Linear Polarization Resistance technique. From Rp to Icorr. Because only a very small perturbation potential (less than ±30 mV, typically ±10 mV versus the open circuit potential, EOC) is applied, this technique does not interfere with corrosion reactions. From the slope, Rp (in Ω cm2 if the current density is plotted or in ohms if the current is plotted) is calculated. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 28 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 28  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Linear Polarization Resistance technique. From Rp to Icorr. It should be noted that the i–E curve around corrosion potential may not be linear. Also, the curve in the anodic and cathodic regions may or may not be symmetrical. The symmetrical i–E curve is obtained only when both βa and βc are equal. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 29 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 29  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Linear Polarization Resistance technique. From Rp to Icorr. βa and βc values that are required to calculate corrosion current could either be determined by the Tafel extrapolation method (discussed previously) or could be assumed. For majority of cases the values of β fall between 60 and 120 mV. Therefore in many instances a value of 120 mV is assumed for both βa and βc. Consequently equation: may reduce to: Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 30 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 30  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Linear Polarization Resistance technique. Measurement in practice. Rp measurements can be obtained by the potentiodynamic method or by the step-wise potentiostatic polarization method. In both methods the corrosion potential is first measured, typically for one hour (during which time corrosion potentials of most electrodes are stabilized) or until it is stabilized. After that, a potential step, at increments of ±5 or ±10 or ±20 mV, is applied (potential-step method) or the potential is scanned at a constant rate (typically 60 mV/h) (potentiodynamic method). In both methods, the experiment is started at the negative potential, moving on to the positive potential through the corrosion potential. From the slope of the plot of the potential–current, Rp is determined. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 31 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 31  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Linear Polarization Resistance technique. Example. 32 32  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Linear Polarization Resistance technique. Advantages of LPR technique. 1. The corrosion current is measured rapidly, typically within a few minutes and hence this technique can be used as an online monitoring technique. 2. Only very small amounts of potential are applied (less than ±30 mV, typically less than ±10 mV), hence the corrosion rate is not affected due to measurements. 3. This technique can be used to measure low corrosion rates (less than 2.5μm/yr. 4. Measurements can be taken repeatedly - in other words, the LPR technique is non-destructive. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 33 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 33  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Tafel extrapolation method. About 100 years ago, Tafel found that a linear relationship between E and log I exists if an electrode is polarized to sufficiently large potentials, both in anodic and cathodic directions. The regions in which such relationships exist are known as Tafel regions. Mathematically this relationship is given by Butler-Volmer equation: where: I is the current, Icorr is the current at corrosion potential (Ecorr), E is the applied potential, βa and βc are Tafel constants which are anodic and cathodic slopes of E-log I plots in the Tafel regions. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 34 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 34  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Tafel extrapolation method. Overpotential. The difference between E and Ecorr is called overpotential, η. At sufficiently larger values of η (typically between 100 and 500 mV), in the anodic direction, i.e., ηa, and in the anodic direction, i.e., ηc, the Butler-Volmer equation: simplifies to: Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 35 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 35  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Tafel extrapolation method. Polarization curves. In cases where Tafel regions are observed, Icorr can be determined by the extrapolation of either anodic or cathodic or both Tafel regions to Ecorr. Real plot Theoretical line Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 36 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 36  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization curves. Measurement in practice. Tafel extrapolation measurements can be performed either by the potentiodynamic method or by the step-wise potentiostatic polarization method. As in Rp measurements, in both methods corrosion potential is first measured, typically for one hour (during which time corrosion potentials of most electrodes are stabilized) or until it stabilizes. After that, the potential step – at increments of ±25 or ±50 or ±100 mV, every 5 minutes, recording the current at the end of each 5-minute period – is applied (potential-step method) or the potential is scanned at a constant rate (typically 0.6 V/h). Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 37 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 37  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization curves. Measurement in practice. 38 38  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization curves. Tafel extrapolation – advantages and limitations. From the E–log I plot, three values are determined: the anodic Tafel slope, the cathodic Tafel slope and Icorr (from back-extrapolation of both anodic and cathode curves to Ecorr). The main advantage of this method is that it provides a simple, straightforward method to determine Tafel constants. This method applies a large overpotential to the metal surface therefore it is considered as destructive. This is particularly true during anodic polarization during which the metal surface may be permanently changed / damaged. For this reason it is not used as a monitoring technique in the field. 39 https://www.gamry.com/ 39  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Other parameters that can be determined from the potentiodynamic polarization curves Primary passivation potential (Epp, potential positive to which passive surface layers are formed), The critical current density (Icc, minimum current required before surface layers are formed), The breakdown potential (Eb, potential positive to which passive surface layer is destroyed and transpassive region starts), The protection potential (Eprot, potential at which passive layers are stable and protective), Passive current (Ip, current of the electrode in Eprot), and The area of the hysteresis loop. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 40 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 40  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Other parameters that can be determined from the potentiodynamic polarization curves 41 ASTM G3, ‘Standard Practice for Conventions Applicable to Electrochemical Measurements in Corrosion Testing’, Annual Book of ASTM Standards, 41 Vol. 03.02, ASTM, West Conshohocken, PA.  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Selected limitations of polarization methods of determining the corrosion rate. Solution resistance. 1. The data obtained during electrochemical measurements should be directly relevant to corrosion. 2. In all the calculations the resultant resistance (R) is assumed to be related to corrosion. However the measured R is made up of two components: Rs and Rp. 3. It is assumed that the Rs, i.e. the solution resistance, is low (highly conducting solution), so that the measured R ∼ Rp. 4. If the Rs value is appreciable that the measured corrosion rate will be underestimated (because Rp is inversely proportional to corrosion rate, higher values of Rs exhibit a higher value of R). The error due to Rs in the Rp measurement is normally significant in systems with high corrosion rates and low conductivity. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 42 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 42  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Selected limitations of polarization methods of determining the corrosion rate. Scan rate. 1. The electrode (i.e., corroding element) can be considered as a capacitor. 2. A capacitor is an electrical device that can store energy in the electric field - it builds up an electric charge. The amount of charge stored in a capacitor is measured in terms of capacitance. 3. When a potential is applied at a higher rate, the electrode’s charge build-up is higher. 4. Thus the measured current will have a higher component of capacitance current rather than a current resulting from the corrosion process. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 43 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 43  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Selected limitations of polarization methods of determining the corrosion rate. Scan rate. 5. The current associated with the corrosion process is known as the Faraday current. The relationship between the measured current, capacitance current and the Faraday current (i.e., corrosion current) is given in: where: Itotal is the total current measured, IF is the Faradaic current associated with corrosion rate, C is the electrode capacitance, dV/dt is the scan rate. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 44 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 44  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Selected limitations of polarization methods of determining the corrosion rate. Scan rate. 6. The error due to capacitance increases as the scan rate increases. As a result of this error the corrosion rate is overestimated. To minimize the error due to capacitance current, polarization experiments are conducted at lower scan-rate (typically 0.6 V/h) Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 45 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 45  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Selected limitations of polarization methods of determining the corrosion rate. Presence of oxidation or reduction species. As a result of electrochemical excitation (either potential or current), if electrochemically active species are present in the electrolyte they prefer to undergo a reaction rather than a corrosion reaction. Under this condition measurement of corrosion rates from electrochemical techniques has no meaning. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 46 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 46  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Selected limitations of polarization methods of determining the corrosion rate. Variation of corrosion potential. If the corrosion potential varies during electrochemical measurements, the results obtained are not meaningful. Therefore before conducting any electrochemical measurement, the corrosion potential of the system should be monitored for a sufficiently longer duration to establish that it is stable. If the corrosion potential does not stabilize then electrochemical techniques may not be used. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 47 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 47  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Selected limitations of polarization methods of determining the corrosion rate. Diffusion controll. In order to use electrochemical techniques for measuring corrosion, the reaction should be charge-controlled, i.e., the rate of the reaction is proportional to the rate at which electron transfer occurs at the electrode / electrolyte interface. If the charge-transfer rate is high, a situation is developed – usually near the cathode – when the reduction species is quickly depleted. At this stage the reaction rate is controlled by the rate of diffusion of species on to the cathode, i.e., diffusion-controlled corrosion, under which conditions the results from polarization methods are not accurate. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 48 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 48  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Selected limitations of polarization methods of determining the corrosion rate. Rather the general corrosion. Most electrochemical polarization parameters measured are related to the general corrosion rate only. Initiation and propagation of localized corrosion complicates the response of polarization measurements. Localized corrosion alters the chemistry of the solution locally. It also alters the electrode geometry and the surface area – all of which results in a change in polarization response which is difficult to quantify. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 49 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 49  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Conversion of Icorr into the corrosion current density. For this reason it should be assumed that the current distribution is uniform across the area used in the calculation. With this assumption the current value is divided by the surface area as shown in: where: icorr is the current density (μA/cm2), Icorr is the current (μA), and A is the exposed specimen area, cm2. Other commonly used units for current are mA and A. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 50 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 50  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Conversion of Icorr into the corrosion rate and mass loss rate. Based on Faraday’s law the corrosion rate (CR) or mass loss rate (MR) can be calculated as: where: CR is given in mm/y, icorr in μA/cm2, icorr K1 is 3.27 × 10−3 and has units of mm g/μA cm y, ρ is the density of metal g/cm3. MR is given in g/m2, K2 is 8.954 × 10−3 g cm2/μA m2 d EW is the equivalent weight. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 51 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 51  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Conversion of Icorr into the corrosion rate and mass loss rate. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 52 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 52  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Conversion of Icorr into the corrosion rate. Equivalent weight for a metal. Equivalent weight EW is the mass in grams that will be oxidized by the passage of one Faraday (1 F = 96 489 C/A·s) of electric charge. For pure elements EW is given as: where: W is the atomic weight of the element and n is the number of electrons required to oxidize an atom of the element in the corrosion process, i.e., the valence of the element. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 53 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 53  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Conversion of Icorr into the corrosion rate. Equivalent weight for an alloy. To calculate EW of alloy the following formula is used: where: ni is the valence of the i-th element of the alloy; wi is the atomic weight of the i-th element of the alloy, fi is the mass fraction of the i-th element of the alloy. Problem 1: It is assumed that the process of oxidation (corrosion) is uniform and does not occur selectively for any component of the alloy. If this is not true then the calculation should be adjusted. Problem 2: Valance assignments for elements that exhibit multiple valences can create uncertainty. It is best if an independent technique is used to establish the proper valence for each alloying element. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface 54 Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 54  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Sample holders and corrosion cells - technical solutions. O-ring Graphite CE Corrosion cell for a flat specimen. 55 55  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Sample holders and corrosion cells - technical solutions. Ag|AgCl RE Corrosion cell for a flat specimen. 56 56  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Sample holders and corrosion cells - technical solutions. Specific geometric area of the measurement (part of the surface in contact with the electrolyte). Metal flat specimens (coupons / disks / plates). 57 57  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Sample holders and corrosion cells - technical solutions. Water jacket 58 Multiport corrosion cell. 58  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Sample holders and corrosion cells - technical solutions. Holder O-ring Electrical contact Sample window 59 59  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Sample holders and corrosion cells - technical solutions. Corrosion Sample O-ring cell Sample window Metal contact 60 60  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Sample holders and corrosion cells - technical solutions. Counter electrode Luggin capilary Sample Water holder jacket 61 61  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Measuring system. 62 62  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. Sample holder and corrosion cell - technical solutions. Ag|AgCl reference electrode KCl electrolyte Luggin capilary Junction Junction 63 63  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. IR compensation. When you pass current between two electrodes in a conductive solution, there are always regions of different potentials in the solution. Much of the overall change in potential occurs very close to the surface of the electrodes. Here the potential gradients are largely caused by ionic concentration gradients set up near the metal surfaces. Also, there is always a potential difference (a potential drop) caused by current flow through the resistance in the bulk of the solution. 64 https://www.gamry.com/ 64  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. IR compensation. Careful placement of the Reference Electrode can compensate for some of the IR-drop resulting from the cell current, I, flowing through the solution resistance, R. You can think of the Reference Electrode as sampling the potential somewhere along the solution resistance. The closer it is to the Working Electrode, the closer you are to measuring a potential free from IR errors. However, complete IR compensation cannot be achieved in practice through placement of the reference electrode, because of the finite physical size of the electrode. The portion of the cell resistance that remains after placing the Reference Electrode is called the uncompensated resistance, Ru. 65 https://www.gamry.com/ 65  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. IR compensation. Modern potentiostats can use current-interrupt (CI) or positive- feedback (PF) IR compensation to dynamically correct uncompensated resistance errors. In the CI technique, the cell current is periodically turned off for a very short time. With no current flowing through the solution resistance, its IR drop disappears instantly. The potential drop at the electrode surface remains constant on a rapid time scale. The difference in potential with the current flowing and without is a measure of the uncompensated IR drop. 66 https://www.gamry.com/ 66  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. IR compensation. In the CI technique, the cell current is periodically turned off for a very short time. With no current flowing through the solution resistance, its IR drop disappears instantly. The potential drop at the electrode surface remains constant on a rapid time scale. The difference in potential with the current flowing and without is a measure of the uncompensated IR drop. 67 https://www.gamry.com/ 67  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Polarization measurement in practice. IR compensation. In controlled potential modes, the applied potential can be dynamically corrected for the measured IR error in one of several ways. In the simplest of these, the IR error from the previous point is applied as a correction to the applied potential. For example, if an IR free potential of 1 V is desired, and the measured IR error is 0.2 V, the potentiostat applies 1.2 V. The correction is always one point behind, for the IR error from one point is applied to correct the applied potential for the next point. 68 https://www.gamry.com/ 68  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Literature references: H.H. Uhlig and R.W. Revie, Corrosion and Corrosion Control, An introduction to Corrosion Science and Engineering, 3rd Edition, John Wiley and Sons, Hoboken, NJ, 1985. https://www.gamry.com/ M. Stern and A.L. Geary, ‘Electrochemical Polarization’, Journal of the Electrochemical Society, 104 (1957), p. 56. J.R. Scully, ‘Polarization Resistance Methods for Determination of Instantaneous Corrosion Rates’, Corrosion, 56 (2000), 218. Techniques for Corrosion Monitoring (Woodhead Publishing Series in Metals and surface Engineering) 1st Edition by Lietai Yang (Editor). 2008 Woodhead. 69 69  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Control questions: 1. Characterize the nature of electrochemical corrosion. 2. Relationship between energy and potential. 3. Electrode potential, Nernst equation, standard EMF and galvanic series. 4. Relationship between potential and current. Mixed potential. 5. Tafel equation. Butler-Volmer equation. 6. Linear polarization technique for determination of corrosion rate. 7. Tafel extrapolation for determination of corrosion rate. 8. What information can be derived from polarization curves? 9. Limitations of polarization methods. Developed by : dr hab. inż. Juliusz Winiarski Department of Advanced Material Technologies Faculty of Chemistry, Wrocław University of Science and Technology 70 70  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Advanced research methods in the engineering of materials Lecture 8 Electrochemical impedance spectroscopy (EIS) in the study of corrosion of materials. 71 Wrocław University of Science and Technology, Wrocław, 2020  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. The method. Simply put, EIS is a powerful tool that can simulate real-world electrochemical behaviors using multiple parameters that can be automated, providing a system of measurement and validation. EIS supplies a large amount of information, but it cannot provide all the answers. EIS is usually used for fine-tuning mechanisms and determining the kinetics of processes, resistances, and capacitances, and it allows for the determination of real surface areas in situ. It is a very sensitive technique but must be used with care. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 72 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014; 2 https://www.gamry.com/  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Applications. 1) Interfacial processes: redox reaction at electrodes, adsorption and electrosorption, kinetics of homogeneous reactions in solution combined with redox processes, forced mass transfer, 2) Geometric effects: linear, spherical, cylindrical mass transfer, limited- volume electrodes, determination of solution resistance, porous electrodes, 3) Applications in power sources (batteries, fuel cells, supercapacitors, membranes), corrosion, coatings and paints, electrocatalytic reactions (e.g., water electrolysis, Cl2 evolution), conductive polymers, self- assembled monolayers, biological membranes, sensors, semiconductors, and others. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 73 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 3  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Ohm’s law. The total resistance of complex electrical circuits can be determined using two fundamental laws of Ohm and Kirchhoff. Ohm’s law relates current passing through resistance i in A, with voltage V in V, and resistance R in Ω: It allows one to determine the current if the applied voltage is known or the voltage (ohmic drop) when the current is flowing through the resistance. It also shows that current follows the potential without delay. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 74 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 4  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Ohm’s law. Conclusion: From Ohm’s law it follows that the equivalent resistance, Req, of the connection of resistances, Ri, in series equals the sum of the resistances. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 75 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 5  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Kirchhoff’s laws. 1) The algebraic sum of currents entering one point is equal to the sum of all currents leaving this point. It simply states that there can be no accumulation of charges in conductors. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 76 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 6  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Kirchhoff’s laws. 2) The second law applies to loops and says that the algebraic sum of voltage drops in a closed loop equals zero. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 77 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 7  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Kirchhoff’s laws. Conclusion: two resistances can be replaced by one equivalent resistance, Req, The equivalent resistance is the harmonic mean of two parallel resistances. This formula should always be used for the parallel connection of resistances. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 78 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 8  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Impedance definition. While the Ohm’s law is a well-known relationship, its use is limited to only one circuit element - the ideal resistor. An ideal resistor has several simplifying properties: - It follows Ohm’s Law at all current and voltage levels, - Its resistance value is independent of frequency, and - ac current (alternate current) and voltage signals through a resistor are in phase with each other. 79 https://www.gamry.com/ 9  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Impedance definition. The real world contains circuit elements that exhibit much more complex behavior. These elements force us to abandon the simple concept of resistance, and in its place we use impedance, a more general circuit parameter. Like resistance, impedance is a measure of the ability of a circuit to resist the flow of electrical current, but unlike resistance, it is not limited by the simplifying properties listed on the previous slide. 80 https://www.gamry.com/ 10  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Impedance definition. Electrochemical impedance is usually measured by applying an ac potential to an electrochemical cell and then measuring the current through the cell. Assume that we apply a sinusoidal potential excitation. The response to this potential is an ac current signal. This current signal can be analyzed as a sum of sinusoidal functions (a Fourier series). 81 https://www.gamry.com/ 11  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Impedance definition. Electrochemical impedance is commonly measured using a small excitation signal (several to tens mV). This is done so that the cell’s response is pseudo-linear. In a linear (or pseudolinear) system, the current response to a sinusoidal potential will be a sinusoid at the same frequency but shifted in phase. 82 https://www.gamry.com/ 12  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Impedance definition. The excitation signal, expressed as a function of time, has the form of: where Et is the potential at time t, E0 is the amplitude of the signal, and ω is the radial frequency. The relationship between radial frequency ω (expressed in radians/second) and frequency f (expressed in hertz, Hz) is: 83 https://www.gamry.com/ 13  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Impedance definition. In a linear system, the response signal, It, is shifted in phase (φ) and has a different amplitude than I0: An expression analogous to Ohm’s law allows us to calculate the impedance of the system as: 84 https://www.gamry.com/ 14  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Impedance definition. The impedance is therefore expressed in terms of a magnitude, Zo, and a phase shift, φ. If we plot the applied sinusoidal signal E(t) on the X-axis of a graph and the sinusoidal response signal I(t) on the Y-axis, the result is an oval. This oval is known as a “Lissajous Figure”. Analysis of Lissajous Figures on oscilloscope screens was the accepted method of impedance measurement before the availability of modern EIS instrumentation. 85 https://www.gamry.com/ 15  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Lissajous curves. In general, after application of an ac potential perturbation to an electrochemical system, E(t) = E0 cos(ωt), the obtained current is shifted in phase with respect to the voltage: i(t) = i0 cos(ωt + φ). By applying the voltage to the x-axis and the current (transformed into the corresponding voltage) to the y-axis of the oscilloscope one obtains so-called Lissajous curves. https://www.gamry.com/ A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 86 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 16  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Lissajous curves. When the phase angle difference φ is zero, a straight line at 45° is obtained. When the phase difference is 90 °, a semicircle is obtained. For intermediate phase shifts, ellipses at different angles are φ obtained. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 87 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 17  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Lissajous curves. The ratio of the amplitudes of both signals gives the modulus of the impedance, |Z|, and the phase angle φ is determined from the inclination of the ellipse. From |Z| and φ the real and imaginary parts of the impedance are determined. Such an analysis must be carried out at all frequencies studied. Nonlinearity of the tested system causes the formation of asymmetric curves. This method is time consuming and is rarely used nowadays. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 88 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 18  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Non-linearity. A linear system is one that possesses the important property of superposition: If the input consists of the weighted sum of several signals, then the output is simply the superposition, that is, the weighted sum, of the responses of the system to each of the signals. For a potentiostated electrochemical cell, the input is the potential and the output is the current. Unfortunately, electrochemical cells are not linear! Doubling the voltage will not necessarily double the current. 89 https://www.gamry.com/ 19  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Non-linearity. However, it can be thought of as pseudo- linear. If we look at a small enough portion of a cell’s current versus voltage curve, it appears to be linear 90 https://www.gamry.com/ 20  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Non-linearity. In normal EIS practice, a relatively small (1 to 10 mV) ac signal is applied to the cell. With such a small potential signal, the system is pseudo-linear. We don’t see the cell’s large nonlinear response to the dc potential because we only measure the cell current at the excitation frequency. 91 https://www.gamry.com/ 21  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Steady state requirement. Measuring an EIS spectrum takes time (often up to many hours). The system being measured must be at a steady state throughout the time required to measure the EIS spectrum. A common cause of problems in EIS measurements and analysis is drift in the system being measured. In practice, a steady state can be difficult to achieve. The cell can change through adsorption of solution impurities, growth of an oxide layer, build-up of reaction products in solution, coating degradation, or temperature changes, to list just a few factors. 92 https://www.gamry.com/ 22  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Frequency Response Analyzer (FRA). https://www.ameteksi.com/ A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 93 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 23  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Frequency Response Analyzer (FRA). Frequency response analyzers operate on the basis of the correlation of the studied signal with the reference signal. The measured signal, E = E0 cos(ωt + φ), is multiplied by a cosine and sine signal of the same frequency, and the product is integrated during one or more wave periods. Integrating over n periods gives: A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 94 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 24  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Frequency Response Analyzer (FRA). Note that both equations: correspond to the Fourier transform (FT) of the function E: This operation produces real and imaginary parts of the measured signal. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 95 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 25  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Frequency Response Analyzer (FRA). A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 96 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 26  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. From measurement to the impedance values. Frequency Response Analyzer (FRA). Such an operation is carried out for the potential and current signal. The impedance of the system is calculated as the ratio of the FTs of the potential and current, which is equal to the ratio of the corresponding phasors: A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 97 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 27  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electrochemical impedance spectroscopy. Impedance – two fundamental types of graph. 1) Complex plane plots, also called Argand diagrams (or Nyquist plots). They are plots of imaginary versus real impedance. In these plots -Z” is plotted versus Z’ as the imaginary impedances of the electrochemical systems are usually negative. It should be added that, although the name Nyquist plot is often used in the electrochemical literature, it is not precise because Nyquist plots are used for assessing the stability of a system with feedback. 2) Bode plots. There are two types of Bode plot: a) log |Z| (magnitude) versus log f (frequency) and b) phase angle φ versus log f. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 98 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 28  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Nyquist plot. 99 29  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Nyquist plot. With Euler’s relationship: it is possible to express the impedance as a complex function. The potential is described as, and the current response as, The impedance is then represented as a complex number, A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 100 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 30  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Impedance notation. IUPAC convention: Z” and Z’, i Alternatively: Zreal and Zimag, j 101 31  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Nyquist plot. The expression for Z(ω) is composed of a real and an imaginary part. -Z” If the real part is plotted on the X-axis and the imaginary part is |Z| plotted on the Y-axis of a chart, we get a “Nyquist Plot”. ω→∞ ω→ 0 arg Z In this plot the Y-axis is negative and that each point on the Nyquist plot is the impedance at Z’ one frequency. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 102 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 32  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Nyquist plot. Low frequency data are on the right side of the plot and higher frequencies are on the -Z” left. On the Nyquist plot the |Z| impedance can be represented as a vector ω→∞ ω→ 0 (arrow) of length |Z|. arg Z The angle between this vector and the X-axis, commonly Z’ called the “phase angle”, is f (=arg Z). A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 103 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 33  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Nyquist plot. It should be stressed that in complex plane plots, the unit length of real and imaginary parts should be the same; otherwise, deformation of the plots is observed. Nyquist plots do not contain all the information about frequency, and some frequencies are often added in these plots to better visualize the frequency domain. Nyquist plots are preferred by electrochemists because a model can be more easily found from them (especially by inexperienced researchers). A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 104 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 34  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Bode plot. Combined representation of magnitude and phase angle versus signal frequency. 105 35  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Bode plot. Two Bode plots contain all the necessary information. From a practical point of view, typical data acquisition and analysis programs display both plots. It is strongly recommended that both types of plots be used, especially when comparing experimental data with the fit to the appropriate model. 106 36  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Tridimensional impedance plots. In some cases other plots are also presented, for example, complex admittance plots, complex capacitance plots, and tridimensional impedance plots. A. Lasia, Electrochemical Impedance Spectroscopy and its Applications, 107 DOI 10.1007/978-1-4614-8933-7_2, © Springer Science+Business Media New York 2014. 37  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electric equivalent circuit versus physical model. Circuit elements. 108 Zview software for EIS, Scribner Associates inc. 2004 38  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Electric equivalent circuit versus physical model. Circuit elements. 109 Zview software for EIS, Scribner Associates inc. 2004 39  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. How to read the impedance spectra? How to draw conclusions about the tested system? ? ? ? ? ? 110 40  „ZPR PWr – Zintegrowany Program Rozwoju Politechniki Wrocławskiej” Impedance representation. Comparison between available plots and observable differences. RC model in series connection.