Introduction to electrochemical techniques Valentin Mirčeski Institute of Chemistry Faculty of Natural Sciences and Mathematics “Ss Cyril and Methodius” University, Skopje Republic of Macedonia

Electrochemistry: basic terms Electrochemistry is interdisciplinary science dealing with the interrelation between the chemical and electrical phenomena. Chemical (redox) transformations caused by a flow of electric current Gaining electrical current due to spontaneous chemical transformation Understanding electrochemistry means: Understanding electrode processes Understanding electrical properties of interfaces The main phenomena: Charge transfer across an interfaces formed, most frequently, between an electric conductor of a first kind (an electrode) (electron conductivity) and second kind (electrolyte solution, i.e., a solution of ions) (ion conductivity)

Electrochemical cells Electrolysis cell: non-spontaneous redox (electrode) reactions are driven by the power of an external electric supply! Galvanic cell: Spontaneous redox (electrode) reactions give raise to a current flow.

Electrochemical cells and electrochemical reactions The simples electrochemical experiment involves charge transfer across at least two interfaces Electric potential difference between the electric potential of the two electrodes (the main driving force as a measure for the energy available to drive electric charges through the electrochemical cell)

Electric potential and current Electrical potential (E (V – volt)) is a measure for the potential energy of a charge in an electric field; The difference in the potential (potential energy) causes a charged species to move in the electric field (charge transfer) Potential of 1 V (volt) is equivalent to the potential energy of 1J of a charged species with a charge of 1 C (coulomb) Charge transfer in time is called electric current (I (A – ampere)

Electrode reactions, half reactions… Electrode/electrolyte interface is characterized with a large potential difference , thus a strong electric filed exists at the interface! Electrode reactions Half-reactions The overall reaction Working electrode Reference electrode R (reduced species) O (oxidized species) - e Electrode electrode|solution Interface O + ne- ⇄ R (electrode reaction)

Standard hydrogen electrode The main reference electrode: Standard (normal) hydrogen electrode (SHE) (NHE) Reference callomel electrode Hg/Hg2Cl2/KCl (saturated in water) 0.242 V vs SHE Reference silver-silver chloride electrode Ag/AgCl/KCl (saturated in water) 0.197 V vs SHE In the course of the electrochemical experiment the chemical composition, hence the electric potential, of the reference electrode remains constant! Standard hydrogen electrode Controlling the potential difference between the working and reference electrode, one controls actually the potential of the working electrode only!

Current sign convention, standard redox potential, Faraday law Reduction Reduction current (“ – “) Oxidation Oxidation current (“ + “) Standard redox potential E, which is related to the standard Gibbs energy Synonyms: standard electrode potential; standard reduction potential. O + ne- = R n – number of electrons F – Faraday constant (96 485.3 C mol-1). Thus, the physical meaning of the Faraday constant is that one mole of a single charged species has a charge of 96 485.3 C; e.g., one mole of electrons has a charge of - 96 485.3 C. Faraday law: A charge of 96485.3 C corresponds to the transformation of 1 mol reactant and 1 mol product in a one-electron electrohemical reaction O + e- = R DG  = -nFE 

I – E curve: polarisation curve (working electrode) 2H+ + 2e- = H2 (reference electrode) Ag + Br- = AgBr + e- 2Br- = Br2 + 2e- AgBr + e- = Ag + Br- The overall current flow must be equal at both electrodes, and it is dictated by the working electrode, which has much smaller electrode surface area. Limiting potentials dictated by electrochemical reactions of the supporting electrolyte at particular electrode. Electrode reactions are heterogeneous in their nature. The rate depends on the electric field, i.e., on the electrode potential.

Overpotential: additional energy required than thermodynamically predicted due to the slow electrode kinetics A large overpotential for hydrogen reduction at Hg electrode Hg

Electroactive species in a supporting electrolyte Polarization curve in the presence of traces of electroactive species (Cd2+)

Possible electrode reactions at different electrodes

Faradaic and nonfaradaic processes Faradaic processes: charge transfer due to redox reactions (electrode reaction)-current flow Nonfaradaic processes: no charge transfer across the interface; adsorption, desorption, changes in the structure of the layer of the solution adjacent to the electrode formation of an electic double layer etc. Important: although there is no charge transfer, the nonfaradaic processes cause the current to flow in the electrochemical cell! Ideally polarizable electrode: no charge transfer, e.g. Hg in 1 M KCl in acetonitrile over 2 V (from 0.25 to -2.1 V vs SHE.

Electrode/electrolyte interface: an electric capacitor

Structure of the electrical doubly layer (IHP) - inner Helmholtz plane (OHP) - Outer Helmholtz plane

Potential profile across the double-layer Y = dE/dx The intensity of the electric field is very high due to the potential variation over very small (nanometer range) distance!

Rate of an electrode reaction: the flux R (reduced species) O (oxidized species) - e Electrode electrode|solution Interface Flux (the rate of the heterogeneous electrode reaction) is equal to the amount of reacted material per unit of time per unit of electrode surface area (mol s -1 cm-2). This chemical rate is equal to the ratio of the electric current, number of exchanged electrons in a unit reaction and electrode surface area. O + ne- ⇄ R (electrode reaction) Electric current (I) measured at the electrode is proportional to the rate (v) of the electrode reaction! (q – charge, t – time, F – Faraday constant; A – electrode surface area; n – number of electrons, n(O) – number of moles of the reactant O)

Factors affecting the rate of electrode processes Modes of mass transfer: Migration Diffusion Convection Nernst-Plank equation

Electrode reaction controlled by the mass transport If the mass transfer is the slowest step of the electrode reaction, then the electrode reaction is termed as being “electrochemically reversible”. At each potential difference (DE) of the interface, the electrode reaction is in redox equilibrium, which is described by the Nernst equation: The Nernst eq. reveals that variation of the potential difference at the interface (DE) causes variation of the equilibrium concentrations of the redox species ([O] and [R]). In other words, it shifts the position of the redox equilibrium, which is manifested as a flow of electric current in the system. O O + ne ⇄ R (electrode reaction) Electrode DE = felecc. – fsol. (Potential difference (DE) across the interface is externally controlled by controlling the inner potential (f) of the electrode. In simple words, one controls the activity, i.e., concentration of electrons participating in the electrode reaction, thus affecting both the position of the redox equilibrium O/R and the kinetics of the redox transformation. Note, frequently, the potential difference DE is designated simply as electrode potential with a symbol E) R electrolyte solution

Semi-empirical treatment of a voltammetric experiment when the diffusion layer has a constant thickness: a steady-state mass transfer In this experiment, the flux at the electrode (i.e., the rate of the electrode reaction, thus the current), depends on the diffusion rate only (i.e., depends on the mass transfer only). According to the First Fick law, the rate of diffusion depends on the diffusion coefficient (D) and the concentration gradient (dc/dx); (D – diffusion coefficient (it is the rate constant of the diffusion (cm 2 s-1)). In addition, it is assumed that the diffusion layer has a constant thickness d. The flux of R species must be equal, but opposite in sign, with the flux of O species. R diffuses toward the electrode, while O, formed by oxidation of R, diffuses away from the electrode (in the opposite direction)  R = O + ne- electrode x The maximal flux of R will be if cR(x = 0) = 0. Thus, the corresponding current is termed limiting current, Il

E / V I / A E1/2 Il (limiting current) Typical I-E curve (voltammogram) for an electriochemical experiment with a constant thickness of the diffusion layer (steady state voltammetry)

Kinetics of a simple homogeneous chemical reaction A ⇄ B kf kb The rate of a common chemical reaction depends on the concentrations of participants, and (through the rate constant) on the temperature and activation energy. Symbols and abbreviations f – forward b – backward net – overall reaction K – equilibrium constant [X] - equilibrium concentration of a species X

c – cathodic (reductive) Electrode kinetics R ⇄ O + ne- kf kb c – cathodic (reductive) a – anodic (oxidative) a – electron transfer coefficient (dimensionless number between 0 and 1; most frequently the value is 0.5) k (cm s-1)- standard rate constant (rate constant when the electrode potential is equal to the standard potential of the redox couple, E’) Rate constants depend on the potential! The unique feature of electrochemical rate constants. Thus, the rate of the electrode reaction can be controlled by the potential! Butler-Volmer equation

Dependence of the current on the electrode potential Limiting current The current increases exponentially with the potential as predicted by the dependence of the rate constants on the potential! diffusion O (at the electrode surface) O (in the solution) Electrode v = I/nFA limiting current R Although the rate of the electrode reaction could be very fast due to the large overpotential, the overall rate will by limited by the supply of the electrode surface with the electroactive material by the mass transport, i.e. diffusion!

Electrochemical techniques: chronoamperometry The dependence of the potential and current on time in the course of the chronoamperometric experiment. The experiment is conducted at a given fixed potential (E2), which is sufficiently height (E2 >> E) to cause complete electrochemical (redox) transformation of the electroactive species at the electrode surface. As a consequence, the current is flowing in the cell, and it is being measured as a function of time. R ⇄ O + ne I t

Description of the mathematical model referring to a simple chronoamperometric experiment - Cottrell equation R ⇄ O + ne Cottrell experiment: Chronoamperometric experiment in a homogenous solution containing only R species, at a potential E >> E , thus enabling complete transformation of all R species at the electrode surface. Mass transfer is occurring only by diffusion without any specific adsorption phenomena on the electrode surface. x cR / c*R 1 0,2 t = 0 t = 0,001 s t = 0,01 s t = 0,1 s t = 1 s Concentration profiles. Variation of the concentration of electroactive species with the distance x measured from the electrode surface at different times of the chronoamperometric experiment. As shown above, the thickness of the diffusion layer increases with time.

Chronoamperometry with a double potential step For mechanistic purposes, i.e. to reveal the mechanism of the electrode reaction, the chronoamperometric experiment can be conducted with a double potential step, as shown in the figure below. At the potential E2, the initially present R species undergo electrochemical oxidation at the electrode surface to produce species O, resulting in the first branch of the current, presented in the right plot (i.e.. chronoamperogram). In the second potential step, the potential is changed to a value E3, at which the reduction of previously formed species O is taking place, producing the second branch of the chronoamperogram presented on the right panel. E2 E I t t E3 E1 t t

Chronocoulometry Chronocoulometry is equivalent method to chronoamperometry, the difference being in measuring the charge consumed in the course of the electrode reaction instead of the current. We recall, the definition of the current Hence, the charge is simply calculated as an integral of the current-time function, i.e. In the course of the experiment, contrary to the chronoamerometry, the response of the crhronocoulometry increases with time, as the amount of the material transformed at the electrode increases with time. By integration of the current, the noise effect is usually smoothed out and it is not so significant as in chronoametrometry. The contribution of the double layer as well as from electrode reaction of immobilized species can be easily separated from the contribution of diffusing species. Thus, chronocoulometry is especially valuable for studying surface processes, thus it is of particular importance in studying conducting polymers.

For a Cottrell experiment described on page 27, the chronocoulometric response is defined as: The charge consumed during the experiment of species that diffuses toward the electrode is proportional to the square-root of time and the plot vs. t1/2 is linear with a slop from which some of the constants of the equation above can be obtained, given the knowledge of others. The eq. above shows that at t = 0, the charge is 0. However, in a real experiment the line Q vs t1/2 does not cross through the origin, as shown in the plot. This is due to the charge consumed by the double layer formation and by electrode transformation of species immobilized on the electrode surface. Thus the total charge can be separated in three terms: The first term is due to electrode reaction controlled by the diffusion of the species, homogeneously distributed in the solution, the second term Qdl is due to formation of the double layer and the third is due to electrode transformation of adsorbed species.