Electroanalytical Chemistry. Gary A. Mabbott

of a species. An activity of a species is proportional to its concentration, C_i. a_i = γ_i·C_i, where the proportionality constant, γ_i, is known as an activity coefficient and is dependent upon the ionic strength of the solution. In contrast, voltammetric methods deliberately apply energy in the form of a voltage from an outside source to a cell in order to drive a chemical reaction at a working electrode. In these experiments, the current is related to the number of moles of reactant that is converted in the process. This current can be used to quantify the concentration of the original reactant.

      In addition to the working electrode (or an indicator electrode in a potentiometric experiment), a second electrode is needed to transfer electrons into or out of the cell in order to counterbalance the charge going into or out of the solution at the working or indicator electrode. This second electrode is a reference electrode. It exploits a simple, reliable electron transfer process that occurs at a well‐established voltage. The reference electrode is designed to maintain its potential (voltage) in the process. Consequently, all of the energy applied to the cell from the outside is focused onto the working electrode. Whenever the current level or the cell's electrical resistance, R, is high, some energy is lost as heat in overcoming the electrical resistance of the solution. This causes an error in voltammetric experiments because some voltage is lost from the voltage that was intended to be applied to the working electrode. This error can be calculated from Ohm's law, V_lost = iR_cell.

Interesting things happen at the boundary of any two phases. Charges, either electrons or ions, can cross these boundaries leading to an excess of electrical charge accumulating on one side and a layer of charge of opposite sign accumulating on the other side. This double layer of charge leads to a difference in electrical potential energy across the interface. This is the potential energy measured in potentiometric experiments that is related to the activity of the analyte ion. In voltammetric experiments, the boundary potential between an electrode and the solution controls the rate of the electron transfer between the analyte in solution and the working electrode.

      An electrical capacitor serves as a good model for many aspects of the electrical double layer. The charge, Q, on either side of the double layer can be calculated from Q = CV, where V is the voltage or potential difference across the double layer and the coefficient, C, is the capacitance. There are subtleties to the structure of the double layer that have significance to electron transfer studies, but most of the charge on the solution side accumulates in a layer called the outer Helmholtz plane (OHP), where ions are separated from the electrode by a layer of one or two water molecules.

      The conductance of a solution is the reciprocal of the solution's electrical resistance. Its magnitude depends on the type and concentration of the ions. The measurement of the conductance of a water sample is a semiquantitative measure of ionic concentration. Conductance is also used as a special detector for ionic solutes in ion chromatography.

      Mass transport is a term for the movement of a chemical species in solution. Two mechanisms for material movement are very important to electroanalytical chemistry. The net movement in a given direction that is due to a concentration gradient and is characterized by a random walk of the molecule or the ion in an unstirred solution is known as diffusion. The flux, J_i, of a species is a measure of the net movement of material across a plane perpendicular to the direction of movement. It has units of mol/cm²/s. Fick's first law of diffusion associates the flux to the concentration gradient for the species. J_i = D_i(∂C_i/∂x). This is a key concept in electron‐transfer experiments. The other mechanism for mass transport is convection or stirring of the bulk solution.

      In both voltammetry and potentiometry experiments, a difference in rates of diffusion associated with salt bridges used with reference electrodes leads to a higher flux for either positive or negative ions over those of the opposite charge. The excess of charge “pushes back” against continuing build‐up of charge leading to a steady state situation. The result is a net separation of charge and a junction potential or diffusion potential. Junction potentials are generally small, but they can be serious errors in potentiometric experiments. Later chapters discuss this issue in depth.

1.2 Basic Concepts

      Electrical phenomena are associated with charged particles. Electrons are the most common charge carriers that one encounters, but ions in a solution are also important charge carriers. The purpose of this chapter is to define some electrochemical terms and introduce some fundamental concepts associated with electrical charge and phase boundaries.

All electrochemical techniques involve measuring (and sometimes manipulating) the voltage at an electrode. What is voltage? Voltage is a measure of the electrical energy available to do work on a charged particle. A charged particle has an electric field associated with it that interacts with its environment. An electric field is the force that two charged particles experience as a function of distance between them. Charges with the same sign repel each other and charges of opposite sign attract. Consequently, the arrangement of charged particles surrounding a given location will determine whether a charged particle coming into that place from the outside will be stabilized by net attractive forces or will be destabilized by net repulsive forces. The electric potential energy for a charged particle is defined as the energy spent or released in the process of inserting a positive test charge into a specific environment. For example, consider an arbitrary location in some material, such as point A shown in Figure 1.1.

Figure 1.1 The electric (or electrostatic) potential energy at a point, A, in a given medium is a measure of the net energy required or released in moving a test charge from outer space (where it is assumed to be free of forces to interact with) to point A where other charges attract or repel it.

There exists some collection of charges surrounding the point in question (point A in Figure 1.1). If one were to bring a positively charged particle from outer space, where it is assumed the test charge is free from the influence of any outside electromagnetic fields to point A, one would have to do work (energy would be spent) to overcome other positive charges in the neighborhood. However, if negative charges dominate the neighborhood at point A, there would be a net attractive force on the test charge and energy would be released in moving it from outer space to that position. The energy spent or released in moving a test charge from outer space to point A is the electric potential energy (also known as the electrostatic potential energy) at that point. For simplicity, this energy is often called the potential at point A. If a different arrangement of charges exists at point B (as in Figure 1.2), then moving a test charge from outer space to point B is associated with a different electric potential energy.

There is not a practical way of measuring the absolute electric potential energy at point A or at point B. However, it is possible to measure the electric potential energy difference between points A and B. A common strategy is to define some point in the system under study as a reference point. Then, the potential at any other point in the system is the electric potential energy difference between the point in question and the reference point. In this approach, no absolute electric potential energies need be evaluated. In the field of electronics, the reference point is often the electric potential energy of a conductor in direct contact with the earth (Figure 1.3).