Detection Limits and Selectivity in Electrochemical Detectors Electrochemical detectors are in direct contact with the solution under scrutiny. Electrodes can be used to drive chemical changes that are detected by another sensor, or electrodes can be used to detect the products of chemical changes wrought by other processes. The close chemical relationship between the electrode and the solution allows better analytical systems to be developed and provides challenging questions in the understanding of figures of merit.
INSTRUMENTATION Stephen G. Weber John T. Long Department of Chemistry University of Pittsburgh Pittsburgh, PA 15260
Electrochemistry provides a powerful set of tools for analysis. Its power derives from the fact that electrochemistry is inherently chemical in nature. There are subtle differences in geometry and basicity among related ligands that make only one the basis for a potentiorrietric lithium sensor. Complex 0003-2700/88/0360-903A/$01.50/0 © 1988 American Chemical Society
surface catalysis is demanded by many molecules, such as O2, H2, CO2, and hydrazines, that undergo multiple electron transfers. These are but two examples of the degree to which electrochemical pursuits rely on a sound understanding of chemistry. Electrochemistry also can be used to make things. Electrochemically prepared polymers are the basis for gasphase sensors and electrochemical transistors. Even light can be generated electrochemically. Electroanalytical chemists are making new materials and catalysts, and they are developing new
analytical techniques. Because of the richness of chemistry, there are many ways to create new analytical techniques and improve established ones. Such creations and improvements are necessary for a complete understanding of the complex systems that are so important to our society. This INSTRUMENTATION article will describe developments in currentcarrying electrochemical detectors. It is possible to argue that these detectors, out of all other developments in electroanalytical chemistry, have had the greatest impact on "real" analytical chemistry since the development of ion-selective electrodes. Within the context of electrochemical detectors, we will discuss three topics that are important to all analytical chemists: sig-
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nal and noise generation and signal-tonoise ratio (S/N), the improvement of qualitative information content, and control of selectivity of the detector. In each area there are many opportunities to increase our knowledge; we will describe some relevant research. We hope to demonstrate that there is much to learn and that the electrochemical approach can be made more versatile and powerful than it is today. Predicting signals and noise The foundation of any technique for quantitative analysis is the relationship between the measured quantity and the amount of analyte in the sample. The simplest electrochemical detectors operate at constant potential (constant oxidizing or reducing power). When exposed to a flowing stream of solution, the electrode yields a current that is the sum of a background current and any current caused by the presence of electroactive species. Because one measures current at these electrodes, they are called amperometric. Equations relating the current to the concentration of the analyte are dependent on many factors such as fluid flow rate, U, its kinematic viscosity, v, the solute's diffusion coefficient, D, and the cell's dimensions (I). The kinematic viscosity is the ratio of the fluid's viscosity to density. Examples of electrochemical detectors include the thinlayer cell, the tubular electrode, the impinging flow electrode with large spacer, and the impinging flow electrode with small spacer. Equations for the current generated in these and other electrochemical detectors have recently been tabulated (2, 3). One can appreciate the signal-generating mechanism by considering the example equation for the thin-layer detector (Figure 1) operating at low efficiency (high flow rates or with small electrodes). The sensitivity is the current (0 per concentration (C):
sensitivity = i/C = 1.467nFU1/3(DA/b)m
(1)
In this equation, nF is the number of coulombs of electrons per mole of analyte, A is the electrode area, and b is the height or thickness of the channel. This equation is appropriate when the applied potential is sufficient to keep the concentration of analyte at the surface equal to zero. Several general observations can be made from this equation. The current is time independent. The equation applies to a steady-state cell in which one unit of analyte flows in per second and a fraction, /, equal to if nFCU, is electrolyzed. The complementary fraction, 1—/, flows to waste. The sensitivity increases (although the efficiency decreases) as the flow rate of the mobile phase increases.
Figure 1. Examples of restricted-flow geometry for low-efficiency cells. In each example, laminar flow carries solutions past the electrode where electrolysis occurs, (a) Flow in, (b) flow out, (c) working electrode, (d) spacer. (Adapted from Reference 1.)
In these detectors, molecules are oxidized or reduced after diffusing from a point in the fluid to the electrode surface. The rate at which this process occurs depends on the local concentration gradient (through Fick's laws). In the thin-layer cell, if the cell is well designed, the flow past the electrode is laminar. In laminar flow, the fluid moves parallel to the surface of the electrode; consequently, there is no bulk motion of analyte toward the electrode surface. The effect of the flow on the current is indirect. By replenishing solution that has been depleted of analyte by fresh analyte-containing solution, the flow increases the concentration gradient and thus the flux of analyte to the electrode. Whenever the fluid's viscosity is absent from the sensitivity equation, as above, there is no transport of solute toward or away from the electrode surface by bulk fluid motion alone. Of course, if the diffusion coefficient, D, is increased, the flux caused by dif-
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fusion is increased. (Consequently, electrochemical detectors in supercritical fluid chromatography should be quite sensitive.) When the electrode area, A, is increased, the sensitivity also increases, but the increase in sensitivity is not proportional to the increase in electrode area. This can be understood by imagining that the electrode is made up of a series of adjacent strips running across the direction of flow. The current at the second strip is not as great as that at the first strip because of the depletion of material from electrolysis at the first electrode. Thus an incremental addition of electrode results in a less than proportional increase in signal. Finally, the thickness of the channel, b, can be decreased to increase current. The gradient of fluid velocity at the surface is greater with a lower b. This increases the rate of the replenishment of the solution near the electrode. For cells of typical dimensions and working under typical conditions, the efficiency of the cell, /, is on the order of 0.01. One should be careful not to interpret the term "low efficiency" in a pejorative sense. The flame ionization detector in gas chromatography is a lowefficiency detector, but it is nonetheless important and powerful. The discussion above, in its most general terms, suffices for an understanding of any low-efficiency detector. High-efficiency detectors (/ — 1) are somewhat different. Electrodes of high efficiency have been called coulometric. This is a misnomer; one measures current with these cells. They got the name coulometric because in the ideal case, where / = 1, the analyte is completely consumed by an electrode process, as in a coulometric titration. A preferable name is "high-efficiency cell." Signal production in them has been described in some detail (4). In these cells (Figure 2), which are often made
Figure 2. High-efficiency cells. Increasing the electrode surface area and the length of time that the solution is exposed to the electrode both increase efficiency, (a) Flow in, (b) flow out, (c) working electrode, (d) spacer. (Adapted from Reference 1.)
linearly with an increase in area: σ = 2σχ
(3)
If the noises are completely uncorrect ed, as they would be if the noise came from independent electrochemical pro cesses occurring at each electrode, then ρ would be zero, and one would have σ = V2*!
Figure 3. Simplified version of the detector as an electrical device with generic cur rent and voltage noise. The variable battery represents the auxiliary-reference electrode system and potentiostat. The interfacial impedance is z,, the voltage noise is e„, the current noise is /„, and the value of the feedback resistance is R1.
of a porous material such as reticulated carbon, the current from a small incre ment of the electrode decreases expo nentially along the electrode. This is simply because of the decrease in the bulk concentration of the material be ing electrolyzed. As material is electrolyzed, the rate of electrolysis decreases because the diffusive flux, driven by the difference between the bulk and surface concentrations of analyte, de creases. Although the understanding of sig nal production in both low- and highefficiency cells is fairly good for simple Faradaic reactions, noise is less well understood. Theoretical analysis (5) shows that noise will decrease as one decreases the electrode area to a point, and then it will be constant. Area-de pendent noise includes contributions from the fluctuations in the working electrode-reference electrode potential difference and environmental influ ences on the interfacial impedance. For example, the operational amplifier used to make the current-to-voltage conversion has an input voltage noise; the reference electrode and its liquid junction can also generate voltage noise. To see how this affects the mea surement, think of adding a noise volt age to the voltage being applied in the potentiostat (Figure 3). It will generate a current, ejz\, with a corresponding output voltage from the current-tovoltage converter equal to —Rfejz\. The interfacial impedance, zu is halved when the electrode area is doubled; thus, this noise is proportional to the electrode area. Fluctuations in the interfacial im pedance caused by fluctuations in tem perature or concentration of some adsorbate will lead to a fluctuation in the measured current that is also propor tional to the electrode area (or more precisely, capacitance). Electrical engi neers always assume that capacitances are noiseless, and any noise they gener ate is put into a circuit as an equivalent voltage or current noise. However, we have allowed the interfacial capaci tance to have a "noise" because it is a
physically reasonable assertion that the interfacial capacitance fluctuates in an analytical system. The input current noise in the cur rent-to-voltage converter amplifier is the constant contribution. The current noise, tn, adds to the signal and yields a constant voltage noise, —inRf, in the output of the current-to-voltage con verter. This noise becomes more im portant when R( is large, as it needs to be with small electrodes. This simple picture demonstrates why the consid eration of electrode area is important to the S/N question. The limiting noise at electrodes is mostly instrumental and environmen tal (6), at least in our hands. (Certainly there are ways to study fundamental noise processes of particular electro chemical interest [7], but conditions that reveal this noise do not usually hold in the detector case.) Consequent ly, a parallel array of electrodes feeding current into a single amplifier has a noise that is proportional to electrode area (as long as the total area is large enough so that the constant noise, i n , is not dominant). However, if the noise source were the random nature of the fundamental Faradaic process itself, then the noise at each electrode in the array would be independent. The noise in this case would increase as the square root of the area. This can be explained by the follow ing statistical argument. Consider the simple case of two electrodes of equal area and sensitivity. They are connect ed in parallel. The variance (σ2) of the current signal from the pair is (8) "2 = °i +
