Modern Analytical Cheymistry - Chapter 11 ppt

CChhaapptteerr 11 461 Electrochemical Methods of Analysis In Chapter 10 we examined several analytical methods based on the interaction of electromagnetic radiation with matter. In this chapter we turn our attention to analytical methods in which a measurement of potential, current, or charge in an electrochemical cell serves as the analytical signal. 1400-CH11 9/9/99 2:06 PM Page 461 462 Modern Analytical Chemistry 11A Classification of Electrochemical Methods Although there are only three principal sources for the analytical signal—potential, current, and charge—a wide variety of experimental designs are possible; too many, in fact, to cover adequately in an introductory textbook. The simplest division is be- tween bulk methods, which measure properties of the whole solution, and interfa- cial methods, in which the signal is a function of phenomena occurring at the inter- face between an electrode and the solution in contact with the electrode. The measurement of a solution’s conductivity, which is proportional to the total con- centration of dissolved ions, is one example of a bulk electrochemical method. A determination of pH using a pH electrode is one example of an interfacial electro- chemical method. Only interfacial electrochemical methods receive further consid- eration in this text. 11A.1 Interfacial Electrochemical Methods The diversity of interfacial electrochemical methods is evident from the partial family tree shown in Figure 11.1. At the first level, interfacial electrochemical methods are divided into static methods and dynamic methods. In static methods no current passes between the electrodes, and the concentrations of species in the electrochemical cell remain unchanged, or static. Potentiometry, in which the po- tential of an electrochemical cell is measured under static conditions, is one of the most important quantitative electrochemical methods, and is discussed in detail in Section 11B. The largest division of interfacial electrochemical methods is the group of dy- namic methods, in which current flows and concentrations change as the result of a redox reaction. Dynamic methods are further subdivided by whether we choose to control the current or the potential. In controlled-current coulometry, which is covered in Section 11C, we completely oxidize or reduce the analyte by passing a fixed current through the analytical solution. Controlled-potential methods are subdivided further into controlled-potential coulometry and amperometry, in which a constant potential is applied during the analysis, and voltammetry, in which the potential is systematically varied. Controlled-potential coulometry is dis- cussed in Section 11C, and amperometry and voltammetry are discussed in Section 11D. 11A.2 Controlling and Measuring Current and Potential Electrochemical measurements are made in an electrochemical cell, consisting of two or more electrodes and associated electronics for controlling and measuring the current and potential. In this section the basic components of electrochemical in- strumentation are introduced. Specific experimental designs are considered in greater detail in the sections that follow. The simplest electrochemical cell uses two electrodes. The potential of one of the electrodes is sensitive to the analyte’s concentration and is called the working, or indicator electrode. The second electrode, which is called the counter electrode, serves to complete the electric circuit and provides a reference potential against which the working electrode’s potential is measured. Ideally the counter electrode’s potential remains constant so that any change in the overall cell potential is attrib- uted to the working electrode. In a dynamic method, where the passage of current changes the concentration of species in the electrochemical cell, the potential of the counter electrode may change over time. This problem is eliminated by replacing the counter electrode with two electrodes: a reference electrode, through which no counter electrode The second electrode in a two-electrode cell that completes the circuit. reference electrode An electrode whose potential remains constant and against which other potentials can be measured. indicator electrode The electrode whose potential is a function of the analyte’s concentration (also known as the working electrode). 1400-CH11 9/9/99 2:06 PM Page 462 Figure 11.1 Partial family tree for interfacial electrochemical methods of analysis. current flows and whose potential remains constant; and an auxiliary electrode that completes the electric circuit and through which current is allowed to flow. Although many different electrochemical methods of analysis are possible (Fig- ure 11.1) there are only three basic experimental designs: (1) measuring the potential under static conditions of no current flow; (2) measuring the potential while con- trolling the current; and (3) measuring the current while controlling the potential. Each of these experimental designs, however, is based on Ohm’s law that a current, i, passing through an electric circuit of resistance, R, generates a potential, E; thus E = iR Each of these experimental designs also uses a different type of instrument. To aid in understanding how they control and measure current and potential, these in- struments are described as if they were operated manually. To do so the analyst Chapter 11 Electrochemical Methods of Analysis 463 Static methods ( i = 0) Controlled potential Variable potential Stripping voltammetry Fixed potential Cyclic voltammetry Controlled current Controlled current coulometry Polarography and stationary electrode voltammetry Pulse polarography and voltammetry Dynamic methods ( i ≠ 0) Potentiometry Stirred solution Quiescent solution Voltammetry Hydrodynamic voltammetry Controlled potential coulometry Amperometry Interfacial electrochemical methods auxiliary electrode The third electrode in a three-electrode cell that completes the circuit. Ohm’s law The statement that the current moving through a circuit is proportional to the applied potential and inversely proportional to the circuit’s resistance (E = iR). 1400-CH11 9/9/99 2:06 PM Page 463 Figure 11.2 Schematic diagram of a manual potentiostat: C = counter electrode; W = working electrode; SW = slide-wire resistor; T = tap key; i = galvanometer. observes a change in current or potential and manually adjusts the instrument’s set- tings to maintain the desired experimental conditions. It is important to understand that modern electrochemical instruments provide an automated, electronic means of controlling and measuring current and potential. They do so by using very differ- ent electronic circuitry than that shown here. Further details about such instru- ments can be found in the suggested readings listed at the end of the chapter. Potentiometers Measuring the potential of an electrochemical cell under condi- tions of zero current is accomplished using a potentiometer. A schematic diagram of a manual potentiometer is shown in Figure 11.2. The current in the upper half of the circuit is where E PS is the power supply’s potential, and R ab is the resistance between points a and b of the slide-wire resistor. In a similar manner, the current in the lower half of the circuit is where E cell is the potential difference between the working electrode and the counter electrode, and R cb is the resistance between the points c and b of the slide-wire resis- tor. When i up = i low =0 no current flows through the galvanometer and the cell potential is given by To make a measurement the tap key is pressed momentarily, and the current is noted at the galvanometer. If a nonzero current is registered, then the slide wire is adjusted and the current remeasured. This process is continued until the gal- vanometer registers a current of zero. Using the tap key minimizes the total amount of current allowed to flow through the cell. Provided that the total cur- rent is negligible, the change in the analyte’s concentration is insignificant. For example, a current of 10 –9 A drawn for 1 s consumes only about 10 –14 mol of analyte. Modern potentiometers use operational amplifiers to create a high- impedance voltmeter capable of measuring potentials while drawing currents of less than 10 –9 A. Galvanostats A galvanostat is used for dynamic methods, such as constant-current coulometry, in which it is necessary to control the current flowing through an elec- trochemical cell. A schematic diagram of a manual constant-current galvanostat is shown in Figure 11.3. If the resistance, R, of the galvanostat is significantly larger than the resistance of the electrochemical cell, and the applied voltage from the power supply is much greater than the cell potential, then the current between the auxiliary and working electrodes is equal to i E R = PS E R R E cb ab cell PS =× i E R low cell cb = i E R ab up PS = 464 Modern Analytical Chemistry potentiometer A device for measuring the potential of an electrochemical cell without drawing a current or altering the cell’s composition. acb • T SW Electrochemical cell CW i Power supply galvanostat A device used to control the current in an electrochemical cell. 1400-CH11 9/9/99 2:06 PM Page 464 Figure 11.3 Schematic diagram of a galvanostat: R = resistor; i = galvanometer; A = auxiliary electrode; W = working electrode; R = reference electrode; V = voltmeter or potentiometer (optional). Chapter 11 Electrochemical Methods of Analysis 465 i Power supply R A W R V SW AW i Power supply R V Figure 11.4 Schematic diagram of a manual potentiostat: SW = slide-wire resistor; A = auxiliary electrode; R = reference electrode; W = working electrode; V = voltmeter or potentiometer; i = galvanometer. potentiostat A device used to control the potential in an electrochemical cell. The potential of the working electrode, which changes as the composition of the electrochemical cell changes, is monitored by including a reference electrode and a high-impedance potentiometer. Potentiostats A potentiostat is used for dynamic methods when it is necessary to control the potential of the working electrode. Figure 11.4 shows a schematic dia- gram for a manual potentiostat that can be used to maintain a constant cell poten- tial. The potential of the working electrode is monitored by a reference electrode connected to the working electrode through a high-impedance potentiometer. The desired potential is achieved by adjusting the slide-wire resistor connected to the auxiliary electrode. If the working electrode’s potential begins to drift from the de- sired value, then the slide-wire resistor is manually readjusted, returning the poten- tial to its initial value. The current flowing between the auxiliary and working elec- trodes is measured with a galvanostat. Modern potentiostats include waveform generators allowing a time-dependent potential profile, such as a series of potential pulses, to be applied to the working electrode. 11B Potentiometric Methods of Analysis In potentiometry the potential of an electrochemical cell is measured under static conditions. Because no current, or only a negligible current, flows while measuring a solution’s potential, its composition remains unchanged. For this reason, poten- tiometry is a useful quantitative method. The first quantitative potentiometric ap- plications appeared soon after the formulation, in 1889, of the Nernst equation re- lating an electrochemical cell’s potential to the concentration of electroactive species in the cell. 1 When first developed, potentiometry was restricted to redox equilibria at metallic electrodes, limiting its application to a few ions. In 1906, Cremer discov- ered that a potential difference exists between the two sides of a thin glass mem- brane when opposite sides of the membrane are in contact with solutions contain- ing different concentrations of H 3 O + . This discovery led to the development of the glass pH electrode in 1909. Other types of membranes also yield useful potentials. Kolthoff and Sanders, for example, showed in 1937 that pellets made from AgCl could be used to determine the concentration of Ag + . Electrodes based on mem- brane potentials are called ion-selective electrodes, and their continued develop- ment has extended potentiometry to a diverse array of analytes. 1400-CH11 9/9/99 2:06 PM Page 465 Figure 11.5 Electrochemical cell for potentiometry. 466 Modern Analytical Chemistry 11B.1 Potentiometric Measurements Potentiometric measurements are made using a potentiometer to determine the dif- ference in potential between a working or, indicator, electrode and a counter elec- trode (see Figure 11.2). Since no significant current flows in potentiometry, the role of the counter electrode is reduced to that of supplying a reference potential; thus, the counter electrode is usually called the reference electrode. In this section we in- troduce the conventions used in describing potentiometric electrochemical cells and the relationship between the measured potential and concentration. Potentiometric Electrochemical Cells A schematic diagram of a typical potentio- metric electrochemical cell is shown in Figure 11.5. Note that the electrochemical cell is divided into two half-cells, each containing an electrode immersed in a solu- tion containing ions whose concentrations determine the electrode’s potential. This separation of electrodes is necessary to prevent the redox reaction from occurring spontaneously on the surface of one of the electrodes, short-circuiting the electro- chemical cell and making the measurement of cell potential impossible. A salt bridge containing an inert electrolyte, such as KCl, connects the two half-cells. The ends of the salt bridge are fixed with porous frits, allowing ions to move freely be- tween the half-cells and the salt bridge, while preventing the contents of the salt bridge from draining into the half-cells. This movement of ions in the salt bridge completes the electric circuit. By convention, the electrode on the left is considered to be the anode, where oxidation occurs Zn(s) t Zn 2+ (aq)+2e – and the electrode on the right is the cathode, where reduction occurs Ag + (aq)+e – t Ag(s) The electrochemical cell’s potential, therefore, is for the reaction Zn(s) + 2Ag + (aq) t 2Ag(s)+Zn 2+ (aq) 2 e – Zn e – Ag Ag + Zn 2+ Cl – Cl – Cl – K + KCl Anode Cathode 0.0167 M ZnCl 2 0.100 M AgNO 3 NO 3 – Salt bridge Porous frit Potentiometer salt bridge A connection between two solutions that allows the movement of current in the form of ionic charge. anode The electrode where oxidation occurs. cathode The electrode where reduction occurs. 1400-CH11 9/9/99 2:06 PM Page 466 Chapter 11 Electrochemical Methods of Analysis 467 Also, by convention, potentiometric electrochemical cells are defined such that the indicator electrode is the cathode (right half-cell) and the reference electrode is the anode (left half-cell). Shorthand Notation for Electrochemical Cells Although Figure 11.5 provides a useful picture of an electrochemical cell, it does not provide a convenient repre- sentation. A more useful representation is a shorthand, or schematic, notation that uses symbols to indicate the different phases present in the electrochemical cell, as well as the composition of each phase. A vertical slash (|) indicates a phase boundary where a potential develops, and a comma (,) separates species in the same phase, or two phases where no potential develops. Shorthand cell nota- tions begin with the anode and continue to the cathode. The electrochemical cell in Figure 11.5, for example, is described in shorthand notation as Zn(s) | ZnCl 2 (aq, 0.0167 M) || AgNO 3 (aq, 0.100 M) | Ag(s) The double vertical slash (||) indicates the salt bridge, the contents of which are nor- mally not indicated. Note that the double vertical slash implies that there is a poten- tial difference between the salt bridge and each half-cell. EXAMPLE 11.1 What are the anodic, cathodic, and overall reactions responsible for the potential in the electrochemical cell shown here? Write the shorthand notation for the electrochemical cell. Ag Pt (0.100 M) HCl KCl AgCl Potentiometer (0.0100 M) FeCl 3 FeCl 2 (0.0500 M) SOLUTION The oxidation of Ag to Ag + occurs at the anode (the left-hand cell). Since the solution contains a source of Cl – , the anodic reaction is Ag(s)+Cl – (aq) t AgCl(s)+e – 1400-CH11 9/9/99 2:06 PM Page 467 The cathodic reaction (the right-hand cell) is the reduction of Fe 3+ to Fe 2+ Fe 3+ (aq)+e – t Fe 2+ (aq) The overall cell reaction, therefore, is Ag(s)+Fe 3+ (aq)+Cl – (aq) t AgCl(s)+Fe 2+ (aq) The electrochemical cell’s shorthand notation is Ag(s) | HCl (aq, 0.100 M), AgCl (sat’d) || FeCl 2 (aq, 0.0100 M), FeCl 3 (aq, 0.0500 M) | Pt Note that the Pt cathode is an inert electrode that carries electrons to the reduction half-reaction. The electrode itself does not undergo oxidation or reduction. Potential and Concentration—The Nernst Equation The potential of a potentio- metric electrochemical cell is given as E cell = E c – E a 11.1 where E c and E a are reduction potentials for the reactions occurring at the cathode and anode. These reduction potentials are a function of the concentrations of those species responsible for the electrode potentials, as given by the Nernst equation where E° is the standard-state reduction potential, R is the gas constant, T is the temperature in Kelvins, n is the number of electrons involved in the reduction reaction, F is Faraday’s constant, and Q is the reaction quotient.* Under typical laboratory conditions (temperature of 25 °C or 298 K) the Nernst equation becomes 11.2 where E is given in volts. Using equation 11.2 the potential of the anode and cathode in Figure 11.5 are Note, again, that the Nernst equations for both E c and E a are written for reduction reactions. The cell potential, therefore, is 11.3 EE E cell Ag Ag + Zn Zn 2+ +2+ Ag Zn =−       −−       °° // . log [] . log [] 0 05916 1 0 05916 2 1 EE c Ag Ag + + Ag =− ° / . log [] 0 05916 1 EE a Zn Zn 2+ 2+ Zn =− ° / . log [] 0 05916 2 1 EE n Q=− ° 0 05916. log EE RT nF Q=− ° ln 468 Modern Analytical Chemistry *See Chapter 6 for a review of the Nernst equation. 1400-CH11 9/9/99 2:06 PM Page 468 Chapter 11 Electrochemical Methods of Analysis 469 Substituting known values for the standard-state reduction potentials (see Appen- dix 3D) and the concentrations of Ag + and Zn 2+ , gives a potential for the electro- chemical cell in Figure 11.5 of EXAMPLE 11.2 What is the potential of the electrochemical cell shown in Example 11.1? SOLUTION The potential for the electrochemical cell is In potentiometry, the concentration of analyte in the cathodic half-cell is gen- erally unknown, and the measured cell potential is used to determine its concentra- tion. Thus, if the potential for the cell in Figure 11.5 is measured at +1.50 V, and the concentration of Zn 2+ remains at 0.0167 M, then the concentration of Ag + is deter- mined by making appropriate substitutions to equation 11.3 Solving for [Ag + ] gives its concentration as 0.0118 M. EXAMPLE 11. 3 What is the concentration of Fe 3+ in an electrochemical cell similar to that shown in Example 11.1 if the concentration of HCl in the left-hand cell is 1.0 M, the concentration of FeCl 2 in the right-hand cell is 0.0151 M and the measured potential is +0.546 V? SOLUTION Making appropriate substitutions into the Nernst equation for the electrochemical cell (see Example 11.2) and solving for [Fe 3+ ] gives its concentration as 0.0136 M. E cell 3+ [Fe =+ = + −       −+ −0 546 0 771 0 05916 0 0151 0 2223 0 05916 1 0. . . log . ] [ . . log( . )] E cell + Ag =+ =+ −       −− −       1 0 7996 0 05916 1 0 7618 0 05916 2 1 0 0167 .50 V . . log [] . . log . EE E cell Fe Fe 2+ 3+ AgCl/Ag 3+ 2+ Fe Fe Cl V =−       −− =+ −       −+ − =+ °°− / . log [] [] ( . log[ ]) . . log . . [ . . log ( . )] . 0 05916 0 05916 0 771 0 05916 0 0100 0 0500 0 2223 0 05916 0 100 0 531 E cell V =+ −       −− −       =+ 0 7996 0 05916 1 0 100 0 7618 0 05916 2 1 0 0167 1 555 . . log . . . log . . 1400-CH11 9/9/99 2:06 PM Page 469 Figure 11.6 Origin of liquid junction potential between solutions of 0.1 M HCl and 0.01 M HCl. 470 Modern Analytical Chemistry Despite the apparent ease of determining an analyte’s concentration using the Nernst equation, several problems make this approach impractical. One problem is that standard-state potentials are temperature-dependent, and most values listed in reference tables are for a temperature of 25 °C. This difficulty can be overcome by maintaining the electrochemical cell at a temperature of 25 °C or by measuring the standard-state potential at the desired temperature. Another problem is that the Nernst equation is a function of activities, not con- centrations.* As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe 3+ /Fe 2+ redox couple is +0.767 V in 1 M HClO 4 , +0.70 V in 1 M HCl, and +0.53 in 10 M HCl. The shift toward more negative potentials with an increasing concentration of HCl is due to chloride’s ability to form stronger complexes with Fe 3+ than with Fe 2+ . This problem can be minimized by replacing the standard-state potential with a matrix-dependent for- mal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). A more serious problem is the presence of additional potentials in the electro- chemical cell, not accounted for by equation 11.1. In writing the shorthand nota- tion for the electrochemical cell in Figure 11.5, for example, we use a double slash (||) for the salt bridge, indicating that a potential difference exists at the interface between each end of the salt bridge and the solution in which it is immersed. The origin of this potential, which is called a liquid junction potential, and its signifi- cance are discussed in the following section. Liquid Junction Potentials A liquid junction potential develops at the interface between any two ionic solutions that differ in composition and for which the mo- bility of the ions differs. Consider, for example, solutions of 0.1 M HCl and 0.01 M HCl separated by a porous membrane (Figure 11.6a). Since the concentration of HCl on the left side of the membrane is greater than that on the right side of the membrane, there is a net diffusion of H + and Cl – in the direction of the arrows. The mobility of H + , however, is greater than that for Cl – , as shown by the difference in the H + Cl – 0.1 M HCl 0.01 M HCl 0.1 M HCl 0.01 M HCl Excess of Cl – Excess of H + – – – – – + + + + + (a) (b) liquid junction potential A potential that develops at the interface between two ionic solutions that differ in composition, because of a difference in the mobilities of the ions (E lj ). * See Chapter 6 for a review of activity. 1400-CH11 9/9/99 2:06 PM Page 470 [...]... listed values.3 481 1400-CH11 9/9/99 2:07 PM Page 482 482 Modern Analytical Chemistry To meter — O O — –O—P — — O (C10H21O)2PO2– Figure 11. 13 Structure and formula of di-(n-decyl) phosphate Ag/AgCl reference electrode Di-(n-decyl) phosphate reservoir Standard Ca2+ solution Figure 11. 14 Schematic diagram of a Ca2+ liquid-based ion-selective electrode Membrane saturated with di-(n-decyl) phosphate Below... reference electrode Calcium ion-selective electrodes are also available in which the di-(n-decyl) phosphate is immobilized in a polyvinyl chloride 1400-CH11 9/9/99 2:07 PM Page 483 Chapter 11 Electrochemical Methods of Analysis Table 11. 3 Representative Examples of Liquid-Based Ion-Selective Electrodes Analyte Membrane Composition Selectivity Coefficientsa Ca2+ di-(n-decyl) phosphate in PVC K+ Valinomycin... the analyte One example of a liquid-based ion-selective electrode is that for Ca2+, which uses a porous plastic membrane saturated with di-(n-decyl) phosphate (Figure 11. 13) As shown in Figure 11. 14, the membrane is placed at the end of a nonconducting cylindrical tube and is in contact with two reservoirs The outer reservoir contains di-(n-decyl) phosphate in di-n-octylphenylphosphonate, which soaks... for reaction 11. 10; thus Inner solution Gas-permeable membrane [H3O+ ] = K Figure 11. 15 Schematic diagram of a gas-sensing membrane electrode [CO2 ] [HCO3− ] 11. 11 where K is the equilibrium constant If the amount of HCO3– in the internal solution is sufficiently large, then its concentration is unaffected by the presence of CO2 and remains constant Substituting equation 11. 11 into equation 11. 9 gives... the electrode If the electrode’s response obeys the Nernst equation, Table 11. 5 Representative Examples of Potentiometric Biosensors Analyte Biologically Active Phasea Substance Determined 5′-adenosinemonophosphate (5′-AMP) L-arginine asparagine L-cysteine L-glutamate L-glutamine oxalate penicillin L-phenylalanine sugars urea AMP-deaminase (E) arginase + urease (E) asparaginase (E) Proteus morganii (B)... Example 11. 7 shows how a one-point standard addition can be used to determine the concentration of an analyte EXAMPLE 11. 7 The concentration of Ca2+ in a sample of sea water is determined using a Ca ion-selective electrode and a one-point standard addition A 10.00-mL sample is transferred to a 100-mL volumetric flask and diluted to volume A 50.00-mL aliquot of sample is placed in a beaker with the Ca ion-selective... In one version of the urea electrode, shown in Figure 11. 16, an NH3 electrode is modified by adding a dialysis membrane that physically traps a pH 7.0 buffered solution of urease between the dialysis membrane and the gas-permeable 1400-CH11 9/9/99 2:07 PM Page 485 485 Chapter 11 Electrochemical Methods of Analysis Table 11. 4 Characteristics of Gas-Sensing Membrane Electrodes Analyte Reaction in Inner... ion-selective electrode based on a glass membrane in which the potential develops from an ion-exchange reaction on the membrane’s surface 1400-CH11 9/9/99 2:06 PM Page 478 478 Modern Analytical Chemistry To meter Internal reference (Ag/AgCl) Sample reference (Ag/AgCl) Salt bridge AgCl, KCl 0.1 M HCl, AgCl (sat’d) Figure 11. 12 Schematic diagram of a combination glass electrode for measuring pH pH-Sensitive... the measurement of pH An example of a typical combination electrode is shown in Figure 11. 12 1400-CH11 9/9/99 2:06 PM Page 479 Chapter 11 Electrochemical Methods of Analysis Table 11. 1 479 Representative Examples of Glass Membrane Ion-Selective Electrodes Analyte Membrane Composition Selectivity Coefficientsa Na+ 11% Na2O, 18% Al2O3, 71% SiO2 Li+ 15% Li2O, 25% Al2O3, 60% SiO2 K+ 27% Na2O, 5% Al2O3,... solution 11. 13 NH3 gaspermeable membrane Few potentiometric biosensors are commercially available As shown in Figures 11. 16 and 11. 17, however, available ion-selective and gas-sensing electrodes may be easily converted into biosensors Several representative examples are described in Table 11. 5, and additional examples can be found in several reviews listed in the suggested readings at the end of the chapter . 05916. log EE RT nF Q=− ° ln 468 Modern Analytical Chemistry *See Chapter 6 for a review of the Nernst equation. 1400-CH11 9/9/99 2:06 PM Page 468 Chapter 11 Electrochemical Methods of Analysis 469 Substituting. introduced in Chapter 3. 1400-CH11 9/9/99 2:06 PM Page 477 Figure 11. 12 Schematic diagram of a combination glass electrode for measuring pH. 478 Modern Analytical Chemistry EXAMPLE 11. 4 The selectivity. years. Crystalline Solid-State Ion-Selective Electrodes Solid-state ion-selective elec- trodes use membranes fashioned from polycrystalline or single-crystal inorganic salts. Polycrystalline ion-selective