A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 23
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These relations can be substituted into (2.4.14) togiveRT, (%a+/H+)H+,Na+Na+—— m*(/Ж6+H+—(Z.4.16)Since ^H+,Na+ a n c ^ wNa+/wH+ a r e constants of the experiment, it is convenient to definetheir product as the potentiometric selectivity coefficient, k^+ N a + :RT*]п-УHиH+,NaNa+, ipotУ/0Q1Q4(23.19)If the /3 phase is the internal filling solution (of constant composition) and the aphase is the test solution, then the overall potential of the cell isRTE = constant + ^ r Inг(2.4.20)This expression tells us that the cell potential is responsive to the activities of bothNa + and H + in the test solution, and that the degree of selectivity between these species isdefined АЦ+N a + .
If the product A^+>Na+ #Na+ * s m u c n less than яg+, then the membraneresponds essentially exclusively to H + . When that condition applies, charge exchange between the phases a and m! is dominated by H + .We have formulated this problem in a manner that considers only N a + and H + as active species. Glass membranes also respond to other ions, such as Li + , K + , Ag + , andNH4". The relative responses can be expressed through the corresponding potentiometricselectivity coefficients (see Problem 2.16 for some typical numbers), which are influencedto a great extent by the composition of the glass.
Different types of electrodes, based ondifferent types of glass, are marketed. They are broadly classified as (a) pH electrodeswith a selectivity order H + > > > N a + > K + , Rb + , Cs + > > Ca 2 + , (b) sodium-sensitiveelectrodes with the order Ag + > H + > Na + > > K + , Li + > > Ca 2 + , and (c) a moregeneral cation-sensitive electrode with a narrower range of selectivities in the orderH + > K + > Na + > N H | , Li + »Ca 2 + .There is a large literature on the design, performance, and theory of glass electrodes(37, 46-55).
The interested reader is referred to it for more advanced discussions.2.4 Selective Electrodes79Other Ion-Selective ElectrodesThe principles that we have just reviewed also apply to other types of selective membranes (48, 50-59). They fall generally into two categories.(a) Solid-State MembranesLike the glass membrane, which is a member of this group, the remaining common solidstate membranes are electrolytes having tendencies toward the preferential adsorption ofcertain ions on their surfaces.Consider, for example, the single-crystal LaF3 membrane, which is doped with EuF2to create fluoride vacancies that allow ionic conduction by fluoride.
Its surface selectivelyaccommodates F~ to the virtual exclusion of other species except OH~.Other devices are made from precipitates of insoluble salts, such as AgCl, AgBr, Agl,Ag2S, CuS, CdS, and PbS. The precipitates are usually pressed into pellets or are suspended in polymer matrices. The silver salts conduct by mobile Ag + ions, but the heavymetal sulfides are usually mixed with Ag2S, since they are not very conductive. The surfaces of these membranes are generally sensitive to the ions comprising the salts, as wellas to other species that tend to form very insoluble precipitates with a constituent ion. Forexample, the Ag2S membrane responds to Ag + , S2~~, and Hg 2 + .
Likewise, the AgClmembrane is sensitive to Ag + , Cl~, Br~, I~, CN~, and OH~.(b) Liquid and Polymer MembranesAn alternative structure utilizes a hydrophobic liquid membrane as the sensing element.The liquid is stabilized physically between an aqueous internal filling solution and anaqueous test solution by allowing it to permeate a porous, lipophilic diaphragm.
A reservoir contacting the outer edges of the diaphragm contains this liquid. Chelating agentswith selectivity toward ions of interest are dissolved in it, and they provide the mechanism for selective charge transport across the boundaries of the membrane.A device based on these principles is a calcium-selective electrode. The hydrophobicsolvent might be dioctylphenylphosphonate, and the chelating agent might be the sodiumsalt of an alkyl phosphate ester, (RO)2 PO^Na + , where R is an aliphatic chain having 8-18carbons. The membrane is sensitive to Ca 2+ , Zn 2+ , Fe 2 + , Pb 2 + , Cu 2+ , tetra-alkylammonium ions, and still other species to lesser degrees. "Water hardness" electrodes are basedon similar agents, but are designed to show virtually equal responses to Ca 2+ and Mg 2+ .Other systems featuring liquid ion-exchangers are available for anions, such as NO^~,ClO^, and Cl~.
Nitrate and perchlorate are sensed by membranes including alkylated1,10-phenanthroline complexes of Ni 2 + and Fe 2 + , respectively. All three ions are activeat other membranes based on quaternary ammonium salts.In commercial electrodes, the liquid ion-exchanger is in a form in which the chelatingagent is immobilized in a hydrophobic polymer membrane like poly(vinylchloride) (Figure 2.4.4). Electrodes based on this design (called polymer or plastic membrane ISEs) aremore rugged and generally offer superior performance.Liquid ion-exchangers all feature charged chelating agents, and various ion-exchangeequilibria play a role in their operation.
A related type of device, also featuring a stabilized liquid membrane, involves uncharged chelating agents that enable the transport ofcharge by selectively complexing certain ions. These agents are sometimes called neutralcarriers. Systems based on them typically also involve the presence of some anionic sitesin the membrane, either naturally occurring or added in the form of hydrophobic ions, andthese anionic sites contribute to the ion-exchange process (56-58).
It has also been proposed that electrodes based on neutral carriers operate by a phase-boundary (i.e., adsorption), rather than a carrier mechanism (59).80:JChapter 2. Potentials and Thermodynamics of CellsElectrical contactModule housingAqueous referencesolutionReference element(AgCI)Ion selectivemembraneFigure 2.4.4 A typical plastic membrane ISE.
[Courtesy ofOrion Research, Inc.]For example, potassium-selective electrodes can be constructed with the naturalmacrocycle valinomycin as a neutral carrier in diphenyl ether. This membrane has a muchhigher sensitivity to K + than to Na + , Li + , Mg 2 + , Ca 2 + , or H + ; but Rb + and Cs + aresensed to much the same degree as K + . The selectivity seems to rest mostly on the molecular recognition of the target ion by the complexing site of the carrier.(c) Commercial DevicesTable 2.4.1 is a listing of typical commercial ion-selective electrodes, the pH and concentration ranges over which they operate, and typical interferences.
Selectivity coefficientsfor many of these electrodes are available (55, 57).TABLE 2.4.1 Typical Commercially Available Ion-Selective ElectrodesSpeciesAmmonium (NH4")Barium (Ba 2 + )Bromide (Br~)Cadmium (Cd 2 + )Calcium (Ca 2 + )Chloride (СГ)Copper (Cu 2 + )Cyanide (CN")Fluoride (F~)Iodide ( Г )Lead (Pb 2 + )Nitrate (NO3")Nitrite (NO2)Potassium (K + )Silver (Ag + )Sodium (Na + )Sulfide (S2~)aType*LLSSLSsssssLLLSGSConcentrationRange(M)6КГЧоКГКГЧоКГ 51 to 10~510"1 to 10~71 to 10~71 to 5 X 10~5КГЧоКГ710" 2 to 10" 61 to 10" 71 to 10~71(ГЧо1(Г 61 to 5 X 10~61 to 10~61 to 10" 61 to 10~7Sat'd to 10~61 to 10~7рнRangeInterferences5-85-92-123-74-92-110-710-145-83-120-93-103-104-92-99-1212-14K + ,Na + ,Mg 2 +K + ,Na + ,Ca 2 +I", S 2 ", CN"Ag + ,Hg 2 + ,Cu 2 + ,Pb 2 + ,Fe 3 +Ba 2 + ,Mg 2 + ,Na + ,Pb 2 +I", S2~, CN~, Br"Ag + ,Hg 2+ ,S 2 ~,CT,Br~S2~OH"S2"Ag + ,Hg 2 + ,S 2 -,Cd 2 + ,Cu 2 + ,Fe 3 +Cl",Br",NO2,F",SO5~Cl",Br"",NOJ,F",SO5~Na + , Ca 2 + , Mg 2 +S2",Hg2+Li + , K + , NH^Ag + ,Hg 2 +G = glass; L = liquid membrane; S = solid-state.
Typical temperature ranges are 0-50°C for liquidmembrane and 0-80°C for solid-state electrodes.2.4 Selective Electrodes •« 81(d) Detection LimitsAs shown in Table 2.4.1, the lower limit for detection of an ion with an ISE is generally10~ 6 to 10~ 7 M. This limit is largely governed by the leaching of ions from the internalelectrolyte into the sample solution (60). The leakage can be prevented by using a lowerconcentration of the ion of interest in the internal electrolyte, so that the concentrationgradient established in the membrane causes an ion flux from the sample to the inner electrolyte.
This low concentration can be maintained with an ion buffer, that is, a mixture ofthe metal ion with an excess of a strong complexing agent. In addition, a high concentration of a second potential-determining ion is added to the internal solution. Under theseconditions, the lower detection limit can be considerably improved. For example, fora conventional liquid-membrane Pb 2 + electrode with an internal filling solution of5 X 10 4 M Pb z + and 5 X 10 l M M g z \ the detection limit for Pb:was 4 X 10~6 M. When the internal solution was changed to 10~3 M Pb 2 + and5 X 10~ z M Na2EDTA (yielding a free [Pb z+ ] = 10" i 2 M), the detection limit decreasedto 5 X 10~ 12 M (61). In the internal solution, the dominant potential-determining ionisNa+at0.1M.2.4.4 Gas-Sensing ElectrodesFigure 2.4.5 depicts the structure of a typical potentiometric gas-sensing electrode (62).
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