Selective Ion-sensitive Electrodes G. J. MOODY and J. D. R. THOMAS Department of Chemistry, University of Wales Institute of Science and Technology, Cardig Contents Introduction Classes of electrodes Glass electrodes Homogeneous solid-state electrodes Heterogeneous solid-state electrodes Liquid ion-exchanger electrodes Neutral carrier complex electrodes Organic radical-ion salt electrodes Electroactive hydrophobised graphite ‘Selectrodes’ Enzyme electrodes Plastic electrodes for organic ions Functional potential Speed of response Conditioning and storage Radiation stability Stability of response Effect of temperature Interferences and interference assessment Mechanism of selective response Glass electrodes Solid-state electrodes Liquid ion-exchanger electrodes Neutral carrier complex electrodes Organic radical-ion salt electrodes Activity, ionic strength and concentration Individual activity coefficients of ions Activity coefficients a t high ionic strength Activity coefficients in mixed electrolyte systems Liquid junction potentials Direct potentiometry with selective ion-sensitive electrodes Interference elimination and ionic strength adjustment Standard addition and subtraction methods Gran’s plots Titration procedures with selective ion-sensitive electrodes Differential and null-point potentiometry The study of complexes Reaction rate studies 69 E60 MOODY AND THOMAS Biomedical applications Biological fluids Mineralised tissues and dental materials Studies of general biological interest Plant materials Applications to enzyme reactions Environmental applications Foods, feeds and fertilisers Rocks and soils Water supplies and sea water Air and stack gases Industrial applications Applications to organic and pharmaceutical analysis Miscellaneous applications Applications in potentiometric titrimetry Selective ion-sensitive electrodes in non-aqueous solvents ConclusionSELECTIVE ION-SENSITIVE ELECTRODES 61 Introduction It is convenient that this review should survey developments in selective ion-sensitive electrodes and their applications for the period subsequent to the discovery, in 1966, of the lanthanum fluoride solid-state electrodel and up to mid- 1972.The survey takes cognizance of foundations laid by earlier studies on glass electrodes, and of pioneering work with non-glass membranes, such as barium sulphate and calcium fluoride slices,2 silver halide discs3 and of halide precipitates in inert matrices4 The successful lanthanum fluoride crystal membrane electrode was quickly followed by descriptions of electrodes selectively sensitive to other ions.This new armoury of selective probes based on simple potentiometric response, which attracted the avid attention of analytical and control scientists from diverse fields, has been associated with a variety of review-type papers, lectures, conferences, books and particularly with the Orion Research Incorporated Datasheets and Newsletter. The shorter general reviews5-8 survey the different types of electrodes, empha- sise their analogy with glass electrodes, and mention actual and possible applica- tions. Longer reviews pay more attention to instrumental details, general handling characteristics, limitations with regard to both sensitivity and selectivity, applica- tions and even some discussion of the mechanisms of the generation of membrane potentials.The~e~-~4 give between them a good survey of the state of the art, and the papers by Bucklo and Torren and Buckll have comprehensive reference lists of papers abstracted before November, 1971. Examples of specific reviews include those concerned with precipitate-based and solid-state electrodes, 12920s25s26 liquid ion-exchange micro electrode^,^^ public health and pollution rnonit0ring,2~-3~ process m0nitoring~~-~7 including electro- plating analy~is,~7 chemical studies,38 sea water,39 direct potenti~metry,~~ and the fluoride electrode" and the kind of review that considers new types of electrodes.42 A review on the development, response, selectivity and applications aims at making recommendations concerning investigations on development, applications and the presentation of results for p~blication.~~ There have been several symposia specifically concerned with selective ion- sensitive electrodes, probably the most well known being that at the National Bureau of Standards, Gaithersberg, Maryland, in January, 1969.Its 450 partici- pants clearly indicate the interest aroused in this field and its papers have been published in book form.14 In addition to the classes of electrodes then available, the symposium dealt with reference electrodes, theoretical considerations and general analytical application, including process control ; agricultural, geological, oceanographic and pharmaceutical problems; and the monitoring of water and its pollution. A book by Moody and Thomas*5 gives a broad survey of theoretical and practical aspects and, in addition to a systematic description of electrode types, devotes special attention to functional potential, selectivity assessment and62 MOODY AND THOMAS experimental procedures.A work by Rechnitzq6 has similar aims and is an audio course based on tape and accompanying manual. In dealing with developments since 1966, this review aims at a more compre- hensive literature coverage than those cited above, although the vast, fast-growing literature precludes an exhaustive coverage.The discussion is based on a classifica- tion of electrodes, response characteristics, selectivity, sensitivity and mechanisms of response, activity considerations, experimental methods and applications. Classes of Electrodes The main membrane materials for selective, ion-sensitive electrodes include glass, homogeneous and heterogeneous solid-state materials, liquid ion-exchangers, neutral carrier complexes, semi-conducting organic charge-transfer complexes and ion-radical salts, and electroactive hydrophobised graphite. A convenient practical classification can be based thereon, particularly as all other types, such as micro, gas, and combination electrodes, are subsidiary to these main groups. The detection limits and principal interferences of commercially available electrodes are sum- marised in Table I.The constructional basis of selective ion-sensitive electrodes is similar to the classical glass electrodes, namely : internal reference element - internal reference solution - sensor membrane. The internal reference solution imposes a constraint on an electrode regarding usage in positions other than those approximately vertical. Durst and Taylor47 overcame this problem by making the internal solution of an Orion fluoride electrode into a gel. Certain solid-state electrodes, which contain no internal solu- tion, use a direct wire contact with the back of the sensor membrane.m Silver or platinum wire liquid membrane coated electrodes also come into this categ0ry,4~-~~ the constructional basis for these electrodes being: internal reference wire element - sensor membrane.Glass electrodes These are the first of the selective ion-sensitive electrodes and are cation- sensitive only. One propo~ition5~Jj3 for achieving anion sensitivity, as yet a mere pipe-dream, is based on a ‘mirror-image glass,’ in which the various elements responsible for cation sensitivity would be replaced by oppositely charged counter- parts, for example, 02- by Ba2+, and Si4+ by C4- or Si4- species. The deviation in alkaline solutions from the ideal NernstianS4 response, coupled with the systematic studyS2 of the marked cation sensitivity of electrodes with more than one mole per cent. of aluminium oxide in the glass, led to other com- mercial cation-sensitive glass membrane electrodes (Table I).As the glass electrodes appear to belong to a family of glass compositions, the search for improved electrodes continues, and Stefanac and SimonS6 and Fgrland and ThulinS6 have studied various glass compositions that are sodium selective. Eisenman hasSELECTIVE ION-SENSITIVE ELECTRODES TABLE I COMMERCIAL SELECTIVE ION-SENSITIVE ELECTRODES 63 ~~~ ~ ~~ ~ ~~ ~ ~~ Lower molar* detection Electrode limit Princip a1 in terf eren ts H+ (GI Na+ (S) Na+ (G) NHJ (G)C NH, (Diffusion) Ca2+ (L) Ca2+-Mg2+ (L) Cd2+ (S) Pb2+ (S)a K+.(? K+ ( ) Ag+ (5 P) cu2+ ( S ) d F- ( S ) c1- (S, L, PI I- ( S , P) NO,- (L) BF, (L) c10,- (L) sa- ( S , P) Br- (S, P) CN- (S, P) SCN- (S) 10-14 10-8 10-6 10-6 10-6 10-6 10-8 10-5 10-5 10-7 10-7 10-7 10-5 10-5 10-5 10-5 10-5 10-5 10-17 10-8 10-6 10-6 10-8 OH- a t pH 2: 13 H+ H+, Ag+ H+, Ag+, NHZ, Li+, Na+ Cs+, Rb+ K+, Na+, Rb+, Li+ Volatile amines Zn2+, Fe2+, Pb2+, Cu2+ ~n2+, Fez+, &2+, Ni2+, Baa+, Sr2+ Ag+, Hg2+, Cu2+ Ag+, Hg2+, cu2+ Hg2+ Ag+, Hg2+ OH- S2-, Br-, I-, CN- S2-, I-, CN- S2-, CN- s2-.I- S20g-, S2-, I-, C1-, Br- ClO,, I-, ClOf, Br- I-, c10, T- i None G = Glass; S = Homogeneous solid state; L = Liquid membrane; P = Pungor hetero- a = Normally based on valinomycin. b = The Corning electrode is based on potassium tetra(p-chlorophenyl) borate exchanger. c = The Beckman electrode comprises a solid organic sensor and is 1000 times more d = Orion lead and copper liquid-membrane types now withdrawn because of inferior * These figures will vary, depending on the definition of limit used. geneous type.sensitive to NHZ than to Na+. selectivity performances compared with Orion solid-state counterparts. patented a sodium over potassium electrode glass composition, and his extensive selectivity order study5' has facilitated suggestion~58~5~ for glass compositions pre- dominantly responsive to other univalent ions like lithium, potassium, thallium(1) and silver (I). No commercial multivalent-ion glass electrodes are available, but there are instances of moderately successful investigations. A potassium barium alumino- silicate showed response to alkaline-earth cations in the order: barium > stron- tium > calcium > magnesium, but the selectivity is poor when alkali metal ions are present, thus precluding its use for determining calcium in physiological fluidsg0 An electrode selectively sensitive to iron(II1) and copper(I1) is based on a non-oxide chalcogenide glass of 60 per cent.selenium , 28 per cent. germanium , and 12 per cent. antimony doped with iron, cobalt or nickel.61 Response is observed down to 10-6 M, with Nernstian behaviour over the range 10-1 to 10-5 M.64 MOODY AND THOMAS Homogeneous solid-state electrodes A variety of crystal membrane electrodes with the sensor crystal sealed into the end of a rigid tube of an inert material such as PTFE, has been patented since 1966, when Frant and Ross1 described a lanthanum fluoride membrane electrode. The early patents concern fluoride electrodes with bismuth fluoride62e68 and rare-earth fluoride membrane~.6~*64 Immediately following the fluoride elec- trode, Orion Research Incorporated described other solid-state electrodes respond- ing to chloride, bromide, iodide and sulphide.66s66 The silver halide electrodes are the natural successors of those studied by Kolthoff and SandersS in 1937, who used discs made from solidified silver halide melts.The later Orion Research Incorporated discs are made66s66 by adding a two- fold stoicheiometric excess of silver nitrate to a sodium sulphide solution and, say, sodium chloride of the appropriate molarity. After successive water washing to remove traces of nitrate, the precipitate, an intimate mixture of silver sulphide and silver chloride, is dried at about 110 "C and pressed into disc membranes, which give faster response times and exhibit smaller photoelectric potentials than do simple silver halide membranesg6 While the Ag2S - AgCl discs are believed to be true mixtures, the corresponding bromide and iodide materials might comprise substantial proportions of the compounds Ag3SBr and Ag3SI, formed during the pressing stages.Copper(II), cadmium and lead-sensitive electrodes are also available.67 The membranes are made by compressing mixtures of the appropriate metal sulphide with silver sulphide. Such a mixed metal sulphide electrode records M2+ sample activities in a Nernstian manner and without interference from oxidising and reducing agents.67 The precipitation of an appropriate metal sulphide on to a silver sulphide surface also occurs for copper( 11), cadmium and lead, ion-sensitive elec- trodes, but not for nickel, cobalt and zinc.68 Discs of copper(1) sulphideaQ and copper(1) selenide'O have been studied, but appear to be inferior to the mixed sulphide systems.Hirata, Higashiyama and Date71 found an electrode with a membrane pressed from copper(1) sulphide powder, obtained by heating copper powder and sulphur in the molar ratio of 2 to 1 at between 400 and 800 "C in an atmosphere of hydrogen sulphide, to be selectively responsive to copper(I1). A compressed disc from a mixture of lead, silver and copper( I) sulphides, individually prepared in similar fashion to copper(1) sulphide,7l gives a selective lead-sensitive ele~trode.'~ Contact was made directly to the membrane, which avoided the use of an internal solution. Similarly to the mixed metal sulphide - silver sulphide membrane electrodes, lead selenide and lead telluride mixed with silver sulphide also give a response for lead, although silver, copper(II), mercury(II), iron(III), sulphide and chloride ions interfere seri0usly.7~ A wider range of chalcogenides has also been asses~ed.~*.~~ A silver rod, coated with silver sulphide by anodic oxidation in dilute sodium sulphide solution with added metal nitrate to provide an outer coat of metal sulphide, gives electrodes with rapid selective and Nernstian response to copper(II), cadmium and lead(I1)SELECTIVE ION-SENSITIVE ELECTRODES 66 ions.These electrodes are suitable for end-point detection in potentiometric titrationsss Electrode membranes responding selectively to alkaline-earth cations prepared from alkaline-earth metal stearate doped with another stearate, such as that of silicon(IV), silver, sodium or lanthanum(III), have recently been patented.76 Pressed membranes comprising silver sulphide (32 mole per cent.), lead sulphide (31 mole per cent.) and copper(1) sulphide (5 mole per cent.) with lead sulphate (32 mole per cent.) are used in selective sulphate ion-sensitive membrane electrodes.77 Successful membranes required an applied pressure of 102 000 lb in-* for 18 hours at temperatures of up to 300 "C.While the critical variable appears to be temperature, the pressure of the copper(1) sulphide appears to improve the response time~.7~ Heterogeneous solid-state electrodes It has already been mentioned4 that this class preceded the present surge of interest in selective ion-sensitive electrodes, and for the present purpose includes those electrodes with membranes consisting of active precipitate material dispersed in an inert binder.Their application and study have continued into the period under review, even though they have been somewhat overshadowed by their homogeneous counterparts. Silicone rubber features as the matrix in many of the new electrodes examined, and precipitation procedures for fluorides have been s t ~ d i e d ~ ~ 1 ~ so as to obtain effective membranes. Likewise, Daviesao has considered various parameters of heterogeneous chloride ion electrodes in matrices of the thermoplastic powder component of Tensol Cement No. 3 (I.C.I.). Materova, Grinberg and EvstifeevaB1 have described a fluoride electrode with calcium fluoride in poly(methylpheny1siloxane) resin.The so-called Pungor electrodes are essentially anion-sensitive electrodes, but sulphate and phosphate electrodes of this type have only limited selectivities.8a However, cation-sensitive electrodes based on silicone rubber matrices are some- what different, for example, Coetzee and BassonS3 prepared a caesium-sensitive electrode from caesium 12-molybdophosphate, but thallium(1) and other univalent alkali metal cations interfere. More successful is the copper(I1) ion-selective elec- trodes4 obtained by coating a copper plate or platinum wire with a copper(1) sulphide powder in about 25 per cent. w/w silicone rubber. After heating it at 80 "C, the electrode is conditioned by soaking it in 0.01 M copper sulphate solution for a week.There is no interference from a wide range of cations and anions, but both silver(1) and mercury(I1) interfere by depositing metal on the membrane. The sulphide ion has a significant interference, however, and the sulphide inter- ference can be exploited by using the electrode for this anion.8* A lead(I1) ion electrode has been similarly 0btained.8~ Closely related to the sensors reported by Hirata and Dates4sa5 are the copper(I1) and lead(I1) electrode^^^^^^ in which a mixture of specially prepared silver sulphide and metal sulphide precipitates is mixed with a finely powdered thermoplastic66 MOODY AND THOMAS polymer, such as Lucite 45 or polyethylene, and the membrane is then thermally cast under pressure. The selectivity patterns resemble the Hirata and Date elec- tr0des.8**8~ Selective halide88 and sulphide-sensitive89 electrodes have been simi- larly prepared.A copper(1) iodide membrane, based on a PVC matrix, is responsive to copper(II), copper(1) and to iodide, but the slope for copper(1) is only 40 mV per decade.g0 Liquid ion-exchanger electrodes The most important of the liquid ion-exchanger electrodes is the calcium electrode devised by R o s s . ~ ~ ~ ~ ~ This has superseded other calcium electrodes based on paraffin membranes92 and tributylphosphate - thenoyltrifluoroacetone trapped systems.93 It uses the calcium salt of didecylphosphoric acid dissolved in di-n-octyl- phenylphosphonate; the form of the calcium salt appears to have a bearing on the electrode quality and response.g* Versions of the calcium electrode and those for other ions have been patented.96-101 Barium and strontium ion functions of bis(2-ethylhexy1)phosphoric acid salts in chlorobenzene have been described.lo2 Liquid membranes with salts of dodecylsulphate, tetrapropylene benzene sulphonate, and dioctylsulphosuccinate in nitrobenzene may be used for detecting detergent anions.lo3 Likewise, crystal violet sulphonate, benzene sulphonate, and dodecylbenzene sulphonate ion-associates give useful selectivity and sensitivity to the sulphonate ion.lo4 Picrate ion-selective systems have been examined by Back.lo6 Coetzee and Freiser106J07 have assessed several ion-association extraction systems based on salts of methyltricaprylammonium ion (Aliquat 336s) for their utility in anion-sensitive electrodes.While useful measurements can be made, the electrodes produced were not highly selective. Amino acid responsive electrodes based on their anion salts with Aliquat 336s have been found to be useful for the determina- tion of tryptophane, phenylalanine, leucine, methionine, valine and glutamic acid over the range 5 x l o - 4 ~ to 1 0 - 1 ~ . 1 0 8 Aliquat 336 has also been used as the basis of a divalent phosphate electrode.10g It is also interesting that liquid anion membrane electrodes, formed by benzene solutions of trilaurylammonium and tetraheptylammonium salts of tetrachloro- zinc and tetrachloropalladium(II), are cation-sensitive to zinc and palladium(II), respectively, when the membrane is interposed between aqueous solutions con- taining the metal ions and chloride.110 Selectivity is possible as long as other metal ions either do not form complexes in aqueous solution or form weaker complexes than the metal ion whose anion complex is the counter ion of the alkyl ammonium radical.l1° To overcome certain disadvantages of the above liquid ion-exchanger mem- brane electrodes, the liquid ion-exchanger can be successfully confined within a PVC matrix membrane to give an electrode as simple and convenient as the glass and solid-state membrane types already des~ribed.51,9~,111,~~~ Such c a l ~ i u m , ~ ~ J ~ ~ potassium61 and nitrate112 electrodes are comparable in response with their liquid membrane counterparts.A PVC matrix membrane containing sodiumSELECTIVE ION-SENSITIVE ELECTRODES 67 tetraphenylborate has been used in conjunction with porous glass in a potassium elect rode.113 The functional species in the Orion nitrate-sensitive liquid ion exchanger is tris (subs ti tu t ed o-phenan t hroline)nickel( 11) nitrate . ss~lOO It is , therefore, interesting that a nitrogen - nickel(I1) complex is used for another solid-state type nitrate- sensitive e1ectr0de.l~~ The necessary amino nitrogen groups and nickel are incor- porated in a polymer matrix membrane by polymerising a mixture of phenol, formaldehyde, ammonia and nickel nitrate. The electrode differentiates between nitrate and polyvalent anions such as sulphate and phosphate, but not between nitrate and other univalent ions. Tetra alkyl ammonium nitrates in appropriate solvents have also been used in nitrate ion-selective membrane e l e c t r o d e ~ , ~ ~ ~ J ~ ~ and recently nitron nitrate in benzyl alcohol has been reported to be f~nctiona1.l~~ For a perchlorate selective membrane, Grekovich, Materova and Belinskaya1lS used a toluene solution of tetraoctylammonium perchlorate bounded by cellophane.Ishibashi and KoharaJ1ls however, depend on the more conventional o-phenanthroline, a,a’-bipyridine and bathophenanthroline as sensitive ion-exchangers in their perchlorate-sensitive liquid membranes. The membrane of a nitrobenzene solution of tris(batho- phenanthro1ine)-iron(I1) perchlorate is the most sensitive for perchlorate and shows excellent selectivity for nitrate and iodide.lls A calcium responsive electrode has been described120 and assessed121 in which the membrane is the calcium salt of a dialkylphosphoric acid in collodion.However, Griffiths, Moody and Thomass4 have had little success with collodion matrices for trapping the calcium liquid ion-exchanger. The organic sensor material of the Beckman 39622 potassium122 and 39626 ammonium123 electrodes is contained at the end of a glass insert tube to offset bubble formation at the sensor tip, thus overcoming a disadvantage of some types of membrane electrodes. To prevent protein adsorption, the siliconised glass frit of the Corning Model 476200 acetylcholine-selective electrode is covered with a cellophane film and the silver - silver chloride element immersed directly in the liquid membrane.124 A capillary assembly with the liquid ion-exchanger separated from external aqueous solution is a similar development .I25 The possibilities of coated wire electrodes where the liquid ion-exchanger sensor is contained in a polymer matrix such as PVC and coated on to a platinum wire, have been briefly e~amined,4~-~1 and further developments in this area are likely to produce useful electrodes for micro work and even in vivo monitoring.The interferences by lead(I1) and zinc with the calcium electrode are significantly greater than those observed with the Orion electr0de.4~ Electrodes for polyvalent ions have been rather scarce compared with the relatively large numbers described for uni- and bi-valent ions. One reason is poor selectivity, as was observed in recent studieslo7 of heteropoly compounds in liquid membranes and their response to phosphate126 and of the response127 of the dinonylnaphthalene - sulphonic acid membrane system to various polyvalent cations, including chromium(II1) , lanthanum(II1) and thorium(1V).68 MOODY AND THOMAS Neutral carrier complex electrodes It has been ~ h o ~ n ~ ~ ~ - ~ ~ ~ that certain neutral macrocyclic antibiotics carry a sequence of localised charges (usually lone pair electrons) of sufficient energy to form ion dipole ligands and to give complexes with alkali metal cations.These cationic complexes, electrically balanced by anions, have considerably larger formation constants for potassium than for ~ 0 d i u m . 1 2 8 * ~ ~ ~ , ~ ~ ~ , ~ ~ 4 The parent anti- biotics, such as valinomycin, in nitrobenzene, diphenylether, hexane, octanol, chlorobenzene or bromobenzene can be used as selective potassium ion sensors in an Orion liquid ion-exchanger membrane electrode casing.13sJ36 Other electrode assemblies have also been de~cribed,~~~J~~-~40 and a glass sinter support for solutions of nonactin, monactin, dinactin or trinactin in carbon tetrachloride or benzene is found to be superior to filter-paper, polyethylene film, Thixcin and nylon mesh,ls7 although the sensor trapped in PVC gives effective sensor membranes.'" Potassium electrodes of similar selectivity to valinomycin-based types have also been made142 from cyclic polyethers that have been synthesised by Pederse11,~*~-~4~ but valinomycin is still the most practical sensor.135J39 A recent patentl46 described selective potassium and ammonium ion-sensitive electrodes with (preferably) solid boundary layers containing a macrocyclic compound, a mineral oil, an aromatic compound and a reinforcing lipid.Electrode life can be prolonged by treating the boundary layer with benzophenone or bromodiphenyl ether between ion concen- tration mea~urements.l4~ Another neutral carrier complex sensor, a polyethylene glycol derivative containing twelve ethylene oxide units per mole of barium and two moles of tetra- phenylborate provides the basis for a barium electrode with superior selectivity to calcium over magnesium, but it is slowly poisoned on exposure to ions of c ~ p p e r ( I I ) . ~ ~ J ~ ~ Organic radical-ion salt electrodes It has been shown160J51 that semiconducting organic radical-ion salts function as the active components of solid-state selective ion-sensitive electrodes. Initially, ground salts of the 7,7,8,8- te t rac yanoquinodime t hane (TCNQ) radical, moulded into pellets, were attached to a bright platinum base with graphite paste as adhesive and electrical contact .I50 All surfaces other than the responding one were insulated with a plastic enamel.The copper(I1) selective and silver-sensitive electrodes showed only a few interferences.l50 Subsequent studies with 11,11,12,12-tetra- cyanonaphtho-2,6-quinodimethane (TNAP), 9-dicyanomethylene-2,4,7-tMitro- fluorene (DTP) and 2,4,5,7-tetranitrofluoren-A9, a-malononitrile (TFM) give elec- trodes with improved activity ranges and selectivities for lead(II), copper(I1) and tetraphenylarsonium ions.151 The selective response of electrodes with membranes containing solid perchlorate salts of the radical-cations of several paradiamines show Nernstian behaviour over the activity range of 10-1 to 10-3.s M perch10rate.l~~SELECTIVE ION-SENSITIVE ELECTRODES 69 Electroactive hydrophobised graphite ‘Selectrodes’ Here the ion-sensor consists of a very thin layer of an electroactive material rubbed on to the sensing surface of a plug of graphite hydrophobised with Teflon inserted into a plastic body.163 A stainless-steel contact to the inner surface of the hydrophobised graphite plug obviates the need for an inner reference s0lution.1~~ The ion-sensitive surface can be easily renewed or replaced by materials sensitive to other ions.163 The initial discussion on ‘Selectrodes’ was restricted to silver halide sensors (containing silver sulphide to reduce light sensitivity), but a wider range of sensors gives functional e l e c t r o d e ~ .l ~ ~ - ~ ~ ~ The ‘Selectrode’ has de~elopedl~~-1~7 from a liquid-state precursorlK8-ls0 whose sensor comprised a solution of an electroactive species such as dithizonates, valino- mycin or iodine dissolved in a water-immiscible organic solvent, and which might be more appropriately classified with liquid ion-exchanger membrane electrodes. The novel design principle whereby ‘Selectrodes’ can be made from various electro- active materials and be capable of measuring a wide range of ions does, however, justify the separate classification. Enzyme electrodes Baum has used an electrode with high selectivity for acetylcholinelB1 for determining acetyl cholinesterase.ls2 Rather than monitor substrate consumption, high selectivities can be obtained if an enzyme-soaked matrix is sandwiched between the sample solution and a sensor electrode, which detects one of the enzymatic degradation products.The most important work, pioneered by Guilbault and M o n t a l v ~ , ~ ~ ~ - ~ ~ ~ is based on an ammonium ion-sensitive glass electrode coated with an enzyme-gel (urease-acrylamide), held in place with a nylon net.ls7 Coating with urea protected by cellophane gives an electrode for measuring urease activity.lssJss In these cases, the enzymatic reaction proceeds according to urease CO(NH,), + H20 - 2NHa + CO, (1) with the ammonium ion being detected by the glass electrode. Similarly, other nitrogeneous compounds, such as glutamine, asparagine, and D- and L-amino acids, in the presence of their corresponding enzymes-glutaminase, asparaginase and amino acid oxidase-give ammonium ions whose concentration can be measured by the glass ele~trode.l70-l~~ Enzyme electrodes based on non-glass membranes have been described by Rechnitz and Llenado.174-l76 They covered the polycrystalline sensing element of an Orion 94-06 cyanide electrode with a thin polyacrylamide gel containing im- mobilised p-glucosidase.This modified electrode senses amygladin, as the cyanide ion produced in stoicheiometric proportion to the amygladin in the sample solution70 MOODY AND THOMAS gives the potentiometric response of the electrode system- /3-glucosidase > C,H, - C - H + 2C,H120, + HCN (2) II 0 C,H,- r -H+H,O I OC12H22Oll The cyanide electrode was similarly adapted17, for rhodanese assay- rhodanese S,O,2- + CN- - SCN- + SO;- (3) Plastic electrodes for organic ions Electrodes where only a plastic membrane separates the test solution from an inner solution of 0.1 M potassium bromide and 0.1 M potassium dihydrogenphos- phate in contact with a saturated calomel electrode are difficult to classify.l77 An organic plastic matrix of limited hydrophilicity acts as the gelling component of the membrane.Responses of several membranes, for example, PVC-N,N-dimethyl- oleamide to aqueous tetrabutylammonium bromide, PVC-dioctylphthalate to quaternary ammonium ions, and a nylon-phenol mixed membrane to sodium tetraphenylborate, are described.177 Functional Potential The mathematical relationships that have been derived for the membrane potential of different types of selective ion-sensitive membrane electrodes are largely due to the work of Nicolsky et aZ.178J79 and Eisenman et aZ.142J80J81 For a membrane electrode within a complete cell, the membrane potential, EM + EM/, contributes its share to the over-all cell potential, ECen, which is made up of the various junction potentials Except for EM, which corresponds to the potential arising at the junction of the membrane of the selective ion-sensitive electrode with the test or standardising solution, the remaining contributory potentials are assumed to remain constant.These are the potential, EM,, corresponding to the selective ion-sensitive electrode membrane - inner solution junction ; the inner reference electrode potential, Ex; the reference electrode potential, ERI ; and the liquid junction potential, E,, between the reference electrode and the test or calibrating solution, and in practice, they all remain virtually constant.Hence, E,, is related to changes in EM, although some of the junction potentials, particularly those of the reference electrode, can be t r o u b l e s ~ m e . ~ ~ ~ J ~ Ignoring the mathematical derivation~,l*~J~~--~~~ the selective ion-sensitiveSELECTIVE ION-SENSITIVE ELECTRODES electrode potential, E , with respect to the reference electrode is given by- log [a, + Kti(a3)2’*] 2.303RT E = constant & - zF 71 for a Nernstian response, where the membrane electrode is taken to respond selectively to an ion, i, of activity at and charge z, in the presence of an interfering ion, j , of activity a j and charge y .Kij is the selectivity coefficient. The benefits deriving from this fonnat have been stressed.la4 The constant term incorporates the various junction potentials and a standard potential characteristic of EM, while the second term on the right-hand side of equation (5) takes the positive sign for cations and the negative sign for anions, The e.m.f. response dependence on the logarithm of the activity [equation (5) in the absence of interferent] indicates that E alters by only 2-72 mV for a univalent ion and by 1.36 mV for a bivalent ion for a 10 per cent. decrease in the activity of the primary species, and by only 2.45 mV for a univalent ion and by 1.23 mV for a bivalent ion for a 10 per cent.increase in the activity of the primary species.@J86 These figures mean that a sensitive voltmeter responding to 0.1 mV or better must be recommendedla5 for work of acceptable precision. Although equation (5) indicates that calibration slopes should be 59/z mV at 25 “C, this is far from universally true, although slopes are normally within 2 to 3 mV of the Nernstian value. This is no inconvenience as long as the particular calibration slope does not change with time. However, because calibration slopes are frequently non-Nernstian, a more appropriate general form of equation (5) is where S is the calibration slope. The near-Nernstian calibration slope of selective ion-sensitive electrodes normally embraces a wide pIon range, and in the absence of interference extends down to about l o - 5 ~ (pIon = 5 ) for many liquid ion-exchanger and solid-state membrane electrodes (Table I).Liquid membrane electrodes frequently have shorter calibration ranges.ls2J86 On the other hand, the notably longer range of the solid-state sulphide electrode makes it eminently suitable for monitoring sulphide ion in the paper and pulp i n d ~ s t r y . ~ ~ ~ J ~ ~ Higher calcium activities of test solutions can be monitored provided the electrode internal solution is suitably matched, but this is at the expense of loss of Nernstian behaviour.189 The fact that the range of response of selective ion-selective electrodes can extend to 1 0 - s ~ and beyond is analytically useful, for even the 1 0 - 6 ~ level corresponds to 0.19 p.p.m.of fluoride, 1.27 p.p.m. of iodide, 0.40 p.p.m. of calcium and 2.07 p.p.m. of lead. It has been suggested that these calibration ranges can be extended by using ion buffers in a manner similar to high capacity buffers used when calibrating pH electrodes. Such a method has recently been describedl90 for a precipitate-based copper(I1) ‘Sele~trode’l~~ where the linear near-Nernstian72 MOODY AND THOMAS calibration range of the electrode could be extended to lO-l3 M with appropriate copper-based buffers.155 The buffers have been used for intercomparison of the copper(I1) 'Selectrode' with the corresponding Orion, Beckman and Radiometer solid-state membrane copper(I1) electrodes.15s A set of cadmium buffers has been used for calibrating a cadmium 'Selectrode' activated with cadmium sulphide - silver s~1phide.l~~ Parallel to the above is the use of precipitates in equilibrium with the appro- priate i0n,~6~"J~~ similar to the saturated solutions of silver halides used by Havas, KaszLs and VLrsanyi.lgl These have low buffer capacities owing to changes in solubility or complexation by any one of several parameters.26 With sufficient dilution of sample or standardising solutions the calibration slope ceases to be near-Nernstian and then usually decreases within a pIon unit or so to near zero.It is true that measurements can be made within this 'break' region, but in view of the above comments concerning precision, measurements near detection limits should only be a matter of last resort.In this context it is interesting to recall lower detection limits based on complexation studies. Thus, Mesmer,lg2 while studying beryllium - fluoride complexes found the lowest detect- able fluoride concentration in 1 M sodium chloride solution to be 7 x 10-8 M, while Baumannls3 found that the near-Nernstian response of the fluoride electrode extends to 5 x M in the presence of thorium and zirconium, 8 x 10-7 M in the presence of lanthanum and 3 x M in the presence of perchloric acid. These are to be compared with only 4 x M as the 'break' in linear response in pure fluoride solutions.193 Speed of Response Next to range and precision, the important point about selective ion-sensitive electrodes is that they respond in real time,20J21~194--201 and descriptions of new electrodes usually detail response times. 51~94~111~112~122~139~202*203 Generally, liquid ion-exchanger membrane electrodes respond more slowly than the solid-state type, but the temperature of the fluid in which the ionic species is being measured has a strong effect on the dynamic response, especially near the lower end of the operating temperature Even solid-state electrodes, particularly the heterogeneous membrane type,89 can give sluggish response.The copper(1) sulphide in both a lead72*205 and a sulphate ion77 electrode is claimed to speed response. Perhaps rather too much emphasis has been placed on response speed; this is certainly so for the direct potentiometric determination of activity where response times of some minutes are quite tolerable.However, automatic analysers and continuous-measurement cells require sensors with more rapid response, and times of minutes are too long for kinetic work and potentiometric titrations. Transient phenomena are also relevant in studying mechanism of response, and are reviewed below. Response times are usually measured, either by immersing the electrode in theSELECTIVE ION-SENSITIVE ELECTRODES 73 solution and recording the time to reach equilibrium, or by injecting a solution of appropriate concentration into the system in which the electrode is already immersed. This latter dynamic method approaches the conditions of continuous monitoring noted above, and response times under these conditions are normally much less than those required to reach static equilibrium.For example, a nitrate electrode with a PVC matrix-membrane equilibrates within 1 second when the activity of the solution with which it is in contact changes from 0.9 x 10-2 M to 0.44 x 10-1 M; transferring the electrode from one solution to another requires at least 1 minute for its equilibration.l12 The longer static times partially arise by the ‘upset’ imposed on the electrode by the removal of previous extraneous liquid (by wiping) before immersion.l12 However, even with these static conditions the nitrate electrode is reported to reach 95 per cent. of its equilibrium value in a matter of seconds.l12 The attainment of equilibrium potential can be monitored by a chart recorder, but various w 0 r k e r ~ , ~ ~ ~ ~ ~ * - ~ 0 ~ ~ ~ ~ 3 have used an oscilloscope for times in the milli- second range.Many workers report response time data for potential readings within 1 mV of the equilibrium value.139~202~203 This is a very useful feature, for such times are usually a mere fraction of the full equilibration times and can provide suitable guides for continuous monitoring and potentiometric applications.& Indeed, where full equilibration times are long, the ‘1-mV times’ can be short enough for a rapid potentiometric titration rather than the intermittent start and stop of the burette system that is sometimes necessary2O8 in automatic systems so as to permit equilibration near the equivalence point. Response times in mixed solutions are of the same order as those of single component so1utionsSl~gQ~112~207 unless serious interferents are involved.61J11 Electrode response is very steady during stirring.111.121,122,197.207-209 Without stirring, longer times are needed to reach the expected potential,202 an inconvenient feature with small sample volumes.202 Base-line noise levels of recorders are generally only important at low activities.122 Notes of caution on stirring concern reproducibilityJ210~211 differences in potential response between stirred and un- stirred solutions209 and different stirring rates.121Jg7 For example, differences of 0.4 and 6mV have been observed209 with an Orion 94-49 fluoride electrode for 10-1 M and 10-9 M fluoride solutions, respectively, although at high ionic strengths, for example, in 1 M sodium nitrate, no such differences are evident.209 The inconvenience of long response times can be overcome with Orion Time Response Paper, which gives the solution concentration after a relatively short time from a predicted ‘time-equals-infinity’ millivolt reading.212 An interesting transient phenomenon with some sodium glass electrodes is the brief response to changes in hydrogen ion and potassium ion activity.212 On a transient basis, the electrode shows about equal selectivity for potassium and sodium.212 Conditioning and Storage Like glass electrodes, the new-generation selective ion-sensitive electrodes74 MOODY AND THOMAS frequently need pre-conditioning.Thus, copper(1) sulphides4 and lead sulphide86 impregnated silicone rubber membranes only develop stable potentials when previously stored in solutions of the appropriate ions for some days.Similarly, the Corning potassium electrode needs to be aged in solutions of similar composition to the test solution so as to avoid long response times and hysteresis effects.213 It has also been suggested that sodium-responsive glass electrodes be calibrated in sodium solutions containing the ions of test samples.21* Electrodes can be reconditioned to recover from deterimental circumstances ; for example, liquid ion-exchanger calcium and nitrate electrodes take at least 1 hour to regain proper response potentials to pure calcium chloride solutions after their exposure to zinclll and perch1orate,ll2 respectively. However, restoration of shorter-life PVC matrix-membrane electrodes, such as the potassium electrode,61 cannot be effected by soaking in the original liquid ion-exchanger, although Simon216 greatly extended the lives of valinomycin - PVC sensor matriceslu by similarly soaking in valinomycin solution.The more robust solid-state electrodes also deteriorate in adverse circumstances; for example, after exposure to interfering levels of thiocyanate, silver bromide electrodes become coated with silver thiocyanate, which can be removed by simply wiping or cleaning with a toothbrush and toothpaste.216 Radiation Stability A few studies have been made of the gamma radiation stability of selective ion-sensitive electrodes (Table 11). Usually, the electrodes give essentially the same calibration slope, activity range and response times as they did prior to irradiation.TABLE I1 GAMMA RADIATION STABILITY OF SELECTIVE ION-SENSITIVE ELECTRODES Cobalt-60 gamma Electrode radiation dose Remarks Reference Orion 94-09-fluoride 15000 rad min-1 Orion 92-07-nitrate 15 000 rad min-l Glass 15000 rad min-1 PVC-calcium 6.5 x loa rad PVC-nitrate 1.6 x los rad PVC-potassium 5.1 x lo8 rad over 16 h over 24 h over 68 h Erratic shift after 5 x 10' rad, 217 but slope remains the same Small negative shift in constant 217 term a t los rad 6 to 15-mV shift in constant 217 term after lo7 rad No effect 94 No effect 112 218 16-mV negative shift in constant 61 term (possibly a day to day effect)SELECTIVE ION-SENSITIVE ELECTRODES 75 Glass electrodes are unaffected after they have been immersed for 2 weeks217 in a 244Cm solution of 3 x log a s-l ~ m - ~ activity.Kubota217 established that the major cumulative change following a large gamma radiation dose is associated with the radiation stability of the internal reference solution. Thus, the Orion nitrate electrode studied became erratic after 107rad, but replacing the internal standard with a fresh solution restored it to normal behavio~r.~l~ The reference solution of a glass electrode, usually 0-1 M hydrochloric acid, is relatively stable,219 and neutral alkali chloride solutions or fluoride in the millimolar concentration level are unaffected by long exposure.217 Glass pH and silver - silver chloride reference electrodes are affected by sun- light and ultraviolet r a d i a t i ~ n . ~ ~ O - ~ ~ ~ Normal function is gradually restored on removal of the radiation.Stability of Response Steadiness and reproducibility of electrode response are important in respect to the frequency of re-calibration and suitability for continuous monitoring. Some electrodes have very low drift ; for example, a urea-specific enzyme electrode166 can be stable to & 0.2 or to 0.05 mV, according to conditions. A Beckman potassium valinomycin electrode ‘did not produce a noticeable drift’ when checked daily while being continuously soaked for 10 days in M potassium chloride,122 although variations of up to & 2 mV were recorded after 10 days when compared with the initial response. Data47n207*22a for the well established and widely used Orion 9449 lanthanum fluoride electrode indicate a similar f 2 mV drift, although Srinivasan and Rech- nitz209 report up to 7 mV drifts depending on stirring and activity conditions, the response being steadier at high ionic strengths. Design demands of miniaturisation can lead to specification change; for example, for a fluoride micr~electrode,~~~ the daily zero potential varied by about & 20 mV, while the depth of immersion had little effect on the potential, the e.m.f.shift being about -2 mV over the 1-mm length of the exposed lanthanum fluoride crystal. Drifts of 2 mV may seem insignificant, but are sufficient to cause errors of several per cent. Frequent re-calibration of selective ion-sensitive electrodes is therefore essential,d3 especially for liquid ion-exchanger electrodes for which daily drifts of over 2 mV have been reported.111J12p226 These even extend to 70 mV for an Orion 92-07 nitrate electrode.226 The larger drifts tend to lead to suspicions concerning electrode assembly, and Potterton and Shults202 have commented on significant variations between different assemblings of an Orion nitrate electrode and between different electrodes. A drastic change in calibration slope can often be related to some malfunction of the reference electrode, whereas failure of a functional selective ion-sensitive electrode is generally more gradual, being manifested as a decrease in the calibra- tion slope.Interference by ions of the same charge type as those to which the electrode is76 MOODY AND THOMAS selectively responsive is unfortunately a feature of selective ion-sensitive electrodes and is considered later.It is, however, reassuring to note that ions of different charge type do not usually affect the response. Thus, ammonium, calcium, copper(II), lanthanum and silver nitrates can be used to calibrate nitrate electrodes without any apparent fear of cation interferen~e.ll~~~~7 Similar conditions also hold for the fluoride ele~trode.20~ Effect of Temperature Light and Swartz203 obtained good agreement between experimental and calculated values (-0.4 mV deg.-l) for the temperature coefficient over the 25" to 60 "C temperature range for the response to silver ions by the silver sulphide electrode, but the agreement was poor for sulphide ions,203 with the theoretical value being - 0.03 mV deg.-l compared with an experimental figure of & 0-05 mV deg.-l The discrepancy is attributed to the uncertainty of the activity coefficient of sulphide ion in molar sodium hydroxide.203 Temperature coefficients of the standard potentials of halide membrane electrodes have been compared with those of the corresponding electrodes of the second kind, and such coefficients depend on membrane ~ h a r a c t e r .~ ~ ~ > ~ * ~ Practical application of selective ion-sensitive electrodes ought to aim at constant temperature conditions, and many authors have commented on the similarity of the calibration curves at various temperatures (except for the expected slight variation in slope). There are many instances8q.85.112.198 of electrodes being used up to 60" to 70 "C. Temperature has been found to significantly influence the dynamic character- istics of liquid membrane electrode~.~04 Interferences and Interference Assessment Table I summarises the main instances where the commercial selective ion- sensitive electrodes have difficulty in exercising selective response.It is clear from this list that specificity is exceptional; where there is a complete lack of selectivity for certain ions in the presence of more preferred species, electrodes can be exploited to monitor the preferred interferent ions; for example, cyclohexylammonium ions instead of calcium,230 perchlorate instead of nitrate,231 and perrhenate or thio- ~ y a n a t e ~ ~ ~ instead of nitrate and perchlorate. It must be remembered that glass electrodes are not completely selective to hydrogen ions, and errors caused by sodium ions and certain standard buffer solutions are still the subject of s t ~ d y .~ ~ ~ s ~ ~ * Con- siderable effort has, therefore, been devoted to assessing electrode performance, usually in terms of the selectivity coefficient, K i j , as defined by equations (5) and (6). The methods ~ ~ e d ~ ~ ~ ~ 2 ~ 5 ~ ~ ~ ~ are based on e.m.f. measurements either in separate or, more realistically, in mixed solutions of the primary ion, i, and interfering ion, j . The two separate-solution methods with the solutions producing e.m.f.'s (El) and (EJ, involve either equation (7) or (8) depending, respectively, on equality ofSELECTIVE ION-SENSITIVE ELECTRODES the primary and interferent ion activities and of the e.m.f.'s ( 2 . 2 & ) = logKij+ (;- 1) logai 77 (7) a, = K,j(aj)zlu (8) The left-hand side of equation (7) takes the positive sign for cations, and the negative sign for anions.The second term on the right-hand side disappears when the charges of the primary and interfering ions are equal. Although Kij values have been obtained for separate solution systemsJl1l~2o3 they are not typical of operating conditions and a more common procedure is to measure the e.m.f. in solutions containing a fixed amount of interference, j , with varying activities of the primary ion, i, for which the electrode is designed. The general idealised pattern43**5s67 involves the calculation of Kij by equation (8), the values of ai and aj being those appertaining to the intercept of that part of the calibration curve (of zero slope) corresponding to complete interference by the interferent with that of Nernstian or near-Nernstian slope corresponding to a more or less unfettered response by the primary ion, Equation (8) represents a special case ( x = 0.5) of the equation used by Whitfield and Leyendekker~~~~ to relate Kij to the solution and membrane phase ion-exchanger compositions.The symbol x represents the mole fraction of sites occupied by the i ions, and (1 - x ) the mole fraction of sites occupied by j ions. Equation (9) combined with equation (6) gives E = constant & (Slog ai - S log x ) (10) a form used by Whitfield and Leyendekker~~~' to present selectivity isotherms for the calcium chloride - sodium chloride - water system over a range of solution ionic strengths (0.03 to 6 M) for the Orion 92-20 calcium electrode.This equation, being concerned basically with available sites occupied by interfering ions, gives selectivities of considerable variation according to solution composition and to ionic strength. 237 The benefits of universal and consistent adoption of K i j for listing selectivity data cannot be over-emphasised,ls4 and ShatkayB8 pointed out the confusion that can arise from haphazard values. Inconsistencies , particularly in some manufacturers' literature, can only bewilder both readers and users. The recom- mended system184 consistently indicates that when Kij < 1, the electrode pre- ferentially responds to the primary ion, i. However, care should still be taken Over the interpretation of selectivity values, for selectivity varies with the relative primary ion - interferent ion activities. Thus, for the PVC-type calcium- sensitive electrode,'ll the value of 0.024 for Kcam at a high magnesium content78 MOODY AND THOMAS (am = 5 x 10-3 M), suggests a better selectivity than 0.222 at a lower magnesium level (aMs = 4.3 x 10-5~), while in fact the electrode gives the most extensively useful response at lower magnesium levels.This illustrates the importance of quoting the activity of the interfering ion corresponding to each Kij value.ls4 In this instance, the results obtained from using equation (8) show that the electrode is unlikely to be useful below an activity of 1.2 x 10-4 M calcium in the former case, while 9 x 10-6 M calcium is suggested as the cut-off point in the latter.The considerable variation of selectivity with interferent concentration is also illustrated by the work of La1 and Christian with the Orion 92-82 lead239 and the Orion 92-19 potassium240 electrodes. The former paper emphasises the modifying natured3 of the power term in equation (8). It is this feature which shows that the lead electrode has nearly the same useful range in the presence of M sodium (down to 8.9 x M calcium (down to 2.5 x M lead) even though the respective K i j values differ enormously (Kpb,, = 8.9 x lo6 and KPbCa = 25). The extensive useful range permits potentio- metric titrations of lead ions to be made,239 while a high response to the sodium and potassium salt titrants would hardly permit such an application. An alternative mixed-solution method of expressing selectivity involves varying the interferent activity at a constant primary ion a ~ t i v i t y , ~ ~ * ~ ~ ~ * and is generally used for assessing hydrogen ion and hydroxide ion interference.Several diagrams expressing the constancy of e.m.f. response over a pH range have been p ~ b l i s h e d . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ These confirm that, unless there are unusual features, it is adequate to quote that pH range for which there is unlikely to be interference with electrode behaviour for a particular level of primary ion. Equation (6) can be used directly for calculating Kij values51~67~241 at constant ionic strength, but with various primary ion levels (ai) and a consequent adjust- ment in interferent activity (aj). For Orion liquid membrane ion-sensitive electrodes, Srinivasan and Rechnitz236 used two rather complicated equations, the general form of the one for high K i j values being M lead) as it has in the presence of and that for low Kij values being As before, the positive sign is used for cation-sensitive electrodes and the negative sign for anion-sensitive electrodes.The a values refer to El, and the a’ values to E,. For high Kij values, the calculated value of the left-hand side of the equation is plotted against the powered interferent activity term, (ajl)z’”, whereas for low K i j values the calculated value of the left-hand side of equation (12) is plotted against the term in square brackets on the right-hand side of the equation.SELECTIVE ION-SENSITIVE ELECTRODES 79 In each case linear plots of slope Kif are obtained, but there is little to commend such complicated functions when the desired information can be obtained more easily. The interference mechanism of solid-state electrodes differs from that of liquid ion-exchange and glass electrodes in the manner in which the primary ion and inter- fering ion, or ions, gain access to the all-important membrane.45 This has led to criticism concerning the application of the above separate solution methods for determining the selectivities of precipitate-based selective ion-sensitive elec- t r o d e ~ , ~ ~ ~ ~ ‘ ~ and it has been suggested26s242 that the defects account for the doubtful quality of certain experimental selectivities of precipitate-based e l e c t r o d e ~ .~ ~ ~ J ~ ~ Equation (8) has, however, been used with mixed-solution data for obtaining ‘measured’ selectivities of halide electrodes for comparison with those calculated from solubility product ratios.242 This highlights a common form of interference of crystal membrane and precipitate-impregnated membrane electrodes arising from the interfering ion actually reacting at the membrane surface to form a new in- soluble cornpo~nd.26~~16~242-2~ For this kind of interference, information on the solubility products of both the membrane salt and the new insoluble compound allows predictions of electrode utility to be made.For e ~ a m p l e , 4 ~ J ~ ~ the selectivity ratio, KBrsCN, for thiocyanate interference of the silver bromide electrode, is the ratio of the solubility products of silver bromide and silver thiocyanate.This implies that for the electrode to be functional to bromide in the presence of thio- cyanate, the ratio of interfering thiocyanate to the bromide activity must not exceed the ratio (solubility product of AgSCN)/(solubility product of AgBr). Of course, the inverse relationship holds when the electrode is to be used for thio- cyanate in the presence of bromide interference, the formls4 of the selectivity ratio then being KSmBr. Interference with solid-state electrodes also occurs when the membrane material reacts with the interferent to give a soluble complex, and Boch and Strecker2P6 have examined the effect of substances that may form complexes with fluoride ions. The behaviour of an electrode is also governed by whether the inter- ference is caused by precipitation or complexation.246 In addition there is the possibility of a slight chlorate and nitrate interaction on the Orion iodide selective electrode beyond the anticipated salt-induced alteration of the activity of solution iodide.247 Complexation has been exploited in adapting silver halide membranes as cyanide electrodes.85J99~21~~248~24g Doubt has been expressed on whether the equilibrium alone determines the electrode response,26 and it has been suggested250 that the simple precipitation exchange also plays a role. AgX +2CN- + Ag(CN); + X- (13) AgX + CN- + AgCN + X- (14) It is worth noting that the cyanide ions may leach silver iodide from the80 MOODY AND THOMAS electrode membrane; in a mixed silver sulphide - silver iodide membrane, this leads to a porous silver sulphide diffusion barrier250 and the response of the electrode can be interpreted in terms of the mass transfer of species through the barrier and of the above equilibrium con~iderations.~~O~~~~ Dissolution of the membrane can also be regarded as being responsible for ‘high’ fluoride readings45~207~218 by the lanthanum fluoride electrode in the presence of citrate in dilute fluoride solutions.However, true interference cannot be ruled and a fluoride release mechanism cannot be satisfactorily reconciled with hydroxide interference of the fluoride electrode.207 It also seems unlikely207 that its methyl group. Finally, it must be remembered that all foreign ions affect the ionic strengths of solutions to various degrees and in turn affect the activity of the primary ion.This is well illustrated by the study208 of ionic strength effects on the response of a fluoride electrode to 10 p.p.m. of fluoride. Such effects are considered at greater length when activity considerations are discussed. acetate interference is due to hindrance of the sensing exchange pr0cess~62~~~3 b Y Mechanism of Selective Response The clarification of electrode response mechanism26 and of the behaviour of membranes as electric circuit element~~5~ is still very much in the early stages. Nevertheless, interesting proposals have been made and certain experimental evidence has an important bearing on the development of acceptable theories. Thus, prolonged electrolyses in glass electrode bulbs filled with tritium-labelled sample solutions show that hydrogen ions do not penetrate the glass membrane.2& On the other hand, the permselective membranes of europium-doped lanthanum fluoride and silver sulphide have been used for the electrochemical generation of fluoride256 and silver(1) i0ns,~~7 respectively, and illustrate the solid-state transport of ions through a permselective membrane.Glass electrodes The long-standing view that the glass membrane was completely permeable to hydrogen ions was disproved by Schwabe and Dahms.256 Nevertheless, during the potentiometric measurement some small current must flow through the glass membrane. The charge can be transferred across the solution - hydrated layer interface by ion-exchange and within the hydrated layer by diffusion.58 An ionic mechanism has been proposed for the dry glass portion that consti- tutes the greater bulk of the membrane, which involves the cationic species of lowest charge available in any given glass.58 No single sodium ion (for sodium silicate glass) moves through the entire thickness of the dry glass layer.Instead, the charge is regarded as being transported by an interstitial mechanism where each charge carrier merely needs to move a few atomic diameters before transferring its energy to another carrier.SELECTIVE ION-SENSITIVE ELECTRODES 81 Resistance measurements provide a check on the utility of glass composi- t i o n ~ , ~ ~ ~ but specially designed a.c. and d.c. measurements under well defined ~ o n d i t i o n s ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ indicate that the resistance as well as the time-constant of a glass membrane can be separated into one part originating in the glass body and another in the surface.The glass body time-constant is in the millisecond range, while the surface glass time-constant is of the order of tens of seconds at room temperature.261n262 It has been suggested that when the electrodes behave ideally, the surface resistance of a hydrated electrode is predominantly located at an inner phase boundary between the gel layer and the glass bulk and arises from slow reactions located at this bo~ndary.~83#264 The flux of lithium ions from the glass bulk out to the solution was found to be proportional to the reciprocal of the surface resi~tance.~e* Compatible with the lack of water and hydrogen ions in isopropanol is the glass gel layer ceasing to increase in thickness when the elec- trodes are transferred from redistilled water into the organic s0lvent.~6~ Clearly, events in the hydrated gel layer surface have an important bearing on response and selectivity.Its structure is deemedm6 to be responsible for glass electrode errors, but leaching studies266 of surface layers could be fruitful. Both the kinetics of the ion exchange processes and the diffusion mobilities of ions in this layer are essential for a complete understanding of the time dependence of electrode response.2s1 Eisenman's works8 on the thickly hydrated surface of NAS 274 glass potassium electrode is of relevance, and a ten-fold selectivity that was observed for potassium relative to sodium ions was considered to be the net result of a hundred-fold ion-exchanger preference for potassium over sodium ions opposed to a ten-fold lower mobility of potassium than of sodium ions.The fact that calcium ions have a very low mobility in the hydrated glass surfacem.60 is in accordance with the generally poor mobility of divalent ions in zeolites as well as in dry glass, and suggests that this causes the poor selectivity of such solid ion-exchangers for divalent cations. In addition, tracer experiments show6* that the initial rapid rate of exchange of calcium for sodium ions at glass electrodes decreases markedly as the exchange progresses. Rechnitz and Kug1erlg8 suggest that this might account for decaying transients (about 100 ms) for calcium and strontium activity measurements obtained in the presence of lo-* M potassium ions to provide a stable background potential, and at pH 9 to suppress the hydrogen ion response of the glass electrode.Solid-state electrodes It has been emphasised that differences between the heterogeneous (Pungor type) electrodes and the homogeneous single and pressed crystal type is a matter of composition and not of mechanism and electrode re~ponse.2~-~6?6~ These classes are, therefore, considered together. However, the particulate nature of the precipitate in the heterogeneous membranes could impose additional parameters, such as surface conduction processes through the interface between dispersed solid and inert rnatri~.~'82 MOODY AND THOMAS Response mechanisms in solid-state electrodes have been based on direct ion-transport through the membrane and on a process whereby different ions take part in the ion-transport process from those that partake in the surface equilibria.26 The ion-transport process in lanthanum fluoride and silver chloride is attri- buted to either cation or anion, usually depending on which has the smaller charge and smaller ionic radius.This is suited to the lattice defect conduction mechanism in which the mobile ion moves into an adjacent lattice defect position267 LaF, + vacancy ._c, LaFt + F- (15) Other ions of different dimensions and charge are unable to move in this fashion and cannot participate in the conduction. Interference is not usually caused by the foreign ions entering the crystal lattice, but by chemical reactions such as complexation and precipitation at its surface.Selectivity is by this entry restriction of all ions except the one of analytical concern. However, if i a n d j are of the same size and charge, for example, fluoride and hydroxide ions, then interference can arise by competitive conducti~n.~~ In all this, surface ion-exchange reactions must not be overlooked.26s.268 Buck’s theory,269n270 in terms of the membrane potential comprising interfacial and diffusion contributions, was based on the respective assumptions of rapid and reversible ion-exchange at membrane interfaces and of mobile defects within the crystal membrane. Radioactive measurements12 showing a fast exchange rate of iodide ions on silver iodide dispersed in a silicone rubber matrix strengthened Pungor’s view concerning the leading role of the surface ion-exchange reaction over the ion-transport element.20e26 Impedance measurements also support the surface exchange theory.271 Here, the lanthanum fluoride electrode belongs to the category of two frequency variable impedances in series, one of which is suggested to be due to a surface film of lan- thanum hydroxide, while the other is due to lanthanum fluoride it~elf.~7l Studies of crystal composition and resistance272 are possibly relevant in this context.There was no film impedance for silver chloride, but surface ion-exchange equilibria are again believed to be important.271 For silver bromide, silver iodide, silver sulphide and the divalent metal sulphide - silver sulphide membranes, there is no net ion-transport across the mem- brane cell.271 Coupling between the membrane and solutions is reckoned to have a capacitance effect, that is, an electric field charge accumulates on the ~urface.~7l Of course, the above theory has to be reconciled with the electrolytic genera- tion of fluoride and silver(I)256e257.However, radioactive tracer studies with 18F indicate that the lanthanum fluoride electrode responds to changes in fluoride concentrations by a rapid exchange polarisation at the membrane surface accom- panied by conduction, probably involving a Shottky defect mechanism, and that the actual diffusion of fluoride ions into the bulk of the membrane is ~mall.~73 The divalent metal (M) electrode membranes comprise a metal sulphide (MS) - silver sulphide mixture, the latter providing silver ion conducting path-SELECTIVE ION-SENSITIVE ELECTRODES 83 ways.67~72D7~~86,20~~271 The ultimate silver ion activity level in any non-silver ion sample (due to the finite membrane solubility) is governed by the equilibrias7 MS(s) + M2++S2- Ag,S(s) + 2Ag+ + S2- and and is given by = d % + ( K * ~ g , 8 / K a ~ 8 ) Such mixed sulphide electrodes record M2+ sample activities in a near-Nernstian manner 2.303 RT 2F 1% %+ E = constant+ and without interference from oxidising and reducing agents provided certain conditions, including those of solubility products, K,, are fulfilled.67 Metal chalcogenide - silver sulphide sintered membranes give more sensitive electrodes than do compacted membranes." Liquid ion-exchanger electrodes A general theory of liquid membrane electrodes based on ion-exchange proper- ties has been presented.268~274-278 Potentiometric response to a given counter-ion depends not only on the activity of the ion in solution and the membrane, but also on the equilibrium constant of the ion-exchange process and the mobility of the ion in the membrane. Selectivity in an electrode can depend on a balancing of the ion-exchange process with the mobility of the ion; this was exemplified above for a potassium- sensitive glass electrode, while extraction criteria and relative ionic mobilities are believed to have their separate roles in electrodes based on solvent extraction systems.60 Eisenman268 points out that the mobility constraint is removed in liquid ion-exchange membranes because the mobility of the undissociated species is likely to be independent of the particular (small) counter-ion bound; that is, the mobility ratio of the undissociated species should be of the order of unity.This means that the potential selectivity of liquid ion-exchangers will be dominated largely by their equilibrium ion-exchange selectivity properties. Of course, this presupposes that migration is the process responsible for the passage of current through the membrane. The similar b e h a ~ i o u r ~ l J l ~ J ~ ~ of electrodes made from membranes of ion-exchangers trapped in PVC-matrices to those with the ion- exchanger supported on Rlillipore and similar filters calls for caution with regard to the interpretation of the actual conduction process.This need not affect the dominating role of equilibrium ion exchange on s e l e c t i ~ i t y . ~ 7 ~ ~ ~ * ~ Impedance measurements show that ionic transport need not be the only process responsible for the passage of electricity through the membrane.270*281 The liquid ion-exchanger membrane cell has been recognised as being equivalent to84 MOODY AND THOMAS a resistance - capacitance network, but the electrode processes involved cannot yet be quantified.%‘ Nevertheless, the net summarised result of the impedance study was that ion transport through a liquid membrane and across the membrane solution interface was by electromigration and by a process for which there is no simple physical analogy. Regarding the role of specificity by equilibrium ion-exchange, recent studies on the parameters of calcium-sensitive PVC matrix membrane electrodes suggest that ion-exchange sites need to be available in the liquid ion-ex~hanger.~‘.~~~ Thus, a more effective sensor was found to be CaH,R,, where R is didecylphosphate, rather than the CaR, required by chemical stoicheiometry.Neutral carrier complex electrodes The theory and mode of operation of selective ion-sensitive membranes based on neutral carriers has been described by Eisenman, Ciani and Szab6.283-286 The neutral carrier mechanism differs from that for ion-exchangers in that charged ion-exchange sites are not present. Instead, the ‘sites’ are neutral molecules that form stoicheiometric complexes with cations and function as carriers for them. The resulting mobile charged complex is regarded as the kind of vehicle that over- comes the barrier to ion movement across phospholipid bilayer membranes.28s Selectivity is determined largely by the specificity of the interactions of ions with the neutral sequestering molecules,ld2 and the principle of conformation-dependent cation binding through ion-dipole interactions has been elucidated by Shemyakin et aZ.28s for valinomycin and enniatin.Also, the selectivity coefficient of liquid membrane electrodes using neutral carriers can be predicted, to a first approxi- mation, from the quotient of the formation constants of the respective metal ions with the carrier.141*287 Several mechanisms have been p r o p ~ s e d l ~ l * ~ ~ ~ for the role of neutral carriers in ion transport through the membrane, According to one model, the valinomycin molecule acts only at the phase interface to enable the ions to pass into the mem- brane, wherein they move as free ions by a ‘pore’ mechanism.A second model explains the enhanced permeability on the basis of ‘canal’ [or ‘channel (stack)’! formation, involving the passage of ions through a canal or stacked channel of ordered valinomycin molecules. A third mechanism involves initial complex formation between the valinomycin and the cation, followed by transport of the ion through the membrane in the cavity of the valinomycin ligand, which acts as a ‘carrier’, while a more elaborate version gives a ‘carrier relay’ mechanism. The ‘carrier’ mechanism is supported by the work of Eisenman, Ciani and Szab6 on the actin type a n t i b i o t i ~ s .~ ~ ~ - , ~ ~ To differentiate between these four mechanisms, Eyal and Rechnitzass measured selectivities with the membrane phase (phenylether solutions of valino- mycin) frozen (at 5 “C) while the aqueous phases were still liquid, and compared the results with those determined in the wholly liquid three-phase system. It was reasoned that the ‘freezing’ should not change selectivities if the ‘canal’ modelSELECTIVE ION-SENSITIVE ELECTRODES 85 were the right one, whereas it should change them significantly for the ‘carrier’ mechanism by decreasing the mobility of the bulky valinomycin molecules in the organic phase. The considerable deterioration in KgNa (from about lo-* to about 5 x 10-l) was more consistent with a ‘carrier’ mechanism in which the bulky complex molecule lost most of its mobility in the frozen membrane phase.14C tracer experiments favour the ‘carrier relay’ type of transport ,1419289 although this could degenerate into a ‘free carrier’ for very thin membranes such as those in biological systems. Organic radical-ion salt electrodes The rapid establishment of equilibrium in the surface ion-exchange reaction noted above is important and appears to have repercussions in the development of interphase potential differences between solid and solution phases with ion-radical salts.lS0 The expectation that such potential would reflect changes in the activities of ions in solution has been fulfilled by the responses of semiconducting organic radical-ion salts as the active components of selective ion-sensitive electrode membranes ,150-152 Activity, Ionic Strength and Concentration Individual activity coefficients of ions The potential of well behaved reversible selective ion-sensitive electrodes reflects the activity of single ionic species [equation (5)].As activity is simply the product of concentration and activity coefficient, the development of these elec- trodes has renewed interest in single ion activity coefficient~.1~3~~~1-~0~ The difficulties of separating the well defined properties of an electrolyte into those for individual ions have been examined by Bates and Alfenaarls3 from the standpoint of selective ion-sensitive electrodes. They stress the well known fact that the activity coefficients of such ions can only be derived from relative experi- mental values on the basis of certain arbitrary conventions relating to the splitting of the mean activity coefficient.One such convention is based on the MacInnes proposal302 asserting the equality of the activity coefficients of K+ and of C1- (fK+ and fa-, respectively) in aqueous solutions of potassium chloride. Another is the international pH convention303 for fa-, which then forms a base for the activitv of coefficients of other ions where A is the Debye - Hiickel slope constant and p the ionic strength given by p = QC cz2 where c and z are the concentration and charge, respectively, of each ionic species present.86 MOODY AND THOMAS The chloride ion activity coefficients of equation (20) are nearly the same as the mean activity coefficients of sodium chloride in its pure aqueous solutions, up to an ionic strength of 0.1 M. This makes the pH convention substantially equivalent to a convention based on the equality of fNa+ and fcl- in sodium chloride solu- t i o n ~ .~ * ~ It is therefore analogous to the use by Garrel~~~O of the MacInnes con- vention as a basis for establishing activity standards for selective ion-sensitive electrodes. That this is suitable is confirmed by the good agreement between the values calculated for feat+ by this convention and those determined with a selective calcium-ion sensitive electrode in calcium chloride solutions of ionic strengths of less than 0.1 M.290 Interrelating activity coefficients on the basis of valence relationships set forth in the Debye - Huckel equation300J03~30* confirms the approximate equivalence of single ionic activity coefficients to the mean activity coefficient f* = f+ =f- for uni-univalent electrolytes and gives the relationship fi+ = f: = f: (23) for 2-1 electrolytes, such as calcium chloride.It is claimed183~300 that this has a sounder theoretical basis than Shatkay's assumption238,291,305 of equating f2+ to f*, and for which experimental verification has apparently ignored liquid junction trncertaintie~.~~6*~07 On this basis it would appear that the direct use of the Debye - Huckel equation for calculating single ionic activity coefficients is accept- The above conventions lead to problems of internal consistency in that multiple pathways to the activity coefficients of single ions exist.183 However, the choice of pathway is not very significant at an ionic strength of 0.1 M, and even though it has been recommended183 that cation-responsive electrodes be standardised in solutions of the corresponding, completely dissociated, chloride salts and that anion-responsive electrodes be standardised in solutions of the completely dis- sociated sodium salts of the anions, completely dissociated salts other than those of chloride and sodium, respectively, do not usually affect calibration.51J12J3g~zo7~2z7 able .51,94,111,112 Activity coefficients at high ionic strength At higher ionic strengths, mean ionic activity coefficients of the alkali metal chlorides differ from one another, and quite apart from differences in other salts, this in itself leads to different values for the activity coefficients of ions according to the pathway considered.ls3 A further characteristic of higher ionic strengths is the minimum in activity coefficient predicted by certain modifications of the Debye - Huckel equation.45 This has been experimentally observed during selectiveSELECTIVE ION-SENSITIVE ELECTRODES 87 ion-sensitive electrode studies on sodium and chloride ion activity coefficients in concentrated sodium chloride solutions both before and after corrections for liquid junction p o t e n t i a l ~ .~ ~ ~ t ~ ~ 3 Standard reference data for the activities of ions to which selective ion- sensitive electrodes respond are under consideration by I.U.P.A.C. but, as indicated above, most authors are fully aware of problems in this area.Regarding the greater problems of higher ionic strength, Bates, Staples and Robinson295 have used the Robinson - Stokes309J10 hydration theory by which it is assumed that water bound to ions is no longer part of the bulk solvent, and that the Debye - Huckel expression [first term of equation (24)] gives the true activity coefficient (mole fraction scale) of the solvated ions -lnfk = Az+z-pt+k In a,+ln[l+0~018(v-h) m] 1+Bdpi v where A and B are constants of the Debye - Huckel theory;309 d is an ionic size parameter; p the ionic strength; a, the water activity; v the number of ions pro- duced by a mole of the electrolyte; and h is the hydration number, i.e., the number of moles of water bound to one mole of electrolyte irrespective of distribution among cations and anions.In extending this theory to provide a formula for dividing into ionic components the mean activity coefficients of certain unassociated chlorides calculated by equation (24), Bates, Staples and Robinson296 assumed that the chloride ion is not hydrated. The resultant calculated values of fNa+ showed good agreement with the measurements of Shatkay and L e r m a ~ ~ , ~ ~ ~ particularly up to 3.0 molal. Individual ionic activity coefficients were thus calculated for seven unassociated uni-univalent chlorides and four alkaline earth chl0rides,~~5 and it is recommended that the treatment would be invalid for solutions with molalities in excess of the following : hydrogen chloride, 1.5 ; lithium chloride, 1-7 ; sodium chloride, 3.4 ; magnesium chloride, 0.9 ; calcium chloride 1.0 ; strontium chloride, 1.0; and barium chloride, 1.6.Despite the recomrnendationls3 that sodium salts be used to standardise anion-responsive electrodes, it has recently been suggested311 that because sodium fluoride is associated in moderately concentrated solutions, potassium fluoride is a more satisfactory reference material for the calibration of fluoride-sensitive electrodes. The activity coefficients of potassium and fluoride ions are reasoned to be equal in solutions of potassium fluoride, that is, fK+ =fr- =f* and standard values of pF ( -logar-) are given for potassium fluoride solutions in the 0-01 M to 3.79 M concentration range.311 Activity coefficients in mixed electrolyte systems In practice, the analytical chemist frequently has to deal with rather more complicated mixed electrolyte systems.Most interest has centred on mixed88 MOODY AND THOMAS electrolyte solutions of biological importance,297-300p312-31s but whatever the system, the primary concern is the variation in activity of one electrolyte in the presence of others. Beyond this, the measurement of ion activity with selective ion-sensitive electrodes has raised the question317 of establishing an unambiguous ion activity scale in a manner analogous to that discussed above. The interaction between ions,318 mainly between those of opposite charge, can lead to a variation of activity coefficients with the composition of mixed electrolyte solutions and thus contradict the Debye - Huckel formula prediction that logf, is proportional to p*.In dilute solutions the conflict is minimal, but at higher con- centrations the influence of ion interactions can among other things alter the significance of the ionic size parameter, d, in equation (24). Moore and Ross313 studied mixed sodium and calcium chloride solutions over a total ionic strength range of 0.05 M to 0.5 M by potentiometric measurements with a selective sodium-sensitive electrode / silver - silver chloride electrode system. In this way, the mean sodium chloride activity coefficient was determined over the range of sodium and calcium concentrations encountered in extracellular fluids. At a constant total ionic strength it was found that logfNacl varied linearly with the ionic strength of calcium chloride in the mixture in accordance with Harned’s rule3l0 logfNaC+~x~arel = logfN.aCl~pore) - a12 pCaClS (26) where -al2 is a constant represented by the slope in a plot of log fNacl (mlrture) against pacl,.The activity coefficients of sodium chloride in solutions containing 5 x 10-3 M calcium chloride were shown to be close to those of correspondingly pure sodium chloride solutions, i.e., the effect of calcium chloride on sodium chloride activity in extracellular fluids would be negligible.3l3 On the other hand, calculations involving the alternative version of Harned’s rule (where - a21 is a constant represented by the slope in a plot of log fcacll against the ionic strength of sodium chloride in the mixture) showed that the activity coefficients of calcium chloride in the mixture were considerably less than those of correspondingly pure calcium chloride solutions, i.e., sodium chloride in extracellular fluids would be expected to exert an appreciable effect on calcium chloride activity.31* However, from studies with an Orion 92-20 calcium electrode on mixed solutions of calcium chloride with calcium nitrate, and with nitrates and chlorides of sodium and potassium, Bagg3l6 concluded that, within experimental error, the mean activity coefficients of calcium chloride in mixed solutions up to an ionic strength of 0-3 M are equal to those that would hold for pure calcium chloride solutions of the same ionic strength.of the sodium activity in sodium chloride - calcium chloride solutions with a cation-sensitive glass electrode showed that Harned’s rule was not well obeyed.However, Butler300 used the rules to present the mean activity coefficients of calcium chloride in sodium chloride - calcium chloride Lanier’sSELECTIVE ION-SENSITIVE ELECTRODES 89 mixtures up to 1.0 molal sodium chloride and 0.05 molal calcium chloride. By comparison with isopiestic data,a20 Leyendekkers and Whitfield314*316 consider that useful estimates of Harned’s coefficients can be made with Orion calcium and chloride liquid ion exchanger electrodes for monitoring changes in calcium chloride activity coefficients in aqueous solutions of calcium chloride - magnesium chloride,31* calcium chloride - strontium chloride314 and of calcium chloride - sodium chloride.316 Other ionic components such as potassium and magnesium, which comprise less than 6 per cent.of the total ionic strength of serum, are said298 to have a neg- ligible effect on the activity coefficient of calcium ion at ionic strengths below 1.0 M. There are also theories and empirical relationships aiming at estimates of activity coefficients in multicomponent ~ y ~ t e m ~ . ~ ~ ~ For example, Leyendekker~~~~ has discussed the prediction of Harned coefficients from ionic entropies, but required more data before he could test the general applicability of the relationships. The same author298 has extended the work of Bates, Staples and R0binson~~6 in single electrolyte systems and derived equations for predicting single ion activity coefficients in sodium chloride - sodium fluoride and potassium chloride - sodium fluoride aqueous systems that compare favourably with potentio- metric values.There is poor correlation between the experimental data and an equation that neglects ion association.298 Butler and H ~ s t o n ~ ~ ~ - ~ ~ ~ studied sodium chloride - potassium ~ h l o r i d e ~ ~ ~ s ~ ~ ~ and sodium chloride - sodium fluoride324 sys- tems, and have shown that cation-sensitive glass electrodes can be used to measure sodium ion activity in concentrated solution.s22 Liquid Junction Potentials An important restraint on the accuracy of ‘experimental’ activities involves the difficulty of precisely predicting changes in reference electrode response182J83 and especially of the liquid junction potential (or diffusion potential) resulting from the junction between the potassium chloride salt bridge and the test solutions in cells of the type Hg/Hg2C12(s)/KCl(sat)/Test sample/Selective ion-sensitive electrode Such cells are not at equilibrium because of the liquid junctions between solutions, where mixing is taking place continuously.Of course, the diffusion potential is minimised if the difference between the transport numbers of cation and anion in the salt bridge is small, as with potassium chloride, and also if the salt bridge concentration is large (as in saturated potassium chloride), providing the test solution concentration is small (< 0.1 M). Even though these conditions are obeyed with good commercial reference electrodes, the liquid junction potential can still vary over a range of test solution compositions and an uncertainty of even a few millivolts can lead to substantial repercussions in activity eval~ation.3~~ P i ~ k n e t t ~ ~ ~ has shown that the liquid junction potential between several dilute electrolytes and saturated potassium chloride obeyed a linear relationship with the logarithm of the specific conductance between M and 10-6 M, the potential90 MOODY AND THOMAS tending to a maximum value of 7.69 mV for the junction between water and saturated potassium chloride.Bates and AlfenaaP3 were concerned with the effect of residual liquid junction potential (AEj expressed in pIon units) that occurred in pIon measurements and which arose from the differences in the concentrations and mobilities of the ionic species in the standard (S) and unknown (X) solutions, and suggested the relationship AEj = pIon(X) + log aIon (X) for estimating AEj.Here pIon(X) is the ‘experimental’ value as determined by cells such as the above, while loga,,,(X) is given by the convention adopted and is referred to as the ‘true’ pIon(X). Leyendekker~~~~ found a linear relationship between AEj calculated by equation (28) and ionic strength within the 0.1 molal and 2 molal ionic strength range for potassium chloride, sodium chloride and ammonium chloride solutions by using an Orion 92-17 liquid ion exchanger chloride electrode for determining pCl(X) in conjunction with saturated calomel reference electrodes. The value of dAEj/dp was 0.043 for both potassium chloride and ammonium chloride and 0.095 for sodium chloride. The Henderson equation for estimating liquid junction potentials326 has been used by S h a t k a ~ ~ ~ ’ for showing that the liquid junction potential between the saturated calomel electrode and aqueous phosphoric acid is approximately con- stant to within 3 to 5 mV for concentrations between lo-* M and 1 M.Its values agree with Baumann’s for perchloric acid levels up to 0-5 M for the junction between 2 M sodium chloride or 2 M ammonium chloride and 2 M (sodium perchlorate plus perchloric acid). In this study, B a ~ r n a n n ~ ~ ~ used a solid-state iodide-selective electrode in the presence of M sodium iodide as the constant half-cell, and this technique paves the way for estimating liquid junction potential changes in other potentiometric measurements. Such work will be valuable in showing how large a separation of pIon(X) and pIon(S) can be tolerated before ‘greater than negligible’ liquid junction errors are encountered.ls3 The difficulty of obtaining a linear calibration between pH and the observed e.m.f. because of the variation of liquid junction potential with composition has led to an assessment of different methods of calibrating glass electrodes in cells with liquid junctions.329 A calibration corrected for liquid junction potential by Biedermann and Sillb’s method330 was found to be the best of those studied.329 Direct Potentiornetry with Selective Ion-sensitive Electrodes Selective ion-sensitive electrodes have been termed nearly ideal measurement tools because of their ability to non-destructively monitor ion activities in solu- ti0n.3~1. They have clearly been useful in activity coefficient studies, but there are also several hundred papers describing analytical applications.These depend either on direct potentiometric measurements based on the Nernstian or near-Nernstian logarithmic relationship between e.m.f. and ionic activity or on potentiometric titrations. The two approaches are discussed separately.SELECTIVE ION-SENSITIVE ELECTRODES 91 Given adequate attention to calibration, the electrodes can usefully be used for many direct concentration measurements, especially at low levels and low ionic strength, where activity problems are minimal. At higher concentrations, precau- tions must be taken against activity and selectivity complications. However, high precision is rarely achieved in direct measurements, for quite apart from liquid junction phenomena, laboratory conditions and lack of stability with many elec- trodes are such that readings to within & 0.1 mV are difficult.This in itself leads332 to an error of 20.39 per cent. in the value of a under Nernstian conditions for an univalent ion. Of course, if the error is random it can, in principle, be made as small as is desired by making a sufficient number of replicate determinations,333 and an accuracy of within 20-2 per cent. has been obtained for silver at the 10-'M level. 33p Interference elimination and ionic strength adjustment In analytical systems, interference effects must be tested at realistic levels, For example, bearing in mind equation (8) there is MO point, when assessing sod nitrate of about 1 0 - ' ~ with 2 M potassium chloride as the extracting agent, in attempting to use a nitrate electrode with selectivity coefficient KNOacI = 4 x 10-8 determined for a chloride level of 0.5 M.In these circumstances, 0.01 M copper sulphate would be a more appropriate e ~ t r a c t a n t , ~ ~ ~ although saline soils high in chloride might require supplementary treatment. Interference can frequently be sidetracked; for example, Milham et aZ.,336 used a rather involved buffer system. Thus, a low pH kept the equilibrium bicarbonate low and the water-extractable organic acids undissociated, aluminium ions complexed the anions of organic acids present, and sulphamic acid destroyed any nitrite quantitatively. An exhaustive examination of the effect of ionic strength is necessary in appraising the analytical scope of selective ion-sensitive electrodes.Conductance monitoring may not always be satisfactory, if only because of the relationship [expressed in equation (21)] that the ionic strength, p = &Em2, where c and x are the concentration and charge, respectively, of each ionic species present. However, Lind337 has shown that specific conductance may be used to estimate the ionic strength of natural water providing the major ionic contributions are known from previous analyses and that dilution is the main variable. Such information is useful for preparing calibration standards of the same ionic strength range as the sample under examination. For example, to determine potassium in sea water, calibration standards are made by diluting synthetic potassium sea water samples with demineralised water.45 Direct measurement on the sample is common, but of course it is only when a sample consists largely of one salt that an activity - e.m.f.calibration plot can be used with any degree of ac~uracy.'~ Such situations are unusual in analytical practice ; hence the constant ionic-background method, as mentioned in the dilu- tion of synthetic sea water, is frequently used. This ensures calibration standards of similar composition to the test solution. Alternatively, where samples exhibit 092 MOODY AND THOMAS considerable over-all variation in composition, an ‘ionic strength adjuster’ is added to both sample and calibration solutions to achieve a common ionic strength.In this procedure, it is intended that the ultimate ionic strength should arise almost exclusively from the ionic strength adjustor and not from the sample itself. This is the basis of the involved buffer system used by Milham et aZ.,336 although it was also a judicious recipe to meet the selectivity parameters of the nitrate electrode. Though virtually any substance may serve as an ionic strength adjuster, it must not complex with the primary ion, and the selectivity coefficient, Kij, with regard to the ionic strength adjuster must be negligible. For this reason, tetra- methylammonium nitrate was chosen in the investigation of calcium complexation with tri- and tetrametaphosphate by use of a calcium-sensitive liquid ion-exchange membrane electrode.338 Certain variations may sometimes be necessary in addi- tion to ionic strength adjustment; for example, pH adjustment will release anions of weak acids.Thus, at pH 10.5 the cyanide ion is present and not undissociated hydrocyanic Similarly sodium citrate in TISAB (total ionic strength adjuster buffer) overcomes the possible presence of complexing cations such as iron(II1) and aluminium(II1) in fluoride determination~.~39 (TISAB contains acetic acid sodium acetate, sodium chloride and sodium citrate.) Suspicions concerning the defects of ionic strength adjusters have been reported with TISAB in the potentiometric titration of fluoride with lanthanum nitrate.3@p3*l Such interference has been attributed330 to the carboxylate content (acetate and citrate) and although acetate is still retained, citrate has been replaced3@ by DCTA (1,2-diaminocyclohexane-NNN’N’-tetra-acetic acid).However, for the direct determination of fluoride, the lanthanum fluoride electrode is only minimally affected by these carboxylate anions.207 Standard addition and subtraction methods The standard addition method provides a way of obtaining concentration by direct potentiometry. Both this and the known subtraction method require a change in the concentration of the primary ion, i. For standard addition (other- wise known as the known addition, or spiking or known-increment method) more i is i n t r ~ d u c e d ~ ~ ~ * ~ ~ whereas in known subtraction the level of i is lowered by adding a complexing agent.344J45 DursV has described a method, analate addition, in which known volumes of the unknown solution are added to a known volume of a standard solution of the ion.There need be no large change of ionic strength in these standard addition and subtraction m e t h ~ d ~ , ~ ~ s ~ ~ s ~ ~ ~ and this has led to a growing interest in their appli~ability.~~Os3~~-~~0 In the standard addition to sample method, the potential, E,, between a selective ion-sensitive electrode and a suitable reference electrode is measured for the sample solution of volume, V,, and total molar concentration, C,, of the species sought where S is the electrode calibration slope, fo is the activity coefficient and xo the E, = constant & Slogxojo C, (29)SELECTIVE ION-SENSITIVE ELECTRODES 93 fraction of uncomplexed ions.A new potential, El, is then measured after the addition of a small volume, Vl, of a standard solution (concentration C,) of ions of the species sought, where C, N 100Co where fl and xl correspond to the new activity coefficient and fraction of free ions, respectively. An essential assumption is that x, - xl and fo - fl. Hence the difference between equations (29) and (30) simplifies to For different volumes, V,, V3, ... of standard giving responses E,, E,, ..., the differences in e.m.f.s are AE,, AE3, . . .. The C, term in equation (31) can be resol~ed*~4~ (32) C, c, = I O f A h l S 1+- -- ( F j 2 with similar expressions being valid for volumes, Vz, V3, . . ., of added standard. tion (32) is349 For sample addition to a standard,346 the corresponding version of equa- where Vo1 is the volume of sample solution added.Kar1berg3d9 has described a nomograph based on equations (32) and (33) for the quick computation of C, and summarises the restrictions affecting its use. These concern constructional factors and items concerned with the chemistry of solutions under examination. The former are straightforward, while the latter are implicit in the principle of the standard addition and sample addition methods. Thus, for the standard addition method, C, > C,, while for the sample addition method, C, < C,. For both methods, x and f must remain constant; the slope of the electrode response curve must be known and be linear, interfering species must be absent and, finally, the liquid junction potential between the reference electrode and the solution must not change.By making two additions (to give readings El and E,) for equation (30), and omitting x and f, C, can be computed333 without prior knowledge of the constant or S. In this procedure, C, is initially set equal to zero and equation (30) solved to give the constant and S. The values are then substituted into equation (29) (x, and fo omitted) and a new estimate for C, made. The process is repeated until estimates of C, converge. The procedure is tedious by hand calculation, but is more simply performed by a computing calculator. For the highest accuracy in the94 MOODY AND THOMAS determination of unknown concentrations, multiple additions are made and a least squares curve fitting used to evaluate the unknown concentration, C,, electrode slope and constant.For this, Brand and R e c h n i t ~ ~ ~ ~ used the Fortran IV computer program ADDFIT and obtained results to within 1 per cent. of the actual value except for lead at about M, but this reflects the difficulties of preparing very dilute solutions. The known-subtraction method depends on decreasing the amount of un- complexed ions by the addition of a complexing agent; reasoning along similar lines to the standard addition method leads to the following version of equation (30) where C, is the concentration of the complexing (or precipitating) agent, 1 : 1 com- plexation (or precipitation) being assumed. There are, incidentally, simpler versions of the standard addition and known- subtraction equations, e.g., equation (31) takes the f0rm~~343-345~351 AEl = &Slog (T) CO + c, (35) when no allowance is made for the volume change arising from the addition of standard; C, is the change in concentration after the known addition stage a d is equal to V,C,/V,.Re-arrangement of equation (35) gives 1 1 (antilog ~ ~ n E , / S ) - 1 for which extensive functional computer tables for both monovalent and divalent ions are available.344 Gran’s plots A ~ e c o m m e n d e d ~ ~ ~ * ~ ~ ~ variation of the standard addition method depends on a modification of the method originally described by Gran35Q and later by other~355-35~ for presenting potentiometric titration data in linear form by using a semi-antilog plot. The principle is apparent in the general antilog version of equation (30) where ‘v is the volume of standard solution added, and f and x correspond to the activity coefficient and the fraction of primary free ions, respectively.The positive sign alternative is used for cation-sensitive electrodes and the negative for anion-sensitive electrodes. A plot of (Vo + V ) . versus V gives a straight line that intercepts the abscissa for a Ve value and where C,Vo = -C,V,. TheSELECTIVE ION-SENSITIVE ELECTRODES concentration of the ion under test, C,, is then obtained from 95 The computation of (V, + V ) .10*”‘S is avoided in the semi-antilog Orion Gran’s Plot PaperJss3 which has been corrected for limited volume changes, i.e., for ( Vo + V ) , so that all that is required is to plot the appropriate potential response on the ordinate against the volume of standard addition, with the intercept on the abscissa, V,, yielding the concentration of ion present in the manner of equation (38).Apart from restriction on volume changes, the Orion Gran’s Plot Paper is also dependent on true Nernstian response by the electrode. Statistical360 and systematic3s1 errors have recently been assessed for the Gran procedure and the theory found to be consistent with the experimental errors determined for a Beckman selective fluoride-sensitive electrode used in measuring a fluoride concentration of 10-4~.3e3 Although the assessment was based on potentiometric titrations, it is to be noted that among the conditions to be satisfied for maximal precision are a precise knowledge of calibration slope and a parity in the concentrations of the standard and unknown solutions. The first condition is implicit in equation (37) , while the second condition is more for potentiometrk titrations as VoCo - VC, is the desirable condition in the direct potentiometry of standard addition procedures.333,313-345.352,383 Titration Procedures with Selective Ion-sensitive Electrodes At higher concentrations, potentiometric titrations are superior to direct potentiometry. However, with selective ion-sensitive electrodes, the development of suitable procedures is fraught with a whole variety of possible pitfalls and lead to errors well outside the range of precision (+Om1 to kO.2 per cent.) normally associated with potentiometric titrations.An intuitive appraisal often suggests that interfering ions will distort a titration curve and cause the inflexion point to differ from the equivalence point.If such points are assumed to coincide, an error will result in the titrati0n.~~~*~~~-360 Apart from interferences, other limiting factors include restricted concentration - activity range and response times of electrodes, the chemical factors of suitability of reagents, relative rates of reactions and the effects of pH and various side rea~tions.4~ The variety of successful titration procedures with selective ion-sensitive electrodes indicates that problems associated with response times are surmountable; for example, it has been reported367 that the time needed for the EDTA titration of calcium or of calcium and magnesium with a calcium electrode as the equivalence point indicator, varies from a few seconds to a few minutes. Even so, the point of maximum rate of potential change does not coincide with the equivalence point, and the over-titration must be caused, at least partly, by sluggish response.Clearly, critical appraisal is necessary for the successful application of selective ion-sensitive electrodes in titration work.96 MOODY AND THOMAS In earlier work, Meites et aZ.368-370 derived important fundamental relation- ships, including the effects of dilution on non-matching of equivalence points and inflexion points in acid - base, precipitation, and chelometric titrations. However, these derivations assumed an ideal indicator electrode and the resulting titration errors were small and probably undetectable experimentally.Titration curves specifically for chelometric titrations of calcium and magnesium with calcium and divalent metal ion-sensitive electrodes have been derived.365*371*372 These were used to assess possible problems of locating experimental equivalence points on both chemical and potentiometric considerations. Distortions of the titration curves were evident in the presence of interfering ions. These could be anticipated, as could the limitations imposed by ionic strength and restrictions in electrode response after the end-point. The actual calculation of titration errors caused by interfering ions has been carried out for pre~ipitation~~~s~~d and chelometric tit ration^.^^^^^^^ When the inflexion point of the titration curve is used to locate the end-point, serious errors (> 1 per cent.) can result for precipitation tit ration^.^^^^^^^ These arise from inter- fering ions in the sample solution or titrant, and there is a lack of symmetry in the titration curve causing the inflexion point to precede the equivalence point.The errors are negligible only in the limit of very sparingly soluble materials or in the absence of interfering ions. Increases in the dilution factor and decreases in sample ion concentration cause greater titration errors. Furthermore, the ion charge ratio [n/m for nA+mT + AnTm($)] becomes important when dilution strongly in- fluences the titration error. Chelometric titration errors are significantly smallerunder equivalent experimental conditions,376 especially when Gran’s method is used.376 The above limitations demand experimental alternatives to end-point detection methods in potentiometric titrations with selective ion-sensitive elec- trodes. Providing the mid-point of the ‘potential jump’ coincides with the equiva- lence point, the normal E versus V titration curve can be used instead of the AE/AV (or A2E/AV2) ve~sus V relationships that are only of restricted application with selective ion-sensitive indicator electrodes.371 Independent estimates by several observers help to avoid bias in the location of this point, or a computer program based on a least squares plot can be used.A further method is based on a plot of AV/AE versus V in which the curves normally consist of two straight lines and intersect each other on the volume axis at the equivalence point.377J78 Three main methods of determining the equivalence point in fluoride - thorium titration curves have been e ~ a m i n e d .~ ~ ~ * ~ ~ O They are the sigmoid form of the curve; differential methods; and methods based on the conditions for mass balance. The mass balance methods were found to be the most reliable and of wider validity. The wider implications of computer treatment of theoretical and practical aspects of titration procedures are also d i s c u s ~ e d . ~ ~ ~ - ~ ~ ~ Many useful hints, including the precision and accuracy of the end-point detection, are given,378-380 with special attention to the Gran technique and for which Orion Gran’s Plot Paper can be used.381 For maximum precision, the standard and unknown concentrations should be close and the electrode slope known p r e ~ i s e l y .~ ~ ~ - ~ ~ ~SELECTIVE ION-SENSITIVE ELECTRODES 97 In the titration of fluoride with lanthanum(III), only points well before the end-point should be considered.382 The Gran plot technique has a special virtue in this respect.383 It permits the exploitation of a larger range of titration data than that obtainable in the vicinity of the equivalence point .378--381 These features are claimed376 to circumvent interference effects in precipitation and chelometric titrations, as the ratio of the sample ion to interfering ion concentration is more favourable early in the titration than at the equivalence point. By using a regres- sion analysis of Gran plots, and with due attention to high resolution in voltage measurements, a large number of readings and linearity of plot, Erikssonss3 obtained results to within k0.1 per cent.and k0.5 per cent. in the potentiometric titration of 0.1 M and 0.001 M fluoride, respectively, with lanthanum(II1). Unfortunately, the titrations take several ho~rs.38~ The above discussion presupposes that the indicator electrode is selectively sensitive to the ion being titrated. However, an additional advantage of potentio- metric titrations over direct potentiometry is the possibility of using the ion to which the indicator electrode is selectively sensitive as the titrant in determining species for which selective ion-sensitive electrodes are not even available.384 This greatly extends the utility of selective ion-sensitive electrodes; for example, the precipitation titration in ethanol of lithium with The best pH conditions for more precise potentiometric end-point determina- tions in chelometric titrations can be determined by the method of Reilly et aZ.386*387 In addition, copper(II)155J88-390 and ion-sensitive electrodes are reliable within defined pH limits for the end-point monitoring of EDTA titrations.Differential and Null-point Potentiometry Differential potentiometry is a concentration cell technique involving the use of a matched pair of electrodes whose liquid junction potentials become negligible if a sufficiently large excess of an inert electrolyte is used.38a The unknown solution is placed in one half-cell and a standard solution in the other. The potential difference is related to the ion concentration by a calibration curve.The precision of the differential potentiometric method can be improved by using null-point potentiomet1y.~~1-~~~ The ion concentration is measured, not from a single potential reading, but by adjusting the composition of one of the half-cell solutions to match the other until a potential (the null, or bias potential) is obtained that corresponds to that prevailing when both half-cells contain an identical solution. The null-point technique, which lends itself to the analysis of very small volumes, has been used for the determination of flu0ride~~6 and ~ilver3~7 in the 5 to lop1 volume range. For example, 0.380ng of fluoride was determined3Q6 with an average error of only 0.002 ng, while over the 0-38 to 0.190 ng range, fluoride was determined396 with an average error of about 1 per cent.For silver, it was possible to determine398 0.054 pg in a volume of 100 p1 with an error of 0.001 pg, while over the 0.054 to 54 pg range, the average error was less than 1 per cent.98 MOODY AND THOMAS The differential potentiometric method with a twin pair of solid-state mem- brane selective chloride-sensitive electrodes was superi0r~~9 to that with a pair of silver - silver chloride electrodes for the determination of chloride in high purity waters at the nanogram per litre range. The method involved adding aliquots of standard chloride to the sample and plotting potential readings versus nanograms of chloride per litre.399 On the same graph, the results of a similar titration per- formed with a blank are plotted, and the sample chloride content corresponds to the distance along the chloride concentration axis (nanograms per litre) between the two parallel titration curves. The method has a detection limit of 6 ng 1-1 and a relative standard deviation of 3 per cent.at the 100 ng 1-1 Potentiometric measurements with pairs of selective ion-sensitive electrodes in the null-point and differential methods can lead to excessively high impedance, especially if two glass electrodes are used. Brand and Rechnitz have d e ~ c r i b e d 4 ~ ~ ~ l and assessed4m a new amplification instrument to meet this challenge for sodium ion determinations by using a cell composed of a pH (reference) electrode and a sodium glass (indicator) electrode. The instrument has also been used400 for differen- tial potentiometric titrations with a glass reference electrode and appropriate indicator electrodes for calcium and copper determinations with EDTA.Null-point and differential yotentiometry emphasise the prospective scope for the widespread use of selective ion-sensitive electrodes; for example, the low impedance fluoride electrode,351 as references for direct potentiometry and poten- tiometric titration. The Study of Complexes The remaining parts of this review of selective ion-sensitive electrodes are devoted to a brief classified consideration of their applications in the widest sense. Thus, their ability to measure the activity of unassociated ions has been used to advantage in the direct study of complexes, and for the determination402 of silicon, aluminium, iron(III), calcium and magnesium from the decrease in fluoride con- centration due to complex formation, Even before the surge of interest aroused by the newer developments, cation-sensitive glass electrodes were used for studies of alkali metal malate and citrate ~ y ~ t e m ~ .~ ~ ~ ~ ~ ~ ~ Most categories of selective ion-sensitive electrodes have been used for com- plex formation studies.405 Not unnaturally, it is the lanthanum fluoride membrane electrode that has been most widely used, as its accessibility window331 is restricted only by hydroxide ion interference at high pH and by the formation of hydrogen fluoride species in acid solution. The latter effect has been used to advantage in studying the equilibria H++F- -+ HF (39) HF+F- + HFL by monitoring the decreasing activity of free F- ions while the increasing acidity is monitored with a pH glass ele~trode.40~**~~SELECTIVE ION-SENSITIVE ELECTRODES 99 Formation constants in the range 5.6 x lo2 to 1.55 x lo3, obtained by various worker~4W-4~~ for reaction (39) at 25" C, compare favourably with literature value~414-4~6 of between 8.13 x 102 and 1.49 x lo3.The constants for reaction (40) are, of course, lower,406-408~413 with a range of 3.0 to 9.6 compared with the litera- ture val~e~~4~4~4**~6 of N 4.0. These data are useful in other complex formation studies, and evidence supporting the existence of (HF)n species has been obtained. 417418 Although claimed409 to be less sensitive than the indirect determination of free fluoride via an Fe(II1) - Fe(I1) redox couple, in studying strong fluoride complexes, the fluoride electrode is saidUg to be superior in convenience, sensitivity and accuracy for studying weak complexes.Nevertheless the fluoride electrode has been used for studying thorium fluoride comple~es~~O*4~0 where P1 is 8-51 x 107.421 The long wait (12 hours in one casemo) required for steady potential readings at the the low fluoride levels characterises this system, which effectively extends the near- Nernstian response of the fluoride electrodefg3 to 5 x M. The /I data quoted420 for the thorium(1V) -hydrogen fluoride system are of the same order as those obtained by N0r&n,~2~ who also studied the corresponding uranium(1V) - hydrogen fluoride equilibrium. The value of pl corresponding to LaF2+ formation in molar potassium nitrate and in molar sodium chloride37g is 1.41 x lo6.The weaker metal - fluoride complexes examined include those of beryllium( 11) ,408 magnesi~m,409,419,(L23-427 calci~m,~%U9A2OA23,427 strontium ,419,423 bari~m,41~.4~3 mangane~e(II),4~8 iron(II),428 cobalt (II),428 ni~kel(II),4~4.4~8 C O P per(I1) ,428J29 ~ilver(I),4~4 cadmi~m(II)4~4 and lead(II),d30 and where the values range from less than 1 for barium to about 50 for lead(I1). No complex was o b s e r ~ e d ~ ~ ~ ~ ~ ~ ~ for thallium( I) ; consequently fluoride electrolytes have been found to be suitable as 'non complexing' media to maintain constant ionic strength at 1.0 in polarographic of perchlorate, nitrate and chloride complexes of thallium (I). In accordance with the low stability constants of the second step of weaker complexes, Elgq~ist*~7 was unable to calculate values for either MgF2 or CaF,, but p2 values have been obtained for the stronger fluoro-complexes of gadolinium(III), europium(III), yttrium(III), scandium(II1) and iron(II1) with the fluoride elec- trodeJ4O9 and even /3, values are given for the stronger scandium (18, = 1.7 x and iron(II1) (18, N 10l2) complexes.This confirms Rechnitz's opinion that species such as FeF, are formed at higher fluoride concentrations and that it is possible to evaluate the formation constant.431 The fluoride electrode has also been used to determine multi-step stability constants for several other systems including ti11(11),4~~ vanadi~m(1V)~l~ and uranium(V1) .413 There is reasonable agreement of the independently obtained values for al~minium4ll~~~~ corresponding to zero ionic strength, the respective values being 4-67 x lo6 and 9-55 x lo6.Other work4S3 has shown that cryolite and ralstonite are rather easily precipitated. Niobium and tantalum fluoride systems have been studied;434J35 the tantalum(V) fluoride ~ y s t e m 4 ~ ~ has a value of 2.34 x lo6, and step-wise stability quotients have been determined for a series100 MOODY AND THOMAS up to and including the heptafluorotantalate(V) from free fluoride measurements with the fluoride electrode. A striking feature of fluoroborate complexes is the relative weakness of mono- and tri-fluoroborates in comparison with the di- and tetra-fluoro spe~ies.4~6,'~~ An analysis of complexes formed between hydrogen and fluoride and between dioxouranium(V1) and fluoride has been used by Entwistle and Hayes4= to determine the limitations of the standard addition method when applied to the determinati0n4~~-44~ of low fluoride impurity in uranium materials by using a fluoride electrode.The method depends on a constant ionic strength of the solution and constancy in the ratio of total fluoride to free fluoride. It can be useda8 to determine fluoride in uranium metal and oxides in the range 1 to 100 pg F- per gram of uranium and in uranyl nitrate solutions in the range 0.5 to 50 pg F- per ml. In the above studies with fluoride complexes, polyethylene or Teflon beakers are usually required and in monitoring solutions of systematically varying com- position, constant ionic strength (often obtained by using perchlorate, but some- times by using chloride or nitrate) and temperature have to be maintained.The silver sulphide membrane electrode is well suited for complex formation studies of the sulphide ion, but here the ready tendency of the sulphide ion to interact with the solvent to form HS- and H2S species complicates matters. Some pK, values have been determined for H2S with this electrode,s0 but although in agreement with some literature values, they differ considerably from that deter- mined by Schmidt and P~ngor.~*, The sulphide electrode is best suited to the study of sulphide complexes in alkaline media.s0~331~443 Thus, the formation constant of the SnSi- ion has been evaluated331 at 2-06 x lo5 (previously reported value, 1.1 x lo5) following monitoring of the sulphide - tin (IV) system with pH type and sulphide ion electrodes.The iodide electrode has been used for studying the hydrogen peroxide - iodate reaction in acid medium.444 The general utility of selective ion-sensitive electrodes for complex formation and other ion-association studies405 is further demonstrated by the use of the solid-state copper(I1) electrode to determine the formation constants of copper(I1) complexes with ethane-1-hydroxy-1, 1-diphosphoric and Eriochrome Red B.W The Orion Model 92-29 liquid ion-exchanger copper(I1) electrode has been used for determining the formation constants of complexes between copper(I1) and ligands of biological significance.447 The results for glycine, glutamic acid, tris- (hydroxymethy1)aminoethane and acetate as ligands compared favourably with other reported values.331~4~7 A copper(1) sulphide membrane electrode has been used for studying copper(1) complexes in acetonitrile when the predominant copper(1) - thiourea complex was shown4a8 to be Cu[S: C(NH,),]+ with p2 = 2 x los. Results from the application of the Orion 92-20 calcium-sensitive liquid membrane electrode to the determination of stability constants for the complexa- tion of calcium ions with tetrapolyphosphate, trimetaphosphate and tetrameta- phosphate ions are in good agreement with those obtained by pH tit ration^.^^^^^^ The same electrode has been used for studying the solubility products of calciumSELECTIVE ION-SENSITIVE ELECTRODES 101 fluoride, calcium carbonate and calcium sulphate and again there is satisfactory agreement with literature values.450 Saturated solutions of calcium carbonate under atmospheric carbon dioxide have been shown451 to contain 80 per cent.of Ca2+ with the other 20 per cent. composed of CaCO, and (CaHCO,)+ species. The Orion calcium and divalent electrodes have been used for measuring the dissociation and solubility of calcium sulphate dih~drate.d~~--"= The Orion 92-32 divalent cation electrode has also been ~ s e d 4 ~ ~ to show that the formation of magnesium sulphate ion pairs, Mg2+ + + MgSO,, in an aqueous NaCl- MgCI, - Na,SO, solution was characterised by an association constant of 10.2, which is close to the 1043 that was later found for calcium sulphate ion pairs.456 These have been used to estimate the sulphate species and effective ionic strength in sea ~ater.,55-&~ Magnesium carbonate equilibria have also been by using the Orion 92-32 liquid membrane electrode.The sodium ion-sensitive glass electrode work of Gardner and N a n c ~ l l a s ~ ~ ~ yields association constants for NaP,Oi- and NaP,O:; (25 and 133, respectively) in close agreement with Monk's ~alues.46~ This work shows no evidence for the ion pair, NaHPO,, whose existence has been somewhat contro~ersial.~~~ A 1 : 1 sodium tartrate complex, also determined from measurements with a sodium ion-sensitive glass electrode,d61 has a stability constant of 2.55 at an ionic strength of 0.2. Association constants for the potassium and sodium adenosine triphosphate complexes, KATP3- and NaATP3-, obtained with the valinomycin potassium- sensitive electrode and a sodium-sensitive glass electrode are substantially greater than previous values obtained from indirect mea~urements.~6~,~~~ Recent studies of the calcium ATP system with the calcium electrode have shown the existence of Ca,ATP in addition to the previously established CaATP2- complex.464 Reaction Rate Studies Equilibrium measurements have been logically extended to the kinetics of several reactions.1g7~431~465-47s An early investigation consisted of rate measure- ments with cation-sensitive glass electrodes of certain tetraphenylborate precipita- tion reactions465 when the maximum second-order rate constant detectable was about lo5 M - ~ s-l.Another study showed pH dependence of the exchange reaction path between silver(1) - EDTA and nickel(I1) ; the silver(1) activity was monitored with a cation-sensitive electrode.466 This stimulated the application of the calcium liquid ion-exchange membrane electrode for following the exchange reaction between magnesium - EDTA and cal~ium.1~7 In the iron(II1) - fluoride reaction, pathways involving F- and HF were shown to be possible431 with the primary reactant depending on pH.Different paths were recognised for the reaction of aluminium(II1) with fluoride AP+ + HF -+ A1F2+ + H+ Al(H,O),+ + F- + A10H2+ + HF A10H2+ + HF -+ A1F2+ + H20102 MOODY AND THOMAS At high acidities, reaction (41) is rate limiting and at lower acidities reaction (43) is rate limiting. A study of the iron(II1) - iodide reaction in fluoride media moni- tored with the fluoride electrode shows that Fe3+ (but not FeF2+) reacts with iodide ion.468 An interesting application of an Orion 92-17 chloride electrode is its use for monitoring the rate of chloride ion production during the &l cyclization of methyl-bis( p-chloroethy1)amine hydro~hloride,4~~ but among the most spectacular applications of ion-selective electrodes is the monitoring of the temporal oscillation of bromide ion in the bromination of malonic acid.467~470 A glass electrode system for sodium, potassium and hydrogen ions is well suited for studying the kinetics of transcellular energy-dependent sodium potassium exchanges, as well as for ion-binding properties of tissues.471 A fast flow system developed by Fleet and Rechnit~"~ utilised liquid mem- brane electrodes as sensors and had an upper measurement limit of lo6 tolO7 M - ~ s-l for the second-order rate constant.A more recent rapid-mixing flow technique in which crystal membrane electrode sensors are used can cope with rate constants as large as lo8 M - ~ s-l under favourable conditions.473 Biomedical Applications Because many biological phenomena are fundamentally related to solution ionic activities rather than to ionic concentrations, the development of selective ion-sensitive electrodes represents an important advance in the biomedical sciences. Only the ionised fraction of calcium is physiologically active,476 and the calcium liquid-ion exchanger membrane electrode represents a major breakthrough in the field of electrolyte metabolism ;299 certain early papers were specially collected for the attention of clinical investigators.477 However, the opinion of investigators as to the utility of these electrodes in the biomedical field is frequently one of con- siderable dismay.This is not entirely surprising, as aqueous biological fluids com- prise many different inorganic ions and various colloidal electrolytes, including proteins. Further complications are the need to protect samples from loss of carbon dioxide and the periodic replacement of membranes in commercial liquid ion-exchanger electrodes;*78 however, PVC matrix membrane e l e c t r o d e ~ ~ 1 ~ ~ ~ J offset this last complication. Biological fluids It is proper that the surveys made of the application of selective ion-sensitive electrodes to biological fl~ids~~9~479-484 should detail difficulties and problems.The matter of activity coefficients in the mixed electrolyte systems is of extreme im- portance, and one surveyzm gives this major attention, along with matters of selectivity, calibration and expression of data. Many of the investigations with the various glass electrodes lie outside the time scale of this review, but they have been carefully surveyed by Khuri,480 whoSELECTIVE ION-SENSITIVE ELECTRODES 103 describes both the importance of avoiding carbon dioxide loss and electrode modi- fications for use in in situ, in vivo and in vitro situations. Moore has summarised studies on sodium,299 potassium299 and calcium.479 Serum calcium exists in three forms, namely protein-bound (30 to 55 per cent.of total), complexed (5 to 15 per cent. of total) and ionised. The ionised form seems to play a part in normal physiological processes such as synaptic transmission486 and blood coagulati~n.~~~ Its measurement is an important aid in diagnosing primary hyperparathyroidism, as the calcium activity is usually raised, even when the total calcium may be Moore478 has exhaustively considered matters of technique, selectivity, calibra- tion, freezing, pH and other factors in the application of the liquid ion-exchanger membrane calcium electrode for determining serum calcium. Doubts478~~8 have been expressed over the r e s ~ l t s ~ ~ ~ ~ ~ ~ ~ of an early static model of the electrode, and a flow-through model for ionised calcium studies is f a v o ~ r e d ~ ~ ~ ~ ~ ~ ~ although the static type permits a direct study of pH - CO, effects.478 Raman488 quotes a human serum calcium ion level of 41 to 55 per cent., with a mean value of 49.2 per cent.(4-72 mg per 100 ml), which compares favourably with Moore's values478 (mean 4-56 mg per 100 ml) and those of other ~ o r k e r s ~ ~ ~ - ~ ~ ~ ranging from 43.9 to 61-24 per cent. Moore478 found that for a given individual, the serum ionic calcium level varies by only about 6 per cent. over several months, but even this could account for the lack of correlation of ionic to total serum calcium noted for the twenty-three normal adults of another study.495 Ionic calcium varied inversely with pH, and at pH 6-8 an average of 54.3 per cent.of serum calcium was ionised, while at pH 7.8 it was 37.5 per cent., the pH-induced decrease being surmised to be reflected as a corresponding increase in the protein-bound calcium. The pH effects on heparin- ised whole blood resemble those in corresponding sera, but ionic calcium levels in whole blood are less than in serum at the normal venous pH of 7-3 to 7.4, the difference being 0.18 mg per 100 ml at pH 7.32. This lowering can be accounted for by a calcium - heparin complex. Citrate and oxalate also form complexes with similar c~nsequences.~~~~*~~ Less significant differences were found between serum and plasma,4S0 but an early static calcium electrode was used in this work. However, it is claimed497*498 that a small amount of heparin (up to 30 units per ml of blood) has no effect on calcium ion activity and neither has a short exposure of whole blood to air, as would occur if an air-bubble were present in the syringe during venipuncture. Other studies show that the calcium electrode gives a reliable index of ionised calcium in blood,499*500 but magnesium ions can depress the potential.501 Also, the presence of erythrocytes might change the liquid junction potential between sample and standard rneas~rements.~~~ To overcome uncertainties of ionic activity coefficients in biological fluids, calibration of the calcium electrode was made with calcium chloride standards in 0.150 M sodium chloride to encompass the The calcium electrode has been extended to fundamental biological and clinical studies of serum calcium l e ~ e l ~ .~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ For example, the effects of thyro- expected ~alue~.478,"88,490.496--500104 MOODY AND THOMAS calcitonin and parathyroid extract on total serum calcium and ionised calcium activity in rat serum has been studied,496 and it has been found479 that serum ionised calcium is significantly elevated in patients with hypercalcemia of cancer with a mean of 6.04 mg per 100 ml as compared with a normal figure of 4.64 mg per 100 ml. There is also a variety of other serum calcium ion determination~.236~~~~-~~~ The calcium electrode has also been used for determinations in urine,621 with due attention to preparing standardising solutions with calcium and ionic strength levels similar to the unknowns. The divalent electrode has been carefully used for studying the effect of divalent cations on the adhesiveness of rat polymorphonuclear neutrophils obtained from peritoneal exudates.528 Urine presents problems as conditions of pH, sodium concentration and ionic strength vary considerably.521 Consequently, each urine sample was first analysed for sodium, potassium and ammonium and a set of standards made up to simulate the urine in both ionic strength and sodium c~ncentration.~~~ The potentiometric studies agreed with spectrophotometric and computational techniques and showed the ionised calcium in urine to be about 50 per cent.of the total with the remainder accountable in terms of various soluble citrate, phosphate, sulphate and oxalate complexes.s01 Problems of pH in gastric juice were overcome by bringing the samples to pH 6.2 to 7.2 with sodium hydroxide prior to analysis for the ionised calcium.527 The Orion calcium electrode has facilitated the study of calcium ion activity on membrane alkalinisation in mitochondria,629 on mitosis,53Oe531 and on the rate of cell division.632. It has also been used to show that the protein polysaccharides of cartilage chelate calcium ions very effectively.533 Electrode studies of calcium binding by chondroitin sulphate are said to be subject to interference by the chondroitin sulphate anion.634 The Orion flow-through calcium electrode has clearly made its mark in the study of biological fluids, but further technical advances can be expected and the automation of procedures will be important. Continuous-flow procedures described for a flow-through Orion calcium ion electrode can cope with 40 samples of serum per hour.15**635 Other studies on biological fluids involving the use of selective ion-sensitive electrodes concern potassium135~536-538 and lead.539 Three of the potassium studies are on blood serum and the independent studies with v a l i n o m y ~ i n ~ ~ ~ * ~ ~ ~ and liquid i~n-exchanger~~' electrodes, each with better potassium-over-sodium selectivity than that of glass electrodes, agree with spectroscopically determined levels (N 4 mM per litre), the calibrations being based on serum samples.The valinomycin liquid-membrane electrode has been ~uggested~~6 for use in flow-through electrodes as for calcium, while the Corning liquid ion-exchanger electrode was adapted to a capillary flow-through sy~tem.~~7 The valinomycin electrode might be used540 for a whole variety of biologically- based applications, including potassium monitoring during open heart surgery and renal physiology.A micro-capillary version of the potassium liquid ion- cerebrospinal f l ~ i d , ~ ~ 5 and gastricSELECTIVE ION-SENSITIVE ELECTRODES 105 exchanger electrode has been used in situ for following potassium ion gradients along the proximal convoluted tubule of a rat kidney. The mean ratio of tubular fluid to plasma potassium ion concentration falls significantly from 0.89 for the first convolution to 0.81 for the last convolution of the proximal tub~le.~38 Because of irreproducible readings, the Orion 94-82 solid-state lead-sensitive electrode was unsatisfactory for blood and saliva samples, but in urine, 3.67 x 10-7 M to 4.34 x 10-7 M of lead could be determined directly without pre- treatment.539 These levels are near to the detection limit (Table I) but, nevertheless, are of the same order of magnitude as those obtained by a colorimetric method.530 With regard to fluoride in biological fluids, urinary fluoride has received the most attention,541-551 and the usual method is based on a direct determination with the lanthanum fluoride electrode following pH and ionic strength adjustment.This is justified by recovery values545-550 and by comparison with microdiffusion method~.544-~~0 However, Cernik, Cooke and Hall551 drew attention to the fluoride levels obtained by direct electrode measurement being lower than those obtained after microdiffusion and treatment with perchloric acid at an elevated temperature.This difference is attributed549 to some fluoride being in a non-ionic f0rm,~~1 but this is not confirmed by Tug1.54g The matter, therefore, merits further attention. This is particularly so in the light of the higher values obtained546 for urinary fluoride after diffusion from perchloric acid when compared with direct electrode values. Differential hydrolysis rates of the carbon - fluorine bonds in 5-trifluoromethyl- 2’-deoxyuridine and its metabolite, 5-trifluoromethyluracil, permit their determina- tion in urine with a fluoride-sensitive electrode.552 That some fluoride is bound in biological fluid is indicated by the higher levels in human serum ashed diffusates compared with unashed diffusate~.~~~*~54 The presence of non-ionic fluorine in plasma has also been established.555 Fry and T a v e ~ ~ ~ d recognise problems of low serum fluoride in preparing standards, and recommend the human serum from a normal young adult who has not drunk fluoridated water for 24 hours as an acceptable alternative.However, Gran’s plots recommended for isolated samples are as convenient and reliable,554 although it is to be noted that a pH meter reading to just within 1 mV was used. Fluoride levels of blood serum have received much attention by T a ~ e ~ , ~ ~ ~ e ~ ~ 6 - ~ ~ and those determined by the fluoride electrode agree with those obtained by the fluorescence of a Morin - thorium complex.558 The fluoride level of biological fluids is normally low, and interest in its determination arises through industrial exposure to fluorine materials, medical treatment such as methoxyfluorane anaesthesia, fluoride treatment of patients with bone disease and after haemodialysis in areas with fluoridated water.In saIiva,545*559 the fluoride level was read with the electrode after adjusting the pH to 4-7 to 4.8 with acetic acid. The activity coefficient of fluoride at the prevailing ionic strength was assumed to be 0-82, and the relationship between concentration and measured activity was taken as 0.80 to allow for the fluoride present as HF at this pH.559 There was good agreement between the fluoride readings obtained106 MOODY AND THOMAS with the electrode and those from chemical analyses of ashed salivary samples.a9 Fluoride levels in stimulated duct saliva are in the 0.01 to 0.05 p.p.m. range, but the ingestion of single doses of sodium fluoride increased salivary fluoride after 5 to 10 minutes, to reach a maximum in 30 to 60 minutes, followed by a slow decrease to approach the original concentration in 2 to 6 Representative maximal values for parotid salivary fluoride after the ingestion of 10,5 and 1 mg were 0.3, 0.2 and 0.06 p.p.m.respectively.55g Of milk fluoride s t ~ d i e s , ~ ~ ~ - ~ ~ ~ that on human milk560 was carried out on a fat- free sample after the removal of casein, albumins and globulins at pH 6.8. The data refer to periods before and after the introduction of water fluoridation.560 A more extensive study on cows' milk561 is concerned with free and total fluoride, the latter being determined after the desorption of protein-bound fluorine by the formation of an insoluble complex between Amido Black 10B and milk proteins at pH 2.0.Citrate buffer is added to adjust pH. Both these5so~561 and the salivary determinations are at a level of 1 p.p.m. or less and involve some measurements in the non-linear range of the fluoride ele~trode.~~9 Few diseases can be so readily diagnosed as cystic fibrosis, which is characterised by elevated chloride ion levels in sweat and for which the solid-state silver chloride combination electrode is an effective m o n i t ~ r . ~ ~ - ~ ~ ~ To facilitate the easy and accurate monitoring of newborn babies, infants and children, direct-reading skin chloride electrodes have been developed, the equipment being complete with a sweat-stimulating attachment .5679568 It is stressed, however, that misleading infor- mation will result if the subject fails to sweat.567 The meter is calibrated with 20 and 100 m~ chloride solutions, these values approximating to the mean normal and mean cystic fibrosis chloride levels in sweat.567 Readings between these two values are reproducible to within *2 mmol 1-1 of chloride ion.567 Descriptions of a method for the sequential determination of sodium, chloride and hydrogen ions on the skin surface include data on reproducibility, precision and rationales concerning temperature control, pH dependence of sodium electrode performance and uniform electrode setting for all tests.569 Chloride electrodes have been used for chloride ion measurements in urine, blood and serum without the removal of p r o t e i n ~ .~ ~ O - ~ ~ Just as fluoride levels may be used to monitor toxicity after methoxyfluorane anae~thesia,~~~-~'~ so a knowledge of bromide ion concentration is sometimes required in toxicology and in treatment control with bromine-containing seda- tives.576 To this end, a bromide ion-selective electrode has been used on two blood samples, one taken before and one after bromide ion administration. A quadratic expression describes the relationship between millivolt readings (E) and bromide ion concentrations [Br-li = ao+a,E,+a2Et where a,, a, and a2 are constants determined by additions of bromide ions to the first sample. The coefficient of variation for the range examined was about 1 per cent.SELECTIVE ION-SENSITIVE ELECTRODES 107 Mineralised tissues and dental materials The tedious diffusion methods often used in fluoride determinations can now be avoided with a lanthanum fluoride electrode, thereby simplifying the analytical procedures associated with dental health interest~.5~~~5~’-5~~ Thus, M~Cann~~s des- cribes a method whereby a sample of between 1 and 20 mg of enamel, dentine, bone or calcium phosphate is placed in a disposable plastic tube, dissolved in 1.00 ml of 0.50 M perchloric acid and the pH adjusted to about 5.6. The calcium is then com- plexed with 4.00 ml of 0.05 M sodium citrate and the fluoride determined with a calibrated fluoride electrode.This kind of procedure, but with smaller samples, has been used in a biopsy procedure for fluoride levels in the outer 1 to 2 pm layer of enamel in which the mean concentrations varied from 400 to 2500 p.p.m.in the anterior teeth of different persons.581 Dried dental plaque was submitted to a similar procedure,583 but dried soft tooth deposits were subjected to a diffusion stage following their dissolution in a perchloric acid - nitric acid mixture, when fluoride recoveries were high.584 Duff and Stuart586 dissolved calcium phosphate and dental enamel samples in hydrochloric acid rather than in perchloric acid. Because of the relatively large amount of fluoride introduced by the sodium chloride of TISAB, sodium citrate was used for the adjustment of the ionic strength. However, because mineralogical and biological samples of calcium orthophosphates can contain appreciable amounts of fluoride-complexing ions, the replacement of the citrate - hydrochloric acid system by one based on perchloric acid, triethanolamine and citric acid to give an operating pH of 7 is recommended.588 Only aluminium causes incomplete fluoride recovery, but this is hardly surprising in view of the high stability of the [A1F6]3- complex.A similar system, aimed at an electrode monitoring at pH 2.5, has been discussed for chloride in calcium phosphate.586 A diffusion procedure, designed to cope with submicrogram amounts of fluoride, does not have to cope with complexation in the absorbing 0.1 M sodium hydroxide solution ; hence pH adjustment for the selective ion-sensitive electrode measurement stage is made with acetate The method, however, is not considered to be satisfactory for organic material such as blood serum.Sodium acetate was used for pH adjustment following the dissolution of a bone sample in hydrochloric acid. No complex formation was apparently experienced in the subsequent electrode monitoring for fluoride as the results matched those of a diffusion - colorimetric procedure on the same samples.592 Ionic strength was not fully appreciated in the calibration,592 but the method has been used for bone fluoride determinations in connection with fluoride toxicity in mice.593 Another procedure uses citrate.594 There are several other studies of fluoride in bone.59”598 The use of the fluoride ion electrode to obtain fluoride figures directly for toothpastes containing either sodium fluoride or tin(I1) fluoride correspond with those obtained by a combined diffusion - thorium nitrate titration procedure.599 The sodium fluoride pastes were tested as aqueous solutions or as suspensions, while the tin(I1) fluoride pastes included 400 mg of malic acid in their solutions or H108 MOODY AND THOMAS suspensions in de-oxygenated ~ a t e r .~ 9 ~ No reference is made to possible interference by the base materials of the toothpastes, but separate calibration curves were used for sodium fluoride and tin(I1) fluoride, steady readings taking 4 to 5 minutes for the samples containing tin(I1) fluoride compared with 1 minute for sodium fluoride based samples.6g* Studies of general biological interest A Pungor-type electrode was used for monitoring iodide in a vitamin - mineral formulation,600 and the Orion lanthanum fluoride electrode was used in the deter- mination of fluoride in multivitamin preparations.601 A study of sodium in bovine albumin solutions involving a sodium glass electrode makes pertinent comments on careful standardisation, depth of immer- sion and the possibility of sodium-protein binding.602 A study on dissolved wool solutions emphasises the need for proper electrode conditioning.60s A non-fusion, distillation technique for preparing biological samples such as fish protein concentrate permitted a rapid electrode fluoride determination.6O4p605 The distillate was collected in 0.1 M sodium hydroxide solution and TISAB added for ionic strength, pH adjustment and for the elimination of complexing effects604 A rapid-mixing continuous-flow system utilising sensing liquid membrane selective ion-sensitive electrodes can handle reaction times as short as 10 ms under turbulent flow conditions.472 Reactions of calcium, magnesium and beryllium ions with such biologically important ligands as lactate, gluconate, mallate and tartrate that involve chelation, loss of water from the metal co-ordination shell and hydrolysis of a water molecule in the co-ordination shell have been investigated.478 To avoid streaming potentials, the ionic strength must be greater than 10-2 M and the flow-rate through the electrode must be controlled to avoid membrane pressure eff e~ts.47~ Plant materials The main interest for the application of selective ion-sensitive electrodes in the plant field involves nitrate in plant nutrition st~dies~~6~~~6-6~0 and fluoride in environmental s t ~ d i e s .~ ~ ~ ~ ~ ~ - ~ ~ ~ The nitrate procedures depend on aqueous extrac- tion techniques6W-6l0 and have been designed to overcome interferences by chloride, bicarbonate and nitrite. Paul and Carlson606 recommend removing the chloride with an ion-exchange resin in its silver form, but Baker and Smith607 do not con- sider this to be expedient. Milhamslo has developed a flow-through electrode unit and used336 an extracting buffer (pH 3-0) containing silver sulphate, aluminium sulphate, boric acid and sulphamic acid; the relatively low pH kept the equilibrium amount of bicarbonate low and the water-extractable organic acids were generally undissociated. The anions of organic acids were complexed with aluminium, and sulphamic acid quantitatively destroyed any nitrite present.The plant materials were ashed for fluoride dete~minations.~~~~~~~-~~~ LouwSELECTIVE ION-SENSITIVE ELECTRODES 109 and Richards616 examined three methods of overcoming the interferences of silicon, aluminium and iron, which occur at high levels in sugar cane, and favoured a modification of Edmund's methodsl1 for separating the fluoride from interferences by leaching it from a sodium carbonate - zinc oxide fusion melt, followed by com- plexing residual trace elements with citrate. Baker612 used sodium hydroxide fusion followed by standard addition to the extract. Grasses,611 vegetables,690 tea,613 cocoa613 and tobacco613 have been assayed, but the fluoride figures for tea, cocoa and tobacco are at variance with those of the cerium - alizarin complexan method, probably because of differences in the ionic strength of the standardising and test solutions.613 The solid-state iodide electrode has been used for the determination of iodide levels in feeding stuffs and plants,61s and the solid-state cyanide electrode has been used for the determination of cyanide in forage samples61s and plant hydro- lysates.6200621 In the application to cyanogenic glycosides in Sudan grass samples,621 an emulsin hydrolysis stage on a pH 5 potassium phthalate buffer homogenate precedes the direct potentiometric cyanide determination at pH 12.Advantage was taken of the volatility of hydrogen cyanide in the determination of the blank, whose value was deducted from the total cyanide to give endogenous cyanide levels that agreed with those obtained by a non-potentiometric procedure.621 Of the chloride s t u d i e ~ , ~ 0 ~ ~ 6 ~ ~ direct potentiometric determination gave un- reproducible and extremely high chloride ion values.However, the chloride electrode satisfactorily indicated the end-point in the titration of plant tissue extracts with silver nitrate to give results comparable to those obtained by the Mohr procedure.622 Applications to Enzyme Reactions This part of the discussion reviews some important applications of electrodes for monitoring ion levels in enzyme reactions. In the determination of urea in blood and urine with an urea-sensitive ele~trode,~64-~~~ interferences from sodium, potassium and other species have to be minimised by adding Dowex 5OW-XZ ion exchanger to the sample.623 A similar, but uncoated, glass electrode is used as referen~e.6~~ The urea levels thus obtained are within 2 to 3 per cent. of those obtained using the standard spectrophotometric method.623 The released ammonia, which permits urea assay [equation (l)], illustrates the underlying principle of enzyme electrodes and can alternatively be exploited for determining urease activity,lss and for kinetic studies of deaminase enzyme sy~tems.6~4 /I-Glucosidase has been determined from the cyanide in the hydrolysate of arnygdalin.l'*J75-625 Determination of the fluoride released by the inactivation of chymotrypsin by a diphenylcarbamyl fluoride permits chymotrypsin to be assayeds26with an accuracy of within 3 per cent.at concentrations ranging from 2 x 10-5 to 5 x 10-6 M. A further variation is the use of the substrate selective Corning Model No. 476200 acetylcholine ion-sensitive electrode for determining acetylcholin- esterase activity.le2 The selectivity towards choline, acetyl-, propionyl-, acetyl-110 MOODY AND THOMAS /%methyl-, butyryl-, valeryl- and benzoyl-choline has been determined627 and the result has been used in a kinetic method for characterising cholinestera~es.~~p6~* This is possible because both cholinesterase and acetylcholinesterase hydrolyse acetylcholine; while only cholinesterase will hydrolyse butyrylcholine and only acet ylcholinest erase will h ydrolyse acet yl-P-met hylcholine .627 p628 The different sub- strates thus permit characterisation, but it is necessary to re-equilibrate the acetyl- choline electrode when the substrate is changed or, more expeditiously, to use a separate equilibrated electrode for each substrate.628 Anticholinesterase activity of organophosphate residues and Paraoxan can be determined in the concentration range from 100 to 1000 ng ml-l with a standard deviation of 12 ng ml-1.629 Studies on the interactions of glucose-1-phosphate with magnesium and fluoride ions suggest that fluoride ions could inhibit phosphoglucomutase activity through the formation of a substrate - magnesium - fluorine complex, or by reduc- ing the availability of the metal ion co-factor for binding to the enzyme.630 Environmental Applications Environmental applications concern foods, feeds, fertilisers, rocks, soils, sewage, natural waters, sea water, smoke and air.Weber631 has discussed the scope and limitations of selective ion-sensitive electrodes for pollution control. Foods, feeds and fertilisers Some reference has already been made to foods, e.g., fluoride in milk.56h662 Methods for determining the fluoride levels of dried milk tea562 and a wider range of beverages have been d e s ~ r i b e d . ~ ~ ~ * ~ ~ ~ For these, the only sample pre-treatment usually required is a decarbonation process.632 The measurement is carried out at pH 7 and at high ionic strength in the presence of a known amount of fluoride; in this way, fluoride levels of 2 p.p.m.and less can be determined. Detailed results are not given. Fluoride levels in feeds have been d e t e r m i ~ ~ e d . ~ ~ ~ - ~ ~ ~ TuS16331634 depends on dissolving the sample in aqueous hydrochloric acid and adjusting the pH with a itr rate^^^ or acetate63a buffer, while Torma and Ginther635 resort to steam distilla- tion from perchloric acid. The results obtained by both methods agree with those obtained by using the complexone method following diffusion - di~tillation.~~3-635 Fluoride has been determined in the phosphoric acid and gypsum (CaSO, . 2H20) produced by the reaction of phosphate rock with sulphuric The close agreement of results with those from a reference method justifies the recommenda- tion for the adoption of the fluoride electrode for routine DemotP3' did not verify his results for calcium in milk determined by the liquid ion-exchanger membrane electrode, but Muldoon and Liska's objective was the comparison of calcium electrode results with those from a resin ion-exchange method.638 The average calcium ion level for raw milk by the resin method was 2.52 (sd & 0.15) mM, compared with 2-71 (sd & 0-01) mM by the electrode method.SELECTIVE ION-SENSITIVE ELECTRODES 111 This significant difference, which was not evident in pasteurised and sterilised milks, was attributed to suspected pH changes (caused by microbial action) affecting the ion-exchange resin method. The calcium ion level in sterilised milk was about 2-25 mM, and in pasteurised milk about 2.05 mM.Lower ionic calcium levels are reported for fresh, powdered and condensed m i l k ~ .6 ~ ~ Calcium in animal feeding stuffs can be determined following ashing and pH adjustment to 5.5 to 6.00 with potassium hydroxide s0lution.~40 The chloride content of cheese has been determined with a Pungor-type electrodeul and of milk with Orion liquid membranea2 and solid-state643 membrane electrodes. Variations in ionic strength in the determination of nitrate in spinach are overcome with a 1 per cent. sodium sulphate extract.644 The precision is good, but the nitrate levels slightly exceed those obtained by the xylenol chemical method.644 Sulphide in beer645 and in foods646 has been determined by using a sulphide electrode and the response over the pH range 3 to 12 ~tudied.~~6 Iodide electrodes are useful in l3lI studiesG47 and for determining the isotope in milk.G48 The sodium glass electrode has been the focus of attention for determining sodium in glucose drinks,649 egg y0lk6~0 and for salt in bacon.651 The various results have been compared with established Rocks and soils Fluoride electrodes have been used for fluoride determinations in g l a s .~ , ~ ~ ~ - phosphatic and other mineral~,~ll~6~~-~~7 and s0ils.668~66~ Singer and Armstr~ng~~* relied on a relatively non-complexing acetate buffer to maintain a constant ionic strength, which was, however, unsuitable for rock samples containing more than 1 per cent. of al~mina.~ll-6~~ A 1 M sodium citrate solution buffered to pH 6 could cope with up to 10 per cent. of alumina,611#655 but to avoid such a high citrate concentration, Ingram658 used 0.1 M sodium citrate and quoted aluminium inter- ference studies to support her action. Van Loon659 fuses the rock sample with sodium hydroxide, and after aqueous extraction adjusts the pH to between 7 and 8 with hydrochloric acid.No pre- cautions are taken against complexing interferents, and the results quoted for fluorite, cryolite, topaz, chliolite and matlockite accord with calculated fluoride levels.659. Sodium carbonate fusion has been used,651--86O but Ficklin depends on a sodium carbonate - potassium nitrate flux with a citric acid system buffered to pH 5.5 to 6.5, although his results on standard rock samples only agree to within about 20 per cent. with a distillation method and to just 15 per cent. reproducibility by the electrode method on replicate analysis.661 Peters and Ladd,670 following fusion with sodium peroxide - sodium carbonate and buffering the acidified extract with a pH 6 citrate buffer, favoured a direct potentiometric method over the standard addition method, which gave a positive bias.A further flux is a bismuth oxide, sodium tungst ate and vanadium pent oxide mixture .671 Bromide and iodide interference with the determination of chloride in chloride- containing minerals and other materials is overcome with chromic The112 MOODY AND THOMAS slowing-down of response time was rectified by occasional light buffing of the electrode crystal membrane with fine emery paper.672 Chloride in silicate rocks can be determined with chloride ion electrodes in solutions of sample melts prepared by fusion in platinum crucibles with a zinc oxide flux, or in culture tubes with a sodium carbonate - potassium nitrate Alternatively, the silver sulphide electrode can be used as an indicator in titrations with silver nitrate.67s The applications of nitrate electrodes for nitrate determination in soil extracts rightly avoid using chloride extract~,~~~,~~~,335.538,889.871-880 and depend instead on water or aqueous copper sulphate extracts.Due consideration has been given to various parameters , including possible nitrite Favourable comparisons have also been made with established methods of nitrate Fiskell and Brelandsa9 state that the chloride electrode is also satisfactory with soil extracts and where the chloride level is high a correction is required in nitrate determinations.The non-fusion distillation technique for the sample preparation of biological materia160~605 has also been used for preparing soil samples for fluoride analysis with an Orion model 9pO9 electrode.68l Potassium-sensitive electrode studies have shown that potassium activity in soils is up to 50 per cent. less than total potassium.ss2 The Orion model 92-32 divalent electrode and the Beckman P/N 39047 cationic glass electrode have been used to determine calcium and rubidium , respectively, in bentonite and illite clay suspensions.6s3 The activities of each ion found were valid indexes of radiotracer-measured root uptake and clay retention of the ~ations.6~~-6~5 Calcium in soils has also been measured.669~6s6-688 The distillation step in the total nitrogen analysis of soil by the Kjeldahl method can be eliminated by using the Orion ammonia electrode for determining ammonium ion formed by the Kjeldahl digestion of the soil sample.689 The results agreed with those of the customary distillation-titration method.analysis. 226,227,335,336,674 Water supplies and sea water Frant and Ross339 first introduced TISAB for the determination of fluoride in water supplies. This has stimulated the adoption of the fluoride electrode for monitoring water s ~ p p I i e s ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ and sewage ,698 although some methods are based on direct measurement .545,6901698 Crosby, Dennis and Stevenssg2 evaluated five spectrophotometric procedures and the fluoride electrode method for deter- mining fluoride in water, and concluded that the electrode method was less susceptible than colorimetric methods to interference from other ions in solution and also gave theoretical fluoride recoveries from several drinking water supplies.It has also been shownsg3 that sodium fluorosilicate is dissociated to at least 95 per cent. at the levels normally present in water supplies, but for analysing704 technical fluorosilicic acid solution, the material is made basic with ammonia to precipitate silica and liberate fluoride ions and then buffered with acetate. The first TISAB formulation was not fully satisfactory for overcomingSELECTIVE ION-SENSITIVE ELECTRODES 113 aluminium interference. The CDTA (1,2-diaminocyclohexane-NNN’N’-tetra- acetic acid) later used to overcome such i n t e r f e r e n ~ e ~ ~ ~ ~ ~ ~ ~ is still not completely satisfactory in some cases, and resort has been made to the extraction of interfering polyvalent cations as their 8-hydroxyquinoline complexes.700 A potentiometric titration method701 preceded by ion-exchange concentration of fluoride ions and the removal of interfering ions enables fluoride to be assessed down to 1 p.p.m.to within 1 per cent. Warner703 obtained good precision with a standard addition method for fluoride in river and estuary water containing substantial levels of aluminium, iron(III), calcium and magnesium. Although values for the nitrate levels of well, surface and polluted waters obtained with nitrate ion selective electrodes generally agree with the values obtained by other method~,~~~JO~-~~O Abbot711 concludes that the electrode method is of little value at the low nitrate levels usually encountered in fresh water or marine surveys.Langmuir and Jacobsen709 used a graphical method based on specific conductance measurements to estimate the nitrate ion activity coefficient to within I p.p.m. of the values determined by the brucine method. The ‘approxi- mate’ electrode method, which ignored activity coefficient considerations, gave results similar to the brucine method above 50 p.p.m. of nitrate ion, but below this level the electrode results were systematically greater by 1.8 p.p.m. Some applications of selective ion-sensitive electrodes for determining chloride, bromide, iodide, sulphide and cyanide contaminants in ~ a t e r ~ ~ ~ . ~ ~ .~ describe automated control methods,36~36~714 one being based on a differential potentiometric determination of nanograms per litre of chloride in boiler-feed water by using two solid-state Orion 94-17 chloride electrodes.399 Divalent and calcium electrodes719-721 have been used to monitor water hard- ness, and the limitations imposed by hydrogen and sodium ions and static charges in the continuous monitoring of the hardness of ion-exchange treated water have been described.721 The valinomycin potassium-sensitive electrode has been used for the determination of potassium in Alpine waters.719 Boiler feed and high purity waters continue to attract investigations with cation-sensitive glass electrode~.7~~-726 Low sodium levels can be measured pro- vided attention is given to high pH, interference and junction noise elimination.723 An EIL GEA 33 sodium glass electrode, in a flowing sample system whose pH was raised by ammonia vapour, obeyed the Nernst equation down to 1 pg of Na+ per litre in high purity water.724 The electrode is suitable for continuous monitoring provided surface active amines, such as octadecylamine are absent.72K River and Alpine waters have also been monitored for sodium.715~719 Goodfellow and Webber726 have assessed an ammonium selective glass electrode for use with boiler feed water; the response was Nernstian up to 10 g 1-1 of ammonia and, like C o l l i ~ , ~ ~ ~ they found the need for buffer control.Sodium caused serious interference, with 100 pg 1-1 of Na+ being equivalent to 25 pg 1-1 of ammonia.726 B a r i ~ a ~ ~ ~ used a univalent cation glass electrode to determine high ammonia contents (0.5 mg 1-I) in waters in the presence of a constant backgound of sodium P h s potassium ions.114 MOODY AND THOMAS A recent investigation729 is a potentiometric ammonia probe based on the diffusion of ammonia through a polymer membrane before being detected by a glass electrode.The membrane permits the diffusion of free ammonia but not of ions, and concentrations of ammonia in the range 1-0 to 0.1 p g ml-l have been mea~ured.7~~ The principal advantage over the ammonium-sensitive glass electrode is that no corrections for alkali metal ions are req~ired.7~~ The scope of solid-state electrodes as indicator electrodes in the EDTA titra- tions of river and sea water has been discussed,390 and a wider review of the scope of selective ion-sensitive electrodes in sea and natural waters has been published.730 The use of the electrodes for determining the association constants of sulphate species is of fundamental interest to sea water s t ~ d i e s .~ ~ ~ ~ ~ ~ ~ These are associated with calcium and magnesium measurements, and it was found that 84 per cent. of the calcium731 and 90 per cent. of the magnesium732 existed in the ionic form. Other principal marine interests concern fluoride monitoring705*733-737 and the degree of halite saturation in Dead Sea brines738 with chloride and sodium electrodes. Warner’s fluoride data, based on TISAB treatment of samples,733*734 were made before there was concern over TISAB forrn~lations.6~5~~~~~~~~ Instead of TISAB, Anfalt and used a carbonate buffer system, but with a standard addition titration technique, and the fluoride level of 0.0734 mM compared favourably with the range 0.062 to 0.080 mM for Mediterranean sea water and 0.074 mM for Atlantic sea water.733 Anomalous results between higher colorimetric and electrode methods for the fluoride level of North Atlantic sea waters have been attributed to colloidal materials .737 Air and stack gases Much attention has been given to the determination of fluoride in air and stack g a s e ~ . ~ ~ ~ - 7 * ~ A procedure for determining as little as 2.5 x p.p.m.of water-soluble fluoride in air samples by using an Orion Model 94-09 fluoride ion electrode with a citrate buffer system depends upon the collection of the gaseous and particulate fluoride in a cellulose acetate membrane filter impregnated with sodium formate, a high-volume sequential sampler being used at a flow-rate of 4 ft3 min-l for 4 hours.739 Potassium carbonate treated filter-paper traps and TISAB treatment of the aqueous extract, neutralised with hydrochloric acid, have also been u ~ e d , ~ * ~ but for lime paper traps, simple extraction with TISAB is deemed adequate.748 Gaseous fluorides in stack gases can be collected by reaction with a hot glass probe to form silicon tetrafluoride, which hydrolyses to soluble fluorosilicic acid.739 A Crytor 09-17 fluoride electrode has been used to monitor total fluoride in effluent gases in hydrogen fluoride manufacture from f l u o r ~ p a r .~ ~ ~ Results for the determination of cyanide present in cigarette smoke by using a cyanide electrode after trapping and treatment in a lead nitrate - sodium hydroxide solution compare with those obtained by the pyridine - benzidineSELECTIVE ION-SENSITIVE ELECTRODES 115 colorimetric method.750 Hydrogen sulphide has also been determined in cigarette smoke .751 Methods for determining nitrogen dioxide and nitric oxide in the parts per million range in gases with a nitrate ion-sensitive electrode depend on the continuous oxidation of the oxides at 300" K in ozonised air, followed by absorp- tion in water and the hydrolysis of dinitrogen pentoxide and of unoxidised dini- trogen tetroxide.752 Oxides of nitrogen in cigarette smoke have been determined as nitrite and nitrate after dissolution in basic solution. The procedure involves measuring the potential of a nitrate electrode before and after the oxidation of the nitrite to nitrate.A specially derived equation was then used for calculating the original nitrate concen tration.753 A continuously monitoring device754 for hydrogen chloride in gaseous mixtures involves the aspiration of the gas or aerosol through a glass column containing surface-roughened glass beads through which water is injected as rapidly falling droplets. The resulting solution is monitored with a chloride electrode and the e.m.f. output is proportional to the hydrogen chloride content of the gaseous sample. Industrial Applications Industrial applications impose additional constraints on selective ion-sensitive electrodes.The possible use of high pressures has led to the design of a suitable multicell assembly that permits simultaneous measurements, on two or three galvanic cells, up to 3 kilobars.755 Moving process streams create problems, e.g., open circuits are created by trapped air bubbles, and static charges result from fast-moving streams rubbing against the plastic walling of electrode^.‘^ Although liquid ion-exchanger membranes are particularly prone to leaching in this respect,7s* the scope of application of selective ion-sensitive electrodes to automatic methods of process control is well doc~mented.~56-~63 Suggestions for industrial uses include the continuous monitoring of fluoride in potable waters, multiple electrode process control systems, an electrode system with reagent addition, a continuous process titrator with selective ion-sensitive electrode end-point detector, a continuous gas analyser and a differential cell with a selective ion-sensitive membrane. Additionally, the uses of selective chloride, calcium, magnesium and sulphate ion-sensitive electrodes for on-line monitoring in sugar refineries have been described.757.762~763 Direct fluoride determination can be conducted on metal pickling and plating bath^.^^^^^^^^^^^^^^^ However, there are differences in the response curves of pure sodium fluoride and chromium plating bath liquors, which are caused by complexa- tion at the low pH (0.5) in the latter ~ a s e .~ 6 ~ Added fluorosilicate leads to a lower fluoride activity than does a corresponding amount of Known addition, known subtraction and Gran's plot procedures have been discussed for electro- plating systems, 2509765 With regard to nuclear fuel re-processing systems, fluoride has been determined116 MOODY AND THOMAS in zirconium de-cladding solutions, uranium feed solution and in uranium final product solutions.Sample pre-treatments involve dilution, complexing of metal constituents, or separation on a cation-exchange c0lumn.~66 This study has been complemented by Entwistle and Hayes,438 whose method depends on a constant ionic strength and constancy in the ratio of total fluoride to free fluoride for accurate fluoride determinations in uranium metal and uranium oxides. Other uses of the fluoride electrode are for fluorine determination in wood preservatives and treated fuming nitric acid,768 glass etching769 and silver brazing fluxes.770 The determination of nitric acid in oleum used in the explosives industry is carried out with a nitrate-sensitive electrode on a solution that has been diluted to known volume after a determination of the total acidity.771 The nitrate ion con- centrations obtained from calibration graphs are within k0.2 per cent.of those obtained by the nitrometer method. The perchlorate electrode has been used to monitor the ammonium perchlorate content of plastic-bonded explo~ives,~7* and the chloride electrode for the potentiometric titration of chloride released from the tris(2-chloroethy1)phosphate contained in PBX-9404 explosive, following com- bustion in an oxygen b0mb.77~ Batch materials used in glass manufacture can be monitored for sodium and calcium with selective sodium and calcium ion-sensitive electrodes following acid digestion, dilution and pH In this way, the soda and limestone contents of a batch were determined with precisions of within k0.4 per cent.and kO.72 per cent., respectively. To avoid having to pay strict attention to the pH and ionic strength of solu- tions, an application of the silver sulphide electrode to determining the sulphide content of lime liquors used in leather processing776 depends on it being used as an indicating electrode in potentiometric titrations, where sulphide lime liquor samples are added to standard silver nitrate.776 A more interesting application of the sulphide electrode is for the direct monitoring of the sulphide ion in the paper and pulp industry.777 Here, the spent ‘black liquor’ is purged with air to minhise sulphur losses and to decrease the release of poisonous sulphur compounds; a periodic knowledge of the sulphide level is, therefore, helpful.During the first hour of oxygenation, the sulphide electrode registers a fifteen-decade decrease in free sulphide compared with nine decades for the less selective oxidation - reduction platinum electrode. However, in the next 30-minute period, the sulphide level actually increases by four decades, whereas the platinum electrode continues to record a further four-decade decrease. The sulphide level is finally lowered to about 10-l8 M after 3 hours’ aeration. Swartz and Light777 made an intensive study of the sulphide electrode as an analytical tool in ‘black liquor’ analysis; direct titration with silver nitrate in 1 M ammonium hydroxide solution gave the amount of all inorganic sulphide present, while back-titration gave the total amount of both inorganic and organic sulphides.However, there were errors caused by the reduction of silver ion by polysulphides and aromatic polyhydroxy compounds ;777 mercurimetric titrations were also un-SELECTIVE ION-SENSITIVE ELECTRODES 117 ~atisfactory.7~7 Frant and R0ss~~8 used an anti-oxidant solution to minimise aerial oxidation, and a cadmium ion electrode to overcome problems with the silver titrations. This two-stage procedure involves an initial cadmium electrode reading of an acetate-buffered cadmium solution to which is added a known volume of the ‘black liquor’, followed by another reading of the cadmium a~tivity.7~~9~7~ The sulphide molarity corresponding to the difference in readings is calculated from a standard Silver has to be separated from polythionic acids in fixing baths before the metal ion is determined with a silver sulphide electrode.780 A sodium electrode has been used for sodium determinations in ‘black liquor’781 to which ammonium sulphate has been added, both as an ionic strength adjuster and as a buffer.It has been suggested that ammonium carbonate may serve in this dual role for this and other liquor ~treams.7~~ Sulphur in petroleum has been determined by combustion and oxidation to sulphate, followed by titration with lead perchlorate to a potentiometric end-point with an Orion solid-state lead electrode.783 Applications to Organic and Pharmaceutical Analysis Hot flask combustion,784~785 oxygen flask ~ombustion786-~~~ and fluorine liberation with sodium biphenyl reagent790 have each been used to prepare samples of organic compounds for fluorine analysis.The subsequent stages involved pH adjustment with TISAB or otherwise, regardless of whether the final determina- tion is direct,785~7~~ or by potentiometric t i t r a t i 0 n . 7 ~ 4 ~ ~ ~ 6 ~ ~ ~ ~ ~ ~ ~ ~ Although the subsequent stages are handled in polythene or PTFE vessels, the combustion stage is carried out in glass vessels;784-787 Shearer and modified a polypropylene sample bottle, while Hozumi and A k i m o t ~ ~ ~ ~ used a silica flask to avoid the low results obtained with borosilicate glass flasks.The use of the fluoride electrode as an end-point detector in potentiornetric titrations is beset with problems concerning actual end-point location.7~785*791~70* The conditions necessary for successful titration have been reported by Francis, Deomarine and Per~ing~~d. Pavel, Kuebler and Wagner785 did not dispute the undoubted accuracy of the titration method, if performed slowly and carefully, but used the direct method for its convenience in time and procedure and freedom from sulphur and phosphorus interference. The potentiometric titration procedure is best carried out in a mixed-solvent system.784~786-788~792~793 Organic compounds of pesticidal and pharmaceutical interest have also been analysed for other halide^.^^'-^^^ Thus, the ionisable chloride of the hydrochlorides of drugs have been determined directly794JQ5 with a chloride electrode, while bound chloride, bromide and iodide require a preliminary Schoniger oxygen-flask stage prior to their potentiometric titration with an appropriate halide-sensitive elec- The bromine contents of n-butyl bromide, bromocamphor, 4bromoaceto- phenone, 5-bromosalicylic acid and 4-methoxy-3,5-dibromobenzoyl chloride have trode.795,796,798118 MOODY AND THOMAS been determinedao0 with a Radelkis OP-Br-7 112-C bromide electrode after sodium fusion and adjustment of the samples to pH 10 to 11. A modification is the release of bromide by sodium in iso-butanol.8°1 Iodide that was liberated from the hormones, 3,3’,5’-triido-~-thyronine and 3,5,3’,5’-tetraiodi-~-thyronine, by treat- ment of suspensions of the samples at pH 11 with nascent hydrogen was determined with an Orion iodide electrode after the mixture had been neutralised with hydrochloric acid.802 The chloride content of pharmaceutical-grade aluminium hydroxide gels has been determined with a chloride electrode by using an aqueous suspension of the material.803 The quantitative reduction, or photo-decomposition by illumination with a powerful light source, of cyanocobalamin liberates hydrogen cyanide, and this was used to precede the assay stage804 with a cyanide-sensitive electrode at pH 11.M range has been determined by direct potentio- metry with a sulphide electrode,*05 but a potentiometric titration procedure is based on either silver nitrate or mercury(I1) nitrate for the 10-1 M to M range.The direct titrations in each case exhibit two steps, the first corresponding to a metal sulphide product and the second to a metal cyanamide.805 Thioacetamide has been similarly assayed.80s Hydrogen sulphide release from amino acids has been monitored,807 and the silver sulphide membrane electrode has also been used for the potentiometric titration of thiols, e.g., L-cysteine and 2-mer~aptoethanol.~~~ The thiol is added to standard silver nitrate,808 care being taken over possible halide interferences. For disulphide groups in proteins, a two-stage reduction method is required to effect the potentiometric titration with standard silver nitrate and an Orion silver sulphide electrode.809 An indirect application of the silver sulphide electrode is the deter- mination of chloride and bromide organic materials by potentiometric t i t r a t i ~ n .~ ~ ~ Of more general application to the determination of sulphur in organic compounds is the method of requiring oxygen-flask oxidation, followed by a poten- tiometric titration of the sulphate with standard lead perchlorate and lead ion- sensitive electrode as end-point indicator.810 Halogens, in general, do not interfere, but fluoride is eliminated by complexation with boric acid, and phosphorus must be separated before hand. 810 Thiourea in the 10-1 M to Miscellaneous Applications Apart from instances of direct use of selective ion-sensitive electrodes for determining ion activity, but without reference to any specific applications,811Bs12 there are many miscellaneous applications.These range from the application of halide and sulphide electrodes as gas chromatographic detector~8l~-~l~ and of a copper electrode for ion exchange chromatographic monitoring,90 to the fluoride electrode in the reactions of sulphur hexafluoride8169817 and chlorofluoranes818 with hydrated electrons. There is also the possibility of application to ions where no selective ion-sensitive electrodes are a ~ a i l a b l e . ~ ~ ~ ~ ~ ~ ~ For example, a l u m i n i ~ m ~ ~ ~SELECTIVE ION-SENSITIVE ELECTRODES 119 and nickel(II)820 can be determined with fluoride and cyanide, respectively, as auxiliary ions. The assays of aluminium in specimen samples by this method agree closely with calculated values.s20 Blanks are recommended where magnesium, copper, lead, silicic acid and calcium are likely to be present.Rather different is the determination of boron in water, soils and plant tissue after conversion to tetrafluoroborate to which the liquid ion exchanger nitrate electrode is sensitive.s21a822 Tungsten has been determineds2, by titrating standard silver nitrate with the sodium tungstate sample by using a dithizone-impregnated membrane indicator electrode,sN but the reverse titrations were unsuccessful, A similar electrode has been used for the potentiometric titration of silver with ascorbic acids25 and with sodium oxalate, potassium hexacyanoferrate(I1) and potassium iodide.826 The determination of fluoride in t u n g ~ t e n , ~ ~ ~ - ~ ~ ~ molybdenums29 and rheniuma2' is possible after they have been fused with sodium nitrate and sodium hydroxide.Even though a Dowex 1-X8 anion-exchange column with 0.5 M sodium chloride elutriant is recommended for separating the fluoride from metal constituents, it is possible, when only molybdenum or tungsten, or both, are present, to measure the pF of the aqueous melt directly.829 The methods cover the range from 1 to 1000 p g g-l of sample with a relative standard deviation of & 2 per cent. A Gran plot procedure is necessary to give a clear end-point indication in the precipitation titration of caesium ions with 12-molybdophosphoric acid by using a selective caesium ion-sensitive electrode as an indicator electr0de.8~0 Silver ion at 4.63 x lo-' M has been determined by direct potentiometry with a silver sulphide e l e c t r ~ d e ~ ~ ~ ~ ~ ~ ~ so that a test solution concentration of 2 x 10-6 M (0.2 p.p.m.) was appropriate in a study of trace silver ion adsorption on to surfaces of Vycor, polyethylene, Teflon and A nitrate electrode has been used to measure small amounts of sodium nitrate in sodium nitrite, the nitrite being first destroyed with hydroxylamine sulphate.833 However, the 0.02 per cent.of nitrate (as NaNO,) consistently formed during the reduction of nitrite must be subtracted from the calculated percentage of sodium nitrate. The results agree with those obtained by the more elaborate bracketing method of Potterton and Shults,202 the accuracy being within +O-02 per cent.for 0.06 per cent. to 0.2 per cent. of sodium nitrate. A salicylate ion-sensitive electrode facilitates the monitoring of the electro- reduction of salicylic a ~ i d , ~ ~ a the sample aliquots being diluted to the M salicylate concentration range and the pH adjusted to 8.5 New developments continue to extend the range of possible applications; for example, an electrode with a membrane prepared from sodium tetraphenylborate, and phenoltrifluoroacetone in P-nitrocymene and poly(viny1 chloride) in THF can be expected to be useful for determining large onium ions.s35 Applications in Potentiometric Titrimetry The general principles and limitations of selective ion-sensitive electrodes as indicator electrodes in potentiometric titrations have been discussed above, and120 MOODY AND THOMAS some references to their applications in this role have been made in the classified survey of applications.However, many other papers have been specifically directed to more academic studies of their scope as indicator electrodes. A titration cell - electrode assembly for liquid ion-exchange electrodes has been evaluated for precipitation titrations of perchlorate and nitrate with tetraphenyl- arsonium chloride and diphenylthallium sulphate, respecti~ely.~36 Smith and M a ~ ~ a h a n ~ ~ ~ titrated perchlorate and tetrafluoroborate with tetraphenylarsonium chloride in a temperature-controlled jacketed cell, as a temperature of 2 ° C sharpened the titration curves. The auxiliary role becomes evident in potentiometric titrimetry; e g ., chloride, bromide, iodide, sulphide and silver electrodes have been used to indicate the end-point in the titration of tetraphenylborate ions with silver nitrate,838 and the lead ion-sensitive electrode has been used for sulphate,783~810~83g~840 oxalatesu and phosphate84* with lead perchlorate as titrant. Lead nitrate has also been used as the titrant for various anions.87 This wide use underlines possible risks of inter- ference. Other similar examples include the copper ion-sensitive electrode in titrations with copper nitrate and copper perchlorate, respectively, of nitrilotri- acetic acidj8@ and the back-titration of 1,2-diaminocyclohexane-NNN'N'-tetra- acetic acid (DCTA) in the determination of alumini~m.~'4 The divalent cation electrode has been recommended in a back-titration for copper(II), cobalt(II), cobalt (I1 I), nickel( 11) , iron( 11), iron( 111), mercury( 11), europium( 111) , manganese( 11) or calcium with triethylenetetraminehexa-acetic acid and using a standard solution of the appropriate lead, zinc or calcium salts as the back-titrants.805 Direct titrations of calcium and magnesium with EDTA208~367~390~84~~8~7 and of copper(I1) with EDTAgop8"s have been carried out.The position of the true end- point needs proper appraisal, as emphasised by an automated titration study of calcium with EDTA.847 A sodium-sensitive glass electrode in the complexometric titration of sodium with DCTA is claimed to give 2 per cent. accuracy.849 This titration is possible in the presence of other ions.849 An interesting variation of complexometric titrations is the use of a small amount of copper(I1) ions in titrations of calcium or zinc with EDTA and with the copper(I1) 'Selectrode' as indicator e1ectr0de.l~~ Another is to use copper - EDTA or copper complexed with any other chelating titrating agent as the indicator, again in conjunction with a selective copper-sensitive indicating electrode.155~388-390 The principle here is based on releasing some copper(I1) ions on the addition of the complex to the metal ion solution (4-4 Mn+ + CuEDTA2- + MEDTAn-* + Cu2+ The end-point in each case is revealed by the absence of free copper ions on adding chelating titrant.155~388-390 This method is claimedm9 to be superior to the mercury(I1) - EDTA method of determining lanthanides, and can be adopted for several chelating agents and when two or more metals are present as, for example, in bra~s.~88SELECTIVE ION-SENSITIVE ELECTRODES 121 Silver sulphide electrodes can be used in argentimetric titrations of sulphide J776~850~861 (including halides in sea water8s3), cyanide ,8659866 cyanide and chloride in a single solution,8ss and of bromide and thiocyanate in mixtures following a separation scheme, in which a pH of 7 to 8 is es~ential.~67 Silver sulphide electrodes have also been examined for the sequential titration of chloride, bromide and iodide with silver nitrate, as well as titrations of cyanide and thio- cyanate;s08 the end-point breaks are greater than with a silver-billet electrode.Sulphide hydrolysis prevents the use of the silver sulphide electrode for the argentimetric titration of sulphide at low concentrations for which sodium plumbate(I1) is recommended850 as the titrant.Solid-state cyanide and halide electrodes have also been used as indicator electrodes,20~79s~796~8s~~868~859 mainly for simple halide and cyanide argentimetric titrations, but also for the sequential titration of chloride and azideJas8 and of mercury with sodium iodide.ss9 The non-interference of perchlorate in the direct titration of nitrate with diphenylthallium(II1) sulphate , using the Orion liquid ion-exchanger membrane nitrate electrode, is rather s ~ r p r i s i n g . ~ ~ ~ . ~ ~ ~ Lanthanum fluoride electrodes have figured in many potentiometric titra- t i o n ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ such as fluorine in organic compounds , 784s793 the micro- determination of fluoride in the presence of phosphate,ss1 and aluminium866 by titration with However, most are fairly detailed studies to establish proper titration conditions for titrant and end-point detection, respectively.Thus, Francis, Deomarine and Per~ing~~' favour a slow and constant titration rate of fluoride with standard lanthanum nitrate or thorium nitrate. Lingane791 examined thorium, lanthanum and calcium ions as possible titrants, and late1-7~~ made an extended study for the improvement of the titration curve by the addition of 60 to 70 per cent. v/v of ethanol. In this respect, 80 per cent. v/v of ethanol was used by Light and MannionTg3 as a titration medium, 80 per cent. v/v of dioxan by Selig,861 while Bazelle recommended 60 per cent.v/v of 2-propano1.208 Other titrants assessed include electrochemically generated lanthanum,868 tetraphenylantimony sulphatess4 and aluminium nitrate.865 The fact that fluoride titrations do not produce compounds according to exact stoicheiometry emphasises Lingane's observation791 that the point of maximal slope in the titration curve should not be taken as the end-point, but rather that the titration should be to the true equivalence point potential. Liquid membrane electrodes responding to detergent anions can be used for the potentiometric titration of an ionic detergent in aqueous solutions in the presence of inorganic salts.lo3 Selective Ion-sensitive Electrodes in Non-aqueous Solvents Potentiometric titrations with the fluoride electrode show that it is functional in mixed-solvent media.Hozumi and Akimoto,868 having observed that a sodium glass electrode gave a sharp inflexion close to the equivalence point in an argenti-122 MOODY AND THOMAS metric titration of halides at high concentrations of organic solvent, adopted the phenomenon for the titration of halides from organic halogens in 90 per cent. v/v of acetone. McClure and R e d d ~ ~ ~ ~ have reported cationic glass electrode response to alkali metal ions in propylene carbonate, acetonitrile and dimethylformamide, but the glass electrode ceased to respond in acetonitrile after 3 months. Alkaline errors are also shown by glass electrodes in isopropan~l.~~~ For actual applications in non-aqueous solvents, the response of solid-state copper( I) ,4d8 ~ o p p e r ( I I ) ~ ~ l and cadmiums72 electrodes in non-aqueous media have been described.Even though the copper(I1) response was linear in methanol from 10-1 to 10-4 M, an unaccountable interference arose in more dilute solutions.871 Breaks in the titration curves of complexometric potentiometric titrations in methanol, acetone and acetonitrile show the possible use of the copper ion electrode for complex formation studies in non-aqueous solvents, but the applicability to analytical problems was not adequately e~tablished.87~*~7~ A 50 per cent. v/v dioxan solution has been used for titrating sulphate with lead p e r c h l ~ r a t e . ~ ~ ~ It also im- proves the potentiometric titration of sodium sulphate with lead nitrate, even though the effect of organic solvent generally is to give lower calibration dopes with a heterogeneous-membrane lead electrode than in ~ a t e r .~ 7 Pungor and Kazarj an873-876 conclude that silicone rubber matrix membrane electrodes cannot be used in pure ethanol, acetone, dimethylformamide, aceto- nitrile or benzene-methanol. However, the electrodes can be used in aqueous methanol and aqueous ethanol with 90 per cent. but only in 40 per cent. l-propanol and 2-pr0panoP~~ and 60 per cent. a~etone.~74-~~~ The threshold is governed by the dissolution of membrane materials. However, the restriction to 60 per cent dimethylformamide was imposed by lack of electrode response. Within the functional range of these systems, the standard aqueous media equations con- cerning response and selectivity still hold.874 Conclusion Despite limitations concerning selectivity and the location of true titration end-points, selective ion-sensitive electrodes have clearly given new impetus to analytical potentiometry.Even though considerable research effort is still required for a complete understanding of the underlying mechanism and of the full implica- tions of activity considerations, continuing experimentation will certainly produce valuable criteria for improving and extending their utility. 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