Anal. Chem. 1998, 70, 53R-106R
Kinetic Determinations and Some Kinetic Aspects of Analytical Chemistry Stanley R. Crouch* and Thomas F. Cullen
Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 Alexander Scheeline and Ewa S. Kirkor
University of Illinois, Department of Chemistry, 600 South Mathews Avenue, Urbana, Illinois 61801 Review Contents Books and Reviews Principles of Kinetic-Based Methods Instrumentation, Automation, and Data Processing for Kinetic Methods Kinetic Methods Based on Catalytic Reactions Kinetic Methods Based on Uncatalyzed Reactions Multicomponent (Differential) Kinetic Determinations Kinetics and Mechanisms of Some Reactions of Analytical Interest Kinetic Aspects of Electrochemical and Separation Processes Applications of Luminescence Miscellaneous Kinetic Methods Literature Cited
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In this review, we have attempted to retain the overall organizational structure of the previous review (Mottola, H. A.; Pe´rez-Bendito, D. Anal. Chem. 1996, 68, 257R-289R). With few exceptions, the papers reviewed were selected from those that appeared in Chemical Abstracts during the October 1995-October 1997 period. For the most part, papers considered were published in the English language in refereed journals. References to the patent literature and to dissertations are not included. We have included only those conference proceedings that we felt were readily available to most readers. Where non-English articles are considered, the Chemical Abstracts reference number is given. The number of applications of kinetics to analytical chemistry continues to grow at a rapid pace. This year some 14 000 computer-generated abstracts were screened manually for possible inclusion in this review. The final database included over 2000 references. Because the subject of this review can be interpreted very broadly, we have chosen to narrow our considerations to those references specifically citing some dynamic or kinetic aspect and, where overlap with other reviews seemed probable, to those articles not likely to be cited elsewhere. Previous reviews in this series have not included enzyme-catalyzed reactions, because of the enormous number of papers in this area. We have chosen here to include some papers discussing enzymic reactions. The papers cited were restricted to those that in our opinions illustrate a novel analytical approach or develop some new measurement or chemical principle based on enzyme kinetics. We have chosen not to report on immunoassay techniques including enzyme-based immunoassay methods. In many cases, references could have been placed in multiple categories (e.g., catalytic determination S0003-2700(98)00005-5 CCC: $15.00 Published on Web 04/10/1998
© 1998 American Chemical Society
monitored by electrochemistry). We have attempted to place the articles in the category that seemed most logical based on what was emphasized (e.g., whether catalytic determination was stressed or electrochemistry). The authors are certain to have made many errors in judgment during the classification process. The Sixth International Symposium on Kinetics in Analytical Chemistry is scheduled to take place in Kassandra, Chalkidiki, Greece from September 16 to September 19, 1998. Papers are being invited in the areas of catalytic methods (including enzyme catalyzed reactions), multicomponent (differential) kinetic methods, continuous-flow processing, and any aspect of a kinetic nature with impact on analytical methodology. Organizing Committee Chairpersons are Professors M. I. Karayannis (University of Ioannina) and C. Papadopoulos (Aristotelian University of Thessaloniki). The Fifth International Symposium held in Moscow in 1995 was the subject of a special issue of The Analyst, edited by H. A. Mottola (Analyst 1996, 121, 379-439). A special issue of the Spanish journal Quı´mica Analı´tica, edited by D. Pe´rez-Bendito (Quı´m. Anal. 1996, 15, 266-355) was devoted to applications of kinetics in analytical chemistry. Many of the papers from these two special issues are discussed later in this review. BOOKS AND REVIEWS Mottola (1) has presented a perspective on the developments in the field of kinetics applied to analytical chemistry from the time of the Fourth International Symposium, held in Erlangen, Germany in 1992, until the Moscow Symposium in 1995. He saw an increase in the number of papers devoted to chemiluminescence and bioluminescence measurements and an increase in the number of citations dealing with multicomponent determinations. Genuine changes in direction were not seen during this period. General Information. One of the important trends in kineticbased methods is the continued development of measurement and data-processing approaches aimed at reducing the influence of experimental variables on the quality of results. Pardue (2) has presented a unified view of kinetic methods emphasizing improvements in the overall ruggedness relative to conventional techniques. The general approach of using transient data to compute equilibrium or steady-state values of signals can show improvements in ruggedness of 10-100-fold compared to usual methods. Another review has discussed data analysis of time-resolved spectroscopic measurements (3). Methods used to treat kinetic data from complex chemical and biological systems were stressed using only a minimum amount of mathematics. Analytical Chemistry, Vol. 70, No. 12, June 15, 1998 53R
Pe´rez-Bendito and Silva (4) have referred to the applications of chemometrics to kinetic-based determinations as “kinetometrics” and have described recent applications to error compensation and to multicomponent determinations. The utility of Kalman filtering, multivariate calibration methods, and artificial neural networks were discussed. Another review from this group (5) dealt with advances in the analysis of pharmaceuticals by kinetic methods. Kinetic approaches based on stopped-flow methods combined with fluorescence polarization immunoassay and micelle-stabilized room-temperature phosphorescence were considered along with sensitized luminescence methods and the use of the continuous addition of reagent technique. Other methods based on kinetometric approaches were also reviewed. Selfassembled systems and their applications to kinetic-based determinations were the subject of a review by Lopez Carreto and coworkers (6). The kinetics of self-assembly processes and their implications in kinetic determinations were also considered. The Monte Carlo simulation method as applied to reaction processes was the subject of one comprehensive review (7). Among processes considered were heterogeneous reactions far from equilibrium, irreversible phase transitions, reactions at interfaces, and diffusion-controlled reactions. Several authors included kinetic methods in general reviews of determinations of specific species. Duan (8) discussed the spectrophotometric determination of chromium in metals and alloys, while Zhu and Wu (9) reviewed photometric methods for determining copper. The determination of nitrite by photometric methods including kinetic methods was the subject of a review by Fu and Ying (10). The application of micellar systems to kinetic methods was the subject of a review by Cai and co-workers (11). The discussion included characteristics of micellar catalysis, micellar modification of properties of systems, and applications of micelles in multicomponent determinations. Several reviews have dealt exclusively with multicomponent kinetic determinations. Cerda` and co-workers (12) have reviewed several multicomponent statistical methods as applied to kinetic determinations, including multiple linear regression, various nonlinear optimization techniques, and methods based on factor analysis. These authors have given an excellent description of methods to resolve mixtures by using single-channel detectors, multichannel detectors, or multiple single-channel detectors. Cullen and Crouch (13) have described the application of multivariate calibration techniques to multicomponent kineticbased determinations. Classical least-squares regression, principal component regression, partial least-squares regression, and artificial neural networks were discussed with emphasis on recent applications to kinetic methods. The application of catalytic reactions to trace analysis was the focus of a review by Kawashima and co-workers (14). These authors describe the design of catalytic methods based on redox processes, ligand substitution reactions, and metalloporphyrin formation reactions. Mechanisms of the reactions were described in several cases. Catalytic spectrophotometric techniques are a part of a review (15) on the determination of the oxidation states of iron in natural waters. Also considered were conventional spectrophotometric methods, chemiluminescence, fluorescence, voltammetry, and potentiometry. Catalytic kinetic methods were 54R
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also described in a review by Qu (16) dealing with developments in the determination of precious metals. Other methods considered in this review were those based on atomic spectrometry, conventional spectrophotometry, luminescence spectrometry, electrochemistry, mass spectrometry, flow injection, chromatography, radiochemistry, X-ray spectrometry, and wet analytical techniques. A review has also been published on the determination of molybdenum in plants by automated catalytic procedures (17). A review on spectrometric methods for determination of cyanide includes catalytic kinetic methods (18). Duan has discussed catalytic kinetic methods for determining manganese (19) in mining and metallurgy and has also reviewed catalytic methods for arsenic, antimony, selenium, tellurium, and thallium (20). Cao (21) presented a discussion of organic analytical reagents and their applications. Catalytic spectrophotometric methods were included. Clinical and Bioanalytical Chemistry. Several reviews appeared in the clinical and bioanalytical areas. Shen (22) reviewed enzymes as analytical reagents with a focus on the development of kinetic enzymic methods for the determination of L-phenylalanine and L-tyrosine in physiological fluids. Rubingh (23) has reviewed the influence of surfactants on enzyme activity including the relationship between homogeneous solution activity and that at solid/liquid interfaces. The determination of enzymatic activities, coenzymes, and substrates by capillary electrophoresis has been reviewed (24). Both off-line and on-line assays of enzyme activities are discussed with special emphasis on the electrophoretically mediated microanalysis (EMMA) technique. Recent developments in determining substrates as well as in conducting kinetic studies on-line are summarized. The fundamentals of direct electron transfer in enzymecatalyzed electrode reactions and the electroanalytical applications of bioelectrocatalytic systems have been critically reviewed (25). Concepts underlying the mechanism of electron transfer were discussed along with electroanalytical devices based on amperometry and potentiometry. Blomquist (26) discussed the kinetic analysis of enzyme activities with an emphasis on the analysis of human placental 17β-hydroxysteroid dehydrogenase. Petri and Brenowitz (27) have reviewed thermodynamic and kinetic approaches to nucleic acid fingerprinting and have included applications of stopped-flow methodology. The strategies that can be employed for immunoassays have been reviewed by Kricka (28) with an emphasis on methods that are convenient, simple, reliable, sensitive, and capable of multiple simultaneous determinations. Several recent advances in chemiluminescent and bioluminescent assays for alkaline phosphatase and acetate kinase have been presented (29) along with chemiluminescent and bioluminescent immunoassays using these enzymes as amplifying labels. Electrochemistry. An extensive review of electrochemistry from 1992 to 1995 has been presented by Bockris and co-workers (30). The topics covered include instrumentation, interfacial structure, electrode kinetics, and photoelectrochemistry. The kinetics of electrode processes in nonaqueous and mixed solvents have been examined by Galus (31). In addition, this review includes information on equilibrium electrochemistry in these solvents including a comparison of electrode potentials. Miller (32) has presented an interesting conceptual description of heterogeneous electron-transfer kinetics at metallic electrodes. He
discusses in detail the differences beween homogeneous and heterogeneous electron transfer in terms of the Marcus theory. Fahidy and Gu (33) have considered some of the recent advances that have been made in studying the dynamics of electrode processes including mathematical methods, modeling, and data interpretation. Sepa (34) has revisited the problem of activation energies of electrode reactions, while Amatore (35) has extensively described the progress that has been made in understanding electrochemistry at ultramicroelectrodes. This review includes a discussion of the advantages of ultramicroelectrodes over electrodes of conventional dimensions. Lovric (36) has given a thorough review of square wave voltammetry and polarography including the applications of these methods for determining the kinetics and mechanisms of redox reactions. The contributions of Russian academician A. M. Frumkin have been described (37), with a focus on the development of the general theory of the kinetics and mechanisms of electrode processe. Miscellaneous. Several additional reviews, while not dealing specifically with kinetic aspects of analytical chemistry, should be of interest to readers of this article. Single-molecule detection by various techniques has been reviewed during this period. Kelso (38) has presented an interesting discussion of the biomedical applications of single-molecule detection. The use of confocal and near-field scanning optical microscopy, photon-counting cameras, fluorescence correlation, and time-gated spectroscopy to detect luminescent labels was stressed. The spectroscopy and dynamics of single molecules were the subject of a review by Trautman (39), who described fluorescence intensity-based measurements as well as those based on lifetimes. Bard and Fan (40) have considered two approaches to single-molecule detection by electrochemical methods. One uses electrogenerated chemiluminescence, while the other involves trapping electroactive molecules between an ultramicroelectrode tip and a conductive substrate in a scanning electrochemical microscope. Flow analysis methods, which are often used to automate kinetic-based determinations, were the subject of several reviews. Hansen (41) has considered the principles and applications of flow injection (FI) in flow-through biosensors. Enzyme-based procedures with optical and thermal detection and renewable surface immunoassays were used as examples to demonstrate the enhanced capability of many biosensors when combined with flow injection. An overview of the quality of FI methods for automating food analyses was made by ranking the methods in terms of accuracy, applicability, precision, selectivity, sensitivity, dynamic range, and sample throughput (42). A ranking scale is proposed as a method for choosing the most appropriate analytical method for a given type of food analysis. Baxter and Christian (43) reviewed sequential injection analysis focusing on methods for bioprocess monitoring. Various assays and the chemistry involved in these were presented. The processing and analysis of complex samples including solids using FI methods were reviewed (44). The principles underlying a variety of sample pretreatment methods and their applications in rapid determinations and process monitoring were discussed. Trends in the use of robots in analytical laboratories have been identified (45). Liu and Dasgupta (46) have presented a very interesting review on liquid drops and their applications in analytical chemistry. The use of droplets for renewable gas
sensing, windowless optical cells, and reaction vessels was considered. Micellar and microemulsion systems were the subject of a review by Tondre and Hebrant (47). Of particular interest in this review is a consideration of the removal of metal ions using micellar extraction. Aggregation phenomena and microheterogeneity in surfactant solutions as studied by NMR methods were the subject of another interesting article (48). Topics considered were self-assembly of surfactant systems, NMR relaxation studies, and self-diffusion phenomena. Ross and Xue (49) have presented an interesting review on the application of inorganic membranes to catalytic reactions, while Hubbard and Van Eldik (50) have comprehensively discussed the effect of pressure on inorganic reactions. Among the processes considered were electron-transfer reactions, ligand substitution reactions, and radiation-induced reactions. Also of considerable interest to readers of this review should be the book by Zolotov (51) dealing with macrocyclic compounds in analytical chemistry. Chapter topics include synthesis, selectivity, solvent extraction, sorption and chromatography, ion-selective electrodes, and determination of organic compounds. PRINCIPLES OF KINETIC-BASED METHODS During the time period covered by this review, several novel kinetic determination procedures have been developed. In some cases, instrumentation has been used in a novel manner; in others, workers have developed new means for error compensation. We also touch on some educational aspects. New Kinetic Measurement Methods. Brauner and Shacham (A1) investigated the correlation of traditional linear regression models with modern nonlinear regression applied to the Arrhenius equation. In an important result, the authors concluded that the traditional method is statistically equivalent to the more precise nonlinear method. This implies that constants determined using classical methods and published in the literature are trustworthy. A general progress curve method for the kinetic analysis of enzyme reactions has been developed (A2), and a simplified numerical solution method has been described for the Nernst-Planck multicomponent ion exchange kinetics model (A3). The numerical solution obtained from the method compares well with solutions provided by other methods. A selective kinetic method has been based on detecting the intermediate product in successive reactions (A4). These intermediates, when not the analyte of interest, often act as interferences. The method relies on a two-point kinetic determination. The two points are chosen such that the interfering intermediate (which has a peak-shaped kinetic profile) is at the same concentration at both times. The development of a generalized flow equation for a reactiondiffusion system has been reported (A5). In this work, the author relates the kinetic coefficients of the system to a specific microscopic mechanism of reaction and diffusion. In another paper, procedures for the generation and collection of transient absorbance data were reviewed (A6). Signal generation, collection, and processing were discussed. Several new kinetic methodologies have been based upon novel instrumental methods. A coupled HPLC/NMR system has been used to measure reaction kinetics (A7), and a second-derivative UV spectrophotometric method has been used for kinetic studies (A8). Gas chromatography/mass spectrometry has been used Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
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to measure the transport of glucose in vivo (A9). The authors employed labeled glucose molecules in order to quantitate the rate of glucose appearance and disappearance. A simple method was reported (A10) for determining reaction kinetics from Raman spectra of molecular complexes. The method utilizes the analysis of Raman line shapes for the determination of reaction rates. Friedman et al. (A11) have reported on the use of time-resolved titrations for the determination of Asp-85 in bacteriorhodopsin, while Dianxun and co-workers (A12) have explored the use of He I photoelectron spectroscopy for the kinetic study of a chemical reaction. The latter method depends on the existence of a nonoverlapping band in the photoelectron spectra of the reactant and the product. Ultratrace levels of arsine have been detected with a chemical sensor (A13). The operation of the sensor is based on work function measurements. The authors report detection limits in the parts-per-trillion range with continuous operation based on surface reaction kinetics. An experimental approach for obtaining the kinetic parameters of ribosomes has been described (A14). The approach is based upon gaining knowledge of the other kinetic processes proceeding concurrently with the reaction of interest. Error Analysis and Compensation Methods. It is imperative in kinetics, as in all of science, that the errors inherent in measurements be quantified and, when possible, eliminated or compensated. Several researchers have reported work that is related to these ends. Schuck and Minton (A15) have developed elementary tests for self-consistency that can be applied to kinetic data from biosensors. Workers in Rorabacher’s group (A16) have designed and implemented a mathematical treatment that corrects for the concentration gradient within a stopped-flow observation cell for reversible second-order reaction kinetics studied by longitudinal absorbance measurements. As a result of this implementation, second-order rate constants up to 108 M-1 s-1 have been determined (a 10-fold extension of the previously demonstrated limits for this method). Stewart and Thompson (A17) have studied the uncertainty in computed species concentrations resulting from variations in parameters affecting reaction rate. The study focused on the change in the magnitude of concentration uncertainty as a function of temperature changes and the difference resulting from the selection of mean, rather than median, rates for model calculations. Linear least-squares analysis can be used to solve for rate constant ratios kA/kB by plotting ([A]0/[A]t) vs ln([B]0/[B]t). Other workers (A18) have determined that since the above method does not take into account random error in [A] and [B], a small but systematic bias in the relative rate constants may arise. The authors explored the magnitude of this bias using Monte Carlo simulations. Mauser and Polster (A19) have proposed three theorems for the spectroscopic-kinetic analysis of chemical reactions. The first theorem states that a reaction mechanism can be experimentally disproved, but not proved. The second states that two strictly linear reaction systems that have the same number of steps cannot be distinguished by purely spectroscopic means. The third theorem limits the extent of distinguishability for thermally controlled reaction systems with at least one second-order step in a manner similar to the second theorem. 56R
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Lim and Pardue (A20) have described the adaptation and evaluation of an error-compensating method for kinetic determinations of DNA. The method relies upon background- and flat-field correction of time-dependent fluorescence data. The corrected data are fit to a model to predict the total change in fluorescence that would occur if the reaction were to proceed to equilibrium. Straathof and Heijnen (A21) have explored instances where the rate constants of enzymic reactions cannot be calculated from the steady-state parameter values. The authors have described new constraints that allow them to predict situations in which rate constants are identifiable by steady-state methods. Educational Aspects. Several papers have dealt with new methods for teaching students the general principles of kinetics. One introductory experiment incorporates curve fitting as an alternative to conventional methods for analyzing kinetic data (A22). An undergraduate kinetics experiment has been based on the clock reaction of Methylene Blue and L-ascorbic acid (A23). Another kinetics experiment allows students to determine rate constants in consecutive first-order systems (A24). A computer program was described that can be applied to the experiment. A stopped-flow kinetics experiment that uses low-cost, low-maintainance equipment of straightforward design has been described (A25). The experiment measures the delay in the onset of chemiluminescence. INSTRUMENTATION, AUTOMATION, AND DATA PROCESSING FOR KINETIC METHODS Considerable work has been done in the area of instrumentation and automation of kinetic methods. Papers dealing with novel instruments and instrumental methods, methods of automating kinetic determinations, and techniques for processing kinetic data are discussed in this section. Sample Handling. Several authors have described new methods for handling samples in conjunction with kinetic determinations or measurements. Many of these involve flow methods. For example, an automated flow-reversal extraction method has been described (B1). A Cu(II)-pyridine complex reacts with free fatty acids (FFA), and the resulting Cu(II)-FFA complex extracts into the organic phase. Continuous monitoring at 716 nm provides a multipeak absorbance-time profile. Oliveira and co-workers (B2) have reported on a computerassisted flow-splitting method. The splitting is achieved by a threeway solenoid valve that defines the flow profile and directs portions of the processed sample to different flow streams. The method was applied to the simultaneous determination of copper and zinc in plant digests. Margerum’s group has continued to develop the pulsedaccelerated flow (PAF) method. First-order rate constants as large as 500 000 s-1 have been measured with this technique (B3). The modes by which samples are mixed in PAF systems were also discussed. This group has also described (B4) a pulsed accelerated-flow spectrometer with position-resolved observation. This instrument allows monitoring of the reaction at 128 positions in the flow reactor. The resulting data can be applied to the analysis of fast, multistep reactions. A microdialysis flow cell for Raman spectroscopy was described (B5). This flow cell permits rapid collection of Raman spectra. A channel flow cell has been developed (B6, B7) to allow the investigation of transient phenomena at the solid/liquid interface.
The flow cell was successfully used to monitor the reaction between the dye Orange G and virgin cotton cloth. A thin-layer flow cell has been developed by Osipov and colleagues (B8). The cell is designed so that antibodies can be immobilized on the inner surface of the flow cuvette. Application of the cell to a chemiluminescent immunoassay was discussed. Many sensors use kinetic-based methods. A surface acoustic wave (SAW) conductance sensor was developed for the rapid detection of ribonuclease (B9). This sensor relies on a change in conductance caused by the reaction of RNAase and RNA. In related work, a SAW impedance sensor has been developed for the determination of trypsin (B10), and a study of surface plasmon biosensors for the kinetic analysis of macromolecular interactions has been reported (B11). The technique allows the elucidation of assembly mechanisms and rate constants. One area in which exciting advances have been made is in small-volume kinetic assays. Liu and Sweedler have discussed the use of small-volume rectangular channels for such determinations. In one paper (B12), the authors describe the use of channel electrophoresis with a cylindrical sampling capillary. The system was shown to be capable of effecting time-based dynamic microseparations. The formation of a fluorescent product was monitored. In other work (B13), the authors describe the application of the system to the dynamic separation of fluorescently labeled amino acids. Capillary flow injection has been reported for kinetic methods and applied to the kinetic determination of ascorbic acid (B14). Reagent volumes of ∼20 µL can be employed vs ∼600 µL for a conventional flow injection system. Stopped-flow instruments were the subject of several reports. One involved the construction of a low-cost stopped-flow unit (B15). A high-pressure stopped-flow spectrometer has been described (B16) for kinetic studies of fast reactions with absorbance and fluorescence detection. The dead time of the system was found to be less than 2 ms. A single-sweep nanosecond time resolution laser T-jump apparatus has been reported (B17). The system is designed for aqueous solutions and relies on absorption of laser light by water. This removes the need to add absorbing species only for their ability to produce a temperature change. Automation of kinetic determinations has also received attention during this review period. A modular laboratory unit that is equipped with three different gradientless reactors was described (B18). The application of the system to kinetic determinations was discussed. A mechanized method for the direct determination of boric acid in shellfish has been proposed (B19). The sample preparation and processing is automated, as is sample transport through a flow system. The reaction of boric acid with Azomethine H is monitored spectrophotometrically in a flow-reversal system. The instrumentation available for infrared kinetic studies has been reviewed (B20). Single-wavelength and broad-band techniques are discussed. Data Collection. Several authors have described novel data collection methods for kinetic determinations and kinetic studies. The use of ultraviolet cavity ring-down spectroscopic detection for kinetic studies was the subject of one study (B21). The authors applied the cavity ring-down technique to a laser photolysis reactor and measured the rate constants of several gasphase reactions.
Subnanosecond gated image intensifiers have been proposed (B22) as detectors for various rapid phenomena and for fluorescence lifetime imaging. A photoacoustic cell that is suitable for kinetic measurements has been developed (B23). The cell is capable of nanosecond time resolution and is based on a layered scheme of laser-induced sound excitation and detection. The application of time-resolved Fourier transform emission spectroscopy to kinetic measurements has been explored (B24). The technique is especially well suited for detecting weak fluorescence from small molecules and transient species. Others (B25) have developed a rapid mix flow cytometer with subsecond kinetic resolution. The fast mixing time of this device makes fast, sensitive kinetic measurements possible. Novel Data-Processing Methods for Single-Component Kinetic Determinations. Multicomponent data-processing methods (see next section) have received more attention than singlecomponent methods during this period. A few authors, however, have reported novel methods for kinetic determinations of single species. As one example, partial least-squares regression has been applied to individual kinetic determinations (B26). The method compared favorably with a traditional initial rate method. Malinowski (B27) has used automatic window factor analysis as a method for determining concentration profiles from evolutionary spectra. The proposed method was found to work automatically and efficiently. Love and Pardue (B28) have reviewed data-processing options for kinetic-based single-component determinations of noncatalysts. Special attention was paid to the effect of random noise. Techniques discussed include two-point fixed time, one-rate, partial sums, successive integration, three- and four-point fixed-time, and two-rate options, as well as the predictive curve-fitting approach. Novel Data-Processing Methods for Multicomponent Kinetic Determinations. Several authors have made significant contributions in the area of data-processing methods for multicomponent kinetic determinations. Notable among these contributions are the application of artificial neural networks to and the rise in popularity of multivariate calibration techniques for multicomponent kinetic determinations. Most interestingly, true second-order data-processing techniques (such as generalized rank annihilation, trilinear decomposition, and multivariate curve resolution) are being added to the arsenal of data-processing techniques available. Table 1 lists most of the recent papers that focus on data-processing methods for multicomponent kinetic determinations. The table is arranged alphabetically by the first technique mentioned in each paper. Techniques for Modeling Chemical Kinetics. Several authors have described techniques for determining physical constants of chemical sytems. A nonlinear least-squares model has been applied (B48) to the kinetic determination of stability constants and to cyclodextrin inclusion complexes. A nonlinear regression method for estimating microbial kinetics parameters was reported (B49). The method uses substrate depletion and biomass growth data to estimate a variety of relevant biological kinetics parameters. Artificial neural networks have been used to qualitatively correlate molecular structure to activity (B50). Artificial neural networks were shown to be superior to multiple linear regression for this application. Neural network methodology was also applied to the estimation of kinetic and thermodyAnalytical Chemistry, Vol. 70, No. 12, June 15, 1998
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Table 1. Data Processing Methods for Multicomponent Kinetic Determinations chemometric technique artificial neural networks artificial neural networks artificial neural networks, partial least-squares artificial neural networks, partial least-squares regression, principal component regression artificial neural networks, partial least-squares regression artificial neural networks, principal component regression combination plots component-resolved spectroscopy evolving projection analysis factor analysis, nonlinear least-squares generalized rank annihilation, trilinear decomposition
chemical system
comments
reaction of N,N-diethyl-p-phenylenediamine with 2-chlorophenol and 3-chlorophenol reaction of acetone and 2-butanone with hydroxylamine simulated chemical systems reaction of Fe(III), Co(II), and Zn(II) EGTA complexes with PAR reaction of benzylamine and butylamine with salicylaldehyde
simulated and experimental chromatographic data simulated chemical systems
reaction of diazotized sulfanilamide with p-, o-, and m-aminobenzoic acid and with orciprenaline photoreactions of benzophenone
multidimensional least-squares, factor analysis multivariate curve resolution, trilinear decomposition nonlinear least-squares, Kalman filtering, partial least-squares regression
amino acids reacting with 1,2-naphthoquinone-4-sulfonate reaction of diazotized sulfanilamide with arylamines simulated chemical systems
nonlinear regression
simulated chemical systems
partial least-squares regression
2-furfuraldehyde and 5-(hydroxymethyl)2-furfuraldehyde in wine, spirits, fruit juices, and honey with a modified Winkler’s method
partial least-squares regression proportional equations
simulated chemical systems
singular value decomposition state space-based analysis
simulated and real NMR relaxation signals
ref
effect of rate constant ratio studied; effect of analyte concentration ratio studied effect of rate constant ratio studied applied to second-order kinetics
B29 B30 B31
effect of instrumental noise studied; applied to nonlinear kinetics (synergistic effects)
B32
applied to nonlinear kinetics (pseudo first order with respect to reagent) applied to nonlinear kinetics (synergistic effects) applied to study of interaction of an enzyme and multiple inhibitors applied to pulsed field gradient spin-echo NMR data useful for systems where components appear sequentially KILET-94 multipurpose nonlinear least-squares program, simultaneous evaluation of rate constants, initial concentrations and molar absorptivities applied to true second-order data
B33
B39
applied to resolution of reaction intermediates
B40
applied to true second-order data
B41
detailed comparison of methods
B42
takes into account matrix effects and rate constant changes comparative study
B43
B34 B35 B36 B37 B38
B44
applied to a sequential injection system for analysis of total glucose and biomass derived expressions for optimum reaction time and minimum rate constant ratio as a function of maximum acceptable error applied to NMR relaxation signals; reveals the number of exponentials present in a signal
B45 B46 B47
Table 2. Models of Selected Chemical Kinetic Systems system modeled antibody-antigen interaction batch precipitation reactions chemical sensors enzyme-catalyzed hydrolysis enzyme kinetics enzyme kinetics enzymic reactions with unstable species flow system gas-solid interactions membrane bioreactors
comments
ref
data from an optical biosensor subjected to curve fitting kinetic modeling modeled nitric oxide fiber-optic sensor response as a function of time data from a SAW enzyme sensor disadvantages of Michaelis-Menten kinetics discussed; Monte Carlo simulation of Michaelis-Menten kinetics performed analysis of Michaelis-Menten kinetics in the presence of irreversible inhibitors that react with the substrate analysis of Michaelis-Menten mechanism for the case where the enzyme, enzyme-substrate complex, or product is unstable modeling of free-radical kinetics at high pressure kinetic model for gas adsorption at solid surfaces by surface transient formation simulations show that dynamics of reactor are controlled by chemical kinetics
B77 B78 B79 B80 B81
namic properties using differential scanning calorimetry data (B51). Four software packages have been reviewed (B52) for kinetic evaluations in thermal analysis. The application of combination plots for the determination of dissociation constants using enzyme inhibition data has been described (B53). Perkowski and co-workers (B54) have developed a kinetic approach for the determination of critical micelle concentrations of nonionic surfactants. The method relies upon 58R
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B82 B83 B84 B85 B86
measurement of the reaction kinetics of surfactants with OH radicals formed by water radiolysis. Several authors have described methods for optimizing reaction conditions and the design of kinetic experiments. These include a study detailing an optimization method for simultaneous kinetic analyses (B46). The model was based on the angle between kinetic vectors and on their norm ratio. The authors concluded that the angle between kinetic vectors controls the
quality of the determination, while the norm ratio determines the error distribution between components. In other work, an experimental design methodology was applied to kinetic determinations (B55). The method relies upon a Doehlert uniform design shell. Several new techniques for writing and solving kinetic equations have been described. In one study, two new approaches to writing kinetic equations were presented (B56). A matrix method allows the derivation of the kinetic rate matrix. An integration method applies to species that are consumed in first-order reactions, regardless of the complexity of their formation pathways. A method for solving nonlinear enzymic rate equations with respect to the concentration of a product has been proposed (B57). The method relies on a Taylor series expansion. A numerical method has been developed (B58) for estimating kinetic parameters by solving kinetic models as a set of coupled partial differential equations. In other work, a method for solving the systems of nonlinear differential equations encountered in kinetics was developed (B59). The method is based on the technique of asymptotic approximations. In yet another report, a numerical integration procedure has been proposed for nonisothermal kinetic measurements (B60). The procedure yields rate constants and activation parameters. Several papers have dealt with methods for deriving rate constants and equations. A simple method has been suggested (B61) for determining rate constants of consecutive reactions with second-order formation and first-order decay of an intermediate. The development of a computer program based on Powell’s method has been reported (B62). The program is capable of calculating reaction order, rate constants, and half-lives. The application of a classical differential method with modern computers was the subject of one paper (B63). The method described permits the successful calculation of rate constants of first-order reactions. Font and Fabregat (B64) used an iterative predictor corrector integral method to estimate rate constants in complex reaction networks. Principal component analysis and other related chemometric tools have been used to extract concentration-time profiles from kinetic data (B65). A nonlinear least-squares procedure has been applied to fit exponential decays and extract preexponential factors and decay constants (B66). The use of artificial neural networks for fitting complex kinetic data and estimating an approximate reaction rate equation was the subject of one investigation. In other work, artificial neural networks have been used to model kinetic processes (B67). A matrix algebra method of calculating possible reaction mechanisms from experimental eigenvectors and eigenvalues derived from kinetic data was described (B68). A new computer program (REDAP) is capable of determining kinetic rate expressions for complex systems containing equilibrium processes (B69). Another program (DYNAFIT) can fit either the initial velocities or the time profile of enzymic reactions to a mechanism (B70). A method for reducing the dimensionality of large, complex kinetic systems by partitioning the fast and slow reactions has been suggested (B71). Williams and co-workers (B72) developed a measurement and data-processing method to improve the ruggedness of membrane-based sensors. The method is based on the measurement of response decays toward a steady-state
condition. The iterative Kalman filter has been applied to the study of enzymic kinetics (B73). Initial concentrations and kinetic parameters were estimated. An artificial neural network has been employed to recover a concentration profile from kinetic data (B74). Biertuempel and Schmidtke (B75) have explored the use of curve-fitting methods for evaluating luminescence lifetime data and found them superior to conventional linearization/regression procedures. Seybold et al. (B76) have simulated first-order kinetics using cellular automata. These cellular automata are arrays of cells that change state in a discrete manner according to local, globally applied rules. The method described permits the simulation of a wide array of first-order kinetic processes. Models of Selected Chemical Kinetic Systems. During the time covered by this review, several authors have contributed papers detailing models of chemical and physical kinetic systems. These studies are summarized in Table 2. KINETIC METHODS BASED ON CATALYTIC REACTIONS Many kinetic methods were reported during the last two years based on catalytic reactions. We have divided these into reactions catalyzed by inorganic species, organic species, and enzymes. The review of enzyme-catalyzed reactions is not intended to be comprehensive, but instead considers some novel applications of enzyme catalysis. The theory of catalytic determinations by continuous addition of a catalyst to a reference solution has been extended (C1) to include the case where the initial detector signals from the sample and reference solutions may or may not be the same. The treatment was generalized for pseudo-first-order reactions. The number of reports involving catalytic titrations has continued to decline. Abramovic and co-workers (C2) have developed an expert system that guides the user in choosing an appropriate catalytic titration procedure for the determination of organic acids. Based on information supplied by the user and an extensive knowledge base, a procedure is proposed that includes sampling, preparation of solutions, apparatus, mode of determining the end point, calculation of results, and pertinent literature references. This same group (C3) also reported on a computercontrolled system for catalytic thermometric titrations of organic bases. Both volumetric and coulometric titrant addition systems are supported with a wide variety of monitoring techniques. The automated system was tested on strong, weak, and very weak organic bases and results in good agreement with conventional procedures were obtained. Several indirect determinations involving catalytic reactions were reported. A spectrophotometric procedure has been described for the determination of metamizol (C4). The drug reacts with PbO2 immobilized on a polyester resin bed. The reactor oxidizes the metamizol while liberating Pb(II), which catalyzes the Pyrogallol Red-persulfate reaction. The decrease in the absorbance of the Pyrogallol Red is monitored at 520 nm. Linearity is achieved over the range of 2-16 µg mL-1 with a relative standard deviation in the middle of the linear range of 2.9%. In another interesting study, unsaturated complexes of various organic ligands with Cu(II) were found to catalyze the 1,10-phenanthroline-H2O2 reaction in surfactant media (C5). Based on a kinetic study, flow injection methods for determining Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
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amino acids, polyamines, and salicylic acid were proposed with picomole detection limits. Vanadium(V) has been determined by means of a chemiluminescence flow injection system based on the fast reaction of V(V) with Fe(CN)64- (C6). The resulting V(IV) and Fe(CN)63- both catalyze the oxidation of luminol by dissolved oxygen in alkaline solution. The luminol and Fe(CN)64- reagents were immobilized on an anion-exchange column. The detection of pyrroloquinoline quinone (PQQ) and its derivatives and isomers has been based on a highly sensitive amplification method utilizing the catalysis of redox cycling by PQQ in the presence of glycine, oxygen, and Nitro Blue Tetrazolium (C7). The catalytic bromination of olefinic monomers by TiCl4 has been used to determine the purity of styrene, acrylic acid, hexadecene, vinyl acetate, and other monomers (C8). A fixed reaction time of 30 min was used. The Ti(IV) system was found to eliminate the handling risk and disposal of the currently used mercury (II) acetate catalyst. Enzyme mimetic systems continue to be used for catalytic determinations. Hydrogen peroxide was determined by using the molybdenum-porphyrin complex as an enzyme to mimic peroxidase (C9). The system was coupled with glucose oxidation to determine glucose in serum. A comparative study was performed of some synthetic and commercial fluorogenic substrates for peroxidase and its mimetic enzyme hemin (C10). Flow injection was used to compare potential substrates. In the enzyme catalysis area, one of the most exciting developments has been the ability to detect reactions catalyzed by single enzyme molecules. For example, single molecules of alkaline phosphatase have been captured in a capillary filled with a fluorescence substrate and detected by laser-induced fluorescence (C11). The activity of single molecules showed a wide range with the most active molecules having a 10-fold higher activity than the least active. Single enzyme molecule activation energies were also measured and shown to have a range of values. The average activation energy was within experimental error of that obtained from a bulk sample. Thermal denaturation of individual enzyme molecules was also studied. Reactions of single enzyme molecules have also been studied by Tan and Yeung (C12). Single lactate dehydrogenase molecules were trapped inside femtoliter-size vials filled with excess lactate and NAD+. The fluorescence of NADH was used to monitor the reactions. Heterogeneities in the activities of individual molecules were found. In contrast, single Os(VIII) ions showed uniform activity in catalyzing the Ce(IV)-As(III) reaction. The different activities of otherwise identical enzyme molecules were attributed to the presence of distinct molecular conformations. In previous work, Xue and Yeung (C13) had achieved a detection limit of 10-17 M concentration of enzyme molecules. The kinetics of enzyme systems with unstable enzymesubstrate complexes and products have been analyzed (C14). General equations for the time course of the reaction were presented. A rapid method was presented for determining the kinetic parameters of enzymes that show nonlinear thermal inactivation behavior (C15). A sum of exponentials model was developed based on physical and chemical considerations. The possibility and desirability of using oxidase enzymes for analytical purposes was discussed (C16). Alcohol oxidase and peroxidase were considered as representative enzymes for the determination 60R
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of their substrates and/or activators and inhibitors. Inorganic Catalysts. Methods for the direct determination of inorganic catalysts continue to be popular. Most of the methods were for metal ions although a few were reported for simple inorganic oxo ions. Inorganic catalytic methods are summarized in Table 3. Several other novel and interesting approaches involving catalytic reactions were reported. Synergistic catalytic effects have been exploited for determining mixtures of catalysts. For example, the simultaneous determination of Fe(II) and Fe(III), based on catalysis of the reaction of chromotropic acid with H2O2, uses this concept (C17). The method is based on introducing a synergistic catalytic coefficient to eliminate the deviation from absorbance additivity caused by the synergistic effect. These same authors (C18) used this concept to determine Mo(VI) and W(VI) by catalysis of the H2O2-I- reaction. Stopped-flow, flow injection was employed to determine the two catalysts simultaneously in mixtures. An interesting approach to copper speciation in white wine samples was reported by Wiese and Schwedt (C19). These authors combined differential pulse anodic stripping voltammetry, potentiometry with a copper ion-selective electrode, and a kinetic method to determine free Cu(II) and labile and tightly bound Cu species. Both the kinetic method and the anodic stripping method determine free and labile Cu(II). The kinetic method was based on catalysis of the oxidation of 8-hydroxybenzaldehyde azine by S2O82- in an ammoniacal medium. The ion-selective electrode results determined free Cu(II), while total copper was determined by flame atomic absorption spectroscopy. The tightly bound Cu(II) was obtained by difference. In a novel study, sulfite, thiosulfate, and sulfate were determined individually by taking advantage of their catalytic effects on the ligand substitution reaction between the Hg(II)-4-(2pyridylazo)resorcinol complex and 1,2-cyclohexanediamineN,N,N′,N′-tetracetic acid (C20). Concentrations on the order of 10-8 M sulfite and thiosulfate were determined in the presence of 25 000-fold excesses of sulfate. Sulfur speciation in natural waters was also aided by a catalytic determination (C21). The iodine-azide reaction was used along with coulometry to determine ppb levels of ionic or molecular sulfides, thiosulfates, and H2S in water. Constant current coulometry was used to determine sulfites; sulfates were determined indirectly by coulometry. When combined with a determination of the total sulfur content, the complete distribution of inorganic sulfur species in water was obtained. In another interesting study, the catalytic determination of trace amounts of iridium in a fossil dinosaur egg was reported (C22). Thermal lensing spectrometry was used to monitor the catalytic reaction. Extensive kinetic studies of the chlorpromazine-hydrogen peroxide reaction used in the catalytic determination of iodide were reported (C23). Two parallel reaction paths were studied. The formation of the colored product of the catalytic process was monitored at 525 nm, while absorbance measurements at 335 nm were used to monitor the colorless sulfoxide formation reaction.
Table 3. Direct Determination of Inorganic Catalytic Species by Kinetic Methods species
dynamic range or detection limit, ng mL-1
indicator reaction
cerium
tetrabase + Chloramine T phenylfluorone + H2O2 Cr(III) + Eriochrome Cyanine R Al(III) + Xylenol Orange Cr(III) + EDTA gallocyanine + BrO3-
cobalt
fluorescein + H2O2
copper
Co(III)-2-(5-bromo-2-pyridylazo)5-(N-propyl-N-sulfopropylamino)phenolate + peroxomonosulfate 3-methyl-2-benzothiazolinone hydrazone + N,N-dimethylaniline Rhodamine B + H2O2 3-methyl-2-benzothiazolinone hydrazone + N-ethyl-N-(2-hydroxy3-sulfopropyl)-3,5-dimethylaniline hydroquinone + H2O2
bromide cadmium carbonate
2-100 30 200 200 10-300 5-1000; 1000-10000 0.08-1.40
type of sample
comments photometric monitoring at 600 nm photometric, 1,10-phenanthroline activation photometric monitoring; pH 5.1-5.3 photometric method at 540 nm; pH 2.9-3.1 FI photometric procedure photometric fixed-time method at 525 nm
water alkali halides water waters
ref C24 C25 C26 C27 C28 C29
fluorometric method with triethanolamine as activator autocatalytic degradation monitored by photometry
vitamin B12
C30
water
C31
0.04-0.2; 0.1-0.5
FI photometric method in micellar medium
pepper brush
C32
20-140 0.002-0.1
photometric method in NH3-NH4F buffer photometric method at 525 nm in the presence of H2O2
serum water, biologicals
C33 C34
5.0-100
FI photometric method at 490 nm
C35
N-phenyl-p-phenylenediamine + m-phenyenediamine Hg(I) + Ce(IV) Ce(IV) + As(III)
0.1-2.0 0-0.1 200
FI photometric method with NH3/pyridine activators; surfactant stabilizer fluorometric, stopped-flow method FI photometric
steam condensate, boiler feedwater water
Hg(I) + Ce(IV) pyrogallol-5-sulfonate + H2O2 p-amino-N,N-dimethylaniline + H2O2
5-42 2.0-75.0 0-4.0
continuous-flow photometric method photometric method at 436.8 nm photometric method at 510 nm
N-phenyl-p-phenylenediamine + m-phenylenediamine chloropromazine + H2O2 MeOH + H2O2
0.5-30
FI photometric method in the presence of Tween 80 fixed-time photometric method FI photometric
lead manganese
Pb2+ + resazurin + S2ferroin + IO43,4-dihydroxybenzoic acid + H2O2 3,3′,5,5′-tetramethylbenzidine + IO4-
1 1-1000 10 0.001-2.5
mercury
ferrozine + hexcyanoferrate(II) safranin + IH2O2 + I-
50-4000
metanil + hydrazine ascorbic acid + H2O2
20-160 0-3
gold iodide iridium iron
molybdenum
nitrite
osmium
permanganate rhenium rhodium ruthenium
selenium
0-100
2-500 -
50-1000 0-70 20-1000 0.4-1500
Bromopyrogallol Red + H2O2
0.4-100
gallocyanine + H2O2
0.001
gallocyanine + H2O2 Ce(IV) + As(III)
0.010-100 0.95-18.82
IO4- + As(III) Fe(CN)63- + Sb(III) Fe(II)-1,10-phenanthroline + IO4Sulfonitrazo R + Sn(II) N,N-dimethyldithiooxamide + Sn(II) sulfarsazene + IO4Methyl Orange + IO4-
5-100 19-660 50-400 2-15 0.01-1.0 1-10
phenosafranine + IO4Ce(IV) + formic acid Ce(IV) + ethanol Methylene Blue + S2-
50-500
gallocyanine + Brilliant Cresyl Blue + S2O82Nile Blue A + H2O2
2.5-500 0.1-500 0.0095-0.126
Brilliant Cresyl Blue + S2O82-
0.3-1500
S2-
silver
20
Nile Blue A + BrO3chlorophosphonazo-pN + BrO3 prochlorperazine + BrO3Bromopyrogallol Red + BrO3Thymol Blue + BrO3-
0.06-0.3; 3-74
photometric method at 608.2 nm photometric method at 510 nm FI photometric method photometric method at 650 nm; solution and filter paper reactions compared photometric method at 562 nm FI photometric method at 490 nm; correction for iron interference photometric method fluorometric method with o-phenylenediamine fixed-time (0.5-3.0 min) photometric method at 645 nm FI photometric method at 551 nm photometric rate method at 525 nm fixed-time photometric method at 467 nm fixed-time (2 min) photometric method at 543 nm FI photometric method at 559 nm
industrial and natural waters water water water, chemicals, hair water
C37 C38 C39 C40 C41 C42
water industrial and natural waters water milk salts water
C44 C45 C46 C47
Hg(II) uptake in plants contact lens cleaners, hair plant and food digests
C48 C49 C50
beans water
C51 C52
water, salt
C53
water, soil water water water
C54 C55 C56 C57
ores, chlorination residues ores
C58
photometric, fixed-time method (4 min) at 625 nm FI photometric at 625 nm photometric method at 410 nm using continuous addition of reagent technique photometric method without distillation kinetic study and rate constants determined FI photometric method at 505 nm
iron(III) nitrate and nickel(II) chloride water water water
photometric method at 634 nm
molybdenite standard reference materials
photometric method at 520 nm; kinetic study photometric method or titration in H2SO4 photometric method or titration in H2SO4 photometric method at 660 nm with micellar catalysis FI photometric method at 620 nm photometric method at 630 nm photometric method at 637.5 nm in ethanol solution photometric method at 635 nm with 1,10-phenanthroline as activator
C36
C43 C38
C59 C60 C61 C62 C63 C64 C65 C66 C67 C68
fly ash
C69 C70 C71 C72
wastewater water
C73 C74 C75
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Table 3. (Continued) species
indicator reaction gallocyanine + S2O8
2-
Indigo Carmine + Fe(CN)6
3-
dynamic range or detection limit, ng mL-1 10-4000
FI photometric method at 540 nm
1700-30000
photometric initial rate or fixed-time method at 612 nm divalent sulfur compounds in alcoholic media fixed-time (1.5 min) photometric method for S2- at 663 nm photometric method for S(IV) at 365 nm fixed-time photometric method for Te(IV) at 628 nm initial rate photometric method for W(VI) at 344 nm method for UO22+
I2 + N3 Methylene Blue + Te(IV)
50-2000
tellurium
Co(II) + N3Toluidine Blue + S2-
5 96-1250
tungsten
chlorpromazine + H2O2
2-10000
uranium
2-thiosemicarbazone-1,2-naphthoquinone4-sulfonate + H2O2 o-phenylenediamine + BrO3I- + ClO3o-phenylenediamine + BrO3-
200-1600
gallocyanine + BrO3aniline + BrO3-
0.020-100 0.015
chromotropic acid + H2O2 leuco-Methylene Blue + BrO3-
2000-10000 0-7
gallocyanine + BrO3thoridazine hydrochloride + H2O2 1-Naphthyl Red + BrO3-
0.3-200 2.5-200 1.0-40.0
-
sulfur
vanadium
0-0.8 5000 0-8
Mechanisms consistent with each term in the rate law were presented along with analytical implications of the findings. Organic Catalysts. Only a few papers reported determinations of organic catalysts. Aldehydes, such as formaldehyde, benzaldehyde, and bromoacetaldehyde were determined in mixtures after separation by thin-layer chromatography (C95). Microgram amounts of each aldehyde could be determined. Formaldehyde was found to catalyze the oxidation of 2,5-diaminotoluene or 4-aminodiphenylamine with H2O2 (C96). The former compound was found to give a lower detection limit (11 µg mL-1). Both reagents were applied to determine the formaldehyde emitted from urea-formaldehyde wood-based panels. Nanomolar amounts of ascorbic acid were determined by its catalytic effect on the reaction of copper(II) with 5,10,15,20-tetrakis(1-methylpyridinium-4-yl)porphyrin (C97). Ascorbic acid reduces Cu(II) to Cu(I), which catalyzes the incorporation of Cu(II) into the porphyrin. Determination of 1 × 10-8 M ascorbic acid could be accomplished by a flow injection spectrophotometric method with a relative standard deviation of 2.8%. Oxalic acid was determined by its catalytic effect on the redox reaction between dichromate and Rhodamine B (C98). The absorbance at 555 nm was used to monitor the reaction. The linear range was from 0.06 to 4 µg mL-1 with a detection limit of 20 ng mL-1. Kinetic Methods Based on Activation or Inhibition of Catalytic Activity. Only a few papers were found that based determinations on activation of a catalytic reaction. The oxidation of aniline by bromate catalyzed by V(V) is activated by 8-hydroxyquinoline or pyrocatechol (C89). A thermal lens spectrometer was used to determine both activators at the 10 µM level. The thermal lens signal, after an induction period, exhibits an exponential time dependence. The parameters of the exponential curve depend on the concentration of activator. The basic chemiluminescence reaction of lucigenin, catalyzed by Fe(III), was 62R
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type of sample
comments
fluorometric rate method for V(V) or V(IV) FI photometric method for V(V) FI photometric method for V(V) or V(IV) with gallic acid activator FI photometric method for V(V) thermal lens method for V(V) with 8-hydroxyquinoline or pyrocatechol activators fluorometric method for V(IV) photometric rate method for V(IV) and V(V) at 667 nm voltammetric method for V(V) with HMDE photometric method at 635 nms fixed-time photometric method for V(V) at 525 nm
ref
water, photographic plate photographic film
C77
apples, bananas water
C79 C80
air, rain water
C81 C82
water
C83
water
C84
waters ores waters
C85 C86 C87
serum, water, crude oil water
C88 C89
salts
C90 C91
water, gasoline, serum water water, food
C92 C93 C94
C78
found to be enhanced by ascorbic acid in the presence of Brij 35 (C99). Ascorbic acid in the range of 6.0 × 10-5 to 2.0 × 10-7 M was determined in a flow injection system with a detection limit of 2.0 × 10-9 M. The herbicide bifenox was determined on the basis of activation of the oxidation of carminic acid by hydrogen peroxide in phosphate buffer (C100). Bifenox in the range of 0.34-5.44 µg mL-1 was determined by a photometric kinetic method. Isoproturon also accelerated the reaction and could be determined in a similar manner. Norsulfazole was determined by a kinetic method based on its activation of the oxidation of hydroquinone with H2O2 catalyzed by Cu(II) (C101). The method was applicable for determining (2-8) × 10-13 M norsulfazole. Inhibition of catalysis was much more commonly employed for kinetic determinations. A spectrophotometric method for trace amounts of Al(III) was based on inhibition of the Co(II)-catalyzed oxidation of purpurin by H2O2 (C102). A concentration range of 100-500 ng mL-1 was reported with relative errors in the 1.85.7% range. Trace amounts of Cd(II) were determined on the basis of inhibition of the same reaction (C103). The detection limit for Cd was 60 ng mL-1. The method was used to determine Cd in juice products. The previously mentioned autocatalytic decomposition of Co(III)-2-(5-bromo-2-pyridylazo)-5-(N-propyl-N-sulfopropylamino)phenolate with peroxomonosulfate as oxidant was used not only for the direct catalytic determination of Co(II) but also for the determination of carboxylic acid inhibitors (C31). Organic acids were found to reductively decompose the oxidant. Inhibition increased in the order tartrate, phthalate, citrate, oxalate. The ascorbic acid oxidation of Methylene Blue catalyzed by Cu(II) was found to be inhibited by cesium-137 and strontium-90. A kinetic method for these radionuclides was developed based on this inhibition (C104). Imidazole has been determined with a detection limit of 5.6 ng mL-1 by its inhibition of the Cu(II)catalyzed oxidation of hydroquinone with H2O2 (C105).
Sulfide has been determined in air and in water samples by its inhibition of the Pd(II)-catalyzed reaction between pyronine G and hypophosphite (C106). The reaction was monitored spectrophotometrically by measuring the decrease in absorbance at 548 nm. The linear range was 10-200 ng mL-1. Several other determinations have been reported based on inhibition of uncatalyzed reactions and these are discussed later in this review. Enzyme Activity Measurements. Several papers reported novel measurements of enzyme activities based on kinetic methods. Newton and co-workers (C107) used fast-atom bombardment mass spectrometry to measure the activity of adenylyl cyclase, which catalyzes the conversion of ATP to cyclic AMP. Results were in good agreement with a radiometric assay. Automated methods for the determination of angiotensin-converting enzyme (ACE) were reported by two groups (C108, C109). Both groups reported excellent results on ACE assays in serum. The activity of ACE in tissues was measured by a fixed-time assay using HPLC and UV-visible spectrophotometry (C110). The application of HPLC to the assay enabled the use of very small amounts of tissue (4 mg) and improved the sensitivity and specificity over the conventional determination. The cysteine proteinase enzyme, cathepsin B, was determined in unfixed single human thyroid follicular epithelial cells using a fluorescence image analysis system (C111). The fluorescence emission from a Schiff base product formed by the substrate N-CBZ-Ala-Arg-Arg-4methoxy-2-naphthylamide and the coupling agent 5-nitrosalicylaldehyde was monitored. A chemiluminescent assay was reported for catalase (C112) based on the luminol-hypochlorite reaction. The chemiluminescence depends specifically on the H2O2 concentration and is sensitive to 10-8 M amounts. This allows catalase activity to be obtained at physiological peroxide concentrations. Chemiluminescence was also employed in the assay of cholinesterase (C113). Here, cholinesterase-catalyzed hydrolysis of 2-naphthyl acetate produces 2-naphthol, which acts as an enhancer to the luminolH2O2-peroxidase reaction. A detection limit of 8 µunits mL-1 was obtained. The hydrolysis of 2-methyl-1-propenylbenzoate catalyzed by esterase produces 2-methyl-1-propenol, which can be subsequently oxidized by the H2O2-peroxidase system to give chemiluminescence from excited acetone (C114). The chemiluminescence intensity is proportional to the total amount of esterase, allowing as little as 2 pmol to be detected. A sensitive microtiter plate kinetic assay for serum endopepetidase activity that is suitable for routine and serial measurements has been described (C115). A standard kinetic microplate reader is employed in the determination. The activity of exonuclease was measured on a single DNA molecule with a fluorescence microscopic method (C116). Double-stranded DNA was labeled with a fluorescent microbead. The radius of an approximate circle estimated from the fluorescence image of the microbead was related to the activity of the enzyme. A novel microchip device has been reported for performing automated enzyme assays within a microfabricated network (C117). Nanoliter volume amounts of substrate, enzyme, and inhibitor were mixed by electroosmotic flow. The enzyme β-galactosidase was assayed by a fluorescence technique, and results were comparable to a conventional enzyme assay. Only
120 pg of enzyme and 7.5 ng of substrate were required, a reduction in reagent consumption by 4 orders of magnitude over the conventional method. A chemiluminescence assay of β-galactosidase was also reported (C118) that reduces measurement time and increases sensitivity when compared to fluorometric and photometric methods. A chemiluminescence assay of protein kinase was reported (C119) that measured chemiluminescence on a microtiter plate. The technique was found to be sensitive at low enzyme and substrate concentrations and high ATP levels. Several other advantages over conventional radiometric and photometric techniques were discussed. Two automated flow injection methods were reported for determining laccase activity. The first method (C120) used the stopped-flow technique with fluorometric detection of 2,3-diaminophenazine produced by the oxidation of o-phenylenediamine catalyzed by laccase. Micellar enhancement was employed by using a nonionic surfactant medium. A detection limit of 70 µunits mL-1 was reported using a 5-min reaction time. Ten samples could be determined per hour with this system. The second method (C121) used photometric detection of the same product at 420 nm. With this second system, 30 samples can be determined per hour. Baker (C122) has described a fluorescence assay for determining β-lactamase and penicillin acylase activity in bacteria. The method is based on a fluorescence determination of ampicilloate by heating solutions with ascorbic acid, EDTA, and a modified Lowry reagent prepared with copper sulfate and potassium sodium tartrate in an acetate buffer. The moving boundary sample introduction system was described for the electrophoretically mediated microanalysis of leucine aminopeptidase (C123). The moving boundary method gave an order of magnitude better sensitivity than the zonal injection EMMA method. Chemiluminescence detection was also reported in conjunction with the EMMA technique (C124). Enzyme assays were based on chemiluminescent monitoring of H2O2 after a fixed incubation time with an enzyme. Catalase, glucose oxidase, and galactose oxidase were assayed, and a detection limit of 9300 molecules was obtained for catalase. A dynamic model of the EMMA method has also been presented (C125). The model uses mass balance expressions that describe the effects of electromigration, chemical reaction, and diffusional band broadening on the concentration profiles of various reagent and product species. Simulations using the model were in good agreement with experimental results for the determination of an enzyme (leucine aminopeptidase) and substrate (ethanol). A microcolumn separation method was used to determine the activity of phenylethanolamine N-methyltransferase in single bovine adrenal medullary cells (C126). Single cells were isolated and treated with deuterated norephinephrine substrate. After 6 h, the reaction was quenched and the deuterated epinephrine separated and detected amperometrically. A continuous kinetic assay for acid phosphatase was reported (C127). The spectrophotometric procedure is based on measurements of the phenol produced from the phosphatase-catalyzed reaction using a phenyl phosphate substrate. Three chemiluminescent methods for determining phospholipase activity have been described. In the first method (C128), Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
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the choline produced from the phosphatidylcholine hydrolysis catalyzed by either phospholipase C or D is determined by oxidation with choline oxidase to produce H2O2. The peroxidasecatalyzed oxidation of luminol by H2O2 produces chemiluminescence. The second method (C129) described a determination of phospholipase D by the same reaction. However, flow injection was used to automate the procedure. The correlation between the chemiluminescence signal and the phospholipase D activity was linear in the range of 1-100 munits mL-1. The third method (C130) used choline oxidase immobilized on polymer beads and a flow system to develop a biosensor for phospholipase D. Determination of choline in biological samples was also described. A continuous kinetic assay for phosphorylase kinase was based on two coupled enzyme systems (C131). The final product, 7-methyl-6-thioguanosine, is detected by spectrophotometry. An automated centrifugal analyzer method has been developed for the determination of the activity of Achromobacter lyticus lysylspecific protease (C132). The enzyme catalyzes the liberation of p-nitroaniline, which is detected photometrically at 405 nm. The method was linear in the range of 0.01-0.125 unit mL-1. Valero and co-workers (C133) have developed a mathematical model of an enzyme amplification mechanism by substrate cycling that was applied to the continuous measurement of pyruvate kinase activity. The pyruvate product of the primary enzyme reactant is cycled to lactate by using the enzymes L-lactate dehydrogenase and L-lactate kinase. One molecule of β-NADH is consumed in each turn of the cycle, and the disappearance is monitored spectrophotometrically at 340 nm. An HPLC assay system has been developed for sialytransferases based on fluorescein-labeled acceptor oligosaccharides (C134). The assay was applied to the detection of sialyltransferase activity in commercial enzyme preparations and in a crude preparation of bovine colostrum. Kinetic assays have been reported for trypsin (C135) and antitrypsin (C136) based on a surface acoustic wave impedance sensor. In both studies, results were compared to conventional spectrophotometric assays. Detection of trypsin in the range of 0-300 munits mL-1 was described with excellent agreement with spectrophotometry. A chemiluminescence system was described for the determination of xanthine oxidase activity (C137). The chemiluminescent signal was obtained from the oxidation of hypoxanthine, accelerated and amplified by use of an Fe-EDTA complex, and perborate, which reacts with luminol. Linear response from 5 to 500 munits mL-1 was obtained. Xanthine oxidase activity was determined in various milk samples. Kinetic Methods for Determination of Enzyme Substrates. Methods for the determination of enzyme substrates continue to be very popular, particularly those that use immobilized enzyme catalysts. Determinations considered particularly novel are summarized in Table 4. In many cases, the procedures are kinetic in nature because the enzymatic reactions do not proceed to completion and/or a transient analytical procedure is used (e.g., chemiluminescence or flow injection). Several other interesting approaches were reported during the period of this review. The use of sol-gel glasses for immobilizing enzymes and other materials has been reviewed (C138). These glasses have been used for constructing sensors for glucose and hydrogen peroxide. Adsorption of luciferase on Langmuir64R
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Blodgett films has been studied by FT-IR spectroscopy (C139). Bioluminescent activity was retained upon immobilization, but the kinetic behavior of the enzyme changed because of the close contact with the surface. New methods for coupling urease to various supports were investigated (C140) with the goal of increasing efficiency and cost-effectiveness in industrial applications. Collagen, DEAE-cellulose, and nylon were among the matrixes studied. Rotating-disk and packed-column immobilized enzyme bioreactors were compared in one study (C141). The roles played by chemical kinetics and mass transfer in continuous-flow systems using these reactors were discussed in detail. The rotating-disk reactor more efficiently utilizes immobilized enzyme active sites and permits very small quantities to be employed. Several studies reported on methods for determining kinetic parameters of soluble and immobilized enzyme systems. The enzyme β-galactosidase was studied in solution and immobilized, and three rate models for determining kinetic parameters were compared (C142). Michaelis and inhibitor constants were determined by an open-closed flow injection approach in the alkaline phosphatase/thiophylline system (C143). The values obtained for the Michaelis constant and the inhibitor constant were in good agreement with those obtained by conventional methods. A microbial potentiometric biosensor has been reported (C144) for the determination of saccharides (galactose, fructose, glucose, lactose). A comparison between steady-state and kinetic measurement modes was given. The biosensor was proposed for use in routine quality control procedures, particularly for low-calorie sweeteners. Another interesting kinetic method was used to measure the intracellular concentrations of respiratory substrates in experiments where starved cells were transiently provided with a rich nutrient supply (C145). Substrate uptake rates and dissolved O2 uptake rates were monitored. One interesting study reported on the effect of a static magnetic field on the activity of R-amylase immobilized by glutaraldehyde attachment on polyurethane foam (C146). Flow injection with photometric detection was used to monitor the enzyme activity. Oscillatory behavior in the enzyme reaction was observed when a static magnetic field was present. Kinetic Methods for Determination of Enzyme Activators and Inhibitors. Methods based on inhibition of enzyme catalysis continue to be more popular than those based on activation. A widely used determination is that of organophosphate pesticides based on inhibition of a cholinesterase. A tandem packed-bed reactor flow system was used with reactors containing acetylcholinesterase and choline oxidase (C183). A mobile phase containing acetylcholine and choline as substrates was used. Switching the two reactors allowed detection of substances that inhibit choline oxidase as well as those that inhibit acetylcholinesterase. Hydrogen peroxide generated as a result of the enzyme reaction was detected electrochemically. Detection limits of 1 nM were obtained for paraoxon and physostigmine in drinking water, while micromolar detection limits were obtained for malathion and methyl parathion. Amperometric biosensors based on inhibition of acetylcholinesterase or butyrylcholinesterase have been described for determining organophosphate and carbamate pesticides (C184). The relative inhibition was used to characterize anticholinesterase
Table 4. Direct Determination of Enzyme Substrates by Kinetic Methods substrate acetaldehyde alcohols amino acids
ATP
enzyme aldehyde dehydrogenase (immobilized) alcohol oxidase (soluble) alcohol oxidase (immobilized) leucine dehydrogenase and NADH oxidase (coimmobilized) leucine dehydrogenase and NADH oxidase (coimmobilized) alkaline phosphatase (immobilized)
ATP and glycerol
glycerophosphate oxidase and glycerol kinase (immobilized) bile acids (sulfated) sulfatase and 3β-hydroxy-steroid dehydrogenase (coimmobilized) choline esters cholinesterase and choline oxidase (coimmobilized)
cholesterol citric acid cyanide dopamine glucose
cholinesterase and choline oxidase (coimmobilized) cholesterol oxidase (immobilized) citrate lyase (soluble), pyruvate oxidase and oxaloacetate decarboxylase (immobilized) rhodanase and sulfite oxidase (immobilized) tyrosinase (immobilized) glucose oxidase (soluble) glucose oxidase (immobilized) glucose oxidase (immobilized) glucose oxidase (immobilized) glucose oxidase (immobilized)
glycerol
hypoxanthine inulin
glycerol dehydrogenase (immobilized) glycerol dehydrogenase and NADH oxidase (coimmobilized) xanthine oxidase (immobilized) inulinase (soluble)
lactate
lactate oxidase (immobilized)
malate oxalate
lactate dehydrogenase and lactate oxidase (soluble) malate dehydrogenase, NADH oxidase (coimmobilized) oxalate oxidase, peroxidase (coimmobilized) oxalate oxidase, bovine serum albumin (coimmobilized) on membrane oxalate decarboxylase
dynamic range or detection limit 1-100 µg
mL-1
analyte separated by pervaporation; photometric method at 340 nm 9 µM (EtOH), 0.9 µM (MeOH) photometric method at 540 nm 3-340 µM (EtOH) “reagentless” FI method with electrocatalyzed chemiluminescence 0.5-600 µM FI chemilumnescence method
C148 C149
blood plasma
C150
water
C152
4 µM ATP, 1 µM glycerol
phosphate product reacted to form molydovanadophosphoric acid, which reacts with luminol to give chemiluminescence FI method with string bead reactors
wines
C153
0.1-25 µM
FI chemiluminescence method
urine, blood
C154
2.0-12.0 mM
continuous flow/stopped flow with rotating bioreactor and amperometric detection FI chemiluminescence method
pharmaceutical preparations
C155
neuronal tissue
C156
FI chemiluminescence method FI amperometric method with multiple membranes
blood serum fruits, juices, sport drinks
C157 C158
FI chemiluminescence method
water
C159
drug mixtures fungus
C160 C161
foodstuffs
C162
water
C163
water
C164
tissue fluids and blood wine
C165 C166
wine
C167
fish, meat clinical
C168 C169
600 fmol of acetylcholine, 500 fmol of choline 0.01 mg/100 mL 0.015-0.5 mM 0.12-3.8 µM
3.5 µM (echem), 8.4 µM (phot) FI electrochemical or photometric method sequential injection, chemiluminescence method photometric method based on o-dianisidine at 460 nm 20-160 µM (amperometry) FI amperometric or chemiluminescence 0.056-1.1 µM method; simultaneous determination (chemiluminescence) of lysine possible 0-10 mM glucose amperometric minisensor based on self-assembled phopholipid membrane FI microdialysis, chemiluminescence method 0.3-5.0 µg mL fluorescence monitoring of transiently retained NADH 0.3-300 µM FI chemiluminescence method 0.2-200 µM 0.1-10 mM
0.3-250 µM
2-200 µM 30-80 µM
fungal peroxidase (immobilized)
1-1000 µM
horseradish peroxidase (soluble)
0.2-10 µM
horseradish peroxidase (immobilized)
urea or ammonia
C147
0.01-10 µM
peroxide
pyruvate
fermentation media water water
HPLC postcolumn chemiluminescence
penicillinase (soluble)
purine nucleoside phosphorylase and xanthine oxidase (immobilized) pyruvate oxidase (immobilized), peroxidase (soluble) lactate dehydrogenase/lactate oxidase (soluble) lactate dehydrogenase/lactate oxidase (immobilized) urease (immobilized)
ref
0.3-300 µM
penicillin
phosphate
type of sample
comments
0.1 µM 4.8-160 µM
8.4 µM 0.25 mM (urea), 0.50 mM (NH3)
C151
FI chemiluminescence method automated system with minimal sample prehandling continuous amperometric monitoring with sandwich membrane photometric enzyme cycling assay
rat microdialysate C170
FI chemiluminescence method
wine
enzyme in transparent porous glass matrix; absorbance vs time measured within glass amperometric enzyme electrode; results correlated with photometric method potentiometric, pervaporation, stopped-flow method sequential injection, chemiluminescence method chemiluminescence method also for glucose and lactate photometric method using Eriochrome Black T as hydrogen donor photometric determination in sol-gel matrix; glucose also determined FI chemiluminescence method; inosine phsophorolysis produces hypoxanthine FI chemiluminescence method photometric enzyme cycling method dual-enzyme optrode monitoring fluorescence of NADH pervaporation, potentiometric method
C171 C172 C173 diluted and undiluted urine urine
C174 C175
fungus
C161
water
C176
water
C177
serum
C178
water
C179 C180 C171
water
C181
serum, urine
C182
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toxicity in a river and its tributaries. Inhibition of cholinesterase and acetylcholinesterase using the substrates indoxyl acetate and 2-naphthyl acetate was the basis of four flurometric methods for determining fenitrothion (C185). The substrates are converted to highly fluorescent products. Detection limits ranging from 5.5 to 19.5 µM were obtained, depending on the enzyme and substrate used. A spectrophotometric flow injection method for determining metrifonate by inhibition of immobilized acetylcholinesterase has been described (C186). Acetylcholine is used as the substrate, and the thiocholine product reacts with a chromophoric reagent to produce a measurable absorbance. On-line reactivation of the inhibited enzyme was also proposed. A linear range from 1 to 10 µM metrifonate was obtained. Organophosphate pesticides have also been determined on the basis of inhibition of the lipase-catalyzed hydrolysis of glycerol triacetate monitored with a surface acoustic wave impedance sensor (C187). The frequency response of the transducer was proportional to the pesticide concentration over the range of 2.27227 µg mL-1. The method was applied to the determination of a pesticide residue in the root, stem, and blade of Chinese cabbage. Another enzyme-based detection system for organophosphate pesticides was based on inhibition of alkaline phosphate activity (C188, C189). Chemiluminescence biosensors based on soluble and immobilized alkaline phosphatase were described. The dephosphorylation of a macrocyclic phosphate is catalyzed by the enzyme reaction and gives rise to chemiluminescence. Pesticides such as paraoxon inhibit enzyme activity and decrease the chemiluminescence signal. Detection of paraoxon and methyl parathion at the ppb level was reported. Inhibition of urease activity has been used in the potentiometric determination of salicylhydroxamic acid (C190). The initial rate of the urea hydrolysis catalyzed by urease was monitored by an ammonia gas-sensing electrode. A linear relationship between the degree of inhibition and the drug concentration was obtained over the range 0.5-7.0 µg mL-1. The determination was tested on several pharmaceutical preparations with an average recovery of 98%. Trace quantities of several metal ions (Zn(II), Be(II), and Bi(III)) were determined on the basis of inhibition of the chemiluminescence signal from the alkaline phosphatase-catalyzed hydrolysis of a phosphate derivative of 2,3-dioxetane (C191). Zn(II) could also be determined by reactivation of the apoenzyme. By inhibition of the native enzyme, sub-ppb to ppm detection limits were achieved. Studies with mixtures of metals were also reported. Organomercury compounds were found to liberate peroxidase immobilized on flims and on chromatographic paper in the presence of the inhibitor phenylthiourea (C192). Enzymatic test procedures for the determination of organomercury compounds in the range of 0.002-1000 µM were reported. KINETIC METHODS BASED ON UNCATALYZED REACTIONS The number of papers reporting determinations based on uncatalyzed reactions has increased. Methods based on direct determinations are summarized in Table 5. Several other papers of interest were published during the period of this review and are discussed here. 66R
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The solid-state detection and quantitative determination of cyanide and cyanogenic compounds has been reviewed (D1). Kinetic measurements and studies using microtiter plate readers, portable reflectometers, and graphic scanners were included. An automated system was reported (D2) that processes radiopharmacokinetic data and estimates asialoglycoprotein receptor concentration by a kinetic method. The program automatically processes heart and liver time-activity data from a hepatic functional image. The automatic determination of total aliphatic amines by an on-line photometric liquid-liquid microextraction method has been described (D3). The method is based on the formation of ion pairs between the amines and sodium 1,2-naphthoquinone-4sulfonate that are extracted into chloroform. The increase in the organic-phase concentration with time is monitored photometrically at 460 nm. The measured parameters for determining the amine concentrations are the absorbances at a fixed time and the slopes of the absorbance vs time progress curves. In another interesting study, three-dimensional cyclodextrins were synthesized and developed for analytical and kinetic applications (D4). The new class of receptors was based on trehalose capping of β-cyclodextrin. Kinetic discrimination methods were used for determining quickly reacting aluminum in natural waters (D5). With a short 2.3-s reaction time, aluminum that is not complexed with humic or fulvic acids is detected, while the complexed aluminum is discriminated against. Results were compared to those based on potentiometric titrations and equilibrium dialysis. A potentiometric kinetic method has been developed for drug adsorption studies (D33). The method uses a chlorpromazine ion-selective electrode to monitor the adsorption kinetics of the drug on activated charcoal and two commercial formulations. In another interesting application of a kinetic method, the extrinsic coagulation pathway in which human blood plasma is clotted by the presence of coagulation factors (prothrombin, factor V, factor XB, calcium, phospholipids) in an excess of thromboplastin was evaluated by a flow injection method (D34). The clotting rate was monitored photometrically at 340 nm. A sensitive kinetic method for determining uranium in biological samples utilized phosphorescence decay measurements (D35). The initial luminescence intensity at the onset of decay was used to measure the uranium concentration over the 0.05-1000 ng mL-1 range. The uranium content of tissue samples was measured to validate the method. Several kinetic methods were based on accelerating or inhibiting effects with uncatalyzed reactions. A kinetic spectrophotometric method for carbonate was based on the carbonate acceleration of the U(VI) complex formation reaction with 2-(5bromo-2-pyridylazo)-5-(N-propyl-N-sulfopropylamino)phenol (D36). Small amounts of carbonate could be determined, while a large excess of carbonate over U(VI) completely suppressed the reaction. In another study, the stopped-flow mixing method was used to develop a kinetic method for carminic acid based on its inhibitory effect on the fluorescence of the europium(III)diphacinone-ammonia system in the presence of Triton X-100 (D37). Measurements were made within 10 s of mixing the reactants. The dynamic range of the determination was 0.5-15
Table 5. Direct Kinetic Determination of Species with Uncatalyzed Reactions species aluminum
indicator reaction Al(III) + Eriochrome Red B
dynamic range or detection limit 0-100 µg mL-1
Al(III) + Fampicillin trihydrate
ampicillin + ascorbic acid mL-1
ascorbic acid
ascorbic acid + Toluidine Blue
5-40 µg
bromazepam
bromazepam + Fe(II)
5.0 × 10-41.5 × 10-3 M
cobalt
Co(II) + 2-methylindole-3carboxaldehyde 4-phenyl-3thiosemicarbazone Cu(II) species + 3-propyl-5hydroxy-5-(D-arabinotetrahydroxybutyl)thiozolidine2-thione Jaffe reaction
0.39-1.38 µg mL-1
formaldehyde + 3-methyl-2benzothiazolone (photometric) or formaldehyde + acetylacetone (fluorometric) HCHO + ethylenediammonium chloranilate modifed Winkler method glutamic acid + trinitrobenzenesulfonic acid HCl + porphyrin
0.02-0.6 ng mL-1 (abs), 0.02-1.0 ng mL-1 (fluor)
copper
creatinine formaldehyde
2-furfuraldehyde glutamic acid hydrogen chloride gas 2,4-dinitrophenylhydrazine (DNPH)
DNPH + aliphatic amine
lysozyme
lysozme + SDS
malonaldehyde + thiobarbituric acid malonaldehyde + methylamine (Hantzsch reaction) malonaldehyde + thiobarbituric acid 2-methyl-1,4-naphthoquinone menadione + OH(menadione) malonaldehyde
40-200 µM 0.12-2 µg mL-1 7.5-30.0 µM 2 µg
mL-1
0.5-5.0 µg mL-1
1.1-50 ng mL-1 0.5-2.8 µg
mL-1
0.10-10 µM 7.5-581 mM
morphine
morphine + 1-fluoro-2,4dinitrobenzene
15 µg mL-1
nickel
Ni(II) + 4′-morphilinoacetophenone thiosemicarbazone paracetamol + Fe(CN)63-
0.4-2.0 µg mL-1 0.5-15.0 µg mL-1
sulfide
S2- + resazurin S2- + magenta
25-2500 ng mL-1
sulfites
sulfite + Fe(III)-1,10phenanthroline or Fe(III)2,2′ dipyridyl Sn(II) + Rose Bengal B
paracetamol
tin
0.2 µg mL-1 0.0-17 µg mL-1
µg mL-1. The method was applied to the determination of carminic acid in orange soft drinks. An interesting kinetic fluorometric method was reported for determining gliadins in foods (D38). Stopped-flow mixing was again used. The method reported was based on the reaction between the gliadin proteins and sodium dodecyl sulfate (SDS) and the elimination of the quenching of Cresyl Violet fluorescence
type of sample
comments fluorometric method sensitized by Fstopped-flow, F- ion-selective electrode method photometric fixed-time (30 min) method at 423 nm capillary FI photometric method at 660 nm kinetic study and sequential injection photometric method at 585 nm photometric method at 388 nm and pH 8.8
ref
water and urine
D6
Chinese tea leaves
D7
bulk and drug formulations water
D8 D9
drug formulations
D10
water
D11
kinetic speciation of Cu(II)humic acid species based on ligand displacment
water/soil humic acid
D12
calcium lactate and glucose interferences studied stopped-flow absorption (620 nm) and fluorometric methods
peritoneal dialysis fluids air
D13
variable-time chloranilate electrode method
antiseptics, D15 pharmaceuticals spirit beverages D16 water D17
kinetic study and photometric initial rate method at 420 nm fluorometric method based on reaction with porphyrin in silicone rubber membrane photometric method based on alkaline hydrolysis of product in DMSO stopped-flow fluorometric method with SDS quenching fluorescence of Cresyl Violet fluorometric method at 553 nm (λex) 515 nm) kinetic study and flurometric method cyclodextrin-enhanced fluorometric method photometric method monitoring complex at 405 nm potentiometric initial rate method with Fion-selective electrode photometric method at 390 nm stopped-flow FI fluorometric method at 426 nm (λem) and λex ) 241 nm photometric method fixed-time photometric method at 540 nm photometric method photokinetic fluorometric method at 568 nm (λem) with λex ) 550 nm
D14
D18 pharmaceuticals
D19
pharmaceuticals
D20
human serum
D21
olive oils
D22
meats
D23
pharmaceuticals
D24, D25
ilicit powders
D26 D27
pharmaceuticals
D28
water water
D29 D30
inorganic salts
D31
metals
D32
by SDS. The increase in fluorescence intensity with time was directly related to the gliadin concentration. The dynamic range was 0.5-50 µg mL-1. A flow injection determination of hydrazine was based on its inhibition of the reaction between thionine and nitrite in acidic solutions (D39). The thionine absorbance was monitored at 602 nm. Hydrazine concentrations in the range of 2.0-40 µg mL-1 Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
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Table 6. Methods for Determining Multicomponent Mixtures analytes
reaction
acid and amine vapor mixtures inclusion in a crown ether calcium and magnesium in reaction with Methylthymol Blue mineral water chlorpromazine, perphenazine, oxidative coupling with MBTH and acetopromazine o-, m-, and p-aminophenol oxidative coupling in the presence of octacyanomolybdate o-cresol and m-cresol in urine oxidative coupling with alanine propoxur, carbaryl, and hydrolysis to obtain phenolic ethiofencarb (carbamate compounds; then reaction pesticides) with p-aminophenol resorcinol, m-aminophenol, reaction with p-aminophenol o-cresol, phenol, and m-cresol
detection
Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
ref
piezoelectric quartz crystal used partial least-squares regression and/or E1, E2 sensor artificial neural network for data analysis photometric monitoring used partial least-squares regression for E3 (diode array: 400-700 nm) data analysis photometric monitoring used kinetic wavelength-pair method E4 photometric monitoring used partial least-squares regression (diode array: 340-500 nm) for data analysis photometric monitoring used kinetic wavelength-pair method photometric monitoring used partial least-squares regression for data analysis
E5
photometric monitoring used partial least-squares regression (diode array: 400-700 nm) for data analysis
E8
could be determined. Enasafi and Naghizadeh (D40) have reported a kinetic method for Hg(II) based on its inhibition of the Brilliant Green-sulfite reaction. The reaction was monitored photometrically at 615 nm. A fixed-time method (3.5 min) was used to determine Hg(II) in the range of 5.0-1300 ng mL-1. Determinations of Hg(II) in contact lens cleaning solutions and industrial waste were reported. Another kinetic method for Hg(II) was based on its inhibition of the oxidation of sodium 2-thiosemicarbazone-1,2-naphthoquinone-4-sulfonate by hydrogen peroxide (D41). Concentrations in the range of 0.2-1.0 µg mL-1 could be determined with relative errors ranging between 2.4 and 13.5%. A determination of palladium has been based on its inhibition of the addition reaction between sulfite and Methyl Green (D42). The reaction was monitored photometrically at 630 nm. The fixedtime method was used to determine Pd in the range of 40-280 ng mL-1. The method was applied to the determination of Pd in a sample of activated charcoal. A fixed-time kinetic method was also used in the determination of phytic acid through inhibition of calcium phosphate crystal growth (D43). The method was applied to the determination of phytic acid in pharmaceutical products and in human urine; the detection limit was 0.1 µg mL-1. The concentrations of phenothiazine dyes were determined by a flow injection chemiluminescence photokinetic method (D44). The photooxidation of ascorbic acid can be sensitized by thionine, Azure C, Azure B, Thionine Blue, Toluidine Blue, Methylene Blue, and New Methylene Blue. The products of these photochemical reactions strongly enhance the chemiluminescent lucigenin-ascorbic acid reaction. The rate of the photooxidation reaction is directly related to the dye concentration in the range of 5 × 10-7-1 × 10-4 M. Trace amounts of thiocyanate can be determined on the basis of thiocyanate inhibition of the oxidation of Rhodamine 6G by bromate in sulfuric acid solutions (D45). The decrease in Rhodamine fluorescence was used to monitor the reaction, and a fixed-time kinetic method was developed. The linear range was from 4.82 × 10-9 to 4.13 × 10-8 M. Thiocyanate in urine and in saliva was measured by this approach. Water toxicity was measured by a kinetic method based on the quenching of the luminescent bacterium Vibrio fischeri in a flow system (D46). The slope of the light decay vs time plot was taken as an indication of the relative toxicity. 68R
comments
E6 E7
MULTICOMPONENT (DIFFERENTIAL) KINETIC DETERMINATIONS Kinetic methods are often useful for the determination of multicomponent mixtures. Most commonly, the selectivity of these multicomponent determinations arises from the different rates at which components of a mixture react with a common reagent. These and other similar studies are detailed in Table 6. In addition to the methods reported here, several studies combined novel data-processing techniques with multicomponent methods. Papers based on these studies are described in the instrumentation, automation, and data-processing section. Several studies have used multicomponent kinetic methods for the speciation of metal ions. For example, an experimental scheme was described to determine the dissociation kinetics of metal complexes using an ion-exchange column. Others (E9) have effected a simultaneous determination of iron(II) and iron(III) by taking advantage of the kinetics of the ligand-exchange reaction between the EGTA complexes and 2-(5-bromo-2-pyridylazo)-5-(diethylamino)phenol. The progress of the reaction was monitored by measuring absorbance at 556 nm. Endo and Abe (E10) have also reported a method for the simultaneous determination of iron(II) and iron(III). Their method relies on the copper(II)-catalyzed reaction of the iron species with Tiron. The progress of the reaction was followed through absorbance measurements at 560 nm. Recent work has shown the wide applicability of micelles and micellar media to kinetic measurements. The determination of europium, terbium, and lanthanum has been reported (E11). The method involves the ligand replacement reaction of the Xylenol Orange complexes of these lanthanides by EDTA in a micellar medium. A partial least-squares regression algorithm was used for data processing. Pyridoxal and pyridoxal 5′-phosphate have been determined (E12) by using their cyanide-catalyzed oxidation in the presence of cetyltrimethylammonium bromide micelles. The reaction was monitored by tracking the fluorescence of the reaction products. In other work, the simultaneous kinetic determination of arsenate and phosphate has been reported (E13). The anions react with molybdate to form heteropoly acids which are subsequently reduced by ascorbic acid to form heteropoly blue species. Triton X-100 micelles were used to catalyze the formation of the phosphomolybdenum blue species, but their presence did not affect the kinetics of the arsenate reaction. Several papers describe means by which the inhibition of crystal growth can be applied to differential kinetic determinations.
These papers rely on enantiospecific inhibition of L- and D-histidine. L- and D-aspartic acid were determined in mixtures (E14), as were L- and D-glutamic acid (E15). L-Arginine and L-ornithine were determined through their inhibition of the growth of L-histidine (E16). Giannousios and Papadopoulos (E17) have reported a sensitive kinetic determination of cysteine and cystine. The cystine was first oxidized to cysteine, and then the inhibitory effect of cysteine on the oxidation reaction of 4-methoxy-1,2-diaminobenzene dihydrochloride in the presence of iron(III) was monitored spectrophotometrically by following the absorbance at 470 nm. Molybdenum(VI) and tungsten(VI) have been determined (E18) using a method based on their differential kinetic effect on the oxidation of chloropromazine by hydrogen peroxide. Ampicillin and tetracycline have been determined (E19) in milk by measuring the initial rate of the reaction of ampicillin with penicillinase and mercuric chloride. Tetracycline was determined from the equilibrium signal arising from the reaction of tetracycline with europium ions in the presence of thenoyltrifluoracetone. Workers in Rutan’s group (E20) have utilized kinetic fluorescence detection for the determination of glycine and glutamine that had been partially separated on a TLC plate. Both species react with o-phthalaldehyde to produce a fluorescent intermediate. The progress of the reaction was monitored photometrically with a CCD detector, and the subsequent third-order data (fluorescence intensity as a function of elution distance, reaction time, and sample number) were processed using a trilinear decomposition method. A determination of salicylic acid and diflunisal, based on lanthanide-sensitized luminescence, has been reported (E21). The method relies upon energy transfer from the analytes to terbium(III) which then luminesces. The differential kinetics of a chemiluminescence reaction have been used (E22) to determine several nucleic acids in mixtures. Chemiluminescent derivatives of the nucleic acids were synthesized and characterized. The differential kinetics of the chemiluminescent reactions allow several derivatives to be determined simultaneously. Synergistic effects are a particular problem that can cause difficulty in multicomponent kinetic determinations. Several papers describe ways in which these effects can be overcome and even used to advantage. Two applications where metal cations are determined despite synergistic effects have been described (E23, E24), and these same authors have reported the use of a synergistic effect to calibrate a kinetic determination based upon a catalytic ligand substitution reaction (E25). KINETICS AND MECHANISMS OF SOME REACTIONS OF ANALYTICAL INTEREST Two classes of systems are considered in this section. Oscillating reactions, whose understanding has been significantly enhanced through critical analytical measurements, are discussed. In addition, reactions whose rates are used for quantitative analysis receive attention. Oscillating Reactions. For primarily electrochemical or surface oscillatory phenomena, see the section on electrochemistry. Here, oscillating reactions in homogeneous solution are discussed. In addition, laboratory experiments (F1-F3) and simulations (F4) appropriate for undergraduate laboratories have been presented. Several extensive reviews of nonlinear chemical phenomena have also appeared (F5-F7).
Theory. Substantial headway has been made in theories of selforganization via global coupling, i.e., nonlocal effects of chemical heterogeneity (F8-F14). Among these effects are formation of spiral waves and other complex, three-dimensional spatial structures (F15-F18). Algorithms for performing microscopic simulations of large chemical systems, leading to statistically valid models of wave propagation, were reported (F19). Molecular dynamics (F20), cellular automata (F21), delay differential equations (F22), and neural networks (F23) were all used for simulating oscillatory reactions. Simulations of non-Markovian processes in oscillatory electron-transfer processes were reported (F24). The effects of activation energy (F25) and temperature gradients (F26) on oscillatory processes and traveling waves were studied. For oscillations taking place on the surface of a catalytic pellet, the influence of reaction order was determined (in closed form for zero-order reactions) (F27). In theoretical work not limited in relevance to just oscillating reactions, the validity of the steady-state approximation and means for studying consecutive reactions under isothermal conditions were considered (F28, F29). The coupling of flow effects to measurement of lumped kinetics parameters was critically studied (F30). Photochemical bistability in a closed, isothermal system, potentially of importance for any excitable medium studied spectroscopically, was studied (F31). Models of catalysis involving nonlinear kinetics and diffusional coupling between steps were further studied (F32, F33). It was shown that oscillations can arise close to equilibrium, provided the kinetics involved are sufficiently nonlinear (F34). The effects of fluctuations received significant attention (F35-F37). Theoretical means for computing proton-coupled electrontransfer rate constants were reported (F38). Equilibrium and kinetics considerations applicable both to the simulation of titration error for redox systems and to the modeling of oscillating reactions were discussed (F39). Oscillating Reactions for Quantitative Analysis. Perhaps the most exciting development in the analytical chemistry of oscillating reactions in the past two years is the successful application of perturbations to oscillations for quantitative analysis of useful specimens (F40). This contrasts with earlier work where such analysis was restricted to species in common model reactions, none of which were likely to be determined in this manner due to the inexpensive availability of highly precise and sensitive alternative methods. Species determined at the submicromolar level by perturbation of the H2O2-NaSCN-CuSO4 system include vanillin, paracetamol, ascorbic acid, reduced glutathione (F41), resorcinol (F42), and gallic acid (F43). Vitamin B6 was similarly detected, using chemiluminescence to monitor the oscillations (F44). In a related approach, the oscillatory effect of CO on the surface of a SnO2 gas sensor was reported (F45). Belousov-Zhabotinsky System. The Belousov-Zhabotinsky (BZ) system remains the most-studied oscillatory reaction. Its complexity means that many details of its reaction mechanisms are not understood, yet many interesting and complex spatial and temporal behaviors derive from its chemistry. This review is limited to aspects of the reaction that involve its analytical characterization or in which its behavior has analytical relevance. Purely theoretical aspects are excluded. Observations of spatial Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
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structure are included since the formation, stability, and dissipation of heterogeneous structures are kinetically important aspects of many chemical systems. The importance of microheterogeneity in supposedly wellstirred systems has been highlighted by several papers on the effects of stirring on the BZ system. Vanag (F46) has used cellular automaton-aided modeling to simulate the influence of stirring-induced heterogeneity. Ali and Menzinger have presented another in a series of studies from the Toronto laboratory on stirring effects on the BZ system (F47). They have shown that the extent of inhomogeneity is dependent on the phase of the reaction (not surprising, considering that the relevant homogeneous rates vary significantly during an oscillatory cycle). In the limit of low stirring, Matthiessen and Mueller have identified chemically driven convection in the BZ system (F48). Chaotic transients have also been seen in unstirred BZ media (F49), as has bistability (F50). The influence of noise was theoretically explored for the low flow rate regime of the three-variable Gyo¨rgyi-Field model (F51). At intermediate stirring/mixing rates, Strizhak has identified stirring-induced bifurcations in BZ dynamics, indicating once again the extreme sensitivity of oscillating reaction behavior to subtle details of experiment design (F52). For a closed reactor, stirring/mixing effects on reaction dynamics have been quantitatively modeled (F53). Turbulent, chaotic (and, thus, highly efficient) mixing has been shown to accelerate local homogeneous reaction rates (F54). And, in a study not specifically concerned with oscillatory reactions, the kinetics in steady and turbulent flows for simple second-order reactions have been compared. Regimes in which local concentrations scale as t-1, t-1/2, and t-1/4 were identified (F55). With the complexities arising from gravitationally driven convection, it is thus not surprising that studies of the BZ system in reducedgravity environments have been undertaken. Both instrumentation (F56) and results (F57) confirming that gravity does significantly effect formation of reactive spatial oscillations have been published. Additional theoretical studies on the oscillatory dynamics of the BZ system in flowing systems involving Taylor vortices (F58) may have relevance to interpretation of experimental data. By contrasting behavior in closed and open reactors, the relative dominance of chemical kinetics over thermodynamics in driving oscillations, both transient and steady state, was shown (F59). Additional theoretical and experimental studies of chaotic BZ transients were reported by the Copenhagen group (F60), by the Toronto group (F61), and by Rachwalska (F62). The effect of diffusionally coupling two independent BZ reactors was investigated (F63-F65), though many of the phenomena discussed were seen earlier by Laplante (J. Phys. Chem. 1992, 96, 4931-4934). Synchronization of reactors in circular and linear arrays (F66) also built on Laplante’s earlier work. Coupling of microreactors, actually small ion-exchange beads, was demonstrated, allowing for simple design of very large networks of coupled reactors (F67). Wave propagation in nominally homogeneous BZ medium is typically studied simply by imaging the spirals and waves produced. Typical of observations and computations in the last two years are a review by Mu¨ller (F68) and individual papers by a variety of authors (F69-F76). Such self-organized heterogene70R
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ity has found a number of uses either directly or as indirect diagnostics of reaction mechanisms. A “chemical diode”, in which chemical waves propagate in only one direction, was fabricated (F77). Chemical waves have been used to assemble logic gates (F78) (early efforts in this area have been reviewed (F79)). Such gates are not as fast as silicon but are programmable by laying out the excitable medium with appropriate “wiring”. This work in turn inspired measurements of chemical wave refraction (F80). Interactions among patterns have been used to encode and recall pairs of bits of information (F81, F82), leading to speculation that chaotic chemical reactions might have uses in cryptography (F83). Considering the rate of random bit generation by such reactions compared to electronic nonlinear oscillators, these reviewers think such developments are unlikely to be practical. The work on chemical logic gates also led to design of chemical clocks based on rotating waves in excitable media (F84). Building on earlier work, use of phase behavior in spatial patterns in excitable media formed by exposure to light was suggested as a means of image processing (F85). Development of better three-dimensional diagnostics would be helpful, and some have appeared during the two years being reviewed. Magnetic resonance imaging of propagating waves (F86, F87) was followed by optical tomography (F88). Additional optical monitoring using fluorescence and chemiluminescence (F89) could also have been carried out in a multidimensional fashion. The (not surprising) influence of fluorescence inner filter effects in studying spatial patterns by fluorescence has been noted (F90). In studying spatial structures of monolayers, fluorescence microscopy does not suffer from such problems (F91). One might think of using arrays of electrodes to study propagating redox waves, but perturbation of the system by the electrodes and the varying exchange currents at different electrodes limits this possibility (F92). Optical diagnostics are also problematic for studying BZ (and other oscillatory systems) since excited states react at different rates than ground states, creating additional heterogeneity. Both temporal (F93-F96) and spatiotemporal (F97-F100) effects have been reported. Chemical turbulence has been induced by periodic modulation of a light spot as well as uniform illumination (F101). Returning to three-dimensional spatial structures, the past two years have seen much work on convection-free BZ reactions in membranes and gels (F102-F106). In the ultimate thin-layer spatial studies imaginable, studies of dynamics revealed by placing redox centers in Langmuir layers above BZ medium have appeared (F107, F108). Studies of Turing structures (an active area in the past two years) are beyond the scope of this review. A variety of homogeneous chemical measurements have been made to measure rate constants for individual steps in the BZ system or to replace various reactants with congeners for various purposes. Critical analysis of proposed BZ mechanisms has been a specialty of the Foersterling group, and their HPLC survey of BZ intermediates (F109) should be carefully studied by intrepid theorists as a reality check. The continuing controversy on the effect of molecular oxygen on BZ reaction kinetics received attention (F110), including a statement that the stirring effects previously mentioned in this review are mainly due to the introduction of oxygen (F111)! Margerum’s group has studied the aqueous chemistry of bromine (F112) and hypobromous acid
Table 7. Miscellaneous Kinetics Studies of BZ Reactions with One or More Reactants Substituted for Standard Reactants reactant
comment
amino acids 3,4-dihydroxybenzoic acid bromomalonic acid/Ru(byp)32+ Ce(III) or ferroin + ethyl- or butylmalonic acid citric acid in micellar media citric or other organic substrates perchloric + gallic acid Cu(II) + malic acid fructose, tartaric acid glucose, galactose, and corresponding lactones galactose Mn2+, Fe(phen)3n+
many new oscillators claimed to be discovered dual-frequency oscillations photochemically produced Br- influences dynamics comparative rates for various organic substrates SDS, CTAB, Triton X-100 effect waves and induction times simulation includes activation energy studies Cu(II) complexed with azacyclotetradecadiene many chromatographic studies of speciation; modified control mechanism claims chiral substrates used, but effect of chirality neither stated nor expected dual-frequency oscillations roles of each catalyst identified; “completely inorganic system” (i.e., no purely organic species) influence of trace metals on BZ
Mn2+, V(IV) micelles at varying pH mixed organic substrates organic acids Ru(III) aqua-chloro complex Ru(bipy)32+ Ag+ sugars
waves as well as homogeneous chemistry comment on a Foersterling group paper relevant when using a Ag/AgBr ion-selective electrode to study BZ oscillations seen with Mn2+ catalyst but not Ce3+
(F113), two critical species in BZ and several other oscillatory systems. (While not relevant to the BZ system, Margerum’s group has made analogous measurements on hypoiodous acid dissociation, demonstrating unexpected reaction with acetate buffer (F114).) Temperature effects have been studied (F115, F116), while a theoretical study of the rate of entropy production has been used as a means of identifying the most important reactions in complex models of oscillating systems (F117). The effects of various species substitutions on the kinetics of the BZ system have been studied as shown in Table 7. Briggs-Rauscher System. This well-known “iodine clock” reaction has seen some limited advances. Comparison of experiment to the Furrow-Noyes model of the reaction, using up-dated rate constants, has been made (F138). Vanag’s 1992 work on chain reaction steps in conversion of I2 to I- was only indexed in 1995 (F139). The use of nickel catalysts (F140) showed that, as long as ligands are labile, the standard potential of the catalyst can lie anywhere between 0.7 and 1.7 V vs SHE. A calorimetric and potentiometric study raised questions concerning the exact reaction stoichiometry (F141). Observation of photoinduced bifurcations analogous to those already mentioned for the BZ reaction (F142) rounds out recent work on this reaction. Bray-Liebhafsky System. The H2O2/iodate oscillator, while largely understood, still has behavior not completely explained by existing models. The group in Belgrade has focused on this system. New rate constants applicable to the high-pH regime for this system, together with activation energies, were measured (F143). Additional measurements on iodide ion dynamics demonstrated the importance of some nonradical processes (F144). Ancillary equilibria, which set concentrations of “slow variables” in the oscillator, were also studied (F145). Thermochemical effects and activation energies were also measured (F146, F147). From these efforts, improved models were derived (F148, F149), and dynamical instabilities identified (F150, F151). Elsewhere, effects of pressure and stirring were studied, again emphasizing the importance of transport processes in oscillatory systems (F152). Other Halo-Oscillatory Systems. In an important paper, Lengyel, Li, Kustin, and Epstein report rate constants for the ClO2-ClO2--
ref F118 F119 F120 F121 F122 F123 F124 F125 F126 F127 F128 F129 F130 F131 F132, F133 F134 F135 F136 F137 F119
I- reaction (F153). The fitting precision between model and experiment for this system is astonishingly good, certainly among the best of any oscillatory reaction system. The “dynamical zoo” for this reaction, subject to feedback control, is separately described (F154). Epstein puts this work in historical perspective and shows how detailed knowledge of this oscillator led to the ability to generate experimental Turing structures (F155). Potentiometry has also been employed to characterize this system (F156). The influence of trace Cu(II) on the chlorite-thiocyanate oscillator has been qualitatively explained (F157). Non-BZ bromate systems received significant attention. Intermediates and products in the phenol-bromate oscillator have been identified using HPLC (F158). Both the bromate-ferroin clock reaction (F159) and the uncatalyzed aniline-bromate oscillator (F160) have seen additional work. Oscillations in pH (F161), photosensitivity (F162), and mechanistic origins of chemical instabilities (F163) of the bromate-sulfite system have been studied. The kinetics of formaldehyde oxidation by bromate (F164) and novel oscillators involving pyruvic acid with complexed Cu(II) (F165) or Ni(II) (F166) catalysts and the more common Mn(II) catalyst (F167) have received scrutiny. The ferrocyanideiodate-sulfite reaction’s pattern formation in gels has been quantified and theoretically explained (F168), as have the Liesegang structures in the uncatalyzed bromate-aniline-sulfuric acid gel system (F169). The photosensitivity of the 1,4-cyclohexanedione-bromate system was studied (F170); this system has the asset of not producing gas bubbles (in contrast to BZ), removing one source of uncertainty in analyzing the observed dynamics. A most interesting temperature-dependent oscillation phenomenon was reported for the uncatalyzed para-substituted phenol-bromate system (F171). Depending on reagent concentrations, period doubling can be seen, and transitions between various oscillation patterns display hysteresis as a function of temperature. Oscillators Involving NO or H2O2. Reduction of NO by propane or ethene leads to oscillations when the reaction is catalyzed by Pt or H-ZSM5 (F172, F173). Such oscillations are relevant to reactions in catalytic converters in automobile exhausts. Hydrogen peroxide is an important species in oscillatory reactions, as it can be both oxidized and reduced; it is thus a Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
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convenient and common intermediate for branching mechanisms. The reaction of H2O2 with S2O32- catalyzed by Cu(II) has been described in terms of a four-step mechanism (F174), and its various dynamical bifurcations have been explained (F175). The uncatalyzed and the catalyzed mechanism were categorized into three reaction stages (F176) (positive feedback, uncatalyzed negative feedback, catalyzed negative feedback). Chaos in the closely related oscillator involving HCO3- and CO32- has been observed (F177) and simulated (F178). The dynamics of H2O2 decomposition with a Fe(III) catalyst deposited in poly(vinylpyridine) has been studied (F179). While one would expect Fenton reactions in this instance, the authors added iodate to the system so that Bray-Liebhafsky reactions would also occur. This is an extremely complex system. Even more complex is the carbonate, bisulfate, H2O2, ferricyanide system subjected to illumination in a flowing stream (F180). Chaotic pH oscillations were observed. Peroxidase-Oxidase (PO) Oscillator. This single-enzymecatalyzed oscillator has been the most thoroughly studied biochemical oscillating reaction (excluding physiological systems such as circadian clocks or cardiac pacemakers, where cell structure cannot be separated from chemical phenomenology). This system has been thoroughly reviewed (F181). The Odense group, in some instances in collaboration with others, has been extremely productive during the period covered by this review. Oscillatory dynamics for several different peroxidases was compared, indicating that not all peroxidases are equally capable of catalyzing oscillatory reactions (F182, F183). The currently best-accepted model of the PO system was shown to give rise to quasiperiodicity, in addition to previously observed behaviors, and predictions made as to the circumstances giving rise to such dynamics (F184). Two papers then demonstrated mixed-mode oscillations, homoclinic chaos, and both perioddoubling and period-adding routes to chaos (as a function of pH) (F185, F186). After decades of involving only 2,4-dichlorophenol and Methylene Blue as reaction modifiers, many additional phenols and amines were shown to be acceptable cofactors for inducing period-doubling behavior (F187). Additional important contributions may be expected from this group in the immediate future. Meanwhile, Larter’s group has been suggesting refinements to the Bronnikova-Fed’kina-Schaffer-Olsen (BFSO) model (F188). An interesting suggestion was made concerning damped oscillations (as have been seen in many experiments): these may be due to the interaction of kinetics on multiple time scales among the various PO system reactions (F189). This is a mechanism distinct from the prior hypotheses that the enzyme gradually degrades in situ. It was shown that a chemically realistic model of the PO system can be reduced under many circumstances to a dynamical model quite similar to Olsen’s 1983 abstract model of the reaction (F190). In related areas, PO reaction dynamics were controlled through stochastic resonance (F191). Inhibition and inactivation of the enzyme by m-chloroperoxybenzoic acid was demonstrated (F192). Peroxidase dynamics were observed in nonaqueous solvents (F193) and with Mn(II) substituted for the normal Fe(III) in the enzyme’s central heme (F194). The taxonomy of enzyme oscillators was explicated by Ross’s group (F195). 72R
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Other Biochemical Oscillators, Sensors, and Related Phenomena. Evaporative cooling can give rise to spatial pattern formation in the immobilized lactoperoxidase-catalyzed reaction between I- and H2O2 (F196). The pH dependence of enzyme rate constants may be sufficient to cause oscillatory reactions and pattern formation even in the absence of other sources of nonlinearity (F197). Substrate inhibition in a bioreactor with feedback regulation of chemical composition (a chemostat) can also lead to oscillations in the absence of ancillary sources of nonlinearity (F198). Even the common enzyme lactate dehydrogenase, normally thought of as a simple Michaelis-Menten system, can participate in oscillations in vivo (F199, F200). Ferreira suggests that presumption of time invariance in the concentration or activity of lactate dehydrogenase is ill-founded. An in vivo example of oscillatory oxygen evolution from cyanobacteria has been described (F201), though the enzymic basis is not described. Catalase can support oscillatory reaction between pH 6.0 and 7.6 in the temperature range 25-37 °C when H2O2 is infused to the catalase solution through a semipermeable membrane (F202). An enzymic analogue to neurochemical oscillations has been described (F203). Self-replicating RNA may display dynamics typical of those on a fractal torus (F204). It has been theoretically shown that immobilized proteolytic enzymes should be able to sustain oscillations (F205), which should also imply that immobilized enzyme biosensors may support autonomous oscillation. Traveling waves of NADH and varying pH can be seen in in vitro glycolytic oscillations (F206). A number of novel biosensors based on enzyme kinetics have been reported. Antigen-antibody interactions can be detected with an optical biosensor; response speed is limited by mass transport, not reaction kinetics (F207). Similarly, ligand binding to interleukin-2 can be observed by a surface plasmon resonance optical biosensor (F208). Such sensors may be of general use in studying surface-binding kinetics (F209), for example, in studying the pyruvate dehydrogenase complex (F210) and the affinity and kinetics of anti-carbohydrate antibodies (F211). A general theory of ligand binding to receptors in a polymer matrix in optical biosensors has been presented (F212). Mismatches in complementary coding of DNA strands can be observed by measuring hybridization kinetics optically (F213). The effect of even a single mismatch in a 20-base pair strand is observable. Turning to electrochemical sensors, chiral recognition of redox species has been demonstrated (F214). Not all enzymes are sufficiently selective to perform this feat (F215); unfortunately, glucose oxidase is one such enzyme. The kinetics of immobilized glucose oxidase was studied, and Michaelis constants were measured (F216). A hypoxanthine-selective sensor was demonstrated (F217). Two oscillatory biosensors were described. In the first, a poly(R-amino acid) membrane was shown to give rise to different amplitude oscillations depending on the identity and concentration of the electrolyte adjacent to the membrane (F218). The other showed chaotic response to salicylate; the carbon paste electrode was overcoated with a silica gel containing Meldola’s Blue and salicylate hydroxylase (F219). Methods for elucidating enzyme kinetics under a number of complicated circumstances have been described. These include where the product is unstable (F220), where substrate and inhibitor concentrations are similar (F221), where inhibition is
Table 8. Measurements of Kinetics of Specific Enzymes enzyme adenosine deaminase cytochrome c cytochrome c oxidase metalloporphyrins glucose-6-phosphatase glutamate dehydrogenase glutamate dehydrogenase β-lactamase lysozyme phospholipase C pyrophosphatase pyruvate kinase thermolysin zymogen
measured parameters
comments
ref
Km ) 5.3 × 10-5 M; detection limit: 1.2 fmol of enzyme or 9.2 ng of substrate folding photolytic limiting rate for CO removal and O2 substitution, 106 s-1 metal ion incorporation rates inhibition by N-bromoacetylethanolamine phosphate tryptophan fluorescence quenching NADH and 2-oxoglutarate binding inhibition by penem antibiotic effect of adsorption on Fractogel-EMD on kinetics interaction between Arg-69 and phosphatidylinositol hydrolysis rate seasonal dependence of Km and activation energy hydrolysis of N-dansyl-L-phenylalanine
electrophoretically mediated microanalysis
F225
submillisecond mixing [O2] ) 16 mM
F226 F227
FIA/P-31 NMR model; no experimental data
F228 F229 F230 F231 F232 F233 F234 F235 F236 F237 F238
Table 9. Miscellaneous Oscillatory Reactions reaction
comments
ref
+ Xylenol Orange H2O2 + KSCN + CuSO4 + NaOH [{Au[P(C6H4OMe-p)3]}2-(µ-CtC)] leuco-Methylene Blue and p-benzoquinones Sn-Cu-O2-halide Ru(III) + ethylene glycol+hexacyanoferrate(III) CH2Cl2 + O2 over γ-Al2O3 radicals on zeolite ethanol + O2 + Pd methanol oxidation over Mo-Ca-O/SiO2 propionaldehyde + O2 + Co(II)
spatiotemporal patterns in a capillary batch reactor; pH and complexation oscillate laser-induced, acoustically coupled oscillations relevant to MB-SCN oscillator O2 consumption oscillates oscillations involve intermediate complex with catalyst oscillates when water vapor present adsorption kinetics important Pd on ferroelectric excited at resonant frequency product is methyl formate; both gas-phase and adsorbed intermediates oxidation oscillates in solution; compared to analogous benzaldehyde reaction
F248 F249 F250 F251 F252 F253 F254 F255 F256 F257 F258
Cr3+
irreversible and the enzyme is to some extent consumed in the reaction it catalyzes (F222), and where adsorption (F223) or molecule-specific electron transfer (F224) occur. Studies of specific enzymes of analytical interest are tabulated in Table 8. Miscellaneous Oscillators. Several papers on permanganateMn(II) oscillators have been published. The catalytic effect of Ag+ on the KMnO4-glycine reaction was twice reported (F239, F240). Dynamics using cyclic diketones (F241) and hydroxylamine (F242) as the reductant have appeared. The Mn(II)hexacyanoferrate(III) and MnO2-hexacyanoferrate(II) oscillators have been shown to have mechanisms that include surface reactions on colloidal MnOx particles. Both oxidative and reductive parts of the mechanism are autocatalytic (F243). The dissolution rate of chalcopyrite in NaCl solution was found to be oscillatory rather than monotonic. It is not clear from the abstracts to what extent this is due to mass-transfer effects or to surface chemical mechanisms (F244, F245). Only two papers on oscillatory drug delivery appear to have been published during the period covered by this review (F246, F247). It is likely that such approaches will give rise to demands for chemical characterization of frequency and amplitude of membrane permeability as soon as this technology moves from the conceptual stage to the clinical trial stage. It may well be the technology that most clearly takes chemical oscillations from the realm of “interesting” to “economically important.” Miscellaneous papers on oscillatory reactions are listed in Table 9. Fractal Chemistry. Fractal descriptions of chemical dynamics only rarely appear. Only where scaling behaviors such as diffusion rates or transport through a tortuous channel occur or where
dendritic growth occurs can such descriptions be expected to be useful. Fractal analysis of catalysis (F259, F260) has been employed to explain the interaction between adsorption isotherms and observed reaction rates on porous supports. More tightly focused is a discussion of analyte-receptor binding reactions in the context of biosensors (F261). Both single- and dual-fractal analysis was described. At this point, such modeling is abstract rather than applicable to any specific sensor. A fractal model of surface roughness and its influence on electron transfer at that surface has also been given. The electron-transfer rate was monitored using oxidation current from Fe(II)-1,10-phenanthroline complexes(F262). Synthesis of fractal films of CuS has been reported (F263). Scaling of propagating reaction fronts (F264) has also been explained using the fractal paradigm. Other Reactions of Analytical Interest. Few central themes are discernible among the collection of reactions tabulated here. They are broken down into three subcategories: metallic ions and small anions, gas-phase reactions, and organic reactions. Where organic species are used to complex metal ions, information is tabulated under the metallic ion heading. Metallic Ions and Small Anions. Macrocycle formation rates for a number of lanthanides and transition metals were measured by stopped-flow spectrophotometry (F265). A related study included consideration of how properties of macrocycle-coordinated lanthanides could be chosen for particular applications including magnetic resonance imaging, solvent extraction, and catalysis of nucleic acid cleavage (F266). The pH dependence and equilibrium constants were also measured. Rates and stepwise equilibria for thiocyanate complexes of Hg(II), Ni(II), Fe(III), and Cu(II) were tabulated in an extensive study (F267). General effects on kinetics due to electrolyte solvation including Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
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Table 10. Miscellaneous Metallic Ion and Small Anion Kinetics Measurements reaction Al3+ + IDA and NTA Ba2+ + benzothiazolium styryl crown ether dye Ce3+ and Gd3+ + EDTA bis(lactone) Cr3+ + Xylenol Orange Co2+ + poly[3-(aza crown ether)pyrroles] + O2 Cu3+-tetrapeptide complexes + histidine Cu2+ + dioxotetraamines Cu2+ + bis-macrocycles Cu2+ + macrocycle incorporation into proteins Fe3+ + cysteine and penicillamine Fe3+ + O-Trensox Fe3+ + 1-nitroso-2-naphthol Fe2+ + S2periodate oxidation ferritin-catalyzed ascorbate oxidation HSO2- + O2 with Fe2+ and Fe3+ catalyst oxomanganese(V) porphyrin complex formation Mn ions as catalysts for HSO2- autoxidation Ni2+ + 1,4,7-triazacyclononane-N,N′,N′′-triacetic acid Os-catalyzed asymmetric dihydroxylation Pt2+ + 1,2-cyclohexanediamine isomers Ru-macrocycle exchange with Ni2+ and Cu2+ Ru(bipy)32+ + alkaloids [bis(pyrazine)silver(II)peroxodisulfate] + H2O Ag+ + Eriochrome Black T Na+, Ca2+, and K+ + cryptands alkali hydroxides + crown ethers Sn2+ and Sn4+ Schiff base formation U6+ + SO42U6+ adsorption on ion exchanger V4+ and V6+ complexes electron-exchange reactions V2+ + picolinic acid CN-, N3-, n-butylnitrile assay by rate of exchange with PhS- bound to nitrogenase hydroxyl radical + OHhydroxylamine + I2 I- as catalyst for chlorpromazine + H2O2 IO3- + oxide radical, solvated electron, hydroxyl radical I2 + crown ethers S + O3 NO2- decomposition in acid solution NO3 and SO4- + aromatics S2O82- thermolysis SCN-, OCN-, CS2 reduction with nitrogenase
comments pH < 4; kf ∼ 10 s-1 dynamics from ps to ks Cu(II) as scavenger pattern formation due to reaction-diffusion behavior convoluted with exchange kinetics electrocatalytic O2 reduction studied by cyclic voltammetry and rotating-disk electrode voltammetry proton extraction is rate-determining step pH and temperature dependence of rates measured stopped-flow/photodiode array measurement proteins were radiolabeled monoclonal antibodies rates and equilibria studied as function of pH hexadentate ligand made of three 8-hydroxyquinoline subunits assay labile iron in ocean water rate and equilibrium constant for formation of Fe(HS)+ review of kinetics methods for determination of various analytes using periodate-selective electrodes effects of competitive chelators SIMS indicates isotope effect consistent with different mechanisms for the two different iron catalysts detection and formation rate characterization effects of trace impurities discussed rate law including effects of pH; Ni2+ acts roughly as a Michaelis-Menten enzyme may be useful for dual-rate measurements on stereoisomers chiral recognition during uptake in erythrocytes fluorescence quenching to assay mixture chemiluminescence detection in HClO4 colloid formation followed by Raman spectroscopy stopped-flow study; Na+ and Ca2+ differentiable based on reaction rate kinetics and mechanism in DMSO/water activation energies determined complexation followed by time-resolved fluorescence temperature dependence of kinetics enantioselective reaction rates rates for all three stages of protonation of picolinic acid determined multiple binding sites possible isotope effects measured indirect evidence of intermediate adducts for trace analysis of Irate constants from SCN- competitive reaction in CHCl3 kinetics of sulfur chemiluminescnece detector Raman study; explains drift problems in FIA assorted laser diagnostics of free-radical reactions in water droplets EPR measurement
the effects of inertial and non-Markovian processes have been described (F268). Several additional reactions are tabulated in Table 10. Gas-Phase Reactions. Acoustic oscillation of a flame appears to suppress soot formation, though whether this is due to greater nucleation of small soot particles or improved heat transfer to the soot particles is as yet unclear (F313). Radicals formed in flames have been studied by UV cavity ring-down spectroscopy, with identification of ethyl and ethylperoxy radicals. Self-reaction rates for these species have been measured (F314). The kinetics of metal deposition and changes in surface morphology as a function of deposition rate have been reported (F315). Time-resolved wavelength modulation spectroscopy has been used to measure gas-phase hydroperoxyl radical kinetics (F316). A batch reactor for studying chemical vapor deposition was designed and used to look at reactions of tungsten and silicon fluorides on Si (F317). Polarized reflectance spectroscopy can be used to monitor the rate of surface reactions in a manner similar to spectroellipsom74R
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ref F269 F270 F271 F272 F273 F274 F275 F276 F277 F278, F279 F280 F281 F282 F283 F284 F285 F286 F287 F288 F289 F290 F291 F292 F293 F294 F295 F296 F297 F298 F299 F300 F301 F302 F303 F304 F305 F306 F307 F308 F309 F310 F311 F312
etry, but with better time resolution (F318). The method was used to follow GaP heteroepitaxy. Finally, etching of SiO2 by Fwas monitored in aqueous solution (F319). While not a gas-phase reaction, such etching of SiO2 can also be done by plasma etching, so the chemistry is of interest in the context of CVD and semiconductor etching. Organic and Biochemical Reactions. Micellar media have been used in modifying some kinetic determinations. These include a method for ascorbate assay using an iron-phenanthroline complex (F320). The use of mixed micelles for assaying ionic surfactants has been explored (F321). Intramolecular charge exchange rates have been monitored using ethyl p-(dimethylamino)cinnamate fluorescence and mixed protein-surfactant micelles (F322). Host-guest chemistry has been an area of intense interest in recent years. Several papers have been of particular relevance to chemical analysis. These include a review by Petrucci et al. (F323). A general discussion of multipoint host-guest interac-
Table 11. Additional Organic and Biochemical Reactions reaction acrylate photopolymerization amino acids + p-benzoquinone L-asparagic acid + antimetabolites and alkylating agents barbituric acid + quinones p-chloranil hydrolysis Crystal Violet and Malachite Green oxidation with N3and OH radicals dimethyl sulfide + hydroperoxides hexanal + L-lysine indole-3-acetic acid + Rose Bengal indomethacin degradation in base LDS 750 solvation Methyl Orange and sulfarsazene + periodate oxidation 5,5′-dithiobis(2-nitrobenzoic acid) + thiols peroxynitrite + “biomolecules” poly(ethylene glycol) flash pyrolysis poly(ethylene terephthalate) crystallization polydiacetylene film formation pseudoephidrine enantiometers tartaric and dimethyl acetylacetonate hydrogenation R-lactalbumin refolding kinetics duplex DNA + homopyrimidine peptide nucleic acids glycans + glycanase cAMP-dependent protein kinase phytoene desaturase
comments
ref
reciprocity failure rates as a function of pH additionally suggests assay via titration of Ag+ determination of barbituric acid in range 25-345 µM stopped-flow study azide reactions faster than hydroxyl reactions
F331 F332 F333 F334 F335 F336
relevant to in-cloud detoxification reactions differentiate reactants and products from fluorescence lifetimes chemiluminescence long-lived after photoexcitation of reactants pH and temperature studies using derivative UV spectrophotometry femtosecond IR relaxation study rhodium catalyst “Ellman’s reagent” for determining extent of heat treatment of milk powder possibilities for in vivo assay discussed Arrhenius parameters at elevated pressures measured by FT-IR XPS and FT-IR monitoring rate law for formation on quartz substrate under 364-nm illumination X-ray powder diffraction monitoring Ni/SiO2 enantioselective catalyst. Langmuir-Hinshelwood adsorption; effects of stirring, temperature, catalyst particle size fluorescence monitoring dissociation kinetics a function of site recognition accuracy enzyme activity determined via flow injection analysis pre-steady-state kinetics determined with rapid-quench-flow technique inhibited by tetrazole herbicides; expressed from transformed E. coli
F337 F338 F339 F340 F341 F342 F343
tions has been presented and includes a specific example of a functionalized zinc porphyrin in CDCl3 (F324). Rates of cyclodextrin binding of a number of species including lysine and serine (F325), alcohols (F326, F327) (studied using ultrasonic relaxation), dyes such as Ethyl Orange and Mordant Yellow 7 (F328), riboflavin (F329), and rotaxanes with large, complexed ferrate stoppers (F330) have been reported. Several additional organic and biochemical reactions are tabulated in Table 11. KINETIC ASPECTS OF ELECTROCHEMICAL AND SEPARATION PROCESSES In contrast to the systems discussed in previous sections, here we consider heterogeneous kinetics. Transport phenomena are inescapably linked to both electrochemistry and separations, so that physical as well as chemical rates are important. Electrochemical Processes. Dynamic electrochemistry is inherently a rate-dependent process, since current is an indication of a redox reaction rate. We focus here on interesting rate processes, either as effectors of electrochemical dynamics or in the study of heterogeneous chemical kinetics. Because of the intimate link between electrochemistry and surface chemistry, some solution/solid interfacial reaction kinetics are also discussed here. There is inherent overlap with the review of Dynamic Electrochemistry, and in cases of doubt, we defer coverage to that review. Simulation and Theory. Bieniasz has been working intensively to define a computer language and environment (“ELSIM”) which will allow digital simulation of a wide range of reaction-diffusion electrode initial and boundary value problems. In a series of papers, he has discussed the parameters important in transient electrochemistry (G1), devised a parser to automate generation of the governing differential equations (at least for the case of one-dimensional geometry) (G2), included the effects of bulk and interfacial species reaction kinetics (G3), and then described the
F344 F345 F346 F347 F348 F349 F350 F351 F352 F353 F354
reaction compiler (G4) and the overall ELSIM system (G5). Building on earlier work by Soerensen and Stewart, a similarly general simulation package has been devised by Villa and Chapman (G6). The electrode surface presents a discontinuous boundary condition to a reaction-diffusion system, making numerical integration of the partial differential equations notoriously difficult. Rudolph presents an implicit finite difference method which is stable under such circumstances (G7a). A “strongly implicit” algorithm is presented by Alden et al. (G7b) and its performance contrasted with some other methods for studying reaction-diffusion systems at microelectrodes and ordinary electrodes. Less elegant, but computationally less demanding, simulation has been carried out by a “brute force” simulation (G8). Simulation emphasizing impedance spectroscopy has been described (G9). Integration of these and other ideas into simulation of electrochemical processes has been reviewed (G10). Closed-form models are at times more satisfying than digital simulations, as functional relationships among experimental and kinetics variables may be more readily discerned. Among the efforts in modeling signals and their interpretation in terms of electrochemical kinetics have been several papers on impedance spectroscopy. Except for very low electron-transfer rate constants, it has been shown that impedance measurements can measure rates of chemical reactions preceding electron transfer (G11). Formalisms for treating impedance measurements to extract rate constants of electrochemical and concomitant homogeneous chemical reactions have been given by several authors (G12G14), while others have presented similar theories, under the guise of ac voltammetry (G15). One largely theoretical paper uses as an experimental example the reduction of thallium (G16). More specialized treatments have included the effect of temperature changes (G17), intraelectrode phenomena (G18), and variation in the relative amounts of mixed solvents at constant ionic strength (G19). Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
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Mass transfer influences nearly all electrochemical measurements, as particularly emphasized in papers on modeling its role in thin-layer cells (G20) and under high mass transport conditions in nonaqueous solvents (G21). An overview of kinetics and equilibrium phenomena in electrochemistry has summarized both well-known and recent developments (G22). A paper with important ramifications for both characterizing and employing amperometric sensors, including means to characterize their response speed and selectivity based on electron-transfer kinetics, also described how surface coverage measurements for surfacemodified electrodes could be misleading (G23). The selectivity of electrode response to species capable of undergoing first-order decay or dimerization was also discussed (G24). Nonlinear electrode response to transients has been modeled (G25). The response of hemicylindrical and hemispherical electrodes to ECE electrochemical systems has been derived (G26). Spectroelectrochemistry. A large review of spectroelectrochemistry included a discussion of the use of this set of techniques for measuring electrochemical kinetics (G27). The rate constant (200 s-1) for reduction of cytochrome c3 adsorbed on gold was determined during a single scan by electroreflectance (G28). Electroreflectance combined with ac voltammetry established rate constants for reduction of hemin (4.9 × 103 s-1) and Nile Blue A (5.4 × 102 s-1) adsorbed on glassy carbon (G29). The dimerization rate of Methyl Viologen radical was found to be 104 M-1 s-1 by UV absorption measurements carried out in a channel flow cell (G30). The importance of both proton transfer and electron transfer at a TiO2 surface for metal ligand species being photoreduced was reported (G31). Time-resolved infrared methods were also employed for studying electron-transfer rate processes on Pt (G32). Clearly, much additional spectroelectrochemical work is occurring, but its focus is on speciation rather than dynamics, or else dynamics is a small fraction of the work. Electrodes. McCreery has continued his studies of the structure and electrochemical kinetics of glassy carbon surfaces. Electron-transfer rates are a strong function of surface functionalization and thus of the electrode surface’s history. Studies of the kinetics at surfaces enriched in specific functional groups have used Raman spectrometry, X-ray photoelectron spectroscopy, and scanning tunneling microscopy to elucidate the correlations involved (G33). Polypyrrole is a common material for coating electrodes both to exclude reducible cations from the surface and to enmesh enzymes. Kinetics of composite polypyrrole-carbomethylcellulose growth on Pt electrodes were studied and the accommodation coefficient measured under various conditions (G34). Heterogeneous surfaces give rise to heterogeneous electron-transfer kinetics; the behavior of heterogeneous electrodes including some treatment of independent species fluxes to kinetically distinct domains has been described (G35). Methods to reduce the capacitance at ultramicroelectrodes have been developed (G36). The use of pressure modulation and impedance spectroscopy to study kinetics on solid electrodes has been described (G37). Changes in kinetics and in equilibrium potentials of reference electrodes contaminated with submonolayer quantities of adsorbates represent a subtle source of bias for many experiments (G38). The effects of surfactants on kinetics at mercury electrodes was revisited (G39). 76R
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Electron-transfer kinetics at doped-polymer, coated electrodes have been reviewed (G40). The specific case of Fe(III)/Fe(II) charge transfer at a poly(ethylene oxide)-coated ultramicroelectrode has received individual attention (G41). Fast kinetics take place in small spaces or on short time scales. Thus, the scanning electrochemical microscope (SECM) is a tool for measuring the fastest electron-transfer rates (G42). In principle, the SECM was shown to be useful for measuring firstorder reaction rates in ECE and DISP1 mechanisms up to 1.6 × 105 s-1 and this was confirmed experimentally (G43). Electrontransfer rates for reactions at the boundary between two immiscible liquids have also been successfully studied in this way (G44). Corrosion is typically an electrode surface phenomenon, whose kinetics are briefly reviewed by Landolt (G45). The dynamics of ion exchange at a conducting-polymer film have been studied with cyclic voltammetry (G46). Such dynamics will influence the kinetics at any ion-containing polymer-coated electrode. Electronexchange rates at monolayer-coated electrodes in nonaqueous solvents may vary by over 1 order of magnitude from those in aqueous solution (G47). Pressure may alter electron-transfer rates in self-assembled monolayers to a greater extent than for the same redox centers in solution, depending on the partial molar volume change when the reaction center undergoes oxidation or reduction (G48). Coulometric studies indicate that the mechanism for sulfur adsorption on Ag(111) involves at least three steps, the first being adsorption of SH to form AgSH, leading eventually to Ag2S (G49). Changes in electron-transfer kinetics at (3-mercaptopropyl)trimethoxysilane-modified gold electrodes were used to identify defects in self-organized films (G50). Claims that defects are stable and can be used for molecular recognition were made. Several measurements of semiconductor surface conduction dynamics (G51, G52) and one on electrodeposition of photoresists (G53) round out the period’s publications focusing on electrode kinetics. Species-Specific Electron-Transfer Rate Determinations. Papers reporting measurement of electron-transfer rates are given in Table 12. Note particularly the first entry in part D of the table, where important advances in understanding the kinetics of the most commonly used reaction for quantifying water, the Karl Fischer reaction, are reported. Table 12 is divided into sections: A, elements; B, anions and organics; C, proteins, nucleotides, DNA, and enzymes; D, oxygen species; E, neurotransmitters and related species; and F, saccharides. Where multiple classifications were sensible, the most specific subheading was chosen. Electrochemical Biosensors. Amperometry using enzymes immobilized on or near an electrode is a common way to selectively sense biochemically important species. The general behavior of such sensors is well understood, as enzyme-modified electrodes have been in use for three decades. Sometimes an entire organism is sufficiently active that whole cells can be immobilized without purifying the sensing enzyme. Such is the case for the use of Azotobacter for sensing phenolic compounds (G230). The working range was narrow, 2-35 ppm phenol, provided the bacteria were immobilized in a polyvinyl film. More conventional sensors use one or more enzymes, typically embedded in a polymer, adsorbed, or covalently bonded to the electrically conducting surface. Acetylcholinesterase is inhibited by organo-
Table 12. Electron-Transfer Data for Individual Species (A) Elements species mixed elements Cr(VI) and As(V) + O2 Cr(VI) + Fe(II) Cr(VI) + Fe(II) Cr(VI), O2, Fe(II) Cu(II), Pb(II) EuSaI, Se(IV), Cu(II), cysteine, p-nitrophenol V(IV) + Fe(III)-1,10-phenanthroline complex Zn(II), Co(II) chromium CrCYDTA, CrHEDTRA(H2O) Cr(VI) + L-cysteine Cr(VI) + polypyrrole Cr2O72- + pyridoxine Cr2+ in concentrated LiCl + LiClO4 Cr(III) bipyridyl Cr(III) + MnO4cobalt CoSCNNO+ Co(II)carbendazim Co(II)2-disalophen Co(II)-macrocycle Co(II) Schiff base Co(II) bipyridine complex in NaNO2 [Co(II)Tmtppa]4+ Co(bpy)32+/3+ copper Cu(TTCN)2 CuCl42Cu(II)/Cu(I) + various ligands Cu(II Cu(I) + CO and ethene in AlCl3-EMIC CuSO4 iron Fe-thiocyanate-nitric oxide Fe(III)/Fe(II) Fe(III) complexes Fe(III)(bipy)3 Fe(III) complexes; Fe(II)+ClO2Fe(III) complexes R-iminooxime Fe(II) macrocyclic complex molybdenum Mo(VI) nickel Ni(II) cysteinate LiNiO3 Ni + Mordant Red 74 Ni + 2-methylbenzimidazole Ni3(Fe(CN)6)2 + NADH Ni + albumin, immunoglobulins, and serum proteins zinc Zn(II) Zn(II) + 2,4- or 2,6-diaminotoluene miscellaneous lead cryptates Ag+ + thiosulfate + nitrate Al(III) in cryolite/alumina IrCl62- + As(III) Mn(II) + N-methylformamide Os bipyridyl complexes
comments catalysis by Te(IV) and Te(VI) -d[Cr(VI)]/dt ) 56.3[Fe(II)]0.6[Cr(VI)] -d[Cr(VI)]/dt ) 0.34[Fe2+] +1.41 × 105[FeOH+] + 2.84 × 109[Fe(OH)2][Cr(VI)] immobilized thionine and phenosafranine indicators for sensors nitrilotriacetic acid complexes reduced at rotating-disk electrodes redox kinetics of Eu-SaI complex effect of micelles (SDS) on reaction rate pentanuclear complexes of substituted phthalocyaninessreaction mechanisms and diffusion coefficients
ref G54 G55 G56 G57 G58 G59 G60 G61
solvent effects on electroreduction at Hg reduced to Cr(III); kinetics and mechanism given effect of pH on reaction rate for environmental remediation rate law and activation energy determined reduction kinetics at Hg catalytic enhancement of electron transfer; 20 pM detection limit stopped-flow rate study in alkaline solution
G62 G63 G64 G65 G66 G67 G68
catalytic current when adsorbed on Hg catalytic prewave used to assay barbital adsorbed on carbon electrode; catalyzes O2 reduction catalytic O2 reduction on graphite catalytic O2 reduction on glassy carbon at various pHs catalytic adsorptive stripping determination of Co(II) porphyrin complex adsorbed on graphite catalyzes oxidation of N2H4 and NH2OH electron-transfer rate constants in solvents with known longitudinal relaxation times
G69 G70 G71 G72 G73 G74 G75
rate constants and mechanisms of 1-electron processes. Involves intermolecular steps reduction at glassy carbon or Pt in acetonitrile rate constants for conformational transformations accompanying redox reaction in 80% MeOH-20% water diffusion coefficient for Cu(II) at infinite dilution, 298.1 K, 0-0.5 M H2SO4 ) (7.80 ( 0.25) × 10-10 m2 s-1 electron-transfer kinetics of adducts in molten salt convection-enhanced electrodeposition
G77
G76
G78 G79 G80 G81 G82
hanging Hg drop catalytic-absorptive stripping voltammetry self-exchange rate measured via isotope labels, ion chromatography, and ICP-MS 2-step reduction mechanisms; some rate constants calculated effect of SDS micelles on electron-transfer rate catalytic detection of Fe; acceleration and inhibition of Fe(II)/ClO2- reaction changes in electrokinetics for Fe(CN)63--modified electrodes formation of µ-hydroxo Fe(III) dimer, kf ) 1.8 × 103 M-1 s-1, kr ) 0.18 s-1
G83 G84
catalytic adsorption current enhancement for improved detection limits
G90-G93
catalytic current to form H2; ∼1 ppm detection limit electrocatalysis of sol-gel glass electrocatalytic current enhancement electrocatalytic current enhancement electrocatalytic enhanced NADH oxidation for Au electrode with adsorbed Ni3(Fe(CN)6)2 catalytic reduction of Ni in protein complexes
G94 G95 G96 G97 G98
Hg or Ga electrodessrate constants on Ga 4 times higher than on Hg catalytic effect of 2,4-isomer higher than of 2,6-isomer
G100, G101
self-diffusion coefficient CE reaction mechanism for Ag+ reduction kinetics related to the Hall process rate-determining step is complex disproportionation electron-transfer rate and transfer number determined enhanced electron-transfer rate with monolayer adsorption
G103 G104 G105 G106 G107 G108
G85 G86 G87 G88 G89
G99
G102
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Table 12. (Continued) species Ti(IV) Tl(I) + MnO4U(VI) V(III)EDTAV(IV) + MnO4V + bromate + 2,3-dihydroxynaphthalene various metallic ions reaction alcohol and glycol oxidation aliphatic aldehyde oxidation Alizarin Red S oxidation amines and NH3 oxidation NH3 oxidation 9,10-anthraquinone reduction azobenzene azo dyes (assorted) benzophenone p-benzoquinone + Mg2+ CO sensor CO2 reduction on vinylterpyridine complexes of transition metals CO2 sensor CO2 reduction oxidation of chlorinated hydrocarbons chloroacetic acid reduction DMSO + Ce(IV) diol oxidation on Pt ethanol oxidation heptamethine cyanine dye oxidation with Ru(bpy)32+ N2H4 oxidation L-lysine
and L-phenylalanine oxidation with Mn(III) cyano-macrocyclic crown ether reduction
L-malate
methanol oxidation methanol and formic acid oxidation on Pt(111) 4-methoxyphenylacetate + potassium 12-tungstocobaltate(III) Methylene Blue reduction nitrate reduction nitrite oxidation/sensing nitrite oxidation/sensing nitrophenol reduction NO reduction dipeptide oxidation perchlorate reduction peroxodisulfate reduction phenol + ferrate(VI) and ferrate(V) polyaniline as electrocatalyst thio-derivatized porphyrins as electrocatalysts propargyl alcohol oxidation pyridine-2-aldoxime reduction quinone/hydroquinone redox reactions
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(A) Elements (Continued) comments use of CSTR to evaluate rate constants in ECE mechanism and measure diffusion coefficients oxidation kinetics in HCl and H2SO4 reduction rate calculated ethylene glycol/water, kinetics of solvation of transition state rate law and constants; in H2SO4 catalytically enhanced stripping analysis and polarography review of reduction mechanisms (B) Anions and Organics comments
ref G109, G110 G111, G112 G113 G114 G115 G116, G117 G118 ref
oxidation mechanisms on Au-OH surface Pt/Pd coated glassy carbon electrode; electrocatalysis ks ) 100 s-1 in base, >500 s-1 in acid mechanism of reaction at Ag-Pb eutectic electrode electrocatalysis on Ag-Pb eutectic electrodes reaction mechanism and effect of 1-substituents effect of packing density on electron-transfer kinetics when thiolate is immobilized on Au mechanisms and rate constants for reactions on Hg electron-transfer rate constants in nonaqueous solvents excited complexes fluoresce, allowing elucidation of chemical and redox kinetics Pt or Pd catalyst adsorbed on SnOx reaction in aqueous solution slower than in DMF; completely inhibited by HPO42Ag wire in Na2CO3/BaCO3 electrolyte; mass-transfer kinetics enhancement by silver ions Pd and Co complexes to catalyze reduction at Pt electrodes kinetics with Ag(II), Co(III), and Ce(IV) oxidants catalytic current for porphyrinato Fe(III)-coated electrode for quantitative analysis catalysis by Ru(III) complex kinetics monitored chromatographically catalytic current on Co-Ni electrode for quantification rate constant >2000 M-1 s-1 in tripropylamine
G119 G120 G121 G122 G123 G124 G125
kinetics for Prussian Blue-modified glassy carbon electrode rate law for coulometric reaction derived
G139
mechanism proposed; 1:5 ethanol-water solvent, Hg electrode malate dehydrogenase + diaphorase coimmobilized; yields NADH which is sensed downstream in a flowing system through mediation of hexacyanoferrate(III)/ hexacyanoferrate(II) couple at graphite electrode electrocatalysis on Pt(111), including effects of anion adsorption on reaction rate influence of adsorbed water on kinetics probed kinetic effect of solvents on electron transfer
G141
G126 G127 G128 G129 G130 G131 G132 G133 G134 G135 G136 G137 G138
G140
G142
G143 G144 G145
kinetics on carbon fiber electrode as f(pH) electrocatalysis by Co-cyclam adsorbed on Au Ru(bipy)2 PVP copolymer sensor membrane operates through electrocatalysis heteropolytungstate doped poly(N-methylpyrrole); reaction rate controlled by catalytic reaction, electron, and substrate diffusion mechanism at Hg electrode electrocatalysis with polymerized Cr(v-tpy)23+ Mn(III) electrolytically generated; rates of oxidation of glycine and glycylglycine compared catalytic reduction by tetrachlorothalate(III) on carbon paste electrode electrocatalysis on Au(111) pulse radiolysis observation of second-order kinetics examples using hydroquinone and iron self-assembled monolayers on gold
G146 G147 G148
electrocatalysis on Pt diffusion coefficients and rate constants reported mechanisms on Pt
G158 G159 G160
Analytical Chemistry, Vol. 70, No. 12, June 15, 1998
G149 G150 G151 G152 G153 G154 G155 G156 G157
Table 12. (Continued) (B) Anions and Organics (Continued) comments
reaction quinone/hydroquinone porphyrin complex redox reactions sulfite oxidation sulfite oxidation tetraphenylborate oxidation thiocyanate and thiourea electrocatalysts thiocyanate and thiosemicarbazide + Ce(IV) TMAPD radical 1,3,7 trimethyluric acid uric acid Xylenol Orange reduction species
cytochrome c insulin myoglobin nucleotides NADH electrooxidation
N′-methylnicotinamide DNA DNA enzymes catalytic enzyme assemblies attached to electrodes by antigen-antibody interactions glucose oxidase
reaction Karl Fischer reaction H2 + O2 O3 reduction O2 reduction O2 and CO2 reduction H2O2 and O2-• reduction H2O2 and O2 reduction H2O2 reduction
kinetics and changes in fluorescence quenching with oxidation state
G161
review, including discussion of mechanisms catalyzed by Fe(II) 1,10-phenanthroline complexes kinetics in EC mechanism operating across liquid/liquid interface for oxidation of Cu2Se and Cu2S particles on glassy carbon electrode in HClO4; rate first order in listed reactants; free-radical intermediates suggest oscillatory behavior possible hydroxylamine determination catalyst on glassy carbon comparative rate of oxidation by peroxidase and various electrodes catalytic oxidation at polyglycine-modified electrode kinetics of lanthanum complex reduction
G162 G163 G164 G165 G166 G167 G168 G169 G170
(C) Proteins, Nucleotides, DNA, and Enzymes comments
proteins (not acting in the role of enzymes) cytochrome c
glutamate dehydrogenase urease
ref
ref
on gold electrode, coadsorbed with 4,6-dimethylmercaptopyrimidine; kinetics as a function of adsorption duration development of linear sweep voltammetry methods for studying electron-transfer rates electrocatalytic determination with ruthenium oxide film embedded in ionomer on graphite electrodes; faster electron transfer than in absence of ionomer
G171
review of catalytic dehydrogenase systems for amperometric biosensors dihydroxybenzaldehyde film modified glassy carbon electrode electrocatalysis by ferrocene derivatives and influence of β-cyclodextrin electrocatalysis with Meldola Blue in random block methylsiloxane polymer on graphite determination of reduction mechanism on Hg
G175
viologen-containing self-assembled monolayers on Au catalyze electron transfer
G181
determination of changes in kinetics due to incorporation onto electrode catalytic detection of chlorophenols by amplification of glucose oxidation; chlorophenol + (CF3CO2)2-iodobenzene yields chloroquinones; chloroquinones recycle reduced glucose oxidase to glucose, accelerating reaction (i.e., enhancing oxidation current) effect of lanthanide ions on redox kinetics enzyme-catalyzed polymer dissolutionskinetics measured via impedance changes
G182
(D) Kinetics of Oxygen Species Redox Reactions comments rigorous kinetics study of a venerable reaction. Thorough understanding of kinetics allows lowered detection limits and reduced interferences while speeding titration heterogeneous catalysis of chemisorbed species reviewed mass transport and charge-transfer kinetics for ozone at Nafion-coated Au catalysis by cobaltocene at carbon paste electrode cobalto-porphinato complex catalysis on graphite kinetics for reduction on La0.6(Ca,Sr)0.4Fe0.8Co0.2O3-δ at 700 °C electrocatalytic reduction with polypyrrole/ Co(II) Schiff base-coated electrodes kinetics model of amperometric enzyme sensor electrocatalysis at riboflavin-adsorbed carbon surface; kinetic effects of catalyst orientation discussed kinetics as function of pH and temperature for amperometric immobilized enzyme sensor; Methylene Blue mediated similar to previous citation, but with Meldola Blue and fumed silica on carbon paste electrocatalysis by oxycobalt and other metallooxide films on glassy carbon nitroxide-loaded carbon paste electrode; second-order rate constants reported indium-tin oxide as electrocatalyst Fe(III) porphyrin on glassy carbon in alkaline solution; rate constants reported
G172 G173 G174
G176, G177 G178 G179 G180
G183
G184 G185
ref G186 G187 G188 G189 G190 G191 G192 G193 G194 G195 G196 G197 G198 G199 G200
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Table 12. (Continued) reaction
(E) Neurotransmitters and Related Species comments
acetylcholine sensing ascorbic acid oxidation ascorbic acid + Fe(BHA)3 ascorbic acid + Fe(CN)63ascorbic acid oxidation ascorbic acid oxidation ascorbic acid oxidation ascorbic acid and dopamine oxidation ascorbic acid and dopamine oxidation catecholamine oxidation catecholamine oxidation catecholamine oxidation dopamine oxidation dopamine oxidation dopamine and uric acid oxidation catecholamine, quninone, and phenol oxidation
kinetics of multiple coupled enzymes and mediators at sensor Os(bipy)2(PVP)10Cl+Cl- electrocatalysis first order in each reactant studied with EXAFS kinetics at polypyrrole-coated Pt electrode benzoquinone mediator; kinetics determined by cyclic voltammetry ferriciniumcarboxylic acid mediator ferrocene-derivative mediators at glassy carbon electrocatalysis at polyhistidine-modified electrode electron-transfer kinetics when macrocycle complex adsorbs on Pt (forms potentiometric shape sensor) review of electrocatalysis and kinetics at polymer-modified electrodes kinetics of polyphenol oxidase-based sensors electrocatalysis at polyglycine-modified carbon fiber electrode electrocatalysis at Ni3(Fe(CN)6)2-doped Nafion-coated Pt ultrafast scanning to kinetically resolve these species from ascorbate glucose dehydrogenase on carbon paste electrode. Electrode oxidizes phenols, which reoxidizes enzyme, which is then reduced by glucose in solution
ref G201 G202 G203 G204 G205 G206 G207 G208 G209 G210 G211 G212 G213 G214 G215 G216
(F) Saccharides reaction or system
comments
ref
glucose, CO, or formaldehyde oxidation on Au(100)
influence of gold surface reconstruction on reaction mechanism characterization of pinholes and electron-transfer dynamics using ferricyanide as probe species; saturation in glucose response at 40 mM improves stability of sensors in storage, but decreases stability in use; kinetics of modified system investigated kinetics same as on other metallic electrodes, but stability is
