References

Abraham FF, Tiller WA (Eds) (1972) An Introduction to Computer Simulation in Applied Science. Plenum, New York.

Abramowitz M, Stegun IA (1968) Handbook of Mathematical Functions. Dover, New York.

Acton FS (1970) Numerical Methods that Work. Harper & Row, New York.

Albery WJ, Hitchman ML (1971) Ring-Disc Electrodes. Clarendon Press, Oxford.

Almdal K (1985) Tautomerisering og reduktion af 9-anthron. Dissertation, Copenhagen University.

Amatore C, Sav~ant JM (1979) ECE and disproportionation. Part VI. General resolution. Application to potential step chronoamperometry. J Electroanal Chern 102: 21.

Ames WF (1977) Numerical Methods for Partial Differential Equations. Academic Press, New York.

Anderson JL, Moldoveanu S (1984) Numerical simulation of convective diffusion at a rectangular channel flow electrode. J Electroanal Chern 179: 107.

Aoki K, Osteryoung J (1981) Diffusion-controlled current at the stationary finite disk electrode. Theory. J Electroanal Chern 122: 19.

Arena JV, Rusling JF (1986) Regression analysis of electrochemical data with expanding space grid digital simulation at spherical electrodes. Anal Chern 58: 1481.

Balfour A, Marwick DH (1979) Programming in Standard FORTRAN 77. Heinemann Educational Books, London.

Bard AJ, Faulkner LR (1980) Electrochemical Methods. Wiley, New York.

Bard AJ, Crayston JA, Kittleson GP, Shea TV, Wrighton MS (1986) Digital simulation of the measured electrochemical response of reversible redox couples at microelectrode arrays: consequences arising from closely spaced ultramicroelectrodes. Anal Chern 58: 2321.

215

Batina N, Ruzit I, Cosovic B (1985) An electrochemical study of strongly adsorbable surface-active substances. Determinations of adsorption parameters for Triton-X-I00 at the mercury/sodium chloride interface. J Electroanal Chern 190: 21.

Bauer HH (1972) Electrodics. Thieme, stuttgart.

Bialecki R, Nahlik R, Lapkowski M (1984) Applying the boundary element method to electrochemical calculations of primary current distributions. Electrochim Acta 29: 905.

Bond AM, O'Halloran RJ, Ruzit I, Smith DE (1976) Fundamental and second harmonic alternating current cyclic voltammetric theory and experimental results for simple electrode reactions involving solution-soluble redox couples. Anal Chern 48: 872.

Bond AM, O'Halloran RJ, Ruzit I, Smith DE (1978) Ac cyclic voltammetry: a digital simulation study of the slow scan limit condition for a reversible electrode process. J Electroanal Chern 90: 381.

216

Bond AM, Henderson TLE, Thormann W (1986) Theory and experimental characterization of linear gold microe1ectrodes with submicrometer thickness. J Phys Chern 90: 2911.

Britz D (1980) The point method for electrochemical digital simulation. Anal Chim Acta 122: 331.

Britz D (1981) Digital Simulation in Electrochemistry, 1st Edition. Springer, Berlin.

Britz D (1987) Investigation of the relative merit of some n-point current approximations in digital simulation. Application to an improved algorithm for quasireversib1e systems. Anal Chim Acta 193: 277.

Britz D (1988) Electrochemical digital simulation by Runge-Kutta integration. J Electroanal Chern 240: 17.

Britz D, Thomsen KN (1987) Electrochemical digital simulation: reevaluation of the Crank-Nicolson scheme. Anal Chim Acta 194: 317.

Britz D, Heinze J, Mortensen J, St6rzbach M (1988) Implicit calculation of boundary values in digital simulation, applied to several electrochemical experimental types. J Electroanal Chern 240: 27.

Byrne GD, Hindmarsh AC (1975) A polyalgorithm for the numerical solution of ordinary differential equations. ACM Trans Math Software 1: 71.

Caban R, Chapman TW (1976) Rapid computation of current distribution by orthogonal collocation. J Electrochem Soc 127: 1036.

Caillaud JB, Padmanabhan L (1971) An improved semi-implicit Runge-Kutta method for stiff systems. Chern Eng J 2: 227.

Cassidy JF, Ghoroghchian J, Sarfarazi F, Pons S (1985) Simulation of edge effects in electroanalytical experiments by orthogonal collocation. Part 5. Chronoamperometry at ultramicroelectrode ensembles. Can J Chern 63: 3577.

Clarenbach S, Grabner EW, Brauer E (1973) Digital simulation of a rotating double-ring electrode. Ber Bunsenges phys Chern 77: 908.

Coen S, Cope DK, Tallman DE (1986) Diffusion current at a band electrode by an integral equation method. J Electroanal Chern 215: 29.

Collatz L (1960) The Numerical Treatment of Differential Equations. springer, Berlin.

Cope DK, Tallman DE (1986) Calculation of convective-diffusion current at multiple strip electrodes in a rectangular flow channel. Implications for electrochemical detection. J Electroanal Chern 205: 101.

Courant R, Friedrichs K, Lewy H (1928) tiber die partiellen Differenzen­gleichungen der mathematischen Physik. Math Ann 100: 32.

Crank J, Nicolson P (1947) A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Proc Cambridge Phil Soc 43: 50.

Crank J (1975) The Mathematics of Diffusion. Clarendon Press, Oxford.

Damaskin BB (1967) The Principles of Current Methods for the study of Electrochemical Reactions. Transl. by G Mamantov. McGraw-Hill, New York.

Damaskin BB, Petrii OA, Batrakov VV (1975) Adsorption organischer Verbindungen an Elektroden. Akademie-Verlag, Berlin.

Delahay P, Trachtenberg I (1957) Adsorption kinetics and electrode processes I. J Am Chern Soc 79: 2355.

Delahay P, Mohilner DM (1962) Rate equation for adsorption of a neutral substance at a metal-electrolyte interface. J Am Chern Soc 84: 4247.

Delahay P (1966) Double Layer and Electrode Kinetics. Interscience, New York.

Dillard JW, Turner JA, Osteryoung RA (1977) Digital simulation of differential pulse polarography with incremental time change. Anal Chern 49: 1246.

Duda JL, Vrentas JS (1968) Mathematical analysis of dropping mercury electrode. I. Solution of diffusion equation for variable mercury flow rate. J Phys Chern 72: 1187.

DuFort EC, Frankel SP (1953) Stability conditions in the numerical treatment of parabolic differential equations. Math Tables Aids Comput 7: 135.

Eddowes MJ (1983) Numerical methods for the solution of the rotating disc electrode system. J Electroanal Chern 159: 1.

Emmons HW (1944) The numerical solution of partial differential equations. Quart Appl Math 2: 173.

217

Feldberg SW, Auerbach C (1964) Model for current-reversal chronopotentio­metry with second-order kinetics complications. Anal Chern 36: 505.

Feldberg SW (1969) Digital simulation: a general method for solving electrochemical diffusion-kinetic problems. In: Bard AJ (Ed) Electroanal Chern 3: 199.

Feldberg SW (1972) Digital simulation of electrochemical boundary phenomena: multiple electron transfer and adsorption. Comput Chern Instrum 2: 185.

Feldberg SW (1980) Improvements on computer simulation of electrochemical phenomena involving hydrodynamics: the rotating disk and dropping mercury electrode. J Electroanal Chern 109: 69.

Feldberg SW (1981) Optimization of explicit finite-difference simulation of electrochemical phenomena utilizing an exponentially expanding space grid. Refinement of the Joslin-pletcher algorithm. J Electroanal Chern 127: 1.

Feldberg SW (1987) Propagational inadequacy of the hopscotch finite difference algorithm: the enhancement of performance when used with an exponentially expanding grid for simulation of electrochemical diffusion problems. J Electroanal Chern 222: 101.

Fick A (1855) tiber Diffusion. Pogg Ann 94: 59.

Flanagan JB, Marcoux L (1973) Digital simulation of edge effects at planar disc electrodes. J phys Chern 77: 1051.

Flanagan JB, Marcoux L (1974) Digital simulation of tubular electrode response in stationary and flowing solution. J Phys Chern 78: 718.

218

Flanagan JB, Takahashi K, Anson F (1977) Reactant adsorption in differential pulse polarography. Effects of adsorptive depletion of reactant, non-linear adsorption isotherms and uncompensated resistance. J Electroanal Chern 81: 261.

Fleck RN, Hansen DN, Tobias CW (1964) Numerical evaluation of current distribution in electrical systems. Rept. UCRL-11612. AEC accession no. 4050, avail OTS, 114 pp.

Fleischmann M, Pons S, Rolinson DR, Schmidt PP (1987) Ultramicroelectrodes. Datech Systems Inc, Morganton, NC.

Forsythe GE, Wasow WR (1960) Finite-Difference Methods for Partial Differential Equations. Wiley, New York.

Fourier JB (1822) Theorie Ana1ytique de la Chaleur. Didot, Pere et Fils, Paris. Republished in mvres de Fourier (1888), Gautier-Villars et Fils, Paris, Vol.1.

Fox L (1962) Chebyshev approximation. In: Fox L (Ed) Numerical solution of Ordinary and Partial Differential Equations. Pergammon Press, Oxford, p.113.

Friedman FL, Koffman EB (1981) Problem Solving and Structured Programming in FORTRAN. 2nd Edition. Addison-Wesley, Reading, Mass.

Fu JW (1982) A finite element analysis of corrosion cells. Corrosion (Houston) 38: 295.

Gear CW (1971A) The automatic integration of ordinary differential equations. Comm ACM 14: 176.

Gear CW (1971B) Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, NJ.

Gerald CF (1978) Applied Numerical Analysis. Addison-Wesley, Mass.

Gilb T (1976) Software Metrics. Studentlitteratur, Lund.

Gokhshtein YP, Gokhshtein AY (1960) Multistage electrochemical reactions in oscillographic polarography. In: Longmuir IS (Ed) Advances in Polarography 2: 465.

Gordon P (1965) Nonsymmetric difference equations. J Soc ind app1 Math 13: 667.

Gourlay AR (1970) Hopscotch: a fast second-order partial differential equation solver. J Inst Maths Applics 6: 375.

Graedel TE, Farrow LA, Weber TA (1976) Kinetic studies of the photochemistry of the urban troposphere. Atmos Env 10: 1095.

Gray DG, Harrison JA (1970) Polymerisation of an electroactive species at the rotating disc electrode. J Electroanal Chern 24: 187.

Gregory DP, Riddiford AC (1956) Transport to the surface of a rotating disc. J Chern Soc: 3756.

Hald A (1952) Statistical Theory with Engineering Applications. John Wiley, New York.

Hanafey MK, Scott RL, Ridgway TH, Reilley CN (1978) Analysis of electrochemical mechanisms by finite difference simulation and simplex fitting of double potential step current, charge and absorbance responses. Anal Chern 50: 116.

Hawkridge FM, Bauer HH (1972) Kinetics and mechanistic study of the reduction of CU(II) in LiN03 solution using ac polarography. Anal Chern 44: 364.

Hayes JW, Ruzit I, Smith DE, Booman GL, Delmastro JR (1974A) Fundamental harmonic ac polarography with disproportionation following the charge transfer step. Theory and experimental results with the U(VI)/U(V) couple. J Electroanal Chern 51: 245.

Hayes JW, Ruzit I, Smith DE, Booman GL, Delmastro JR (1974B) Fundamental harmonic ac polarography with irreversible dimerization following the charge transfer step. Theory and experimental results with the benzaldehyde system. J Electroanal Chern 51: 269.

Heinze J (1981) Diffusion processes at finite (micro) disk electrodes solved by digital simulation. J Electroanal Chern 124: 73.

Heinze J, Storzbach M, Mortensen J (1984) Digital simulation of cyclic voltammetric curves by the implicit Crank-Nicolson technique. J Electroanal Chern 165: 61.

Heinze J, Storzbach M (1986) Electrochemistry at ultramicroelectrodes -simulation of heterogeneous and homogeneous kinetics by an improved ADI-technique. Ber Bunsenges Phys Chern 90: 1043.

Hertl P, Speiser B (1987) Electroanalytical investigations. Part IV. The simulation of fast chemical equilibrium reactions in cyclic voltammetric reaction-diffusion models with spline collocation. J Electroanal Chern 217: 225.

Hicks JS, Wei J (1967) Numerical solution of parabolic differential equations with two point boundary conditions by use of the method of lines. JACM 14: 549.

219

van der Houwen PJ (1977) Construction of Integration Formulas for Initial Value Problems. North-Holland, Amsterdam.

van der Houwen PJ, Sommeijer BP (1980) On the internal stability of explicit, m-stage Runge-Kutta methods for large m-values. Z Angew Math Mech 60: 479.

van der Houwen PJ, Sommeijer BP (1983) Predictor-corrector methods with improved absolute stability regions. lMA J Numer Anal 3: 417.

Hoyer B, Kryger L (1985) A theoretical and experimental study of the waveform in potentiometric stripping analysis with a rotating mercury-film electrode - the reversible case. Talanta 32: 839.

Jain MK (1984) Numerical Solution of Differential Equations (2nd. Ed.). Wiley Eastern Ltd.

Joslin T, Pletcher D (1974) The digital simulation of electrode processes. Procedures for conserving computer time. J Electroanal Chern 49: 171.

Keast P, Mitchell AR (1966) On the instability of the Crank Nicolson formula under derivative boundary conditions. Computer J 9: 110.

220

Koryta J (1953) tiber den Einfluss der Farbstoffe der Eosin-Gruppe auf die reversible Oxydo-Reduktion an der tropfenden Quecksilberelektrode. ColI Czech Chern Commun 18: 206.

Koutecky J (1953) Correction for spherical diffusion to the Ilkovie equation. Czech J Phys 2: 50.

Koutecky J, von Stackelberg M (1962) Die Gleichung fUr polarographische Diffusionsstrome und die Grenzen ihrer GUltigkeit. In: Zuman P, Kolthoff IR (Eds) Progress in Polarography 1: 21.

Ksenzhek OS, Lobach GA (1981) End-face microelectrode. Potentiostatic mode. sov Electrochem 17: 220.

Ksenzhek OS, Lobach GA (1982) The end-face microelectrode. Electrochemical processes under mixed control. sov Electrochem 18: 954.

Kvaratskheliya RK (1978) Elektrokhimicheskoye Vosstanovlyeniye Kislorodnikh Coyedinyenii Azota (Electrochemical reduction of oxygen compounds of nitrogen). Metsniereba Publishers, Tbilisi.

Laasonen P (1949) tiber eine Methode zur Losung der warmeleitungsgleichung. Acta Math 81: 309.

Lapidus L, Seinfeld JH (1971) Numerical Solution of Ordinary Differential Equations. Academic Press New York.

Lapidus L, pinder GF (1982) Numerical Solution of partial Differential Equations in Science and Engineering. John Wiley, New York.

Lasia A (1983) Comparison and application of finite difference methods to electroanalytical problems. J Electroanal Chern 146: 397.

Levich VG (1962) Physicochemical Hydrodynamics. Prentice-Hall, NJ.

Liu S (1969) Stable explicit difference approximations to parabolic partial differential equations. Cited in Lapidus and Pinder (1982). AIChE J 15: 334.

Lorenz W (1958) tiber die Geschwindigkeit der Adsorption und der zweidimensionalen Assoziation h6herer Fettsauren an der Grenzflache Quecksilber-ElectrolytI6sung. Z Elektrochem 62: 192.

Lovrie M (1981) 0 adsorpciji kontroliranoj difuzjom. Bull Soc Chim Beograd 46: 93.

Magno F, Bontempelli G, Perosa 0 (1983) A comparison of some recently developed procedures for digital simulation in electroanalytical research. Anal Chim Acta 147: 65.

Magno F, Perosa 0, Bontempelli G (1985) Digital simulation of electrochemical processes involving very fast chemical reactions. Part 1. A simple general approach. Anal Chim Acta 173: 211.

Markowitz JM, Elving PJ (1958) The polarographic diffusion current. Chern Rev 58: 1047.

Mastragostino M, Nadjo L, Sav~ant JM (1968) Disproportionation and ECE mechanisms. I. Theoretical analysis. Relationships for linear sweep voltammetry. Electrochim Acta 13: 721.

Mohilner OM (1966) The electrical double layer, Part I: Elements of double-layer theory. In: Bard AJ (Ed) Electroanal Chern 1: 241.

Moldoveanu S, Anderson JL (1985) Numerical simulation of convective diffusion at a microarray channel electrode. J Electroanal Chern 185: 239.

Nernst W (1904) Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen. Z phys Chern 47: 52.

Newman J (1967) Note. The Koutecky correction to the Ilkovit equation. J Electroanal Chern 15: 309.

Nicolit S (1983) Digitalna simulacija elektrodnih reakcija za pulsnu polarografiju i srodne tehnike. Dissertation, zagreb University.

Nielsen MF (1985) Reaction mechanism analysis in organic electrochemistry. Thesis, Copenhagen University.

Nielsen MF, Almdal K, Hammerich 0, Parker VD (1987) The application of Runge-Kutta integration in digital simulation of electroanalytica1 experiments. An accurate treatment of the homogeneous kinetics. Acta Chern Scand A41: 423.

221

Nisancioglu K, Newman J (1974) Transient convective diffusion to a disk electrode. J Electroanal Chern 50: 23.

Noye J (1982) Finite difference methods for partial differential equations. In: Noye J (Ed) Numerical Solutions of Partial Differential Equations, North-Holland Publishing Co, Amsterdam: 3.

Oldham KB (1979) Analytical expressions for the reversible Randles-Sevcik function. J Electroanal Chern 105: 373.

Oldham KB (1981) Edge effects in semi infinite diffusion. J Electroanal Chern 122: 1.

Pao Y-H, Daugherty RJ (1969) Time-dependent viscous incompressible flow past a finite flat plate. Boeing Scientific Research Labs Report Dl-82-0822. [Cited by Noye (1982)].

Peaceman DW, Rachford HH (1955) The numerical solution of parabolic and elliptic differential equations. J Soc Indust Appl Maths 3: 28.

Pedersen SU, Svensmark B (1987) Simulated data for electrochemical determination of rate constants for homogeneous electron transfer reactions with a second order homogeneous follow-up reaction. I. Coupling between mediator and reduced form of the substrate. Acta Chern Scand A40: 607.

Penczek M, Stojek Z, Osteryoung J (1984) The finite element method for solution of electroanalytical problems. Part I. Oxidation of amalgam thin films. J Electroanal Chern 170: 99.

Penczek M, Stojek Z (1984) The finite element method for solution of electroanalytical problems. Part II. Hermite approximation with variable space grid. J Electroanal Chern 181: 83.

Penczek M, stojek Z (1987) Current distribution at a submicrodisc electrode. J Electroanal Chern 227: 271.

Polcyn DS, Shain I (1966) Multistep charge transfers in stationary electrode polarography. Anal Chern 38: 370.

Pons BS (1981A) Approximation of chronopotentiometric responses by orthogonal collocation. Electrochim Acta 25: 601.

222

Pons BS (1981B) Simulation of electrochemical processes by orthogonal collocation. Spherical electrode geometry. Can J Chem 59: 1538.

Pons S, Speiser B, McAleer JF (1982A) Orthogonal collocation simulation of the rotating disc electrode. Electrochim Acta 27: 1177.

Pons S, Speiser B, McAleer JF, Schmidt PP (1982B) Simulation of the dropping mercury electrode by orthogonal collocation. Electrochim Acta 27: 1711.

Pons S (1984) Polynomial approximation techniques for differential equations in electroanalytical problems. In: Bard AJ (Ed) Electroanal Chem 13: 115.

Prater KB, Bard AJ (1970) Rotating ring-disk electrodes. 1. Fundamentals of the digital simulation approach. Disk and ring transients and collection efficiencies. J Electrochem Soc 117: 207.

Press WH, Flannery BP, Teukolsky SA, vetterling WT (1986) Numerical Recipes. The Art of Scientific Computing. cambridge university Press.

Randles JEB (1948) A cathode-ray polarograph. Part II - The current­voltage curves. Trans Faraday Soc 44: 327.

Reddy IN (1984) An Introduction to the Finite Element Method. International Student Edition, McGraw-Hill, New York.

Reinert KE, Berg H (1962) Theorie der polarographischen Verfolgung schneller chemischer Reaktionen in Losung mittels reaktionsbedingter Diffusionsstrom-Zeit Kurven. Monatsber Deut Akad wiss Berlin 4: 26.

Reller H, Kirowa-Eisner E, Gileadi E (1982) Ensembles of microelectrodes. A digital simulation. J Electroanal Chem 138: 65.

Reller H, Kirowa-Eisner E, Gileadi E (1984) Ensembles of microelectrodes: Digital simulation by the two-dimensional expanding grid method. Cyclic voltammetry, iR effects and applications. J Electroanal Chem 161: 247.

Richardson LF (1911) The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam. phil Trans A210: 307.

Rizzo FJ, Shippy DJ (1970) A method of solution for certain problems of transient heat conduction. AlAA J 8: 2004.

Ruzit I, Feldberg S (1974) The heterogeneous equivalent: a method for digital simulation of electrochemical systems with compact reaction layers. J Electroanal Chem 50: 153.

Ruzit I (1983) Digital simulation of very rapid chemical reactions coupled by electrode reaction. An amended approach. J Electroanal 144: 433.

Ruzit I (1985) Extension of the improved "heterogeneous equivalent" method to the digital simulation of the slow pseudo-first order homogeneous reactions coupled to the electrode reaction. J Electroanal Chem 189: 221.

Ruzit I (1986) Comments on the paper 'Hopscotch: an algorithm for the numerical solution of electrochemical problems' by Shoup and Szabo. J Electroanal Chem 199: 431.

Sau1'yev VK (1964) Integration of Equations of Parabolic Type by the Method of Nets. Pergamon Press, NY.

Schindler EW Jr, Weaver MJ (1983) A parallel simulation sch~me for the rapid accurate calculation of nonidea1 electrochemical transients. Anal Chim Acta 147: 347.

223

Seeber R, Stefani S (1981) Explicit finite difference method in simulating electrode processes. Anal Chem 53: 1011.

Seger1ind L (1984) Applied Finite Element Analysis. 2nd Ed. John Wiley.

Shoup 0, Szabo A (1982) Chronoamperometric current at finite disk electrodes. J E1ectroana1 Chem 140: 237.

Shoup 0, Szabo A (1986) Explicit hopscotch and implicit finite-difference algorithms for the Cottrell problem: exact analytical results. J E1ectroana1 Chem 199: 437.

Speiser B, Rieker A (1979) E1ectroana1ytica1 investigations. Part II. Application of the orthogonal collocation technique to the simulation of cyclic vo1tammograms. J E1ectroana1 Chem 102: 1.

Speiser B (1980) E1ectroana1ytica1 investigations. Part III. optimization of the dimensionless parameter ~ in orthogonal collocation simulations of cyclic vo1tammograms. J E1ectroana1 Chem 110: 69.

Speiser B, Pons S (1982) Simulation of edge-effects in e1ectroana1ytica1 experiments by orthogonal collocation. Part 1. Two-dimensional collocation and theory for chronoamperometry. Can J Chem 60: 1352.

Speiser B, Pons S, Rieker A (1982) E1ectroana1ytica1 investigations - IV. Use of orthogonal collocation for the simulation of quasireversib1e electrode processes under potential scan conditions. E1ectrochim Acta 27: 1171.

Speiser B (1984) E1ectroana1ytica1 investigations. Part V. The simulation of fast chemical reactions in cyclic vo1tammetry by a combination of the orthogonal collocation method and the heterogeneous equivalent approach. J E1ectroana1 Chem 171: 95.

Stephens MM, Moorhead ED (1987) A global finite element Ga1erkin/B-sp1ine (GBS) numerical model of electrochemical kinetics, transport and mechanism for multi-geometry working electrodes. Part 1. Modeled Nernstian vo1tammetry. J E1ectroana1 Chem 220: 1.

Taylor JK, Smith RE, Cooter IL (1949) Polarographic limiting currents. J Res Nat1 Bur Stand 42: 387.

Testa AC, Reinmuth WH (1961) Stepwise reactions in chronopotentiometry. Anal Chem 33: 1320.

Thanos ICG (1986) An in-situ Raman spectroscopic study of the reduction of HN03 on a rotating silver electrode. J E1ectroanal Chem 200: 231.

Tokuda K, Gueshi T, Aoki K, Matsuda H (1985) Finite-element method approach to the problem of the IR-potentia1 drop and overpotentia1 measurements by means of a Luggin-Haber capillary. J E1ectrochem Soc 132: 2390.

Vetter K (1961) E1ektrochemische Kinetik. Springer, Berlin.

224

Vielstich W (1953) Der Zusammenhang zwischen Nernstscher Diffusions­schicht und Prandtlscher Stromungsgrenzschicht. Z Elektrochem 57: 646.

Villadsen JV, stewart WE (1967) Solution of boundary-value problems by orthogonal collocation. Chern Eng Sci 22: 1483.

Villadsen J (1970) Selected Approximation Methods for Chemical Engineering Problems. Reproset, Copenhagen.

Villadsen J, Michelsen ML (1978) Solution of differential equation models by polynomial approximation. Prentice-Hall, New Jersey.

Weinberg GM (1971) The Psychology of Computer Programming. Van Nostrand Reinhold, NY.

Wiesner K (1947) Pokus 0 vyposet absolutnich hodnot rychlostnich konstant pro disociac: slabych kyselin. [Calculation of the absolute dissociation rate of weak acids]. Chern Listy 41: 6.

Whiting LF, Carr PW (1977) A simple, fast numerical method for the solution of a wide variety of electrochemical diffusion problems. J Electroanal Chern 81: 1.

Winograd N (1973) An implicit finite-difference method. Simulation of spectro-electrochemical working curves. J Electroanal Chern 43: 1.

Yen S-C, Chapman TW (1982) Simulation of voltammetry by orthogonal collocation. J Electroanal Chern 135: 305.

Index

ac vo1tammetry 176, 177 accumulation of errors 60, 119 accuracy 115, 116, 117, 119, 121, 130, 134 adaptability of OC 109 ADI 167, 169, 172, 175 adsorption isotherms 20, 59, 90 adsorption kinetics 19-22, 59-63, 71, 90 advanced methods 73-alkyl halide 145, 147 alternating directions: see ADI analogue computers 1, 81 arbitrary parameters 109, 122 aromatic 145 asymmetric form 178 atmospheric chemistry backward differences backward recursion band electrode 112 BEM 112 benzophenone 158 benzopinaco1 158

154 28, 30

85, 188

boundary element method (BEM) 112 boundary problems 45-, 79, 86, 108 box method 2, 6, 24, 32-34, 46, 47, 63, 67-69, 73, 90, 91, 95, 116,

122-125,127,134,142,159,160,162,163,166 bugs, debugging 179, 181, 182 catalytic mechanism 145 central differences 28, 30, 37, 82, 118, 123, 159, 178 Chebyshev series 175 chemical reactions: see homogeneous .. chronoamperometry 88 chronopotentiometry 79, 86-88, 108, 120, 121, 129, 188 combustion chemistry 154

225

concentration profile, (discrete) 16, 45, 46, 50, 59, 60, 61, 68, 88, 90, 91, 94, 101, 107, 109, 111, 120, 121, 147, 148, 154-158, 174, 181

concentration samples, distribution 33, 46, 47, 52, 63, 64, 66, 67, 85, 100,103,117,122,127,134,142,182

consistency, -ent 116, 121, 122, 126, 141, 143 controlled current 46, 47, 53, 60, 68, 176 controlled potential 14, 49, 53, 69, 176 convection 1, 5, 8, 9, 11, 33, 37, 79, 118, 159, 160, 165, 175, 176 convection velocity 9, 118, 159-161, 164 convergence, -ent 86, 94, 115, 126-129, 132, 134 convergence plots 127-129, 131, 134 Cottrell equation, -experiment 79, 86, 95, 120, 124, 125, 127, 128,

130, 133, 188, 190 coverage: see surface coverage cpu 116, 126, 128, 129, 131-134, 148, 180, 182 Crank-Nicolson 68, 73, 74, 80, 81, 83, 84, 86, 87, 90, 96, 98, 99,

109, 110, 111, 115, 118, 119, 127, 128, 141, 169, 174, 175, 176, 178, 181, 182

- roundoff errors with 119 - solving 84 - with implicit boundary values 86 - with unequal intervals 90

cumulative error 60, 63, 119

226

current 12, 13, 15, 48, 50, 52-55, 57, 58, 63, 107, 108, 112, 130, 132, 173

- approximation 34, 45, 51, 55, 63, 87, 99, 117, 120, 121 - calculation 107, 173 - controlled-: see controlled

8, 128 current, chronopotentiometry

- diffusion-- at dme 162 - at rde 165

- error 42 - migration- 10 - in multistep reaction 53, 54 - peak- (CV, LSV) 132, 147, 149 - relation to concentration gradient

cyclic voltammetry 110, 146 cylindric geometry 7, 34, 36, 38 debugging: see bugs .. dehydration reaction 137, 156 depletion 15, 61, 163 desorption 59 diagnostic, in debugging didiagonal equation system differences

- backward 28, 30

181 85, 188

8, 162

- central 28, 30, 37, 82, 118, 123, 159, 178 - forward 28, 30, 31, 46, 81, 118, 149

diffusion coefficient 1, 6, 7, 10, 12, 46, 48, 52, 60, 140, 176 diffusion equation

- cartesian coordinates 1, 7 - cylindrical coordinates 7 - discretisation 32, 81, 82, 86, 98, 143, 150, 152, 172, 174, 177,

- dme 160 - Fick's first 6, 25 - general form 7 - Laplace transform solution method 112 - microdisk 171 - polynomial approximation 103 - rde 165, 166 - semidiscretisation of 77 - solution, Cottrell case 15 - spherical 8, 37 - steady state 174, 175 - transformation to unequal intervals 94, 95 - two-dimensional 167 - with chemical reactions 139, 140, 146 - with convection 159

diffusion layer 10, 14, 16, 41, 141, 142, 156, 161, 190 - dme 162 - rde 163-164

178

dimensionless forms, variables 14, 17, 18, 21, 42, 46, 60, 62, 65, 95, 140, 142, 161

dimerisation 12, 138, 139, 150, 177

discretisation 23, 150, 153, 160, 169, 170, 175, 177, 178 - at microdisk 170

box-method 24, 34 - common sense 27, 28

Crank-Nicolson 81-82, 85, 96-98 errors 29-31, 117, 118 higher-order schemes 177 incorrect, at end (box-) 122 point-method 27, 28, 32, 37

- with ~h-shift 33 - semi- 77 - Taylor expansion, by 29 - two dimensional 168-170 - steady state 174 - with ADI 169 - with unequal intervals 96-98

disk electrode: see rotating disk electrode disproportionation 12, 138, 177 dme: dropping mercury electrode (dme) 9, 22, 52, 160-163 DuFort and Frankel scheme 178 EC mechanism 141 ECE mechanism 107 edge effect 165-167, 171, 173 efficiency 73,74, 79, 81, 90, 93, 110, 111, 115, 116, 117, 126,

130-134, 151, 172, 180 egoless programming 182 elliptic equations 175, 176 end element expression 27, 122, 123, 126, 134 equilibrium 13, 19, 20, 48, 49, 59, 61,154,155,157 error(s)

- accumulated 60, 119 - cancelling 117, 120-124, 127, 133 - current approximation 63, 117, 120 - discretisation- 29, 76, 83, 94, 117, 118, 134 - polynomial fit (in OC) 101 - programming 74, 90, 180-182 - roundoff 119 - simulation- 40, 47, 76, 94, 111, 113, 116, 128

Euler method 24, 75 expanding plane model explici t method

160, 162, 190

- box- 24-27, 34-37 - point- 3, 27, 31-34, 37-38 - RKI 74-81

exponentially expanding intervals fast reactions 10, 141, 154, 157

92, 96, 168

Feldberg 2, 24, 37, 59, 73, 74, 79, 91, 92, 93, 95, 96, 99, 111, 115, 116, 128, 142, 149, 155, 157, 160, 161, 162, 163, 166, 168

FEM 112, 115, 180 Fick 1, 5, 6, 24, 31, 32 finite differences 1, 23, 24, 38, 41, 73, 75, 81, 110 finite element method (FEM) 112, 115, 180 flash photolysis 11, 141 flow cell 175 following reaction FORTRAN language forward difference Fourier 1, 6, 177

138 42, 126, 179-181

28, 30, 31, 46,

fudge factor 37, 115, 122, 124, 127 heterogeneous equivalent 155-157

81, 118, 149

227

228

(homogeneous) chemical reactions

hopscotch 73, 110-111, 126, 172 hydrodynamics 9, 163, 164, 166

1, 5, 11, 21, 52, 74, 79, 101, 108, 109, 118, 130, 132, 137-157

implicit boundary values 86, 108, 115, 120, 130, 152, 170, 188 implicit methods

- Crank-Nicolson - Laasonen - hopscotch

73, 81-90, 115, 120, 169 83, 110, 169, 170, 176 73, 110-111, 126, 172

inert walls 51, 171 inorganic reactions 137 instability 159, 160 irreversible systems 49, 51, 147 iterative procedure 121, 175, 176 Jacobi polynomials 101, 105 Laasonen 83, 110, 169, 170, 176 Laplace equation 112, 176 Laplace transform method 112, 173 Levich 163, 164, 166, 175, 190 library routines 120, 182 linearising approximations 151 linear sweep voltammetry (LSV) lines, method of 81

116, 132-134, 171, 177, 190

mechanism studies 107, 109, 113, 134, 137-149, 153-155 mediated electron transfer 145, 146 mercury electrode: see dropping .. method of lines 81 microdisk, -electrode 166-168, 170, 172-174, migration effects 5, 9, 10, 11 multistep reactions 52, 55, 57, 58, 70, 90 nonlinear terms 79, 141, 150-151 normalisation: see dimensionless .. observation time 14, 141, 154 ordinary differential equations 106, 118, 173 organic reactions (see also mechanism studies) 113, 134, 137 orthogonal collocation (OC) 73, 81, 100, 118, 173 orthogonal polynomial 110, 155 oscillation 38, 40, 115 oxyanions 137 "parallel" method 143, 144 parallel simulation 112 Pascal language 179, 180, 188 Peaceman and Rachford 94, 169 peak current 132, 148, 149, 190 peak potential 116, 132, 133, 148, 190 pentadiagonal equation system 169 photolysis 11, 141 pinaco1 158 point method 2, 23, 31-33, 37-38, 47, 63, 68, 85, 87, 96, 115, 117,

120,125,127,134,142,160,162,163,166,182 - with ~h-shift 33, 79

polynomial approximation: see orthogonal collocation Prandtl number 163, 164 program bugs, debugging 179, 181, 182 programming language: see FORTRAN, Pascal programs 42, 71, 79, 120, 126, 132, 140, 163, 179, 180, 182, 188, 190 propagation effects 111, 181 pulse techniques 94 quasi reversible systems 47, 48, 49, 51, 57, 58, 69, 70, 88 radical species 145, 147, 158 Randles 2, 73, 83 reaction layer 109, 141-142, 147-149, 154-157, 190 recursive expressions 53, 55, 56, 85, 86, 189

Reinert and Berg mechanism 130, 131, 141, 143, 144, 154, 181 reversible reactions, systems 47-49, 55, 58, 69, 70, 132 Richardson 1, 115, 178 ring-disk electrodes etc: see rotating disk ... RKI: see Runge-Kutta integration roots of Jacobi polynomials 101, 102, 105, 110 rotating disk electrodes 122, 160, 163, 166, 174, 175, 190 Runge-Kutta integration

- chemical terms only 143, 144, 151 - general 74-76, 118

229

- whole-system method 77-81, 118, 128-129, 131, 132, 134, 144, 151, 153-154, 190

Saul'yev 178 semidiscretisation 77 "sequential" method 143-144, 147, 149 settling time at rde 165 shell elements 34, 35, 37, 162, 163 sinusoidal signals 177 spherical geometry 6, 7, 19, 33, 34, 36, 37, 110, 161 sphericity 161, 162 spline collocation 109, 155, 157, 158 stability (conditions) 38, 79, 111, 159, 160, 168, 172 steady state 59, 94, 100, 112, 135, 145, 146, 156, 165, 166, 174-176,

190 surface coverage 19-21, 59-61 symbol convention 4 Taylor expansions 29, 66, 122, 123, 177, 178 tridiagononal equation system 83, 98 unequal intervals 73, 74, 90-100, 103, 112, 113, 115, 117, 119, 128,

velocity vetter weighted x-limit

of convection 9, 10, 12, 141, 142, residuals method

42, 92, 103, 109

129, 149, 155, 158, 168, 190 118, 159-161, 164 162 101

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

G. Henze, Universitiit Trier; R. Neeb, Universitiit Mainz

Elektrochemische Analytik 1986. 150 Abbildungen. X, 383 Seiten. ISBN 3-540-15048-X

Das Buch gibt einen Uberblick tiber Grundlagen und Leistungsfahigkeit aller elektrochemischen Analysenmethoden. In dieser umfassenden Darstellung gibt es keine vergleichbare Monographie. Die Entwicklungen der letzten zwei Jahrzehnte wurden dafiir nahezu li.ickenlos berticksich­tigt. Ftir den Interessenten dtirften die sehr vielen Literaturhinweise in den anwen­dungsbezogenen Kapiteln ntitzlich sein. Das Buch wird weniger den Studierenden als vielmehr den in der Praxis tiitigen Analytiker interessieren. Ftir den Einsatz der elektrochemischen Analysenmethoden in der Umweltanalytik, der Pharmazie, Medizin, Lebensmittelchemie und filr die Untersuchung geologischer und biologi­scher Matrices findet der Leser zahlreiche Beispiele und Anregungen.

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

E.Steckhan (Ed.)

Electrochemistry I 1987. 19 figures, 51 tables. IX, 195 pages. (Topics in Current Chemistry, Volume 142). Hard cover. ISBN 3-540-17871-6

Contents: E. Steckhan: Organic Syntheses with Electrochemically Regenerable Redox Systems. -M. A. Fox: Selective Formation of Organic Compounds by Photoelectrosynthesis at Semi­conductor Particles. - H.-I Schafer: Oxidation of Organic Compounds at the Nickel Hydroxide Electrode. - H.I P. Utley: Electrogenerated Bases. - K. Uneyama: The Chemistry of Electrogenerated Acids (EGA); How to Generate EGA and How to Utilize It?

E. Steckhan (Ed.)

Electrochemistry II 1988. 79 figures, 9 tables. XII, 187 pages. (Topics in Current Chemistry, Volume 143). Hard cover. ISBN 3-540-18226-8

Contents: C. E. Lunte, W. R. Heineman: Electro­chemical Techniques in Bioanalysis. - G. S. Cala­brese, K. M. O'Connell: Medical Applications of Electrochemical Sensors and Techniques.-R. Memming: Photoelectrochemical Solar Energy Conversion. - A. Henglein: Mechanism of Reac­tions on Colloidal Microelectrodes and Size Quan­tization Effects.