edited by JOHN W. MOORE computer mrie~. 28 Eastern Michigan university, ypsilanti, 48197

Microcomputer Demonstrations in the Teaching of Electrochemical Kinetics Oliver R. Brown The University. Newcastle upon Tyne NE1 7RU, United Kingdom

Several articles published recently in THIS JOURNAL have drawn attention to the use of inexpensive microcomputers as aids in teaching chemistry (1-3). In particular the value of graphics facilities has been stressed (4). However, if the title "A Tool, Not a Gimmick" of the initial paper (5) in the "Computer Series" is to be valid, it is necessary to exploit fully the uniqtle ad\,antages offered by the wmputw UIIPII crmi- pared u'ith alternative demt,nstrafim techniques. Stutir displays that merely show a diagram have no advantage over a slide projection. Even dynamic displays offer only conve- nience when compared with videotape or cine-film presen- tation. One cansuggest that the major advantage of the mi- crocomputer in a teaching role lies in its combination of possibilities for interactive operation, either by the teacher or the pupil, and for dynamic display.

This paper describes the application of this philosophy to the teaching of elementary electrode kinetics with the help of an Apple I1 Plus (48K RAM) microcomputer equipped with a floppy disk drive; however, many of the ideas discussed will be specific neither to the Apple nor to electrochemistry. The Apple was chosen for its excellence in the following features: high-resolution color graphics, storage and manipulation of shapes, games controls, and instruction handbooks. Inci- dentally, Apples are used extensively in our research lahora- tory for the total control of elaborate experiments (6) and were therefore available and familiar to us.

In Britain, electrochemistry is generally a neglected area of chemical education. Electrochemistrv questions set in na- tional exaninations tor High Srhud pul;ila r~.st th~~pr~,ximity of the ouoil's rn i~~:onc~~pl lms imd i1:veln i f iworance 111 those . . ot. the examiners i n s t & I oiprohiug the ;tareof knowledge and undt.rititnding rnl the candidate. In parricular the kinetic.< and mechanisms bf electrode processes receive little serious at- tention; indeed, it is only in recent editions that some, other- wise commendable, student textbooks in physical chemistry have acknowledged the existence of this long-established branch of science which underpins some of the most important commercial chemical processes. Therefore, it is considered that this subject area is deserving of efforts toward the im- provement of teaching methods so that the vicious circle of ignorance should be broken.

This paper describes some of the demonstrations that have been employed in presenting, to find-year undergraduate and first-year postgraduate students, the concepts of diffusion and convection near an electrode and those concerned with the rates of electron-transfer Drocesses at the surface. In narticular the SEDD (simulated kxperiment with divided display) techniaue is described in which two hieh-resolution disolavs . . of inter-dependent relationships are shown side-by-side. For examole, the left half of the screen can be used to disolav g r i q ~ h i ~ n l l ~ a the~rretical interpretation u r the srate of thk system under studv whilr rhr right half ~ l i s ~ I a \ ~ s th~ : cxperl- mental result that would correspond to that state.

Techniques used in Programming for Teaching Displays

The programs we have used are broadly of two types: in- teractive and non-interactive. The latter type show the same seauence of disolav "frames" each time the Droeram is run. . . . "

Each frame contains one or more images whose shapes must be programmed. If the shapes are single points or straight lines then it is possible to calculate and plot their positions by means of the HPLOT command provided that there are only a few shape changes between successive frames. Alternating displays of the Apple's two high-resolution graphics (HGR) pages enable each picture to he prepared fully while the pre- vious one is being shown. However, in many cases the shapes to be displayed are curved, the lines often corresponding to a function (e.g., a higher transcendental function) that re- quires a good deal of calculation time, so that successive dis- plays would be separated hy many seconds. Therefore, it is often necessary to calculate and store the shapes in advance of running the program. Usually this is done most conve- niently and with minimum demands upon the memory space by creating a shape table. The shapes are drawn on the screen as required when the program is running. Those shapes which can he expressed as a continuous single-valued function can be calculated and stored by means of an auxiliary pro- gram. Other shapes must he specified and entered manually into the table: a tedious process. Storage of complete HGR pages on disc as datafiles is both demanding upon disc space and unacceptably slow in display.

I t is in interactive display that the microcomputer reaches its full potential in teaching. The operator is ahle to change the conditions of the simulated experiment either through keyboard input or, more conveniently, by the potentiometers known as games controls. These analog controls can cope si- multaneously with a maximum of four variables. The current values of the variables can be written on the screen below the graphic display ii the first graphics page IHGK I I is in \.iew or, smith mure diiliculty, un the second orsottics page r I 1,

The major prohlem-in interactive o&&n & t h a t of re- sponse speed. If a large number of experimental variables are to he adiusted. then the number of combinations of conditions is too &eat to'he able to store all the possible result figures within the available memory space. The only alternative to being ahle to draw the result shape appropriate to the set conditions is to calculate and HPLOT the result within the display program. In general the BASIC language takes too lone to do this: whereas. machine-lannuane oroerams of this . . . . . . . romplexit\. take most programer ttx, lung r u writ^^. Tht:n.li~re. thenoerator i i likel\.tt,ltri~~thr f ~ i l of initan1 rcirjonci, unlcss the displayed figu;es consist of only a few or lines and/or involve a choice of various sizes (SCALE) and orien- tations (ROT) of fewer than a few hundred alternative stored shapes. Careful programming usually allows these criteria to he achieved. For example, a variable need not he allowed the

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full resolution of the control potentiometer; i t is usually only necessarv to have a ranee of about ten alternative values. In this waythe memory can usually accommodate all of the 100 possible results obtainable usiua two variables.

Listings of programs describid below are, for reasons of economy and space, omitted from this paper but are available from the author a t a nominal cost of $20 (f 10) to cover expense of copying and postage.

Influence of Electrode Potentlal on Rates of Redox Reactions

A suite of six simple programs illustrate the concepts of the svmmetrv factor 13 and activation enerev AG* in electron- tiansfer ieactions a t an electrode and show how these pa- rameters vary with the electrode potential E. The measured quantities that depend upon the values of /3 and AG* are the current density, i, the exchange current density, io, and the transfer coefficient a, which is related to the Tafel slope, dEld logi, by

d log i/dE = aF12.303RT (1)

when the overvoltage is large (n > 2.303RT/F) Program 1 (Fig. 1) shows a pair of intersecting parabolas,

representing the potential energy curves of the reactant and product states for a reaction

The game controls allow the curves (stored as a single parahola in the shape table) to be displaced vertically relative to each other, corresponding to changes in the electrode potential. The symmetry factor, defined (7) according to eqn. (3), is calcu- lated and displayed below the graphics.

pa = dAc:/dAc. (3)

The subscript "a" denotes the anodic reaction. This program shows that pa falls with increasing electrode potential, hut, that over the narrow range of potential typically covered in electrode kinetic measurements, i t remains constant within a few per cent. As the transfer coefficient of one-electron redox reactions performed under usual conditions is equal to the symmetry factor, it is seen that the Tafel slope is expected to he independent of E. This conclusion justifies the represen-

Figure t . Intersecting potential-energy curves representing the reaction profile of the redox reaction: Rd = Ox + e-

Figure 2. Potentiai-energy shapes with adjustable slopes so that the symmetry factor can be varied.

tation of potential energy curves by V-shapes in subsequent proarams. This is common practice in textbooks on electro- chemistry (8) and is a convenience when writing programs.

In program 2 (Fig. 2) the relative displacement of the po- tential energy curves is controlled by PDL(0); the other games control, PDL(l), adjusts the slope of the mobile "V" and so enables the importance of the value of the symmetry factor to he considered. It can he seen that

Pa = (dC~d/dx)/((dC~d/dx) - (dCo,/dx)) (4)

where x denotes the distance along the reaction profile mea- sured from rieht to left.

Program 3 i ~ i g . 3) uses the SEDD method; the left half of the screen contains the V - s h a d curves of o r o m 2. but the right side is a Tafel plot. FO; each combiiatiin of electrode ~o ten t i a l and svmmetrv factor set uo on the left. a corre- sponding experi&ental point is plotted on the right. The op- erator can plot out hoth the anodic and cathodic branches of a Tafel presentation for a given value of symmetry factor. Then he or she can change /3 and scan again through the range of E. This program ignores the non-Tafel region of potential that lies between the anodic and cathodic branches and occurs when the anodic and cathodic partial currents are of compa- rahle magnitude. Consequently, this illustration is applicable onlv to a reaction that is kineticallv irreversible. We can sup"pose that the scales of the Tafel axes are small.

Proeram 4 (Fie. 4) uses the SEDD techniaue to demonstrate the mire generarcase. The program uses a fixed value for the svmmetrv factor (13 = 0.5) and allows the loa i versus E rela- tionship he plotted out, point-by-point, over the Tafel and non-Tafel regions. Further emphasis is given to the non-Tafel region in program 5 (Fig. 5) which also uses the SEDD method. In this case hoth halves of the display are of the same experi- mental results; I versus E is plotted on the left and log r versus E o n the right. Contrulled variahles an, thr symmetry factor (PDI.IOI) and exchanee current densitv IPDLIIII and the . .. - . . .. electrude putential is scanned automatically.

Program 6 (Fig. 61 demonstrates the vit~mtions of the sol- vation sheath of an ion adjacent to the electrode surface. The theories of Marcus ( 9 ) and of I.e~,irh (10) regard the activation process in a rt.dox-typeclectron-transfer prtwss as the rear. rangement of the solvept molecules to a set of positims that

Figure 3. Point-by-point plots of Tafel relations produced by "awing the elechode potential at selected values of the symmetry factor. The lower plot has been obtained using 0 < 0.5. The upper plot is being taken with f l > 0.5

Figure 4. Point-by-point plot of polarization data from the cathodic Tafel region via the nan-Tafel region to the anodic Tale1 region.

410 Journal of Chemical Education

is intermediate between the equilibrium positions of the re- duced and oxidized ions. Electron tunnellina between the ion and the electrode can occur only when the energy of the sys- tem is the same, regardless of whether the system is in the reduced (Rd) or oxidized (Ox + e-,) state. Such afavorable arrangement of nuclei can be achieved either when the over- potential is numerically high or when the reactant ion is ex- cited. The control parameters are the vibrational level iPDL(0)) which lies between 0 and 3 and the electrode no- tential (PDL(~)) which sets an overpotential between *0.7 V. The particular system supposed to be under consideration is

Fe(III)(aq) + e- = Fe(II)(aq) (5 )

The graphics portray the ions as puckered circles (the puck- ered nature results from the finite resolution of the graphics) whose diameters vary rhythmically. The Fe(II1) ion is smaller than the F e U ion, and the electron transfer event when it . . occurs is evident from the change of size as well as from the appearance or disappearance of a letter "E" within the elec-

Effect of Mass Transfer on Rates of Redox Electrode Reactions

Programs 3 and 4 showed polarization data that were un- affected by the supply of reactant or the dispersal of the product. In fact the mass transfer of material to and from the electrode surface can be ignored only when the currents are low and the reaction is not kinetically reversible. General treatments of the combined effects of diffusion, convection, and mimation (11 ) are unsuited to undereraduate courses. and . . so i t is Gsual to simplify the presentation by ignoring migration (justifiable when a large excess of supporting electrolyte is used in the experimental system) and by supposing the entire electrode surface to behave uniformly-in particular, stirring is supposed to be uniform. With these conditions, the Nernst diffusion layer model of mass transfer can be adopted pro- vided that no coupled chemical reactions occur.

A further set of programs use the SEDD method to show side-by-side the prifdei of concentration versus distance from the electrode for the reactant and product species and the corresponding point on the polarization (i versus E ) curve. The controlled variables are electrode potential (PDL(1)) and the thickness of the Nernst laver (PDL(0)). As the Nernst

stagnant layer within the distanced, i t follows that the con- centration must vary linearly with distance inside the layer. The slope of that profile must, according to Fick's Law, be proportional to the current flowing a t the electrode. Mass- transfer-limited currents are observed when the reactant concentration falls to zero a t the surface.

Program 7 treats the case of an irreversible electrode reac- tion when only one half of the redox couple is present in the bulk of the electrolyte solution. Program 8 deals with the re- versible reaction under similar circumstances. Program 9 differs from it only insofar as both species are supposed to be present in the electrolyte. Program 10 treats the more general case of a quasi-reversible reaction. Changing the vigor of stirring (i.e., changing the thickness of the Nernst layer) is seen not to affect currents at the foot of an irreversible wave (Fig. 7); however, currents on a reversible wave are, at all potentials,

Figure 6. (A) Fe(1ll) (aq) ion in the vibrational ground state, adjacent to the elec- node, which is at a positive overpotential so reduction cannot occur. (6) Fe(1l) (aq) ion unable to be oxidized because the overpotential of the electrode is very negative.

model separates the effects ofdiffusion'kd convection by su~nosine the solution to be of uniform concentration from thkbulkio a distance d from the electrbde surface, with a

Figure 7. Polarization curves for an irreversible redox reaction plotted point- by-paint when the product isabsent from the bulk of solution. The upper CUNe

has been plotted when me diffusion layer mickness was 1 X lo-' cm, The lower curve is being plotted as it is 5 X cm.

Figure 5. Simultaneous representation of polarization data in linear and loga- rilhmicforms. (A)Case of 6 = 0.5 and (6) case of 0 = 0.24. The reaction i s W simple redox process: Rd = Ox + 8-.

Figure 8. Polarization curves for a quasi-reversible redox reaction. Conditions 85 lor Figure 7.

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Figure 9. Polarization curves for a quasi-reversible redox reaction when ko is 0.1 cm s-'. me lower curve has been plotted when We diffusion layer Wick- was 5 X cm, and the upper curve is being plotted as it is 1 X cm.

Figure 10. Same curvesas for Figure 9 with thedifference that therate constam ko is now 5 X 10-'cm s-'.

inversely proportional to the diffusion layer thickness, as are the limiting currents of all waves (Fig. 8).

Program 10 has provision for keyboard input of the stan- dard rate constant ko and the concentration ratio cRa/co,. By oerformine successive runs with different values of kn. the system can he seen to change from reversible to irreversible behavior, the irreversible behavior beginning a t lower values of ko when the diffusion layer is thin. This is a particularly vivid demonstration of the factors that determine reversibilitv in electrode reaction; (Figs. 9 and 10).

Coupled Chemical Reactions Most real electrochemical reactions, unlike the simole

one-electron redox process considered so far, consist of several mechanistic steps. Of particular interest are those in which chemical evemi orcurhefore or after the elertrnn-transfer process (12). For such reactions the SF:I)I) method can be used in conjunction with a shape table to display side-by-side the polarieation wave and the concentration versus distance orofiles of the soecies invohd: esoeciallv the reaction inter- mediates. The number of possible model schemes that can he treated in this way is clearly large, and so we will consider only one, relatively simple, example: a first-order irreversible chemical step following a reversible redox event. The case is considered in which the chemical rate constant is sufficiently high for the reaction to he essentially complete before the intermediate has had time to diffuse across the Nernst layer.

The controlled variables are electrode ootential (PDL(1)) and the chemical rate constant, k (PDL(~)). The ~ k r n s t zf: fusion laver thickness is supoosed fixed a t 1.0 X 1 0 - h . a value easily attainable using a rotating-disc electrode. o n the left of the screen is shown the concentration versus distance profile of the eledrogenerated intermediate, and on the right the plot of steady-state current density versus potential is shown. For each combination of k and E that is imposed on the system one point is plotted on the i versus E plane. In realitv, the intermediate usually reacts with another species in the elertrolyte solution. If that species is in excess, then our model remains relevant and the fikt-order rate constant must be replaced by a pseudo-first-order rate constant whose value can he varied from zero hy adjusting the concentration of the extra species. The polarization curves each consist of points

Figure 11. For the reaction scheme A = e + B; B - 6, the concentration of B is shown as a function of distance x from the electrode surface at each valve Of electrode potential examined. The right-hand-side wave has been obtained for the case of no chemical reaction (k = 0) and the left-side wave is being plotted for the case where k = 6688 6-'.

Figlre 12 A arge-ampilt~d~ step neleclrode potent a nar orenapplocd loan electrode at wn ch tne react on Rd = Ox T C occrrs me concentrat on at Rd is ohawn as a t m c t m of d stance x from me electrode %dace as the c ~ n s n t versus time relation is recorded.

Figure 13. As the dropping mercury electrode expands. the tracks of particles of solute (or solvent) are seen to move Outward only slightly.

a t 22 values of potential. Six values of rate constant (300 s-I to 5 X lo4 sS-l) as well a s k = 0 are possible.

The demonstration shows that, with increasing values of the chemical rate constant, the polarization wave moves to progressively less extreme values of the electrode potential ( W d log k = -2.303RT/ZF), but i t retains the shape shown by the simple redox reaction (Fig. 11).

Non-Steady-State Displays Many, if not most, electrochemical kinetic measurements

are not of the steadv-state tvne discussed so far. When a perturbation in either the electrode potential or the current density is applied to a svstem a time-deoendent resnonse ensues (13)'i)ne of the c&nmonest and &ost useful pertur- batims is the sinprle step of electrode potential; it allows the electrode reaction to he switched from an off state to an on state.

The one example of a non-steady-state SEDD program that we will consider here is a relatively simple situation; a po- tential step of large magnitude is applied to an electrode a t which reaction 2 can occur. Immediately the reactant con- centration adiacent to the surface is essentiallv decreased to zero so that the measured currents (simulatedas an i versus time. t. olot on the rieht-hand side of the screen) are diffu- sion-.c&rolled and tcerefore follow the Cottrell equation:

i h F = ~ ( D l a t ) ' / ~ (6)

412 Journal of Chemical Education

Here, D arid c are the diffusion coefficient and the concen- tration, respectively, of the reactant species. On the left of the screen is shown the relationship hetween c and the distance from the electrode, a function that is time-dependent. Thus, the demonstration shows the "concentration wave" spreading out from the electrode as the current falls with time. The rate of display, a t ahout 7 frames per second is in simulated real time. One frame is shown in Figure 12.

An example of a non-graphical, time-dependent display used in teaching electrochemistry is shown in Figure 13. Its purpose is to show the manner in which the dropping mercury electrode produces convective diffusion. As the drop expands, it is seen that points in the solution, representing solute par- ticles, remain almost stationary as their tracks are displayed. Therefore, their relative movement is toward the electrode surface.

Student Response The underaraduate class was more alert and receptive than

were their predecessors who, in previous yeamhad been taught similar material without the aid of the microcomputer. m ow ever, the opportunity has not arisen to make a con&olled comparison of the relative efficacy of the knowledge-transfer process with and without the computer.

The postgraduate class was explicitly appreciative of the method of presentation hut many of the students were meeting the material for a second or third time, and they

would probably have achieved a full understanding even without the innovation. Certainly, there were no obvious disadvantages involved in the use of the computer so, with hardware prices tumbling, there is a strong case for extensive implementation of these methods.

Further Applications

The display techniques described here have been applied and will continue to he applied to many presentations of electrochemical and chemical concepts. Examples include the distrihutions of ions in the diffuse double layer as a function of electrode potential and salt concentration.

Literature Cited (11 Myers, G. H., J. CHEM. EDUC. 57.702 11980). (21 Moore, J. W.. Gerhold. G.. Bishop, R. D.. Gelder, J. I., Pollnaw, G. F., andOwen, G. S.,

;. CHEM EDUC.57.93 (1980). 13) Moore, J., Gerhold, G., Breneman, G. L.. Owen, G. S., Butler, W., Smith. S. G., and

Lyndrup,M. L., J.CHEM. EDUC.,56,776(19791. (41 Soitzberg. L. J., J. CHEM. EDUC., 56,644 11979). (5) Moore, J. W., and Collins, R. W., J . CHEM. EDUC.. 56,140 (19791. (6) Brown,O.R.,El~efrochim. Aeto.,27,33 (1982). (71 Delahsy, P.,"Double Layer and Electrode Kinetics," Interscience, New York. 1965. (8) Boekris, J. O.'M., and Reddy. A. K. N., "Modern Eleetroehemistry," MaeDonaid,

London, 1970, Vol. 2. p. 975. (91 Marcus, R.A.,Ann.Rro. Phys Cham., 15. 155 119641.

(10) Levich, V. G., in "Advances in Eleaoehemi~try and Electrochemical Engineering." (Editor Delshay, P.1. Interrcience, New York, 1965. p. 249.

I l l ) Newman. J., "Electrochemical Systems.). Prentice-Hall, New Jersey. 1973. (121 Opekar F.,and Beran!P., J. El~c t roo~ol . Chem.69.51 (19761. (13) MacDonald, D. D., ','Transient Technique8 in Electrochemistry," Plenum. New York,

1977. (14) Bishop, R. Daniel, Kilobaud Mieroeompufing, 5(71. 108 (July 1981).

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