25:
359:
412:= 300 Ω•s. Values of the charge transfer resistance and Warburg coefficient depend on physico-chemical parameters of a system under investigation. To obtain the Randles circuit parameters, the fitting of the model to the experimental data should be performed using complex nonlinear least-squares procedures available in numerous EIS data fitting computer programs.
163:(CPE) replacing the double layer capacity. The Randles equivalent circuit is one of the simplest possible models describing processes at the electrochemical interface. In real electrochemical systems, impedance spectra are usually more complicated and, thus, the Randles circuit may not give appropriate results.
171:
Figure 1 shows the equivalent circuit initially proposed by John Edward Brough
Randles for modeling of interfacial electrochemical reactions in presence of semi-infinite linear diffusion of electroactive particles to flat electrodes. A simple model for an electrode immersed in an electrolyte is
90:
313:
371:
In a simple situation, the
Warburg element manifests itself in EIS spectra by a line with an angle of 45 degrees in the low frequency region. Figure 2 shows an example of EIS spectrum (presented in the
208:. The key assumption is that the rate of the faradaic reaction is controlled by diffusion of the reactants to the electrode surface. The diffusional resistance element (the Warburg impedance,
230:
450:
A. Lasia. Electrochemical impedance spectroscopy and its applications. In: Modern
Aspects of Electrochemistry. Volume 32. Kluwer Academic/Plenum Pub. 1999, Ch.2, p. 143.
190:. If a faradaic reaction is taking place then that reaction is occurring in parallel with the charging of the double layer – so the charge transfer resistance,
259:
54:
156:
76:
47:
106:
123:
37:
463:
127:
41:
33:
160:
58:
139:
8:
331:
439:
351:
431:
152:
98:
251:
341:
308:{\displaystyle Z_{\mathrm {w} }={\frac {A_{\mathrm {w} }}{\sqrt {j\omega }}},}
457:
443:
373:
229:
In this model, the impedance of a faradaic reaction consists of an active
435:
110:
422:
Randles, J. E. B. (1947). "Kinetics of rapid electrode reactions".
358:
89:
199:, associated with the faradaic reaction is in parallel with
159:(EIS) for interpretation of impedance spectra, often with a
172:
simply the series combination of the ionic resistance,
262:
241:
and a specific electrochemical element of diffusion
366:
307:
16:Equivalent circuit for an electrochemical reaction
455:
46:but its sources remain unclear because it lacks
362:Simulated EIS spectrum of the Randles circuit.
376:) simulated using the following parameters:
77:Learn how and when to remove this message
357:
88:
421:
456:
157:electrochemical impedance spectroscopy
181:, with the double layer capacitance,
126:with the parallel combination of the
18:
13:
424:Discussions of the Faraday Society
286:
269:
14:
475:
23:
367:Identifying the Warburg element
217:), is therefore in series with
166:
1:
415:
107:equivalent electrical circuit
7:
109:that consists of an active
10:
480:
231:charge transfer resistance
93:Randles circuit schematic.
155:. It is commonly used in
128:double-layer capacitance
32:This article includes a
61:more precise citations.
363:
309:
161:constant phase element
94:
361:
310:
92:
436:10.1039/df9470100011
260:
332:Warburg coefficient
250:, represented by a
364:
305:
95:
34:list of references
352:angular frequency
300:
299:
153:faradaic reaction
87:
86:
79:
471:
447:
411:
402:
393:
384:
349:
339:
329:
314:
312:
311:
306:
301:
292:
291:
290:
289:
279:
274:
273:
272:
249:
240:
225:
216:
207:
198:
189:
180:
150:
137:
121:
99:electrochemistry
82:
75:
71:
68:
62:
57:this article by
48:inline citations
27:
26:
19:
479:
478:
474:
473:
472:
470:
469:
468:
464:Analog circuits
454:
453:
418:
410:
404:
401:
395:
392:
386:
383:
377:
369:
347:
337:
328:
322:
285:
284:
280:
278:
268:
267:
263:
261:
258:
257:
252:Warburg element
248:
242:
239:
233:
224:
218:
215:
209:
206:
200:
197:
191:
188:
182:
179:
173:
169:
149:
143:
136:
130:
120:
114:
103:Randles circuit
83:
72:
66:
63:
52:
38:related reading
28:
24:
17:
12:
11:
5:
477:
467:
466:
452:
451:
448:
417:
414:
408:
403:= 100 Ω,
399:
394:= 25 μF,
390:
381:
368:
365:
356:
355:
345:
342:imaginary unit
335:
326:
316:
315:
304:
298:
295:
288:
283:
277:
271:
266:
246:
237:
222:
213:
204:
195:
186:
177:
168:
165:
147:
134:
118:
85:
84:
42:external links
31:
29:
22:
15:
9:
6:
4:
3:
2:
476:
465:
462:
461:
459:
449:
445:
441:
437:
433:
429:
425:
420:
419:
413:
407:
398:
389:
385:= 20 Ω,
380:
375:
360:
353:
346:
343:
336:
333:
325:
321:
320:
319:
302:
296:
293:
281:
275:
264:
256:
255:
254:
253:
245:
236:
232:
227:
221:
212:
203:
194:
185:
176:
164:
162:
158:
154:
146:
141:
133:
129:
125:
117:
112:
108:
104:
100:
91:
81:
78:
70:
67:December 2010
60:
56:
50:
49:
43:
39:
35:
30:
21:
20:
427:
423:
405:
396:
387:
378:
374:Nyquist plot
370:
323:
317:
243:
234:
228:
219:
210:
201:
192:
183:
174:
170:
144:
131:
115:
102:
96:
73:
64:
53:Please help
45:
167:Explanation
113:resistance
111:electrolyte
59:introducing
416:References
444:0366-9033
297:ω
140:impedance
458:Category
350:is the
330:is the
318:where
151:) of a
138:and an
55:improve
442:
430:: 11.
340:is an
124:series
105:is an
40:, or
440:ISSN
101:, a
432:doi
122:in
97:In
460::
438:.
426:.
400:ct
391:dl
238:ct
226:.
223:ct
205:dl
196:ct
187:dl
135:dl
44:,
36:,
446:.
434::
428:1
409:W
406:A
397:R
388:C
382:S
379:R
354:.
348:ω
344:;
338:j
334:;
327:W
324:A
303:,
294:j
287:w
282:A
276:=
270:w
265:Z
247:W
244:Z
235:R
220:R
214:W
211:Z
202:C
193:R
184:C
178:S
175:R
148:w
145:Z
142:(
132:C
119:S
116:R
80:)
74:(
69:)
65:(
51:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
