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Cottrell equation

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505: 20: 292:, dissociation of a ligand, or a change in geometry. Deviations from linearity can be expected at very short time scales due to non-ideality in the potential step. At long time scales, buildup of the diffusion layer causes a shift from a linearly dominated to a radially dominated diffusion regime, which causes another deviation from linearity. 159: 343: 385: 229: 249: 89: 546: 80: 75:
that is planar but can also be derived for spherical, cylindrical, and rectangular geometries by using the corresponding
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Bard, A. J.; Faulkner, L. R. “Electrochemical Methods. Fundamentals and Applications” 2nd Ed. Wiley, New York. 2001.
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Cottrell, F. G. (1903-01-01). "Der Reststrom bei galvanischer Polarisation, betrachtet als ein Diffusionsproblem".
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sometimes indicate that the redox event is associated with other processes, such as association of a
410: 298: 358: 202: 76: 520: 8: 234: 40: 484: 466: 44: 512: 456: 448: 415: 188: 36: 28: 516: 420: 559: 470: 461: 48: 452: 63:/ferrocenium couple, the current measured depends on the rate at which the 504: 405: 47:. Specifically it describes the current response when the potential is a 154:{\displaystyle i={\frac {nFAc_{j}^{0}{\sqrt {D_{j}}}}{\sqrt {\pi t}}}} 72: 60: 177:= number of electrons (to reduce/oxidize one molecule of analyte 64: 67:
diffuses to the electrode. That is, the current is said to be "
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Variation of current density following the Cottrell equation
19: 361: 301: 237: 205: 92: 71:". The Cottrell equation describes the case for an 349:
is the collection of constants for a given system (
379: 337: 243: 223: 153: 295:In practice, the Cottrell equation simplifies to 231:= initial concentration of the reducible analyte 557: 540: 79:and boundary conditions in conjunction with 547: 533: 278:Deviations from linearity in the plot of 460: 438: 18: 558: 197:= area of the (planar) electrode in cm 39:with respect to time in a controlled 499: 441:Zeitschrift fĂĽr Physikalische Chemie 13: 447:(1). Walter de Gruyter GmbH: 385. 14: 582: 503: 477: 432: 81:Fick's second law of diffusion 1: 426: 519:. You can help Knowledge by 338:{\displaystyle i=kt^{-1/2},} 16:Equation in electrochemistry 7: 399: 51:in time. It was derived by 10: 587: 498: 53:Frederick Gardner Cottrell 566:Electrochemical equations 411:Electroanalytical methods 380:{\displaystyle c_{j}^{0}} 224:{\displaystyle c_{j}^{0}} 171:= current, in units of A 35:describes the change in 571:Electrochemistry stubs 515:-related article is a 453:10.1515/zpch-1903-4229 381: 339: 245: 225: 155: 55:in 1903. For a simple 24: 382: 340: 262:diffusion coefficient 246: 226: 156: 43:experiment, such as 22: 359: 299: 235: 203: 90: 69:diffusion controlled 376: 220: 125: 59:event, such as the 377: 362: 335: 241: 221: 206: 151: 111: 25: 528: 527: 462:2027/uc1.b2655532 244:{\displaystyle j} 149: 148: 138: 45:chronoamperometry 33:Cottrell equation 578: 549: 542: 535: 513:electrochemistry 507: 500: 491: 481: 475: 474: 464: 436: 416:Limiting current 395: 388: 386: 384: 383: 378: 375: 370: 352: 348: 344: 342: 341: 336: 331: 330: 326: 287: 281: 273: 267: 259: 250: 248: 247: 242: 230: 228: 227: 222: 219: 214: 196: 189:Faraday constant 186: 180: 176: 170: 160: 158: 157: 152: 150: 141: 140: 139: 137: 136: 127: 124: 119: 100: 77:Laplace operator 37:electric current 29:electrochemistry 586: 585: 581: 580: 579: 577: 576: 575: 556: 555: 554: 553: 496: 494: 482: 478: 437: 433: 429: 402: 394: 390: 371: 366: 360: 357: 356: 354: 350: 346: 322: 315: 311: 300: 297: 296: 283: 279: 271: 265: 258: 254: 236: 233: 232: 215: 210: 204: 201: 200: 194: 184: 178: 174: 168: 132: 128: 126: 120: 115: 101: 99: 91: 88: 87: 17: 12: 11: 5: 584: 574: 573: 568: 552: 551: 544: 537: 529: 526: 525: 508: 493: 492: 476: 430: 428: 425: 424: 423: 421:Anson equation 418: 413: 408: 401: 398: 392: 374: 369: 365: 334: 329: 325: 321: 318: 314: 310: 307: 304: 276: 275: 269: 256: 252: 240: 218: 213: 209: 198: 192: 182: 181:, for example) 172: 162: 161: 147: 144: 135: 131: 123: 118: 114: 110: 107: 104: 98: 95: 15: 9: 6: 4: 3: 2: 583: 572: 569: 567: 564: 563: 561: 550: 545: 543: 538: 536: 531: 530: 524: 522: 518: 514: 509: 506: 502: 501: 497: 490: 489:0-471-04372-9 486: 480: 472: 468: 463: 458: 454: 450: 446: 443:(in German). 442: 435: 431: 422: 419: 417: 414: 412: 409: 407: 404: 403: 397: 372: 367: 363: 332: 327: 323: 319: 316: 312: 308: 305: 302: 293: 291: 286: 270: 263: 253: 238: 216: 211: 207: 199: 193: 191:, 96485 C/mol 190: 183: 173: 167: 166: 165: 145: 142: 133: 129: 121: 116: 112: 108: 105: 102: 96: 93: 86: 85: 84: 82: 78: 74: 70: 66: 62: 58: 54: 50: 49:step function 46: 42: 38: 34: 30: 21: 521:expanding it 510: 495: 479: 444: 440: 434: 294: 284: 277: 274:= time in s. 264:for species 163: 32: 26: 406:Voltammetry 560:Categories 427:References 251:in mol/cm; 471:2196-7156 317:− 143:π 73:electrode 61:ferrocene 41:potential 400:See also 387:⁠ 355:⁠ 351:n, F, A 268:in cm/s 164:where, 65:analyte 487:  469:  345:where 290:ligand 31:, the 511:This 57:redox 517:stub 485:ISBN 467:ISSN 282:vs. 457:hdl 449:doi 445:42U 396:). 27:In 562:: 465:. 455:. 389:, 353:, 260:= 187:= 83:. 548:e 541:t 534:v 523:. 473:. 459:: 451:: 393:j 391:D 373:0 368:j 364:c 347:k 333:, 328:2 324:/ 320:1 313:t 309:k 306:= 303:i 285:t 280:i 272:t 266:j 257:j 255:D 239:j 217:0 212:j 208:c 195:A 185:F 179:j 175:n 169:i 146:t 134:j 130:D 122:0 117:j 113:c 109:A 106:F 103:n 97:= 94:i

Index


electrochemistry
electric current
potential
chronoamperometry
step function
Frederick Gardner Cottrell
redox
ferrocene
analyte
diffusion controlled
electrode
Laplace operator
Fick's second law of diffusion
Faraday constant
diffusion coefficient
ligand
Voltammetry
Electroanalytical methods
Limiting current
Anson equation
doi
10.1515/zpch-1903-4229
hdl
2027/uc1.b2655532
ISSN
2196-7156
ISBN
0-471-04372-9
Stub icon

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