17:
906:
552:
503:
where the difference on the left-hand side is the
Galvani potential difference between the phases (1) and (2). Thus, the Galvani potential difference is determined entirely by the chemical difference of the two phases; specifically by the difference of the chemical potential of the charge carriers in
507:
The
Galvani potential difference between an electrode and electrolyte (or between other two electrically conductive phases) forms in an analogous fashion, although the chemical potentials in the equation above may need to include all species involved in the electrochemical reaction at the interface.
146:
First, consider the
Galvani potential between two metals. When two metals are electrically isolated from each other, an arbitrary voltage difference may exist between them. However, when two different metals are brought into electronic contact, electrons will flow from the metal with a lower voltage
922:
From the above equation, two metals in electronic contact (i.e., under electronic equilibrium) must have the same electrode potential. Also, the electrochemical potentials of the electrons within the two metals will be the same. However, their
Galvani potentials will be different (unless the metals
151:
of the electrons in the bulk of both phases are equal. The actual numbers of electrons that passes between the two phases is small (it depends on the capacitance between the objects), and the occupancies of the electron bands are practically unaffected. Rather, this small increase or decrease in
516:
The
Galvani potential difference is not directly measurable using voltmeters. The measured potential difference between two metal electrodes assembled into a cell does not equal the difference of the Galvani potentials of the two metals (or their combination with the solution Galvani potential)
901:{\displaystyle E^{(2)}-E^{(1)}=\left(\phi ^{(2)}-\phi ^{(S)}-{\frac {\mu _{j}^{(2)}}{z_{j}F}}\right)-\left(\phi ^{(1)}-\phi ^{(S)}-{\frac {\mu _{j}^{(1)}}{z_{j}F}}\right)=\left(\phi ^{(2)}-\phi ^{(1)}\right)-\left({\frac {\mu _{j}^{(2)}-\mu _{j}^{(1)}}{z_{j}F}}\right)}
498:
236:
1191:
1010:
which is effectively negative of the reduced electrochemical potential of electrons given in units of volts. It is noted that what one experimentally measures using an inert metallic probe and a voltmeter is
348:
1004:
269:
81:
61:
38:
1029:
944:
382:
1080:
165:
281:
Now, the electrochemical potential of a species is defined as a sum of its chemical potential and the local electrostatic potential:
287:
1256:
960:
1251:
539:
M is the additional metal (here assumed to be the metal (1)) that must be inserted into the circuit to close it,
153:
274:
j denotes the species which are the carrier of electric current in the system (which are electrons in metals)
159:
The equality of the electrochemical potential between the two different phases in contact can be written as:
1040:
1163:
Virkar, Anil V. (2010). "Mechanism of oxygen electrode delamination in solid oxide electrolyzer cells".
247:
517:
because the cell needs to contain another metal-metal interface, as in the following schematic of a
1192:"The Course of Oxygen Partial Pressure and Electric Potentials across an Oxide Electrolyte Cell"
1203:
104:
66:
46:
23:
1014:
929:
8:
1045:
1207:
1227:
1145:
493:{\displaystyle \phi ^{(2)}-\phi ^{(1)}={\frac {\mu _{j}^{(1)}-\mu _{j}^{(2)}}{z_{j}F}}}
358:
1219:
1231:
1149:
1090:
1211:
1176:
1172:
1135:
1094:
1085:
1061:
367:
363:
z is the electrical charge carried by a single charge carrier (unity for electrons)
88:
83:
in one phase. The corresponding potential differences computed between two phases.
16:
1056:
41:
152:
charge results in a shift in all the energy levels in the metals. An electrical
108:
1124:"The absolute electrode potential: an explanatory note (Recommendations 1986)"
1245:
1223:
1109:
1089:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
518:
135:
1140:
1123:
1098:
231:{\displaystyle {\overline {\mu }}_{j}^{(1)}={\overline {\mu }}_{j}^{(2)}}
148:
128:
1215:
124:
120:
116:
1050:
112:
343:{\displaystyle {\overline {\mu }}_{j}=\mu _{j}+z_{j}F\phi }
1053:(interface between two immiscible electrolyte solutions)
546:
Instead, the measured cell potential can be written as:
141:
511:
1017:
963:
932:
555:
385:
290:
277:(1) and (2) denote phase 1 and phase 2, respectively.
250:
168:
69:
49:
26:
156:is formed at the interface between the two phases.
1023:
998:
938:
900:
492:
342:
263:
230:
75:
55:
32:
1190:Jacobsen, Torben; Mogensen, Mogens (2008-12-18).
999:{\displaystyle \pi =-{\frac {\mu _{e}}{F}}+\phi }
1243:
1189:
147:to the metal with the higher voltage until the
542:the vertical bar, |, denotes a phase boundary.
1117:
1115:
1139:
915:E is the potential of a single electrode,
1165:International Journal of Hydrogen Energy
1121:
15:
1112:
1244:
1162:
107:between two points in the bulk of two
918:(S) denotes the electrolyte solution.
533:M and M are the two different metals,
134:The Galvani potential is named after
142:Galvani potential between two metals
111:. These phases can be two different
512:Relation to measured cell potential
13:
1086:Compendium of Chemical Terminology
264:{\displaystyle {\overline {\mu }}}
14:
1268:
103:, Δφ, delta phi) is the electric
372:Φ is the electrostatic potential
271:is the electrochemical potential
1122:Trasatti, S. (1 January 1986).
1183:
1177:10.1016/j.ijhydene.2010.06.058
1156:
1103:
1074:
871:
865:
847:
841:
811:
805:
792:
786:
746:
740:
720:
714:
701:
695:
655:
649:
629:
623:
610:
604:
586:
580:
567:
561:
467:
461:
443:
437:
416:
410:
397:
391:
376:From the two equations above:
223:
217:
192:
186:
1:
1067:
1091:Galvani potential difference
1041:Absolute electrode potential
297:
256:
206:
175:
97:Galvani potential difference
7:
1034:
10:
1273:
1257:Electrochemical potentials
1128:Pure and Applied Chemistry
952:electromotive potential in
536:S denotes the electrolyte,
119:joined), or a solid and a
101:inner potential difference
1252:Electrochemical concepts
1141:10.1351/pac198658070955
1099:10.1351/goldbook.G02574
1025:
1000:
940:
902:
494:
344:
265:
232:
84:
77:
63:and surface potential
57:
34:
1026:
1001:
941:
903:
495:
345:
266:
233:
78:
76:{\displaystyle \chi }
58:
56:{\displaystyle \psi }
35:
33:{\displaystyle \phi }
19:
1024:{\displaystyle \pi }
1015:
961:
939:{\displaystyle \pi }
930:
926:Moreover, if define
553:
383:
288:
248:
166:
105:potential difference
67:
47:
24:
1208:2008ECSTr..13z.259J
1046:Electrode potential
875:
851:
750:
659:
471:
447:
227:
196:
1021:
996:
948:electric potential
936:
898:
855:
831:
730:
639:
490:
451:
427:
359:chemical potential
340:
261:
228:
200:
169:
85:
73:
53:
30:
20:Galvani potential
1216:10.1149/1.3050398
1171:(18): 9527–9543.
988:
892:
766:
675:
488:
300:
259:
209:
178:
93:Galvani potential
1264:
1236:
1235:
1196:ECS Transactions
1187:
1181:
1180:
1160:
1154:
1153:
1143:
1119:
1110:
1107:
1101:
1078:
1062:Donnan potential
1030:
1028:
1027:
1022:
1005:
1003:
1002:
997:
989:
984:
983:
974:
945:
943:
942:
937:
923:are identical).
907:
905:
904:
899:
897:
893:
891:
887:
886:
876:
874:
863:
850:
839:
829:
820:
816:
815:
814:
796:
795:
772:
768:
767:
765:
761:
760:
749:
738:
729:
724:
723:
705:
704:
681:
677:
676:
674:
670:
669:
658:
647:
638:
633:
632:
614:
613:
590:
589:
571:
570:
504:the two phases.
499:
497:
496:
491:
489:
487:
483:
482:
472:
470:
459:
446:
435:
425:
420:
419:
401:
400:
368:Faraday constant
349:
347:
346:
341:
333:
332:
320:
319:
307:
306:
301:
293:
270:
268:
267:
262:
260:
252:
237:
235:
234:
229:
226:
215:
210:
202:
195:
184:
179:
171:
127:submerged in an
89:electrochemistry
82:
80:
79:
74:
62:
60:
59:
54:
39:
37:
36:
31:
1272:
1271:
1267:
1266:
1265:
1263:
1262:
1261:
1242:
1241:
1240:
1239:
1202:(26): 259–273.
1188:
1184:
1161:
1157:
1120:
1113:
1108:
1104:
1079:
1075:
1070:
1057:Volta potential
1037:
1016:
1013:
1012:
979:
975:
973:
962:
959:
958:
931:
928:
927:
882:
878:
877:
864:
859:
840:
835:
830:
828:
824:
804:
800:
785:
781:
780:
776:
756:
752:
751:
739:
734:
728:
713:
709:
694:
690:
689:
685:
665:
661:
660:
648:
643:
637:
622:
618:
603:
599:
598:
594:
579:
575:
560:
556:
554:
551:
550:
514:
478:
474:
473:
460:
455:
436:
431:
426:
424:
409:
405:
390:
386:
384:
381:
380:
328:
324:
315:
311:
302:
292:
291:
289:
286:
285:
251:
249:
246:
245:
216:
211:
201:
185:
180:
170:
167:
164:
163:
144:
123:(e.g., a metal
68:
65:
64:
48:
45:
44:
42:Volta potential
25:
22:
21:
12:
11:
5:
1270:
1260:
1259:
1254:
1238:
1237:
1182:
1155:
1134:(7): 955–966.
1111:
1102:
1072:
1071:
1069:
1066:
1065:
1064:
1059:
1054:
1048:
1043:
1036:
1033:
1020:
1008:
1007:
995:
992:
987:
982:
978:
972:
969:
966:
935:
920:
919:
916:
909:
908:
896:
890:
885:
881:
873:
870:
867:
862:
858:
854:
849:
846:
843:
838:
834:
827:
823:
819:
813:
810:
807:
803:
799:
794:
791:
788:
784:
779:
775:
771:
764:
759:
755:
748:
745:
742:
737:
733:
727:
722:
719:
716:
712:
708:
703:
700:
697:
693:
688:
684:
680:
673:
668:
664:
657:
654:
651:
646:
642:
636:
631:
628:
625:
621:
617:
612:
609:
606:
602:
597:
593:
588:
585:
582:
578:
574:
569:
566:
563:
559:
544:
543:
540:
537:
534:
527:
526:
513:
510:
501:
500:
486:
481:
477:
469:
466:
463:
458:
454:
450:
445:
442:
439:
434:
430:
423:
418:
415:
412:
408:
404:
399:
396:
393:
389:
374:
373:
370:
364:
361:
351:
350:
339:
336:
331:
327:
323:
318:
314:
310:
305:
299:
296:
279:
278:
275:
272:
258:
255:
239:
238:
225:
222:
219:
214:
208:
205:
199:
194:
191:
188:
183:
177:
174:
143:
140:
72:
52:
29:
9:
6:
4:
3:
2:
1269:
1258:
1255:
1253:
1250:
1249:
1247:
1233:
1229:
1225:
1221:
1217:
1213:
1209:
1205:
1201:
1197:
1193:
1186:
1178:
1174:
1170:
1166:
1159:
1151:
1147:
1142:
1137:
1133:
1129:
1125:
1118:
1116:
1106:
1100:
1096:
1092:
1088:
1087:
1082:
1077:
1073:
1063:
1060:
1058:
1055:
1052:
1049:
1047:
1044:
1042:
1039:
1038:
1032:
1018:
993:
990:
985:
980:
976:
970:
967:
964:
957:
956:
955:
953:
949:
933:
924:
917:
914:
913:
912:
894:
888:
883:
879:
868:
860:
856:
852:
844:
836:
832:
825:
821:
817:
808:
801:
797:
789:
782:
777:
773:
769:
762:
757:
753:
743:
735:
731:
725:
717:
710:
706:
698:
691:
686:
682:
678:
671:
666:
662:
652:
644:
640:
634:
626:
619:
615:
607:
600:
595:
591:
583:
576:
572:
564:
557:
549:
548:
547:
541:
538:
535:
532:
531:
530:
525:M | S | M | M
524:
523:
522:
520:
519:galvanic cell
509:
505:
484:
479:
475:
464:
456:
452:
448:
440:
432:
428:
421:
413:
406:
402:
394:
387:
379:
378:
377:
371:
369:
365:
362:
360:
356:
355:
354:
337:
334:
329:
325:
321:
316:
312:
308:
303:
294:
284:
283:
282:
276:
273:
253:
244:
243:
242:
220:
212:
203:
197:
189:
181:
172:
162:
161:
160:
157:
155:
150:
139:
137:
136:Luigi Galvani
132:
130:
126:
122:
118:
114:
110:
106:
102:
98:
95:(also called
94:
90:
70:
50:
43:
27:
18:
1199:
1195:
1185:
1168:
1164:
1158:
1131:
1127:
1105:
1084:
1076:
1009:
951:
947:
925:
921:
910:
545:
528:
515:
506:
502:
375:
352:
280:
240:
158:
154:double layer
145:
133:
100:
96:
92:
86:
149:Fermi level
129:electrolyte
115:(e.g., two
1246:Categories
1068:References
1224:1938-6737
1019:π
994:ϕ
977:μ
971:−
965:π
934:π
857:μ
853:−
833:μ
822:−
802:ϕ
798:−
783:ϕ
732:μ
726:−
711:ϕ
707:−
692:ϕ
683:−
641:μ
635:−
620:ϕ
616:−
601:ϕ
573:−
453:μ
449:−
429:μ
407:ϕ
403:−
388:ϕ
366:F is the
357:μ is the
338:ϕ
313:μ
298:¯
295:μ
257:¯
254:μ
207:¯
204:μ
176:¯
173:μ
125:electrode
71:χ
51:ψ
28:ϕ
1232:97315796
1150:31768829
1035:See also
950:(or the
1204:Bibcode
911:where:
529:where:
353:where:
241:where:
1230:
1222:
1148:
954:), as
946:, the
121:liquid
117:metals
113:solids
109:phases
91:, the
1228:S2CID
1146:S2CID
1081:IUPAC
1051:ITIES
99:, or
1220:ISSN
1212:doi
1173:doi
1136:doi
1095:doi
1093:".
131:).
87:In
1248::
1226:.
1218:.
1210:.
1200:13
1198:.
1194:.
1169:35
1167:.
1144:.
1132:58
1130:.
1126:.
1114:^
1083:,
1031:.
521::
138:.
40:,
1234:.
1214::
1206::
1179:.
1175::
1152:.
1138::
1097::
1006:,
991:+
986:F
981:e
968:=
895:)
889:F
884:j
880:z
872:)
869:1
866:(
861:j
848:)
845:2
842:(
837:j
826:(
818:)
812:)
809:1
806:(
793:)
790:2
787:(
778:(
774:=
770:)
763:F
758:j
754:z
747:)
744:1
741:(
736:j
721:)
718:S
715:(
702:)
699:1
696:(
687:(
679:)
672:F
667:j
663:z
656:)
653:2
650:(
645:j
630:)
627:S
624:(
611:)
608:2
605:(
596:(
592:=
587:)
584:1
581:(
577:E
568:)
565:2
562:(
558:E
485:F
480:j
476:z
468:)
465:2
462:(
457:j
444:)
441:1
438:(
433:j
422:=
417:)
414:1
411:(
398:)
395:2
392:(
335:F
330:j
326:z
322:+
317:j
309:=
304:j
224:)
221:2
218:(
213:j
198:=
193:)
190:1
187:(
182:j
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