26:
34:
42:
278:, and ideal mixtures are enough to describe many common solutions. Thus, in many cases, mixing (or phase separation) is driven primarily by the entropy of mixing. It is generally the case that the entropy will increase whenever a particle (an atom, a molecule) has a larger space to explore; and thus, the entropy of mixing is generally positive: the components of the mixture can increase their entropy by sharing a larger common volume.
127:-water system has an LCST of 61 °C, and also a UCST of 210 °C at pressures high enough for liquid water to exist at that temperature. The components are therefore miscible in all proportions below 61 °C and above 210 °C (at high pressure), and partially miscible in the interval from 61 to 210 °C.
281:
Phase separation is then driven by several distinct processes. In one case, the enthalpy of mixing is positive, and the temperature is low: the increase in entropy is insufficient to lower the free energy. In another, considerably more rare case, the entropy of mixing is
286:", that is to say, it is negative. In this case, even if the change in enthalpy is negative, phase separation will occur unless the temperature is low enough. It is this second case which gives rise to the idea of the lower critical solution temperature.
76:
are formed by phase separation, though not all phase separations forms colloids - for example oil and water can form separated layers under gravity rather than remaining as microscopic droplets in suspension.
108:: staying mixed (or unmixed) absent some large disturbance. The region beyond the spinodal curve is absolutely unstable, and (if starting from a mixed state) will spontaneously phase-separate.
368:
335:
591:
Shin, Y.; Zwierlein, M. W.; Schunck, C. H.; Schirotzek, A.; Ketterle, W. (2006-07-18). "Observation of Phase
Separation in a Strongly Interacting Imbalanced Fermi Gas".
192:
260:
236:
212:
157:
652:
Zwierlein, Martin W.; Schirotzek, André; Schunck, Christian H.; Ketterle, Wolfgang (2006-01-27). "Fermionic
Superfluidity with Imbalanced Spin Populations".
1410:
386:
123:, above which or below which the components of a mixture are miscible in all proportions. It is rare for systems to have both, but some exist: the
306:) in a certain range of temperatures and concentrations separates into parts. The initial mix of the two isotopes spontaneously separates into
820:
1112:
721:
Kopyciński, Jakub; Pudelko, Wojciech R.; Wlazłowski, Gabriel (2021-11-23). "Vortex lattice in spin-imbalanced unitary Fermi gas".
923:
788:
506:
116:
112:
104:. On one side of the binodal, mixtures are absolutely stable. In between the binodal and the spinodal, mixtures may be
1481:
1157:
813:
459:
1105:
1014:
1471:
1247:
139:, with phase separation or mixing occurring for whichever case lowers the Gibbs free energy. The free energy
1400:
1072:
976:
806:
1330:
1098:
885:
530:
Carlson, J.; Reddy, Sanjay (2005-08-02). "Asymmetric Two-Component
Fermion Systems in Strong Coupling".
1385:
992:
85:
1277:
900:
868:
72:
liquids, such as oil and water. This type of phase separation is known as liquid-liquid equilibrium.
1262:
1197:
1041:
1036:
997:
340:
309:
53:
of helium, showing at bottom a range of temperatures and ratios at which they will phase-separate.
1217:
398:
474:
P.W. Atkins and J. de Paula, "Atkins' Physical
Chemistry" (8th edn, W.H. Freeman 2006) pp. 186-7
1315:
1310:
1167:
1060:
950:
781:
Phase
Separation in Soft Matter Physics: Micellar Solutions, Microemulsions, Critical Phenomena
81:
1415:
1395:
1053:
1048:
1026:
971:
878:
858:
162:
1129:
1121:
935:
918:
829:
740:
671:
610:
549:
120:
8:
1242:
1212:
1031:
1009:
895:
853:
65:
744:
675:
614:
553:
1019:
910:
843:
756:
730:
703:
661:
634:
600:
573:
539:
267:
245:
221:
197:
142:
1476:
1420:
1379:
1282:
1065:
945:
873:
863:
784:
760:
695:
687:
626:
565:
512:
502:
455:
271:
136:
707:
638:
1355:
1350:
1142:
1004:
748:
679:
618:
557:
447:
25:
622:
577:
561:
33:
1340:
1325:
1257:
1222:
1207:
1202:
1187:
1152:
966:
93:
752:
439:
1390:
1345:
1335:
1252:
1147:
1137:
1077:
382:
375:
371:
61:
1465:
1435:
1272:
1232:
1177:
930:
691:
516:
408:
275:
89:
46:
683:
451:
1292:
1287:
699:
630:
569:
1445:
1360:
666:
605:
544:
239:
1440:
1430:
1425:
1302:
940:
413:
105:
69:
41:
798:
1450:
1405:
1320:
1090:
848:
378:
1267:
735:
303:
299:
215:
124:
101:
651:
266:. Thus, the change of the free energy in mixing is the sum of the
1370:
1172:
1162:
418:
403:
263:
97:
73:
50:
20:
16:
Creation of two phases of matter from a single homogenous mixture
381:
case. The phase separation can compete with other phenomena as
295:
590:
1192:
374:
systems. It has been shown experimentally in a two-component
720:
446:(2nd ed.). Oxford: Blackwell Scientific Publications.
68:. The most common type of phase separation is between two
444:
IUPAC Compendium of
Chemical Terminology (the "Gold Book")
29:
Mixing of liquids A and B and subsequent phase separation
80:
A common form of spontaneous phase separation is termed
343:
312:
248:
224:
200:
165:
145:
1411:
List of boiling and freezing information of solvents
501:(3rd rev. and expanded ed.). Berlin: Springer.
778:
362:
329:
254:
230:
206:
186:
151:
442:. In McNaught AD, Wilkinson A, Jenkins A (eds.).
289:
1463:
370:-rich regions. Phase separation also exists in
37:When mixed, oil and vinegar will phase-separate
437:
1106:
814:
96:. There are two boundary curves of note: the
529:
92:in which phase separation occurs are called
1113:
1099:
821:
807:
734:
665:
604:
543:
779:Khabibullaev PK, Saidov A (April 2013).
40:
32:
24:
828:
1464:
1120:
499:Matter and methods at low temperatures
496:
387:Fulde-Ferrell-Larkin-Ovchinnikov phase
1094:
802:
487:(Oxford University Press 1999) p. 175
468:
274:. The enthalpy of mixing is zero for
477:
117:lower critical solution temperature
113:upper critical solution temperature
13:
771:
159:can be decomposed into two parts:
14:
1493:
438:Nic M, Jirat J, Kosata B (1997).
130:
60:is the creation of two distinct
783:. Berlin Heidelberg: Springer.
714:
645:
584:
523:
490:
431:
363:{\displaystyle {\ce {{}^3He}}}
330:{\displaystyle {\ce {^{4}He}}}
290:Phase separation in cold gases
1:
623:10.1103/PhysRevLett.97.030401
562:10.1103/PhysRevLett.95.060401
424:
1401:Inorganic nonaqueous solvent
7:
753:10.1103/PhysRevA.104.053322
392:
10:
1498:
1386:Acid dissociation constant
135:Mixing is governed by the
18:
1369:
1301:
1231:
1128:
985:
959:
909:
901:Thermodynamic equilibrium
836:
358:
325:
98:binodal coexistence curve
84:; it is described by the
1482:Condensed matter physics
1054:Distribution coefficient
998:Hammett acidity function
977:Liquid–liquid extraction
886:Le Chatelier's principle
353:
347:
320:
314:
1351:Solubility table (data)
1218:Apparent molar property
684:10.1126/science.1122318
593:Physical Review Letters
532:Physical Review Letters
485:Properties of Materials
452:10.1351/goldbook.P04534
399:Biomolecular condensate
385:formation or an exotic
1316:Total dissolved solids
1311:Solubility equilibrium
1236:and related quantities
1015:Coordination complexes
951:Thermodynamic activity
497:Pobell, Frank (2007).
364:
331:
256:
232:
208:
188:
187:{\displaystyle G=H-TS}
153:
86:Cahn–Hilliard equation
82:spinodal decomposition
54:
38:
30:
1472:Equilibrium chemistry
1416:Partition coefficient
1396:Polar aprotic solvent
1027:Dissociation constant
972:Equilibrium unfolding
859:Equilibrium chemistry
365:
332:
257:
233:
209:
189:
154:
121:critical temperatures
44:
36:
28:
1331:Enthalpy of solution
1258:Volume concentration
1253:Number concentration
936:Predominance diagram
919:Equilibrium constant
341:
310:
246:
222:
198:
163:
143:
1243:Molar concentration
1213:Dilution (equation)
1010:Binding selectivity
986:Specific equilibria
896:Reversible reaction
854:Dynamic equilibrium
830:Chemical equilibria
745:2021PhRvA.104e3322K
676:2006Sci...311..492Z
615:2006PhRvL..97c0401S
554:2005PhRvL..95f0401C
66:homogeneous mixture
1283:Isotopic abundance
1248:Mass concentration
1122:Chemical solutions
1020:Macrocyclic effect
844:Chemical stability
440:"Phase separation"
360:
327:
268:enthalpy of mixing
252:
228:
204:
184:
149:
55:
39:
31:
1459:
1458:
1088:
1087:
1066:Common-ion effect
993:Acid dissociation
946:Reaction quotient
864:Equilibrium stage
790:978-3-662-09278-1
723:Physical Review A
660:(5760): 492–496.
508:978-3-540-46356-6
354:
352:
351:
350:
321:
319:
318:
317:
294:A mixture of two
272:entropy of mixing
255:{\displaystyle S}
231:{\displaystyle T}
207:{\displaystyle H}
152:{\displaystyle G}
137:Gibbs free energy
1489:
1356:Solubility chart
1183:Phase separation
1143:Aqueous solution
1115:
1108:
1101:
1092:
1091:
1005:Binding constant
891:Phase separation
823:
816:
809:
800:
799:
794:
765:
764:
738:
718:
712:
711:
669:
667:cond-mat/0511197
649:
643:
642:
608:
606:cond-mat/0606432
588:
582:
581:
547:
545:cond-mat/0503256
527:
521:
520:
494:
488:
481:
475:
472:
466:
465:
435:
369:
367:
366:
361:
359:
348:
346:
336:
334:
333:
328:
326:
315:
261:
259:
258:
253:
237:
235:
234:
229:
213:
211:
210:
205:
193:
191:
190:
185:
158:
156:
155:
150:
94:miscibility gaps
58:Phase separation
1497:
1496:
1492:
1491:
1490:
1488:
1487:
1486:
1462:
1461:
1460:
1455:
1365:
1326:Solvation shell
1297:
1235:
1227:
1223:Miscibility gap
1208:Serial dilution
1203:Supersaturation
1153:Buffer solution
1124:
1119:
1089:
1084:
1037:Self-ionization
981:
967:Buffer solution
955:
905:
832:
827:
797:
791:
774:
772:Further reading
769:
768:
719:
715:
650:
646:
589:
585:
528:
524:
509:
495:
491:
482:
478:
473:
469:
462:
436:
432:
427:
395:
345:
344:
342:
339:
338:
313:
311:
308:
307:
292:
247:
244:
243:
223:
220:
219:
199:
196:
195:
164:
161:
160:
144:
141:
140:
133:
119:(LCST) are two
115:(UCST) and the
88:. Regions of a
23:
17:
12:
11:
5:
1495:
1485:
1484:
1479:
1474:
1457:
1456:
1454:
1453:
1448:
1443:
1438:
1433:
1428:
1423:
1418:
1413:
1408:
1403:
1398:
1393:
1391:Protic solvent
1388:
1383:
1375:
1373:
1367:
1366:
1364:
1363:
1358:
1353:
1348:
1343:
1338:
1336:Lattice energy
1333:
1328:
1323:
1318:
1313:
1307:
1305:
1299:
1298:
1296:
1295:
1290:
1285:
1280:
1275:
1270:
1265:
1260:
1255:
1250:
1245:
1239:
1237:
1229:
1228:
1226:
1225:
1220:
1215:
1210:
1205:
1200:
1195:
1190:
1188:Eutectic point
1185:
1180:
1175:
1170:
1165:
1160:
1155:
1150:
1148:Solid solution
1145:
1140:
1138:Ideal solution
1134:
1132:
1126:
1125:
1118:
1117:
1110:
1103:
1095:
1086:
1085:
1083:
1082:
1081:
1080:
1070:
1069:
1068:
1058:
1057:
1056:
1046:
1045:
1044:
1034:
1029:
1024:
1023:
1022:
1012:
1007:
1002:
1001:
1000:
989:
987:
983:
982:
980:
979:
974:
969:
963:
961:
957:
956:
954:
953:
948:
943:
938:
933:
928:
927:
926:
915:
913:
907:
906:
904:
903:
898:
893:
888:
883:
882:
881:
876:
866:
861:
856:
851:
846:
840:
838:
834:
833:
826:
825:
818:
811:
803:
796:
795:
789:
775:
773:
770:
767:
766:
713:
644:
583:
522:
507:
489:
476:
467:
460:
429:
428:
426:
423:
422:
421:
416:
411:
406:
401:
394:
391:
383:vortex lattice
357:
324:
291:
288:
276:ideal mixtures
251:
227:
203:
183:
180:
177:
174:
171:
168:
148:
132:
131:Physical basis
129:
102:spinodal curve
64:from a single
15:
9:
6:
4:
3:
2:
1494:
1483:
1480:
1478:
1475:
1473:
1470:
1469:
1467:
1452:
1449:
1447:
1444:
1442:
1439:
1437:
1434:
1432:
1429:
1427:
1424:
1422:
1419:
1417:
1414:
1412:
1409:
1407:
1404:
1402:
1399:
1397:
1394:
1392:
1389:
1387:
1384:
1381:
1377:
1376:
1374:
1372:
1368:
1362:
1359:
1357:
1354:
1352:
1349:
1347:
1344:
1342:
1339:
1337:
1334:
1332:
1329:
1327:
1324:
1322:
1319:
1317:
1314:
1312:
1309:
1308:
1306:
1304:
1300:
1294:
1291:
1289:
1286:
1284:
1281:
1279:
1278:Mass fraction
1276:
1274:
1273:Mole fraction
1271:
1269:
1266:
1264:
1261:
1259:
1256:
1254:
1251:
1249:
1246:
1244:
1241:
1240:
1238:
1234:
1233:Concentration
1230:
1224:
1221:
1219:
1216:
1214:
1211:
1209:
1206:
1204:
1201:
1199:
1196:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1178:Phase diagram
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1159:
1158:Flory–Huggins
1156:
1154:
1151:
1149:
1146:
1144:
1141:
1139:
1136:
1135:
1133:
1131:
1127:
1123:
1116:
1111:
1109:
1104:
1102:
1097:
1096:
1093:
1079:
1076:
1075:
1074:
1071:
1067:
1064:
1063:
1062:
1059:
1055:
1052:
1051:
1050:
1047:
1043:
1040:
1039:
1038:
1035:
1033:
1030:
1028:
1025:
1021:
1018:
1017:
1016:
1013:
1011:
1008:
1006:
1003:
999:
996:
995:
994:
991:
990:
988:
984:
978:
975:
973:
970:
968:
965:
964:
962:
958:
952:
949:
947:
944:
942:
939:
937:
934:
932:
931:Phase diagram
929:
925:
924:determination
922:
921:
920:
917:
916:
914:
912:
908:
902:
899:
897:
894:
892:
889:
887:
884:
880:
877:
875:
872:
871:
870:
867:
865:
862:
860:
857:
855:
852:
850:
847:
845:
842:
841:
839:
835:
831:
824:
819:
817:
812:
810:
805:
804:
801:
792:
786:
782:
777:
776:
762:
758:
754:
750:
746:
742:
737:
732:
729:(5): 053322.
728:
724:
717:
709:
705:
701:
697:
693:
689:
685:
681:
677:
673:
668:
663:
659:
655:
648:
640:
636:
632:
628:
624:
620:
616:
612:
607:
602:
599:(3): 030401.
598:
594:
587:
579:
575:
571:
567:
563:
559:
555:
551:
546:
541:
538:(6): 060401.
537:
533:
526:
518:
514:
510:
504:
500:
493:
486:
483:M. A. White,
480:
471:
463:
461:0-9678550-9-8
457:
453:
449:
445:
441:
434:
430:
420:
417:
415:
412:
410:
409:Phase diagram
407:
405:
402:
400:
397:
396:
390:
388:
384:
380:
377:
373:
372:ultracold gas
355:
322:
305:
301:
297:
287:
285:
279:
277:
273:
269:
265:
249:
241:
225:
217:
201:
181:
178:
175:
172:
169:
166:
146:
138:
128:
126:
122:
118:
114:
109:
107:
103:
99:
95:
91:
90:phase diagram
87:
83:
78:
75:
71:
67:
63:
59:
52:
48:
47:phase diagram
43:
35:
27:
22:
1341:Raoult's law
1293:Ternary plot
1288:Mixing ratio
1182:
1073:Vapor–liquid
960:Applications
890:
780:
726:
722:
716:
657:
653:
647:
596:
592:
586:
535:
531:
525:
498:
492:
484:
479:
470:
443:
433:
293:
283:
280:
134:
110:
79:
57:
56:
1446:Lyonium ion
1361:Miscibility
1346:Henry's law
1078:Henry's law
869:Free energy
284:unfavorable
240:temperature
1466:Categories
1441:Amphiphile
1436:Lipophilic
1431:Hydrophile
1426:Hydrophobe
1303:Solubility
1198:Saturation
1168:Suspension
1061:Solubility
1032:Hydrolysis
941:Phase rule
736:2109.00427
425:References
414:Phase rule
337:-rich and
298:isotopes (
106:metastable
70:immiscible
19:See also:
1451:Lyate ion
1406:Solvation
1321:Solvation
1263:Normality
1049:Partition
879:Helmholtz
849:Chelation
761:237372963
692:0036-8075
517:122268227
379:Fermi gas
376:ultracold
176:−
1477:Solvents
1421:Polarity
1380:Category
1268:Molality
1130:Solution
1042:of water
837:Concepts
708:13801977
700:16373535
639:11323402
631:16907486
570:16090928
393:See also
304:helium-4
300:helium-3
270:and the
216:enthalpy
125:nicotine
100:and the
74:Colloids
51:isotopes
49:for two
1371:Solvent
1173:Colloid
1163:Mixture
741:Bibcode
672:Bibcode
654:Science
611:Bibcode
550:Bibcode
419:UNIQUAC
404:Colloid
264:entropy
194:, with
21:Colloid
911:Models
787:
759:
706:
698:
690:
637:
629:
578:448402
576:
568:
515:
505:
458:
296:helium
242:, and
62:phases
1193:Alloy
874:Gibbs
757:S2CID
731:arXiv
704:S2CID
662:arXiv
635:S2CID
601:arXiv
574:S2CID
540:arXiv
785:ISBN
696:PMID
688:ISSN
627:PMID
566:PMID
513:OCLC
503:ISBN
456:ISBN
302:and
262:the
238:the
214:the
111:The
749:doi
727:104
680:doi
658:311
619:doi
558:doi
448:doi
1468::
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