28:
966:
co-workers. The Mie potential has also been used for coarse-grain modeling. Electronic tools are available for building Mie force field models for both united atom force fields and transferable force fields. The Mie potential has also been used for modeling small spherical molecules (i.e. directly the Mie substance - see above). The Table below gives some examples. There, the molecular models have only the parameters of the Mie potential itself.
705:
773:, where a theoretical substance exists that is defined by particles interacting by the Lennard-Jones potential, a substance class of Mie substances exists that are defined as single site spherical particles interacting by a given Mie potential. Since an infinite number of Mie potentials exist (using different
965:
Due to its flexibility, the Mie potential is a popular choice for modelling real fluids in force fields. It is used as an interaction potential many molecular models today. Several (reliable) united atom transferable force fields are based on the Mie potential, such as that developed by Potoff and
823:
Also, many theoretical (analytical) models have been developed for describing thermophysical properties of Mie substances and chain molecules formed from Mie particles, such as several thermodynamic equations of state and models for transport properties.
793:, have successfully been modelled as homogeneous chains of Mie particles. As such, the Mie potential is useful for modelling far more complex systems than those whose behaviour is accurately captured by "free" Mie particles.
375:
97:
describing the interactions between particles on the atomic level. It is mostly used for describing intermolecular interactions, but at times also for modeling intramolecular interaction, i.e. bonds.
292:
789:, where larger molecules, or even a collection of molecules, are simplified in their structure and described by a single Mie particle. However, more complex molecules, such as long-chained
796:
Thermophysical properties of both the Mie fluid, and chain molecules built from Mie particles have been the subject of numerous papers in recent years. Investigated properties include
932:
1170:
1015:
450:
1395:
1346:
1219:
1297:
1258:
1121:
1050:
1754:
994:
955:
470:
516:
138:
851:
759:
496:
79:
1093:
1072:
733:
404:
158:
53:
694:
625:
430:
649:
596:
576:
556:
536:
2335:"Revised Enskog theory for Mie fluids: Prediction of diffusion coefficients, thermal diffusion coefficients, viscosities, and thermal conductivities"
301:
2745:
Lafitte, Thomas; Apostolakou, Anastasia; Avendaño, Carlos; Galindo, Amparo; Adjiman, Claire S.; Müller, Erich A.; Jackson, George (2013-10-16).
1560:
Lafitte, Thomas; Apostolakou, Anastasia; Avendaño, Carlos; Galindo, Amparo; Adjiman, Claire S.; Müller, Erich A.; Jackson, George (2013-10-21).
3042:
1730:
1772:
1771:
Lafitte, Thomas; Apostolakou, Anastasia; Avendaño, Carlos; Galindo, Amparo; Adjiman, Claire S.; Müller, Erich A.; Jackson, George (2013).
2817:"Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium"
777:
parameters), equally many Mie substances exist, as opposed to
Lennard-Jonesium, which is uniquely defined. For practical applications in
2945:"Simultaneous Description of Equilibrium, Interfacial, and Transport Properties of Fluids Using a Mie Chain Coarse-Grained Force Field"
2880:
Mick, Jason R.; Soroush
Barhaghi, Mohammad; Jackman, Brock; Rushaidat, Kamel; Schwiebert, Loren; Potoff, Jeffrey J. (2015-09-16).
3037:
1899:
Galliero, Guillaume; Piñeiro, Manuel M.; Mendiboure, Bruno; Miqueu, Christelle; Lafitte, Thomas; Bessieres, David (2009-03-14).
2649:
Schmitt, Sebastian; Kanagalingam, Gajanan; Fleckenstein, Florian; Froescher, Daniel; Hasse, Hans; Stephan, Simon (2023-11-27).
762:
3032:
2984:"Accurate non-asymptotic thermodynamic properties of near-critical N2 and O2 computed from molecular dynamics simulations"
805:
715:
of a fluid consisting of particles interacting through a Mie potential with different values for the repulsive exponent (
165:
631:, whereas no justification for a certain value for the repulsive exponent is known. The repulsive steepness parameter
659:. Therefore, the Mie potential is a more flexible intermolecular potential than the simpler Lennard-Jones potential.
104:; yet the history of intermolecular potentials is more complicated. The Mie potential is the generalized case of the
2554:"Comparison of Force Fields for the Prediction of Thermophysical Properties of Long Linear and Branched Alkanes"
2466:
Mick, Jason R.; Soroush
Barhaghi, Mohammad; Jackman, Brock; Schwiebert, Loren; Potoff, Jeffrey J. (2017-06-08).
2217:"Development of thermodynamically consistent machine-learning equations of state: Application to the Mie fluid"
2882:"Optimized Mie potentials for phase equilibria: Application to noble gases and their mixtures with n-alkanes"
2611:
3027:
812:
properties. Based on such studies the relation between the shape of the interaction potential (described by
786:
770:
709:
663:
628:
105:
82:
32:
2612:"Force-Field Parameters from the SAFT-γ Equation of State for Use in Coarse-Grained Molecular Simulations"
2983:
2893:
2828:
2758:
2704:
Dufal, Simon; Lafitte, Thomas; Galindo, Amparo; Jackson, George; Haslam, Andrew J. (September 2015).
2412:
2401:"A corresponding-states framework for the description of the Mie family of intermolecular potentials"
2346:
2228:
2173:
1977:
1955:
1912:
1849:
1784:
1573:
1443:
862:
809:
778:
1000:
435:
2925:
2862:
2686:
2589:
2448:
2378:
2315:
2142:
2001:
1967:
1881:
1748:
1701:
1646:
1626:
1539:
1143:
797:
667:
1901:"Interfacial properties of the Mie n−6 fluid: Molecular simulations and gradient theory results"
1368:
1319:
1192:
1020:
2982:
Nichele, Jakler; Abreu, Charlles R. A.; Alves, Leonardo S. de B.; Borges, Itamar (2018-05-01).
2815:
Aasen, Ailo; Hammer, Morten; Ervik, Åsmund; Müller, Erich A.; Wilhelmsen, Øivind (2019-08-13).
2507:"Mie Potentials for Phase Equilibria Calculations: Application to Alkanes and Perfluoroalkanes"
2068:"Mie Potentials for Phase Equilibria Calculations: Application to Alkanes and Perfluoroalkanes"
1280:
1241:
1104:
518:
is generally indicative of the size of the particles involved in the collision. The parameters
3003:
2964:
2917:
2909:
2854:
2794:
2786:
2727:
2706:"Developing intermolecular-potential models for use with the SAFT - VR M ie equation of state"
2678:
2670:
2631:
2581:
2573:
2534:
2526:
2487:
2440:
2370:
2362:
2307:
2264:
2256:
2197:
2189:
2134:
2095:
2087:
2048:
2040:
1993:
1936:
1928:
1873:
1865:
1812:
1736:
1726:
1693:
1685:
1607:
1599:
1531:
1492:
696:, whereas the repulsive exponent is used as an adjustable parameter during the model fitting.
2627:
979:
940:
651:
has a significant influence on the modeling of thermodynamic derivative properties, e.g. the
455:
2995:
2956:
2901:
2844:
2836:
2776:
2766:
2747:"Accurate statistical associating fluid theory for chain molecules formed from Mie segments"
2717:
2662:
2623:
2565:
2518:
2479:
2430:
2420:
2354:
2299:
2246:
2236:
2181:
2126:
2079:
2032:
1985:
1956:"Simultaneous description of bulk and interfacial properties of fluids by the Mie potential"
1920:
1857:
1802:
1792:
1773:"Accurate statistical associating fluid theory for chain molecules formed from Mie segments"
1677:
1638:
1589:
1581:
1562:"Accurate statistical associating fluid theory for chain molecules formed from Mie segments"
1523:
1482:
1451:
1512:"A child of prediction. On the History, Ontology, and Computation of the Lennard-Jonesium"
801:
652:
114:
830:
738:
501:
475:
58:
2897:
2832:
2762:
2416:
2350:
2232:
2177:
1981:
1916:
1853:
1788:
1577:
1447:
2282:
Pohl, Sven; Fingerhut, Robin; Thol, Monika; Vrabec, Jadran; Span, Roland (2023-02-27).
1078:
1057:
718:
656:
143:
94:
38:
383:
3021:
2866:
2690:
2593:
2552:
Schmitt, Sebastian; Fleckenstein, Florian; Hasse, Hans; Stephan, Simon (2023-03-02).
2382:
2319:
2146:
1705:
1650:
1543:
854:
712:
673:
604:
409:
2944:
2929:
2650:
2553:
2467:
2452:
2162:"Transport properties of Mie(14,7) fluids: Molecular dynamics simulation and theory"
2020:
2005:
1885:
1666:"Thermophysical Properties of the Lennard-Jones Fluid: Database and Data Assessment"
1665:
634:
581:
561:
541:
521:
17:
2425:
2400:
2160:
Eskandari
Nasrabad, Afshin; Oghaz, Nader Mansoori; Haghighi, Behzad (2008-07-10).
2114:
1989:
2999:
2130:
1900:
1837:
1561:
1511:
2468:"Optimized Mie Potentials for Phase Equilibria: Application to Branched Alkanes"
1642:
1527:
1487:
1470:
1431:
1838:"Second virial coefficient properties of the n - m Lennard-Jones/Mie potential"
704:
370:{\displaystyle C={\frac {n}{n-m}}\left({\frac {n}{m}}\right)^{\frac {m}{n-m}}}
101:
3007:
2968:
2960:
2913:
2858:
2790:
2731:
2674:
2666:
2635:
2577:
2569:
2530:
2506:
2491:
2483:
2444:
2366:
2311:
2260:
2193:
2138:
2091:
2067:
2044:
2036:
2021:"Long Range Corrections for Inhomogeneous Simulations of Mie n – m Potential"
1997:
1932:
1869:
1740:
1689:
1681:
1603:
1535:
1496:
1455:
781:, the Mie substances are mostly relevant for modelling small molecules, e.g.
2251:
1954:
Werth, Stephan; Stöbener, Katrin; Horsch, Martin; Hasse, Hans (2017-06-18).
782:
27:
2943:
Hoang, Hai; Delage-Santacreu, Stéphanie; Galliero, Guillaume (2017-08-16).
2921:
2849:
2798:
2781:
2682:
2585:
2538:
2435:
2374:
2268:
2201:
2099:
2052:
1940:
1877:
1816:
1807:
1697:
1611:
1594:
1627:"Review and comparison of equations of state for the Lennard-Jones fluid"
1664:
Stephan, Simon; Thol, Monika; Vrabec, Jadran; Hasse, Hans (2019-10-28).
2399:
Ramrattan, N.S.; Avendaño, C.; Müller, E.A.; Galindo, A. (2015-05-19).
2283:
2905:
2840:
2771:
2746:
2722:
2705:
2522:
2358:
2303:
2241:
2216:
2185:
2083:
2019:
Janeček, Jiří; Said-Aizpuru, Olivier; Paricaud, Patrice (2017-09-12).
1924:
1861:
1797:
1585:
1720:
790:
2881:
2816:
2334:
2161:
1972:
498:, which is sometimes called the "collision radius." The parameter
380:
The
Lennard-Jones potential corresponds to the special case where
1510:
Lenhard, Johannes; Stephan, Simon; Hasse, Hans (February 2024).
2651:"Extension of the MolMod Database to Transferable Force Fields"
1625:
Stephan, Simon; Staubach, Jens; Hasse, Hans (November 2020).
2505:
Potoff, Jeffrey J.; Bernard-Brunel, Damien A. (2009-11-05).
2066:
Potoff, Jeffrey J.; Bernard-Brunel, Damien A. (2009-11-05).
1471:"On the history of key empirical intermolecular potentials"
827:
It has been observed that many combinations of different (
1383:
1334:
1207:
1158:
820:) and the thermophysical properties has been elucidated.
857:, and that this degeneracy is captured by the parameter
160:, the distance between two particles, and is written as
108:, which is perhaps the most widely used pair potential.
2616:
Annual Review of
Chemical and Biomolecular Engineering
676:
637:
607:
584:
564:
544:
524:
504:
412:
386:
100:
The Mie potential is named after the German physicist
2333:
Jervell, Vegard G.; Wilhelmsen, Øivind (2023-06-08).
1371:
1322:
1283:
1244:
1195:
1146:
1107:
1081:
1060:
1023:
1003:
982:
943:
865:
833:
741:
721:
670:. Typically, the attractive exponent is chosen to be
478:
458:
438:
304:
168:
146:
117:
61:
41:
937:
where fluids with different exponents, but the same
2288:
r,6) fluid with a repulsive exponent from 11 to 13"
2113:Stephan, Simon; Urschel, Maximilian (August 2023).
287:{\displaystyle V(r)=C\,\varepsilon \left,~~~~~~(1)}
55:), all depicted curves use the attractive exponent
2215:Chaparro, Gustavo; Müller, Erich A. (2023-05-10).
1469:Fischer, Johann; Wendland, Martin (October 2023).
1389:
1340:
1291:
1252:
1213:
1164:
1115:
1087:
1066:
1044:
1009:
988:
949:
926:
845:
753:
727:
688:
643:
619:
590:
570:
550:
530:
510:
490:
464:
444:
424:
398:
369:
286:
152:
132:
73:
47:
35:, for different values of the repulsive exponent (
2605:
2603:
957:-parameter will exhibit the same phase behavior.
2610:Müller, Erich A.; Jackson, George (2014-06-07).
1432:"Zur kinetischen Theorie der einatomigen Körper"
2949:Industrial & Engineering Chemistry Research
700:Thermophysical properties of the Mie substance
578:describes the character of the repulsion and
8:
2655:Journal of Chemical Information and Modeling
1753:: CS1 maint: multiple names: authors list (
1670:Journal of Chemical Information and Modeling
1516:Studies in History and Philosophy of Science
31:The potential curve of the Mie potential in
598:describes the character of the attraction.
2472:Journal of Chemical & Engineering Data
2025:Journal of Chemical Theory and Computation
2848:
2780:
2770:
2721:
2434:
2424:
2250:
2240:
1971:
1806:
1796:
1593:
1486:
1382:
1377:
1372:
1370:
1333:
1328:
1323:
1321:
1284:
1282:
1245:
1243:
1206:
1201:
1196:
1194:
1157:
1152:
1147:
1145:
1108:
1106:
1080:
1059:
1033:
1028:
1022:
1002:
981:
942:
901:
880:
864:
832:
740:
720:
675:
636:
606:
583:
563:
558:characterize the shape of the potential:
543:
523:
503:
477:
457:
437:
411:
385:
348:
334:
311:
303:
243:
229:
215:
201:
187:
167:
145:
116:
60:
40:
2628:10.1146/annurev-chembioeng-061312-103314
2115:"Characteristic curves of the Mie fluid"
968:
961:Mie potential used in molecular modeling
703:
662:The Mie potential is used today in many
26:
1422:
1746:
2810:
2808:
2394:
2392:
81:. The black curve corresponds to the
7:
1766:
1764:
1555:
1553:
735:), all with the attractive exponent
2988:The Journal of Supercritical Fluids
2558:The Journal of Physical Chemistry B
2511:The Journal of Physical Chemistry B
2072:The Journal of Physical Chemistry B
1722:The theory of intermolecular forces
25:
2284:"Equation of state for the Mie (
1836:Sadus, Richard J. (2018-08-21).
472:indicates the distance at which
2886:The Journal of Chemical Physics
2821:The Journal of Chemical Physics
2751:The Journal of Chemical Physics
2339:The Journal of Chemical Physics
2292:The Journal of Chemical Physics
2221:The Journal of Chemical Physics
2166:The Journal of Chemical Physics
1905:The Journal of Chemical Physics
1842:The Journal of Chemical Physics
1777:The Journal of Chemical Physics
1566:The Journal of Chemical Physics
627:is physically justified by the
927:{\displaystyle \alpha =C\left}
452:is the dispersion energy, and
281:
275:
178:
172:
127:
121:
1:
3043:Quantum mechanical potentials
2426:10.1080/00268976.2015.1025112
1990:10.1080/00268976.2016.1206218
3000:10.1016/j.supflu.2018.01.011
2131:10.1016/j.molliq.2023.122088
2119:Journal of Molecular Liquids
1165:{\displaystyle {\ce {CH_4}}}
1010:{\displaystyle \varepsilon }
445:{\displaystyle \varepsilon }
106:Lennard-Jones (LJ) potential
1643:10.1016/j.fluid.2020.112772
1528:10.1016/j.shpsa.2023.11.007
1488:10.1016/j.fluid.2023.113876
1390:{\displaystyle {\ce {O_2}}}
1341:{\displaystyle {\ce {N_2}}}
1214:{\displaystyle {\ce {H_2}}}
3059:
1292:{\displaystyle {\ce {Kr}}}
1253:{\displaystyle {\ce {He}}}
1116:{\displaystyle {\ce {Ar}}}
1045:{\displaystyle k_{B}^{-1}}
761:. The cross indicates the
432:in Eq. (1). In Eq. (1),
2961:10.1021/acs.iecr.7b01397
2667:10.1021/acs.jcim.3c01484
2570:10.1021/acs.jpcb.2c07997
2484:10.1021/acs.jced.6b01036
2037:10.1021/acs.jctc.7b00212
1682:10.1021/acs.jcim.9b00620
1456:10.1002/andp.19033160802
806:vapor-liquid equilibrium
601:The attractive exponent
3038:Computational chemistry
989:{\displaystyle \sigma }
950:{\displaystyle \alpha }
629:London dispersion force
465:{\displaystyle \sigma }
83:Lennard-Jones potential
1725:. Oxford Univ. Press.
1719:J., Stone, A. (2013).
1631:Fluid Phase Equilibria
1475:Fluid Phase Equilibria
1391:
1342:
1293:
1254:
1215:
1166:
1117:
1089:
1068:
1046:
1011:
990:
951:
928:
847:
787:coarse grain modelling
766:
755:
729:
690:
645:
621:
592:
572:
552:
532:
512:
492:
466:
446:
426:
400:
371:
288:
154:
134:
86:
75:
49:
3033:Intermolecular forces
1392:
1343:
1294:
1255:
1216:
1167:
1118:
1090:
1069:
1047:
1012:
991:
952:
929:
848:
756:
730:
707:
691:
646:
622:
593:
573:
553:
533:
513:
493:
467:
447:
427:
401:
372:
289:
155:
135:
76:
50:
30:
1430:Mie, Gustav (1903).
1369:
1320:
1281:
1242:
1193:
1144:
1105:
1079:
1058:
1021:
1001:
980:
941:
863:
853:) can yield similar
831:
739:
719:
674:
635:
605:
582:
562:
542:
522:
511:{\textstyle \sigma }
502:
476:
456:
436:
410:
384:
302:
166:
144:
133:{\displaystyle V(r)}
115:
59:
39:
2898:2015JChPh.143k4504M
2833:2019JChPh.151f4508A
2763:2013JChPh.139o4504L
2517:(44): 14725–14731.
2417:2015MolPh.113..932R
2351:2023JChPh.158v4101J
2233:2023JChPh.158r4505C
2178:2008JChPh.129b4507E
2078:(44): 14725–14731.
1982:2017MolPh.115.1017W
1966:(9–12): 1017–1030.
1917:2009JChPh.130j4704G
1854:2018JChPh.149g4504S
1789:2013JChPh.139o4504L
1578:2013JChPh.139o4504L
1448:1903AnP...316..657M
1385:
1336:
1209:
1160:
1041:
970:
846:{\displaystyle n,m}
798:virial coefficients
779:molecular modelling
754:{\displaystyle m=6}
491:{\displaystyle V=0}
74:{\displaystyle m=6}
18:Draft:Mie potential
1436:Annalen der Physik
1387:
1373:
1338:
1324:
1289:
1250:
1211:
1197:
1162:
1148:
1113:
1085:
1064:
1042:
1024:
1007:
986:
969:
947:
924:
843:
767:
751:
725:
686:
668:molecular modeling
641:
617:
588:
568:
548:
528:
508:
488:
462:
442:
422:
396:
367:
284:
150:
130:
111:The Mie potential
93:is an interaction
87:
71:
45:
2955:(32): 9213–9226.
2906:10.1063/1.4930138
2841:10.1063/1.5111364
2772:10.1063/1.4819786
2723:10.1002/aic.14808
2661:(22): 7148–7158.
2523:10.1021/jp9072137
2411:(9–10): 932–947.
2405:Molecular Physics
2359:10.1063/5.0149865
2304:10.1063/5.0133412
2242:10.1063/5.0146634
2186:10.1063/1.2953331
2084:10.1021/jp9072137
1960:Molecular Physics
1925:10.1063/1.3085716
1862:10.1063/1.5041320
1798:10.1063/1.4819786
1732:978-0-19-175141-7
1676:(10): 4248–4265.
1586:10.1063/1.4819786
1414:
1413:
1376:
1327:
1287:
1248:
1200:
1151:
1111:
1088:{\displaystyle m}
1067:{\displaystyle n}
917:
896:
728:{\displaystyle n}
399:{\textstyle n=12}
364:
342:
327:
274:
271:
268:
265:
262:
259:
237:
209:
153:{\displaystyle r}
140:is a function of
48:{\displaystyle n}
16:(Redirected from
3050:
3012:
3011:
2979:
2973:
2972:
2940:
2934:
2933:
2877:
2871:
2870:
2852:
2812:
2803:
2802:
2784:
2774:
2742:
2736:
2735:
2725:
2716:(9): 2891–2912.
2701:
2695:
2694:
2646:
2640:
2639:
2607:
2598:
2597:
2564:(8): 1789–1802.
2549:
2543:
2542:
2502:
2496:
2495:
2478:(6): 1806–1818.
2463:
2457:
2456:
2438:
2428:
2396:
2387:
2386:
2330:
2324:
2323:
2279:
2273:
2272:
2254:
2244:
2212:
2206:
2205:
2157:
2151:
2150:
2110:
2104:
2103:
2063:
2057:
2056:
2031:(9): 4482–4491.
2016:
2010:
2009:
1975:
1951:
1945:
1944:
1896:
1890:
1889:
1833:
1827:
1826:
1824:
1823:
1810:
1800:
1768:
1759:
1758:
1752:
1744:
1716:
1710:
1709:
1661:
1655:
1654:
1622:
1616:
1615:
1597:
1557:
1548:
1547:
1507:
1501:
1500:
1490:
1466:
1460:
1459:
1427:
1396:
1394:
1393:
1388:
1386:
1384:
1381:
1374:
1347:
1345:
1344:
1339:
1337:
1335:
1332:
1325:
1298:
1296:
1295:
1290:
1288:
1285:
1259:
1257:
1256:
1251:
1249:
1246:
1220:
1218:
1217:
1212:
1210:
1208:
1205:
1198:
1171:
1169:
1168:
1163:
1161:
1159:
1156:
1149:
1122:
1120:
1119:
1114:
1112:
1109:
1094:
1092:
1091:
1086:
1073:
1071:
1070:
1065:
1051:
1049:
1048:
1043:
1040:
1032:
1016:
1014:
1013:
1008:
995:
993:
992:
987:
971:
956:
954:
953:
948:
933:
931:
930:
925:
923:
919:
918:
916:
902:
897:
895:
881:
852:
850:
849:
844:
771:Lennard-Jonesium
760:
758:
757:
752:
734:
732:
731:
726:
695:
693:
692:
689:{\textstyle m=6}
687:
650:
648:
647:
642:
626:
624:
623:
620:{\textstyle m=6}
618:
597:
595:
594:
589:
577:
575:
574:
569:
557:
555:
554:
549:
537:
535:
534:
529:
517:
515:
514:
509:
497:
495:
494:
489:
471:
469:
468:
463:
451:
449:
448:
443:
431:
429:
428:
425:{\textstyle m=6}
423:
405:
403:
402:
397:
376:
374:
373:
368:
366:
365:
363:
349:
347:
343:
335:
328:
326:
312:
293:
291:
290:
285:
272:
269:
266:
263:
260:
257:
253:
249:
248:
247:
242:
238:
230:
220:
219:
214:
210:
202:
159:
157:
156:
151:
139:
137:
136:
131:
80:
78:
77:
72:
54:
52:
51:
46:
21:
3058:
3057:
3053:
3052:
3051:
3049:
3048:
3047:
3018:
3017:
3016:
3015:
2981:
2980:
2976:
2942:
2941:
2937:
2879:
2878:
2874:
2814:
2813:
2806:
2744:
2743:
2739:
2703:
2702:
2698:
2648:
2647:
2643:
2609:
2608:
2601:
2551:
2550:
2546:
2504:
2503:
2499:
2465:
2464:
2460:
2398:
2397:
2390:
2332:
2331:
2327:
2281:
2280:
2276:
2214:
2213:
2209:
2159:
2158:
2154:
2112:
2111:
2107:
2065:
2064:
2060:
2018:
2017:
2013:
1953:
1952:
1948:
1898:
1897:
1893:
1835:
1834:
1830:
1821:
1819:
1770:
1769:
1762:
1745:
1733:
1718:
1717:
1713:
1663:
1662:
1658:
1624:
1623:
1619:
1559:
1558:
1551:
1509:
1508:
1504:
1468:
1467:
1463:
1429:
1428:
1424:
1419:
1367:
1366:
1318:
1317:
1279:
1278:
1240:
1239:
1191:
1190:
1142:
1141:
1103:
1102:
1077:
1076:
1056:
1055:
1019:
1018:
999:
998:
978:
977:
963:
939:
938:
906:
885:
879:
875:
861:
860:
855:phase behaviour
829:
828:
737:
736:
717:
716:
702:
672:
671:
653:compressibility
633:
632:
603:
602:
580:
579:
560:
559:
540:
539:
520:
519:
500:
499:
474:
473:
454:
453:
434:
433:
408:
407:
382:
381:
353:
330:
329:
316:
300:
299:
225:
224:
197:
196:
195:
191:
164:
163:
142:
141:
113:
112:
57:
56:
37:
36:
23:
22:
15:
12:
11:
5:
3056:
3054:
3046:
3045:
3040:
3035:
3030:
3028:Thermodynamics
3020:
3019:
3014:
3013:
2974:
2935:
2872:
2804:
2737:
2696:
2641:
2622:(1): 405–427.
2599:
2544:
2497:
2458:
2388:
2325:
2274:
2252:10044/1/104154
2207:
2152:
2105:
2058:
2011:
1946:
1911:(10): 104704.
1891:
1828:
1760:
1731:
1711:
1656:
1617:
1572:(15): 154504.
1549:
1502:
1461:
1442:(8): 657–697.
1421:
1420:
1418:
1415:
1412:
1411:
1409:
1406:
1403:
1400:
1397:
1380:
1363:
1362:
1360:
1357:
1354:
1351:
1348:
1331:
1314:
1313:
1311:
1308:
1305:
1302:
1299:
1275:
1274:
1272:
1269:
1266:
1263:
1260:
1236:
1235:
1233:
1230:
1227:
1224:
1221:
1204:
1187:
1186:
1184:
1181:
1178:
1175:
1172:
1155:
1138:
1137:
1135:
1132:
1129:
1126:
1123:
1099:
1098:
1095:
1084:
1074:
1063:
1053:
1039:
1036:
1031:
1027:
1006:
996:
985:
975:
962:
959:
946:
922:
915:
912:
909:
905:
900:
894:
891:
888:
884:
878:
874:
871:
868:
842:
839:
836:
763:critical point
750:
747:
744:
724:
701:
698:
685:
682:
679:
657:speed of sound
644:{\textstyle n}
640:
616:
613:
610:
591:{\textstyle m}
587:
571:{\textstyle n}
567:
551:{\textstyle m}
547:
531:{\textstyle n}
527:
507:
487:
484:
481:
461:
441:
421:
418:
415:
395:
392:
389:
362:
359:
356:
352:
346:
341:
338:
333:
325:
322:
319:
315:
310:
307:
283:
280:
277:
256:
252:
246:
241:
236:
233:
228:
223:
218:
213:
208:
205:
200:
194:
190:
186:
183:
180:
177:
174:
171:
149:
129:
126:
123:
120:
70:
67:
64:
44:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3055:
3044:
3041:
3039:
3036:
3034:
3031:
3029:
3026:
3025:
3023:
3009:
3005:
3001:
2997:
2993:
2989:
2985:
2978:
2975:
2970:
2966:
2962:
2958:
2954:
2950:
2946:
2939:
2936:
2931:
2927:
2923:
2919:
2915:
2911:
2907:
2903:
2899:
2895:
2891:
2887:
2883:
2876:
2873:
2868:
2864:
2860:
2856:
2851:
2850:10044/1/72226
2846:
2842:
2838:
2834:
2830:
2826:
2822:
2818:
2811:
2809:
2805:
2800:
2796:
2792:
2788:
2783:
2782:10044/1/12859
2778:
2773:
2768:
2764:
2760:
2756:
2752:
2748:
2741:
2738:
2733:
2729:
2724:
2719:
2715:
2711:
2710:AIChE Journal
2707:
2700:
2697:
2692:
2688:
2684:
2680:
2676:
2672:
2668:
2664:
2660:
2656:
2652:
2645:
2642:
2637:
2633:
2629:
2625:
2621:
2617:
2613:
2606:
2604:
2600:
2595:
2591:
2587:
2583:
2579:
2575:
2571:
2567:
2563:
2559:
2555:
2548:
2545:
2540:
2536:
2532:
2528:
2524:
2520:
2516:
2512:
2508:
2501:
2498:
2493:
2489:
2485:
2481:
2477:
2473:
2469:
2462:
2459:
2454:
2450:
2446:
2442:
2437:
2436:10044/1/21432
2432:
2427:
2422:
2418:
2414:
2410:
2406:
2402:
2395:
2393:
2389:
2384:
2380:
2376:
2372:
2368:
2364:
2360:
2356:
2352:
2348:
2344:
2340:
2336:
2329:
2326:
2321:
2317:
2313:
2309:
2305:
2301:
2297:
2293:
2289:
2287:
2278:
2275:
2270:
2266:
2262:
2258:
2253:
2248:
2243:
2238:
2234:
2230:
2226:
2222:
2218:
2211:
2208:
2203:
2199:
2195:
2191:
2187:
2183:
2179:
2175:
2172:(2): 024507.
2171:
2167:
2163:
2156:
2153:
2148:
2144:
2140:
2136:
2132:
2128:
2124:
2120:
2116:
2109:
2106:
2101:
2097:
2093:
2089:
2085:
2081:
2077:
2073:
2069:
2062:
2059:
2054:
2050:
2046:
2042:
2038:
2034:
2030:
2026:
2022:
2015:
2012:
2007:
2003:
1999:
1995:
1991:
1987:
1983:
1979:
1974:
1969:
1965:
1961:
1957:
1950:
1947:
1942:
1938:
1934:
1930:
1926:
1922:
1918:
1914:
1910:
1906:
1902:
1895:
1892:
1887:
1883:
1879:
1875:
1871:
1867:
1863:
1859:
1855:
1851:
1848:(7): 074504.
1847:
1843:
1839:
1832:
1829:
1818:
1814:
1809:
1808:10044/1/12859
1804:
1799:
1794:
1790:
1786:
1782:
1778:
1774:
1767:
1765:
1761:
1756:
1750:
1742:
1738:
1734:
1728:
1724:
1723:
1715:
1712:
1707:
1703:
1699:
1695:
1691:
1687:
1683:
1679:
1675:
1671:
1667:
1660:
1657:
1652:
1648:
1644:
1640:
1636:
1632:
1628:
1621:
1618:
1613:
1609:
1605:
1601:
1596:
1595:10044/1/12859
1591:
1587:
1583:
1579:
1575:
1571:
1567:
1563:
1556:
1554:
1550:
1545:
1541:
1537:
1533:
1529:
1525:
1521:
1517:
1513:
1506:
1503:
1498:
1494:
1489:
1484:
1480:
1476:
1472:
1465:
1462:
1457:
1453:
1449:
1445:
1441:
1438:(in German).
1437:
1433:
1426:
1423:
1416:
1410:
1407:
1404:
1401:
1398:
1378:
1365:
1364:
1361:
1358:
1355:
1352:
1349:
1329:
1316:
1315:
1312:
1309:
1306:
1303:
1300:
1277:
1276:
1273:
1270:
1267:
1264:
1261:
1238:
1237:
1234:
1231:
1228:
1225:
1222:
1202:
1189:
1188:
1185:
1182:
1179:
1176:
1173:
1153:
1140:
1139:
1136:
1133:
1130:
1127:
1124:
1101:
1100:
1096:
1082:
1075:
1061:
1054:
1037:
1034:
1029:
1025:
1004:
997:
983:
976:
973:
972:
967:
960:
958:
944:
935:
920:
913:
910:
907:
903:
898:
892:
889:
886:
882:
876:
872:
869:
866:
858:
856:
840:
837:
834:
825:
821:
819:
815:
811:
807:
803:
799:
794:
792:
788:
784:
780:
776:
772:
764:
748:
745:
742:
722:
714:
713:phase diagram
711:
706:
699:
697:
683:
680:
677:
669:
665:
660:
658:
654:
638:
630:
614:
611:
608:
599:
585:
565:
545:
525:
505:
485:
482:
479:
459:
439:
419:
416:
413:
393:
390:
387:
378:
360:
357:
354:
350:
344:
339:
336:
331:
323:
320:
317:
313:
308:
305:
297:
294:
278:
254:
250:
244:
239:
234:
231:
226:
221:
216:
211:
206:
203:
198:
192:
188:
184:
181:
175:
169:
161:
147:
124:
118:
109:
107:
103:
98:
96:
92:
91:Mie potential
84:
68:
65:
62:
42:
34:
33:reduced units
29:
19:
2991:
2987:
2977:
2952:
2948:
2938:
2889:
2885:
2875:
2824:
2820:
2754:
2750:
2740:
2713:
2709:
2699:
2658:
2654:
2644:
2619:
2615:
2561:
2557:
2547:
2514:
2510:
2500:
2475:
2471:
2461:
2408:
2404:
2342:
2338:
2328:
2295:
2291:
2285:
2277:
2224:
2220:
2210:
2169:
2165:
2155:
2122:
2118:
2108:
2075:
2071:
2061:
2028:
2024:
2014:
1963:
1959:
1949:
1908:
1904:
1894:
1845:
1841:
1831:
1820:. Retrieved
1780:
1776:
1721:
1714:
1673:
1669:
1659:
1634:
1630:
1620:
1569:
1565:
1519:
1515:
1505:
1478:
1474:
1464:
1439:
1435:
1425:
964:
936:
859:
826:
822:
817:
813:
795:
774:
768:
664:force fields
661:
600:
379:
298:
295:
162:
110:
99:
90:
88:
2994:: 225–233.
1522:: 105–113.
802:interfacial
783:noble gases
769:As for the
3022:Categories
2125:: 122088.
1973:1611.07754
1822:2023-09-11
1637:: 112772.
1481:: 113876.
1417:References
785:, and for
102:Gustav Mie
3008:0896-8446
2969:0888-5885
2914:0021-9606
2867:202083098
2859:0021-9606
2791:0021-9606
2732:0001-1541
2691:265103133
2675:1549-9596
2636:1947-5438
2594:257068027
2578:1520-6106
2531:1520-6106
2492:0021-9568
2445:0026-8976
2383:259119498
2367:0021-9606
2320:257249977
2312:0021-9606
2261:0021-9606
2194:0021-9606
2147:258795513
2139:0167-7322
2092:1520-6106
2045:1549-9618
1998:0026-8976
1933:0021-9606
1870:0021-9606
1749:cite book
1741:915959704
1706:204545481
1690:1549-9596
1651:224844789
1604:0021-9606
1544:266440296
1536:0039-3681
1497:0378-3812
1035:−
1005:ε
984:σ
945:α
911:−
899:−
890:−
867:α
810:transport
506:σ
460:σ
440:ε
358:−
321:−
232:σ
222:−
204:σ
189:ε
95:potential
2930:43211598
2922:26395716
2799:24160524
2683:37947503
2586:36802607
2539:19824622
2453:27773511
2375:37290070
2269:37161943
2202:18624538
2100:19824622
2053:28742959
2006:49331008
1941:19292546
1886:52068374
1878:30134705
1817:24160524
1698:31609113
1612:24160524
655:and the
2894:Bibcode
2829:Bibcode
2759:Bibcode
2413:Bibcode
2347:Bibcode
2229:Bibcode
2174:Bibcode
1978:Bibcode
1913:Bibcode
1850:Bibcode
1785:Bibcode
1574:Bibcode
1444:Bibcode
1353:105.79
1304:176.10
1262:3.3530
1226:17.931
1223:3.2574
1177:153.36
1174:3.7412
1131:12.085
1128:117.84
974:Specie
791:alkanes
710:reduced
3006:
2967:
2928:
2920:
2912:
2892:(11).
2865:
2857:
2797:
2789:
2757:(15).
2730:
2689:
2681:
2673:
2634:
2592:
2584:
2576:
2537:
2529:
2490:
2451:
2443:
2381:
2373:
2365:
2345:(22).
2318:
2310:
2267:
2259:
2227:(18).
2200:
2192:
2145:
2137:
2098:
2090:
2051:
2043:
2004:
1996:
1939:
1931:
1884:
1876:
1868:
1815:
1783:(15).
1739:
1729:
1704:
1696:
1688:
1649:
1610:
1602:
1542:
1534:
1495:
1402:118.0
1356:14.08
1350:3.609
1301:3.645
1268:14.84
1180:12.65
1125:3.404
808:, and
273:
270:
267:
264:
261:
258:
2926:S2CID
2863:S2CID
2827:(6).
2687:S2CID
2590:S2CID
2449:S2CID
2379:S2CID
2316:S2CID
2298:(8).
2143:S2CID
2002:S2CID
1968:arXiv
1882:S2CID
1702:S2CID
1647:S2CID
1540:S2CID
1405:12.0
1399:3.46
1307:14.0
1265:4.44
1097:Ref.
296:with
3004:ISSN
2965:ISSN
2918:PMID
2910:ISSN
2855:ISSN
2795:PMID
2787:ISSN
2728:ISSN
2679:PMID
2671:ISSN
2632:ISSN
2582:PMID
2574:ISSN
2535:PMID
2527:ISSN
2488:ISSN
2441:ISSN
2371:PMID
2363:ISSN
2308:ISSN
2265:PMID
2257:ISSN
2198:PMID
2190:ISSN
2135:ISSN
2096:PMID
2088:ISSN
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