833:
Collisions between two dissimilar particles occur when a beam of fast particles is fired into a gas consisting of another type of particle, or two dissimilar molecules randomly collide in a gas mixture. For such cases, the above formula for scattering cross section has to be modified.
49:
of molecules in a gas. Mean free path is the average distance that a particle will travel without collision. For a fast moving particle (that is, one moving much faster than the particles it is moving through) the kinetic diameter is given by,
1132:
1015:
30:
that expresses the likelihood that a molecule in a gas will collide with another molecule. It is an indication of the size of the molecule as a target. The kinetic diameter is not the same as
195:
900:
1352:
Matteucci, Scott; Yampolskii, Yuri; Freeman, Benny D.; Pinnau, Ingo, "Transport of gases and vapors in glassy and rubbery polymers" in, Yampolskii, Yuri; Freeman, Benny D.; Pinnau, Ingo,
958:
99:
1337:
Li, Jian-Min; Talu, Orhan, "Effect of structural heterogeneity on multicomponent adsorption: benzene and p-xylene mixture on silicalite", in Suzuki, Motoyuki (ed),
837:
The scattering cross section, Ļ, in a collision between two dissimilar particles or molecules is defined by the sum of the kinetic diameters of the two particles,
135:
However, a more usual situation is that the colliding particle being considered is indistinguishable from the population of particles in general. Here, the
1040:
38:, which is generally a lot smaller, depending on the exact definition used. Rather, it is the size of the sphere of influence that can lead to a
1301:
969:
145:
136:
843:
1361:
1346:
1331:
1316:
1286:
934:
56:
928:, the scattering coefficient Ī±, as the product of the gas number density and the scattering cross section,
1377:
1281:
Breck, Donald W., "Zeolite
Molecular Sieves: Structure, Chemistry, and Use", New York: Wiley, 1974
785:
920:
are, half the kinetic diameter (ie, the kinetic radii) of the two particles, respectively.
8:
764:
925:
1357:
1342:
1327:
1312:
1282:
514:
1297:
710:
492:
410:
1127:{\displaystyle l={1 \over \sigma n}={1 \over 4\pi r^{2}n}={1 \over \pi d^{2}n}}
643:
575:
128:
46:
35:
1371:
596:
31:
453:
205:
The following table lists the kinetic diameters of some common molecules;
139:
of energies must be considered, which leads to the modified expression,
39:
550:
364:
224:
664:
428:
389:
243:
27:
963:
The mean free path is the inverse of the scattering coefficient,
806:
728:
685:
618:
303:
282:
471:
264:
746:
532:
324:
1354:
Materials
Science of Membranes for Gas and Vapor Separation
346:
23:
1307:
Ismail, Ahmad Fauzi; Khulbe, Kailash; Matsuura, Takeshi,
1010:{\displaystyle l={1 \over \alpha }={1 \over \sigma n}}
1043:
972:
937:
846:
148:
59:
1126:
1009:
952:
894:
189:
93:
1309:Gas Separation Membranes: Polymeric and Inorganic
190:{\displaystyle d^{2}={1 \over {\sqrt {2}}\pi ln}}
1369:
895:{\displaystyle \sigma =\pi (r_{1}+r_{2})^{2}}
1208:
1206:
1204:
1202:
1200:
1198:
1196:
1194:
34:defined in terms of the size of the atom's
1171:
1169:
1167:
1165:
1163:
1161:
1159:
1191:
1356:, pp. 1-47, John Wiley & Sons, 2006
1300:, 2004 unpublished draft, retrieved and
1246:
1244:
1242:
1240:
1238:
1236:
1234:
1232:
1230:
1228:
1226:
1224:
1222:
1156:
828:
1370:
1322:Joos, Georg; Freeman, Ira Maximilian,
953:{\displaystyle \alpha \equiv n\sigma }
94:{\displaystyle d^{2}={1 \over \pi ln}}
1219:
200:
45:Kinetic diameter is related to the
13:
14:
1389:
16:Measurement in molecular physics
1275:
115:is the kinetic radius, r = d/2,
1341:, pp. 373-380, Elsevier, 1993
1262:
1253:
1182:
1147:
883:
856:
137:MaxwellāBoltzmann distribution
1:
1140:
1326:, Courier Corporation, 1958
7:
10:
1394:
1339:Fundamentals of Adsorption
1153:Joos & Freeman, p. 573
121:is the mean free path, and
229:
218:
213:
210:
109:is the kinetic diameter,
22:is a measure applied to
1020:For similar particles,
1128:
1011:
954:
896:
191:
95:
1259:Li & Talu, p. 373
1129:
1012:
955:
897:
192:
96:
1041:
970:
935:
844:
829:Dissimilar particles
786:Carbon tetrachloride
146:
57:
1324:Theoretical Physics
765:Sulfur hexafluoride
1124:
1007:
950:
926:intensive quantity
892:
187:
91:
1378:Molecular physics
1311:, Springer, 2015
1294:Molecular Physics
1122:
1094:
1063:
1005:
987:
826:
825:
515:Hydrogen chloride
201:List of diameters
185:
173:
89:
1385:
1304:18 October 2015.
1269:
1266:
1260:
1257:
1251:
1248:
1217:
1210:
1189:
1186:
1180:
1173:
1154:
1151:
1133:
1131:
1130:
1125:
1123:
1121:
1117:
1116:
1100:
1095:
1093:
1089:
1088:
1069:
1064:
1062:
1051:
1016:
1014:
1013:
1008:
1006:
1004:
993:
988:
980:
959:
957:
956:
951:
901:
899:
898:
893:
891:
890:
881:
880:
868:
867:
711:Hydrogen bromide
493:Hydrogen sulfide
208:
207:
196:
194:
193:
188:
186:
184:
174:
169:
163:
158:
157:
100:
98:
97:
92:
90:
88:
74:
69:
68:
20:Kinetic diameter
1393:
1392:
1388:
1387:
1386:
1384:
1383:
1382:
1368:
1367:
1278:
1273:
1272:
1268:Freude, pp. 3-4
1267:
1263:
1258:
1254:
1249:
1220:
1211:
1192:
1187:
1183:
1174:
1157:
1152:
1148:
1143:
1112:
1108:
1104:
1099:
1084:
1080:
1073:
1068:
1055:
1050:
1042:
1039:
1038:
1033:
1026:
997:
992:
979:
971:
968:
967:
936:
933:
932:
919:
912:
886:
882:
876:
872:
863:
859:
845:
842:
841:
831:
814:
793:
772:
697:
693:
672:
651:
630:
626:
604:
583:
562:
558:
500:
479:
440:
436:
411:Carbon monoxide
397:
376:
372:
332:
311:
290:
251:
222:
220:
215:
203:
168:
167:
162:
153:
149:
147:
144:
143:
78:
73:
64:
60:
58:
55:
54:
32:atomic diameter
17:
12:
11:
5:
1391:
1381:
1380:
1366:
1365:
1350:
1335:
1320:
1305:
1290:
1277:
1274:
1271:
1270:
1261:
1252:
1218:
1190:
1181:
1155:
1145:
1144:
1142:
1139:
1135:
1134:
1120:
1115:
1111:
1107:
1103:
1098:
1092:
1087:
1083:
1079:
1076:
1072:
1067:
1061:
1058:
1054:
1049:
1046:
1031:
1024:
1018:
1017:
1003:
1000:
996:
991:
986:
983:
978:
975:
961:
960:
949:
946:
943:
940:
922:
921:
917:
910:
905:
902:
889:
885:
879:
875:
871:
866:
862:
858:
855:
852:
849:
830:
827:
824:
823:
821:
818:
815:
812:
809:
803:
802:
800:
797:
794:
791:
788:
782:
781:
779:
776:
773:
770:
767:
761:
760:
758:
755:
752:
749:
743:
742:
740:
737:
734:
731:
725:
724:
722:
719:
716:
713:
707:
706:
704:
701:
698:
695:
691:
688:
682:
681:
679:
676:
673:
670:
667:
661:
660:
658:
655:
652:
649:
646:
644:Sulfur dioxide
640:
639:
637:
634:
631:
628:
624:
621:
615:
614:
612:
609:
606:
602:
599:
593:
592:
590:
587:
584:
581:
578:
576:Carbon dioxide
572:
571:
569:
566:
563:
560:
556:
553:
547:
546:
544:
541:
538:
535:
529:
528:
526:
523:
520:
517:
511:
510:
508:
505:
502:
498:
495:
489:
488:
486:
483:
480:
477:
474:
468:
467:
465:
462:
459:
456:
450:
449:
447:
444:
441:
438:
434:
431:
425:
424:
422:
419:
416:
413:
407:
406:
404:
401:
398:
395:
392:
386:
385:
383:
380:
377:
374:
370:
367:
361:
360:
358:
355:
352:
349:
343:
342:
340:
337:
334:
330:
327:
321:
320:
318:
315:
312:
309:
306:
300:
299:
297:
294:
291:
288:
285:
279:
278:
276:
273:
270:
267:
261:
260:
258:
255:
252:
249:
246:
240:
239:
236:
232:
231:
228:
217:
212:
202:
199:
198:
197:
183:
180:
177:
172:
166:
161:
156:
152:
133:
132:
129:number density
122:
116:
110:
104:
101:
87:
84:
81:
77:
72:
67:
63:
47:mean free path
36:electron shell
15:
9:
6:
4:
3:
2:
1390:
1379:
1376:
1375:
1373:
1363:
1359:
1355:
1351:
1348:
1344:
1340:
1336:
1333:
1329:
1325:
1321:
1318:
1314:
1310:
1306:
1303:
1299:
1295:
1291:
1288:
1284:
1280:
1279:
1265:
1256:
1247:
1245:
1243:
1241:
1239:
1237:
1235:
1233:
1231:
1229:
1227:
1225:
1223:
1215:
1209:
1207:
1205:
1203:
1201:
1199:
1197:
1195:
1185:
1178:
1172:
1170:
1168:
1166:
1164:
1162:
1160:
1150:
1146:
1138:
1118:
1113:
1109:
1105:
1101:
1096:
1090:
1085:
1081:
1077:
1074:
1070:
1065:
1059:
1056:
1052:
1047:
1044:
1037:
1036:
1035:
1030:
1023:
1001:
998:
994:
989:
984:
981:
976:
973:
966:
965:
964:
947:
944:
941:
938:
931:
930:
929:
927:
924:We define an
916:
909:
906:
903:
887:
877:
873:
869:
864:
860:
853:
850:
847:
840:
839:
838:
835:
822:
819:
816:
810:
808:
805:
804:
801:
798:
795:
789:
787:
784:
783:
780:
777:
774:
768:
766:
763:
762:
759:
756:
753:
750:
748:
745:
744:
741:
738:
735:
732:
730:
727:
726:
723:
720:
717:
714:
712:
709:
708:
705:
702:
699:
689:
687:
684:
683:
680:
677:
674:
668:
666:
663:
662:
659:
656:
653:
647:
645:
642:
641:
638:
635:
632:
622:
620:
617:
616:
613:
610:
607:
600:
598:
597:Nitrous oxide
595:
594:
591:
588:
585:
579:
577:
574:
573:
570:
567:
564:
554:
552:
549:
548:
545:
542:
539:
536:
534:
531:
530:
527:
524:
521:
518:
516:
513:
512:
509:
506:
503:
496:
494:
491:
490:
487:
484:
481:
475:
473:
470:
469:
466:
463:
460:
457:
455:
452:
451:
448:
445:
442:
432:
430:
427:
426:
423:
420:
417:
414:
412:
409:
408:
405:
402:
399:
393:
391:
388:
387:
384:
381:
378:
368:
366:
363:
362:
359:
356:
353:
350:
348:
345:
344:
341:
338:
335:
328:
326:
323:
322:
319:
316:
313:
307:
305:
302:
301:
298:
295:
292:
286:
284:
281:
280:
277:
274:
271:
268:
266:
263:
262:
259:
256:
253:
247:
245:
242:
241:
237:
234:
233:
226:
209:
206:
181:
178:
175:
170:
164:
159:
154:
150:
142:
141:
140:
138:
130:
126:
123:
120:
117:
114:
111:
108:
105:
102:
85:
82:
79:
75:
70:
65:
61:
53:
52:
51:
48:
43:
41:
37:
33:
29:
25:
21:
1353:
1338:
1323:
1308:
1293:
1292:Freude, D.,
1276:Bibliography
1264:
1255:
1213:
1188:Freude, p. 4
1184:
1176:
1149:
1136:
1028:
1021:
1019:
962:
923:
914:
907:
836:
832:
454:Nitric oxide
204:
134:
131:of particles
124:
118:
112:
106:
44:
19:
18:
1137:as before.
1362:0470029048
1347:0080887724
1332:0486652270
1317:3319010956
1287:0471099856
1212:Matteucci
1141:References
40:scattering
1298:chapter 2
1106:π
1078:π
1057:σ
999:σ
985:α
948:σ
942:≡
939:α
854:π
848:σ
551:Propylene
365:Acetylene
214:Molecular
176:π
80:π
28:molecules
1372:Category
1302:archived
665:Chlorine
429:Ethylene
390:Nitrogen
244:Hydrogen
238:Formula
221:diameter
211:Molecule
1179:, p. 14
1175:Ismail
807:Bromine
729:Krypton
686:Benzene
619:Propane
304:Ammonia
283:Methane
219:Kinetic
127:is the
42:event.
1360:
1345:
1330:
1315:
1285:
1216:, p. 6
1214:et al.
1177:et al.
904:where.
472:Oxygen
265:Helium
103:where,
1250:Breck
1034:and,
747:Xenon
533:Argon
325:Water
24:atoms
1364:. Ų¦Ų¦
1358:ISBN
1343:ISBN
1328:ISBN
1313:ISBN
1283:ISBN
347:Neon
235:Name
230:ref
216:mass
26:and
820:350
817:160
799:590
796:154
790:CCl
778:550
775:146
757:396
754:131
739:360
721:350
715:HBr
703:585
678:320
657:360
636:430
611:330
589:330
568:450
543:340
525:320
519:HCl
507:360
485:346
464:317
446:390
421:376
403:364
382:330
357:275
339:265
317:260
296:380
275:260
257:289
1374::
1296:,
1221:^
1193:^
1158:^
1027:=
913:,
811:Br
769:SF
751:Xe
736:84
733:Kr
718:81
700:78
675:70
669:Cl
654:64
648:SO
633:44
608:44
586:44
580:CO
565:42
540:40
537:Ar
522:36
504:34
482:32
461:30
458:NO
443:28
418:28
415:CO
400:28
379:26
354:20
351:Ne
336:18
314:17
308:NH
293:16
287:CH
269:He
225:pm
1349:.
1334:.
1319:.
1289:.
1119:n
1114:2
1110:d
1102:1
1097:=
1091:n
1086:2
1082:r
1075:4
1071:1
1066:=
1060:n
1053:1
1048:=
1045:l
1032:2
1029:r
1025:1
1022:r
1002:n
995:1
990:=
982:1
977:=
974:l
945:n
918:2
915:r
911:1
908:r
888:2
884:)
878:2
874:r
870:+
865:1
861:r
857:(
851:=
813:2
792:4
771:6
696:6
694:H
692:6
690:C
671:2
650:2
629:8
627:H
625:3
623:C
605:O
603:2
601:N
582:2
561:6
559:H
557:3
555:C
501:S
499:2
497:H
478:2
476:O
439:4
437:H
435:2
433:C
396:2
394:N
375:2
373:H
371:2
369:C
333:O
331:2
329:H
310:3
289:4
272:4
254:2
250:2
248:H
227:)
223:(
182:n
179:l
171:2
165:1
160:=
155:2
151:d
125:n
119:l
113:r
107:d
86:n
83:l
76:1
71:=
66:2
62:d
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