730:. Since the anionic polymerization dispersity for a batch reactor or PFR is basically uniform, the molecular weight distribution takes on the distribution of the CSTR residence times, resulting in a dispersity of 2. Heterogeneous CSTRs are similar to homogeneous CSTRs, but the mixing within the reactor is not as good as in a homogeneous CSTR. As a result, there are small sections within the reactor that act as smaller batch reactors within the CSTR and end up with different concentrations of reactants. As a result, the dispersity of the reactor lies between that of a batch and that of a homogeneous CSTR.
112:
104:
726:, the reactive anion intermediates have the ability to remain reactive for a very long time. In batch reactors or PFRs, well-controlled anionic polymerization can result in almost uniform polymer. When introduced into a CSTR however, the residence time distribution for reactants in the CSTR affects the dispersity of the anionic polymer due to the anion lifetime. For a homogeneous CSTR, the residence time distribution is the
703:(PFRs), the dispersities for the different polymerization methods are the same. This is largely because while batch reactors depend entirely on time of reaction, plug flow reactors depend on distance traveled in the reactor and its length. Since time and distance are related by velocity, plug flow reactors can be designed to mirror batch reactors by controlling the velocity and length of the reactor.
711:
disproportionation. The rate of reaction for free radical polymerization is exceedingly quick, due to the reactivity of the radical intermediates. When these radicals react in any reactor, their lifetimes, and as a result, the time needed for reaction are much shorter than any reactor residence time. For FRPs that have a constant monomer and initiator concentration, such that the
734:
out of the reactor before achieving high molecular weight, while others stay in the reactor for a long time and continue to react. The result is a much more broad molecular weight distribution, which leads to much larger dispersities. For a homogeneous CSTR, the dispersity is proportional to the square root of the
733:
Step growth polymerization is most affected by reactor type. To achieve any high molecular weight polymer, the fractional conversion must exceed 0.99, and the dispersity of this reaction mechanism in a batch or PFR is 2.0. Running a step-growth polymerization in a CSTR will allow some polymer chains
623:
The reactor polymerization reactions take place in can also affect the dispersity of the resulting polymer. For bulk radical polymerization with low (<10%) conversion, anionic polymerization, and step growth polymerization to high conversion (>99%), typical dispersities are in the table below.
710:
The effects of reactor type on dispersity depend largely on the relative timescales associated with the reactor, and with the polymerization type. In conventional bulk free radical polymerization, the dispersity is often controlled by the proportion of chains that terminate via combination or
615:, a special case of addition polymerization, leads to values very close to 1. Such is the case also in biological polymers, where the dispersity can be very close or equal to 1, indicating only one length of polymer is present.
718:
is constant, the dispersity of the resulting monomer is between 1.5 and 2.0. As a result, reactor type does not affect dispersity for free radical polymerization reactions in any noticeable amount as long as conversion is low.
818:
427:
291:(often referred to as a monodisperse polymer) is composed of molecules of the same mass. Nearly all natural polymers are uniform. Synthetic near-uniform polymer chains can be made by processes such as
314:
A polymer material is denoted by the term disperse, or non-uniform, if its chain lengths vary over a wide range of molecular masses. This is characteristic of man-made polymers.
555:
526:
493:
460:
585:
Typical dispersities vary based on the mechanism of polymerization and can be affected by a variety of reaction conditions. In synthetic polymers, it can vary greatly due to
147:
distribution; a population of particles can be described by size, surface area, and/or mass distribution; and thin films can be described by film thickness distribution.
707:(CSTRs) however have a residence time distribution and cannot mirror batch or plug flow reactors, which can cause a difference in the dispersity of final polymer.
742:. Thus, for the similar reasons as anionic polymerization, the dispersity for heterogeneous CSTRs lies between that of a batch and a homogeneous CSTR.
918:
Okita, K.; Teramoto, A.; Kawahara, K.; Fujita, H. (1968). "Light scattering and refractometry of a monodisperse polymer in binary mixed solvents".
131:
if the objects have the same size, shape, or mass. A sample of objects that have an inconsistent size, shape and mass distribution is called
775:
143:, droplets in a cloud, crystals in a rock, or polymer macromolecules in a solution or a solid polymer mass. Polymers can be described by
334:
substances having respectively higher and lower molecular weights. Another interpretation of dispersity is explained in the article
171:(pronounced D-stroke) which can refer to either molecular mass or degree of polymerization. It can be calculated using the equation
373:
819:"The impact of smoke from forest fires on the spectral dispersion of cloud droplet size distributions in the Amazonian region"
1101:
1049:
1011:
862:
307:. Uniform collections can be easily created through the use of template-based synthesis, a common method of synthesis in
1126:
1076:
127:
is a measure of the heterogeneity of sizes of molecules or particles in a mixture. A collection of objects is called
1145:
275:
instead. The terms monodisperse and polydisperse are however still preferentially used to describe particles in an
704:
496:
463:
557:
is more sensitive to molecules of high molecular mass. The dispersity indicates the distribution of individual
755:
751:
1170:
17:
206:
is the number-average molar mass. It can also be calculated according to degree of polymerization, where
35:
1165:
31:
531:
502:
469:
436:
783:
765:
712:
335:
945:
944:
Stepto, R. F. T.; Gilbert, R. G.; Hess, M.; Jenkins, A. D.; Jones, R. G.; Kratochvíl P. (2009). "
779:
700:
569:
has a value equal to or greater than 1, but as the polymer chains approach uniform chain length,
338:(cumulant method subheading). In this sense, the dispersity values are in the range from 0 to 1.
1001:
727:
606:
315:
136:
723:
612:
300:
877:
833:
739:
735:
8:
1160:
1094:
Introduction to
Polymer Science and Chemistry: A Problem-Solving Approach, Second Edition
1027:
881:
837:
893:
846:
1175:
1122:
1097:
1072:
1045:
1007:
1000:
Brown, William H.; Foote, Christopher S.; Iverson, Brent L.; Anslyn, Eric V. (2012).
897:
771:
738:, but for a heterogeneous CSTR, dispersity is proportional to the natural log of the
973:
927:
885:
841:
761:
601:
can range around 5 to 20. For typical step polymerization, most probable values of
319:
796:
331:
304:
241:
is the number-average degree of polymerization. In certain limiting cases where
1067:
Dotson, Neil A.; Galván, Rafael; Laurence, Robert L.; Tirrell, Matthew (1996).
594:
590:
558:
356:
308:
144:
965:
901:
299:
to produce chains that are similar in length. This technique is also known as
1154:
978:
89:
889:
111:
103:
327:
154:
931:
323:
120:
168:
586:
322:) also has a pronounced polydispersed character. It is the case of
296:
318:
produced by the decomposition of plants and wood debris in soils (
562:
360:
292:
288:
276:
140:
799: – Polymers whose repeating units bear an electrolyte group
355:) or heterogeneity index, is a measure of the distribution of
150:
528:
is more sensitive to molecules of low molecular mass, while
1066:
917:
422:{\displaystyle \quad PDI=M_{\mathrm {w} }/M_{\mathrm {n} }}
84:
is the number-average molar mass (or molecular weight).
76:
is the mass-average molar mass (or molecular weight) and
999:
27:
Measure of heterogeneity of particle or molecular sizes
267:, which is considered redundant, preferring the terms
972:. International Union of Pure and Applied Chemistry.
580:
534:
505:
472:
439:
376:
263:, which is considered to be self-contradictory, and
1028:"Definition of polydisperse - Chemistry Dictionary"
234:is the weight-average degree of polymerization and
549:
520:
487:
454:
421:
816:
1152:
573:approaches unity (1). For some natural polymers
303:. It is used commercially for the production of
1044:, 9th edition (Oxford University Press, 2010,
1006:(6 ed.). Cengage Learning. p. 1161.
593:went to completion, etc. For typical addition
966:"monodisperse polymer (See: uniform polymer)"
817:Martins, J. A.; Silva Dias, M. A. F. (2009).
1119:Chemical Reaction Engineering, Third Edition
955:(2): 351–353. DOI:10.1351/PAC-REC-08-05-02.
863:"Measurement of crystal size distributions"
776:matrix-assisted laser desorption/ionization
351:), also known as the polydispersity index (
1116:
295:polymerization, a method using an anionic
1071:. VCH Publishers, Inc. pp. 260–279.
977:
845:
618:
745:
110:
102:
860:
115:A non-uniform (polydisperse) collection
14:
1153:
1091:
722:For anionic polymerization, a form of
259:. IUPAC has also deprecated the terms
938:
199:is the weight-average molar mass and
1062:
1060:
1058:
135:. The objects can be in any form of
609:limits Đ to values of 2 and below.
163:, having replaced it with the term
107:A uniform (monodisperse) collection
24:
705:Continuously stirred-tank reactors
581:Effect of polymerization mechanism
541:
512:
479:
446:
413:
396:
367:(PDI) of a polymer is calculated:
25:
1187:
1139:
1055:
1040:Peter Atkins and Julio De Paula,
920:The Journal of Physical Chemistry
550:{\displaystyle M_{\mathrm {w} }}
521:{\displaystyle M_{\mathrm {n} }}
488:{\displaystyle M_{\mathrm {n} }}
455:{\displaystyle M_{\mathrm {w} }}
1110:
1085:
1069:Polymerization Process Modeling
497:number average molecular weight
464:weight average molecular weight
377:
1034:
1020:
993:
958:
911:
854:
826:Environmental Research Letters
810:
255:, it is simply referred to as
13:
1:
946:Dispersity in Polymer Science
803:
756:size-exclusion chromatography
752:Gel permeation chromatography
861:Higgins, Michael D. (2000).
847:10.1088/1748-9326/4/1/015002
167:, represented by the symbol
7:
1117:Levenspiel, Octave (1999).
790:
647:Radical Polymerization (RP)
282:
36:Dispersion (disambiguation)
10:
1192:
1042:Atkins' Physical Chemistry
728:most probable distribution
699:With respect to batch and
577:is almost taken as unity.
32:Dispersal (disambiguation)
29:
1121:. John Wiley & Sons.
139:, such as particles in a
1146:Introduction to Polymers
784:tandem mass spectrometry
766:dynamic light scattering
336:Dynamic light scattering
30:Not to be confused with
979:10.1351/goldbook.M04012
780:electrospray ionization
770:Direct measurement via
636:Plug Flow Reactor (PFR)
1092:Chanda, Manas (2013).
664:Anionic Polymerization
619:Effect of reactor type
551:
522:
489:
456:
423:
316:Natural organic matter
116:
108:
86:
890:10.2138/am-2000-8-901
870:American Mineralogist
764:measurements such as
746:Determination methods
724:living polymerization
630:Polymerization Method
613:Living polymerization
589:ratio, how close the
552:
523:
490:
457:
424:
301:living polymerization
114:
106:
44:
605:are around 2 —
532:
503:
470:
437:
374:
160:polydispersity index
157:the use of the term
1171:Colloidal chemistry
932:10.1021/j100847a053
882:2000AmMin..85.1105H
838:2009ERL.....4a5002M
693:Unbounded (~20-25)
607:Carothers' equation
137:chemical dispersion
701:plug flow reactors
547:
518:
485:
452:
419:
117:
109:
1166:Polymer chemistry
1103:978-1-4665-5384-2
1050:978-0-19-954337-3
1013:978-0-8400-5498-2
1003:Organic chemistry
772:mass spectrometry
697:
696:
16:(Redirected from
1183:
1133:
1132:
1114:
1108:
1107:
1089:
1083:
1082:
1064:
1053:
1038:
1032:
1031:
1024:
1018:
1017:
997:
991:
990:
988:
986:
981:
962:
956:
950:Pure Appl. Chem.
942:
936:
935:
915:
909:
908:
906:
900:. Archived from
876:(9): 1105–1116.
867:
858:
852:
851:
849:
823:
814:
762:Light scattering
740:Damköhler number
736:Damköhler number
642:Segregated CSTR
639:Homogeneous CSTR
627:
626:
559:molecular masses
556:
554:
553:
548:
546:
545:
544:
527:
525:
524:
519:
517:
516:
515:
494:
492:
491:
486:
484:
483:
482:
461:
459:
458:
453:
451:
450:
449:
428:
426:
425:
420:
418:
417:
416:
406:
401:
400:
399:
320:humic substances
305:block copolymers
99:
97:, 81(2), 351-353
91:Pure Appl. Chem.
42:IUPAC definition
21:
1191:
1190:
1186:
1185:
1184:
1182:
1181:
1180:
1151:
1150:
1142:
1137:
1136:
1129:
1115:
1111:
1104:
1090:
1086:
1079:
1065:
1056:
1039:
1035:
1026:
1025:
1021:
1014:
998:
994:
984:
982:
970:IUPAC Gold Book
964:
963:
959:
943:
939:
916:
912:
904:
865:
859:
855:
821:
815:
811:
806:
797:Polyelectrolyte
793:
754:(also known as
748:
716:
690:Unbounded (~50)
621:
583:
540:
539:
535:
533:
530:
529:
511:
510:
506:
504:
501:
500:
478:
477:
473:
471:
468:
467:
445:
444:
440:
438:
435:
434:
412:
411:
407:
402:
395:
394:
390:
375:
372:
371:
332:polyelectrolyte
285:
254:
247:
240:
233:
226:
219:
212:
205:
198:
191:
184:
177:
101:
88:
83:
77:
75:
68:
67:
66:
59:
52:
43:
39:
28:
23:
22:
15:
12:
11:
5:
1189:
1179:
1178:
1173:
1168:
1163:
1149:
1148:
1141:
1140:External links
1138:
1135:
1134:
1127:
1109:
1102:
1084:
1077:
1054:
1033:
1019:
1012:
992:
957:
937:
910:
907:on 2017-08-08.
853:
808:
807:
805:
802:
801:
800:
792:
789:
788:
787:
768:
759:
747:
744:
714:
695:
694:
691:
688:
685:
682:
678:
677:
674:
671:
668:
665:
661:
660:
657:
654:
651:
648:
644:
643:
640:
637:
634:
631:
620:
617:
595:polymerization
591:polymerization
582:
579:
561:in a batch of
543:
538:
514:
509:
481:
476:
448:
443:
431:
430:
415:
410:
405:
398:
393:
389:
386:
383:
380:
357:molecular mass
309:nanotechnology
284:
281:
252:
245:
238:
231:
224:
217:
210:
203:
196:
189:
182:
175:
145:molecular mass
81:
73:
64:
57:
50:
46:
41:
40:
26:
9:
6:
4:
3:
2:
1188:
1177:
1174:
1172:
1169:
1167:
1164:
1162:
1159:
1158:
1156:
1147:
1144:
1143:
1130:
1128:0-471-25424-X
1124:
1120:
1113:
1105:
1099:
1096:. CRC Press.
1095:
1088:
1080:
1078:1-56081-693-7
1074:
1070:
1063:
1061:
1059:
1051:
1047:
1043:
1037:
1029:
1023:
1015:
1009:
1005:
1004:
996:
980:
975:
971:
967:
961:
954:
951:
947:
941:
933:
929:
925:
921:
914:
903:
899:
895:
891:
887:
883:
879:
875:
871:
864:
857:
848:
843:
839:
835:
832:(1): 015002.
831:
827:
820:
813:
809:
798:
795:
794:
785:
781:
777:
773:
769:
767:
763:
760:
757:
753:
750:
749:
743:
741:
737:
731:
729:
725:
720:
717:
708:
706:
702:
692:
689:
686:
683:
680:
679:
675:
672:
669:
666:
663:
662:
658:
655:
652:
649:
646:
645:
641:
638:
635:
633:Batch Reactor
632:
629:
628:
625:
616:
614:
610:
608:
604:
600:
596:
592:
588:
578:
576:
572:
568:
564:
560:
536:
507:
498:
474:
465:
441:
408:
403:
391:
387:
384:
381:
378:
370:
369:
368:
366:
362:
358:
354:
350:
349:
344:
339:
337:
333:
329:
325:
321:
317:
312:
310:
306:
302:
298:
294:
290:
280:
278:
274:
270:
266:
262:
258:
251:
244:
237:
230:
223:
216:
209:
202:
195:
188:
181:
174:
170:
166:
162:
161:
156:
152:
148:
146:
142:
138:
134:
130:
126:
122:
113:
105:
100:
98:
96:
92:
85:
80:
72:
63:
56:
49:
37:
33:
19:
1118:
1112:
1093:
1087:
1068:
1041:
1036:
1022:
1002:
995:
983:. Retrieved
969:
960:
952:
949:
940:
923:
919:
913:
902:the original
873:
869:
856:
829:
825:
812:
732:
721:
709:
698:
622:
611:
602:
598:
584:
574:
570:
566:
432:
364:
352:
347:
346:
342:
340:
328:fulvic acids
313:
286:
272:
268:
265:polydisperse
264:
261:monodisperse
260:
256:
249:
242:
235:
228:
221:
214:
207:
200:
193:
186:
179:
172:
164:
159:
158:
149:
132:
128:
124:
118:
94:
90:
87:
78:
70:
61:
54:
47:
45:
18:Polydisperse
926:: 278–285.
786:(ESI-MS/MS)
778:(MALDI) or
681:Step-Growth
359:in a given
324:humic acids
273:non-uniform
133:non-uniform
1161:Copolymers
1155:Categories
985:25 January
804:References
343:dispersity
330:, natural
287:A uniform
165:dispersity
155:deprecated
125:dispersity
898:101422067
121:chemistry
1176:Colloids
791:See also
774:, using
676:1.0-2.0
659:1.5-2.0
587:reactant
563:polymers
363:sample.
297:catalyst
283:Overview
227:, where
192:, where
878:Bibcode
834:Bibcode
670:1.0 + ε
667:1.0 + ε
656:1.5-2.0
653:1.5-2.0
650:1.5-2.0
495:is the
462:is the
361:polymer
293:anionic
289:polymer
277:aerosol
269:uniform
141:colloid
129:uniform
1125:
1100:
1075:
1048:
1010:
896:
433:where
123:, the
69:where
905:(PDF)
894:S2CID
866:(PDF)
822:(PDF)
782:with
151:IUPAC
1123:ISBN
1098:ISBN
1073:ISBN
1046:ISBN
1008:ISBN
987:2012
466:and
341:The
326:and
271:and
153:has
95:2009
974:doi
928:doi
886:doi
842:doi
687:2.0
684:2.0
673:2.0
353:PDI
119:In
34:or
1157::
1057:^
968:.
953:81
948:"
924:72
922:.
892:.
884:.
874:85
872:.
868:.
840:.
828:.
824:.
713:DP
597:,
565:.
499:.
311:.
279:.
248:=
213:=
178:=
93:,
53:=
1131:.
1106:.
1081:.
1052:)
1030:.
1016:.
989:.
976::
934:.
930::
888::
880::
850:.
844::
836::
830:4
758:)
715:n
603:Đ
599:Đ
575:Đ
571:Đ
567:Đ
542:w
537:M
513:n
508:M
480:n
475:M
447:w
442:M
429:,
414:n
409:M
404:/
397:w
392:M
388:=
385:I
382:D
379:P
365:Đ
348:Đ
345:(
257:Đ
253:X
250:Đ
246:M
243:Đ
239:n
236:X
232:w
229:X
225:n
222:X
220:/
218:w
215:X
211:X
208:Đ
204:n
201:M
197:w
194:M
190:n
187:M
185:/
183:w
180:M
176:M
173:Đ
169:Đ
82:n
79:M
74:w
71:M
65:n
62:M
60:/
58:w
55:M
51:M
48:Đ
38:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
