3256:
29:
3226:
556:
4773:, blend composition, and chain length was discarded. Specifically, interactions beyond the nearest neighbor may be highly relevant to the behavior of the blend and the distribution of polymer segments is not necessarily uniform, so certain lattice sites may experience interaction energies disparate from that approximated by the mean-field theory.
3210:, is a free energy parameter, thus including an entropic component. This means that aside to the regular mixing entropy there is another entropic contribution from the interaction between solvent and monomer. This contribution is sometimes very important in order to make quantitative predictions of thermodynamic properties.
3964:, which is very small for large polymers. The amount of polymer in the solvent-rich/polymer-poor coexisting phase is extremely small for long polymers. The solvent-rich phase is close to pure solvent. This is peculiar to polymers, a mixture of small molecules can be approximated using the Flory–Huggins expression with
4267:
4776:
One well-studied effect on interaction energies neglected by unmodified Flory–Huggins theory is chain correlation. In dilute polymer mixtures, where chains are well separated, intramolecular forces between monomers of the polymer chain dominate and drive demixing leading to regions where polymer
4567:
Flory–Huggins theory tends to agree well with experiments in the semi-dilute concentration regime and can be used to fit data for even more complicated blends with higher concentrations. The theory qualitatively predicts phase separation, the tendency for high molecular weight species to be
4777:
concentration is high. As the polymer concentration increases, chains tend to overlap and the effect becomes less important. In fact, the demarcation between dilute and semi-dilute solutions is commonly defined by the concentration where polymers begin to overlap
3844:
4462:
1286:, but is weighted to take account of the relative sizes of the molecules. For a small solute, the mole fractions would appear instead, and this modification is the innovation due to Flory and Huggins. In the most general case the mixing parameter,
3267:
curves for a semi-dilute polymer solution. The light blue region indicates a metastable solution where phase separation occurs and the white region corresponds to well-mixed states. The dark blue unstable region corresponds to states where
4072:
3710:
3402:
3124:
1849:
750:
3617:
5196:
3537:
2626:
4872:
2184:
4749:; however, polymers blends have been observed where this parameter is highly asymmetric. In certain blends, mixing entropy can dominate over monomer interaction. By adopting the mean-field approximation,
2530:
2456:
4980:
1668:
1978:
2259:
3721:
2964:
4336:
4039:
Synthetic polymers rarely consist of chains of uniform length in solvent. The Flory–Huggins free energy density can be generalized to an N-component mixture of polymers with lengths
2775:
1042:
3887:
4029:
4747:
873:
835:
630:
4602:
1426:
4706:
3162:
4906:
4633:
3921:
2916:
3024:
2997:
1700:
4557:
4531:
4498:
4262:{\displaystyle f{\Bigl (}\{\phi _{i},r_{i}\}{\Bigr )}=\sum _{i=1}^{N}{\frac {\phi _{i}}{r_{i}}}\ln \phi _{i}+{\frac {1}{2}}\sum _{i,j=1}^{N}\phi _{i}\phi _{j}\chi _{ij}}
3214:
2376:
1761:
1734:
1188:
1106:
3962:
3188:
2345:
773:
3451:
2312:
2101:
2070:
2043:
4802:
4767:
4660:
4328:
4301:
4064:
3425:
3250:
3208:
2886:
2859:
2832:
2805:
1483:
1456:
1304:
1228:
1161:
1079:
3988:
3926:
The unusual feature of the liquid/liquid phase separation is that it is highly asymmetric: the volume fraction of monomers at the critical point is approximately
5095:
5045:
3294:
2282:
2001:
1503:
1276:
1252:
1208:
1134:
4948:. Flory suggested that Huggins' name ought to be first since he had published several months earlier: Flory, P.J., "Thermodynamics of high polymer solutions",
2284:
is the coordination number, the number of nearest neighbors for a lattice site, each one occupied either by one chain segment or a solvent molecule. That is,
3302:
5690:
4604:
interaction-temperature dependence and other features commonly observed in polymer mixtures. However, unmodified Flory–Huggins theory fails to predict the
3031:
3543:
The polymer solution is stable with respect to small fluctuations when the second derivative of this free energy is positive. This second derivative is
2378:
that any such site is occupied by a solvent molecule, we obtain the total number of polymer-solvent molecular interactions. An approximation following
1768:
666:
3276:
Polymers can separate out from the solvent, and do so in a characteristic way. The Flory–Huggins free energy per unit volume, for a polymer with
4467:
As in the case for dilute polymer solutions, the first two terms on the right-hand side represent the entropy of mixing. For large polymers of
3463:
2545:
3628:
5392:
4810:
3549:
2385:
The enthalpy change is equal to the energy change per polymer monomer-solvent interaction multiplied by the number of such interactions
2382:
is made by following this procedure, thereby reducing the complex problem of many interactions to a simpler problem of one interaction.
542:
3889:
the monomer-solvent effective interaction is weakly repulsive, but this is too weak to cause liquid/liquid separation. However, when
137:
2109:
2473:
2391:
2103:. Each of the last occurs at the expense of the average of the other two, so the energy increment per monomer-solvent contact is
1369:
5206:
5179:
5151:
5364:
5258:
Berry, J; et al. (2018). "Physical principles of intracellular organization via active and passive phase transitions".
3715:
are both equal to zero. A little algebra then shows that the polymer solution first becomes unstable at a critical point at
1529:
1333:
and polymer – everywhere we look we find a molecule. Of course, any notion of "finding" a molecule in a given location is a
4605:
80:
75:
5761:
1864:
2195:
5321:
5108:
In fact, two of the sites adjacent to a polymer segment are occupied by other polymer segments since it is part of a
307:
122:
5385:
1368:
in molecular sizes by assuming that individual polymer segments and individual solvent molecules occupy sites on a
169:
3839:{\displaystyle \chi _{\text{cp}}\simeq 1/2+N^{-1/2}+\cdots \qquad \phi _{\text{cp}}\simeq N^{-1/2}-N^{-1}+\cdots }
4457:{\displaystyle f(\phi )={\frac {\phi }{N_{A}}}\ln \phi +{\frac {1-\phi }{N_{B}}}\ln(1-\phi )+\chi \phi (1-\phi )}
2970:
2008:
5766:
5527:
5234:
4770:
3923:, there is separation into two coexisting phases, one richer in polymer but poorer in solvent, than the other.
2924:
535:
5113:
2637:
904:
292:
3852:
1520:
5680:
3993:
4711:
884:
840:
802:
597:
5610:
5378:
4956:
4571:
322:
117:
112:
90:
5142:
Burchard, W (1983). "Solution
Thermodyanmics of Non-Ionic Water Soluble Polymers.". In Finch, C. (ed.).
5751:
5665:
5101:, which is the natural form of free energy from the Flory–Huggins lattice theory, to Gibbs free energy.
1113:
792:
636:. Although it makes simplifying assumptions, it generates useful results for interpreting experiments.
317:
146:
5557:
1279:
528:
70:
4662:. Additionally, it can be shown that for a binary blend of polymer species with equal chain lengths
1382:
5542:
5477:
4665:
3132:
1342:
645:
583:
285:
4884:
4611:
3892:
2894:
5497:
3002:
2975:
1676:
567:
387:
382:
156:
4536:
4503:
4470:
5595:
5590:
5447:
3269:
2354:
1739:
1712:
1166:
1084:
1048:
780:
268:
5367:, Chapter 3 of Book Title: Polymer Science and Technology; by Joel R. Fried; 2nd Edition, 2003
3929:
3170:
5695:
5675:
5170:
Franks, F (1983). "Water
Solubility and Sensitivity-Hydration Effects.". In Finch, C. (ed.).
5098:
4973:
2317:
895:
758:
482:
302:
297:
3430:
2287:
2079:
2048:
2021:
5409:
5401:
5267:
4934:
4780:
4752:
4638:
4306:
4279:
4042:
3410:
3235:
3193:
2864:
2837:
2810:
2783:
1461:
1434:
1289:
1213:
1139:
1057:
784:
151:
45:
1322:
8:
5522:
5492:
3967:
492:
60:
5271:
5756:
5341:
5291:
5080:
5030:
5013:
4909:
4608:
observed in some polymer blends and the lack of dependence of the critical temperature
3397:{\displaystyle f={\frac {\phi }{N}}\ln \phi +(1-\phi )\ln(1-\phi )+\chi \phi (1-\phi )}
3279:
3255:
2267:
1986:
1703:
1488:
1334:
1325:
about the locations of the molecules when they are interspersed. In the pure condensed
1261:
1237:
1193:
1119:
455:
438:
397:
221:
5700:
5659:
5562:
5337:
5317:
5283:
5240:
5230:
5202:
5175:
5147:
4969:
2889:
2379:
1346:
1315:
591:
587:
448:
412:
231:
226:
55:
5635:
5630:
5462:
5422:
5295:
5275:
3454:
3229:
3119:{\displaystyle \chi _{12}={\frac {V_{\rm {seg}}(\delta _{a}-\delta _{b})^{2}}{RT}}}
575:
402:
372:
312:
127:
4945:
4533:
these terms are negligibly small. This implies that for a stable mixture to exist
5620:
5605:
5537:
5502:
5487:
5482:
5467:
5432:
5074:
5063:
5020:
475:
417:
367:
194:
1844:{\displaystyle \phi _{1}={\frac {N_{1}}{N}},\quad \phi _{2}={\frac {xN_{2}}{N}}}
65:
5670:
5625:
5615:
5532:
5427:
5417:
5279:
4927:
1326:
745:{\displaystyle \Delta G_{\rm {mix}}=\Delta H_{\rm {mix}}-T\Delta S_{\rm {mix}}}
571:
509:
362:
105:
5745:
5715:
5552:
5512:
5457:
4273:
2535:
It depends on the nature of both the solvent and the solute, and is the only
2073:
2004:
1858:, is occupied by a solvent molecule or a polymer segment, respectively. Thus
1358:
1350:
1283:
407:
216:
211:
189:
4559:, so for polymers A and B to blend their segments must attract one another.
3622:
and the solution first becomes unstable when this and the third derivative
2018:
change. There are three molecular interactions to consider: solvent-solvent
5572:
5567:
5287:
5244:
5097:. We are not making any distinction here. This allows the approximation of
2919:
2462:
1255:
649:
499:
443:
392:
377:
201:
184:
5725:
5640:
5109:
5024:
4993:
due to molecular disorder in liquids and amorphous solids as compared to
3532:{\displaystyle \Pi ={\frac {\phi }{N}}-\ln(1-\phi )-\phi -\chi \phi ^{2}}
2621:{\displaystyle \Delta H_{\rm {mix}}=k_{\rm {B}}TN_{1}\phi _{2}\chi _{12}}
1509:
1372:. Each site is occupied by exactly one molecule of the solvent or by one
1361:
1052:
653:
514:
460:
248:
236:
28:
3705:{\displaystyle f'''=-{\frac {1}{N\phi ^{2}}}+{\frac {1}{(1-\phi )^{2}}}}
5720:
5710:
5705:
5582:
5017:
4938:
2314:
is the total number of polymer segments (monomers) in the solution, so
1855:
891:
357:
337:
179:
1854:
These are also the probabilities that a given lattice site, chosen at
5730:
5685:
5600:
5370:
4867:{\displaystyle c^{*}={\frac {m}{{\frac {4}{3}}\pi R_{\text{g}}^{3}}}}
3225:
332:
263:
253:
206:
50:
1306:, is a free energy parameter, thus including an entropic component.
5547:
5067:
5059:
3612:{\displaystyle f''={\frac {1}{N\phi }}+{\frac {1}{1-\phi }}-2\chi }
3264:
1365:
876:
657:
579:
487:
465:
327:
5346:
5650:
5452:
5442:
5117:
5048:
4998:
4994:
4931:
3260:
2969:
The value of the interaction parameter can be estimated from the
1983:
For a small solute whose molecules occupy just one lattice site,
1513:
1373:
1330:
1109:
880:
796:
788:
633:
5340:(2010). "Theory and Simulation of Multiphase Polymer Systems".
5316:. Great Clarendon Street, Oxford, UK: Oxford University Press.
5071:
3232:
for a polymer solution in two regimes of interaction parameter
1354:
1231:
776:
504:
5365:"Conformations, Solutions and Molecular Weight" (book chapter)
2179:{\displaystyle \Delta w=w_{12}-{\tfrac {1}{2}}(w_{22}+w_{11})}
5472:
2076:, but between different chain sections), and monomer-solvent
1517:
1338:
5001:
and solute molecules are really the same size, are the main
2525:{\displaystyle \chi _{12}={\frac {z\Delta w}{k_{\rm {B}}T}}}
2451:{\displaystyle \Delta H_{\rm {mix}}=N_{1}\phi _{2}z\Delta w}
470:
258:
132:
795:
considered separately. The objective is to find explicit
3296:
monomers, can be written in a simple dimensionless form
555:
5257:
2780:
where we have converted the expression from molecules
2136:
1663:{\displaystyle \Delta S_{\rm {mix}}=-k_{\rm {B}}\left}
1632:
1594:
1485:
is the number of polymer molecules, each of which has
1376:
of the polymer chain, so the total number of sites is
5083:
5033:
4887:
4813:
4783:
4755:
4714:
4668:
4641:
4614:
4574:
4539:
4506:
4473:
4339:
4309:
4282:
4075:
4045:
3996:
3970:
3932:
3895:
3855:
3724:
3631:
3552:
3466:
3433:
3413:
3305:
3282:
3238:
3196:
3173:
3135:
3034:
3005:
2978:
2927:
2897:
2867:
2840:
2813:
2786:
2640:
2548:
2476:
2394:
2357:
2351:
the polymer segments. Multiplying by the probability
2320:
2290:
2270:
2198:
2112:
2082:
2051:
2024:
2014:
In addition to the entropic effect, we can expect an
1989:
1867:
1771:
1742:
1715:
1679:
1532:
1491:
1464:
1437:
1385:
1292:
1264:
1240:
1216:
1196:
1169:
1142:
1122:
1087:
1060:
907:
843:
805:
761:
669:
600:
5691:
List of boiling and freezing information of solvents
2539:
parameter in the model. The enthalpy change becomes
3213:More advanced solution theories exist, such as the
5172:Chemistry and Technology of Water-Soluble Polymers
5144:Chemistry and Technology of Water-Soluble Polymers
5089:
5039:
4900:
4866:
4796:
4761:
4741:
4700:
4654:
4627:
4596:
4551:
4525:
4492:
4456:
4322:
4295:
4261:
4058:
4023:
3982:
3956:
3915:
3881:
3838:
3704:
3611:
3531:
3445:
3419:
3396:
3288:
3244:
3202:
3182:
3156:
3118:
3018:
2991:
2958:
2910:
2880:
2853:
2826:
2799:
2769:
2631:Assembling terms, the total free energy change is
2620:
2524:
2450:
2370:
2339:
2306:
2276:
2253:
2178:
2095:
2064:
2037:
1995:
1972:
1843:
1755:
1728:
1694:
1662:
1497:
1477:
1450:
1420:
1298:
1270:
1246:
1234:of interdispersing polymer and solvent molecules.
1222:
1202:
1182:
1155:
1128:
1100:
1073:
1036:
867:
829:
767:
744:
624:
578:which takes account of the great dissimilarity in
4117:
4081:
3220:
1973:{\displaystyle \Delta S_{\rm {mix}}=-k_{\rm {B}}}
5743:
5195:Dijk, Menno A. van; Wakker, Andre (1998-01-14).
2254:{\displaystyle xN_{2}z\phi _{1}=N_{1}\phi _{2}z}
5220:
5218:
5137:
5135:
4944:, August 1941, Volume 9, Issue 8, p. 660
4031:and both coexisting phases are far from pure.
5386:
536:
5165:
5163:
4112:
4086:
1523:) as a result of mixing solute and solvent.
559:Mixture of polymers and solvent on a lattice
5215:
5132:
4881:is the mass of a single polymer chain, and
3164:is the actual volume of a polymer segment.
2347:is the number of nearest-neighbor sites to
2003:equals one, the volume fractions reduce to
5393:
5379:
5229:. Ithaca, N.Y.: Cornell University Press.
5194:
4979:, May 1941 Volume 9, Issue 5, p. 440
2461:The polymer-solvent interaction parameter
1282:. The volume fraction is analogous to the
543:
529:
5345:
5307:
5305:
5224:
5160:
3167:In the most general case the interaction
2959:{\displaystyle R=k_{\rm {B}}N_{\text{A}}}
2763:
2674:
1966:
1910:
1030:
941:
138:Nitroxide-mediated radical polymerization
5141:
3254:
3224:
1210:), with the introduction of a parameter
554:
2770:{\displaystyle \Delta G_{\rm {mix}}=RT}
1458:is the number of solvent molecules and
1037:{\displaystyle \Delta G_{\rm {mix}}=RT}
652:change accompanying mixing at constant
5744:
5400:
5336:
5302:
5169:
3882:{\displaystyle 0<\chi \lesssim 1/2}
883:increments associated with the mixing
5374:
4708:the critical concentration should be
4024:{\displaystyle \phi _{\text{cp}}=1/2}
3427:the volume fraction of monomers, and
2189:The total number of such contacts is
1341:locations the size of molecules. The
4742:{\displaystyle \psi _{\text{c}}=1/2}
868:{\displaystyle \Delta S_{\rm {mix}}}
830:{\displaystyle \Delta H_{\rm {mix}}}
625:{\displaystyle \Delta G_{\rm {mix}}}
590:. The result is an equation for the
5311:
5227:Scaling concepts in polymer physics
4606:lower critical solution temperature
4597:{\displaystyle \chi \propto T^{-1}}
13:
5198:Concepts in Polymer Thermodynamics
5112:; and one more, making three, for
3849:This means that for all values of
3467:
3190:and the ensuing mixing parameter,
3174:
3148:
3145:
3142:
3063:
3060:
3057:
2940:
2656:
2653:
2650:
2641:
2579:
2564:
2561:
2558:
2549:
2510:
2496:
2442:
2410:
2407:
2404:
2395:
2113:
1901:
1883:
1880:
1877:
1868:
1686:
1566:
1548:
1545:
1542:
1533:
1512:on a lattice we can calculate the
923:
920:
917:
908:
859:
856:
853:
844:
821:
818:
815:
806:
762:
736:
733:
730:
721:
709:
706:
703:
694:
685:
682:
679:
670:
616:
613:
610:
601:
27:
16:Lattice model of polymer solutions
14:
5778:
5358:
5225:de Gennes, Pierre-Gilles (1979).
4034:
1353:is no longer reasonable when the
123:Controlled radical polymerization
4997:. This, and the assumption that
4769:parameter complex dependence on
4276:, where one species consists of
2971:Hildebrand solubility parameters
1337:since we can't actually examine
3779:
1805:
1349:of small molecules in terms of
5330:
5260:Reports on Progress in Physics
5251:
5188:
5174:. Springer. pp. 157–178.
5146:. Springer. pp. 125–142.
5104:
5054:
5008:
4985:
4964:
4922:
4695:
4669:
4562:
4451:
4439:
4427:
4415:
4349:
4343:
3690:
3677:
3504:
3492:
3391:
3379:
3367:
3355:
3346:
3334:
3221:Liquid-liquid phase separation
3096:
3069:
2764:
2671:
2173:
2147:
1967:
1907:
1421:{\displaystyle N=N_{1}+xN_{2}}
1031:
938:
791:minus the values for the pure
1:
5201:. CRC Press. pp. 61–65.
5125:
5005:approximations in this model.
4701:{\displaystyle (N_{A}=N_{B})}
3157:{\displaystyle V_{\rm {seg}}}
1364:. We take account of this dis
1309:
564:Flory–Huggins solution theory
86:Flory–Huggins solution theory
5681:Inorganic nonaqueous solvent
4915:
4901:{\displaystyle R_{\text{g}}}
4628:{\displaystyle T_{\text{c}}}
4330:monomers this simplifies to
3916:{\displaystyle \chi >1/2}
2911:{\displaystyle N_{\text{A}}}
632:for mixing a polymer with a
582:sizes in adapting the usual
7:
4977:Journal of Chemical Physics
4942:Journal of Chemical Physics
4804:which can be estimated as
3019:{\displaystyle \delta _{b}}
2992:{\displaystyle \delta _{a}}
2007:, and we recover the usual
2005:molecular or mole fractions
1695:{\displaystyle k_{\rm {B}}}
1190:of polymer (component
152:Condensation polymerization
118:Free-radical polymerization
113:Chain-growth polymerization
10:
5783:
5666:Acid dissociation constant
4552:{\displaystyle \chi <0}
4526:{\displaystyle N_{B}\gg 1}
4493:{\displaystyle N_{A}\gg 1}
147:Step-growth polymerization
5762:Thermodynamic free energy
5649:
5581:
5511:
5408:
4968:"Solutions of Long Chain
2371:{\displaystyle \phi _{1}}
1756:{\displaystyle \phi _{2}}
1729:{\displaystyle \phi _{1}}
1183:{\displaystyle \phi _{2}}
1101:{\displaystyle \phi _{1}}
1047:The right-hand side is a
639:
5280:10.1088/1361-6633/aaa61e
5116:sites, but only one for
3957:{\displaystyle N^{-1/2}}
3183:{\displaystyle \Delta w}
1516:change (the increase in
5631:Solubility table (data)
5498:Apparent molar property
5077:at constant (external)
4303:monomers and the other
2340:{\displaystyle xN_{2}z}
1314:We first calculate the
1230:to take account of the
1136:), the number of moles
890:The result obtained by
768:{\displaystyle \Delta }
157:Addition polymerization
91:Coil–globule transition
5596:Total dissolved solids
5591:Solubility equilibrium
5516:and related quantities
5091:
5041:
4902:
4868:
4798:
4763:
4743:
4702:
4656:
4629:
4598:
4553:
4527:
4494:
4458:
4324:
4297:
4263:
4225:
4145:
4060:
4025:
3984:
3958:
3917:
3883:
3840:
3706:
3613:
3533:
3457:(in reduced units) is
3447:
3446:{\displaystyle N\gg 1}
3421:
3398:
3290:
3273:
3270:spinodal decomposition
3252:
3246:
3204:
3184:
3158:
3120:
3020:
2993:
2960:
2912:
2882:
2855:
2828:
2801:
2771:
2622:
2526:
2452:
2372:
2341:
2308:
2307:{\displaystyle xN_{2}}
2278:
2255:
2180:
2097:
2096:{\displaystyle w_{12}}
2066:
2065:{\displaystyle w_{22}}
2039:
2038:{\displaystyle w_{11}}
1997:
1974:
1845:
1757:
1730:
1696:
1664:
1499:
1479:
1452:
1422:
1321:, the increase in the
1300:
1272:
1248:
1224:
1204:
1184:
1157:
1130:
1102:
1075:
1038:
869:
831:
769:
746:
646:thermodynamic equation
626:
560:
269:Self-healing hydrogels
32:
5767:Statistical mechanics
5696:Partition coefficient
5676:Polar aprotic solvent
5099:Helmholtz free energy
5092:
5042:
4903:
4869:
4799:
4797:{\displaystyle c^{*}}
4764:
4762:{\displaystyle \chi }
4744:
4703:
4657:
4655:{\displaystyle r_{i}}
4630:
4599:
4554:
4528:
4495:
4459:
4325:
4323:{\displaystyle N_{B}}
4298:
4296:{\displaystyle N_{A}}
4264:
4199:
4125:
4061:
4059:{\displaystyle r_{i}}
4026:
3985:
3959:
3918:
3884:
3841:
3707:
3614:
3534:
3448:
3422:
3420:{\displaystyle \phi }
3399:
3291:
3258:
3247:
3245:{\displaystyle \chi }
3228:
3215:Flory–Krigbaum theory
3205:
3203:{\displaystyle \chi }
3185:
3159:
3121:
3021:
2994:
2961:
2913:
2883:
2881:{\displaystyle n_{2}}
2856:
2854:{\displaystyle n_{1}}
2829:
2827:{\displaystyle N_{2}}
2802:
2800:{\displaystyle N_{1}}
2772:
2623:
2527:
2453:
2373:
2342:
2309:
2279:
2256:
2181:
2098:
2067:
2040:
1998:
1975:
1846:
1758:
1731:
1706:. Define the lattice
1697:
1665:
1500:
1480:
1478:{\displaystyle N_{2}}
1453:
1451:{\displaystyle N_{1}}
1423:
1301:
1299:{\displaystyle \chi }
1273:
1249:
1225:
1223:{\displaystyle \chi }
1205:
1185:
1158:
1156:{\displaystyle n_{2}}
1131:
1103:
1076:
1074:{\displaystyle n_{1}}
1039:
870:
832:
770:
755:A change, denoted by
747:
627:
558:
483:Cookware and bakeware
435:Industrial production
303:X-ray crystallography
31:
5611:Enthalpy of solution
5538:Volume concentration
5533:Number concentration
5081:
5031:
5016:polymer, there is a
4989:We are ignoring the
4885:
4811:
4781:
4753:
4712:
4666:
4639:
4612:
4572:
4537:
4504:
4471:
4337:
4307:
4280:
4073:
4043:
3994:
3968:
3930:
3893:
3853:
3722:
3629:
3550:
3464:
3431:
3411:
3303:
3280:
3236:
3194:
3171:
3133:
3032:
3003:
2976:
2925:
2895:
2888:by transferring the
2865:
2838:
2811:
2784:
2638:
2546:
2474:
2392:
2355:
2318:
2288:
2268:
2196:
2110:
2080:
2049:
2022:
1987:
1865:
1769:
1740:
1713:
1677:
1530:
1489:
1462:
1435:
1383:
1290:
1280:absolute temperature
1262:
1238:
1214:
1194:
1167:
1163:and volume fraction
1140:
1120:
1085:
1081:and volume fraction
1058:
905:
841:
803:
759:
667:
598:
5523:Molar concentration
5493:Dilution (equation)
5314:Soft Matter Physics
5312:Doi, Masao (2013).
5272:2018RPPh...81d6601B
4960:No. 18, May 6, 1985
4860:
3983:{\displaystyle N=1}
456:Protective Coatings
71:Mark–Houwink theory
5563:Isotopic abundance
5528:Mass concentration
5402:Chemical solutions
5338:Schmid, Friederike
5087:
5066:corrected for any
5037:
4974:Maurice L. Huggins
4910:radius of gyration
4898:
4864:
4846:
4794:
4759:
4739:
4698:
4652:
4625:
4594:
4549:
4523:
4490:
4454:
4320:
4293:
4259:
4056:
4021:
3980:
3954:
3913:
3879:
3836:
3702:
3609:
3529:
3443:
3417:
3394:
3286:
3274:
3253:
3242:
3200:
3180:
3154:
3116:
3016:
2989:
2956:
2908:
2878:
2851:
2824:
2797:
2767:
2618:
2522:
2448:
2368:
2337:
2304:
2274:
2251:
2176:
2145:
2093:
2062:
2045:, monomer-monomer
2035:
1993:
1970:
1841:
1753:
1726:
1704:Boltzmann constant
1692:
1660:
1653:
1610:
1495:
1475:
1448:
1418:
1335:thought experiment
1296:
1268:
1244:
1220:
1200:
1180:
1153:
1126:
1098:
1071:
1034:
865:
827:
765:
742:
622:
561:
33:
5752:Polymer chemistry
5739:
5738:
5266:(46601): 046601.
5208:978-1-56676-623-4
5181:978-1-4757-9661-2
5153:978-1-4757-9661-2
5090:{\displaystyle P}
5040:{\displaystyle x}
4895:
4862:
4853:
4841:
4722:
4622:
4407:
4370:
4197:
4168:
4004:
3787:
3732:
3700:
3666:
3598:
3577:
3481:
3320:
3289:{\displaystyle N}
3259:Schematic of the
3114:
2953:
2905:
2890:Avogadro constant
2537:material-specific
2520:
2380:mean field theory
2277:{\displaystyle z}
2144:
2009:entropy of mixing
1996:{\displaystyle x}
1839:
1800:
1652:
1609:
1498:{\displaystyle x}
1347:entropy of mixing
1271:{\displaystyle T}
1247:{\displaystyle R}
1203:{\displaystyle 2}
1129:{\displaystyle 1}
1051:of the number of
592:Gibbs free energy
588:entropy of mixing
576:polymer solutions
553:
552:
466:Consumer products
5774:
5636:Solubility chart
5463:Phase separation
5423:Aqueous solution
5395:
5388:
5381:
5372:
5371:
5352:
5351:
5349:
5334:
5328:
5327:
5309:
5300:
5299:
5255:
5249:
5248:
5222:
5213:
5212:
5192:
5186:
5185:
5167:
5158:
5157:
5139:
5107:
5096:
5094:
5093:
5088:
5057:
5046:
5044:
5043:
5038:
5011:
4988:
4967:
4958:Citation Classic
4925:
4907:
4905:
4904:
4899:
4897:
4896:
4893:
4873:
4871:
4870:
4865:
4863:
4861:
4859:
4854:
4851:
4842:
4834:
4828:
4823:
4822:
4803:
4801:
4800:
4795:
4793:
4792:
4768:
4766:
4765:
4760:
4748:
4746:
4745:
4740:
4735:
4724:
4723:
4720:
4707:
4705:
4704:
4699:
4694:
4693:
4681:
4680:
4661:
4659:
4658:
4653:
4651:
4650:
4635:on chain length
4634:
4632:
4631:
4626:
4624:
4623:
4620:
4603:
4601:
4600:
4595:
4593:
4592:
4568:immiscible, the
4558:
4556:
4555:
4550:
4532:
4530:
4529:
4524:
4516:
4515:
4499:
4497:
4496:
4491:
4483:
4482:
4463:
4461:
4460:
4455:
4408:
4406:
4405:
4396:
4385:
4371:
4369:
4368:
4356:
4329:
4327:
4326:
4321:
4319:
4318:
4302:
4300:
4299:
4294:
4292:
4291:
4268:
4266:
4265:
4260:
4258:
4257:
4245:
4244:
4235:
4234:
4224:
4219:
4198:
4190:
4185:
4184:
4169:
4167:
4166:
4157:
4156:
4147:
4144:
4139:
4121:
4120:
4111:
4110:
4098:
4097:
4085:
4084:
4065:
4063:
4062:
4057:
4055:
4054:
4030:
4028:
4027:
4022:
4017:
4006:
4005:
4002:
3989:
3987:
3986:
3981:
3963:
3961:
3960:
3955:
3953:
3952:
3948:
3922:
3920:
3919:
3914:
3909:
3888:
3886:
3885:
3880:
3875:
3845:
3843:
3842:
3837:
3829:
3828:
3813:
3812:
3808:
3789:
3788:
3785:
3772:
3771:
3767:
3745:
3734:
3733:
3730:
3711:
3709:
3708:
3703:
3701:
3699:
3698:
3697:
3672:
3667:
3665:
3664:
3663:
3647:
3639:
3618:
3616:
3615:
3610:
3599:
3597:
3583:
3578:
3576:
3565:
3560:
3538:
3536:
3535:
3530:
3528:
3527:
3482:
3474:
3455:osmotic pressure
3452:
3450:
3449:
3444:
3426:
3424:
3423:
3418:
3403:
3401:
3400:
3395:
3321:
3313:
3295:
3293:
3292:
3287:
3251:
3249:
3248:
3243:
3230:Osmotic pressure
3209:
3207:
3206:
3201:
3189:
3187:
3186:
3181:
3163:
3161:
3160:
3155:
3153:
3152:
3151:
3125:
3123:
3122:
3117:
3115:
3113:
3105:
3104:
3103:
3094:
3093:
3081:
3080:
3068:
3067:
3066:
3049:
3044:
3043:
3025:
3023:
3022:
3017:
3015:
3014:
2998:
2996:
2995:
2990:
2988:
2987:
2965:
2963:
2962:
2957:
2955:
2954:
2951:
2945:
2944:
2943:
2917:
2915:
2914:
2909:
2907:
2906:
2903:
2887:
2885:
2884:
2879:
2877:
2876:
2860:
2858:
2857:
2852:
2850:
2849:
2833:
2831:
2830:
2825:
2823:
2822:
2806:
2804:
2803:
2798:
2796:
2795:
2776:
2774:
2773:
2768:
2762:
2761:
2752:
2751:
2742:
2741:
2729:
2728:
2713:
2712:
2700:
2699:
2684:
2683:
2661:
2660:
2659:
2627:
2625:
2624:
2619:
2617:
2616:
2607:
2606:
2597:
2596:
2584:
2583:
2582:
2569:
2568:
2567:
2531:
2529:
2528:
2523:
2521:
2519:
2515:
2514:
2513:
2502:
2491:
2486:
2485:
2457:
2455:
2454:
2449:
2438:
2437:
2428:
2427:
2415:
2414:
2413:
2377:
2375:
2374:
2369:
2367:
2366:
2346:
2344:
2343:
2338:
2333:
2332:
2313:
2311:
2310:
2305:
2303:
2302:
2283:
2281:
2280:
2275:
2260:
2258:
2257:
2252:
2247:
2246:
2237:
2236:
2224:
2223:
2211:
2210:
2185:
2183:
2182:
2177:
2172:
2171:
2159:
2158:
2146:
2137:
2131:
2130:
2102:
2100:
2099:
2094:
2092:
2091:
2074:covalent bonding
2071:
2069:
2068:
2063:
2061:
2060:
2044:
2042:
2041:
2036:
2034:
2033:
2002:
2000:
1999:
1994:
1979:
1977:
1976:
1971:
1965:
1964:
1949:
1948:
1936:
1935:
1920:
1919:
1906:
1905:
1904:
1888:
1887:
1886:
1850:
1848:
1847:
1842:
1840:
1835:
1834:
1833:
1820:
1815:
1814:
1801:
1796:
1795:
1786:
1781:
1780:
1762:
1760:
1759:
1754:
1752:
1751:
1735:
1733:
1732:
1727:
1725:
1724:
1708:volume fractions
1701:
1699:
1698:
1693:
1691:
1690:
1689:
1669:
1667:
1666:
1661:
1659:
1655:
1654:
1648:
1647:
1646:
1633:
1624:
1623:
1611:
1605:
1604:
1595:
1586:
1585:
1571:
1570:
1569:
1553:
1552:
1551:
1504:
1502:
1501:
1496:
1484:
1482:
1481:
1476:
1474:
1473:
1457:
1455:
1454:
1449:
1447:
1446:
1427:
1425:
1424:
1419:
1417:
1416:
1401:
1400:
1305:
1303:
1302:
1297:
1277:
1275:
1274:
1269:
1253:
1251:
1250:
1245:
1229:
1227:
1226:
1221:
1209:
1207:
1206:
1201:
1189:
1187:
1186:
1181:
1179:
1178:
1162:
1160:
1159:
1154:
1152:
1151:
1135:
1133:
1132:
1127:
1107:
1105:
1104:
1099:
1097:
1096:
1080:
1078:
1077:
1072:
1070:
1069:
1043:
1041:
1040:
1035:
1029:
1028:
1019:
1018:
1009:
1008:
996:
995:
980:
979:
967:
966:
951:
950:
928:
927:
926:
874:
872:
871:
866:
864:
863:
862:
836:
834:
833:
828:
826:
825:
824:
774:
772:
771:
766:
751:
749:
748:
743:
741:
740:
739:
714:
713:
712:
690:
689:
688:
631:
629:
628:
623:
621:
620:
619:
545:
538:
531:
449:Applied coatings
286:Characterization
19:
18:
5782:
5781:
5777:
5776:
5775:
5773:
5772:
5771:
5742:
5741:
5740:
5735:
5645:
5606:Solvation shell
5577:
5515:
5507:
5503:Miscibility gap
5488:Serial dilution
5483:Supersaturation
5433:Buffer solution
5404:
5399:
5361:
5356:
5355:
5335:
5331:
5324:
5310:
5303:
5256:
5252:
5237:
5223:
5216:
5209:
5193:
5189:
5182:
5168:
5161:
5154:
5140:
5133:
5128:
5123:
5082:
5079:
5078:
5064:internal energy
5032:
5029:
5028:
4918:
4908:is the chain's
4892:
4888:
4886:
4883:
4882:
4855:
4850:
4833:
4832:
4827:
4818:
4814:
4812:
4809:
4808:
4788:
4784:
4782:
4779:
4778:
4754:
4751:
4750:
4731:
4719:
4715:
4713:
4710:
4709:
4689:
4685:
4676:
4672:
4667:
4664:
4663:
4646:
4642:
4640:
4637:
4636:
4619:
4615:
4613:
4610:
4609:
4585:
4581:
4573:
4570:
4569:
4565:
4538:
4535:
4534:
4511:
4507:
4505:
4502:
4501:
4478:
4474:
4472:
4469:
4468:
4401:
4397:
4386:
4384:
4364:
4360:
4355:
4338:
4335:
4334:
4314:
4310:
4308:
4305:
4304:
4287:
4283:
4281:
4278:
4277:
4250:
4246:
4240:
4236:
4230:
4226:
4220:
4203:
4189:
4180:
4176:
4162:
4158:
4152:
4148:
4146:
4140:
4129:
4116:
4115:
4106:
4102:
4093:
4089:
4080:
4079:
4074:
4071:
4070:
4050:
4046:
4044:
4041:
4040:
4037:
4013:
4001:
3997:
3995:
3992:
3991:
3969:
3966:
3965:
3944:
3937:
3933:
3931:
3928:
3927:
3905:
3894:
3891:
3890:
3871:
3854:
3851:
3850:
3821:
3817:
3804:
3797:
3793:
3784:
3780:
3763:
3756:
3752:
3741:
3729:
3725:
3723:
3720:
3719:
3693:
3689:
3676:
3671:
3659:
3655:
3651:
3646:
3632:
3630:
3627:
3626:
3587:
3582:
3569:
3564:
3553:
3551:
3548:
3547:
3523:
3519:
3473:
3465:
3462:
3461:
3432:
3429:
3428:
3412:
3409:
3408:
3312:
3304:
3301:
3300:
3281:
3278:
3277:
3237:
3234:
3233:
3223:
3195:
3192:
3191:
3172:
3169:
3168:
3141:
3140:
3136:
3134:
3131:
3130:
3106:
3099:
3095:
3089:
3085:
3076:
3072:
3056:
3055:
3051:
3050:
3048:
3039:
3035:
3033:
3030:
3029:
3010:
3006:
3004:
3001:
3000:
2983:
2979:
2977:
2974:
2973:
2950:
2946:
2939:
2938:
2934:
2926:
2923:
2922:
2902:
2898:
2896:
2893:
2892:
2872:
2868:
2866:
2863:
2862:
2845:
2841:
2839:
2836:
2835:
2818:
2814:
2812:
2809:
2808:
2791:
2787:
2785:
2782:
2781:
2757:
2753:
2747:
2743:
2737:
2733:
2724:
2720:
2708:
2704:
2695:
2691:
2679:
2675:
2649:
2648:
2644:
2639:
2636:
2635:
2612:
2608:
2602:
2598:
2592:
2588:
2578:
2577:
2573:
2557:
2556:
2552:
2547:
2544:
2543:
2509:
2508:
2504:
2503:
2492:
2490:
2481:
2477:
2475:
2472:
2471:
2433:
2429:
2423:
2419:
2403:
2402:
2398:
2393:
2390:
2389:
2362:
2358:
2356:
2353:
2352:
2328:
2324:
2319:
2316:
2315:
2298:
2294:
2289:
2286:
2285:
2269:
2266:
2265:
2242:
2238:
2232:
2228:
2219:
2215:
2206:
2202:
2197:
2194:
2193:
2167:
2163:
2154:
2150:
2135:
2126:
2122:
2111:
2108:
2107:
2087:
2083:
2081:
2078:
2077:
2056:
2052:
2050:
2047:
2046:
2029:
2025:
2023:
2020:
2019:
1988:
1985:
1984:
1960:
1956:
1944:
1940:
1931:
1927:
1915:
1911:
1900:
1899:
1895:
1876:
1875:
1871:
1866:
1863:
1862:
1829:
1825:
1821:
1819:
1810:
1806:
1791:
1787:
1785:
1776:
1772:
1770:
1767:
1766:
1747:
1743:
1741:
1738:
1737:
1720:
1716:
1714:
1711:
1710:
1685:
1684:
1680:
1678:
1675:
1674:
1642:
1638:
1634:
1631:
1619:
1615:
1600:
1596:
1593:
1581:
1577:
1576:
1572:
1565:
1564:
1560:
1541:
1540:
1536:
1531:
1528:
1527:
1490:
1487:
1486:
1469:
1465:
1463:
1460:
1459:
1442:
1438:
1436:
1433:
1432:
1412:
1408:
1396:
1392:
1384:
1381:
1380:
1312:
1291:
1288:
1287:
1263:
1260:
1259:
1239:
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1195:
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1174:
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1147:
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1121:
1118:
1117:
1092:
1088:
1086:
1083:
1082:
1065:
1061:
1059:
1056:
1055:
1024:
1020:
1014:
1010:
1004:
1000:
991:
987:
975:
971:
962:
958:
946:
942:
916:
915:
911:
906:
903:
902:
852:
851:
847:
842:
839:
838:
814:
813:
809:
804:
801:
800:
760:
757:
756:
729:
728:
724:
702:
701:
697:
678:
677:
673:
668:
665:
664:
656:and (external)
642:
609:
608:
604:
599:
596:
595:
549:
520:
519:
431:
423:
422:
353:
345:
344:
288:
278:
277:
195:Polyisobutylene
176:Functional type
172:
162:
161:
108:
98:
97:
41:
22:Polymer science
17:
12:
11:
5:
5780:
5770:
5769:
5764:
5759:
5754:
5737:
5736:
5734:
5733:
5728:
5723:
5718:
5713:
5708:
5703:
5698:
5693:
5688:
5683:
5678:
5673:
5671:Protic solvent
5668:
5663:
5655:
5653:
5647:
5646:
5644:
5643:
5638:
5633:
5628:
5623:
5618:
5616:Lattice energy
5613:
5608:
5603:
5598:
5593:
5587:
5585:
5579:
5578:
5576:
5575:
5570:
5565:
5560:
5555:
5550:
5545:
5540:
5535:
5530:
5525:
5519:
5517:
5509:
5508:
5506:
5505:
5500:
5495:
5490:
5485:
5480:
5475:
5470:
5468:Eutectic point
5465:
5460:
5455:
5450:
5445:
5440:
5435:
5430:
5428:Solid solution
5425:
5420:
5418:Ideal solution
5414:
5412:
5406:
5405:
5398:
5397:
5390:
5383:
5375:
5369:
5368:
5360:
5359:External links
5357:
5354:
5353:
5329:
5322:
5301:
5250:
5235:
5214:
5207:
5187:
5180:
5159:
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5127:
5124:
5122:
5121:
5102:
5086:
5052:
5036:
5006:
4983:
4962:
4955::51-61 (1942)
4950:J. Chem. Phys.
4928:Thermodynamics
4919:
4917:
4914:
4891:
4875:
4874:
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4109:
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4088:
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4053:
4049:
4036:
4035:Polymer blends
4033:
4020:
4016:
4012:
4009:
4000:
3979:
3976:
3973:
3951:
3947:
3943:
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3390:
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3384:
3381:
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3375:
3372:
3369:
3366:
3363:
3360:
3357:
3354:
3351:
3348:
3345:
3342:
3339:
3336:
3333:
3330:
3327:
3324:
3319:
3316:
3311:
3308:
3285:
3241:
3222:
3219:
3199:
3179:
3176:
3150:
3147:
3144:
3139:
3127:
3126:
3112:
3109:
3102:
3098:
3092:
3088:
3084:
3079:
3075:
3071:
3065:
3062:
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2551:
2533:
2532:
2518:
2512:
2507:
2501:
2498:
2495:
2489:
2484:
2480:
2467:is defined as
2459:
2458:
2447:
2444:
2441:
2436:
2432:
2426:
2422:
2418:
2412:
2409:
2406:
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2397:
2365:
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2331:
2327:
2323:
2301:
2297:
2293:
2273:
2262:
2261:
2250:
2245:
2241:
2235:
2231:
2227:
2222:
2218:
2214:
2209:
2205:
2201:
2187:
2186:
2175:
2170:
2166:
2162:
2157:
2153:
2149:
2143:
2140:
2134:
2129:
2125:
2121:
2118:
2115:
2090:
2086:
2059:
2055:
2032:
2028:
1992:
1981:
1980:
1969:
1963:
1959:
1955:
1952:
1947:
1943:
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1934:
1930:
1926:
1923:
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1779:
1775:
1750:
1746:
1723:
1719:
1688:
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1671:
1670:
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1651:
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1637:
1630:
1627:
1622:
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1614:
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1599:
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1575:
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1559:
1556:
1550:
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1539:
1535:
1494:
1472:
1468:
1445:
1441:
1429:
1428:
1415:
1411:
1407:
1404:
1399:
1395:
1391:
1388:
1359:macromolecular
1351:mole fractions
1311:
1308:
1295:
1267:
1243:
1219:
1199:
1177:
1173:
1150:
1146:
1125:
1095:
1091:
1068:
1064:
1045:
1044:
1033:
1027:
1023:
1017:
1013:
1007:
1003:
999:
994:
990:
986:
983:
978:
974:
970:
965:
961:
957:
954:
949:
945:
940:
937:
934:
931:
925:
922:
919:
914:
910:
861:
858:
855:
850:
846:
823:
820:
817:
812:
808:
764:
753:
752:
738:
735:
732:
727:
723:
720:
717:
711:
708:
705:
700:
696:
693:
687:
684:
681:
676:
672:
641:
638:
618:
615:
612:
607:
603:
572:thermodynamics
551:
550:
548:
547:
540:
533:
525:
522:
521:
518:
517:
512:
510:Plastic bottle
507:
502:
497:
496:
495:
493:Food Container
490:
480:
479:
478:
468:
463:
458:
453:
452:
451:
446:
436:
432:
429:
428:
425:
424:
421:
420:
415:
410:
405:
400:
395:
390:
385:
380:
375:
370:
365:
360:
354:
351:
350:
347:
346:
343:
342:
341:
340:
335:
325:
320:
315:
310:
305:
300:
295:
289:
284:
283:
280:
279:
276:
275:
274:
273:
272:
271:
256:
251:
246:
242:
241:
240:
239:
234:
229:
224:
217:Vinyl polymers
214:
209:
204:
199:
198:
197:
192:
187:
177:
173:
170:Classification
168:
167:
164:
163:
160:
159:
154:
149:
143:
142:
141:
140:
135:
130:
120:
115:
109:
104:
103:
100:
99:
96:
95:
94:
93:
88:
83:
78:
73:
66:Phase behavior
63:
58:
53:
48:
42:
39:
38:
35:
34:
24:
23:
15:
9:
6:
4:
3:
2:
5779:
5768:
5765:
5763:
5760:
5758:
5755:
5753:
5750:
5749:
5747:
5732:
5729:
5727:
5724:
5722:
5719:
5717:
5714:
5712:
5709:
5707:
5704:
5702:
5699:
5697:
5694:
5692:
5689:
5687:
5684:
5682:
5679:
5677:
5674:
5672:
5669:
5667:
5664:
5661:
5657:
5656:
5654:
5652:
5648:
5642:
5639:
5637:
5634:
5632:
5629:
5627:
5624:
5622:
5619:
5617:
5614:
5612:
5609:
5607:
5604:
5602:
5599:
5597:
5594:
5592:
5589:
5588:
5586:
5584:
5580:
5574:
5571:
5569:
5566:
5564:
5561:
5559:
5558:Mass fraction
5556:
5554:
5553:Mole fraction
5551:
5549:
5546:
5544:
5541:
5539:
5536:
5534:
5531:
5529:
5526:
5524:
5521:
5520:
5518:
5514:
5513:Concentration
5510:
5504:
5501:
5499:
5496:
5494:
5491:
5489:
5486:
5484:
5481:
5479:
5476:
5474:
5471:
5469:
5466:
5464:
5461:
5459:
5458:Phase diagram
5456:
5454:
5451:
5449:
5446:
5444:
5441:
5439:
5438:Flory–Huggins
5436:
5434:
5431:
5429:
5426:
5424:
5421:
5419:
5416:
5415:
5413:
5411:
5407:
5403:
5396:
5391:
5389:
5384:
5382:
5377:
5376:
5373:
5366:
5363:
5362:
5348:
5343:
5339:
5333:
5325:
5323:9780199652952
5319:
5315:
5308:
5306:
5297:
5293:
5289:
5285:
5281:
5277:
5273:
5269:
5265:
5261:
5254:
5246:
5242:
5238:
5232:
5228:
5221:
5219:
5210:
5204:
5200:
5199:
5191:
5183:
5177:
5173:
5166:
5164:
5155:
5149:
5145:
5138:
5136:
5131:
5119:
5115:
5111:
5106:
5103:
5100:
5084:
5076:
5073:
5069:
5065:
5061:
5056:
5053:
5050:
5034:
5026:
5022:
5019:
5015:
5010:
5007:
5004:
5000:
4996:
4992:
4987:
4984:
4982:
4978:
4975:
4971:
4966:
4963:
4961:
4959:
4954:
4951:
4947:
4943:
4940:
4939:Paul J. Flory
4936:
4933:
4929:
4924:
4921:
4920:
4913:
4911:
4889:
4880:
4856:
4847:
4843:
4838:
4835:
4829:
4824:
4819:
4815:
4807:
4806:
4805:
4789:
4785:
4774:
4772:
4756:
4736:
4732:
4728:
4725:
4716:
4690:
4686:
4682:
4677:
4673:
4647:
4643:
4616:
4607:
4589:
4586:
4582:
4578:
4575:
4560:
4546:
4543:
4540:
4520:
4517:
4512:
4508:
4487:
4484:
4479:
4475:
4448:
4445:
4442:
4436:
4433:
4430:
4424:
4421:
4418:
4412:
4409:
4402:
4398:
4393:
4390:
4387:
4381:
4378:
4375:
4372:
4365:
4361:
4357:
4352:
4346:
4340:
4333:
4332:
4331:
4315:
4311:
4288:
4284:
4275:
4274:polymer blend
4272:For a binary
4254:
4251:
4247:
4241:
4237:
4231:
4227:
4221:
4216:
4213:
4210:
4207:
4204:
4200:
4194:
4191:
4186:
4181:
4177:
4173:
4170:
4163:
4159:
4153:
4149:
4141:
4136:
4133:
4130:
4126:
4122:
4107:
4103:
4099:
4094:
4090:
4076:
4069:
4068:
4067:
4051:
4047:
4032:
4018:
4014:
4010:
4007:
3998:
3977:
3974:
3971:
3949:
3945:
3941:
3938:
3934:
3924:
3910:
3906:
3902:
3899:
3896:
3876:
3872:
3868:
3865:
3862:
3859:
3856:
3833:
3830:
3825:
3822:
3818:
3814:
3809:
3805:
3801:
3798:
3794:
3790:
3781:
3776:
3773:
3768:
3764:
3760:
3757:
3753:
3749:
3746:
3742:
3738:
3735:
3726:
3718:
3717:
3716:
3694:
3686:
3683:
3680:
3673:
3668:
3660:
3656:
3652:
3648:
3643:
3640:
3636:
3633:
3625:
3624:
3623:
3606:
3603:
3600:
3594:
3591:
3588:
3584:
3579:
3573:
3570:
3566:
3561:
3557:
3554:
3546:
3545:
3544:
3524:
3520:
3516:
3513:
3510:
3507:
3501:
3498:
3495:
3489:
3486:
3483:
3478:
3475:
3470:
3460:
3459:
3458:
3456:
3440:
3437:
3434:
3414:
3388:
3385:
3382:
3376:
3373:
3370:
3364:
3361:
3358:
3352:
3349:
3343:
3340:
3337:
3331:
3328:
3325:
3322:
3317:
3314:
3309:
3306:
3299:
3298:
3297:
3283:
3271:
3266:
3262:
3257:
3239:
3231:
3227:
3218:
3216:
3211:
3197:
3177:
3165:
3137:
3110:
3107:
3100:
3090:
3086:
3082:
3077:
3073:
3052:
3045:
3040:
3036:
3028:
3027:
3026:
3011:
3007:
2984:
2980:
2972:
2967:
2947:
2935:
2931:
2928:
2921:
2899:
2891:
2873:
2869:
2846:
2842:
2819:
2815:
2792:
2788:
2758:
2754:
2748:
2744:
2738:
2734:
2730:
2725:
2721:
2717:
2714:
2709:
2705:
2701:
2696:
2692:
2688:
2685:
2680:
2676:
2668:
2665:
2662:
2645:
2634:
2633:
2632:
2613:
2609:
2603:
2599:
2593:
2589:
2585:
2574:
2570:
2553:
2542:
2541:
2540:
2538:
2516:
2505:
2499:
2493:
2487:
2482:
2478:
2470:
2469:
2468:
2466:
2465:
2445:
2439:
2434:
2430:
2424:
2420:
2416:
2399:
2388:
2387:
2386:
2383:
2381:
2363:
2359:
2350:
2334:
2329:
2325:
2321:
2299:
2295:
2291:
2271:
2248:
2243:
2239:
2233:
2229:
2225:
2220:
2216:
2212:
2207:
2203:
2199:
2192:
2191:
2190:
2168:
2164:
2160:
2155:
2151:
2141:
2138:
2132:
2127:
2123:
2119:
2116:
2106:
2105:
2104:
2088:
2084:
2075:
2057:
2053:
2030:
2026:
2017:
2012:
2010:
2006:
1990:
1961:
1957:
1953:
1950:
1945:
1941:
1937:
1932:
1928:
1924:
1921:
1916:
1912:
1896:
1892:
1889:
1872:
1861:
1860:
1859:
1857:
1836:
1830:
1826:
1822:
1816:
1811:
1807:
1802:
1797:
1792:
1788:
1782:
1777:
1773:
1765:
1764:
1763:
1748:
1744:
1721:
1717:
1709:
1705:
1681:
1656:
1649:
1643:
1639:
1635:
1628:
1625:
1620:
1616:
1612:
1606:
1601:
1597:
1590:
1587:
1582:
1578:
1573:
1561:
1557:
1554:
1537:
1526:
1525:
1524:
1522:
1519:
1515:
1511:
1506:
1492:
1470:
1466:
1443:
1439:
1413:
1409:
1405:
1402:
1397:
1393:
1389:
1386:
1379:
1378:
1377:
1375:
1371:
1367:
1363:
1360:
1356:
1352:
1348:
1344:
1340:
1336:
1332:
1328:
1324:
1320:
1318:
1307:
1293:
1285:
1284:mole fraction
1281:
1265:
1257:
1241:
1233:
1217:
1197:
1175:
1171:
1148:
1144:
1123:
1115:
1111:
1093:
1089:
1066:
1062:
1054:
1050:
1025:
1021:
1015:
1011:
1005:
1001:
997:
992:
988:
984:
981:
976:
972:
968:
963:
959:
955:
952:
947:
943:
935:
932:
929:
912:
901:
900:
899:
897:
893:
888:
886:
882:
878:
848:
810:
798:
794:
790:
786:
782:
778:
725:
718:
715:
698:
691:
674:
663:
662:
661:
659:
655:
651:
647:
637:
635:
605:
593:
589:
585:
581:
577:
573:
569:
568:lattice model
565:
557:
546:
541:
539:
534:
532:
527:
526:
524:
523:
516:
513:
511:
508:
506:
503:
501:
498:
494:
491:
489:
486:
485:
484:
481:
477:
474:
473:
472:
469:
467:
464:
462:
459:
457:
454:
450:
447:
445:
442:
441:
440:
437:
434:
433:
427:
426:
419:
416:
414:
411:
409:
406:
404:
401:
399:
396:
394:
391:
389:
386:
384:
381:
379:
376:
374:
371:
369:
366:
364:
361:
359:
356:
355:
349:
348:
339:
336:
334:
331:
330:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
304:
301:
299:
296:
294:
291:
290:
287:
282:
281:
270:
267:
266:
265:
262:
261:
260:
257:
255:
252:
250:
247:
244:
243:
238:
235:
233:
230:
228:
225:
223:
220:
219:
218:
215:
213:
212:Polycarbonate
210:
208:
205:
203:
200:
196:
193:
191:
190:Polypropylene
188:
186:
183:
182:
181:
178:
175:
174:
171:
166:
165:
158:
155:
153:
150:
148:
145:
144:
139:
136:
134:
131:
129:
126:
125:
124:
121:
119:
116:
114:
111:
110:
107:
102:
101:
92:
89:
87:
84:
82:
79:
77:
74:
72:
69:
68:
67:
64:
62:
59:
57:
54:
52:
49:
47:
44:
43:
37:
36:
30:
26:
25:
21:
20:
5621:Raoult's law
5573:Ternary plot
5568:Mixing ratio
5437:
5332:
5313:
5263:
5259:
5253:
5226:
5197:
5190:
5171:
5143:
5105:
5055:
5047:would be an
5027:lengths, so
5021:distribution
5009:
5002:
4990:
4986:
4976:
4965:
4957:
4952:
4949:
4941:
4923:
4878:
4876:
4775:
4566:
4466:
4271:
4038:
3925:
3848:
3714:
3621:
3542:
3406:
3275:
3212:
3166:
3128:
2968:
2920:gas constant
2779:
2630:
2536:
2534:
2463:
2460:
2384:
2348:
2263:
2188:
2015:
2013:
1982:
1853:
1707:
1672:
1507:
1430:
1316:
1313:
1256:gas constant
1046:
889:
754:
650:Gibbs energy
643:
563:
562:
500:Vinyl record
444:Blow molding
430:Applications
202:Polyurethane
185:Polyethylene
85:
46:Architecture
5726:Lyonium ion
5641:Miscibility
5626:Henry's law
5018:statistical
5012:For a real
4991:free volume
4771:temperature
4563:Limitations
3990:, and then
1521:uncertainty
1510:random walk
1323:uncertainty
654:temperature
515:Plastic bag
461:3D printing
249:Homopolymer
237:Polystyrene
61:Degradation
5746:Categories
5721:Amphiphile
5716:Lipophilic
5711:Hydrophile
5706:Hydrophobe
5583:Solubility
5478:Saturation
5448:Suspension
5236:080141203X
5126:References
1505:segments.
1343:expression
1310:Derivation
793:components
584:expression
476:Whitewalls
398:Staudinger
368:MacDiarmid
352:Scientists
338:Viscometry
180:Polyolefin
56:Morphology
40:Properties
5757:Solutions
5731:Lyate ion
5686:Solvation
5601:Solvation
5543:Normality
5347:1001.1265
5118:terminals
5114:branching
5014:synthetic
5003:geometric
4970:Compounds
4935:Solutions
4916:Footnotes
4844:π
4820:∗
4790:∗
4757:χ
4717:ψ
4587:−
4579:∝
4576:χ
4541:χ
4518:≫
4485:≫
4449:ϕ
4446:−
4437:ϕ
4434:χ
4425:ϕ
4422:−
4413:
4394:ϕ
4391:−
4379:ϕ
4376:
4358:ϕ
4347:ϕ
4248:χ
4238:ϕ
4228:ϕ
4201:∑
4178:ϕ
4174:
4150:ϕ
4127:∑
4091:ϕ
3999:ϕ
3939:−
3897:χ
3866:≲
3863:χ
3834:⋯
3823:−
3815:−
3799:−
3791:≃
3782:ϕ
3777:⋯
3758:−
3736:≃
3727:χ
3687:ϕ
3684:−
3657:ϕ
3644:−
3607:χ
3601:−
3595:ϕ
3592:−
3574:ϕ
3521:ϕ
3517:χ
3514:−
3511:ϕ
3508:−
3502:ϕ
3499:−
3490:
3484:−
3476:ϕ
3468:Π
3438:≫
3415:ϕ
3389:ϕ
3386:−
3377:ϕ
3374:χ
3365:ϕ
3362:−
3353:
3344:ϕ
3341:−
3329:ϕ
3326:
3315:ϕ
3240:χ
3198:χ
3175:Δ
3087:δ
3083:−
3074:δ
3037:χ
3008:δ
2981:δ
2834:to moles
2755:χ
2745:ϕ
2722:ϕ
2718:
2693:ϕ
2689:
2642:Δ
2610:χ
2600:ϕ
2550:Δ
2497:Δ
2479:χ
2443:Δ
2431:ϕ
2396:Δ
2360:ϕ
2240:ϕ
2217:ϕ
2133:−
2114:Δ
2072:(not the
1958:ϕ
1954:
1929:ϕ
1925:
1893:−
1869:Δ
1808:ϕ
1774:ϕ
1745:ϕ
1718:ϕ
1629:
1591:
1558:−
1534:Δ
1319:of mixing
1294:χ
1218:χ
1172:ϕ
1114:component
1090:ϕ
1022:χ
1012:ϕ
989:ϕ
985:
960:ϕ
956:
909:Δ
845:Δ
807:Δ
775:, is the
763:Δ
722:Δ
716:−
695:Δ
671:Δ
602:Δ
580:molecular
439:Extrusion
418:Braconnot
408:Baekeland
388:de Gennes
373:Shirakawa
333:Rheometry
264:Hydrogels
254:Copolymer
245:Structure
207:Polyester
106:Synthesis
51:Tacticity
5701:Polarity
5660:Category
5548:Molality
5410:Solution
5288:29313527
5068:pressure
5060:enthalpy
4999:monomers
4995:crystals
4981:Abstract
4946:Abstract
4930:of High
3637:‴
3558:″
3265:spinodal
2016:enthalpy
1366:symmetry
1345:for the
1049:function
877:enthalpy
797:formulas
785:solution
781:variable
658:pressure
648:for the
586:for the
488:Bakelite
403:Goodyear
328:Rheology
5651:Solvent
5453:Colloid
5443:Mixture
5296:4039711
5268:Bibcode
5245:4494721
5062:is the
5049:average
4932:Polymer
3272:occurs.
3261:binodal
2918:to the
1702:is the
1518:spatial
1514:entropy
1374:monomer
1370:lattice
1339:spatial
1331:solvent
1317:entropy
1278:is the
1254:is the
1110:solvent
896:Huggins
885:process
881:entropy
789:mixture
634:solvent
594:change
570:of the
413:Hayward
393:Ziegler
383:Edwards
5320:
5294:
5286:
5243:
5233:
5205:
5178:
5150:
5072:volume
4877:Here,
3453:. The
3129:where
2264:where
1856:random
1673:where
1508:For a
1431:where
1355:solute
1327:phases
1232:energy
1116:
875:, the
783:for a
640:Theory
505:Kevlar
363:Heeger
5473:Alloy
5342:arXiv
5292:S2CID
5110:chain
5025:chain
1362:chain
1357:is a
1053:moles
892:Flory
779:of a
777:value
566:is a
471:Tires
378:Natta
358:Flory
5318:ISBN
5284:PMID
5241:OCLC
5231:ISBN
5203:ISBN
5176:ISBN
5148:ISBN
5075:work
5058:The
4544:<
4500:and
3900:>
3860:<
3407:for
3263:and
2999:and
2861:and
2807:and
1736:and
1258:and
894:and
879:and
837:and
799:for
644:The
298:FTIR
259:Gels
232:PVAc
133:RAFT
128:ATRP
81:LCST
76:UCST
5276:doi
5023:of
4972:",
4937:",
4066:by
2464:chi
2349:all
1108:of
898:is
787:or
660:is
574:of
323:DMA
318:TGA
313:NMR
308:DSC
293:GPC
227:PVA
222:PVC
5748::
5304:^
5290:.
5282:.
5274:.
5264:81
5262:.
5239:.
5217:^
5162:^
5134:^
4953:10
4912:.
4410:ln
4373:ln
4171:ln
4003:cp
3786:cp
3731:cp
3487:ln
3350:ln
3323:ln
3217:.
3041:12
2966:.
2759:12
2715:ln
2686:ln
2614:12
2483:12
2169:11
2156:22
2128:12
2089:12
2058:22
2031:11
2011:.
1951:ln
1922:ln
1626:ln
1588:ln
1329:–
1026:12
982:ln
953:ln
887:.
5662:)
5658:(
5394:e
5387:t
5380:v
5350:.
5344::
5326:.
5298:.
5278::
5270::
5247:.
5211:.
5184:.
5156:.
5120:.
5085:P
5070:-
5051:.
5035:x
4926:"
4894:g
4890:R
4879:m
4857:3
4852:g
4848:R
4839:3
4836:4
4830:m
4825:=
4816:c
4786:c
4737:2
4733:/
4729:1
4726:=
4721:c
4696:)
4691:B
4687:N
4683:=
4678:A
4674:N
4670:(
4648:i
4644:r
4621:c
4617:T
4590:1
4583:T
4547:0
4521:1
4513:B
4509:N
4488:1
4480:A
4476:N
4452:)
4443:1
4440:(
4431:+
4428:)
4419:1
4416:(
4403:B
4399:N
4388:1
4382:+
4366:A
4362:N
4353:=
4350:)
4344:(
4341:f
4316:B
4312:N
4289:A
4285:N
4255:j
4252:i
4242:j
4232:i
4222:N
4217:1
4214:=
4211:j
4208:,
4205:i
4195:2
4192:1
4187:+
4182:i
4164:i
4160:r
4154:i
4142:N
4137:1
4134:=
4131:i
4123:=
4118:)
4113:}
4108:i
4104:r
4100:,
4095:i
4087:{
4082:(
4077:f
4052:i
4048:r
4019:2
4015:/
4011:1
4008:=
3978:1
3975:=
3972:N
3950:2
3946:/
3942:1
3935:N
3911:2
3907:/
3903:1
3877:2
3873:/
3869:1
3857:0
3831:+
3826:1
3819:N
3810:2
3806:/
3802:1
3795:N
3774:+
3769:2
3765:/
3761:1
3754:N
3750:+
3747:2
3743:/
3739:1
3695:2
3691:)
3681:1
3678:(
3674:1
3669:+
3661:2
3653:N
3649:1
3641:=
3634:f
3604:2
3589:1
3585:1
3580:+
3571:N
3567:1
3562:=
3555:f
3539:.
3525:2
3505:)
3496:1
3493:(
3479:N
3471:=
3441:1
3435:N
3392:)
3383:1
3380:(
3371:+
3368:)
3359:1
3356:(
3347:)
3338:1
3335:(
3332:+
3318:N
3310:=
3307:f
3284:N
3178:w
3149:g
3146:e
3143:s
3138:V
3111:T
3108:R
3101:2
3097:)
3091:b
3078:a
3070:(
3064:g
3061:e
3058:s
3053:V
3046:=
3012:b
2985:a
2952:A
2948:N
2941:B
2936:k
2932:=
2929:R
2904:A
2900:N
2874:2
2870:n
2847:1
2843:n
2820:2
2816:N
2793:1
2789:N
2765:]
2749:2
2739:1
2735:n
2731:+
2726:2
2710:2
2706:n
2702:+
2697:1
2681:1
2677:n
2672:[
2669:T
2666:R
2663:=
2657:x
2654:i
2651:m
2646:G
2604:2
2594:1
2590:N
2586:T
2580:B
2575:k
2571:=
2565:x
2562:i
2559:m
2554:H
2517:T
2511:B
2506:k
2500:w
2494:z
2488:=
2446:w
2440:z
2435:2
2425:1
2421:N
2417:=
2411:x
2408:i
2405:m
2400:H
2364:1
2335:z
2330:2
2326:N
2322:x
2300:2
2296:N
2292:x
2272:z
2249:z
2244:2
2234:1
2230:N
2226:=
2221:1
2213:z
2208:2
2204:N
2200:x
2174:)
2165:w
2161:+
2152:w
2148:(
2142:2
2139:1
2124:w
2120:=
2117:w
2085:w
2054:w
2027:w
1991:x
1968:]
1962:2
1946:2
1942:N
1938:+
1933:1
1917:1
1913:N
1908:[
1902:B
1897:k
1890:=
1884:x
1881:i
1878:m
1873:S
1837:N
1831:2
1827:N
1823:x
1817:=
1812:2
1803:,
1798:N
1793:1
1789:N
1783:=
1778:1
1749:2
1722:1
1687:B
1682:k
1657:]
1650:N
1644:2
1640:N
1636:x
1621:2
1617:N
1613:+
1607:N
1602:1
1598:N
1583:1
1579:N
1574:[
1567:B
1562:k
1555:=
1549:x
1546:i
1543:m
1538:S
1493:x
1471:2
1467:N
1444:1
1440:N
1414:2
1410:N
1406:x
1403:+
1398:1
1394:N
1390:=
1387:N
1266:T
1242:R
1198:2
1176:2
1149:2
1145:n
1124:1
1112:(
1094:1
1067:1
1063:n
1032:]
1016:2
1006:1
1002:n
998:+
993:2
977:2
973:n
969:+
964:1
948:1
944:n
939:[
936:T
933:R
930:=
924:x
921:i
918:m
913:G
860:x
857:i
854:m
849:S
822:x
819:i
816:m
811:H
737:x
734:i
731:m
726:S
719:T
710:x
707:i
704:m
699:H
692:=
686:x
683:i
680:m
675:G
617:x
614:i
611:m
606:G
544:e
537:t
530:v
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