1740:
being detected. Accurate interpretation becomes exceedingly difficult for systems with non-negligible contributions from multiple scattering. In many commercial instruments where analysis of the scattering signal is automatically performed, the error may never be noticed by the user. Particularly for larger particles and those with high refractive index contrast, this limits the application of standard static light scattering to very low particle concentrations. On the other hand, for soluble macromolecules that exhibit a relatively low refractive index contrast versus the solvent, including most polymers and biomolecules in their respective solvents, multiple scattering is rarely a limiting factor even at concentrations that approach the limits of solubility.
1761:, colligative properties, and other macromolecular interactions as it yields, in addition to size and molecular weight, information on the affinity and stoichiometry of molecular complexes formed by one or more associating macromolecular/biomolecular species. In particular, static light scattering from a dilution series may be analyzed to quantify self-association, reversible oligomerization, and non-specific attraction or repulsion, while static light scattering from mixtures of species may be analyzed to quantify hetero-association.
1235:
86:, different gains, and are looking at different geometrical scattering volumes. In this case, a normalization of the detectors is absolutely needed. To normalize the detectors, a measurement of a pure solvent is made first. Then an isotropic scatterer is added to the solvent. Since isotropic scatterers scatter the same intensity at any angle, the detector efficiency and gain can be normalized with this procedure. It is convenient to normalize all the detectors to the 90° angle detector.
62:
measurements of both molar mass and size for all macromolecules of radius above 1â2% of the incident wavelength. Hence simultaneous measurements at several angles relative to the direction of the incident light, known as multi-angle light scattering (MALS) or multi-angle laser light scattering (MALLS), are generally regarded as the standard implementation of static light scattering. Additional details on the history and theory of MALS may be found in
1609:
1731:
the Debye plot is the possibility to determine the second virial coefficient. This parameter describes the interaction between particles and the solvent. In macromolecule solutions, for instance, it can assume negative (particle-particle interactions are favored), zero, or positive values (particle-solvent interactions are favored).
69:
To measure the average molecular weight directly without calibration from the light scattering intensity, the laser intensity, the quantum efficiency of the detector, and the full scattering volume and solid angle of the detector need to be known. Since this is impractical, all commercial instruments
1769:
One of the main applications of static light scattering for molecular mass determination is in the field of macromolecules, such as proteins and polymers, as it is possible to measure the molecular mass of proteins without any assumption about their shape. Static light scattering is usually combined
1739:
Static light scattering assumes that each detected photon has only been scattered exactly once. Therefore, analysis according to the calculations stated above will only be correct if the sample has been diluted sufficiently to ensure that photons are not scattered multiple times by the sample before
1730:
As the Debye plot is a simplification of the Zimm equation, the same limitations of the latter apply, i.e., samples should present a monodisperse nature. For polydisperse samples, the resulting molecular mass from a static light-scattering measurement will represent an average value. An advantage of
61:
For static light scattering experiments, a high-intensity monochromatic light, usually a laser, is launched into a solution containing the macromolecules. One or many detectors are used to measure the scattering intensity at one or many angles. The angular dependence is required to obtain accurate
1743:
However, as shown by
Schaetzel, it is possible to suppress multiple scattering in static light scattering experiments via a cross-correlation approach. The general idea is to isolate singly scattered light and suppress undesired contributions from multiple scattering in a static light scattering
1756:
Samples that change their properties after dilution may not be analyzed via static light scattering in terms of the simple model presented here as the Zimm equation. A more sophisticated analysis known as 'composition-gradient static (or multi-angle) light scattering' (CG-SLS or CG-MALS) is an
1022:
There are typically several analyses developed to analyze the scattering of particles in solution to derive the above-named physical characteristics of particles. A simple static light scattering experiment entails the average intensity of the sample that is corrected for the scattering of the
1536:
418:
1540:
The analysis performed with the Zimm plot uses a double-extrapolation to zero concentration and zero scattering angle resulting in a characteristic rhomboid plot. As the angular information is available, it is also possible to obtain the radius of gyration
763:
1744:
experiment. Different implementations of cross-correlation light scattering have been developed and applied. Currently, the most widely used scheme is the so-called 3D-dynamic light scattering method,. The same method can also be used to correct
1600:, due to the absence of the variable concentration of the sample. More specifically, the value of the second virial coefficient is either assumed to equal zero or is inputted as a known value in order to perform the partial Zimm analysis.
211:
2406:
1715:
1011:
531:
620:
1304:
1356:
238:
1151:
840:
926:
A Zimm plot is built from a double extrapolation to zero angle and zero concentration from many angles and many concentration measurements. In its simplest form, the Zimm equation is reduced to:
629:
1719:
Note that this is also the result of an extrapolation to zero scattering angle. By acquiring data on concentration and scattering intensity, the Debye plot is constructed by plotting
82:
For a light scattering instrument composed of many detectors placed at various angles, all the detectors need to respond the same way. Usually, detectors will have slightly different
30:
of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the
2454:
1582:
2128:
Urban, C.; Schurtenberger, P. (1998). "Characterization of turbid colloidal suspensions using light scattering techniques combined with cross-correlation methods".
1758:
91:
50:
Static light scattering is also commonly utilized to determine the size of particle suspensions in the sub-Îźm and supra-Îźm ranges, via the Lorenz-Mie (see
1589:
1168:
1024:
1629:
931:
427:
1593:
1585:
2314:"Large-Scale Supramolecular Structure in Solutions of Low Molar Mass Compounds and Mixtures of Liquids: I. Light Scattering Characterization"
1727:
vs. concentration. The intercept of the fitted line gives the molecular mass, while the slope corresponds to the 2nd virial coefficient.
540:
1531:{\displaystyle {\frac {Kc}{\Delta R(\theta ,c)}}={\frac {1}{M_{w}}}\left(1+{\frac {q^{2}R_{g}^{2}}{3}}+O(q^{4})\right)+2A_{2}c+O(c^{2})}
413:{\displaystyle {\frac {Kc}{\Delta R(\theta ,c)}}={\frac {1}{M_{w}}}\left(1+{\frac {q^{2}R_{g}^{2}}{3}}+O(q^{4})\right)+2A_{2}c+O(c^{2})}
233:, is the Zimm equation (the right-hand side of the Zimm equation is provided incorrectly in some texts, as noted by Hiemenz and Lodge):
1250:
878:
the change in the refractive index of the solution with change in concentration. The intensity of the analyte measured at an angle is
1064:
886:. In these equations, the subscript A is for analyte (the solution) and T is for the toluene with the Rayleigh ratio of toluene,
2063:
2001:
772:
2017:
2407:"Dimerization of Bovine Serum Albumin As Evidenced By Particle Size and Molecular Mass Measurement :: Anton-Paar.com"
74:
since the
Rayleigh ratio of toluene and a few other solvents were measured using an absolute light scattering instrument.
1791:
1828:"Theorie der Opaleszenz von homogenen Flßssigkeiten und Flßssigkeitsgemischen in der Nähe des kritischen Zustandes"
1806:
1779:
1306:) as determined by static light scattering, a Zimm plot is a conventional means of deriving the parameters such as
40:. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient,
758:{\displaystyle \ R(\theta )={\frac {I_{A}(\theta )n_{0}^{2}}{I_{T}(\theta )n_{T}^{2}}}{\frac {R_{T}}{N(\theta )}}}
1771:
1957:
B.H. Zimm (1948). "The
Scattering of Light and the Radial Distribution Function of High Polymer Solutions".
2439:
63:
2474:
2464:
2434:
2175:(2010). "Modulated 3D cross-correlation light scattering: Improving turbid sample characterization".
2043:
2469:
2085:
Schaetzel, K. (1991). "Suppression of multiple-scattering by photon cross-correlation techniques".
1796:
1775:
1745:
1584:
and at least 4 concentrations. Performing a Zimm analysis on a single concentration is known as a
2236:
Pusey, P.N. (1999). "Suppression of multiple scattering by photon cross-correlation techniques".
1551:
55:
1048:
The scattered intensity can be plotted as a function of the angle to give information on the
2361:"Glycerol polymerization degree effect on the emulsifying properties of polyglycerol esters"
1865:
C.V. Raman (1927). "Relation of
Tyndall effect to osmotic pressure in colloidal solutions".
2194:
2137:
2094:
1966:
1928:
1893:
1839:
223:
is the scattering intensity measured for the
Rayleigh scatterer by the 90° angle detector.
2359:
DĂazâLasprilla, Ana M.; Mercado, Ronald A.; RamĂrezâCaballero, Gustavo E. (20 June 2021).
23:
that measures the intensity of the scattered light to obtain the average molecular weight
8:
2459:
206:{\displaystyle \ N(\theta )={\frac {I_{R}(\theta )-I_{S}(\theta )}{I_{R}(90)-I_{S}(90)}}}
2360:
2198:
2141:
2098:
1970:
1932:
1897:
1843:
2388:
2289:
2264:
2218:
2184:
2110:
2055:
1597:
1324:
83:
31:
20:
2249:
2392:
2380:
2341:
2333:
2294:
2210:
2153:
2114:
2059:
1997:
1612:
Calculation of molecular mass by static light scattering measurement using Debye plot
863:
2106:
2372:
2325:
2284:
2276:
2245:
2222:
2202:
2145:
2102:
2051:
1974:
1936:
1901:
1847:
1801:
1624:â1). Therefore, the Zimm equation is simplified to the Debye equation, as follows:
2018:"Molecular mass measurement using static light scattering :: Anton Paar Wiki"
1056:
2172:
1314:
51:
2280:
2448:
2384:
2337:
2313:
1851:
1710:{\displaystyle {\frac {Kc}{\Delta R(\theta ,c)}}={\frac {1}{M_{w}}}+2A_{2}c}
1548:). Experiments are performed at several angles, which satisfy the condition
2345:
2298:
2214:
2149:
1919:
B.H. Zimm (1945). "Molecular Theory of the
Scattering of Light in Fluids".
2157:
1006:{\displaystyle \ Kc/\Delta R(\theta \rightarrow 0,c\rightarrow 0)=1/M_{w}}
526:{\displaystyle \ K=4\pi ^{2}n_{0}^{2}(dn/dc)^{2}/N_{\text{A}}\lambda ^{4}}
1238:
Evaluation of the static light-scattering measurement using the Zimm plot
1216:
911:, are also calculated from this equation. The refractive index increment
226:
The most common equation to measure the weight-average molecular weight,
894:
2376:
2358:
2329:
2206:
1978:
1940:
1905:
1827:
1212:
615:{\displaystyle \ \Delta R(\theta ,c)=R_{A}(\theta )-R_{0}(\theta )}
2189:
1616:
If the measured particles are smaller than Îť/20, the form factor
1299:{\displaystyle \scriptstyle \mu _{2}/{\bar {\Gamma }}^{2}<0.3}
1220:
71:
1996:(2nd ed.). Boca Raton, Fla. : CRC Press. pp. 307â308.
1751:
1208:
1015:
for measurements made at low angle and infinite dilution since
2265:"Light Scattering Based Analysis of Biomolecular Interactions"
1608:
1234:
767:
and the scattering vector for vertically polarized light is
2127:
1146:{\displaystyle \ln(\Delta R(\theta ))=1-(R_{g}^{2}/3)q^{2}}
1588:
analysis and is only valid for dilute solutions of strong
1247:
For polymers and polymer complexes that are monodisperse (
2048:
Colloid and
Interface Chemistry for Water Quality Control
1770:
with other particle characterization techniques, such as
923:
and can be measured with a differential refractometer.
2455:
Scattering, absorption and radiative transfer (optics)
2170:
1254:
1211:
plot is typically used to analyze the conformation of
835:{\displaystyle \ q=4\pi n_{0}\sin(\theta /2)/\lambda }
1632:
1554:
1359:
1253:
1067:
934:
775:
632:
543:
430:
241:
94:
70:
are calibrated using a strong, known scatterer like
1759:
methods to investigate proteinâprotein interactions
2238:Current Opinion in Colloid & Interface Science
1709:
1576:
1530:
1298:
1145:
1005:
834:
757:
614:
525:
412:
205:
1884:P.Debye (1944). "Light Scattering in Solutions".
915:characterizes the change of the refractive index
2446:
1340:is not implemented, a Zimm plot will only yield
1187:. However, this approximation is only true for
1031:as a function of the angle or the wave vector
897:. As described above, the radius of gyration,
1195:. Note that for a Guinier plot, the value of
1992:Hiemenz, Paul C.; Lodge, Timothy P. (2007).
1991:
1752:Composition-gradient static light scattering
1748:data for multiple scattering contributions.
1336:One must note that if the material constant
2235:
1825:
1952:
1950:
1864:
2288:
2188:
2084:
1956:
1918:
1055:which can simply be calculated using the
2262:
1792:Differential static light scatter (DSLS)
1607:
1233:
1223:. A Kratky plot can be made by plotting
1947:
1883:
2447:
2435:Application of static light scattering
2311:
1734:
2041:
1199:and the concentration is not needed.
904:, and the second virial coefficient,
851:the refractive index of the solvent,
855:the wavelength of the light source,
2318:The Journal of Physical Chemistry B
1596:however, does not yield the second
1351:will yield the following equation:
1159:also known as the form factor with
13:
2365:Journal of Applied Polymer Science
2056:10.1016/b978-0-12-809315-3.00004-9
1644:
1371:
1274:
1077:
949:
547:
253:
14:
2486:
2428:
870:the solution concentration, and d
2177:Review of Scientific Instruments
1780:electrophoretic light scattering
1167:. Hence a plot of the corrected
1038:
2399:
2352:
2312:SedlĂĄk, MariĂĄn (1 March 2006).
2305:
2256:
2229:
2164:
2121:
1764:
1215:but can be used to analyze the
1043:
2078:
2035:
2010:
1985:
1912:
1877:
1858:
1819:
1662:
1650:
1525:
1512:
1479:
1466:
1389:
1377:
1277:
1202:
1130:
1104:
1092:
1089:
1083:
1074:
979:
973:
961:
955:
821:
807:
749:
743:
706:
700:
670:
664:
645:
639:
609:
603:
587:
581:
565:
553:
489:
468:
407:
394:
361:
348:
271:
259:
197:
191:
175:
169:
154:
148:
132:
126:
107:
101:
1:
2250:10.1016/S1359-0294(99)00036-9
1812:
1772:size-exclusion chromatography
1603:
2050:, Elsevier, pp. 37â47,
1807:Proteinâprotein interactions
1242:
893:being 1.35Ă10 cm for a
64:multi-angle light scattering
7:
1785:
1577:{\displaystyle qR_{g}<1}
10:
2491:
1059:approximation as follows:
58:formalisms, respectively.
2281:10.1007/s12551-013-0107-1
2107:10.1088/0953-8984/2/S/062
1225:sin(θ/2)ÎR(θ) vs sin(θ/2)
77:
2130:J. Colloid Interface Sci
1852:10.1002/andp.19103381612
1797:Dynamic light scattering
1776:dynamic light scattering
1746:dynamic light scattering
2183:(12): 123107â123107â7.
1023:solvent will yield the
919:with the concentration
17:Static light scattering
2150:10.1006/jcis.1998.5769
1711:
1613:
1578:
1532:
1300:
1239:
1147:
1007:
836:
759:
616:
527:
414:
207:
56:Fraunhofer diffraction
1712:
1611:
1579:
1533:
1347:. Hence implementing
1301:
1237:
1148:
1008:
837:
760:
617:
528:
415:
208:
47:, can be calculated.
2042:Chang, Qing (2016),
1826:A. Einstein (1910).
1630:
1552:
1357:
1251:
1065:
932:
773:
630:
541:
428:
239:
92:
2199:2010RScI...81l3107B
2142:1998JCIS..207..150U
2099:1990JPCM....2..393S
1971:1948JChPh..16.1093Z
1933:1945JChPh..13..141Z
1898:1944JAP....15..338D
1844:1910AnP...338.1275E
1757:important class of
1735:Multiple scattering
1453:
1179:will yield a slope
1121:
723:
687:
467:
335:
2475:Physical chemistry
2044:"Osmotic Pressure"
1707:
1620:can be neglected (
1614:
1598:virial coefficient
1574:
1528:
1439:
1325:virial coefficient
1296:
1295:
1240:
1157:ln(ÎR(θ)) = lnP(θ)
1143:
1107:
1003:
832:
755:
709:
673:
612:
523:
453:
410:
321:
203:
84:quantum efficiency
32:radius of gyration
21:physical chemistry
19:is a technique in
2465:Polymer chemistry
2377:10.1002/app.50566
2330:10.1021/jp0569335
2263:Some, D. (2013).
2207:10.1063/1.3518961
2065:978-0-12-809315-3
2003:978-1-57444-779-8
1994:Polymer chemistry
1979:10.1063/1.1746738
1941:10.1063/1.1724013
1906:10.1063/1.1707436
1832:Annals of Physics
1686:
1666:
1458:
1413:
1393:
1280:
1173:ÎR(θ) vs sin(θ/2)
937:
864:Avogadro constant
778:
753:
725:
635:
546:
510:
433:
340:
295:
275:
201:
97:
2482:
2422:
2421:
2419:
2417:
2403:
2397:
2396:
2356:
2350:
2349:
2324:(9): 4329â4338.
2309:
2303:
2302:
2292:
2260:
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2253:
2233:
2227:
2226:
2192:
2168:
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2125:
2119:
2118:
2082:
2076:
2075:
2074:
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2039:
2033:
2032:
2030:
2028:
2014:
2008:
2007:
1989:
1983:
1982:
1954:
1945:
1944:
1916:
1910:
1909:
1881:
1875:
1874:
1862:
1856:
1855:
1823:
1802:Light scattering
1716:
1714:
1713:
1708:
1703:
1702:
1687:
1685:
1684:
1672:
1667:
1665:
1642:
1634:
1590:point scatterers
1583:
1581:
1580:
1575:
1567:
1566:
1537:
1535:
1534:
1529:
1524:
1523:
1502:
1501:
1486:
1482:
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1477:
1459:
1454:
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1438:
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1414:
1412:
1411:
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1392:
1369:
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1305:
1303:
1302:
1297:
1288:
1287:
1282:
1281:
1273:
1269:
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1150:
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1144:
1142:
1141:
1126:
1120:
1115:
1012:
1010:
1009:
1004:
1002:
1001:
992:
948:
935:
841:
839:
838:
833:
828:
817:
800:
799:
776:
764:
762:
761:
756:
754:
752:
738:
737:
728:
726:
724:
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717:
699:
698:
688:
686:
681:
663:
662:
652:
633:
621:
619:
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580:
579:
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497:
496:
481:
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384:
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359:
341:
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329:
320:
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293:
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243:
212:
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209:
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190:
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168:
167:
157:
147:
146:
125:
124:
114:
95:
2490:
2489:
2485:
2484:
2483:
2481:
2480:
2479:
2470:Polymer physics
2445:
2444:
2431:
2426:
2425:
2415:
2413:
2405:
2404:
2400:
2357:
2353:
2310:
2306:
2261:
2257:
2234:
2230:
2169:
2165:
2126:
2122:
2093:: SA393âSA398.
2083:
2079:
2070:
2068:
2066:
2040:
2036:
2026:
2024:
2016:
2015:
2011:
2004:
1990:
1986:
1955:
1948:
1917:
1913:
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1863:
1859:
1824:
1820:
1815:
1788:
1767:
1754:
1737:
1698:
1694:
1680:
1676:
1671:
1643:
1635:
1633:
1631:
1628:
1627:
1606:
1562:
1558:
1553:
1550:
1549:
1546:
1519:
1515:
1497:
1493:
1473:
1469:
1448:
1443:
1433:
1429:
1428:
1426:
1419:
1415:
1407:
1403:
1398:
1370:
1362:
1360:
1358:
1355:
1354:
1345:
1331:
1323:and the second
1321:
1311:
1283:
1272:
1271:
1270:
1265:
1259:
1255:
1252:
1249:
1248:
1245:
1205:
1192:
1184:
1164:
1137:
1133:
1122:
1116:
1111:
1066:
1063:
1062:
1053:
1046:
1041:
997:
993:
988:
944:
933:
930:
929:
909:
902:
891:
883:
861:
850:
824:
813:
795:
791:
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739:
733:
729:
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713:
694:
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682:
677:
658:
654:
653:
651:
631:
628:
627:
597:
593:
575:
571:
542:
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538:
517:
513:
507:
503:
498:
492:
488:
477:
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426:
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401:
397:
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355:
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252:
244:
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220:
185:
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163:
159:
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142:
138:
120:
116:
115:
113:
93:
90:
89:
80:
45:
38:
28:
12:
11:
5:
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2478:
2477:
2472:
2467:
2462:
2457:
2443:
2442:
2437:
2430:
2429:External links
2427:
2424:
2423:
2398:
2351:
2304:
2275:(2): 147â158.
2255:
2244:(3): 177â185.
2228:
2163:
2136:(1): 150â158.
2120:
2077:
2064:
2034:
2009:
2002:
1984:
1946:
1911:
1876:
1867:Indian J. Phys
1857:
1817:
1816:
1814:
1811:
1810:
1809:
1804:
1799:
1794:
1787:
1784:
1766:
1763:
1753:
1750:
1736:
1733:
1706:
1701:
1697:
1693:
1690:
1683:
1679:
1675:
1670:
1664:
1661:
1658:
1655:
1652:
1649:
1646:
1641:
1638:
1605:
1602:
1573:
1570:
1565:
1561:
1557:
1544:
1527:
1522:
1518:
1514:
1511:
1508:
1505:
1500:
1496:
1492:
1489:
1485:
1481:
1476:
1472:
1468:
1465:
1462:
1457:
1451:
1446:
1442:
1436:
1432:
1425:
1422:
1418:
1410:
1406:
1402:
1397:
1391:
1388:
1385:
1382:
1379:
1376:
1373:
1368:
1365:
1343:
1329:
1319:
1315:molecular mass
1309:
1294:
1291:
1286:
1279:
1276:
1268:
1262:
1258:
1244:
1241:
1204:
1201:
1190:
1182:
1169:Rayleigh ratio
1162:
1140:
1136:
1132:
1129:
1125:
1119:
1114:
1110:
1106:
1103:
1100:
1097:
1094:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1051:
1045:
1042:
1040:
1037:
1025:Rayleigh ratio
1000:
996:
991:
987:
984:
981:
978:
975:
972:
969:
966:
963:
960:
957:
954:
951:
947:
943:
940:
907:
900:
889:
881:
859:
848:
831:
827:
823:
820:
816:
812:
809:
806:
803:
798:
794:
790:
787:
784:
781:
751:
748:
745:
742:
736:
732:
721:
716:
712:
708:
705:
702:
697:
693:
685:
680:
676:
672:
669:
666:
661:
657:
650:
647:
644:
641:
638:
611:
608:
605:
600:
596:
592:
589:
586:
583:
578:
574:
570:
567:
564:
561:
558:
555:
552:
549:
520:
516:
506:
501:
495:
491:
487:
484:
480:
476:
473:
470:
465:
460:
456:
450:
446:
442:
439:
436:
409:
404:
400:
396:
393:
390:
387:
382:
378:
374:
371:
367:
363:
358:
354:
350:
347:
344:
339:
333:
328:
324:
318:
314:
307:
304:
300:
292:
288:
284:
279:
273:
270:
267:
264:
261:
258:
255:
250:
247:
229:
218:
199:
196:
193:
188:
184:
180:
177:
174:
171:
166:
162:
156:
153:
150:
145:
141:
137:
134:
131:
128:
123:
119:
112:
109:
106:
103:
100:
79:
76:
52:Mie scattering
43:
36:
26:
9:
6:
4:
3:
2:
2487:
2476:
2473:
2471:
2468:
2466:
2463:
2461:
2458:
2456:
2453:
2452:
2450:
2441:
2438:
2436:
2433:
2432:
2412:
2408:
2402:
2394:
2390:
2386:
2382:
2378:
2374:
2371:(24): 50566.
2370:
2366:
2362:
2355:
2347:
2343:
2339:
2335:
2331:
2327:
2323:
2319:
2315:
2308:
2300:
2296:
2291:
2286:
2282:
2278:
2274:
2270:
2266:
2259:
2251:
2247:
2243:
2239:
2232:
2224:
2220:
2216:
2212:
2208:
2204:
2200:
2196:
2191:
2186:
2182:
2178:
2174:
2173:Scheffold, F.
2167:
2159:
2155:
2151:
2147:
2143:
2139:
2135:
2131:
2124:
2116:
2112:
2108:
2104:
2100:
2096:
2092:
2088:
2081:
2067:
2061:
2057:
2053:
2049:
2045:
2038:
2023:
2019:
2013:
2005:
1999:
1995:
1988:
1980:
1976:
1972:
1968:
1964:
1960:
1959:J. Chem. Phys
1953:
1951:
1942:
1938:
1934:
1930:
1926:
1922:
1921:J. Chem. Phys
1915:
1907:
1903:
1899:
1895:
1891:
1887:
1886:J. Appl. Phys
1880:
1872:
1868:
1861:
1853:
1849:
1845:
1841:
1837:
1833:
1829:
1822:
1818:
1808:
1805:
1803:
1800:
1798:
1795:
1793:
1790:
1789:
1783:
1781:
1777:
1773:
1762:
1760:
1749:
1747:
1741:
1732:
1728:
1726:
1722:
1717:
1704:
1699:
1695:
1691:
1688:
1681:
1677:
1673:
1668:
1659:
1656:
1653:
1647:
1639:
1636:
1625:
1623:
1619:
1610:
1601:
1599:
1595:
1591:
1587:
1571:
1568:
1563:
1559:
1555:
1547:
1538:
1520:
1516:
1509:
1506:
1503:
1498:
1494:
1490:
1487:
1483:
1474:
1470:
1463:
1460:
1455:
1449:
1444:
1440:
1434:
1430:
1423:
1420:
1416:
1408:
1404:
1400:
1395:
1386:
1383:
1380:
1374:
1366:
1363:
1352:
1350:
1346:
1339:
1334:
1332:
1326:
1322:
1316:
1312:
1292:
1289:
1284:
1266:
1260:
1256:
1236:
1232:
1230:
1226:
1222:
1218:
1214:
1210:
1200:
1198:
1194:
1186:
1178:
1174:
1170:
1166:
1158:
1153:
1138:
1134:
1127:
1123:
1117:
1112:
1108:
1101:
1098:
1095:
1086:
1080:
1071:
1068:
1060:
1058:
1054:
1039:Data analyses
1036:
1034:
1030:
1026:
1020:
1018:
1013:
998:
994:
989:
985:
982:
976:
970:
967:
964:
958:
952:
945:
941:
938:
927:
924:
922:
918:
914:
910:
903:
896:
892:
885:
877:
873:
869:
865:
858:
854:
847:
842:
829:
825:
818:
814:
810:
804:
801:
796:
792:
788:
785:
782:
779:
768:
765:
746:
740:
734:
730:
719:
714:
710:
703:
695:
691:
683:
678:
674:
667:
659:
655:
648:
642:
636:
625:
622:
606:
598:
594:
590:
584:
576:
572:
568:
562:
559:
556:
550:
536:
533:
518:
514:
504:
499:
493:
485:
482:
478:
474:
471:
463:
458:
454:
448:
444:
440:
437:
434:
423:
420:
402:
398:
391:
388:
385:
380:
376:
372:
369:
365:
356:
352:
345:
342:
337:
331:
326:
322:
316:
312:
305:
302:
298:
290:
286:
282:
277:
268:
265:
262:
256:
248:
245:
234:
232:
224:
222:
213:
194:
186:
182:
178:
172:
164:
160:
151:
143:
139:
135:
129:
121:
117:
110:
104:
98:
87:
85:
75:
73:
67:
65:
59:
57:
53:
48:
46:
39:
33:
29:
22:
18:
2414:. Retrieved
2410:
2401:
2368:
2364:
2354:
2321:
2317:
2307:
2272:
2269:Biophys. Rev
2268:
2258:
2241:
2237:
2231:
2180:
2176:
2166:
2133:
2129:
2123:
2090:
2086:
2080:
2069:, retrieved
2047:
2037:
2027:23 September
2025:. Retrieved
2021:
2012:
1993:
1987:
1965:(12): 1093.
1962:
1958:
1924:
1920:
1914:
1889:
1885:
1879:
1870:
1866:
1860:
1838:(16): 1275.
1835:
1831:
1821:
1768:
1765:Applications
1755:
1742:
1738:
1729:
1724:
1720:
1718:
1626:
1621:
1617:
1615:
1594:partial Zimm
1586:partial Zimm
1542:
1539:
1353:
1348:
1341:
1337:
1335:
1327:
1317:
1307:
1246:
1228:
1224:
1206:
1196:
1188:
1180:
1176:
1172:
1160:
1156:
1154:
1061:
1049:
1047:
1044:Guinier plot
1035:as follows:
1032:
1028:
1021:
1016:
1014:
928:
925:
920:
916:
912:
905:
898:
887:
879:
875:
871:
867:
856:
852:
845:
843:
769:
766:
626:
623:
537:
534:
424:
421:
235:
227:
225:
216:
214:
88:
81:
68:
60:
49:
41:
34:
24:
16:
15:
2171:Block, I.;
2087:J. Mod. Opt
1778:(DLS), and
1229:qÎR(θ) vs q
1217:random walk
1203:Kratky plot
2460:Scattering
2449:Categories
2411:Anton Paar
2022:Anton Paar
1927:(4): 141.
1892:(4): 338.
1813:References
1604:Debye plot
1165:sin(θ/2)/Ν
895:HeNe laser
2440:Litesizer
2393:233888953
2385:0021-8995
2338:1520-6106
2190:1008.0615
2115:250745836
1654:θ
1645:Δ
1381:θ
1372:Δ
1278:¯
1275:Γ
1257:μ
1243:Zimm plot
1219:model of
1102:−
1087:θ
1078:Δ
1072:
1019:(0) = 1.
974:→
962:→
959:θ
950:Δ
830:λ
811:θ
805:
789:π
747:θ
704:θ
668:θ
643:θ
607:θ
591:−
585:θ
557:θ
548:Δ
515:λ
445:π
263:θ
254:Δ
179:−
152:θ
136:−
130:θ
105:θ
2346:16509731
2299:23646069
2215:21198014
1786:See also
1221:polymers
1213:proteins
2416:14 June
2290:3641300
2223:9240166
2195:Bibcode
2158:9778402
2138:Bibcode
2095:Bibcode
2071:14 June
1967:Bibcode
1929:Bibcode
1894:Bibcode
1840:Bibcode
1782:(ELS).
1774:(SEC),
1161:q = 4Ďn
1057:Guinier
72:toluene
2391:
2383:
2344:
2336:
2297:
2287:
2221:
2213:
2156:
2113:
2062:
2000:
1592:. The
1209:Kratky
1193:< 1
1155:where
936:
777:
634:
545:
432:
422:where
215:where
96:
78:Theory
54:) and
2389:S2CID
2219:S2CID
2185:arXiv
2111:S2CID
1725:ÎR(θ)
1197:dn/dc
913:dn/dc
844:with
624:with
2418:2022
2381:ISSN
2342:PMID
2334:ISSN
2295:PMID
2211:PMID
2154:PMID
2073:2022
2060:ISBN
2029:2022
1998:ISBN
1873:: 1.
1622:P(θ)
1618:P(θ)
1569:<
1290:<
1207:The
862:the
535:and
221:(90)
2373:doi
2369:138
2326:doi
2322:110
2285:PMC
2277:doi
2246:doi
2203:doi
2146:doi
2134:207
2103:doi
2052:doi
1975:doi
1937:doi
1902:doi
1848:doi
1293:0.3
1227:or
1175:or
884:(θ)
802:sin
2451::
2409:.
2387:.
2379:.
2367:.
2363:.
2340:.
2332:.
2320:.
2316:.
2293:.
2283:.
2271:.
2267:.
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2217:.
2209:.
2201:.
2193:.
2181:81
2179:.
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2144:.
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2109:.
2101:.
2091:38
2089:.
2058:,
2046:,
2020:.
1973:.
1963:16
1961:.
1949:^
1935:.
1925:13
1923:.
1900:.
1890:15
1888:.
1869:.
1846:.
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1834:.
1830:.
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2420:.
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2328::
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2205::
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2148::
2140::
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2054::
2031:.
2006:.
1981:.
1977::
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1939::
1931::
1908:.
1904::
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
