208:
when studying anisotropic particles. Earlier measurements, before the introduction of lasers, were performed using focused, though unpolarized, light beams from sources such as Hg-arc lamps. Another required element is an optical cell to hold the sample being measured. Alternatively, cells incorporating means to permit measurement of flowing samples may be employed. If single-particles scattering properties are to be measured, a means to introduce such particles one-at-a-time through the light beam at a point generally equidistant from the surrounding detectors must be provided.
220:
also collected data sequentially as a single detector was moved from one collection angle to the next. The MALS implementation is of course much faster, but the same types of data are collected and are interpreted in the same manner. The two terms thus refer to the same concept. For differential light scattering measurements, the light scattering photometer has a single detector whereas the MALS light scattering photometer generally has a plurality of detectors.
1156:
984:
1197:
33:
1167:(SEC), MALS measurements began to be used in conjunction with an on-line concentration detector to determine absolute molar mass and size of sample fractions eluting from the column, rather than depending on calibration techniques. These flow mode MALS measurements have been extended to other separation techniques such as
1310:
is the mean square radius of branched and linear macromolecules with identical molar masses. By utilizing MALS in conjunction with a concentration detector as described above, one create a log-log plot of the root-mean-square radius vs molar mass. The slope of this plot yields the branching ratio, g.
346:
Scattering data is usually represented in terms of the so-called excess
Rayleigh ratio defined as the Rayleigh ratio of the solution or single particle event from which is subtracted the Rayleigh ratio of the carrier fluid itself and other background contributions, if any. The Rayleigh Ratio measured
1213:
As MALS can provide molar mass and size of molecules, it permits study into protein-protein binding, oligomerization and the kinetics of self-assembly, association and dissociation. By comparing the molar mass of a sample to its concentration, one can determine the binding affinity and stoichiometry
995:
in his paper "Apparatus and
Methods for Measurement and Interpretation of the Angular Variation of Light Scattering; Preliminary Results on Polystyrene Solutions" involved using a single detector rotated about a sample contained within a transparent vessel. MALS measurements from non-flowing samples
231:
The application of the Litton detector by
Salzman et al. provided measurement at 32 small scattering angles between 0° and 30°, and averaging over a broad range of azimuthal angles as the most important angles are the forward angles for static light scattering. By 1980, Bartholi et al. had developed
139:
Until the advent of lasers and their associated fine beams of narrow width, the width of conventional light beams used to make such measurements prevented data collection at smaller scattering angles. In recent years, since all commercial light scattering instrumentation use laser sources, this need
1182:
The angular dependence of light scattering data is shown below in a figure of mix of polystyrene spheres which was separated by SEC. The two smallest samples (farthest to the right) eluted last and show no angular dependence. The sample, second to the right shows a linear angular variation with the
377:
from which scattered light reaches the detector is determined by the detector's field of view generally restricted by apertures, lenses and stops. Consider now a MALS measurement made in a plane from a suspension of N identical particles/molecules per ml illuminated by a fine beam of light produced
219:
The traditional differential light scattering measurement was virtually identical to the currently used MALS technique. Although the MALS technique generally collects multiplexed data sequentially from the outputs of a set of discrete detectors, the earlier differential light scattering measurement
164:
Measurements were generally expressed as scattered intensities or scattered irradiance. Since the collection of data was made as the detector was placed at different locations on the arc, each position corresponding to a different scattering angle, the concept of placing a separate detector at each
160:
measurement. Historically, such measurements were made using a single detector rotated in an arc about the illuminated sample. The first commercial instrument (formally called a "scattered photometer") was the Brice-Phoenix light scattering photometer introduced in the mid-1950s and followed by the
1314:
In addition to branching, the log-log plot of size vs. molar mass indicates the shape or conformation of a macromolecule. An increase in the slope of the plot indicates a variation in conformation of a polymer from spherical to random coil to linear. Combining the mean-square radius from MALS with
247:
Company, in 1983, followed in 1984 with the sale of the first 15 detector flow instrument (Dawn-F) to AMOCO. By 1988, a three-dimensional configuration was introduced specifically to measure the scattering properties of single aerosol particles. At about the same time, the underwater device was
207:
or focused light beam (usually from a laser source producing a collimated beam of monochromatic light) that illuminates a region of the sample. In modern instruments, the beam is generally plane-polarized perpendicular to the plane of measurement, though other polarizations may be used especially
143:
The "multi-angle" term refers to the detection of scattered light at different discrete angles as measured, for example, by a single detector moved over a range that includes the particular angles selected or an array of detectors fixed at specific angular locations. A discussion of the physical
1204:
Coupling MALS with an in-line concentration detector following a sample separation means like SEC permits the calculation of the molar mass of the eluting sample in addition to its root-mean-square radius. The figure below represents a chromatographic separation of BSA aggregates. The 90° light
279:
is the simplest and describes elastic scattering of light or other electromagnetic radiation by objects much smaller than the incident wavelength. This type of scattering is responsible for the blue color of the sky during the day and is inversely proportional to the fourth power of wavelength.
223:
Another type of MALS device was developed in 1974 by
Salzmann et al. based on a light pattern detector invented by George et al. for Litton Systems Inc. in 1971. The Litton detector was developed for sampling the light energy distribution in the rear focal-plane of a spherical lens for sampling
211:
Although most MALS-based measurements are performed in a plane containing a set of detectors usually equidistantly placed from a centrally located sample through which the illuminating beam passes, three-dimensional versions also have been developed wherein the detectors lie on the surface of a
1146:
When plotted one can extrapolate to both zero angle and zero concentration, and analysis of the plot will give the mean square radius of the sample molecules from the initial slope of the c=0 line and the molar mass of the molecule at the point where both concentration and angle equal zero.
272:
The interpretation of scattering measurements made at the multiangular locations relies upon some knowledge of the a priori properties of the particles or molecules measured. The scattering characteristics of different classes of such scatterers may be interpreted best by application of an
169:
have different response and hence needs to be normalized in this scheme. An interesting system based upon the use of high speed film was developed by
Brunsting and Mullaney in 1974. It permitted the entire range of scattered intensities to be recorded on the film with a subsequent
212:
sphere with the sample controlled to pass through its center where it intersects the path of the incident light beam passing along a diameter of the sphere. The former framework is used for measuring aerosol particles while the latter was used to examine marine organisms such as
776:
248:
built to measure the scattered light properties of single phytoplankton. Signals were collected by optical fibers and transmitted to individual photomultipliers. Around
December 2001, an instrument was commercialized, which measures 7 scattering angles using a
196:, both of which are referred to by the initials DLS. The latter refers to a technique that is quite different, measuring the fluctuation of scattered light due to constructive and destructive interference, the frequency being linked to the thermal motion,
322:, then such particles may be considered as composed of very small elements, each of which may be represented as a Rayleigh-scattering particle. Thus each small element of the larger particle is assumed to scatter independently of any other.
996:
such as this are commonly referred to as "batch measurements". By creating samples at several known low concentrations and detecting scattered light about the sample at varying angles, one can create a Zimm plot by plotting :
621:
255:
The literature associated with measurements made by MALS photometers is extensive. both in reference to batch measurements of particles/molecules and measurements following fractionation by chromatographic means such as
473:
857:
232:
a new approach to measuring the scattering at discrete scattering angles by using an elliptical reflector to permit measurement at 30 polar angles over the range 2.5° ⤠θ ⤠177.5° with a resolution of 2.1°.
2498:
2345:
Podzimek, Stepan (1994). "The Use of GPC Coupled with a
Multiangle Laser Light Scattering Photometer for the Characterization of Polymers. On the Determination of Molecular Weight, Size and Branching".
637:
188:
expressed in milli-barns/steradian. Differential cross section measurements were commonly made, for example, to study the structure of the atomic nucleus by scattering from them nucleons, such as
912:
1222:
The branching ratio of a polymer relates to the number of branch units in a randomly branched polymer and the number of arms in star-branched polymers and was defined by Zimm and
Stockmayer as
1279:
1089:
174:
scan providing the relative scattered intensities. The then-conventional use of a single detector rotated about an illuminated sample with intensities collected at specific angles was called
1141:
1040:
2028:"Absolute on-line molecular mass analysis of basic fibroblast growth factor and its multimers by reversed-phase liquid chromatography with multi-angle laser light scattering detection"
958:
1381:
1147:
Improvements to the Zimm plot, which incorporate all collected data (commonly referred to as a "global fit"), have largely replaced the Zimm plot in modern batch analyses.
1437:
B. A. Zimm (1948). "Apparatus and methods for measurement and interpretation of the angular variation of light scattering; preliminary results on polystyrene solutions".
2233:
V.A. Erma (1969). "Exact solution for the scattering of electromagnetic waves from bodies of arbitrary shape: III. Obstacles with arbitrary electromagnetic properties".
51:
1340:
1308:
1858:
M. Bartholdi; G. C. Salzman; R. D. Hiebert & M. Kerker (1980). "Differential light scattering photometer for rapid analysis of single particles in flow".
378:
by a laser. Assuming that the light is polarized perpendicular to the plane of the detectors. The scattered light intensity measured by the detector at angle
515:
2179:
V.A. Erma (1968a). "An exact solution for the scattering of electromagnetic waves from conductors of arbitrary shape: I. Case of cylindrical symmetry".
991:
MALS is most commonly used for the characterization of mass and size of molecules in solution. Early implementations of MALS such as those discussed by
343:
LorenzâMie theory may be generalized to spherically symmetric particles per reference. More general shapes and structures have been treated by Erma.
631:" of the suspending fluid, i.e. RayleighâGans approximation, the scattering function in the scattering plane is the relatively complex quantity
165:
angular location of interest was well understood, though not implemented commercially until the late 1970s. Multiple detectors having different
239:
systems began in 1977 when
Science Spectrum, Inc. patented a flow-through capillary system for a customized bioassay system developed for the
2076:
2010:
388:
783:
2373:
Waghwani HK, Douglas, T (March 2021). "Cytochrome C with peroxidase-like activity encapsulated inside the small DPS protein nanocage".
1183:
intensity increasing at lower scattering angles. The largest sample, on the left, elutes first and shows non-linear angular variation.
2206:
V.A. Erma (1968b). "Exact solution for the scattering of electromagnetic waves from conductors of arbitrary shape: II. General case".
1916:
1472:
B. A. Brice; M. Halwer & R. Speiser (1950). "Photoelectric light scattering photometer for determining high molecular weights".
69:
771:{\displaystyle i(\theta )={\frac {k^{2}V^{2}\left|{m-1}\right|^{2}}{4\pi ^{2}}}G^{2}\left({2ka\sin {\frac {\theta }{2}}}\right)}
328:
theory is used to interpret the scattering of light by homogeneous spherical particles. The
RayleighâGans approximation and the
284:
627:
Even for a simple homogeneous sphere of radius a whose refractive index, n, is very nearly the same as the refractive index "n
2513:
2449:
Wang Y, Uchida M, Waghwani HK, Douglas, T (December 2020). "Synthetic Virus-like Particles for Glutathione Biosynthesis".
1176:
1164:
862:
261:
257:
109:
2508:
1400:
287:
is a means of interpreting MALS measurements with the assumption that the scattering particles have a refractive index,
148:, including some applications, data analysis methods and graphical representations associated therewith are presented.
1900:
L. V. Maldarelli, D. T. Phillips, W. L. Proctor, P. J. Wyatt, and T. C. Urquhart, Programmable action sampler system,
1227:
1172:
1045:
132:
was intended to reassure those used to making light scattering measurements with conventional light sources, such as
243:. The first commercial MALS instrument incorporating 8 discrete detectors was delivered to S.C. Johnson and Son, by
1106:
999:
2111:
P. J. Wyatt (1962). "Scattering of Electromagnetic Plane Waves from Inhomogeneous Spherically Symmetric Objects".
329:
325:
2027:
1620:
P. J. Wyatt (1968). "Differential Light Scattering: A Physical Method for Identifying Living Bacterial Cells".
1404:
1168:
917:
193:
1345:
180:
157:
145:
2002:
Modern Size-Exclusion Liquid Chromatography: Practice of Gel Permeation and Gel Filtration Chromatography
2503:
249:
983:
2092:
L. V. Lorenz (1890). "Light propagation in and outside a sphere illuminated by plane waves of light".
2319:
2242:
2215:
2188:
2151:
2120:
1867:
1773:
1721:
1712:
P. J. Wyatt; Y. J. Chang; C. Jackson; R. G. Parker; et al. (1988). "Aerosol Particle Analyzer".
1681:
1629:
1576:
1481:
1446:
105:
2518:
1408:
1396:
1205:
scattering signal from a MALS detector and the molar mass values for each elution slice are shown.
276:
97:
2474:
166:
133:
156:
The measurement of scattered light from an illuminated sample forms the basis of the so-called
2466:
2431:
2390:
2072:
2047:
2006:
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1824:
1737:
1645:
1602:
1545:
1155:
2458:
2421:
2382:
2355:
2327:
2277:
2268:
Wyatt, P.J. (1993). "Light Scattering and the Absolute Characterization of Macromolecules".
2250:
2223:
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2159:
2128:
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1814:
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1535:
1489:
1454:
1196:
295:
244:
225:
17:
1318:
1286:
2310:
Zimm, Bruno H. (1949). "The Dimensions of Chain Molecules Containing Branches and Rings".
352:
197:
113:
2323:
2246:
2219:
2192:
2155:
2124:
1871:
1777:
1725:
1685:
1633:
1580:
1485:
1450:
203:
A MALS measurement requires a set of ancillary elements. Most important among them is a
1597:
1564:
362:
is defined as the intensity of light per unit solid angle per unit incident intensity,
1588:
2492:
2478:
2281:
2043:
992:
616:{\displaystyle R(\theta )={\frac {I(\theta )r^{2}}{I_{0}\Delta V}}=Ni(\theta )/k^{2}}
213:
1412:
1392:
171:
140:
to mention the light source has been dropped and the term MALS is used throughout.
2066:
2000:
1819:
1802:
1540:
1523:
2410:"Virus-Like Particles (VLPs) as a Platform for HierarchicalCompartmentalization"
1803:"A Flow-System Multiangle Light-Scattering Instrument for Cell Characterization"
1524:"A Flow-System Multiangle Light-Scattering Instrument for Cell Characterization"
356:
273:
appropriate theory. For example, the following theories are most often applied.
2426:
2409:
2359:
1844:
2462:
2164:
2139:
1902:
1786:
1761:
1693:
1662:
Cf. L. I. Schiff, Quantum Mechanics (McGraw-Hill Book Company, New York 1955).
1508:
204:
93:
2254:
2227:
2200:
2132:
1801:
G. C. Salzmann; J. M. Crowell; C. A. Goad; K. M. Hansen; et al. (1975).
1672:
S. Fernbach (1958). "Nuclear Radii as Determined by Scattering of Neutrons".
1522:
G. C. Salzmann; J. M. Crowell; C. A. Goad; K. M. Hansen; et al. (1975).
120:
source is most often used, in which case the technique can be referred to as
96:
by a sample into a plurality of angles. It is used for determining both the
2470:
2435:
2394:
1887:
1741:
1649:
1493:
505:
is the vacuum wavelength of the incident light. The excess Rayleigh ratio,
192:. It is important to distinguish between differential light scattering and
2051:
1828:
1606:
1549:
1975:
1940:
1879:
1733:
332:
theory produce identical results for homogeneous spheres in the limit as
101:
1641:
2386:
468:{\displaystyle I(\theta )={\frac {I_{0}N\Delta V}{(kr)^{2}}}i(\theta )}
189:
2331:
1458:
1407:
or zeta potential. MALS techniques have been adopted for the study of
852:{\displaystyle G(\xi )={\frac {3}{\xi ^{2}}}(\sin \xi -\xi \cos \xi )}
2295:
Trainoff, S.P. (November 18, 2003). "U.S. Patent No. 6,651,009 B1".
1999:
A. M. Striegel; W. W. Yau; J. J. Kirkland & D. D. Bly (2009).
240:
117:
90:
1762:"Discrimination of Phytoplankton via Light-Scattering Properties"
252:
detector (BI-MwA: Brookhaven Instruments Corp, Hotlsville, NY).
1565:"Differential Light Scattering from Spherical Mammalian Cells"
26:
382:
in excess of that scattered by the suspending fluid would be
1342:
attained from DLS measurements yields the shape factor Ď =
228:
distribution of objects recorded on film transparencies.
200:
of the molecules or particles in solution or suspension.
47:
2499:
Scattering, absorption and radiative transfer (optics)
2065:
M. Schimpf; K. Caldwell; J. C. Giddings, eds. (2000).
1963:
1348:
1321:
1289:
1230:
1109:
1048:
1002:
920:
865:
786:
640:
518:
498:
is the refractive index of the suspending fluid, and
391:
2026:
I. V. Astafieva; G. A. Eberlein; Y. J. Wang (1996).
907:{\displaystyle k={\frac {2\pi n_{0}}{\lambda _{0}}}}
970:is the wavelength of the incident light in vacuum.
42:
may be too technical for most readers to understand
1375:
1334:
1302:
1273:
1135:
1083:
1034:
952:
906:
851:
770:
615:
467:
483:is the scattering function of a single particle,
2408:Waghwani HK, Uchida M, Douglas, T (April 2020).
1274:{\displaystyle g={\frac {R_{b}^{2}}{R_{l}^{2}}}}
1084:{\displaystyle \sin ^{2}{\frac {\theta }{2}}+kc}
161:Sofica photometer introduced in the late 1960s.
136:that low-angle measurements could now be made.
1136:{\displaystyle \sin ^{2}{\frac {\theta }{2}}}
1035:{\displaystyle {\frac {K^{*}c}{R_{\theta }}}}
8:
264:(RPC), and field flow fractionation (FFF).
1842:N. George, A. Spindel, J. T. Thomasson in
1563:A. Brunsting & P. F. Mullaney (1974).
89:) describes a technique for measuring the
2425:
2163:
1818:
1785:
1755:
1753:
1751:
1596:
1539:
1383:, for each macromolecular size fraction.
1365:
1355:
1349:
1347:
1326:
1320:
1294:
1288:
1263:
1258:
1248:
1243:
1237:
1229:
1123:
1114:
1108:
1062:
1053:
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1024:
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1001:
953:{\displaystyle V={\frac {4}{3}}\pi a^{3}}
944:
927:
919:
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885:
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811:
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534:
517:
444:
414:
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390:
369:, per unit illuminated scattering volume
70:Learn how and when to remove this message
54:, without removing the technical details.
1707:
1705:
1703:
1195:
1154:
982:
1432:
1430:
1428:
1424:
1095:is the concentration of the sample and
1376:{\displaystyle {\frac {r_{g}}{r_{h}}}}
1760:P. J. Wyatt & C. Jackson (1989).
52:make it understandable to non-experts
7:
1917:"Evolution of Wyatt Technology Corp"
1218:Branching and molecular conformation
1159:MALS signals for polystyrene spheres
1964:See, for example Chemical Abstracts
2348:Journal of Applied Polymer Science
1200:BSA Separation and MM distribution
571:
423:
178:after the quantum mechanical term
25:
2068:Field-Flow Fractionation Handbook
122:multiangle laser light scattering
2375:Journal of Materials Chemistry B
1391:Other MALS applications include
1099:is a stretch factor used to put
347:at a detector lying at an angle
224:geometric relationships and the
31:
1143:into the same numerical range.
979:Zimm plot and batch collection
846:
819:
796:
790:
650:
644:
595:
589:
546:
540:
528:
522:
462:
456:
441:
431:
401:
395:
1:
1589:10.1016/S0006-3495(74)85925-4
1177:reversed-phase chromatography
1165:size exclusion chromatography
262:reversed phase chromatography
258:size exclusion chromatography
176:differential light scattering
128:). The insertion of the word
2282:10.1016/0003-2670(93)80373-S
2044:10.1016/0021-9673(96)00134-3
1766:Limnology & Oceanography
1401:protein-protein interactions
1187:Utility of MALS measurements
18:Multi-angle light scattering
2032:Journal of Chromatography A
1173:ion exchange chromatography
298:of the surrounding medium,
285:RayleighâGans approximation
144:phenomenon related to this
83:Multiangle light scattering
2535:
2427:10.1021/acs.biomac.0c00030
2360:10.1002/app.1994.070540110
1921:www.americanlaboratory.com
1820:10.1093/clinchem/21.9.1297
1541:10.1093/clinchem/21.9.1297
1214:of interacting molecules.
181:differential cross section
158:classical light scattering
2463:10.1021/acssynbio.0c00368
2165:10.1103/physrev.134.ab1.2
1787:10.4319/lo.1989.34.1.0096
1694:10.1103/RevModPhys.30.414
235:The commercialization of
2255:10.1103/physrev.179.1238
2228:10.1103/physrev.176.1544
2201:10.1103/physrev.173.1243
2133:10.1103/PhysRev.127.1837
1405:electrophoretic mobility
1315:the hydrodynamic radius
1169:field flow fractionation
373:. The scattering volume
194:dynamic light scattering
108:, by detecting how they
100:and the average size of
2094:Videnski.Selsk.Skrifter
2005:. John Wiley and Sons.
146:static light scattering
2270:Analytica Chimica Acta
2138:BalĂĄzs, Louis (1964).
1494:10.1364/JOSA.40.000768
1377:
1336:
1304:
1275:
1209:Molecular interactions
1201:
1160:
1137:
1085:
1036:
988:
954:
908:
853:
772:
617:
469:
2514:Scientific techniques
2451:ACS Synthetic Biology
1903:U.S. patent 4,140,018
1509:U.S. patent 3,624,835
1411:stability and use in
1378:
1337:
1335:{\displaystyle r_{h}}
1305:
1303:{\displaystyle R^{2}}
1276:
1199:
1158:
1138:
1086:
1037:
986:
955:
909:
854:
773:
618:
470:
1880:10.1364/AO.19.001573
1845:U.S. patent 3689772A
1734:10.1364/AO.27.000217
1346:
1319:
1287:
1228:
1107:
1046:
1000:
918:
914:,
863:
784:
638:
516:
389:
294:, very close to the
2509:Colloidal chemistry
2324:1949JChPh..17.1301Z
2247:1969PhRv..179.1238E
2220:1968PhRv..176.1544E
2193:1968PhRv..173.1243E
2156:1964PhRv..134....1B
2125:1962PhRv..127.1837W
1976:"MALS Bibliography"
1872:1980ApOpt..19.1573B
1778:1989LimOc..34...96W
1726:1988ApOpt..27..217W
1686:1958RvMP...30..414F
1642:10.1364/AO.7.001879
1634:1968ApOpt...7.1879W
1581:1974BpJ....14..439B
1486:1950JOSA...40..768B
1451:1948JChPh..16.1099Z
1409:pharmaceutical drug
1397:protein aggregation
1268:
1253:
1192:Molar mass and size
1163:With the advent of
778:, where
509:, is then given by
277:Rayleigh scattering
98:absolute molar mass
2387:10.1039/d1tb00234a
1906:(1979) filed 1977.
1848:(1972) filed 1971.
1807:Clinical Chemistry
1528:Clinical Chemistry
1512:(1971) filed 1968.
1387:Other applications
1373:
1332:
1300:
1271:
1254:
1239:
1202:
1161:
1133:
1081:
1032:
989:
950:
904:
849:
768:
613:
465:
319:|m - 1| << 1
167:quantum efficiency
2457:(12): 3298â3310.
2414:Biomacromolecules
2381:(14): 3168â3179.
2332:10.1063/1.1747157
2078:978-0-471-18430-0
2012:978-0-471-20172-4
1866:(10): 1573â1581.
1628:(10): 1879â1896.
1459:10.1063/1.1746740
1445:(12): 1099â1116.
1371:
1269:
1151:SEC and flow mode
1131:
1070:
1030:
935:
902:
817:
761:
721:
578:
451:
80:
79:
72:
16:(Redirected from
2526:
2483:
2482:
2446:
2440:
2439:
2429:
2420:(6): 2060â2072.
2405:
2399:
2398:
2370:
2364:
2363:
2342:
2336:
2335:
2307:
2301:
2300:
2297:US Patent Office
2292:
2286:
2285:
2265:
2259:
2258:
2241:(5): 1238â1246.
2231:
2214:(5): 1544â1553.
2204:
2187:(5): 1243â1257.
2176:
2170:
2169:
2167:
2136:
2119:(5): 1837â1843.
2108:
2102:
2101:
2089:
2083:
2082:
2062:
2056:
2055:
2023:
2017:
2016:
1996:
1990:
1989:
1987:
1986:
1972:
1966:
1961:
1955:
1954:
1952:
1951:
1941:"museum | about"
1937:
1931:
1930:
1928:
1927:
1913:
1907:
1905:
1898:
1892:
1891:
1855:
1849:
1847:
1840:
1834:
1832:
1822:
1813:(9): 1297â1304.
1798:
1792:
1791:
1789:
1757:
1746:
1745:
1709:
1698:
1697:
1669:
1663:
1660:
1654:
1653:
1617:
1611:
1610:
1600:
1560:
1554:
1553:
1543:
1534:(9): 1297â1304.
1519:
1513:
1511:
1504:
1498:
1497:
1469:
1463:
1462:
1434:
1382:
1380:
1379:
1374:
1372:
1370:
1369:
1360:
1359:
1350:
1341:
1339:
1338:
1333:
1331:
1330:
1309:
1307:
1306:
1301:
1299:
1298:
1280:
1278:
1277:
1272:
1270:
1267:
1262:
1252:
1247:
1238:
1142:
1140:
1139:
1134:
1132:
1124:
1119:
1118:
1090:
1088:
1087:
1082:
1071:
1063:
1058:
1057:
1041:
1039:
1038:
1033:
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1029:
1028:
1019:
1015:
1014:
1004:
959:
957:
956:
951:
949:
948:
936:
928:
913:
911:
910:
905:
903:
901:
900:
891:
890:
889:
873:
858:
856:
855:
850:
818:
816:
815:
803:
777:
775:
774:
769:
767:
763:
762:
754:
732:
731:
722:
720:
719:
718:
705:
704:
703:
698:
694:
678:
677:
668:
667:
657:
622:
620:
619:
614:
612:
611:
602:
579:
577:
570:
569:
559:
558:
557:
535:
474:
472:
471:
466:
452:
450:
449:
448:
429:
419:
418:
408:
339:
320:
316:and assume that
296:refractive index
245:Wyatt Technology
226:spectral density
75:
68:
64:
61:
55:
35:
34:
27:
21:
2534:
2533:
2529:
2528:
2527:
2525:
2524:
2523:
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2488:
2487:
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2448:
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2407:
2406:
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2367:
2344:
2343:
2339:
2309:
2308:
2304:
2294:
2293:
2289:
2267:
2266:
2262:
2235:Physical Review
2232:
2208:Physical Review
2205:
2181:Physical Review
2178:
2177:
2173:
2144:Physical Review
2137:
2113:Physical Review
2110:
2109:
2105:
2091:
2090:
2086:
2079:
2064:
2063:
2059:
2025:
2024:
2020:
2013:
1998:
1997:
1993:
1984:
1982:
1974:
1973:
1969:
1962:
1958:
1949:
1947:
1939:
1938:
1934:
1925:
1923:
1915:
1914:
1910:
1901:
1899:
1895:
1857:
1856:
1852:
1843:
1841:
1837:
1800:
1799:
1795:
1759:
1758:
1749:
1711:
1710:
1701:
1671:
1670:
1666:
1661:
1657:
1619:
1618:
1614:
1562:
1561:
1557:
1521:
1520:
1516:
1507:
1506:P. J. Wyatt in
1505:
1501:
1480:(11): 768â778.
1474:J. Opt. Soc. Am
1471:
1470:
1466:
1436:
1435:
1426:
1421:
1389:
1361:
1351:
1344:
1343:
1322:
1317:
1316:
1290:
1285:
1284:
1226:
1225:
1220:
1211:
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1105:
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1043:
1020:
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998:
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976:
968:
940:
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807:
782:
781:
733:
723:
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706:
680:
679:
669:
659:
658:
636:
635:
630:
603:
561:
560:
549:
536:
514:
513:
503:
496:
492:
488:
440:
430:
410:
409:
387:
386:
367:
333:
318:
314:
310:
303:
292:
270:
198:Brownian motion
154:
114:collimated beam
76:
65:
59:
56:
48:help improve it
45:
36:
32:
23:
22:
15:
12:
11:
5:
2532:
2530:
2522:
2521:
2516:
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2506:
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2490:
2485:
2484:
2441:
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2365:
2337:
2302:
2287:
2260:
2171:
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2084:
2077:
2071:. Wiley-IEEE.
2057:
2038:(2): 215â229.
2018:
2011:
1991:
1967:
1956:
1932:
1908:
1893:
1860:Applied Optics
1850:
1835:
1793:
1747:
1720:(2): 217â221.
1714:Applied Optics
1699:
1680:(2): 414â418.
1674:Rev. Mod. Phys
1664:
1655:
1622:Applied Optics
1612:
1575:(6): 439â453.
1555:
1514:
1499:
1464:
1423:
1422:
1420:
1417:
1388:
1385:
1368:
1364:
1358:
1354:
1329:
1325:
1297:
1293:
1266:
1261:
1257:
1251:
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1236:
1233:
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1216:
1210:
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1130:
1127:
1122:
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1113:
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1077:
1074:
1069:
1066:
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1056:
1052:
1027:
1023:
1018:
1013:
1009:
980:
977:
975:
972:
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961:
960:
947:
943:
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888:
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848:
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810:
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308:
301:
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2357:
2353:
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2317:
2313:
2312:J. Chem. Phys
2306:
2303:
2298:
2291:
2288:
2283:
2279:
2275:
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2264:
2261:
2256:
2252:
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2186:
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2161:
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2153:
2149:
2145:
2141:
2140:"Errata Ibid"
2134:
2130:
2126:
2122:
2118:
2114:
2107:
2104:
2099:
2095:
2088:
2085:
2080:
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2070:
2069:
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2058:
2053:
2049:
2045:
2041:
2037:
2033:
2029:
2022:
2019:
2014:
2008:
2004:
2003:
1995:
1992:
1981:
1980:www.wyatt.com
1977:
1971:
1968:
1965:
1960:
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1946:
1945:www.wyatt.com
1942:
1936:
1933:
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1918:
1912:
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1873:
1869:
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1854:
1851:
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1839:
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1830:
1826:
1821:
1816:
1812:
1808:
1804:
1797:
1794:
1788:
1783:
1779:
1775:
1772:(I): 96â112.
1771:
1767:
1763:
1756:
1754:
1752:
1748:
1743:
1739:
1735:
1731:
1727:
1723:
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1715:
1708:
1706:
1704:
1700:
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1691:
1687:
1683:
1679:
1675:
1668:
1665:
1659:
1656:
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1647:
1643:
1639:
1635:
1631:
1627:
1623:
1616:
1613:
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1582:
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1483:
1479:
1475:
1468:
1465:
1460:
1456:
1452:
1448:
1444:
1440:
1439:J. Chem. Phys
1433:
1431:
1429:
1425:
1418:
1416:
1414:
1410:
1406:
1402:
1398:
1394:
1386:
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1102:
1098:
1094:
1078:
1075:
1072:
1067:
1064:
1059:
1054:
1050:
1025:
1021:
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1011:
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993:Bruno H. Zimm
985:
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973:
971:
969:
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941:
937:
932:
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924:
921:
897:
893:
886:
882:
878:
875:
869:
866:
843:
840:
837:
834:
831:
828:
825:
822:
812:
808:
804:
799:
793:
787:
780:
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758:
755:
750:
747:
744:
741:
738:
734:
728:
724:
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711:
707:
700:
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691:
688:
685:
681:
674:
670:
664:
660:
653:
647:
641:
634:
633:
632:
608:
604:
599:
592:
586:
583:
580:
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415:
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398:
392:
385:
384:
383:
381:
376:
372:
368:
361:
358:
354:
350:
344:
341:
337:
331:
327:
323:
321:
315:
304:
297:
293:
286:
281:
278:
274:
267:
265:
263:
259:
253:
251:
246:
242:
238:
233:
229:
227:
221:
217:
215:
214:phytoplankton
209:
206:
201:
199:
195:
191:
187:
183:
182:
177:
173:
168:
162:
159:
151:
149:
147:
141:
137:
135:
131:
127:
123:
119:
115:
111:
110:scatter light
107:
103:
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95:
92:
88:
84:
74:
71:
63:
53:
49:
43:
40:This article
38:
29:
28:
19:
2504:Spectroscopy
2454:
2450:
2444:
2417:
2413:
2403:
2378:
2374:
2368:
2351:
2347:
2340:
2318:(12): 1301.
2315:
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2305:
2296:
2290:
2273:
2269:
2263:
2238:
2234:
2211:
2207:
2184:
2180:
2174:
2150:(7AB): AB1.
2147:
2143:
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2112:
2106:
2097:
2093:
2087:
2067:
2060:
2035:
2031:
2021:
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1994:
1983:. Retrieved
1979:
1970:
1959:
1948:. Retrieved
1944:
1935:
1924:. Retrieved
1920:
1911:
1896:
1863:
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1413:nanomedicine
1393:nanoparticle
1390:
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305:. If we set
299:
288:
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275:
271:
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236:
234:
230:
222:
218:
210:
202:
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179:
175:
172:densitometer
163:
155:
142:
138:
134:Hg-arc lamps
129:
125:
121:
86:
82:
81:
66:
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41:
357:solid angle
2519:Scattering
2493:Categories
2354:: 91â103.
1985:2017-02-23
1950:2017-02-23
1926:2017-02-23
1569:Biophys. J
1419:References
353:subtending
338:| â 0
334:|1 â
330:LorenzâMie
326:LorenzâMie
237:multiangle
205:collimated
152:Background
2479:227167991
1399:studies,
1126:θ
1121:
1065:θ
1060:
1026:θ
1012:∗
987:Zimm plot
938:π
894:λ
879:π
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841:
835:ξ
832:−
829:ξ
826:
809:ξ
794:ξ
756:θ
751:
712:π
689:−
648:θ
593:θ
572:Δ
544:θ
526:θ
460:θ
424:Δ
399:θ
102:molecules
94:scattered
2471:33232156
2436:32319761
2395:33885621
2276:: 1â40.
1888:20221079
1742:20523583
1650:20068905
1395:sizing,
190:neutrons
106:solution
60:May 2014
2320:Bibcode
2243:Bibcode
2216:Bibcode
2189:Bibcode
2152:Bibcode
2121:Bibcode
2100:: 1â62.
2052:8765649
1868:Bibcode
1829:1149235
1774:Bibcode
1722:Bibcode
1682:Bibcode
1630:Bibcode
1607:4134589
1598:1334522
1577:Bibcode
1550:1149235
1482:Bibcode
1447:Bibcode
485:k = 2Ďn
260:(SEC),
116:from a
46:Please
2477:
2469:
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2075:
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2009:
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1283:Where
1175:, and
1091:where
479:where
268:Theory
2475:S2CID
307:m = n
241:USFDA
130:laser
126:MALLS
118:laser
91:light
2467:PMID
2432:PMID
2391:PMID
2073:ISBN
2048:PMID
2007:ISBN
1884:PMID
1833:>
1825:PMID
1738:PMID
1646:PMID
1603:PMID
1546:PMID
1103:and
963:and
507:R(θ)
481:i(θ)
351:and
283:The
186:Ď(θ)
112:. A
87:MALS
2459:doi
2422:doi
2383:doi
2356:doi
2328:doi
2278:doi
2274:272
2251:doi
2239:179
2224:doi
2212:176
2197:doi
2185:173
2160:doi
2148:134
2129:doi
2117:127
2040:doi
2036:740
1876:doi
1815:doi
1782:doi
1730:doi
1690:doi
1638:doi
1593:PMC
1585:doi
1536:doi
1490:doi
1455:doi
1112:sin
1051:sin
1042:vs
838:cos
823:sin
748:sin
493:, n
250:CCD
104:in
50:to
2495::
2473:.
2465:.
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2416:.
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1978:.
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1919:.
1882:.
1874:.
1864:19
1862:.
1823:.
1811:21
1809:.
1805:.
1780:.
1770:34
1768:.
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1750:^
1736:.
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1427:^
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1101:kc
489:/Îť
375:ÎV
371:ÎV
360:ÎΊ
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