Multiangle light scattering

Multiangle Light Scattering (MALS) and Differential Light Scattering (DLS)

The term Multiangle Light Scattering, or MALS, refers generally to the measurement of light scattered by a single particle or an ensemble of particles/molecules, illuminated by a collimated beam of light, into a discrete set of scattering angles at each of which lies an associated detector. (Figure 1 is a schematic of such measurement wherein all detectors lie in a plane.) MALS is a special form of the more general Differential Light Scattering (earlier known as DLS) that is discussed in further detail below. Associated with a MALS measurement are a variety of ancillary elements. Most important among them is a collimated light source (nowadays, usually a laser) producing a fine beam of monochromatic light to illuminate a small region of the sample. The beam is generally plane polarized, though other polarizations may be used especially when studying anisotropic particles. Essential, as well, is an optical cell containing the sample being measured, manifold elements to hold the cell and light source and permit, for the case of a flowing system, the insertion or injection into the cell a variety of samples. If single-particles scattering properties in air 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.

Although most MALS-based measurements are performed in a plane per Fig. 1 containing a set of detectors ¹ usually equidistantly placed from a centrally located sample through which the illuminating beam passes, three dimensional versions ^2,3 also have been developed wherein the detectors lie on the surface of a 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. These structures are shown in Figs. 2 and 3. The former framework is used for measuring aerosol particles while the latter was used to examine marine organisms such as phytoplankton.

Another type of MALS measurement was developed in 1974 by Salzmann⁴ et al. based on a light pattern detector invented by George⁵ 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 geometric relationships and the spectral density distribution of objects recorded on film transparencies. This detector is shown in Fig. 4 with the Salzman et al. implementation shown in Fig. 5. Salzman et al. used only the top set of detectors that captured scattered light at different small forward polar scattering angles $\theta$ integrated over azimuthal scattering angles $\phi$ between 0° and 180°.

Although the Salzman et al. approach was restricted to 32 small scattering angles between 0° and 30°, and averaging over a broad range of azimuthal angles, by 1980 Bartholi⁶ et al. had overcome this limitation using an elliptical reflector to permit measurement at 30 polar angles over the range 2.5° $\leqslant \theta \leqslant$ 177.5° with a resolution of 2.1° as shown in Figs. 6 and 7.

Scattering data are usually expressed 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 at a detector lying at an angle $\theta$ and subtending a solid angle $\Delta v$ is defined as the intensity of light per unit solid angle per unit incident intensity, $I_{0}$ , per unit illuminated scattering volume $\Delta v$. The scattering volume $\Delta v$ 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 by a laser. Assume that the light is plane polarized perpendicular to the plane of the detectors such as shown in Fig. 1. The scattered light intensity detected by the detector at angle $\theta$ in excess of that scattered by the suspending fluid would be $I(\theta )={\frac {I_{0}N\Delta v}{(kr)^{2}}}i(\theta )$ , where $i(\theta )$ is the scattering function ⁷ of a single particle, $k=2\pi n_{0}/\lambda _{0}$, $n_{0}$ is the refractive index of the suspending fluid, and $\lambda _{0}$ is the vacuum wavelength of the incident light. The excess Rayleigh ratio, $R(\theta )$ , is then given by $R(\theta )={\frac {I(\theta )r^{2}}{I_{0}\Delta v}}=Ni(\theta )/k^{2}.$

Even for a simple homogeneous sphere of radius a whose refractive index, n, is very nearly the same as the refractive index of the suspending fluid, n0, i. e. , the scattering function in the scattering plane of Fig. 1 is the relatively complex quantity , where

,  ,  , and  is the wavelength of the incident light in vacuum.

History

The measurement of scattered light from an illuminated sample forms the basis of the so-called classical light scattering measurement. Historically, such measurements were made using a single detector ^7,8 rotated in an arc about the illuminated sample. Some early examples of instruments used to make these measurements are shown, respectively, in Figs. 8 and 9. 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 angular location of interest ⁹ was well understood, though not implemented commercially ⁴ until the late 1970s. An interesting system based upon the use of high speed film was developed by Brunsting and Mullaney ¹⁰ in 1974 permitted the entire range of scattered intensities to be recorded on the film, as shown in Fig. 10, with a subsequent densitometer 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 differential light scattering¹¹ after the quantum mechanical term differential cross section ¹², 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 ¹³, such as neutrons.

The commercialization of multiangle systems began in 1977 when Phillips ¹⁴ introduced a flow-through capillary surrounded by 8 discrete detectors for a customized bioassay system developed for the USFDA. His implementation was commercialized in 1984 with the introduction of a 15 detector instrument (Dawn-F: Wyatt Technology Corporation, Santa Barbara, CA). By 1985 a three dimensional configuration of Fig. 2 was introduced ² specifically to measure the scattering properties of single aerosol particles. At about the same time, the underwater device of Fig. 5 was built to measure the scattered light properties of single phytoplankton ³. Signals were collected by optical fibers and transmitted to individual photomultipliers.

The commercial introduction of conventional light scattering instrumentation in the early 1970s that incorporated a laser light source ¹⁵ was the impetus for the development of a new class of photometers. In 1972 Beckman Instruments, recognizing that the use of a laser source would permit scattered light measurements to be made at very small angles (for example for determining the weight average molar mass of a sample following the method of Zimm⁷), introduced their low angle laser light scattering instrument, developed by Wilber Kaye ^{16, 17, 18} and his colleagues, at the American Chemical Society’s 1972 National meeting in Los Angeles. Figure 11 shows an optical diagram of their instrument ¹⁸. They referred to their instrument as a LALLS (Low-Angle Laser Light Scattering) photometer with the word “laser” added to emphasize the ability to measure at low angles since the very narrow beam produced by a laser would permit measurement at correspondingly smaller scattering angles than achievable using conventional light sources. By 1992 the first commercial light scattering photometer providing a plurality of discrete detectors was introduced ¹. Although the term DLS (differential light scattering) was initially associated with such multiangle detectors (the term is now most commonly used to refer to “dynamic light scattering”), following Beckman’s popularization of the term “LALLS”, MALLS became a common descriptive. The laser reference was finally dropped and MALS has survived. Two angle devices have appeared with the descriptor DALS (dual angle light scattering) or TALS, but in general any device with more than a single detector and with a laser light source have now become universally referred to as a MALS photometer.

The literature associated with measurements made by MALS photometers is extensive¹⁹ both in reference to batch measurements of particles/molecules and measurements following fractionation by chromatographic means such as size exclusion chromatography²⁰ (SEC), reversed phase chromatography²¹ (RPC), and field flow fractionation²² (FFF).

References

1. http://www.wyatt.com/solutions/hardware/ ; http://www.BIC.com

2. P. J. Wyatt, Y. J. Chang, C. Jackson, R. G. Parker, D.T. Phillips, S.D. Phillips, J. R. Bottiger, and K. L. Schehrer, “Aerosol Particle Analyzer,” Applied Optics 27, 217-221 (1988).

3. P. J. Wyatt and C. Jackson, “Discrimination of Phytoplankton via Light-Scattering Properties,” Limnology & Oceanography 34(I) 96 (1989).

4. G. C. Salzmann, J. M. Crowell, C. A. Goad, K. M. Hansen, R. D. Hiebert, P. M. LaBauve, J. C. MartIn, M. L. Ingram, and P. F. Mullaney, “A Flow-System Multiangle Light-Scattering Instrument for Cell Characterization,” CLINICAL CHEMISTRY 21, 1297-1304 (1975).

5. N. George, J. T. Thomasson, and A. Spindel. U. S. Patent 3,689,772 (1972).

6. M. Bartholdi, G. C. Salzmann, R. D. Hiebert, and M. Kerker, “Differential light scattering photometer for rapid analysis of single particles in flow,“ Applied Optics 19, 1573-1581 (1980).

7. B. A. Zimm, “Apparatus and methods for measurement and interpretation of the angular variation of light scattering; preliminary results on polystyrene solutions,” J. Chem. Phys. 16, 1099-1116 (1948).

8. B. A. Brice, M. Halwer, and R. Speiser, “Photoelectric light scattering photometer for determining high molecular weights,” J. Opt. Soc. Am. 40, 768-778 (1950).

9. P. J. Wyatt in U. S. Patent 3,624,835 (1971) filed 1968.

10. A. Brunsting and P. F. Mullaney, “Differential Light Scattering from Spherical Mammalian Cells,” Biophys. J. 14, 439-453 (1974).

11. P. J. Wyatt, “Differential Light Scattering: A Physical Method for Identifying Living Bacterial Cells,” Applied Optics 7, 1879-1896 (1968).

12. Cf. L. I. Schiff, Quantum Mechanics (McGraw-Hill Book Company, New York 1955).

13. S. Fernbach, “Nuclear Radii as Determined by Scattering of Neutrons,” Revs. Modern Phys. 30, 414-418 (1958).

14. L. V. Maldarelli, D. T. Phillips, W. L. Proctor, P. J. Wyatt, and T. C. Urquhart, Programmable action sampler system, U. S. Patent 4,140,018 (1979) filed 1977.

15. D. T. Phillips “Evolution of a light scattering photometer,” BioScience 21, 865-867 (1971).

16. W. Kaye, “Low-angle laser light scattering,” Anal. Chem. 45, 221A-225A (1973).

17. W. Kaye and A. J. Havlik, “Low-angle laser light scattering—Absolute Calibration,” Applied Optics 12, 541-550 (1973).

18. W. Kaye and J. B. McDaniel, “Low-angle laser light scattering—Rayleigh factors and depolarization ratios,” Applied Optics 13, 1934-1937 (1974).

19. http://www.wyatt.com/literature/bibliography.cfm includes over 5300 references.

20. A. M. Striegel, W. W. Yau, J. J. Kirkland, and D. D. Bly, Modern size-exclusion liquid chromatography (John Wiley & Sons, Inc., Hoboken 2009)

21. Need Reference

22. Need Reference

Figure 1. Schematic of MALS measurement in a plane.

Figure 2. Three dimensional detector framework for MALS measurement of aerosol particles.

Figure 3. Framework to hold optical fibers for under water MALS measurements.

Figure 4. The photodiode light pattern detector of George et al.

Figure 5. The scattering arrangement of Salzman et al.

Figure 6. The optical basis of the Bartholdi et al. instrument showing the intersection of the laser beam and particle stream at the primary focus of a circular strip on an ellipsoidal reflector and also the reflected scattered rays converging to the detector array.

Figure 7. Schematic diagram of the detector array of Fig. 6.

Figure 8. A schematic diagram of Zimm’s earliest scanning photometer with temperature controlled sample cell.

Figure 9. Schematic of the optical system of the Brice Phoenix light scattering photometer.

Figure 10. Schematic diagram of the film photometer. The laser provides the incident light to the scatterers in the cuvette and the film records the scattered light.

Figure 11. Optical diagram of the Beckman low-angle laser light-scattering photometer: LA, laser; W1-W2, sample cell windows; … DE, photomultiplier.