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| '''Multiangle light scattering''' (MALS) is a technique for determining, independently, the [[absolute molar mass]] and the average size of particles in solution, by detecting [[light scattering|how they scatter light]]. Collimated light from a [[laser]] source is most often used, in which case the technique can be referred to as '''multiangle laser light scattering''' (MALLS). The insertion of the word “laser” was intended to reassure those used to making light scattering measurements with conventional light sources such as Hg-arc lamps that low angle measurements could now be made. Until the advent of lasers and their associated fine beams of very 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 to mention the light source has been dropped and the term MALS used throughout.
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| 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. <!--(Figure 1 is a schematic of such measurement wherein all detectors lie in a plane.)--> A discussion of the physical phenomenon related to this [[static light scattering]], including some applications, data analysis methods and graphical representations associated therewith are presented.
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| Associated with a MALS measurement are a variety of ancillary elements. Most important among them is a collimated or focused light source (nowadays, usually a laser) producing a fine beam of monochromatic light to illuminate a region of the sample. In modern instruments, the beam is generally polarized, though other polarizations may be used especially when studying anisotropic particles. Early work in the field was performed with unpolarized sources such as Hg-arc lamps. Essential is an optical cell containing the sample being measured. Alternatively manifold elements can be used for the case of a flowing system. 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.
| | It involves expertise and knowledge of various tools and technologies used for creating websites. Offshore expert Word - Press developers high level of interactivity, accessibility, functionality and usability of our website can add custom online to using. * A community forum for debate of the product together with some other customers in the comments spot. In the recent years, there has been a notable rise in the number of companies hiring Indian Word - Press developers. Over a million people are using Wordpress to blog and the number of Wordpress users is increasing every day. <br><br>Any business enterprise that is certainly worth its name should really shell out a good deal in making sure that they have the most effective website that provides related info to its prospect. Best of all, you can still have all the functionality that you desire when you use the Word - Press platform. This may possibly also permit it currently being seriously straightforward to modify the hues within your Ad - Sense code so the ads blend nicely with the many term broad internet word wide web web page in case you can come to your conclusion to run the adverts. Apart from these, you are also required to give some backlinks on other sites as well. You can also get a free keyword tool that is to determine how strong other competing sites are and number of the searches on the most popular search sites. <br><br>ve labored so hard to publish and put up on their website. If you beloved this write-up and you would like to get much more data about [http://www.heroesandvillains.info/forumv3/index.php?thememode=full;redirect=https://wordpress.org/plugins/ready-backup/ wordpress backup] kindly pay a visit to our web page. When a business benefits from its own domain name and a tailor-made blog, the odds of ranking higher in the search engines and being visible to a greater number of people is more likely. Possibly the most downloaded Word - Press plugin, the Google XML Sitemaps plugin but not only automatically creates a site map linking to everyone your pages and posts, it also notifies Google, Bing, Yahoo, and Ask. Storing write-ups in advance would have to be neccessary with the auto blogs. Have you heard about niche marketing and advertising. <br><br>The next thing I did after installing Wordpress was to find myself a free good-looking Wordpress-theme offering the functionality I was after. Find more information about Design To Wordpress here. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. A whole lot worse, your site will likely be useless as well as your merchandise won't sell if no one has the endurance to wait for the web pages to load. Now all you have to do is log into your Word - Press site making use of the very same username and password that you initially had in your previous site. <br><br>This advice is critical because you don't want to waste too expensive time establishing your Word - Press blog the exact method. In fact portfolio Word - Press themes is a smooth and attractive but considerably flawed Word - Press theme in creating simpler to the photographers or designers to develop a specific internet site showcasing their most current perform since it appear modern-day and has fantastic typography and large photographs which would develop an attractive wanting portfolio internet site. It can be concluded that white label SEO comprise of a third party who resells a contract involving IT expert or consultant, SEO professional and end user. Web developers and newbies alike will have the ability to extend your web site and fit other incredible functions with out having to spend more. Press CTRL and the numbers one to six to choose your option. |
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| <!--{{clearright}}
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| [[File:MALS detector framework.png|thumb|right|Figure 2. Three-dimensional detector framework for MALS measurement of aerosol particles.]]
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| [[File:MALS optical framework.png|thumb|right|Figure 3. Framework to hold optical fibers for under water MALS measurements.]]-->
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| 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<ref name=Wyatt1>{{cite journal|author=P. J. Wyatt, Y. J. Chang, C. Jackson, R. G. Parker, D.T. Phillips, S.D. Phillips, J. R. Bottiger, and K. L. Schehrer|title=Aerosol Particle Analyzer|journal=Applied Optics|volume=27|issue=2|pages=217–221|year=1988|pmid=20523583|doi=10.1364/AO.27.000217|bibcode = 1988ApOpt..27..217W }}</ref><ref name=Wyatt2>{{cite journal|author=P. J. Wyatt and C. Jackson|title=Discrimination of Phytoplankton via Light-Scattering Properties|journal=Limnology & Oceanography|volume=34|issue=I|pages=96|year=1989|doi=10.4319/lo.1989.34.1.0096}}</ref> 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]].
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| ==Background==
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| <!--{{clearright}}
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| [[File:Zimm photometer schematic.png|thumb|right|Figure 8. A schematic diagram of Zimm’s earliest scanning photometer with temperature controlled sample cell.]]
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| [[File:Brice Phoenix light scattering photometer.png|thumb|right|Figure 9. Schematic of the optical system of the Brice Phoenix light scattering photometer.]]
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| [[File:Film photometer schematic.png|thumb|right|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.]]-->
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| The measurement of scattered light from an illuminated sample forms the basis of the so-called [[static light scattering|classical light scattering]] measurement. Historically, such measurements were made using a single detector<ref name=Zimm1 /><ref>{{cite journal|author=B. A. Brice, M. Halwer, and R. Speiser|title=Photoelectric light scattering photometer for determining high molecular weights|journal=J. Opt. Soc. Am.|volume=40|pages=768–778|year=1950|doi=10.1364/JOSA.40.000768}}</ref> 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 Sofica photometer introduced in the late 1960s.<!-- 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<ref>P. J. Wyatt in {{US patent|3624835}} (1971) filed 1968.</ref> was well understood, though not implemented commercially<ref name=CC21>{{cite journal|author=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|title=A Flow-System Multiangle Light-Scattering Instrument for Cell Characterization|journal=Clinical Chemistry|volume=21|pages=1297–1304|year=1975|pmid=1149235|issue=9}}</ref> until the late 1970s. Multiple detectors having different [[quantum efficiency]] 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<ref>{{cite journal|author=A. Brunsting and P. F. Mullaney|title=Differential Light Scattering from Spherical Mammalian Cells|journal=Biophys. J.|volume=14|pages=439–453|year=1974|doi=10.1016/S0006-3495(74)85925-4|pmid=4134589|issue=6|pmc=1334522|bibcode = 1974BpJ....14..439B }}</ref> in 1974. It 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 scattering''<ref name=Wyatt5>{{cite journal|author=P. J. Wyatt|title=Differential Light Scattering: A Physical Method for Identifying Living Bacterial Cells|journal=Applied Optics|volume=7|pages=1879–1896|year=1968|doi=10.1364/AO.7.001879|pmid=20068905|issue=10|bibcode = 1968ApOpt...7.1879W }}</ref> after the quantum mechanical term ''[[Cross section (physics)|differential cross section]]'',<ref>Cf. L. I. Schiff, Quantum Mechanics (McGraw-Hill Book Company, New York 1955).</ref> ''σ(θ)'' 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,<ref>{{cite journal|author=S. Fernbach|title=Nuclear Radii as Determined by Scattering of Neutrons|journal=Revs. Modern Phys.|volume=30|pages=414–418|year=1958|doi=10.1103/RevModPhys.30.414|bibcode = 1958RvMP...30..414F }}</ref> such as neutrons. It is important to distinguish between [[differential light scattering]] and [[dynamic light scattering]], 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, [[Brownian motion]] of the molecules or particles in solution or suspension.
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| 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 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.
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| Another type of MALS device was developed in 1974 by Salzmann et al.[3] based on a light pattern detector invented by George et al.[4] 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.
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| The innovative 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.[5] had developed 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°.
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| The commercialization of ''multiangle'' systems began in 1977 when Phillips<ref>L. V. Maldarelli, D. T. Phillips, W. L. Proctor, P. J. Wyatt, and T. C. Urquhart, Programmable action sampler system, {{US patent|4140018}} (1979) filed 1977.</ref> 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<ref name=Wyatt1 /> 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.<ref name=Wyatt2 /> Signals were collected by optical fibers and transmitted to individual photomultipliers. A more recent instrument was commercialized, which measures 7 scattering angles using a [[Charge-coupled device|CCD]] detector (BI-MwA: [[Brookhaven Instruments]] Corp, Hotlsville, NY).
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| <!--{{clearright}}
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| [[File:Beckman low-angle laser light-scattering photometer.png|thumb|right|Figure 11. Optical diagram of the Beckman low-angle laser light-scattering photometer: LA, laser; W1-W2, sample cell windows; … DE, photomultiplier.]]-->
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| The commercial introduction of conventional light scattering instrumentation in the early 1970s that incorporated a ''laser'' light source<ref>{{cite journal|author=D. T. Phillips|title=Evolution of a light scattering photometer|journal=BioScience|volume=21|pages=865–867|date= August 15, 1971 |doi=10.2307/1295813|issn=00063568|issue=16|first=D. T.|url=http://jstor.org/stable/1295813|publisher=American Institute of Biological Sciences}}</ref> 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 Zimm<ref name=Zimm1 />), introduced their low angle laser light scattering instrument, developed by Wilber Kaye<ref name=Kaye1>{{cite journal|author=W. Kaye|title=Low-angle laser light scattering|journal=Anal. Chem.|volume=45|pages=221A–225A|year=1973|doi=10.1021/ac60325a068|last2=Grossman|first2=D. M.|last3=Jacobs|first3=A. L.|last4=Michaelis|first4=A. F.|last5=Salstiz|first5=B.}}</ref><ref name=Kaye2>{{cite journal|author=W. Kaye and A. J. Havlik|title=Low-angle laser light scattering—Absolute Calibration|journal=Applied Optics|volume=12|pages=541–550|year=1973|doi=10.1364/AO.12.000541|pmid=20125341|issue=3|bibcode = 1973ApOpt..12..541K }}</ref><ref name=Kaye3>{{cite journal|author=W. Kaye and J. B. McDaniel|title=Low-angle laser light scattering—Rayleigh factors and depolarization ratios|journal=Applied Optics|volume=13|pages=1934–1937|year=1974|doi=10.1364/AO.13.001934|pmid=20134598|issue=8|bibcode = 1974ApOpt..13.1934K }}</ref> and his colleagues, at the American Chemical Society’s 1972 National meeting in Los Angeles. <!-- Figure 11 shows an optical diagram of their instrument.<ref name=Kaye3 /> --> They referred to their instrument as a LALLS (Low-Angle Laser Light Scattering) photometer with the word “laser” added, as discussed earlier, 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. The only LALS system currently available is commercialized by Viscotek/Malvern. By 1992, the first commercial light scattering photometer providing a plurality of discrete detectors was introduced. 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. The classic 90° detection angle is referred to as right-angle light scattering, RALS.
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| The literature associated with measurements made by MALS photometers is extensive.<ref>[http://www.cas.org See, for example Chemical Abstracts]</ref> both in reference to batch measurements of particles/molecules and measurements following fractionation by chromatographic means such as [[size exclusion chromatography]]<ref>{{cite book|author=A. M. Striegel, W. W. Yau, J. J. Kirkland, and D. D. Bly|title=Modern Size-Exclusion Liquid Chromatography: Practice of Gel Permeation and Gel Filtration Chromatography|publisher=John Wiley and Sons|year=2009|isbn=0-471-20172-3|pages=|url=http://books.google.com/?id=JF4f4eLBkJ8C&printsec=frontcover}}</ref> (SEC), [[Reversed-phase_chromatography|reversed phase chromatography]]<ref>{{cite journal|author=I. V. Astafieva, G. A. Eberlein, Y. J. Wang|title=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|journal=Journal of Chromatography A|volume=740|pages=215–229|year=1996|doi=10.1016/0021-9673(96)00134-3|pmid=8765649|issue=2}}</ref> (RPC), and field flow fractionation<ref>{{cite book|editor=M. Schimpf, K. Caldwell, and J. C. Giddings|title=Field-Flow Fractionation Handbook|publisher=Wiley-IEEE|year=2000|isbn=0-471-18430-6|url=http://books.google.com/?id=zJzJvs4LQAwC&printsec=frontcove}}</ref> (FFF).
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| ==Theory==
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| [[Rayleigh scattering]] is the elastic scattering of light or other electromagnetic radiation by objects much smaller than the wavelength of the incoming light. It often can occur when light travels in transparent solids and liquids, but is more prevalent in gases. This type of scattering is responsible for the blue color of the sky during the day. [[Rayleigh scattering]] is inversely proportional to the fourth power of wavelength, which means that the shorter wavelength of blue light will be scattered more intensely than the longer wavelengths (e.g. green and red). This gives the sky a blue appearance.
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| So-called Rayleigh-Gans scattering, a generalization of Rayleigh scattering, assumes that the scattering particles have a refractive index, ''n<sub>1</sub>'', very close to the [[refractive index]] of the surrounding medium, ''n<sub>0</sub>''. If we set ''m = n<sub>1</sub>/n<sub>0</sub>, |1 − m| = 1'', then such particles may be considered as composed of very small elements, each of which may be represented as a Rayleigh particle. Thus each small element of the larger particle is assumed to scatter independently of any other.
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| [[Lorenz-Mie scattering|Lorenz-Mie]] scattering refers to the scattering of light by spherical particles. Rayleigh-Gans scattering and [[Lorenz-Mie scattering|Lorenz-Mie]] scattering produce identical results for spheres in the limit as {{nowrap||1 − ''m''| → 0}}.
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| Scattering data are 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 at a detector lying at an angle ''θ'' and subtending a solid angle ''ΔΩ'' is defined as the intensity of light per unit solid angle per unit incident intensity, ''I<sub>0</sub>'', per unit illuminated scattering volume ''ΔV''. The scattering volume ''ΔV'' 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. Assuming that the light is polarized perpendicular to the plane of the detectors. The scattered light intensity measured by the detector at angle ''θ'' in excess of that scattered by the suspending fluid would be
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| :<math>I(\theta ) = \frac{{I_0 N\Delta V}} {{(kr)^2}}i(\theta )</math>,
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| where ''i(θ)'' is the scattering function<ref name=Zimm1>{{cite journal|author=B. A. Zimm|title=Apparatus and methods for measurement and interpretation of the angular variation of light scattering; preliminary results on polystyrene solutions|journal=J. Chem. Phys.|volume=16|pages=1099–1116|year=1948|doi=10.1063/1.1746740|bibcode = 1948JChPh..16.1099Z }}</ref> of a single particle, ''k = 2πn<sub>0</sub>/λ<sub>0</sub>, n<sub>0</sub>'' is the refractive index of the suspending fluid, and ''λ<sub>0</sub>'' is the vacuum wavelength of the incident light. The excess Rayleigh ratio, ''R(θ)'', is then given by
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| :<math>R(\theta ) = \frac{{I(\theta )r^2}}{{I_0 \Delta V}} = Ni(\theta )/k^2</math>.
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| 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, ''n<sub>0</sub>'' that is ''n/n<sub>0</sub> = m = 1'', the scattering function in the scattering plane is the relatively complex quantity
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| :<math>i(\theta ) = \frac{{k^2 V^2 \left| {m - 1} \right|^2}}{{4\pi ^2}}G^2 \left( {2ka\sin \frac{\theta }{2}} \right)</math>, where
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| :<math>G(\xi ) = \frac{3}{{\xi ^2}}(\sin \xi - \xi \cos \xi )</math>, <math>k = \frac{{2\pi n_0}}{{\lambda _0}}</math>, <math>V = \frac{4}{3}\pi a^3 </math>
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| and ''λ<sub>0</sub>'' is the wavelength of the incident light in vacuum. | |
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| ==References==
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| {{reflist|2}}
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| [[Category:Scattering, absorption and radiative transfer (optics)]]
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| [[Category:Spectroscopy]]
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| [[Category:Colloidal chemistry]]
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| [[Category:Scientific techniques]]
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