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Dynamic light scattering is a powerful technique in physics, which can be used to determine the size distribution profile of small particles in solution. This article needs additional references or sources for verification. ...
A particle is Look up Particle in Wiktionary, the free dictionary In particle physics, a basic unit of matter or energy. ...
Making a saline water solution by dissolving table salt (NaCl) in water This article is about chemical solutions. ...
Description
When light hits small particles the light scatters in all directions (Rayleigh scattering) so long as the particles are small compared to the wavelength (< 250 nm). If the light source is a laser, and thus is monochromatic and coherent, then one observes a time-dependent fluctuation in the scattering intensity. These fluctuations are due to the fact that the small molecules in solutions are undergoing Brownian motion and so the distance between the scatterers in the solution is constantly changing with time. This scattered light then undergoes either constructive or destructive interference by the surrounding particles and within this intensity fluctuation information is contained about the time scale of movement of the scatterers. Rayleigh scattering causing the blue hue of the sky and the reddening at sunset Rayleigh scattering (named after Lord Rayleigh) is the scattering of light, or other electromagnetic radiation, by particles much smaller than the wavelength of the light. ...
A nanometre (American spelling: nanometer, symbol nm) is a unit of length in the metric system, equal to one thousand-millionth of a metre, which is the current SI base unit of length. ...
Experiment with a laser (US Military) In physics, a laser is a device that emits light through a specific mechanism for which the term laser is an acronym: Light Amplification by Stimulated Emission of Radiation. ...
A photograph of a sign in grayscale The same photograph in black and white Monochrome comes from the two Greek words mono (μωνο, meaning one), and chroma (χÏωμα, meaning surface or the color of the skin). A monochromatic object has a single color. ...
Coherence is the property of wave-like states that enables them to exhibit interference. ...
Three different views of Brownian motion, with 32 steps, 256 steps, and 2048 steps denoted by progressively lighter colors. ...
There are several ways to derive dynamic information about particles’ movement in solution by Brownian motion. One of such methods is dynamic light scattering, also known as quasi elastic laser light scattering. The dynamic information of the particles is derived from an autocorrelation of the intensity trace recorded during the experiment. The second order autocorrelation curve is generated from the intensity trace as follows:
where is the autocorrelation function at a particular wave vector, and delay time, and is the intensity. At short time delays the correlation is high because the particles do not have a chance to move to a great extent from the initial state that they were in. The two signals are thus essentially unchanged when compared after only a very short time interval. As the time delays become longer, the correlation starts to exponentially fall off to zero, meaning that there is no correlation between the intensity of scattering of the initial state with the final state after a long time period has elapsed (relative to the motion of the particles). This exponential decay is obviously then related to the motion of the particles specifically, the diffusion coefficient. To fit the decay (i.e. the autocorrelation function), numerical methods are used based on calculations of assumed distributions. If the sample was monodisperse the decay would simply be a single exponential. The Siegert equation, relates the second order autocorrelation curve with the first order autocorrelation function as follows: A plot showing 100 random numbers with a hidden sine function, and an autocorrelation of the series on the bottom. ...
A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...
where is a parameter which is a correction factor depending on the geometry and alignment of the laser beam of the light scattering setup. Once the autocorrelation curve has been generated, different mathematical approaches can be employed to fit the curve and thus determine the z-averaged translational diffusion coefficient. The simplest approach is to treat the first order autocorrelation function as the sum of single exponential decays with fractions where is the decay rate.
Data analysis
Cumulant method One of the most common methods is the cumulant method [1], from which in addition to the sum of the exponentials above, more information can be derived about the variance of the system as follows: // Cumulants of probability distributions In probability theory and statistics, the cumulants κn of the probability distribution of a random variable X are given by In other words, κn/n! is the nth coefficient in the power series representation of the logarithm of the moment-generating function. ...
In probability theory and statistics, the variance of a random variable (or somewhat more precisely, of a probability distribution) is a measure of its statistical dispersion, indicating how its possible values are spread around the expected value. ...
where is the average decay rate and is the second order polydispersity index (or an indication of the variance). A third order polydispersity index may also be derived but this is only necessary if the particles of the system are highly polydisperse. The z-averaged translational diffusion coefficient may be derived at a single angle or at a range of angles depending on the wave vector . The polydispersity index, or PDI, is the ratio of the weight average molecular weight to the number average molecular weight. ...
with where is the incident laser wavelength, is the refractive index of the sample and is angle at which the detector is located with respect to the sample cell.
Depending on the anisotropy and polydispersity of the system, a resulting plot of vs. may or may not show an angular dependence. Spherical particles will show no angular dependence, hence no anisotropy. A plot of vs. will result in a horizontal line. Particles with a shape other than a sphere will show anisotropy and thus an angular dependence when plotting of vs. .[2] The intercept will be in any case the . The can be calculated into the hydrodynamic radius for a sphere through the Stokes-Einstein equation. Look up anisotropy in Wiktionary, the free dictionary. ...
The polydispersity index, or PDI, is the ratio of the weight average molecular weight to the number average molecular weight. ...
In physics (namely, in kinetic theory) the Einstein relation is a previously unexpected connection revealed by Einstein in his 1905 paper on Brownian motion: linking D, the Diffusion constant, and μ, the mobility of the particles; where is Boltzmanns constant, and T is the absolute temperature. ...
One must note that the cumulant method is valid for small and sufficiently narrow .[3] One should seldom use parameters beyond , because overfitting data with many parameters in a power-series expansion will render all the parameters including and , less precise [4].
CONTIN algorithm An alternative method for analyzing the autocorrelation function can be achieved through an inverse Laplace transform known as CONTIN developed by Steven Provencher.[5].[6] The CONTIN analysis is ideal for heterodisperse, polydisperse and multimodal systems which cannot be resolved with the cumulant method. The resolution for separating two different particle populations is approximately a factor of five or higher and the difference in relative intensities between two different populations should be less than 1 : 1E-5. A polydisperse polymer is one with a wide range of molecular masses. ...
Maximum entropy method The Maximum entropy method is an analysis method that has great developmental potential. The method is also used for the quantification of sedimentation velocity data from analytical ultracentrifugation. The maximum entropy method involves a number of iterative steps to minimize the deviation of the fitted data from the experimental data and subsequently reducing the of the fitted data. The principle of maximum entropy is a method for analyzing the available information in order to determine a unique epistemic probability distribution. ...
A Svedberg (symbol S, sometimes Sv, not to be confused with Sv for Sverdrup) is a non-SI physical unit used to characterize the behaviour of a particle type in ultracentrifugation. ...
The ultracentrifuge is a centrifuge optimized for spinning a rotor at very high speeds, capable of generating acceleration as high as 1,000,000 G (9,800 km/s²) There are two kinds of ultracentrifuges, the preparative and the analytical ultracentrifuge. ...
See also The Diffusion Coefficient is given by where D is the diffusion coefficient in dimensions of [length2 time-1] T is the temperature in dimensions of Kelvin R is the gas constant in dimensions of [energy temperature-1 parts-1] See also Ficks law of diffusion Categories: Science stubs ...
Also known as FCS Categories: Science stubs | Spectroscopy | Biochemistry | Cell biology | Biotechnology | Microscopes | Biophysics ...
Nanoparticle Tracking Analysis is a technique developed by nanosight which allows nano-particles (smaller than the wave length of light) to be seen via a microscope. ...
The Stokes radius or hydrodynamic diameter is the radius of a hydrated atom, but can also be applied to molecules. ...
Static light scattering is a technique in physical chemistry that uses the intensity traces at a number of angles to derive information about the radius of gyration and molecular mass of the polymer or polymer complexes, for example, micellar formation (1-5). ...
In particle physics, scattering is a class of phenomena by which particles are deflected by collisions with other particles. ...
References - ^ *Koppel, D. E. Analysis of Macromolecular Polydispersity in Intensity Correlation Spectroscopy: The Method of Cumulants. (1972), J. Chem. Phys., 57, 4814-4820.
- ^ *Gohy, J.-F., Varshney, S. K., Jérôme, R. Water-soluble complexes formed by poly(2-vinylpyridinium)-block-poly(ethylene oxide) and poly(sodium methacrylate)-block-poly(ethylene oxide) copolymers. (2001), Macromolecules, 34, 3361-3366.
- ^ *Hassan, P. A., Kulshreshtha, S. K. Modification to the cumulant analysis of polydispersity in quasielastic light scattering data. (2006) J. Colloid Interface Sci., 300, 744-748.
- ^ *Chu, B. Laser Light scattering: Basic Principles and Practice, 2nd Edition. Academic Press (1992)
- ^ *Provencher, S. W. CONTIN: A GENERAL PURPOSE CONSTRAINED REGULARIZATION PROGRAM FOR INVERTING NOISY LINEAR ALGEBRAIC AND INTEGRAL EQUATIONS. (1982), Comp. Phys. Commun., 27, 229-242.
- ^ *Provencher, S. W. CONSTRAINED REGULARIZATION METHOD FOR INVERTING DATA REPRESENTED BY LINEAR ALGEBRAIC OR INTEGRAL EQUATIONS. (1982), Comp. Phys. Commun., 27, 213-227.
External links - http://physics.ucsd.edu/neurophysics/courses/physics_173_273/dynamic_light_scattering_03.pdf
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