Dynamic light scattering

Principle of dynamic light scattering using the example of large and small particles

In the dynamic light scattering (DLS) is an analysis method in which the scattered light of a laser in a dissolved or suspended is determined sample. It is most commonly used with polymers and biopolymers such as proteins to determine the hydrodynamic radius of the molecules. Dynamic light scattering is also known under the names photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QELS). ${\displaystyle R_{\mathrm {h} }}$

description

When light hits small particles, it is scattered in all directions ( Rayleigh scattering ). This also applies to macromolecules in solution or suspension . The scattered light from different scattering centers will then interfere with one another . If laser light is used, which is coherent and monochromatic , this interference leads to small fluctuations in the scattering intensity, since the distances between the scattering centers are constantly changing due to Brownian molecular motion . If these fluctuations are analyzed with regard to the time scale on which they occur, information about the speed at which the particles move in solution is obtained. From this, in turn, a diffusion coefficient can be determined, from which, for example, the hydrodynamic radius can be calculated according to the Stokes-Einstein relationship .

Measuring equipment

Traditionally, a goniometer is used for light scattering experiments . The laser unit is located on a fixed arm and the detector, usually a secondary electron multiplier (SEV) or an avalanche photodiode (APD), is located on a pivoting arm . The measuring cell is located in the middle of the arrangement so that it can work in any angular arrangement, usually a cylindrical quartz cell. With modern devices, the possibility of being able to record the angle dependence is often sacrificed for a compact arrangement. These devices measure at a fixed angle of e.g. B. 90 °, but can also be used with simple cuboid cuvettes with very small volumes. This reduces the volume required for a measurement from sometimes more than 10 ml to a few µl. Since large particles and particles that are not to a certain extent spherical scatter anisotropically , an exact analysis of the size of these particles is no longer possible with such a structure.

Data analysis

In order to determine the dynamic parameters of the particles, an autocorrelation of the measurement signal is carried out. The autocorrelation function for a discrete time series can be calculated as follows:

${\displaystyle R(k)={\frac {1}{(n-k)\cdot \sigma ^{2}}}\sum _{t=1}^{n-k}[X_{t}-\mu ][X_{t+k}-\mu ]}$

where is the mean, the variance, the signal intensity, the number of data points and the value of the autocorrelation. is a counter variable that specifies the distance between the start and end value. An exponential function can now be adapted from the curve determined in this way. The rate of decline that can be determined correlates directly with the diffusion coefficient. If the viscosity of the solvent is known, the hydrodynamic radius of the measured particles can be determined from this using the Stokes-Einstein equation. With this information, the molar mass can be determined indirectly. In order to determine not just a single variable, but entire distributions, e.g. B. sums from several exponential functions adapted to the autocorrelation function. So that the noise is not also interpreted, sophisticated methods are required to obtain reliable results. ${\displaystyle \mu }$ ${\displaystyle \sigma ^{2}}$ ${\displaystyle X}$ ${\displaystyle n}$ ${\displaystyle R}$ ${\displaystyle k}$

See also

• Fluorescence Correlation Spectroscopy

literature

• Günter Jakob Lauth, Jürgen Kowalczyk: Introduction to the physics and chemistry of interfaces and colloids . Springer Spectrum, Berlin, Heidelberg 2016, ISBN 978-3-662-47017-6 .
• Roland Winter, Frank Noll, Claus Czeslik: Methods of biophysical chemistry . 2., revised. and exp. Edition. Vieweg + Teubner, Wiesbaden 2011, ISBN 978-3-8348-1316-9 .