Laser Light Scattering is one of the most important techniques for the characterization of polymers and particles in solution. Based on different physical principles, a variety of Laser Light Scattering techniques has been developed. Some of these Laser Light Scattering techniques are presented in the following listing.

1) Static Laser Light Scattering Techniques

Typical molar mass range: ca. 103 g/mol to ca. 109 g/mol
Typical particle size range: ca. 10 nm to ca. 500 nm

Multi Angle Static Laser Light Scattering - MALS
The only way to overcome the inherent limitations of the Low, Right and Dual Angle Static Laser Light Scattering technique is the use of Multi Angle Static Laser Light Scattering. Molar mass and size can be calculated not only for smaller but also for bigger macromolecules and even nanoparticles. In Multi Angle Static Laser Light Scattering the data of a series of different scattering angles is plotted into the Zimm Plot and the resulting function allows the determination of molar mass (slope of curve at angle 0° angle) and size (intercept value of graph with y-axis). Thus Multi Angle Static Laser Light Scattering is the only light scattering technique capable of providing precise and correct molar mass and size values for macromolecules and nanoparticles.

2) Dynamic Laser Light Scattering Techniques

Typical particle size range: ca. 1 nm to ca. 5000 nm

Dynamic Laser Light Scattering - DLS: Dynamic Laser Light Scattering is also called Photon Correlation Spectroscopy (PCS) or Quasi Elastic Laser Light Scattering (QELS). Dynamic Laser Light Scattering is primarily used for the determination of particle size of macromolecules and particulates in solution. In Dynamic Laser Light Scattering the fluctuation of the scattered light caused by the Brownian Motion of the molecules, is detected by a photon detector. The collected data is used to establish a correlation function from which the Hydrodynamic Radius can be calculated. Molar mass can only be calculated from the hydrodynamic size when certain assumptions concerning the conformation (sphere, rod, etc.) are made.
Multi Angle Dynamic Laser Light Scattering - DLS: In most cases Dynamic Laser Light Scattering is done at a 90° scattering angle. In some complex mixtures and when high or low sample concentrations are present, also other scattering angles (e.g. back scattering angles) can be used. The most advanced Dynamic Laser Light Scattering technologies work with multiple angles to provide a maximum of information concerning the sample.

Static Light Scattering

In Static Light Scattering a beam of polarized light is focused onto a polymer/particle and the scattered light is detected with a photodiode detector. In Static Light Scattering the intensity of this scattered light is measured, which is proportional to the molar mass and the concentration of the particles or polymers in solution. In Static Light Scattering the accessible molar mass range is ca. 103 Da to 109 Da and the particles size range covered is ca. 10 nm to 500 nm. Because in Static Light Scattering the intensity of the scattered light is directly proportional to the product of molar mass (Mw) and sample concentration (c) the following formula can be used to describe the phenomena:

ILS ~ Mw * c

ILS = Light scattering intensity; Mw = Molar mass weight-average; c = Sample concentration

In more detail Static Light Scattering in dilute polymer solutions can be expressed by the following equation:

[(K’ * c) / R(θ)] = [1 /(Mw * P(θ)] + [2 * A2 * c]

If one incorporates some defined assumptions and approximations, e.g. dilute solutions, single angle detection, molecules small compared to wavelength of light, then the equation above can be simplified to the following formula:

[(K’ * c) / R(θ)] = [1 / Mw]

This means that by using Static Light Scattering the molar mass of a macromolecule can be calculated when the detector constant K’ has been determined and the sample concentration and the intensity of the scattered light is measured.

top

Dynamic Light Scattering

Dynamic Laser Light Scattering, also called Photon Correlation Spectroscopy (PCS) or Quasi Elastic Laser Light Scattering (QELS) is a technique for the determination of Hydrodynamic Radius of macromolecules and particulates in solution. In Dynamic Light Scattering the fluctuation of the scattered light, caused by the Brownian Motion of the molecules, is detected by a photon counting detector. Therefore a laser beam is focused in the sample causing the particles in the scattering volume to scatter light in all directions. In Dynamic Laser Light Scattering these scattered photons are counted. Small particles diffuse “faster” and show a higher scattering frequency than larger particles which diffuse “slower”, showing a lower scattering frequency.

The collected data is used to establish an autocorrelation function from which the Diffusion Coefficient directly can be derived. Using the Stokes-Einstein equation, the Hydrodynamic Radius and the size distribution can be calculated.

D = (kB *T) / (6πη * Rh)

top

Multi Angle Light Scattering

The basic principle of Static Light Scattering at multiple angles (Multi Angle Light Scattering) is the same as the principle of Static Light Scattering at one single angle. A beam of polarized light is focused onto the sample molecule and the scattered light is detected with a photo detector. But in Multi Angle Light Scattering the scattered light is detected at various different angles at the same time. The intensity of the scattered light at each angle is proportional to the molar mass and the concentration of the molecules under investigation. For smaller macromolecules with no angular dependence of the scattered light, the detection of one single angle is sufficient. But when the sample molecules get larger, more and more light is scattered in the forward direction at smaller detection angles. In this case it is absolutely necessary to detect the scattered light at multiple angles at the same time.

In Multi Angle Light Scattering the basic equation from Static Light Scattering can be used. Multi Angle Light Scattering in dilute polymer solutions can be expressed by the following equation:

[(K’ * c) / R(θ)] = [1 /(Mw * P(θ)] + [2 * A2 * c]

R(θ) = Excess intensity of scattered light at a given angle (θ);
c = Sample concentration
Mw = Molar mass weight-average
A2 = Second viral coefficient
K’ = Optical constant equal to 4π2n2 (dn/dc)2 / (λo4NA)
n = Solvent refractive index and dn/dc is the refractive index increment
NA = Avogadro’s number
λo = Wavelength of the scattered light
P(θ) = Complex function describing the angular dependence of the scattered light

Based on this formula the following Multi Angle Light Scattering equation can be obtained:

R(θ)/(K’*c) = M [ 1 – (2/3!) <rg2> [(4πn/λ) sin(θ/2)] 2 + (2/5!) <rg4> [(4πn/λ) sin(θ/2)] 4 ± ...]

Using this formula R(θ)/(K’*c) can be plotted against sin2(θ/2) and the gyration radius rg as well as the molar mass Mw can be calculated. Rg is the slope of the function at angle 0° and Mw can be derived from the intercept of the curve with the y-axis.

top

back to products