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.