Dynamic Light Scattering Recap Part 2

Stokes-Einstein equation

Stokes-Einstein equation

Last month we recapped on the basic principles of dynamic light scattering. This month I’d like to add some further detail.

A key point was that the particles we are trying to measure in our samples are subject to constant collision with the molecules of the solvent, which makes them move around in a random way which we describe as Brownian Motion. When particles move like this we can apply the Stokes-Einstein equation, which relates the velocity of a particle in solution to its hydrodynamic radius.

For reference, the formula is:

D=kT ÷6πηR

D is the particle’s diffusion velocity and R is its hydrodynamic radius, while T is the temperature, ηis the solution’s viscosity and k is the Boltzmann constant. As the particle’s diffusion velocity is inversely proportional to its radius, we can expect a small particle to diffuse faster than a large one.

The constantly changing distance between particles in a sample subject to Brownian Motion produces a Doppler Shift between the incoming light’s frequency and that of the scattered light. Because the phase overlap of the diffracted light is affected by the distances between the particles, the speckled pattern that I mentioned in the last article constantly changes; the brightness of its spots fluctuating in intensity as the positions of the particles change in relation to each other. How quickly the intensity fluctuates depends on how quickly the particles are moving, and we know that large particles move faster than slow ones. So if we can gather data on the scattered light fluctuations, we can make deductions on particle size.

This, in a nutshell, explains how irradiating a sample in solution or suspension with laser light gives us a means of measuring particle size. Dynamic light scattering instruments developed by Beckman Coulter, culminating in today’s DelsaMax range of analysers, have taken this principle and advanced it to deliver extraordinary speed, accuracy and reliability.