# Dynamic Light Scattering: An Introduction in 30 Minutes

## Introduction

Dynamic Light Scattering (DLS), sometimes referred to as Photon Correlation Spectroscopy or Quasi-Elastic Light Scattering, is a technique classically used for measuring the size of particles typically in the sub-micron region, dispersed in a liquid. The sensitivity of some modern systems is such that it can also now be used to measure the size of macromolecules in solution, e.g. proteins

## Brownian Motion

DLS measures Brownian motion and relates this to the size of the particles. Brownian motion is the random movement of particles due to the bombardment by the solvent molecules that surround them. The larger the particle or molecule, the slower the Brownian motion will be. Smaller particles are "kicked" further by the solvent molecules and move more rapidly. An accurately known temperature is necessary for DLS because knowledge of the viscosity is required (because the viscosity of a liquid is related to its temperature). The temperature also needs to be stable, otherwise convection currents in the sample will cause non-random movements that will ruin the correct interpretation of size.

The velocity of the Brownian motion is defined by a property known as the translational diffusion coefficient (usually given the symbol, D).

## The Hydrodynamic Diameter

The size of a particle is calculated from the translational diffusion

coefficient by using the Stokes-Einstein equation;

where:-

d(H) = hydrodynamic diameter

D = translational diffusion coefficient

k = Boltzmann's constant

T = absolute temperature

η = viscosity

Note that the diameter that is measured in DLS is a value that refers to how a particle diffuses within a fluid so it is referred to as a hydrodynamic diameter. The diameter that is obtained by this technique is the diameter of a sphere that has the same translational diffusion coefficient as the particle.

The particle translational diffusion coefficient will depend not only on the size of the particle "core", but also on any surface structure that will affect the diffusion speed, as well as the concentration and type of ions in the medium. Factors that can affect the diffusion speed discussed in the following sections.

## Ionic Strength of Medium

The ions in the medium and the total ionic concentration can affect the particle diffusion speed by changing the thickness of the electric double layer which is called the Debye length (K-1). Thus a low conductivity medium will produce an extended double layer of ions around the particle, reducing the diffusion speed and resulting in a larger, apparent hydrodynamic diameter. Conversely, higher conductivity media will suppress the electrical double layer reducing the measured hydrodynamic diameter.

The performance of a DLS instrument is normally verified by measurement of a suitable polystyrene latex standard. If the standard needs to be diluted prior to measurement, then dilution in an appropriate medium is important. The International Standard on DLS (ISO22412:2008) says that dilution of any polystyrene standard should be made in 10mM NaCl. This concentration of salt will suppress the electrical double layer and ensure that the hydrodynamic diameter reported will be the same as the hydrodynamic diameter on the certificate or the expected diameter. For a 60nm monodisperse latex, dispersion in demineralised water rather than 10mM NaCl can result in 15% higher size reported.