Dynamic Light Scattering (DLS) is a measurement technique that provides a fast and simple method for submicron and nanoparticle sizing.
DLS relies on the fact that freely diffusing particles, moving randomly due to Brownian motion, will produce rapid fluctuations in scattered laser light. These fluctuations are rapid, on the order of tens of nanoseconds to hundreds of milliseconds, and are directly related to the motion of particles. Temporal autocorrelation is used to quantify the speed at which these photo pulses become decorrelated from some initial state, which is then related directly to the motion of particles.
Turning Scattered Light into Particle Size Information
The signal that arises from the scattered intensity from the laser light is collected and transformed into an autocorrelation function which is the basis for measuring a particle size distribution. In this technique, rapid fluctuations in the intensity of scattered light arise from the random motion of dispersed particles. This random, or Brownian, motion of particles and proteins is analyzed by autocorrelation to give either a simple mean size and polydispersity, or more complete distribution data even for multimodal distributions. The diameter obtained from Dynamic Light Scattering is often referred to as the hydrodynamic diameter and is inversely proportional to the diffusion coefficient. Large particles scatter more light and diffuse more slowly than small particles. The hydrodynamic diameter is related to the diffusion coefficient via the Stokes-Einstein equation, where size is inverse with the rate of diffusion.
When a distribution of sizes is present, the effective diameter measured is an average diameter which is weighted by the intensity of light scattered by each particle. This intensity weighting is not the same as the population or number weighting used in a single particle counter such as in electron microscopy. However, even for narrowly dispersed samples, the average diameters obtained are usually in good agreement with those obtained by single particle techniques.
The Stokes-Einstein Equation and Dynamic Light Scattering
The relationship between Dt, the primary quantity measured in DLS, and hydrodynamic particle size, dh, is inverse, and is given by the Stokes-Einstein Equation:
Dt = Kb T / 3πηdh
Where the Boltzmann constant (Kb), Temperature (T), and bulk viscosity (η) are all known values, and only the particle size, dh, is a property of the particle.
For a known scattering angle, θ, and refractive index, n, the scattering vector q is calculated from the following expression where λo is wavelength of the laser:
q = 4πn/λo sin(θ/2)
A given autocorrelation function (ACF), typically represented as a function of delay time, C(τ) is deconvoluted into either a single-exponential, stretched-exponential, or sum of exponentials. Where B, is a constant background term, and A, an optical constant determined by instrument design:
The result of this deconvolution is a characteristic linewidth or decay rate, Г, and typically also a polydispersity index (PDI).This linewidth, Г, is related to the translational diffusion coefficient (Dt) as follows:
Г = Dt⋅q2
Dynamic Light Scattering is sometimes referred to as Quasi-Elastic Light Scattering (QELS) or Photo-Correlation Spectroscopy (PCS).