Dynamic Light Scattering

The Beckman Coulter Delsa Nano C is a combined particle size and zeta potential analyser with the facility to titrate pH and record zeta potentials of both suspensions and solid phase samples. Principle of Operation Size Measurement

Particles suspended in liquids are in Brownian motion due to random collisions with solvent molecules. This motion causes the particles to diffuse through the medium. The diffusion coefficient, D, is inversely proportional to the particle size according to the Stokes-Einstein equation:

d

TkB

03πη

where D is the diffusion coefficient, kB is Boltzmann’s constant, T is absolute temperature, η0 is viscosity and d is the hydrodynamic diameter

When laser light is directed onto the particles, light is scattered in all directions. The scattered light that is observed comes from a collection of scattering elements within a scattering volume that is defined by the scattering angle and detection apertures. The observed intensity of the scattered light at any instant will be a result of the interference of light scattered by each element; and thus, will depend on the relative positions of the elements. If the particles are in motion, the relative positions of particles will change in time; and thus, fluctuations in time of the scattered light intensity will be observed.

Because particles in Brownian motion move about randomly, the scattered intensity fluctuations are random. The fluctuations will occur rapidly for smaller, faster moving particles and more slowly for larger, slower moving particles. The fluctuations of the scattered light are recorded and then analyzed using the autocorrelation function to give the size (or distribution of size) of the particles in the sample.

Zeta Measurement

When an electric field is applied to charged particles in the suspension, particles move toward an electrode opposite to its surface charge. Because the velocity is proportional to the amount of charge of the particles, zeta potential can be estimated by measuring the velocity of the particles. Electrophoretic light scattering is the method most generally used to determine the velocity of the particles. To determine the speed of the particles movement, the particles are irradiated with a laser light, and the scattered light emitted from the particles is detected. Because the frequency of the scattered light is shifted from the incident light in proportion to the speed of the particles movement, the electrophoretic mobility of the particles can be measured.

Results Size Analysis

The Delsa Nano C provides much information regarding the size of the particles in suspension: the cumulant result, the intensity, volume and number distributions and the polydispersity index (PDI). It is also possible to record the autocorrelation function, size distribution table and a realtime size table.

Figure 1 shows the results from the size analysis of nanoparticles. It can be seen (Figure 2) that the cumulant result is 304.4 nm with a PDI of 0.009. The PDI is an indication of variance in the sample, a low PDI (usually less than 0.2) indicates that the sample is monodispersed. The intensity distribution (Figure 3) result shows a weighted mean (or peak value) of 307.4 nm. It can be seen from the histogram that the sample has a single population and narrow distribution.

Figure 1. Size Results showing the autocorrelation function, realtime size result, intensity distribution

and the cumulant result.

Figure 2. Cumulant Result and PDI

Figure 3. Intensity Distribution

Zeta Analysis

The zeta potential of particles in suspension is obtained by measuring the mobility of the particles when an electric field is applied. The zeta potential can then be calculated from the Smoluchowski equation:

UZrεε

η0

=

where ε0 and εr are dielectric constants in vacuum and of the solvent, respectively and U is the mobility of the particles.

Figure 4 and 5 show the zeta measurement result for nanoparticles in suspension. It can be seen that these particles have a zeta potential of -47.82 mV. The zeta potential is measured at 5 regions in the cell and a weighted mean is calculated, as can be seen in Figure 6. These five measurements are used to correct for electroosmotic flow that is induced in the cell due to the surface charge of the cell wall.

Figure 4. Results showing zeta potential, mobility, conductivity, the autocorrelation function,

distribution and a 3D graph of the particle mobility.

Figure 5. Measured zeta potential, particle mobility and conductivity.

Figure 6. 3D graph of the particle mobility at different positions within the cell.