Measuring zeta potential using phase analysis light scattering (PALS)

Introduction In previous instruments, Doppler shift analysis was performed by Fourier The measurement of zeta potential in transformation. Analysis of the the Zetasizer range of instruments is Doppler shift in the Zetasizer Nano made using the technique of laser series is done by using phase Doppler electrophoresis. This analysis light scattering (PALS). This technique is discussed at length in technical note attempts to explain another technical note available from what PALS is. the Malvern Instruments website Figure 1: For high mobility particles, (www.malvern.co.uk). In brief, laser enough data is collected within the Doppler electrophoresis measures Phase Analysis Light measurement time to produce an small frequency shifts in the scattered Scattering (PALS) accurate determination of the particle light that arise due to the movement PALS is a technique that uses the motion. of particles in an applied electric field. same optical setup as conventional ∆ The frequency shift f is equal to: laser Doppler electrophoresis. However, a different signal processing θ method is employed. Instead of the ∆f = 2vsin( ) / λ frequency shift being measured, the 2 phase shift is determined instead. The measured phase change is where proportional to the change in the v is the particle velocity, position of the particles. Phase, by λ the laser wavelength and definition, is frequency x time. θ the scattering angle. PALS can give an increase in Figure 2: For low mobility particles, In microelectrophoresis, the particle performance of greater than 100 only a fraction of an oscillation may velocities that are measured are very times than that associated with have been completed within the small, typically around 10’s of standard measurement techniques. measurement time. In this case, microns/second, and hence the This allows the measurement of high determination of the particle's frequency shifts are ~ 10Hz. In the conductivity samples where low mobility would not be possible using Zetasizer Nano, measurement of the applied voltages need to be used to Fourier transformation. Malvern zeta potential standard avoid any risk of sample effects due The effect of the field on low mobility DTS0050 in an applied field of 150V to Joule heating. In addition, PALS particles is much weaker and across the roughly 50mm length of gives the ability to accurately measure consequently, to compensate, the the folded capillary cell have a other samples that have low particle electric field needs to be increased. frequency shift of around 50Hz. mobilities, for example high viscosity However, increasing the electric field or non-aqueous applications. The velocity of the particles for high conductivity samples results undergoing electrophoresis is The electrophoretic contribution to the in significant Joule heating which determined by comparing the beat motion can only be detected by destroys any random motion and can frequency detected with that of a sampling many oscillations of the denature the sample. reference frequency. This reference frequency-shifted signal. This is fine For low mobility particles only a frequency is produced by modulating for high mobility particles since they fraction of an oscillation may have one of the laser beams with an pick up a lot of energy from the been completed within the oscillating mirror. The mobility of the electric field that moves them quickly measurement time (figure 2). particles in an applied field will through the beam, producing many therefore produce a frequency shift oscillations in a short space of time away from that of the modulator (figure 1). frequency.

1 Zetasizer Nano application note MRK571-01

In this case it would be impossible to As an example, imagine two determine the particle’s motion using frequencies that are both 50Hz (figure standard Fourier transform analysis. 3). If the phase difference (in radians) However, if we consider phase, a between these two signals is plotted particle moving just half a wavelength over time, a flat line is obtained. Now represents a large measurable shift in consider two signals that have phase terms. different frequencies (in this example, they are 50 and 51Hz respectively). A By measuring the phase difference plot of the phase difference between between the beat frequency and a the two signals shows a gradient reference frequency, the changes in (figure 4). The rate of change in the position of the particle can be phase difference is related to the determined more accurately when the velocity at which the particles are particle displacements are small. moving. Therefore the mean zeta

potential value can be determined. The reference frequency used in the Figure 5 shows a typical phase plot Zetasizer Nano is that of the optical obtained from a zeta potential modulator. The mean phase shift with measurement performed on the time gives us information on the Zetasizer Nano. During the electrophoretic motion of the particle. measurement sequence, the applied PALS measures the rate of change of voltage is rapidly reversed a number the phase difference between the two of times. This plot shows well defined, signals. alternating slopes of the phase difference with time that result from the rapid reversal of the applied field.

These slopes are averaged to determine the mean phase difference and hence mean zeta potential.

Figure 3: Schematic diagram showing the phase Figure 4: Schematic diagram showing the phase difference between two signals of different difference between two signals with the same frequency (50Hz) frequencies (50 and 51Hz)

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Figure 5: Typical phase plot from a zeta potential measurement performed on a

Zetasizer Nano instrument

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3 Zetasizer Nano application note MRK571-01