 How can the zeta deviation be larger than the mean?
We recently received a phone call from a customer asking about their zeta potential results: When they are measuring electrophoretic light scattering, the zeta potential value for their sample is 15.4mV and the Standard Deviation is 24mV. Why is the Standard Deviation larger than the actual mean Zeta potential ?

To understand this better let’s first look at the concept of M3-PALS . M3 stands for mixed mode measurement: while traditional electrophoretic measurements are performed by measurement of particles at the stationary layer (= a precise position near the cell wall), with M3 the measurement can be performed anywhere in the cell. In the Zetasizer Nano series it is performed in the center of the cell. M3 consists of both Slow Field Reversal (SFR) and Fast Field Reversal (FFR) measurements, hence the name ‘Mixed Mode Measurement’. An M3 measurement is performed in the following manner:

• A fast field reversal measurement is performed at the cell center.
This gives an accurate determination of the mean.
• A slow field reversal measurement is made.
This gives better resolution, but mobility values are shifted by the effect of electroosmosis.
• The mean zeta potentials calculated from the FFR and SFR measurements are subtracted to determine the electroosmotic flow.
This value is used to normalize the slow field reversal distribution.
• The value for electroosmosis is used to calculate the zeta potential of the cell wall.

With this scheme both measurement repeatability and accuracy are improved, on top of the fact that alignment to find the stationary layer is no longer needed. The method can also be combined with phase analysis light scattering PALS to the patented M3-PALS, but this should be the topic of another blog post. (For further details consult the M3-PALS application note)

From the Zetasizer manual, chapter 4 page 16:

## Zetasizer Deviation The zeta deviation displays 1 standard deviation of the zeta potential distribution  around the mean result, in millivolts (mV).

In other words: the Zeta deviation value comes from the distribution. Yes the deviation is really only related to the distribution. So when the distribution is “bad” the zeta deviation may be considered a useless number. On the other extreme: if the sample is measured in monomodal analysis, then the zeta deviation is zero.
Usually, the zeta quality report should indicate something about the distribution not being ideal, to help understand that the zeta deviation just points out that the zeta distribution is not very reliable  because it is very broad.

## Electrophoresis or electroosmosis?

Electrophoretic light scattering (ELS) investigates the behavior of samples under the influence of an applied electric field by studying the electrophoretic mobility. Two terms often used in connection with ELS experiments are electroosmosis and electrophoresis. They refer to slightly different phenomena, one treating the liquid and the other treating the particles as a reference:

• Electroosmosis = motion of liquid due to an imposed electric field
• Electrophoresis = motion of charged particles due to an imposed electric field

The main interest in ELS studies is the characterization of the charge of particles. Therefore, modern ELS instrumentation attempts to minimize electroosmotic effects and measure only electrophoresis by the phase analysis or PALS method. The standard deviation of the distribution of electrophoretic mobilities is an indication of the width of the charge distribution obtained in the experiment. The distribution is obtained from a Fourier transform of the Slow Field Reversal or SFR mode in the data analysis. The initial use of fast field reversal FFR identifies the overall mean zeta potential. The mixed mode analysis result parameters in the Malvern Zeta report therefore come from two different measurement techniques: the mean zeta is from FFR and the zeta deviation is from SFR.

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