The plates were made as follows: a grain of the clay mineral powder is assembled from many single particles (we refer to “a single particle” as a particle composed of stacked crystallographic sheets). Typically, the single particles that form the grain are oriented in different directions. In order to form a plate-shaped clay mineral aggregate composed of large number of single particles oriented in one direction we performed the following steps: We dispersed clay powder in distilled water, ultrasonicated (10 min) and mechanically shook (2 h) to disassemble into single clay mineral particles. The dispersion was then transferred into a Petri dish and left covered to dry at room temperature. While sedimenting and drying the particles align (on average) with their stacking direction along the direction of gravity [16]. We controlled the thickness of the dry sheet by adding an adequate amount of the dispersion to the Petri dish. After drying for 3 days the thickness obtained was 70 ± 2 μm. As the water evaporates the Na-FH single particles will settle, lying flat on top of one another (Figure 1A).The final plate-shaped clay aggregates composed of single clay mineral particles, orientated (on average) with their stacking direction perpendicular to the longest axis of the aggregate (Figure 1A), are cut out from the dry sheet (Figure 1C). Whereas, for the rectangular-shape aggregates of clay mineral particles with their stacking direction parallel to the direction of the longest axis of the aggregate (Figure 1B) are made by stacking approximately 64 layers of sample (a) on top of each other and slicing a strip of the plate to obtain the desired shape.

The experimental set-up is sketched in Figure 2. The plate orientation and motion is observed using a microscope. The plate is immersed in silicone oil (Sigma Aldrich, 1000 cSt). A standard 10 × 10 × 50 mm transparent cuvette made from PMMA was used as a sample cell. Two copper electrodes are attached to the inside of the cuvette, each of which is connected to a high voltage amplifier (Trek Model 2220). Before each measurement, the plate is aligned using a metal needle such that its longest axis is perpendicular to the electric field, and its surface normal to the camera view. Rotation time in comparison to sedimentation time is insignificant, and hence does not influence the measurement. When the external electric field is applied across the copper electrodes, the plate will rotate to align itself with the field.

After a full rotation the plate is brought back to (approximately) the same initial location in the cell and aligned as above and the experiment is repeated.

As these experiments are performed in an AC field, with an oscillation period that is at least 100 times shorter than the typical alignment period, we do not expect any permanent dipole to effect the measurements. Experimental observations of frequencies on the order of 1 Hz only showed velocity oscillations consistent with the applied sinusoidal waveform and showed no tendency to change the rotation direction as we would expect from a permanent dipole.

In order to access the effects of geometrical changes (shape of particle), a plate, with perpendicular stacking, was consecutively trimmed such that the width:length ratio is different for each set of measurements. We choose to trim a plate rather than make new ones as this way we guarantee the same thickness and length. The plate is trimmed by placing it between two glass slides and slicing off a thin sliver along the long edge with a scalpel. The measurement is then made using the method described above.

We also wished to assess the effect of the electric field, using two plates, 7 and 8 (Table 1), the magnitude of the electric field is adjusted from 50 to 293 V/mm and the method outlined above is performed at each field strength.

In order to access the effect of the presence of water, a sample is kept in a 110 °C oven for 3 days. Hot (110 °C) silicone oil is poured over the plate before being removed from the oven, ensuring limited exposure to the humid air. The sample cuvette is then cooled as quickly as possible using room temperature metal plates held against the cuvette allowing the initial measurements to be performed soon after the removal from the oven. Upon removal from the oven the plate and oil will be exposed to lab conditions and thus the humid air, we expect over time this humidity will make its way into the clay mineral plate aggregate via the suspending oil.

The plate aggregates are placed in the cuvette as in the previous experiments and measurements made.

The video of the plate rotating is split into its respective frames and a threshold is applied to the image such that the plate can be easily differentiated from the background. Each frame is then analyzed and the angle of the plate with respect to the electrodes is estimated. We subsequently calculated the rotation rate of the particle, which is defined in Equation (1). The rotation rate is related to both the electric field torque and the hydrodynamic drag. Since the latter depends on the angular velocity, which is related to the initial angle (θ₀), we had to assure the same starting conditions in all experiments. It was challenging to pre-align the plate identically (with respect to θ₀) before each measurement. However, we tackled the problem by adjusting the starting point of the rotation while fitting the data (see explanation further on in the text).

At low Reynolds number the torque due to the electric field and hydrodynamic forces will balance each other (see Appendix A for details) leading to:

Where θ is the angle between the longest axis of the plate and the electric field, θ˙ is the angular velocity, E is the strength of the electric field, ξ is the rotational friction constant which is proportional to the viscosity η, and Δα is the difference in the longitudinal and transverse polarizability (Δα = α_∥ − α_⊥) of the particle. Solving Equation (1), for tanθ we obtain:

Where τ is given as:

and t is the elapsed time, and θ₀ is the angle with respect to the field of the particle at t = t₀.

Using two fitting parameters (t₀, τ) on Equation (2) we can fit the experimental data using:

Parameter t₀ shifts the curve on the horizontal time axis and is used to adjust the starting point of the rotation and τ adjusts the width and slope of the curve. When plotting the curves such that they all intersect at θ0=-45°, multiple intersecting curves can thus be compared.

We are free to choose the zero time and can therefore set the time at which the plate is at θ0=-45° to 0, thus shifting the curve. A typical fit is shown in Figure 3. Usually the residuals lie within 1° and its distribution is similar for all the datasets and plate rotations.

For plates with their stacking direction parallel (Figure 1B) to the field we saw no difference in the dynamics of the rotation. We are unable to make a comparison of the rotation rate due to the size differences between these and the perpendicularly stacked plates. Due to the way the plates are stacked they become quite fragile and hence we are unable to trim them to the same dimensions as the perpendicularly stacked plate Figure 1A.

The plate ratio is varied as described in Section 2.3 and analyzed. The results from these experiments are shown in Figures 4, 5.

Figure 4 shows a typical data series for single measurements of a plate rotating, where rotation angle is plotted as a function of time for each of the different ratios (see Table 1 for the particle sizes used). We observe that as the ratio is decreased, thus producing a more needle-like plate, the curve becomes steeper. The average characteristic rotation time for alignment of a plate is shown in Figure 5, where each data point represents at least 22 independent measurements. We can see that the effect of changing the ratio becomes quite substantial and there is a sharp increase in the rotation time, starting from a plateau at low ratio values. This may correspond to either an increase of magnitude of the dipole moment or a decrease in the friction coefficient or both. After removing the effect of the hydrodynamic drag (for details see Appendix 20), we can still clearly see the shape dependency on the time of rotation. In Figure 6 we plot the difference in the polarizability (Δα) vs. the plate aspect ratio (the correction for the hydrodynamic drag was already included).

In Na-FH clay there is, order of magnitude, 1 unit electron charge per nm³ of material [17]. Here, the typical plate aggregates have a volume of order of magnitude 10⁶ × 10⁷ × 10⁷nm³ = 10²⁰ nm³, giving a total order of magnitude 10 C charge associated with physically bound charge compensating ions in our plate aggregate. In the extreme event that the induced polarization in our plate aggregates involves physical transportation of all charge compensating cations to the edge of the sample, this would thus correspond to an induced dipole of order of magnitude 0.1 Cm (our samples are in the centimeter range), which at an applied field of about 100 V/mm would give an order of magnitude polarizability Δα of about 10⁻⁶ Cm²∕V. This is 11 orders of magnitude larger than our observed Δα. Thus, as we expect, our observations are consistent with plate aggregate polarizability due to local charge displacements on the nanoscale rather than on the sample scale. This is also strongly supported by the observation that parallel stacked plates show the same order of magnitude rotation times as the perpendicularly stacked ones, i.e., that the polarization is due to clay mineral particle surface charges rather than due to charges that are intercalated in the clay mineral nanostructure.

The electric field is varied and the experiments are performed as described in the Section 2.4. The analyzed results for these measurements are shown in Figure 7A. As the voltage is increased the rotation rate increases, giving a steeper curve. We can see a very simple relationship between the applied field and rotation time. Scaling the time with E² we obtain a data collapse as can be seen in Figure 7B. Thus, we can conclude, the characteristic rotation time scales as E⁻².

This is as expected and confirms the model including the E⁻² dependency on the characteristic rotation time. Similar behavior is found when electro-orientating a plate with a different width:length ratio. Figure 8 shows an increased plate ratio as compared to Figure 7.

The effects of hydration on the rotation time were measured as described in Section 2.5. Figure 9 shows the characteristic rotation time as a function of the aging time. The rotation time is the highest for the measurement taken just after the sample was removed from the oven. The magnitude of the characteristic rotation time decreased from around 9.7 to 8.2 s. We see two possible explanation to this, this is either due to the increased number of dipoles, or possibly due to the enhanced polarizability because of the local displacement of charge compensating cations.

In Na-FH the polar water molecules will intercalate the clay mineral nanostructure [18–20], in addition to adhering to the outer clay mineral particle surfaces.

In presence of an external electric field, clay particle aggregates undergo electro-orientation due to the induced electric torque. The magnitude of the electric torque is related to the strength of the electric dipoles induced on the clay particle aggregates. Since the rate of rotation of the plate is related to both the magnitude of the induced electric torque and the hydrodynamic drag, by ruling out the latter factor we were able to measure the difference between the longitudinal and vertical polarizability Δα. The small value of Δα measured in our experiments is consistent with plate aggregate polarizability of bounded charge displacements on the nanoscale rather than on the sample scale. This is also supported by the observation that the parallel stacked plates show approximately the same characteristic rotation time as the perpendicular stacked ones. We also observed the influence of water molecules on the characteristic rotation time, i.e., as the plate aggregate is hydrated the rate of rotation increases substantially, which indicates that water serves to increase the polarizability, and thus increases the torque due to the electric field. The geometry of a plate-shaped clay aggregate affects the polarizability. Interestingly, the magnitude of the polarizability has its peak value for plates with length-to-width ratio of around 0.25. We also validated the theoretical predictions on both electric field strength and viscosity dependency on the rate of rotation (Appendix B). The measurements showed that the characteristic rotation time scale as E⁻² and η.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.