When it comes to sedimenting opals there are some problems. The first one is the time required to obtain an opal. If the silica spheres are too small (under 300 nm of diameter), several weeks are needed or even they may not settle at all because thermal agitation compensates gravitational forces. The other difficulty is related to heavy spheres (over 550 nm of diameter); their sedimentation velocity is such that it is quite hard to achieve an ordered array and it becomes completely impossible if the diameter is further increased. It is known that when gravitational energy is much larger than thermal energy (kBT) the sedimentation occurs far from equilibrium and non-crystalline sediment is obtained. Both problems make it quite unpleasant to work out of the limits of this reduced diameter range (300 nm – 550 nm) which corresponds to sedimentation velocities from 0.2 mm/hour to 0.7 mm/hour according to Stokes law.

The forces between particles and the effects of electric fields over colloidal particles have been widely observed, e.g. modulation of lateral attraction between particles and particle clustering. Using the electric field to drive the sedimentation velocity and keep it around 0.4 mm/hour would solve the difficulties mentioned before.

The cell where electrophoresis was performed (Figure 1) consisted of a cylindrical tube (2 cm of diameter) of methyl acrylate fixed to the basis where the opal should settle, obtained from a standard silicon wafer sputtered with titanium (with less than 0.1 nm of rugosity and thick enough to assure a good conductivity). We use platinum for the upper electrodes because they have the highest Redox potential. Then, both electrodes were connected to a dc source used to obtain an electrical field. With this method compacts with thickness ranging between a few monolayers and 1 mm (depending on the amount of silica spheres used) with surfaces about 3.1 cm2 are produced. To measure the sedimentation velocity, the height descended by the colloid/clear water interface was monitored with time. The velocity results from experimental fit of height vs. time.

The model of constant velocity particle packing is based on the interaction of gravitational (Fg=1/6prsgd3), Archimedes (FA=1/6prwgd3) and frictional forces (Ff=3phvd). Here densities, gravity acceleration, viscosity of water, and sphere diameter are involved. When all forces are balanced, the Stokes law is obtained. Experimental observations fit to this expression in an excellent way. SiO2 and TiO2 in colloidal suspension have a surface charge density when they are away from the point of zero charge (PZC). Taking into consideration the force produced by an electric field E parallel to all other forces, the following equation is obtained for the velocity:

where, the first part of this equation is the classical Stokes law and the second part corresponds to the contribution of the electric field to the sedimentation velocity, related to the mobility of the spheres u. Since Stokes velocity without electric field is determined with great accuracy, the electrophoretic mobility can be obtained in a straightforward manner if Stokes velocity is subtracted from the experimental velocity of the sample under a known electric field. Once the mobility is determined, the electric field necessary to achieve a given velocity can be stated beforehand. Moving away from the PZC increases the particle’s charge, so variations of the pH must involve changes in the mobility values.

First, the response of SiO2 spheres was studied. An electric field was applied to colloidal suspensions of SiO2 spheres in which the original pH was varied by adding HCl to change the surface charge. The PZC of silica occurs at a pH=2.5, so pHs of the suspensions were chosen to be different enough without being close to the PZC: pH=3.8 and the reference value (no acid added) of pH=8.4. The results of the sedimentation velocities for silica spheres of 500 nm of diameter are graphically compared with the theoretical Stokes fall of a sample without electric field in the left panel of Figure 2. It can be clearly seen that, as we move away from the PZC, the mobility increases and so does uE.

In order to study the effects of velocity variations on silica particle ordering, two more sedimentations were prepared from the same sample. One of them was left to fall without electric field, whereas in the other one the electrodes were inverted to decrease the sedimentation velocity by opposing the electric field to gravity. Since the mobility can be extracted from the previous experiment (u= -3.9 mm cm/V), the electric field needed to get the desired velocity (0.4 mm/hour) was calculated to be 0.5 V/m. The experimental value (v=0.35 mm/hour, see right graph in Figure 2) was close to it. The results from this experiments are numerically compared in the Table.

Electronic and optical microscopy studies of all these samples were made and it was observed that the slowed sedimentation sample presented a better ordering than the one settled without field, while the accelerated samples from the previous experiment presented no order at all. Bragg diffraction was performed as well showing that the slowed opal presented well-defined Bragg peaks.

To prove how useful this method could be, SiO2 spheres with a diameter of 870 nm were used. The purpose was to obtain a well ordered array by decreasing the natural velocity of this colloid (no electric field applied). Figure 3 shows a scanning electron microscopy (SEM) of a cleaved edge of the naturally settled opal. A high velocity (1.54 mm/hour) is obtained for these large spheres and no long-range order is achieved as by the Fourier transformed image shown in the inset of Figure 3. An equal colloid of the same spheres was prepared and settled under a slowing electric field, in which the velocity was kept close to 0.35 mm/hour. Figures 3 and 4 show that only very small domains appear when electrophoretic technique is not applied while large domains are obtained when sedimentation is performed under an appropriate electric field.

A Bragg diffraction study from the slowed opal was performed after sintering, and very clear peaks were measured as shown in Figure 5.a) while the other sample did not present any kind of peak as a result of the lack of large enough ordered domains. In addition, a little percentage of small spheres was present in this sample. They were observed in SEM images of the natural settled sample but they were not present in the other one because electric force compensated the gravity force. This suggests that the electrophoretic concept could be used to control the presence of small spheres in sedimentation when monodispersity is not granted.

A sample of quite small (205 nm of diameter) SiO2 spheres, which would take two months to be settled, was prepared for sedimentation. It was accelerated from 0.09 mm/hour (natural velocity) to 0.35 mm/hour in order to complete the sedimentation in less than two weeks without decreasing the optical quality. Again, the diffraction study from the as-grown opal presented Bragg peaks as shown in Figure 5.b), which denoted the presence of order within the opal.

To check the effects of electric fields on other species, spheres of TiO2 with a nucleus of SiO2, (silica core of 250 nm diameter covered with a 180 nm layer of TiO2) having a different PZC (pH=6.6) from silica, were prepared. In this case, the average density of these heterogeneous spheres was used; once its value was introduced into the first part of Equation (1), the natural sedimentation velocity was deduced. Taking this data into account, the first experiment was repeated with different pH values (1.5, and 5.1). The results shown in Figure 6 confirmed what was expected: moving away from the PZC involves a change in mobility and the ability of these spheres to be driven by an applied electric field.