Condensation of Charged Spheres and Swelling of Clay Platelets (01PR1983: Antti-Pekka Hynninen)

The explanation of the experimentally observed phenomena of (i) attraction between like-charged colloidal spheres and (ii) the sol-gel transition in clay suspensions are two of the most profound problems in colloid science. We propose to study both phenomena by simulation using the classical analogue of the Car-Parinello method. In this recently introduced method the mesoscopic (colloidal) particles are treated explicitly by Molecular Dynamics simulation, whereas the microions are treated on the level of their density profiles that follow from minimising the free energy functional. We plan to extend this novel method to systems coupled to a salt-reservoir, and to combine it with standard techniques for determining phase equilibria, such as the Gibbs Ensemble method and thermodynamic integration. This combination of extensions allows us to determine the phase diagram and the structure of suspensions of colloidal spheres and clay particles, not only in the well-understood regime of high salt concentrations, but also in the low-salt regime, where the unexplained phenomena (i) and (ii) were observed.

Colloidal Rods at Interfaces (UU: Svyatoslav Savenko)

In this project we plan to study suspensions of rodlike particles in contact with a planar hard wall in which rodlike particles are embedded parallel to the wall. In order to investigate the wetting behaviour, we recently developed a new Monte-Carlo method for simulating fluids in contact with a single wall. In this method, we simulate the suspension in contact with a single wall, while a flat density profile is imposed far from this wall using a penalty function that suppresses large density fluctuations from a self-consistently determined averaged bulk density. In this way, we can avoid simulations with two walls, which can induce capillary condensation/nematization. Using this technique, we were indeed able to follow the logarithmic growth of a thick nematic film at the wall-isotropic interface (see figure on the cover page). We propose to investigate the interfacial behaviour of hard-rod fluids in contact with corrugated walls by extending this technique to structured walls. We hope that our simulations can give some insight in the origin of the alignment effects of LC molecules on corrugated/rubbed surfaces.

Entropic Wetting in Colloidal Mixtures (01SFFSM22: Andrea Fortini)

The focus of this proposal is on two different systems where the bare interactions are either hard o r ideal: (i) a simple model for a mixture of colloids and ideal polymer and (ii) a mixture of thin a nd thick rod-like particles. Our group has a proven track record in the determination of the bulk phase behaviour of both systems with theory and simulations, which gives us an excellent position to study the wetting behaviour. For both systems, we plan to investigate how the topology of the phase diagram influences the location of wetting transitions.

Colloidal Epitaxy

Colloidal epitaxy provides a means to direct the growth of colloidal crystals. Under the influence of gravity colloids settle at the bottom of the container, forming close packed crystalline domains. By using a corrugated wall where the pattern of holes equals a well chosen crystal plane, a colloidal crystal can be grown epitaxially. In this way an almost perfect face centered cubic crystal of hard-sphere like silica particles was grown. At the moment we are trying to grow a hexagonal close packed crystal, which, for hard spheres, has a slightly higher free energy.

Manipulation of colloidal crystal growth has applications for the production of photonic crystals. Understanding the dynamics of epitaxial crystal growth is on the other hand an interesting and fundamental research question. Even the role of gravity in the epitaxial growth process, which is not yet understood, can be examined by using particles that can be density matched with their suspending liquid.

fcc air-sphere crystal
SEM image of an fcc air-sphere crystal in a backbone of silicon (image by D.C. 't Hart)

Inverse Photonic Crystals (02POM10: J.H.J. Thijssen)

Photonic crystals are 3D structures in which the refractive index varies periodically throughout space. Such structures form a periodic potential for photons, causing strong interactions with light. In a way, these interactions can be considered as Bragg-reflections. Provided the refractive index contrast is large enough and a suitable structure is chosen, photonic crystals can exhibit a photonic band gap. This means that light of a certain frequency range cannot propagate within the crystal in any direction regardless of its polarization. In other words, light of a frequency within the gap will be Bragg-reflected such that standing waves are formed in all directions for all polarizations. Thus, a photonic band gap is the optical analogue of an electronic band gap in semiconductors. However, since Maxwell's equations are scale-invariant, a structure can be designed to have a band gap at any desired wavelength. For example, if the gap is tuned at a wavelength of 1.3 or 1.5 micron, photonic crystals could be used in fibres for longe-distance telecommunication. 

One way of fabricating photonic crystals is by colloidal self-assembly. Colloids are particles with sizes on the order of 1 nm up to 1 micron. These colloidal particles could be ideal building blocks for photonic crystals, for they feature sizes on the order of visible and near-infrared light, and they are known to self-assemble under the right conditions. Furthermore, the single particle properties of colloids can be chemically modified. Regular structures of colloids are called colloidal crystals and if the refractive index of the colloids is different from that of the host, which is almost always the case, these crystals are photonic crystals, by definition.

In our group, two routes towards photonic crystals are explored. One of them uses monodisperse colloidal silica spheres to form colloidal crystals that serve as a template. The spheres are usually labelled with a fluorescent dye, which allows individual imaging of touching particles using confocal microscopy. Other characterisation techniques that are used include laser diffraction, x-ray diffraction (see figure), Vis-NIR spectroscopy and electron microscopy.

With a little bit of effort, it is possible to grow face-centred cubic (fcc) colloidal crystals by sedimentation of monodisperse colloidal spheres. It has been calculated that an fcc crystal of air-spheres in silicon has a band gap with a relative width of 5%. However, this gap is not very robust and its width is not spectecular. For example, a diamond crystal of air spheres in silicon exhibits a much larger and much more robust gap at a much lower index contrast However, up till now, nobody has succeeded in fabricating a photonic crystal with diamond symmetry and a sufficient index contrast.

In our group, we try to grow colloidal crystals with symmetries other than the fcc one as well. For example, sedimentation of highly charged spheres with a long-range interaction yields a body-centred cubic (bcc) crystal. Sedimentation in an electric field perpendicular to gravity yields crystals with body-centred tetragonal (bct) or face-centred orthorhombic (fco) symmetry, depending on the charge of the colloids. For example, the figure shows a confocal microscope images of the bct hexagonal (110) plane; the lower figure is a side-view ((100) plane), clearly showing bct AB-stacking. In this way, using external fields to influence the crystallization of colloidal particles, it might be possible in the future to obtain even more different structures.

Usually, silica colloids are used for fabricating colloidal crystals. The refractive index of silica equals 1.45 (compare 1.33 for water and 1.5 for glass). If air is the host medium, the index contrast of such a silica colloidal crystal is 1.45, which is too low to open up a band gap. Thus, in a final step, the colloidal crystal is used as a template for infiltration using chemical vapor deposition (CVD). The colloidal crystal is infiltrated with a high-index material, such as silicon (see figure). Silicon has the advantage that it has a large refractive index (3.5) and absorption is small for wavelengths larger than 1.1 micron. Furthermore, silicon photonic crystals should be compatible with existing technologies from the semiconductor industry. In a last step, the original silica template is removed by wet etching, enlarging the index contrast (from 2.41 to 3.5).

FCC-BCT crystal transition
FCC-BCT crystal transition

Electro-Rheological Fluids

When a dispersion of uncharged colloidal spheres is placed in a (uniform) electric field the dielectric constant difference between particles and solvent creates dipolar interaction potentials between the spheres. If the fields are so high that the dipolar interactions between the spheres are several times kT non-equilibrium string-like structures are formed spanning the container and the dispersion starts behaving like a solid. This ability to change viscosity over several orders of magnitude in milliseconds is useful for applications like shock absorbers or a variable transmission. The proposed lowest energy structure for monodisperse spheres at high fields is a body centered tetragonal crystal (BCT). At relatively low fields (~0.5 V/mm), where interaction forces between the spheres were only several times kT, we observed such BCT crystals (figure on the right). Furthermore, intriguing metastable sheet-like structures, not yet predicted by theory, were seen as precursor to the BCT crystals (left three Figures). At higher concentrations, where the equilibrium phase without field is an FCC colloidal crystal, an interesting martensitic FCC-BCT transition was found.