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UNIVERSITY OF WATERLOO
Waterloo Institute for Nanotechnology (WIN); Department of Chemical Engineering; Department of Physics & Astronomy
Prof. Mark W. Matsen

SCFT is a fantastically successful theory, but it is also notoriously computational. Although it can cope with general three-dimensional problems, it can only do so with very limited numerical accuracy. The one exception is the calculations for triply-periodic block-copolymer morphologies, but this has been possible because of their periodic symmetry. In general, researchers tend to focus on systems with sufficient symmetry (e.g., planar, cylindrical, or spherical) so as to reduce the SCFT to a one-dimensional calculation. The class of problems that we are currently interested in are those with a single axis of rotational symmetry. These are still two-dimensional problems, but accurate calculations are now becoming feasible. Roan [1] was the first to apply SCFT to a problem of this symmetry, when he examined the interaction between two brush-coated nano-particles. His calculations predicted an unusual attraction, that contradicted the less sophisticated treatments based on one-dimensional calculations for planar brushes supplemented with the Derjaguin approximation. However, I have recently proved [2] that attractions are impossible, which implies that Roan's numerical accuracy was insufficient for the problem at hand. The aim of the present project is to develop sufficiently accurate and efficient SCFT algorithms to cope with this class of two-dimensional problems, and then to apply them to a representative selection of interesting systems.

Block-copolymer based nanocomposites: Block-copolymer materials possess useful and interesting mechanical properties due to their periodically-ordered nano-domains. By mixing the block copolymer with nano-sized inorganic particles, the resulting nano-composites can display, for example, directional heat or electric conductance, improved strength, added heat resistance, or decreased gas permeability. The limitless combination of polymeric materials with inorganic particles has simulated a great deal of activity in this area. In another high-tech application where block copolymer materials are being investigated as optical-wavelength photonic crystals, nano-particles can be inserted so as to boost the dielectric contrast between the internal domains.

Micelle interactions: Block copolymer solutions have become a system of considerable interest for a range of diverse reasons. Much of this focus has been on the micellar phases where the block copolymer forms spherical or cylindrical micelles, analogous to those of surfactant- and lipid-based lyotropic liquid crystals. One particularly trendy idea is to use block-copolymer micelles/vesicles for drug delivery, by selecting block copolymers that self-assembles with the drug at its centre while the micelles passes through the environment over which the drug has to be transported. The behaviour of these micelles in solution is largely affected by the pair-wise interactions between their coronae, and as a general rule attractive interactions are to be avoided. There is also the interesting fact that concentrated solutions sometimes crystallize into body-centred cubic (bcc) arrays and in other cases into face-centred cubic (fcc) packings. Our investigation of the pair-wise interaction may shed some light onto the underlying factors controlling the packing preference.

Colloidal stabilization: The ability to create dispersions of colloidal particles has massive technological importance, but such efforts are always impeded by the tendency of colloids to aggregate due to the ever-present van der Waals attraction. One of the most effective methods of preventing flocculation is to graft polymer brushes to the surface of the colloids. Theoretical efforts to model the resulting repulsion are usually based on one-dimensional calculations between flat planar brushes. The particle curvature is then accounted for by the Derjaguin approximation, which assumes the separation between the opposing particles varies gradually as is the case for large colloids. However, I have done a calculation [3] based on a simple scaling theory that shows the underlying assumptions of the Derjaguin approximation breakdown for particle radii less than ~100 times the thickness of the brush. Roan has used SCFT to investigate actual spherical substrates, but the numerical intensity of the calculation limited him to very small colloids, and even then numerical inaccuracies seem to have corrupted the calculation. We aim to revisit this system equipped with our improved algorithms. This problem is much the same as the interacting micelles but now the cores are no longer deformable and the grafting density must remain strictly uniform. Furthermore, we need to investigate considerably larger particles in order to test the applicability of the Derjaguin approximation, and these facts will make the problem somewhat more challenging than the micelle one.