(Martin Grant, Derek Gray, Reghan Hill, Maria Kilfoil, Alejandro Rey, David Ronis, Teo van de Ven, and Jorge Viñals).
One particular example of a complex system that is receiving widespread attention by MIAM faculty concerns colloidal suspensions, often polymer coated. At a fundamental level, dilute colloidal suspensions mimic atomic systems, and hence can be used as a prototype to study basic static and dynamic processes such as solidification, rheology, shear induced melting, and shear induced order, or pattern formation just to name a few [T. Croteau and D. Ronis. “Nonequilibrium velocity distributions in liquids: Systems under shear”. Phys. Rev. E 66, 066109 (2002)]. However, they are also under active scrutiny for a number of applications that include hydrodynamic and colloidal interactions in dispersions and emulsions, optical properties of suspensions, adsorption of polymers and polyelectrolytes on colloidal particles and pulp fibres, particle deposition and removal from solid surfaces, fines and filler retention in papermaking, wetting of solids by liquids, and stability of foams [L. Craciun, T. van de Ven et al., “Rheological properties of concentrated latex suspensions of poly(styrene-butadiene)”. Rheol. Acta 42, 410 (2003)]. A particular class of applications concerns the papermaking chemistry and the paper industry. This includes chiral nematic phases of colloidal suspensions of cellulose crystallites that have very unusual properties as they are stable dilute aqueous dispersions with optical properties identical to conventional cholesteric liquid crystals. The liquid crystalline phase may be oriented in a magnetic field so that a gentle orientation of proteins is imparted by suspensions of the crystallites, for example facilitating NMR structural studies of the protein. The liquid crystalline structure of the suspensions can be preserved on drying, giving iridescent films of cellulose. There is commercial interest in using these films as optically variable pigments, showing different colors depending on the angle of viewing [M. Yu, D. Grey et al., “Evidence for a chiral internal stress in paper sheets”. J. Pulp and Paper Sci. 30, 91 (2004)].
Beyond the equilibrium and structural studies of colloidal systems just enumerated, research is conducted on their very slow dynamics and long term stability, and the relationship of both to microstructure evolution. These studies will shed light on similar slow relaxational phenomena in many other systems, such as gels and glasses, as these phenomena are generic across many soft condensed matter systems. One addresses structural relaxation at the many scales that are simultaneously active by real space imaging of colloidal gels at controlled time intervals to probe suitable metrics of both translational and orientational order. In particular, the local origin of cage rearrangements near the glass transition has been directly observed by using real space imaging of hard sphere colloids. More generally, the relationship between glassy states and a nonequilibrium jamming transitions are being investigated as it is possible that a unified theoretical framework can be developed encompassing both classes of phenomena. [M. Kilfoil et al., “Dynamics of weakly aggregated colloidal particles”. Phil. Trans. R. Soc. London Ser. A 361, 753 (2003)].
A second area of research in colloidal systems concerns polymer coated colloids. Polymer coatings provide an economical means of tailoring off-the-shelf “bare” colloidal particles for traditional applications of colloid chemistry and emerging (micro and nanoscale) technologies. Theoretical analyses are being developed to describe the coupled intra- and inter-particle interactions in systems comprised of colloidal particles coated with charged or neutral, polymeric chains in order to quantitatively obtain answer particle distributions, counter ion distributions, and an understanding of absorbed polymer conformation [D. Ronis, “Equilibrium structure in polymer-coated colloids”. Physica A 231, 220 (1996)]. Additional research concerns electro-kinetic effects, namely their transport under externally imposed electric fields, to aid in several classes of experimental studies involving colloids such as electrophoresis, dielectric spectroscopy and electro-kinetic-sonic amplitude. A computer package has been developed that provides numerically 'exact' steady and dynamic electrophoretic mobilities and polarizabilities, drag coefficients, and other single-particle and dilute-suspension properties, for colloids with neutral and charged coatings [R. Hill et al., “Electrophoresis of spherical polymer-coated colloidal particles”. J. Coll. Int. Sci. 258, 56 (2003)].
At a more fundamental level, research is conducted on the theoretical underpinnings of mesoscopic and macroscopic dynamical equations for complex systems outside of thermodynamic equilibrium, including complex fluids, mesophases –phases that by reason of symmetry are intermediate between completely unstructured fluids and perfectly ordered crystalline solids-, and microstructured systems displaying long range order at the mesoscopic scale, but that are macroscopically disordered. For example, transport in models of porous media is analyzed to understand ionic transport in membranes and zeolites, both analytically and through Lattice Boltzmann simulations. Pores or channels selectively allow ions or neutral molecules to pass through the system, and play important roles in cell biology and industrial filtration processes. [B. Palmieri and D. Ronis, “Diffusion in channeled structures: Xenon in a crystalline sodalite”. Phys. Rev. E 68, 046127 (2003)]. Another example concerns coupling between flows in complex fluids and surface instabilities, as for example defect texturing seen on the surfaces of extruded plastics. Successful theories need to combine hydrodynamics and rheology, reptation physics, kinetics of phase transitions, and dynamical systems analysis and chaos. The same thermodynamic principles and transport equations are being applied to polymer blends, liquid crystalline materials, carbonaceous mesophases, biological fluids, emulsions, and suspensions to understand their rheology and possible flow instabilities, facts that will aid in their processing [D. Grecov and A.D. Rey, “Multiscale simulation of flow-induced texture formation in polymer liquid crystals and carbonaceous mesophases”. Mol. Simul. 31, 185 (2005)]. Processing flows are also being explicitly considered in a number of industrial applications, that include carbon fiber spinning, structure-processing relations in polymer-liquid crystal blends, fiber coating flows, migration phenomena in plastic food packaging, and rheological properties of cosmetics and pharmaceutical products [D. Grecov and A.D. Rey, “Impact of texture on stress growth in thermotropic liquid crystalline polymers subjected to step-shear”. Rheol. Acta 44, 135 (2004)].
In fact, many of these topics exist at the boundary between condensed matter physics and materials science, whereas the mathematical apparatus is common to various fields of application such as crystal and epitaxial growth, the motion of unstable interfaces as applied to reaction fronts or combustion, or the kinetics of phase transformations as exemplified by spinodal decomposition and nucleation [N. Provatas, M. Grant et al., “Seaweed to dendrite transition in directional solidification”. Phys. Rev. Lett. 91, 155502 (2003)]. By their very nature, these problems are interdisciplinary overlapping Physics, Chemistry, Computational Science, Applied Mathematics, and Materials Science [K. Elder, M. Grant, “Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals”. Phys. Rev. E 70, 051605 (2004)]. Research at MIAM focuses on the underlying principles that lead to mesoscopic and macroscopic theoretical models, and application to several different fields within materials science. Beyond those studies mentioned above, recent examples of applications include eutectic growth, unstable motion of flame fronts growing in a random background of reactants during slow combustion, elastic effects on morphological instabilities in thin film growth, mesoscopic models of dislocation motion and plasticity, defect motion and coarsening of mesophases, or grain boundary migration in block copolymer under shears [Z.F. Huang and J. Viñals, “Tilt grain boundary instabilities in three-dimensional lamellar patterns”. Phys. Rev. E 71, 031501 (2005)].
Finally, promising recent research focuses on the development of nanotubes made of alternating copolymers and nanorods, not of carbon as is conventionally done. Applications of polymeric nanotubes are anticipated in Biological and Biotechnology. Examples include cell adhesion and coagulation, liposome suspensions and the flow of blood. [C. Malardier-Jugroot, T. van de Ven et al., “Characterization of a novel self-association of an alternating copolymer into nanotubes in solution”. Molec. Simul. 31, 173 (2005)].