We investigate the ordered morphologies occurring in thin-films diblock copolymer. For temperatures above the order-disorder transition and for an arbitrary two-dimensional surface pattern, we use a Ginzburg-Landau expansion of the free energy to obtain a linear response description of the copolymer melt. The ordering in the directions perpendicular and parallel to the surface are coupled. Three dimensional structures existing when a melt is confined between two surfaces are examined. Below the order-disorder transition we find tilted lamellar phases in the presence of striped surface fields.

When sheets of layeredmaterial like C., WS2 or BN are restricted to [ ]nite sizes, they generally form single- and multi-walled hollow nanoparticles in order to avoiddangling bonds. Using contin uum approaches to model elastic deformation and van der Waals in teractions of spherical nanoparticles, we predict the variation of mechanical stability, adhesive properties and phase behavior with radius R and thickness h. We find that mechanical stability is limited by forces in the nN range and pressures in the GPa range. Adhesion energies scale linearly with R, but depend only weakly on h. Deformation due to van der Waals adhesion occurs for single-walled particles for radii of few nm, but is quickly suppressed for increasing thickness. As R is increased, the gas-liquid coexistence disappears from the phase diagram for particle radii in the range of 1-3 nm (depending on wall thickness) since the in teraction rangedecreases like 1/R.

Recent advances in the development and application of self-assembly templating techniques have opened up the possibility of tailoring membranes for specific separation problems. A new self-assembly processing route to generate inorganic membrane films has made it feasible to finely control both the three-dimensional (3D) porosity and the chemical nature of the adsorbing structures. Chemical sites can be added to a porous membrane either after the inorganic scaffolding has been put in place or, alternatively, chemical sites can be co-assembled in a one-step process. To provide guidance to the optimized use of these ‘designer’ membranes we have developed a substantial modeling program that focuses on permeation through porous materials. The key issues that need to be modeled concern 1) the equilibrium adsorption behavior in a variety of 3D porous structures, ranging from straight pore channels to fractal structures, 2) the transport (i.e. diffusion) behavior in these structures. Enriching the problem is the presence of reactive groups that may be present on the surface. An important part of the design of actual membranes is to optimize these reactive sites with respect to their strength as characterized by the equilibrium constant, and the positioning of these sites on the adsorbing surface. What makes the technological problem challenging is that the industrial application requires both high flux and high selectivity. What makes the modeling challenging is the smallness of the length scale (molecular) that characterizes the surface reaction and the confinement in the pores. This precludes the use of traditional continuum engineering methods. However, we must also capture the 3D connectivity of the porous structure which is characterized by a larger than molecular length scale. We will discuss how we have used lattice models and both Monte Carlo and 3D density functional theory methods to tackle these modeling challenges.