Predicting the mesophases of copolymer-nanoparticle composites.

The interactions between mesophase-forming copolymers and nanoscopic particles can lead to highly organized hybrid materials. The morphology of such composites depends not only on the characteristics of the copolymers, but also on the features of the nanoparticles. To explore this vast parameter space and predict the mesophases of the hybrids, we have developed a mean field theory for mixtures of soft, flexible chains and hard spheres. Applied to diblock-nanoparticle mixtures, the theory predicts ordered phases where particles and diblocks self-assemble into spatially periodic structures. The method can be applied to other copolymer-particle mixtures and can be used to design novel composite architectures.

Kinetic model of phase separation in binary mixtures with hard mobile impurities.

We develop a mean-field rate-equation model for the kinetics of phase separation in binary mixtures with hard mobile impurities. For impurities preferentially wet by one of the components, the phase separation is arrested in the late stage. The "steady-state" domain size depends strongly on both the particle diffusion constant and the particle concentration. We compare theoretical results with the simulation data and find good qualitative agreement.

The use of graft copolymers to bind immiscible blends.

Computer simulations and experimental studies were combined to design copolymers that enhance the strength of polymer composites. These copolymers contain side chains that associate across the boundary between phase-separated regions to form a "molecular velcro" that effectively binds the regions together. This behavior significantly improves the structural integrity and mechanical properties of the material. Because the side chains can be fabricated from a large class of compounds, the technique greatly increases the variety of copolymers that can be used in forming high-strength polymer blends.

The aggregation of reverse micelles. A computer simulation.

We have developed a computer simulation to model the formation of reverse micelles in two dimensions. Several of the qualitative results obtained from these calculations agree with experimental observations. Specifically, we have shown that the chain length has a large influence in determining the size and shape of the aggregate. We predict the existence of a critical tail length: Chains below this value will form an extended lamella-like structure, whereas chains longer than this value will form clusters that appear ellipsoid or circular in cross-section. Finally, we obtained a scaling law that relates the aggregation number (N) to the length of the tail (L): N approximately L-1.14. A physical model to account for the observed exponent will be developed in a future paper.

The role of polymer matrix structure and interparticle interactions in diffusion-limited drug release.

A lattice random-walk model is used to simulate diffusion in a porous polymer. This model may be useful for the practical design of drug-release systems. Both interacting and noninteracting particles (random walkers) were allowed to diffuse through a pore with a single exit hole. It was found that the specific interactions among the diffusing particles have little influence on the overall release rate. Diffusion through more complicated structures was investigated by simulating the diffusion of particles through two pores connected by a constricted channel whose length and width were varied. The overall rate of release was found to be proportional to the width of the constricted channel. When the length of the channel was greater than or equal to the length of the pore, the rate of release was also inversely proportional to the channel length. From a practical standpoint, release rates can be decreased (and times for release increased) by one or two orders of magnitude by decreasing the width and expanding the length of the interconnecting channels in the polymer matrix.

Kinetic model for the interaction of myosin subfragment 1 with regulated actin.

A one-dimensional kinetic Ising model is developed to describe the binding of myosin subfragment 1 (SF-1) to regulated actin. The model allows for cooperative interactions between individual actin sites with bound SF-1 ligands rather than assuming that groups of actin monomer sites change their state in a cooperative fashion. With the triplet closure approximation, the model yields a set of 16 independent differential (master) equations which may be solved numerically to yield the extent of binding as a function of time. The predictions of the model are compared with experiments on the transient binding of SF-1 to regulated actin in the presence of Ca2+ and in the absence of Ca2+ with varying amounts of SF-1 prebound to the actin filament and on the equilibrium binding of SF-1 X ADP to regulated actin in the absence of Ca2+. In all cases, the calculations fit the data to within the experimental errors. In the case of SF-1 X ADP, the results suggest that a repulsive interaction exists between adjacently bound SF-1 at the ends of two neighboring seven-site actin units.