289. Patterned structures from a binary mixture of particles

This is a guest blog post by Carlos Mendoza from Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico.

Let me start by thanking Dmitry for the invitation to write a guest blog entry about my recent paper arXiv:0901.4153. This has been done in collaboration with Erasmo Batta and has been accepted for publication in EPL.

Self-assembly is the spontaneous aggregation of the components of a disordered system into an ordered one by virtue of their mutual interactions. The search of particles in the mesoscopic scales that self-organize into potentially useful patterned structures is extremely important for technological applications like nanoelectricity. However, usually nanoparticles self-assemble into hexagonal arrays that are incompatible with industry-standard circuits. Recently a system formed by a blend of block copolymers has been designed to form nanoparticles that self-assemble into square arrays that would enable simplified circuit interconnection. The blend consists of two kinds of diblock copolymers, A-B and B’-C, being the A and C blocks mutually repulsive and incompatible with blocks B and B’. Block B contains small numbers of groups that form hydrogen bonds to complementary groups in block B’ (Section a on the Fig. below).

The attractive interactions between complementary hydrogen bonds suppress macrophase separation in favor of microphase separation, thereby producing large-scale assembly of nanoscale features. By controlling the amount of hydrogen bonding units, the molecular weights and compositions of the block copolymers, diverse families of ordered structures are achieved, including square arrays of cylinders that are the result of the competition between the different interactions. In this contribution I describe a recent work in which such a system is modeled by a simple binary mixture of particles interacting via isotropic potentials (arXiv:0901.4153). It is argued that this system represents a plausible model for micelles of block copolymers. It consists of a two-dimensional binary mixture of particles, like-species of which interact via a repulsive square shoulder potential while unlike species via an attractive square well (Sections b and c on the Fig. above). The system produces a rich variety of low-temperature phases and microphases including the technologically important stripes, squares and honeycomb structures:

At the origin of the pattern formation is the tendency of the system to maximize the number of favorable overlaps between particles of different species avoiding at the same time unfavorable overlaps between particles of the same type (insets on Fig. above). This study shows how simple models can lead to rich patterned structures which might have applications for nanotechnology.