Block copolymers phase separate into domains which are quite regular, and are hence often referred to as 'self-organizing systems'. The domains have been studied and characterized by a variety of periodic morphologies, including triply periodic ones. The translation periods in the model correspond to distances in the polymer of a few hundred nanometers. The phase transitions in simple block copolymers are abrupt and are described as interfaces or surfaces, or specifically, Inter Material Dividing Surfaces, or IMDS. These are sufficiently regular to be amenable to mathematical modeling using some of the surface families described in the Geometry section of this website. While the sphere, cylinder, and lamellar phases are easily observed and characterized, the labyrinth phases are not, and have been the subject of considerable research.

Deciphering Structure

It is possible to infer what morphologies are present by examining samples of the copolymer material. Various instruments have been employed to this end, including transmission electron microscopes (TEM), atomic force microscopes (AFM), and X-ray scattering machines. TEM and to some extent AFM images can be simulated using volume projection techniques. Inferences about the morphology of a sample can be made when there is a good match between its TEM image and a simulated volume projection using a known mathematical IMDS model. Other approaches to inferrring structure include using tilt series of TEM images to construct IMDS models through tomography, and using X-Ray diffraction data to compute amplitude terms in a general Fourier series representation of periodic structures.

TEMsim is a tool designed to infer the three-dimensional structure of morphologies observed in block copolymers in TEM images, by matching those images to simulated projections of of volumes separated by mathematically modelled surfaces. It was used to create the Standard Projections of G, D, and P surface models of grain boundarys are provided as a reference for similar structures observed using microscopy.

Block Copolymer Web Resources

• ^ Information on block copolymers is provided in a ^ brochure by the ^ Max Planck Institute for Polymer Research in Mainz, Germany.
• The ^ Glossary of the PLC Virtual Textbook defines ^ polymer, and the different kinds of ^ copolymers
• The ^ Glossary of Basic Terms in Polymer Science defines ^monomer, ^polymer, ^copolymer, and ^block copolymer.
• The article ^ Copolymer films: Watching molecules organize themselves gives a primarily two-dimensional view of phase separation in block copolymers.