# Block Copolymers

## Definition

A block copolymer is a polymer that consists of multiple different types of polymer chains that are covalently attached to each other. The polymerized subunits that make up a block copolymer are chemically different, and they form adjacent blocks. For instance, a monomer A might bond at both of its ends to polymer B, forming a triblock BAB structure.

An important property of block copolymers is the propensity for the blocks to self-assemble into nanostructures, the size of which is determined by the length of the constituent monomers. This results in regions that are highly enriched for a single type of monomer, with the covalent bonds between blocks crowding at the interphases between the domains. Such copolymer structures will disappear and be replaced with a disordered structure upon an increase in temperature of a sufficient magnitude. If there were no covalent bond between the blocks of a copolymer there would be a macrophase (rather then microphase) separation, such as one sees when oil and vinegar separate into droplets in a salad dressing.

## Theory

In the simplest case of a block copolymer that is made up of two homopolymers, which we can call A and B. The free energy of the blend is approximated by the Flory-Higgins equation:

$\frac{\Delta G_{mix}}{k_bT}=\frac{\ln f_A}{N_A}+\frac{f_B}{N_B}+f_A f_B \chi$

In which:

• N is the degree of polymerization, which is the number of molecules per macromolecule;
• $N_a$ and $N_b$ are the degree of polymerization of block A and B, respectively;
• f is composition, which is defined as $f_i=\frac{N_i}{N}$
• $\chi$ is the A-B Flory-Huggins interaction parameter, which describes the free-energy cost monomer of contact between A and B, where a positive values represents a net repulsion between the monomers.
The geometry of microdomains change as function of the ratio of the lengths of the two blocks

## References

• International Union of Pure and Applied Chemistry Macromolecular Division Commission on Macromolecular Nomenclature. Glossary of Basic Terms in Polymer Science (IUPAC Recommendations 1996). Pure Appl. Chem. 1996, 68: 2287-2311.
• Polymer Research Laboratory at Princeton
• Segalman R.A., Patterning with block copolymer thin ﬁlms. Mater. Sci. Eng. 2005, 48: 191-226.
• Bates F.S and Frendrickson G.H., Block Copolymers - Designer Soft Materials. Phys. Today 1999, 52: 32-38