Polymer with screw axis arranged monomers

Symmetries of polymers are described by the line groups which are classified and their irreducible representations are tabulated. The magnetic (i.e. time reversal symmetry included) line groups, together with their correpresentations are derived.

These results are the basis for the research of diverse physical properties of polymers (phase transitions, selection rules, physical tensors). The complete classification of the phonon spectra has been performed, and the vibronic (in)stability of polymers has been established (Jahn-Teller theorem for polymers). The Molien functions for the line groups have been calculated what enabled complete determination of the most general forms of the invariant potentials for the all quasi-1D systems (applied in analysis of commensurate and incommensurate phase transition in polymers and 3D crystals).

The computer program POLSym ® enables the efficient analysis of the polymer properties, implementing their symmetry through the modified group projector technique. Such studies are easily performed even for complex polymers as the DNA macromolecule.