Biopolymers, as proteins and DNA-molecules may be interpreted from a theoretical point of view as macromolecules with quenched random disorder along the chain. This idealzed model requires that monomer sequences show pronounced Markovian behaviour. Furthermore, the thermodynamic behaviour of compositionally randomized polymer chains is mainly controlled by the monomer-monomer interaction. In this talk we may distinguish between short and long range interactions.
In the first section of the present talk we focus on the thermodynamic properties of linear biopolymers with long and short range interactions on the basis of a generalized charge model. We demonstrate by application of a perturbation expansion and a proper subsummation of the leading terms that such models describe the main properties of biopolymers, for instance the swelling-collaps transition, very well. In the second part of this talk we investigate diluted solutions and dense melts of such biopolymers by numerical Monte Carlo simulations. The equilibrium structural properties of such systems are characterized by the mean square end-to-end distance and the static structure factor of the polymer chains. Both temperature and density determine the structure (collapse, swelling or screening regime). A description of this behavior is given using generalized scaling arguments and proven by the numerical MC--simulations.
Finally, we analyze of the thermodynamic properties of random cross-linked polymer networks made of phantom chains with compositional disorder. We start our investigations from an extended Edwards Hamiltonian and end with the discussion of the free energy and mechanical properties. Using replica field theory we determine and solve the saddle point equations. The physically relevant ground state is invariant against translations in the real space, but it depends strongly on the coupling parameters for interactions, topology and compositional disorder of the network. We predict three different thermodynamic states for random copolymer networks. For two regimes the saddle point shows a rotational symmetry after elimination of translation effects. Here the network behaves similar to a homogeneous network. The third regime corresponds to a ground state with broken replica symmetry similar. Here, the behavior of the random copolymer network shows similarities to the thermodynamical properties of spin glasses and the network state is comparable to diluted proteins.