PHASE-TRANSITIONS IN POLYMERIC SYSTEMS - A CHALLENGE FOR MONTE-CARLO SIMULATION

Polymers are more difficult to simulate than small molecule systems, due to the large size of random polymer coils (and their slow relaxation, that is observed when dynamic simulation algorithms are used). However, variation of the chain length N of a flexible polymer chain provides a very useful additional control parameter, allowing stringent tests of theories, and new physical phenomena may emerge. As an example of these concepts, critical phenomena in polymer mixtures are described. It is shown that unmixing of symmetrical mixtures (N-A = N-B = N) is described by an equation for the critical temperature T-c(N) = aN + b rather than T-c alpha root N as claimed by some theories. While for finite N the critical behavior is Ising-like, for N --> infinity it becomes mean-field like, and this crossover creates interesting problems for the finite size scaling analysis of Monte Carlo data. Special problems occur also for asymetric mixtures (semi-grandcanonical algorithms involve chain splitting and fusion, and finite size scaling analyses must take ''field mixing'' into account). Finally, studies of interfaces between coexisting phases require huge systems (> 10 million lattice sizes), but can be handled on parallel computers. Less well understood, however, are ordering phenomena in block copolymers: type and wavelength of the resulting mesophases change with temperature and composition, and since the ordering is typically incommensurate with the lattice linear dimension, no simple finite-size behavior emerges.