Introduction to Monte Carlo simulations of polymers

In this lecture the basic aspects of Monte Carlo simulations are introduced, choosing models of polymers as examples. First the distinction between simple sampling and the Metropolis importance sampling algorithm is discussed, and the main limitations of the latter are discussed: lack of information on the partition function; "dynamical" correlation of "observations" and the resulting interpretation in terms of master equations, which also is the basis for applications to simulate the dynamics of fluctuations, diffusion processes and relaxation processes far from equilibrium; finite size effects, and their analysis in the context of simulations of second-order and first-order phase transitions. Examples discussed will include the dynamics of polymer melts, dynamics of translocation of polymers through membranes, and mixing of symmetrical binary mixtures, as well as asymmetrical polymer solutions. Also an introduction to path integral quantum Monte Carlo will be given, mentioning the application to crystalline orthorhombic polyethylene as an example.