ABSTRACT
There is a large number of different methods (algorithms) used for simulation of polymers on the coarse grained molecular scale [1-6]. Models of polymers considered in this range usually disregard the details of the chemical constitution of macromolecules and represent them as assemblies of beads connected by nonbreakable bonds. In order to speed up recognition of neighboring beads, the simplified polymers are often considered to be on lattices with beads occupying lattice sites and bonds coinciding with lines connecting neighboring sites. The methods used for simulation of the lattice polymers can be considered within two groups. The first group includes algorithms that can operate only in systems with a relatively large fraction of lattice sites left free and the second group includes algorithms suitable for lattice systems in which all lattice sites are occupied by molecular elements. Whereas, the systems considered within the first group should be regarded as lattice gases, the systems treated within the second group of methods can be considered as lattice liquids. This reflects the differences in the mechanisms of molecular rearrangements used within these two groups to move the systems through the phase space in order to reach equilibrium. The latter problem concerns the physical nature of molecular rearrangements in dense polymer systems and is related to the microscopic mechanism of motion in molecular liquids. Unfortunately, this is not yet solved entirely. The most popular picture is that a molecule, or a molecular segment in the case of polymers, needs a free space in its neighborhood in order to make a translational step beyond the position usually occupied for quite a long time. Most simulation methods assume this picture and consequently a relatively large portion of the space in the form of free lattice sites has to be left free to allow a reasonable mobility [15]. On the other hand, there is only one simulation method that assumes a cooperative nature of molecular rearrangements on the local scale and which does not require such a reserve space to allow the molecular mobility. The method, which uses the mechanism of cooperative rearrangements for polymer systems is the Cooperative Motion Algorithm (CMA) suggested originally in [6] and presented in improved form in subsequent
publications [7-10]. A mechanism of this kind has been formulated recently also for low molecular weight liquids, based on assumptions taking into account both a dense packing of molecules interacting strongly due to excluded volume and a condition of preservation of local continuity of the system. The later version of the microscopic mechanism, called the Dynamic Lattice Liquid (DLL) model, has been described in detail [11-14].
