ARTICLE NO. CP975650
NOTE Large-Scale Simulations on Polymer Melts
Recently the discussion of the behavior of polymer melts cell. For more details on the bond-fluctuation model see [16,17]. The chains in the melts were grown in a random in the different time regimes of their diffusion process has attracted new attention [1][2][3]. Special features during the process, ensuring self-and cut-avoiding. Subsequent to the generation the melts were subjected to a random dynamics transition to the center of mass diffusion of the entire chain in the melt were proposed using certain computer for a duration of 1,000,000 Monte Carlo steps (MCS). One
Monte Carlo step denotes one attempted jump per mono-simulations and were opposed using other simulations. This recent discussion illuminates a major problem in the mer. Afterward the measurements were begun, lasting 20 ϫ 10 6 MCS. However, the largest system was measured area of computer simulations of polymers, namely the size of the system and the duration of the simulation. Concern-for 200 ϫ 10 6 MCS. The chain length was 199 segments.
Two different densities were investigated, 0.45 and 0.6. ing the size, the simulations can be divided into two groups, a larger one using 500 to 2,000 repeat units (e.g., [4-10]) The density is defined as the lattice sites occupied divided by the total number of lattice sites. For the lower density, and a smaller one using 15,000 to 450,000 units [2,[11][12][13][14][15]. To obtain dense systems the first group puts these mono-systems with 200 chains in a simulation box of 91 ϫ 91 ϫ 91 grid units, 30 chains in 48 ϫ 48 ϫ 48, 13 chains in mers into relatively small boxes with periodic boundary conditions. Once more two groups of simulations can be 36 ϫ 36 ϫ 36, 4 chains in 24 ϫ 24 ϫ 24, and 1 chain in 15 ϫ 15 ϫ 15 were chosen. The parameters for the higher distinguished. The first simulates many, but short, chains. Thus, no entanglements can be found in these polymer density were 280 chains in a box of 91 ϫ 91 ϫ 91 and 41 chains in a box of 48 ϫ 48 ϫ 48. All systems were averaged systems. The other group prefers long, but few, chains, and some just one chain [6, 9, 10], within the simulation box. over several independent configurations, the numbers increasing to 200 runs with decreasing segment content in They presume that, due to the periodic boundary conditions, self-entanglement of these few chains resembles the the simulation box, except for the largest one, which was time averaged using about 5 ϫ 10 6 MCS as the sampling situation of many chains. The simulations using low numbers of monomer units are unfortunately on the rise since interval. Within the bond-fluctuation model the entanglement length N e for the low-density systems is about 38 most heretofore commercially available products have handled at best a few chains within endurable CPU time. segments and for the high-density systems is 24 segments [18]. Hence the chain length of 200 monomers is about The simulation with large numbers of monomers [2,[11][12][13][14][15] can combine both properties, many and long chains, within 5.2 N e and 8 N e , respectively.
The simulations were run on a Cray-YMP8. The pro-a reasonably large simulation box. The large simulation (64,000 units) by Brown et al. [15] was performed by molec-gram was vectorized mainly by three means. First, the three-dimensional lattice coordinates were written in a ular dynamics. Even the application of state-of-the-art computers and programs limited these simulations to a one-dimensional linearized manner. Second, the lattice of the system was divided into cubes of size 7 ϫ 7 ϫ 7 or duration of about 8 ns.
As an example, for the case of melts we will show that 6 ϫ 6 ϫ 6, with the exception of the smallest system. In the athermal case a distance of at least 5 grid units ensures a certain system size is vital in obtaining reliable data. Furthermore, large-scale fluctuations will be presented, that parallel movement of monomers can be performed without their influencing one another. Within each cube suggesting that even simulations which are commonly considered long lasting must be treated carefully when ex-the same randomly chosen lattice site was subject to the following vector compression procedure, the third tool. If tracting structural properties.
The approach presented is based on the well-known monomers are found at these sites in the different cubes, these monomers are noted in a list. Next, the possibility three-dimensional bond-fluctuation algorithm [16]. In this coarse-grained lattice model the polymer chains are repre-of their jumping in a randomly chosen direction is checked.
If this is not possible for a certain monomer due to occupa-sented by mutually and self-avoiding walks on a cubic lattice, each monomer occupying eight corners of the unit tion of the site, this monomer is removed from the list.