Effects of chain topology on polymer dynamics: Bulk melts

Abstract

We introduce a new lattice-based Monte Carlo model of polymer dynamics in which the polymer chain topology can be altered without perturbing any static properties or the local segment mobility. Chain entanglements can then simply be switched ‘‘on’’ and ‘‘off,’’ and their effects on global dynamics can be clearly isolated. Two sets of simulations have been conducted for bulk polymer melts. In the first set chain crossing is rigorously forbidden, but in the second set the polymer chains are allowed to cross through each other. When the chains are not allowed to cross, the self-diffusion coefficient exhibits the classic signature of the crossover from unentangled to entangled dynamics. For short chains, D∼N−1, while for long chains, D∼N−2, where D is the diffusion coefficient and N is the number of polymer segments. Furthermore, the longest noncrossing chains show a clear preference for anisotropic motion along their own contours—they appear to move by reptation. When the chains are allowed to cross, however, D∼N−1 at all chain lengths, characteristic of unentangled dynamics. No crossover is indicated in this case, and no signs of reptation are present. Since the structure and local mobility are nearly identical in the two cases, the dynamical differences are due only to the chain topology through the crossing condition. We discuss how the results illustrate the role of entanglements in bulk polymers and how the model may be used in the future as a tool to examine entanglement effects in adsorbed layers and confined polymer fluids.

Energy Landscape and Isotropic Tensile Strength of n-Alkane Glasses

“…Their work suggests that chains of length greater than n ) 8 should contain topological interchain entanglements, even though they might not exhibit rheological entanglement dynamics. Although the topological problem of identifying chain entanglements at the atomistic level remains unsolved, 37,[80][81][82][83][84][85][86] visual inspection of the configurations for the longer chains, n ) 16, 24, and 48, confirms that the molecules tend to adopt curled or folded conformations and tend to intertwine, indicating there is some degree of entanglement present. However, results from the landscape equations of state and the deformation curves show a counterintuitive trend, namely that the tensile strength decreases with chain length beyond n ) 3.…”

Monte Carlo simulation of a single ring among linear chains: Structural and dynamic heterogeneity

“…All this makes it possible to obtain equilibrium conformation for noncrossing chains ͑or real chains͒ within a relatively short period by starting from equilibrated crossing chains. 37 In our simulations, monomers are placed on a 3D cubic lattice with size L box ϫ L box ϫ L box ͑for details see Table I͒. Admittedly, our box size for the linear-1000 system ͑40 ϫ 40ϫ 40͒ is not very large, and as a result, the system may suffer from some "overlap" artifacts due to the periodic boundary conditions.…”

“…One is that the number of chain segments between entanglements ͑N e ͒ ͑Ref. 39͒ for linear chains in melt, is quite small ͑N e Ϸ 30͒, 37,38,40 which makes it easy to simulate entangled linear chains with a relatively large N Linear / N e . The other advantage is that the chain crossing can be simply switched "on" and "off," which can be used to control the entanglement between chains without affecting the static properties or the local segment mobility.…”

“…In this step, chain crossing for linear-linear and linear-ring is allowed; as for the ring itself, however, chain crossing is always forbidden to avoid concatenated or knotted rings. eq is determined using a similar method as Shaffer's, 37 i.e., eq is at least ten times as big as the longest relaxation time of the crossing linear chains in melt. After that we run the simulation for more than eq / 10 to gradually remove those chain crossing.…”

Coarse-grained models for macromolecular systems

“…The most widely used lattice algorithm is the bond-fluctuation model [10,11] (see Figure 2, left). It can be seen as an intermediate between cubic lattice models and continuum models, since the bond between two monomers can take many different values (36 in 2d and 108 in 3d, compared to 4 in 2d and 6 in 3d for a simple cubic lattice).…”