Visualizing Local Dynamics of Polymers

Jutta Luettmer-Strathmann
Department of Physics

Rammohan Tangirala
Department of Computer Science

The University of Akron
Akron, OH 44325-4001

Introduction 

Processes on different length scales affect dynamic properties of polymers. The figure below contrasts a coarse-grained view of polymer chains in a melt with a close-up view of a monomeric unit displaying the local architecture. Properties on small scales (the scale of monomeric units) have a large effect on the overall mobility of the chains. Since this is reflected in bulk dynamic properties like the viscosity, research in local chain dynamics has potential applications in the design and processing of polymeric materials [1]. 

There are several factors that influence the motion of short chain segments of polymers in a melt. In related work we investigate the effects of chain properties like local architecture [2] with the aid of small-scale simulations. Here we focus on the role of the local environment and employ Monte Carlo simulations of a simple model for a polymer (a so-called generalized bond-fluctuation model [3]) to illustrate some aspects of local chain dynamics.

The figure illustrates a section of a single polymer chain represented by beads on the sites of a simple cubic lattice. The beads are connected by bonds that can have a length of 1 (along a side of a small cube), ?2 (along the face diagonal) and ?3 (along the body diagonal). In the simulations, attempts are made to move the beads to one of their nearest neighbor sites. A move is allowed if the new site is empty, no bonds are overstretched, and no bonds have to cross in the process. In the simulations shown below, 200 chains of 20 beads each are simulated on a lattice of dimension 20×20×20. 

Movies of Simulation Results

The movie clips shown below were generated with the aid of AVS from the simulation results. The basic time unit is one Monte Carlo step (MCS), which corresponds to one attempted move per bead. After a long equilibration period, four configurations per MCS were recorded for the following 100 MCS. 

All chains

The animation illustrates the dynamics of the whole system. The beads on the chains are shown as spheres, the bonds as white lines. In the beginning all beads have a blue color. During the run, the color value increases by one unit each time a bead moves. In this way, the most mobile beads change their color from blue to bright green over the time (100MCS) of the simulation, while the most immobile beads retain their blue color. The images show regions of high mobility (greenish color) and regions of low mobility (blue). There are, in fact, chain segments that do not move at all during the simulations, while other beads are much more mobile than the average. 

Individual chains

During the simulation, we identified the most mobile bead, the most mobile bead in the center of a chain, and the slowest bead. To make the movements more visible, we show only the chain to which the “special” bead belongs after transferring it to the center of the cube. The color scheme is shifted compared to the previous animation (this will allow us later to distinguish the chains in their environments). Mobile beads gradually change their color from green (the initial color for all) over orange to red.

1. As we might have expected, the most mobile bead finds itself at the end of a chain. In general, chain ends are more mobile than chain centers, since they have only one rather than two bonded neighbors. Note, however, that with all its whipping about, the bead ends up only two steps removed from its starting position.

2. The mobility of a central bead is a better indicator for the mobility of a whole. Note here, how the whole chain is displaced in the course of the simulation.

3. Finally, we present a chain where one bead, the fourth from the lower end, does not move at all. To find out why this chain is so immobile, we will look at its environment.

Local environments

In the following clips, we show the chains (green to red) in their local environments (blue to bright green) given by the first, second, and third nearest neighbors of the chain segments. 

1. Notice how the very active end bead is surrounded by many empty sites and some mobile beads of other chains. You may also note how a dense region in the upper right corner holds the chain in place. 

2. The mobile central bead finds itself in a low-density environment during the last third of the clip and takes advantage of it to explore its surroundings. 

3. The slowest bead (the fourth from the lower end of the chain) is at all times surrounded by a number of beads from other chains. A closer look at the bonds reveals that the chain is intertwined with neighboring chains. Since bonds cannot penetrate each other, it is very difficult for the chain to free itself.

Discussion

The animations give an impression about the effect of the local environment on the mobility of chain segments. They confirm the importance of the role of the local density, which is the subject of the so-called free-volume theories [1]. They also illustrate that fast beads sometimes belong to slow chains and that a polymer melt comprises a whole range of different environments. One of the objectives of this work is to identify the local environments that determine segmental mobility and to arrive at a quantitative description of their nature and effect. A second objective is to investigate the relationship between the mobility of individual beads and the average mobility of polymer chains in the melt. The simple polymer model [3] in the simulations already shows some of the characteristic dynamics of polymer melts. It will be extended [4] in order to investigate how the chain structure affects the mobility of the polymer.

Acknowledgements

The authors would like to thank the OSC for computational resources and for making AVS available.Financial support through the Petroleum Research Fund and the National Science Foundation is gratefully acknowledged. 

References

[1] J. D. Ferry, Viscoelastic Properties of Polymers, Wiley, New York (1980).

[2] J. Luettmer-Strathmann. Effect of small-scale architecture on polymer mobility. J. Chem. Phys. 112, 5473 (2000). Segmental mobility of polyolefin melts.Int. J. Thermophys., in press.

[3] J. S. Shaffer, Effects of chain topology on polymer dynamics: Bulk melts. J. Chem.
Phys. 101, 4205 (1994).

[4] J. Baschnagel, K. Binder, P. Doruker, A. A. Gusev, O. Hahn, K. Kremer, W. L. Mattice, F. Müller-Plathe, M. Murat, W. Paul, S. Santos, U. W. Suter, and V. Tries. Bridging the gap between atomistic and coarse-grained models of polymers: Status and perspectives. Adv. Polym. Sci. 152, 41 (2000).