MATERIALS SCIENCE AND CHEMISTRY

A supramolecular polymer (SMP) refers to a polymer, a part of which is functionalized by a chemical group allowing to form physical bonds with each other. Because the physical association is, in general, reversible and is sensitive to external stimuli, e.g., temperature, mechanical force, pH, the rheological property of the SMP is can be reversibly controlled. Therefore, SMPs have gained a lot of attention in various fields of studies because their potential application as smart materials.

From the physical point of view, one of the most important factors determining rehological properties of SMPs is the topology of aggregates, as polymers of different topology, e.g., linear, ring or branched polymers, without functional groups have very difference mechanisms of diffusion and stress relaxation. Ring polymers, as an example, have a topology whose ends are intrinsically connected to each other, which leads to a different structure relaxation mechanism from linear polymers.

Many experimental and simulation studies have shown that a threading configuration between rings reduces diffusivity of the rings and affects the rheology of the melt. When a very small amount of rings is added to a linear polymer melt, the diffusion of the linear polymer is also slowed down because it is additionally entangled by ring polymers. For SMPs with functional groups which can make only a pairwise association, linear- and ring-shaped aggregates are formed. The numbers and sizes of the aggregates thermally fluctuate, which will eventually determine the rheology of the SMP. However, although several functional groups used for SMPs are known to be pairwise, the topological effect of aggregates on the SMP rheology is poorly understood. Therefore, we performed molecular dynamics simulations of SMPs with pairwise-associating stickers at melt-like density and investigated the relation between the topology of aggregates and the dynamic properties.[1]

In this work, we used a coarse-grained polyethylene glycol model which was developed by ourselves.[2,3] A bead-spring description with Lennard-Jones nonbonded and harmonic bond length potentials for a polymer is used, and the Gaussian attraction potential is employed to describe a hydrogen bond between two stickers. The directionality of the hydrogen bond can be controlled by the width of the Gaussian, so as to restrict our sticker to associate only by a pairwise manner.

We simulated six different linear polymer lengths from 16 to 512 in terms of the number of beads in a polymer including the sticker beads replaced at both ends. The total number of beads in a simulation box is 131,072. Due to the long lifetime of the association and the slow relaxation of the resulting aggregates, we need long simulation time for longer than 2 μs. For each polymer length, we performed simulations for three different association strengths. Simulations were carried out at the JUWELS supercomputer with the ESPResSo++ package in which the Gaussian attraction potential is implemented. Roughly 3 million core hours of computing time were consumed for the project.

Figure 1 highlights ring-shaped aggregates from our simulation snapshot for the number of beads in a polymer of 16. This figure shows that linear aggregates are much more probable than ring aggregates. Moreover, a short ring is more probable than a long ring because the probability of two ends of a linear aggregate meeting each other in space gets smaller as the length of the linear aggregates increases. We found that even the small fraction of rings critically affect the dynamics of the whole SMP. We also found that the fraction of ring aggregates increases with increasing the association strength.

The threading configuration shown in Figure 2 clearly shows the stress relaxation mechanism of the SMP. When a ring-shaped aggregate is formed by association between stickers, a few linear aggregates are enclosed in the ring. Because the majority of rings are small-sized, the motion of the linear polymer perpendicular to its contour is highly suppressed. The only way to relax its stress is either to diffuse along its contour or to break the association of the ring aggregate. We found that the segmental structure relaxation time of a single polymer is proportional to the average lifetime of associations in ring aggregates (the right graph of Figure 2), which implies that ring breaking is the dynamically controlling mechanism.