Dynamics of Branched Polymers: A Combined Study by Molecular Dynamics Simulations and Tube Theory

Abstract

We present large-scale computer simulations of entangled polymers with symmetric star-like and Cayley tree-like architectures. Unlike the usual observation for repational behaviour of linear chains, the simulated systems exhibit a strong dispersion, over several decades, of the relaxation times after the local reptative ('Rouse in tube') regime. Relaxation is dramatically slowed down by approaching the branch point from the outer segments. This is consistent with the expected retraction mechanism for strongly entangled branched polymers. In order to describe fluctuations around the branch point, we introduce a Rouse-like model adapted to star-like polymers and incorporate entanglements by means of localizing springs. Model predictions for localization of the branch point are compared with simulations with fixed arm ends, which suppress retraction and tube dilution. Strikingly, the simulations reveal a localization of the branch point weaker than expected. This suggests the presence of early constraint-release effects that are not captured by the standard mechanism of tube dilution. We quantify, as a function of time, the strength of such effects and the fraction of relaxed material directly from the simulations with free ends. This allows us to renormalize the tube diameter and entanglement time in our model as time-dependent quantities. With this renormalization, the model provides an excellent description of the early relaxation of the branch point.

Branch-Point Motion in Architecturally Complex Polymers: Estimation of Hopping Parameters from Computer Simulations and Experiments

“…A detailed description of the protocol can be found in Ref. 38 After equilibration, production MD runs were performed, extending over typically one to five billion MD steps. The MD runs were integrated by using the velocity-Verlet algorithm with time step ∆t = 0.01τ 0 .…”

“…In our previous work, we confronted our choice of the coefficients with the predictions of the Rouse model. 38 …”

5D Entanglement in Star Polymer Dynamics

“…Its motion is quantified in terms of the MSD g (t) = (R(t) − R(0)) 2 (4) shown in Figure 4. The longest trajectory of star polymers available in the current literature is by Bačová et al, [18] using the standard Kremer-Grest model, with an added bending stiffness to decrease the entanglement length. On the short timescale, all N follow the same law of a free random walk g ∝ t/τ .…”

“…[7] Branched polymers, and stars in particular, [8] are becoming more accessible, thanks to recent innovations in their chemical synthesis. [18] The current consensus is in favor of arm retraction, although a broad mesoscopic time range remains unexplored and some open questions remain. While the static structure of star polymer systems has been well studied in both bulk [11] and interfaces, [12] their dynamics pose considerable challenges, as they can be many orders of magnitude slower compared to linear chains of the same molecular weight N. It has been recognized that reptation is impossible for branched polymers, and a new relaxation pathway of arm retraction has been proposed.…”

“…While the static structure of star polymer systems has been well studied in both bulk [11] and interfaces, [12] their dynamics pose considerable challenges, as they can be many orders of magnitude slower compared to linear chains of the same molecular weight N. It has been recognized that reptation is impossible for branched polymers, and a new relaxation pathway of arm retraction has been proposed. [18] The speedup quoted here is an order-of-magnitude estimate, whose precise value cannot be guaranteed, as it depends on the specific hardware, driver, compiler, and kernel optimization, the random number generator, as well as details of the physical model such as the algorithm used to constrain the bond length and (optionally) the bond stiffness. The exponential scaling was first observed in rheology and diffusion experiments.…”