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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Molecular dynamics studies of knotted polymers

Molecular dynamics calculations have been used to explore the influence of knots on the strength of a polymer strand. In particular, the mechanism of breaking 31, 41, 51, and 52 prime knots has been studied using two very different models to represent the polymer: (1) the generic coarse-grained (CG) bead model of polymer physics and (2) a state-of-the-art machine learned atomistic neural network (NN) potential for polyethylene derived from electronic structure calculations. While there is a broad overall agreement between the results on the influence of the pulling rate on chain rupture based on the CG and atomistic NN models, for the simple 31 and 41 knots, significant differences are found for the more complex 51 and 52 knots. Notably, in the latter case, the NN model more frequently predicts that these knots can break not only at the crossings at the entrance/exit but also at one of the central crossing points. The relative smoothness of the CG potential energy surface also leads to stabilization of tighter knots compared to the more realistic NN model.

DelloStritto, Mark (ORCID:0000000206785860)↗
DOE OSTI2022

Random Knotting in Fractal Ring Polymers

Many ring polymer systems of physical and biological interest exhibit both pronounced topological effects and nontrivial self-similarity, but the relationship between these two phenomena has not yet been clearly established. Here, we use theory and simulation to formulate such a connection by studying a fundamental topological property—the random knotting probability—for ring polymers with varying fractal dimension, d f . Using straightforward scaling arguments, we generalize a classic mathematical result, showing that the probability of a trivial knot decays exponentially with chain size, N, for all fractal dimensions: P 0 (N) ∝ exp(–N/N 0 ). However, no such simple considerations can account for the dependence of the knotting length, N 0 , on d f , necessitating a more involved analytical calculation. This analysis reveals a complicated double-exponential dependence, which is well supported by numerical data. By contrast, functional forms typical of simple scaling theories fail to adequately describe the observations. These findings are equally valid for two-dimensional ring polymer systems, where “knotting” is defined as the intersection of any two segments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends

Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, in this work, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τ d,R for rings of length N R blended with linear chains of length N l to scale as τ d,R ~ N$^2_R$N$^{3.4}_L$.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Topological Effects Near Order–Disorder Transitions in Symmetric Diblock Copolymer Melts

The effects of polymer chain topology on the order–disorder transition of symmetric AB diblock copolymer melts are studied using coarse-grained molecular dynamics simulations. Specifically, we compared chain conformations near the lamellar-disordered transition in melts of symmetric (i.e., 50–50) AB diblock copolymers of linear chains, rings, and trefoil knots at the same chain lengths. The order (lamellar)–disorder transition temperature and the domain sizes both shifted to lower values with the introduction of topological constraints, leading to the following sequence: linear chains > rings > trefoil knots. Furthermore, investigation of the polymer chain conformations in terms of their radii of gyration, their writhe values (a measure for the degree of intertwining of a chain around itself), and their Jones polynomials (a method to measure entanglement of curves) showed that linear chains and rings remained stretched, while knots were stretched and tightened in disordered melts close to the lamellar-disorder transition. This work highlights chain topology as an important factor in affecting microphase separation in block copolymers.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A Note on the Effects of Linear Topology Preservation in Monte Carlo Simulations of Knotted Proteins

Monte Carlo simulations are a powerful technique and are widely used in different fields. When applied to complex molecular systems with long chains, such as those in synthetic polymers and proteins, they have the advantage of providing a fast and computationally efficient way to sample equilibrium ensembles and calculate thermodynamic and structural properties under desired conditions. Conformational Monte Carlo techniques employ a move set to perform the transitions in the simulation Markov chain. While accepted conformations must preserve the sequential bonding of the protein chain model and excluded volume among its units, the moves themselves may take the chain across itself. We call this a break in linear topology preservation. In this manuscript, we show, using simple protein models, that there is no difference in equilibrium properties calculated with a move set that preserves linear topology and one that does not. However, for complex structures, such as those of deeply knotted proteins, the preservation of linear topology provides correct equilibrium results but only after long relaxation. In any case, to analyze folding pathways, knotting mechanisms and folding kinetics, the preservation of linear topology may be an unavoidable requirement.

Especial, João N. C. (ORCID:0000000254765370)↗