Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics

Abstract

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, R 2 g , was found to scale as N 4/5 for an intermediate regime and N 2/3 for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper 1 . Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.

Density effects in entangled solutions of linear and ring polymers

“…2, right panels). Furthermore, now the observed scaling law is different, p c (l) ∼ l −1 , and in particular compatible with the predictions of crumpled globules [14,20,41]. This analysis is complemented by considering separately the two contributions to the average number of contacts of each monomer of the chain: the first arising from contacts between monomers inside the same chain, ρ c intra , and the second arising from contacts between monomers belonging to different chains, ρ c inter .…”

“…More recently a new class of systems has emerged and started receiving similar systematic attention: entangled solutions and melts of unconcatenated and unknotted circular (ring) polymers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Why are ring polymers so special and, as we will shortly see, challenging?…”

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

“…Indeed there are no really dense 'melt-like' regions in the stiff SCNPs (see bottom panels in Fig. 5) resembling the 'territories' observed in melts of rings and chromatime [32,33,36]. These would indeed involve strong folding of chain segments and consequently a large bending penalty.…”

“…These would indeed involve strong folding of chain segments and consequently a large bending penalty. The second, and more relevant, difference is that the SCNPs do not show the approximate scaling P (s) ∼ s −1 expected for crumpled globules [32,33,36,43]. The decay of P (s) at long contour distances is, for all the investigated values of k and f , compatible with power-law behaviour, P (s) ∼ s −x , but with an exponent 1.5 ≤ x ≤ 1.8 (see results for f = 0.4 as a function of k and for k = 0 as a function of f in both panels of Fig.…”

“…As a consequence of their molecular architecture with permanent loops, SCNPs exhibit a peculiar collapse behaviour in concentrated solutions and melts. Instead of the Gaussian conformations displayed by linear chains, they adopt fractal or 'crumpled' globular conformations [31,32] resembling those found for melts of ring polymers or chromatin loops [32,33,34,35,36], suggesting this scenario for the effect of purely steric crowding on IDPs in cell environments.…”