Melt Structure and Dynamics of Unentangled Polyethylene Rings: Rouse Theory, Atomistic Molecular Dynamics Simulation, and Comparison with the Linear Analogues

Abstract

Atomistic configurations of model unentangled ring polyethylene (PE) melts ranging in chain length from C 24 up to C 400 have been subjected to detailed molecular dynamics (MD) simulations in the isothermal-isobaric statistical ensemble at temperature T = 450 K and P = 1 atm. Strictly monodisperse samples were employed in all cases. We present and discuss in detail simulation results for a variety of structural, thermodynamic, conformational and dynamic properties of these systems, and their variation with chain length. Among others, these include the mean chain radius of gyration, the pair correlation function, the intrinsic molecular shape, the local dynamics, the segmental mean square displacement (msd), the chain center-of-mass self-diffusion coefficient D G , the chain terminal relaxation time τ d , the characteristic spectrum of the Rouse relaxation times τ p , and the dynamic structure factor S(q,t). In all cases, the results are compared against the corresponding data from simulations with linear PE melts of the same chain length (the linear analogues) and the predictions of the Rouse theory for polymer rings which we derive here in its entirety. The Rouse theory is found to provide a satisfactory description of the simulation findings, especially for rings with chain length between C 50 and C 170 . An important finding of our work (from the observed dependence of D G , τ p , ζ, and η 0 on chain length N) is that PE ring melts follow approximately Rouse-like dynamics even when their chain length is as long as C 400 ; this is more than twice the characteristic crossover chain length (∼C 156 ) marking the passage from Rouse to reptation dynamics for the corresponding linear PE melts. In a second step, and by mapping the simulation data onto the Rouse model, we have managed to extract the friction coefficient ζ and the zero-shear rate viscosity η 0 of the simulated ring melts. Overall, and in agreement with previous theoretical and experimental studies, our simulation results support that the structure of ring polymers in the melt is more compact than that of their linear analogues due to their nonconcatenated configurations. Additional results for the intermolecular mer-mer and center-of-mass pair correlation functions confirm that the effective correlation hole effect is more pronounced in melts of rings than in melts of linear chains.

Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics

“…These theories make use of the fact that linear chains have free ends but ring polymers do not have free ends so the application of these theories, and especially reptation theory, is questionable. However, the Rouse model can be solved for a Gaussian ring 22 . The diffusion times from Rouse theory for the linear and ring models are given in Table II.…”

Conformation of Ring Polymers in 2D Constrained Environments

“…Thus we show further that spatially confined molecules fold into specific conformations close to those found for linear chains, and strongly dependent on the size of the confining box. DOI: 10.1103/PhysRevLett.106.248301 PACS numbers: 82.35.Gh, 87.64.Dz, 36.20.Ey, 87.14.gk Ring closure of a polymer is one of the important factors influencing its statistical mechanical properties [1], e.g., scaling [2,3], shape [4,5], and diffusion [6][7][8], because it restrains the accessible phase space. The theoretical description of circular chains (knots or catenanes) is a challenging problem, owing to the difficulties inherent to a systematic theoretical analysis of such objects constrained to a unique topology.…”

“…Ring closure of a polymer is one of the important factors influencing its statistical mechanical properties [1], e.g., scaling [2,3], shape [4,5], and diffusion [6][7][8], because it restrains the accessible phase space. The theoretical description of circular chains (knots or catenanes) is a challenging problem, owing to the difficulties inherent to a systematic theoretical analysis of such objects constrained to a unique topology.…”

Conformational evolution under steady shear flow: a comparison between cyclic and linear block copolymers

“…For example, all segments of a cyclic homopolymer chain are equivalent due to a lack of free chain ends (Iatrou et al 2002;Watanabe et al 2006;Tsolou et al 2010). Then, the mean orientational anisotropy appears to be the same for these segments under the steady shear flow (Watanabe et al 2006;Tsolou et al 2010).…”