Highly entangled polymer primitive chain network simulations based on dynamic tube dilation

Abstract

The concept of dynamic tube dilation (DTD) is here used to formulate a new simulation scheme to obtain the linear viscoelastic response of long chains with a large number of entanglements. The new scheme is based on the primitive chain network model previously proposed by some of the authors, and successfully employed to simulate linear and nonlinear behavior of moderately entangled polymers. Scaling laws are generated by the DTD concept, and allow for prediction of the linear response of very long chains on the basis of suitable simulations performed on shorter ones, without introducing adjustable parameters. Tests of the method against existing data for linear monodisperse polyisoprene and polystyrene show good quantitative agreement.

Challenges in Multiscale Modeling of Polymer Dynamics

“…The longest relaxation time was found to scale with the number of entanglements, Z, as Z 3.5±0.1 , while the self-diffusion coefficient was found to scale as D cm ∼ Z −2.4±0.2 ; both agree well with experimental results [144]. Later on, the PCN model was extended to study the relationship between entanglement length and plateau modulus [145][146][147][148][149]. It was also extended to study star and branched polymers [150], nonlinear rheology [151][152][153], phase separation in polymer blends [154,155], block copolymers [156] and the dynamics of confined polymers [157].…”

Quantitative comparison of primitive chain network simulations with literature data of linear viscoelasticity for polymer melts

“…With respect to our previous paper [15], it may be noted that different values of M 0 and G 0 are reported for polystyrene and polyisoprene in Table 1. In our earlier study we used for the vertical shift the values of G (0) N as provided by the literature, and then fitted values of M 0 = 8.3 kDa for polystyrene and M 0 = 3.4 kDa for polyisoprene.…”

“…Conversely, in our primitive chain network simulations [12][13][14][15] the primitive chains are dispersed in real 3-D space just as in microscopic simulations, and force balance among the chains is explicitly considered.…”

Analytical Rheology of Polymer Melts: State of the Art

“…In addition to the tube model, there are a number of other simulation methods, such as sliplink [167][168][169][170][171][172][173][174][175][176][177][178], lattice [179][180][181][182][183][184][185][186][187][188][189][190][191], and molecular dynamics [192][193][194][195][196][197][198][199][200][201][202][203][204][205] models, to model polymer dynamics. These methods are more "accurate" since they avoid the central simplification of the mean-field tube theory, namely, the phenomenological approximation of the effects of a complex multi-chain environment into a mean-field "tube."…”