Quantitative Theory for Linear Dynamics of Linear Entangled Polymers

Abstract

We present a new quantitative development of the reptation picture of de Gennes−Doi−Edwards. It is well-known that the original reptation theory is unable to fit linear relaxation spectra (G‘ and G‘ ‘) as it misses several important physical processes: (1) contour length fluctuations, (2) constraint release, and (3) longitudinal stress relaxation along the tube. All of these processes were treated theoretically before; however, the treatment used either uncontrolled approximations or failed to include all of them at the same time. The aim of this work is to combine self-consistent theories for contour length fluctuations and constraint release with reptation theory. First, we improve the treatment of contour length fluctuations using a combined theoretical and stochastic simulation approach. This allows us to obtain an expression for the single chain relaxation function μ(t) without any adjustable parameters and approximations. To include constraint release, we use the scheme proposed by Rubinstein and Colby, which provides an algorithm for calculating the full relaxation function G(t) from the single chain relaxation μ(t). Then longitudinal modes are added, and a detailed comparison with different experimental data is given. One of the conclusions is that polystyrene is described by theory very well, but polybutadiene shows problems, which may be a first indication of nonuniversality of polymer dynamics.

Single-Chain Slip-Link Model of Entangled Polymers: Simultaneous Description of Neutron Spin−Echo, Rheology, and Diffusion

“…Than, there is a rather sharp transition to approximately η ∼ N 3.6 behavior, with crossover around N c ) 16 (with CR). This is slightly different from our earlier analytical model, 19 which goes through higher slope around 3.8-3.9 before smooth transition to slope 3. Similarly, the diffusion coefficient shows -2.4 slope (-0.4 on this graph).…”

“…Now I will briefly make a connection with our previous analytical solution for the "standard" tube model. 19 Figure 10shows comparison of the linear rheology predicted by the single-chain slip-link model with and without constraint release with our previous analytical model. 19 The fitting parameters for the analytical model are Looking at the left graph, one can conclude that if both models do not have constraint release, the agreement is satisfactory even for N ) 48, which corresponds to about Z ) 7 entanglements in analytical model.…”

“…19 Figure 10shows comparison of the linear rheology predicted by the single-chain slip-link model with and without constraint release with our previous analytical model. 19 The fitting parameters for the analytical model are Looking at the left graph, one can conclude that if both models do not have constraint release, the agreement is satisfactory even for N ) 48, which corresponds to about Z ) 7 entanglements in analytical model. When one adds constraint release, there is an additional choice of constraint release parameter in the analytical model c ν (see ref 19 for details).…”

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

“…This unique behaviour is intimately related to the uncrossability of chains which effectively leads to topological constraints between chains in the form of entanglements (deGennes, 1980;Doi and Edwards, 1988). The original reptation theory, based on the tube model, and more recent theoretical concepts have captured qualitatively and quantitatively the effect of entanglements on polymer dynamics and rheology (deGennes, 1980;Doi and Edwards, 1988;Kroger, 2004;Likhtman, 2005;Likhtman and McLeish, 2002;Marrucci, 1996;Marrucci and Ianniruberto, 2004;McLeish and Larson, 1998;Ramirez et al, 2007;Stephanou et al, 2011;Wang et al, 2012). Additionally, density is one of the key factors which affect profoundly the static, dynamic and rheological properties of entangled polymers (Daoud et al, 1975;Doi and Edwards, 1988;Edwards, 1966;Fleer et al, 1993).…”

Polymer dynamics: long time simulations and topological constraints

“…This primitive path is the backbone of the appropriately coarse grained chain contour [7,8]. Recent, more refined analytical [3,9] and numerical models [10][11][12][13][14] concentrate on the dynamics of these primitive paths. These models are able to quantitatively describe many rheological and single chain dynamics data with a small set of material-specific parameters such as the tube diameter, d T .…”