Direct Observation of Nonaffine Tube Deformation in Strained Polymer Networks

Abstract

We present a one-to-one comparison of polymer segmental fluctuations as measured by small angle neutron scattering in a network under deformation with those obtained by neutron spin echo spectroscopy. This allows an independent proof of the strain dependence of the chain entanglement length. The experimentally observed nonaffine square-root dependence of the tube channel on strain is in excellent agreement with theoretical predictions and permits us to exclude an often invoked nondeformed as well as affinely deformed tube.

Nematic effects and strain coupling in entangled polymer melts under strong flow

“…In conclusion, we confirm the ruling out of both nondeformed and affinely deformed tubes in entangled melts akin to crosslinked networks [21]. In the pure short chain melt we confirm the non-affine mean-field result ν = 0.5 for the strain coupling, even subjecting the sample to a significantly increased stretch and strain rate than previously documented.…”

“…If we focus on the relaxation of the SiS sample first, the fit for t = 0 basically confirm the ν = 0.5 non-affine strain coupling from [21] even for the much stronger flow conditions employed here (a factor ∼15 higher strain ratio). For t > 0 the fits to the SiS data predict that at the Rouse time the system is almost relaxed and from the effective strain ratio we find that at the 320s mark, the system has fully relaxed.…”

“…It is important to recognise that the microscopic and macroscopic strain ratios are not necessary the same [18] and a number of models have attempted to relate the two theoretically [19]. In particular, the value of the strain coupling has been a topic of discussion for some time [14,20,21] but for moderate strain ratios has been clearly demonstrated experimentally to be non-affine with ν = 0.5 [21] confirming various theoretical predictions [22,23]. However, it is unclear if this scaling also applies for the much higher strain ratio described here and how the exponent would change in a system influenced by nematic effects.…”

Structural Studies of Three-Arm Star Block Copolymers Exposed to Extreme Stretch Suggests a Persistent Polymer Tube

“…Important parameters for the flow behavior include both the molecular chemistry and the molecular architecture, but also the exact flow condition. The tube model of polymers proposed and described by de Gennes [1] and Doi and Edwards [2] has proven to make a very good theoretical basis for the observed flow characteristics of linear chains [3,4], even though some modifications have been proposed to account for details in the experimental findings [4][5][6][7][8]. Large strain amplitudes can be expected to show further complications beyond the properties of the linear regime described in the tube model [9,10].…”

Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers

“…The above formulations have been found to work well in describing the viscous behavior of polymer chains under small deformation (Li et al, 2012b). However, under the finite strain deformation it cannot be used to capture the viscous energy dissipation of chains, since several important physical mechanisms have been neglected in the original formulation (Li et al, 2012b) ; more specifically, primitive chain length and tube diameter should be changed by the deformation gradient, which has already been observed through experiments (Straube et al, 1995;Pyckhout-Hintzen et al, 2013;Ott et al, 2014). Therefore, we have made the following important assumptions for these physical mechanisms 1.…”