Direct Assessment of Tube Dilation in Entangled Polymers

Abstract

A key ingredient within theories focusing on the rheology of entangled polymers is the way how the topological constraints of an entangled chain are lifted by unconstrained segments, i.e., how the constraining tube is dilated. This important question has been addressed by directly measuring the tube diameter d at the scale of the tube by neutron spin echo spectroscopy. The tube diameter d and plateau modulus G 0 N of highly entangled polyethylene oxide (PEO) chains of volume fraction c that are diluted by low molecular PEO show a concentration dependence d ∝ c a=2 and G 0 N ∝ c 1þa with an exponent a close to 4=3. This result allows the clear discrimination between different theoretical models that predict 4=3 or other values between 1 and 2 and provides an important ingredient to tube model theories.

Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

“…In polymer melts, the reptation model has been confirmed and tested by both equilibrium [11,26,27] and nonequilibrium simulations [28,29,30,31], and experiments [32,33,34]. The problem of entangled polymer diffusion [35] with obstacles (nanoparticles) has been addressed by a few studies, but in nanocomposites, there are several parameters that can affect the reptational tube, such as nanoparticle type or loading, confinement, polymer–nanoparticle type of interaction [36].…”

Self-Similar Polymer Ring Conformations Based on Elementary Loops: A Direct Observation by SANS

“…For PEO N e has been determined by neutron spin echo spectroscopy on the scale of the reptation tube size resulting in N e = 59. 29 There the entanglement distance is directly derived from the topological confinement acting on the moving chain. From the plateau modulus in rheological measurements N e = 37 is found.…”

“…The different theories suggest that N e,0 is to be expected close to N e , the length of an entanglement strand in the corresponding linear melt. For PEO N e has been determined by neutron spin echo spectroscopy on the scale of the reptation tube size resulting in N e = 59 . There the entanglement distance is directly derived from the topological confinement acting on the moving chain.…”

Viscosity reduction in polymer nanocomposites: Insights from dynamic neutron and X‐ray scattering

“…Such phenomena have been object of research 59–61 and further discussion is beyond the scope of this paper focusing on dynamics. As far as the NSE measurement is concerned, the main requirement is that scattering signal overwhelmingly originates by the polymer chains and that a Gaussian conformation is retained 62 …”

“…As far as the NSE measurement is concerned, the main requirement is that scattering signal overwhelmingly originates by the polymer chains and that a Gaussian conformation is retained. 62 Within the Gaussian approximation, the dynamics probed by NSE in these conditions relates to the mean squared segment correlation function: 41…”