Direct Assessment of Tube Dilation in Entangled Polymers

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(N)(0) of highly entangled polyethylene oxide (PEO) chains of volume fraction c that are diluted by low molecular PEO show a concentration dependence d proportional to c(a/2) and G(N)(0) proportional to c(1+a) 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.