Where ρ is the polymer density, A is number, and MC is the
average molecular weight of the polymer between cross-linking
points. A simple NMR method is used to determine MC. Using Eqs.
(3) and (4), the Vc is calculated as shown in Table 1. It clearly
showed that the Vc of MRE increased with increasing in Fe3O4
doping content. The result was attributed to the formation of
physical cross-links between NR chain and Fe3O4 nanoparticles, in
which there were more NR chains for one physical cross-link
comparing to one chemical cross-link as shown in Scheme 2. In
addition to this, it was found that there were less cross-linking
chains and more dangling chains for the MRE comparing to the
neat NR. The result was attributed to form less cross-links for MRE
comparing to the neat NR.