Relating Chain Structure to Physical Properties of Branched Polymers*

We investigated linear and branched polyethylene (PE) using small-angle neutron scattering (SANS). The experiments were conducted on dilute solutions of PE in deuterated p-xylene. A variety of structural information$^{\dag }$ such as fractal dimension ($d_{f})$, connectivity dimension ($c)$, minimum path dimension ($d_{min})$, long chain branch fraction ($\phi _{br})$, radius of gyration ($R_{g})$ and persistence length ($l_{p})$ were obtained. Such information presents a qualitative and quantitative assessment of branching in polymers. Theoretical models such as `binary contacts per pervaded volume' model$^{\ast }$ were employed to correlate the structural information of the polymer to its entanglement molecular weight ($M_{e})$. $M_{e}$ was used to predict physical properties such as plateau modulus ($G_N^0 )$ and zero-shear viscosity (\textit{$\eta $}$_{0})$. We relate physical properties of branched polymers to their structural properties.$^{ \dag }$Beaucage G. \textit{Physical Review E} \textbf{70},031401 (2004) $^{\ast }$Colby \textit{et al}.\textit{ Macromolecules }\textbf{25,} p.996 (1992)