Rolie-Double-Poly LVE

Summary

Rolie-Double-Poly equation for the linear predictions of polydispere entangled linear polymers

• Function

  \[\begin{split}\begin{eqnarray} G'(\omega) & = & \sum_{i=1}^{n_{modes}}\sum_{j=1}^{n_{modes}} G \phi_i \phi_j \frac{(\omega\tau)^2}{1+(\omega\tau)^2} \\ G''(\omega) & = & \sum_{i=1}^{n_{modes}}\sum_{j=1}^{n_{modes}} G \phi_i \phi_j \frac{\omega\tau}{1+(\omega\tau)^2} \end{eqnarray}\end{split}\]

  where, \(\tau = (\tau_{\text D,i}^{-1} + \tau_{\text D, j}^{-1})^{-1}\), and, if the “modulus correction” button is clicked, \(G=G_N^0 \times g(Z_\text{eff})\), with \(g\) the Likthman-McLeish CLF correction function, otherwise \(G=G_N^0\)

• Parameters

  • nmodes : number of molecular mass components.

  • G_N^0 : Plateau modulus

  • phi0i : Volume fraction of component \(i\)

  • tauD0i : Reptation time of component \(i\)