Dynamic dilution equation for stars

Summary

Fit DTD Theory for stars. Theory of stress relaxation in star polymer melts with no adjustable parameters beyond those measurable in linear melts

• Function

  See Milner-McLeish (1997) and Larson et al. (2003) for details.

• Parameters

  • G0 \(\equiv G_N^0\): Plateau modulus

  • tau_e \(\equiv \tau_\mathrm e = \left(\dfrac{M_\mathrm e^\mathrm G}{M_0}\right)^2 \dfrac{\zeta b^2}{3\pi^2k_\mathrm B T}\): Entanglement equilibration time

  • Me \(\equiv M_\mathrm e^\mathrm G = \dfrac 4 5 \dfrac{\rho R T} {G_N^0}\): Entanglement molecular weight

  • alpha: Dilution exponent

  where:

  • \(\rho\): polymer density

  • \(\zeta\): monomeric friction coefficient

  • \(b\): monomer-based segment length

  • \(k_\mathrm B T\): thermal energy

  • \(M_0\): molar mass of an elementary segment