We recently showed that two systems
have the same nonlinear flow
dynamics if they have (1) the same number of entanglements, Z, (2) the same number of Kuhn segments between entanglements, N
e, and (3) a single monomeric friction reduction
between all species. Because differences in polymer chemistry result
in different values of (1)–(3), these results show that the
likelihood of two melts having the same nonlinear behavior is improbable.
This work determines the dependence of the nonlinear extensional flow
behavior on N
e for three polymer melts:
polystyrene, poly(methyl methacrylate), and poly(tert-butylstyrene). We show that polymer melts with the same Z have almost identical scaled linear viscoelasticity. Extensional
rheology at constant strain rate shows strain hardening depends strongly
on the value of N
e. More specifically,
our data suggest a power-law dependence of steady state stress on
the Weissenberg number which increases with increasing N
e.
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