31 research outputs found
Mesoscopic theory of the viscoelasticity of polymers
We have advanced our previous static theory of polymer entanglement involving
an extended Cahn-Hilliard functional, to include time-dependent dynamics. We go
beyond the Gaussian approximation, to the one-loop level, to compute the
frequency dependent storage and loss moduli of the system. The three parameters
in our theory are obtained by fitting to available experimental data on
polystyrene melts of various chain lengths. This provides a physical
representation of the parameters in terms of the chain length of the system. We
discuss the importance of the various terms in our energy functional with
respect to their contribution to the viscoelastic response of the polymeric
system.Comment: Submitted to Phys. Rev.
Onset of entanglement
We have developed a theory of polymer entanglement using an extended
Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive
term, operating over mesoscales, which is interpreted as giving rise to
entanglement, and the other a local repulsive term indicative of excluded
volume interactions. We show how such a functional can be derived using notions
from gauge theory. We go beyond the Gaussian approximation, to the one-loop
level, to show that the system exhibits a crossover to a state of entanglement
as the average chain length between points of entanglement decreases. This
crossover is marked by critical slowing down, as the effective diffusion
constant goes to zero. We have also computed the tensile modulus of the system,
and we find a corresponding crossover to a regime of high modulus.Comment: 18 pages, with 4 figure