Vol.2, No 8, 1998 pp. 605 - 627
EQUATIONS FOR VOLUME RECOVERY IN AMORPHOUS POLYMERS ?
Aleksey D. Drozdov
Institute for Industrial Mathematics,
4 Hanachtom Street, Beersheba 84249 Israel
Abstract. Constitutive relations are
derived for the kinetics of volume recovery in amorphous polymers. The
model is based on the theory of temporary networks in the version of a
concept of adaptive links. A glassy polymer is treated as a network of
permanent chains and temporary chains, whose breakage and reformation are
caused by micro-Brownian motion. The relative rates of reformation for
temporary chains, as well as the equilibrium concentration of permanent
chains are determined by the current temperature. Simple kinetic equations
are proposed for the evolution of these parameters.
A polymer is modeled as a compressible
viscoelastic medium whose specific mechanical energy equals the sum of
the energies of individual links and the energy of their interaction. In
nonisothermal processes these energies are changed due to thermal expansion
(contraction) of the network. Volume recovery of polymeric glasses (slow
changes in the specific volume after quenching or rapid heating) is explained
by some misfit between the coefficients of thermal expansion for individual
links and for the network as a whole. A difference between the coefficients
of thermal expansion leads to internal stresses in a temporary network.
Relaxation of these stresses caused by reformation of temporary links is
revealed in tests as structural relaxation.
Constitutive relations for a temporary
network at finite strains are derived using the laws of thermodynamics.
Nonlinear ordinary differential equations are developed for the kinetics
of volume recovery. To verify these equations, experimental data are fitted
for polystyrene and poly(vinyl acetate). Fair agreement is demonstrated
between observations and the model's predictions.
JEDNAČINE ZAPREMINSKOG OPORAVKA (OBNAVLJANJA)
U AMORFNIM POLIMERIMA
Rad sadrži model vremenskih mreža, termičkih
deformacija mreža, termodinamičke potencijale i konstitutivne relacije.
Nove konstitutivne relacije su izvedene
za kinetiku zapreminskog oporavka (obnavljanja) nakon naglog grejanja i
hlađenja. Konstitutivne jednačine su bazirane na konceptu promenljivih
mreža u obliku modela sa adaptivnim vezama.