Vol.2, No 8, 1998 pp. 605 - 627
UDC: 532.135:539.3
CONSTITUTIVE EQUATIONS FOR VOLUME RECOVERY IN AMORPHOUS POLYMERS ?
Aleksey D. Drozdov
Institute for Industrial Mathematics, 4 Hanachtom Street, Beersheba 84249 Israel
e-mail: aleksey@indigo.bgu.ac.il
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.
KONSTITUTIVNE 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.