Time-cure superposition during crosslinking

Abstract

Using a dynamic scaling theory for the viscoelasticity of cross-linking polymers near the gel point, we predict the superposition of viscoelastic functions at differing extents of reactions. For example, to superpose the stress relaxation modulus, a vertical shift is needed to account for the increase in the equilibrium modulus with cure, G" ~e8/3, and a horizontal shift for the divergence of the characteristic relaxation time, ~e~4, where < is the critical extent of reaction. Experiments on model epoxies show excellent superposition both below and above the gel point and give G" ~e2-8±0•2 and rz ~c~3'9±0•2. The critical regime where this superposition is valid is surprisingly wide, encompassing over half of the reaction.

Measuring dynamic cell–material interactions and remodeling during 3D human mesenchymal stem cell migration in hydrogels

“…When α → 0, probe particles are completely arrested in the gel network. All values of α between 0 and 1 are an elastic solid or viscoelastic liquid, and this transition is defined by the critical relaxation exponent, n. The value of n has been previously determined from measurements of the kinetics of degradation analyzed using time-cure superposition (30)(31)(32)(33). To determine the state of a material, α is compared with n; if α > n, the material is a viscoelastic fluid, and if α < n, the material is an elastic solid (30).…”

Relaxation Patterns of Nearly Critical Gels

“…22,24,41 A constant n value would allow time-cure superposition, which was first proposed by Adolf and Martin. 22 Hodgson and Amis 41 confirmed this principle on a slightly different system. Both studied gelation in epoxy systems, starting from monomer precursors.…”

Universal aspects of hydrogel gelation kinetics, percolation and viscoelasticity from PA-hydrogel rheology

“…0.4% (above the gel point). The spectra are shifted with factors a $ s l $ Ày and b $ G À1 $ Àz [23] along the abscissa and ordinate, respectively. The resulting master curve shows the lowfrequency plateau for G 0 and G 00 at low s l x, and the frequency-independent power-law scaling of G 0 and G 00 with…”

“…For example, Adam and Delsanti [22] found z ¼ 2.1 6 0.3, k ¼ 0.78 6 0.05, and D % 0.73 for radical copolymerization (polystyrene/divinylbenzene/benzene), and z ¼ 3:260:6; k ¼ 0:7860:05, and D % 0:80 for polycondensation (diisocyanate/triol). Adolf and Martin [23] [19], often furnishing 0:7 k 1:4 and 0:6 D 0:8. However, several studies with excess crosslinker at the gel point furnish D % 0:5.…”