You may be familiar with the WLF equation and Time-Temperature Superposition (TTS). But did you know Williams, Landel & Ferry justified their famous equation with the theory of Free Volume? The idea was that open spaces between polymer chains drive the material’s viscoelasticity. Modulus is a function of time and given sufficient time under load, Free Volume opens up, softening the material. Increasing temperature accelerates molecular motion and therefore accelerates the process, justifying horizontal shifting.
It stands to reason that other state variables that affect free volume should also reduce time. Indeed, environmental and mechanical deformation effects on Free Volume have been developed in the technical literature for decades:
-
Temperature: Williams, Landel & Ferry (1955)
-
Pressure: Fillers & Tschoegl (1977)
-
Solvents: Knauss & Kenner (1980)
-
Large Strain: Knauss & Emri (1981)
-
Distortion: Popelar & Liechti (1997)
-
Damage: Schapery (1997)
Free Volume is a powerful nonlinear viscoelastic concept, capable of handling time and environmental effects. Even so, it is not perfect, with problems capturing unloading and also large strain elastomer stiffening.
I can accept that Free Volume is a necessary condition for nonlinear viscoelasticity, but is it sufficient? Just because Free Volume is available doesn’t mean a polymer chain or side branch is available to utilize that space. Randomness is a better state variable to accelerate time. Psylotech’s VISCA is an entropy based reduced time model that solves Free Volume’s limitations while keeping its strengths.
