Free volume theory and nonlinear thermoviscoelasticity

Abstract

The rheological behavior of polymers in the neighborhood of the glass transition is investigated in the framework of the free volume theory of nonlinear viscoelastic behavior. Free volume theory as normally applied above the glass transition is modified to account for the effect of the residual volume of vacancies below the glass transition; this modification is accomplished by modeling the changes in the state of the polymer as the sum of viscoelastic changes and a random disturbance deriving from the thermal collisions between molecule segments. The changes in mechanical properties in passing across the glass transition follow from the freezing‐in of relaxation mechanisms and of free volume; the model, which also incorporates a time‐dependent coefficient of thermal expansion under isobaric conditions, does not require additional parameters other than those characterizing the rubbery state. The pressure dependence of the glass transition is found to be in qualitiative agreement with measurements on PVAc, while the ratio of the glassy and rubbery heat capacities is found to coincide with the ratio of the equilibrium bulk compliances in the glassy and rubbery domains.

An experimentally-based viscoelastic constitutive model for polyurea, including pressure and temperature effects

“…For the cases considered in the present paper, this is a significant effect. The well-established explanation for this phenomenon is found in works of Ferry [25], Knauss and Emri [26,27], and Losi and Knauss [28]. It is based on the free-volume content of a polymer: the less available free volume the harder it becomes for the chains to move.…”

Finite viscoelasticity of filled rubbers: the effects of pre-loading and thermal recovery

“…This conclusion contradicts the strain-time superposition principle [24,30], which is conventionally developed within the free-volume theory [7]. According to that concept, mechanical loading of a specimen results in the growth of the free volume, which, in turn, accelerates the reformation process for mobile units (cooperatively rearranging regions).…”

A constitutive model for the dynamic and high‐pressure behaviour of a propellant‐like material: Part II: Model development and applications

“…Additionally, it was shown that high pressures commonly found during dynamic penetration produce compaction and induced sti!ening. This can be interpreted in terms, for example, of time}pressure equivalence as in most amorphous polymers (see, for instance Reference [2]), or of free-volume collapse (see, in particular, Reference [3]). This part of the material's behaviour is thus linked to viscoelasticity and elastomeric behaviour.…”