Polymer Thermal Relaxation Processes

What does the terminal relaxation time ($ au_t$) represent in the context of super Tg relaxation?

How does the elastic modulus (E) relate to the concentration of entanglement points in a transient network?

Which statement correctly describes the behavior of polymer strain ($e(t)$) at short times during super Tg relaxation?

What factor significantly influences the viscosity ($ au_t$) of a polymer?

What is the relationship between viscosity ($ au_t$) and chain length (N) in polymers?

In the context of super Tg relaxation, what does the creep compliance J(t) represent?

What happens to polymer chains when they are above the glass transition temperature (Tg)?

What is indicated by the equation $ au_t ext{ is approximately equal to } rac{ ext{E}}{ ext{η}}$ when discussing super Tg relaxation?

Super Tg Relaxation

Super Tg relaxation is a prolonged thermal relaxation process occurring above the glass transition temperature (Tg)
For polymers near the rubbery state, a small stress (σ) is applied, and the induced strain (e(t)) is observed.
For small stress, the strain is a linear function of the stress: e(t) = σJ(t)
J(t) is the creep compliance, and J = 1/E (where E is the elastic modulus)

Short Time Conformations

At short times, chain conformations remain unchanged.
This behavior resembles a polymeric glass, where conformations are frozen.
The mechanical response is similar to a polymeric glass.

Longer Time Conformations

At longer times, chain conformations do adjust.
The strain becomes more significant.
There's a time range (t < tt) where chains remain entangled like a rubber network, resulting in a plateau in the strain.

Elastic Modulus of the Transient Network

Plateau modulus (E) is independent of chain length for long chains.
E measures the number of entanglement points per unit volume in the transient network, particularly for flexible chains.
c (~1/a³) is the concentration and Ne is the average interval between entanglement points, typically around 100.

Viscosity and Terminal Time

Viscosity (η) is highly sensitive to chain length.
Both viscosity and terminal time (τt) increase proportionally to a power of N (chain length), where the exponent m (m~ ≈3.3 to 3.4).
The value of m represents an unsolved problem in polymer physics.

Molar Mass Dependence

A plot of log G' (storage modulus) versus log(ω) (angular frequency) shows a linear relationship for various molar masses of polystyrene.
The plot is measured at a temperature of 160°C.
The data come from a study on polystyrene samples with a narrow molar mass distribution.

Explore the concepts of Super Tg relaxation and the mechanical responses of polymers above the glass transition temperature (Tg). This quiz covers short and long-time chain conformations and the elastic modulus of transient polymer networks. Test your understanding of these essential polymer behaviors.