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Questions and Answers
What does the terminal relaxation time ($ au_t$) represent in the context of super Tg relaxation?
What does the terminal relaxation time ($ au_t$) represent in the context of super Tg relaxation?
- The time it takes for polymer conformations to adjust after stress application (correct)
- The shortest relaxation time observed in mechanical measurements
- The period during which the strain remains linear with respect to stress
- The maximum time the polymer remains in the rubbery state
How does the elastic modulus (E) relate to the concentration of entanglement points in a transient network?
How does the elastic modulus (E) relate to the concentration of entanglement points in a transient network?
- E increases with increasing chain length
- E measures the density of entanglement points per unit volume (correct)
- E is independent of the configuration of polymer chains
- E is directly proportional to the amount of stress applied
Which statement correctly describes the behavior of polymer strain ($e(t)$) at short times during super Tg relaxation?
Which statement correctly describes the behavior of polymer strain ($e(t)$) at short times during super Tg relaxation?
- The response can be described by viscous flow equations
- Strain is highly influenced by temperature changes
- Conformations of the chains remain unchanged (correct)
- Strain becomes nonlinear with increasing stress
What factor significantly influences the viscosity ($ au_t$) of a polymer?
What factor significantly influences the viscosity ($ au_t$) of a polymer?
What is the relationship between viscosity ($ au_t$) and chain length (N) in polymers?
What is the relationship between viscosity ($ au_t$) and chain length (N) in polymers?
In the context of super Tg relaxation, what does the creep compliance J(t) represent?
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 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?
What is indicated by the equation $ au_t ext{ is approximately equal to } rac{ ext{E}}{ ext{η}}$ when discussing super Tg relaxation?
Flashcards
Super Tg Relaxation
Super Tg Relaxation
A prolonged relaxation process that occurs in polymers above the glass transition temperature (Tg) where polymer chains can rearrange despite being in a solid-like state.
Terminal Relaxation Time (Ï„t)
Terminal Relaxation Time (Ï„t)
The time it takes for a polymer to reach its equilibrium state after a stress is applied. It represents the longest relaxation time observed in mechanical measurements.
Viscosity-Terminal Time Relationship
Viscosity-Terminal Time Relationship
The relationship between viscosity and terminal relaxation time in polymers. Viscosity is proportional to the product of the elastic modulus and the terminal relaxation time.
Plateau Modulus (E)
Plateau Modulus (E)
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Entanglement Points (Ne)
Entanglement Points (Ne)
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Power Law Dependence of Viscosity and Terminal Time
Power Law Dependence of Viscosity and Terminal Time
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Exponent (mη)
Exponent (mη)
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Study Notes
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.
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