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Questions and Answers
What happens to the shear modulus of atactic polystyrene as the testing temperature increases?
What happens to the shear modulus of atactic polystyrene as the testing temperature increases?
- It remains constant.
- It fluctuates without trend.
- It increases steadily.
- It decreases sharply at the glass transition. (correct)
At what temperature is the β-peak located in the tan δ curve for atactic polystyrene?
At what temperature is the β-peak located in the tan δ curve for atactic polystyrene?
- Approximately 150°C
- Approximately 100°C
- Approximately 50°C (correct)
- Approximately 0°C
What is believed to cause the γ-peak in the tan δ curve for polymers?
What is believed to cause the γ-peak in the tan δ curve for polymers?
- Head-to-head repeat sequences. (correct)
- Disruption in the polymer backbone.
- Formation of side-chain entanglements.
- Growth of crystallinity in the material.
What does the equation $E_1 = \frac{E \tau_0^2 \omega^2}{\tau_0 \omega + 1}$ represent?
What does the equation $E_1 = \frac{E \tau_0^2 \omega^2}{\tau_0 \omega + 1}$ represent?
What is the significance of the peak (α) in the tan δ curve according to the content?
What is the significance of the peak (α) in the tan δ curve according to the content?
Which of the following statements is true regarding viscoelastic materials?
Which of the following statements is true regarding viscoelastic materials?
In the provided equations, what is represented by $\tau_0$?
In the provided equations, what is represented by $\tau_0$?
How does the frequency $\omega$ affect the β-peak in tan δ?
How does the frequency $\omega$ affect the β-peak in tan δ?
What term describes the relative angular displacement of stress and strain in a viscoelastic material?
What term describes the relative angular displacement of stress and strain in a viscoelastic material?
What is the form of stress when expressed in relation to strain and the phase angle?
What is the form of stress when expressed in relation to strain and the phase angle?
Which component of stress in a viscoelastic material is in phase with the strain?
Which component of stress in a viscoelastic material is in phase with the strain?
How is dynamic modulus E1 defined in terms of stress and strain?
How is dynamic modulus E1 defined in terms of stress and strain?
Which of the following equations represents the relationship of complex modulus in a viscoelastic material?
Which of the following equations represents the relationship of complex modulus in a viscoelastic material?
What is the relationship between E2 and E1 as described by tangent of the phase angle?
What is the relationship between E2 and E1 as described by tangent of the phase angle?
In what way does strain behave in a viscoelastic material under sinusoidal stress?
In what way does strain behave in a viscoelastic material under sinusoidal stress?
What model can be used to demonstrate the frequency dependence of viscoelastic properties?
What model can be used to demonstrate the frequency dependence of viscoelastic properties?
Flashcards
Complex Viscoelastic Response
Complex Viscoelastic Response
The relationship between stress and strain for a viscoelastic material when the stress is varied sinusoidally with frequency ω.
Viscoelastic Modulus (E)
Viscoelastic Modulus (E)
A viscoelastic material's tendency to deform and recover under stress, measured at a specific frequency.
Storage Modulus (E1)
Storage Modulus (E1)
The real part of the viscoelastic modulus, representing the elastic component of deformation.
Loss Modulus (E2)
Loss Modulus (E2)
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Loss Tangent (tan δ)
Loss Tangent (tan δ)
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Glass Transition (Tg)
Glass Transition (Tg)
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Secondary Transitions
Secondary Transitions
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β-Peak
β-Peak
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Dynamic mechanical testing
Dynamic mechanical testing
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Phase Angle (δ)
Phase Angle (δ)
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Complex Modulus (E*)
Complex Modulus (E*)
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Frequency Dependence of Viscoelastic Behavior
Frequency Dependence of Viscoelastic Behavior
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Maxwell Model
Maxwell Model
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Viscoelastic Behavior
Viscoelastic Behavior
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Study Notes
Dynamic Mechanical Behaviors
- Dynamic mechanical testing is used to analyze materials when a sinusoidal load is applied at a specific frequency.
- Applied stress (σ) varies as a function of time (σ = σ₀sinωt), where σ₀ is the stress amplitude and ω is the angular frequency.
- Elastic materials exhibit strain (e) in a similar sinusoidal manner as stress (e = e₀sinωt).
- Viscoelastic materials exhibit a phase lag (δ) between stress and strain, meaning strain doesn't occur simultaneously with stress. Strain lags behind the stress during creep.
- The phase angle (δ), or phase lag, represents the relative angular displacement between stress and strain.
- Stress can be represented as two components: one in phase with strain (σ₀cosδ) and another 90° out of phase with strain (σ₀sinδ).
- Two dynamic moduli (E₁, E₂) can be defined: E₁ is in phase with strain, and E₂ is 90° out of phase with strain.
- The stress and strain variation, given by
e = e₀sin(ωt + δ)andσ = σ₀sin(ωt + δ), where δ reflects the phase shift.
Frequency Dependence of Viscoelastic Behavior
- The Maxwell model helps understand the frequency dependence of viscoelastic properties.
- The relationship between stress (
σ) and strain (e) with time (t) can be represented by complex equations if stress is sinusoidally varied asσ = σ₀ exp i(ωt + δ)ande = e₀ exp iωtwhere ω is the angular frequency. - Stress (
σ) and strain (e) values vary with time (t) .
Transitions and Polymer Structure
- Shear modulus (G₁) and tan δ (the tangent of the phase angle) vary with temperature for amorphous polymers (e.g., atactic polystyrene).
- A significant drop in shear modulus occurs at the glass transition temperature (Tg) in amorphous polymers.
- Minor peaks in tan δ at lower temperatures correspond to secondary transitions.
- The relaxation time (τ) significantly affects how stress and strain behave at different frequencies
- Crystallinity influences α' and α relaxations decreasing in intensity in a reduction in crystallinity and implying that they are associated with motion within the crystalline regions.
- Y-relaxation increases with a reduction in crystallinity and is related to amorphous material.
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