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Questions and Answers
What characteristic change occurs in polymers when the temperature is decreased or the frequency is increased?
What characteristic change occurs in polymers when the temperature is decreased or the frequency is increased?
What does the shift factor aT relate to in time-temperature superposition?
What does the shift factor aT relate to in time-temperature superposition?
According to the WLF equation, what happens to the constants C1 and C2 when the reference temperature Ts is taken as Tg?
According to the WLF equation, what happens to the constants C1 and C2 when the reference temperature Ts is taken as Tg?
How is the fractional free volume fV in a polymer defined?
How is the fractional free volume fV in a polymer defined?
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What is the relationship defined by the Maxwell model between viscosity and spring modulus?
What is the relationship defined by the Maxwell model between viscosity and spring modulus?
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Which of the following statements is true regarding the testing conditions of polymers?
Which of the following statements is true regarding the testing conditions of polymers?
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What empirical observation supports time-temperature superposition in polymers?
What empirical observation supports time-temperature superposition in polymers?
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What happens to a polymer's properties as it transitions from a rubbery state to a glassy state?
What happens to a polymer's properties as it transitions from a rubbery state to a glassy state?
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What does the shift factor $a_T$ represent in the context of time–temperature superposition?
What does the shift factor $a_T$ represent in the context of time–temperature superposition?
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Which equation relates viscosity to free volume according to Doolittle?
Which equation relates viscosity to free volume according to Doolittle?
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In the equation $\ln \eta(T) = \ln A + B(\frac{1}{V_f} - 1)$, what does $B$ represent?
In the equation $\ln \eta(T) = \ln A + B(\frac{1}{V_f} - 1)$, what does $B$ represent?
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What does $T_g$ signify in the context of the equations presented?
What does $T_g$ signify in the context of the equations presented?
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What is the approximate value of $\alpha_f$ mentioned for most amorphous polymers?
What is the approximate value of $\alpha_f$ mentioned for most amorphous polymers?
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How is the shift factor $a_T$ defined when using $T_g$ as the reference temperature?
How is the shift factor $a_T$ defined when using $T_g$ as the reference temperature?
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Which statement is true regarding the rearranged equation for viscosity?
Which statement is true regarding the rearranged equation for viscosity?
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What is the order of magnitude of $f_g$ for most amorphous polymers?
What is the order of magnitude of $f_g$ for most amorphous polymers?
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Study Notes
Time-Temperature Superposition
- Time-temperature superposition suggests a relationship between time and temperature dependence of viscoelastic polymer properties.
- A polymer exhibiting rubbery behavior at specific conditions can show glassy behavior with reduced temperature or increased testing rate/frequency.
- This behavior is shown in the variation of shear compliance (J) with frequency at various temperatures near the glass transition temperature (Tg).
- At high temperatures and low frequencies, the material is more rubbery, showing high compliance.
- As temperature decreases and frequency increases, the material becomes glassy with lower compliance.
- Curves for different temperatures can be aligned by horizontal shifts parallel to the log frequency axis. A reference temperature (Ts) is used to align curves, with shift (log ws – log w) corresponding to the shift factor.
WLF Equation
- Williams-Landel-Ferry equation (WLF) describes time-temperature superposition.
- The equation relates the shift factor (log ar) to temperature difference (T-Ts) from a reference temperature (Ts).
- Constants C₁ and C2 in the equation are often assigned specific values (e.g., C1g = 17.4 and C2g = 51.6 K when reference temperature is Tg) and are used for fitting curves that are largely universal.
- WLF equation is useful for fitting experimental data, though its theoretical justification comes from considerations of free volume.
Free Volume and Viscosity
- Fractional free volume (fv) of a polymer can be represented as fv=fg + (T-Tg) * af. Where fg and af are constants.
- Viscosity (η) is related to free volume (Vf).
- Doolittle's equation connects viscosity to free volume changes.
- The equation ln η = ln A + B (Vf - Vf / Vf) relates viscosity (η) to total volume (V), constant A and B, and free volume (Vf)
- Log (η(T) / η(Tg)) can be represented as (B / 2.303* fg) * (T-Tg) / (fg/af + (T-Tg)), where constant fg approximately 0.025 and af is approximately 4.8 x 10⁻⁴ K⁻¹.
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Description
Test your understanding of time-temperature superposition and the WLF equation in polymer science. This quiz covers the relationship between temperature, frequency, and the viscoelastic properties of polymers, emphasizing their behavior near the glass transition temperature (Tg). Explore how these concepts apply to shear compliance and material behavior.
