32.7: Questions
- Page ID
- 33019
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Explain why cooling a liquid very fast (quenching) can lead to the formation of a glass. Your answer should use what you have learnt about the kinetics of glass formation.
- Answer
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At lower temperatures the mobility of the polymer molecules is reduced. By quenching a liquid the mobility of the molecules is reduced in less time than it takes for the molecules to order themselves in a crystalline manner. Because of this the polymer becomes an amorphous solid, or glass.
What is meant by the 'free volume' of a polymer?
- Answer
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Unlike the ordered molecular arrangement of a crystalline material, amorphous polymers are made up of disordered polymer chains. At the end of each chain there is a small amount of unfilled space, which is called free volume. The sum of all the small free volumes makes a total free volume for the material.
What is the significance of the theoretical 'Kauzmann temperature'?
- Answer
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The Kauzmann temperature is the temperature below which the entropy of a liquid would be less than that of the corresponding solid. This is paradoxical and cannot be the case. The glass transition must occur above the Kauzmann temperature.
Why is the measured value of Tg dependent on the method of measurement?
- Answer
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The glass transition temperature is dependent on the strain rate during measurement. Measurements which take place over a large timescale will result in a lower glass transition temperature, and hence rubbery behaviour at lower temperatures. Measurements which take place on a short timescale will result in a higher value of Tg and hence glassy behaviour at higher temperatures. This can be seen by watching the videos of silly putty flowing like a liquid over a long timescale and smashing like a glass over a short timescale. Both experiments were performed at room temperature.
Using what you understand about the way polymer chains behave above and below Tg, why do you think glasses tend to be brittle whereas rubbers are not?
- Answer
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The polymer chains in a glass are immobile. They cannot change their conformation so the glass cannot deform plastically. When the glass suffers an impact mechanical energy is transferred into the glass. This energy cannot be dissipated as the molecules are immobile and so the glass will crack, forming new interfaces to expend the input mechanical energy.
In contrast the polymer molecules in a rubber are able to change their conformation and slide past each other. When mechanical energy is transferred into the rubber the energy is expended by the conformation changes taking place in the polymer chains. Macroscopically this leads to plastic deformation and rubbery, rather than brittle behaviour.
What is meant by the conformation of a polymer? Using a Newman projection show what is meant by the 'trans' and 'gauche' states.
- Answer
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The conformation of a polymer molecule is the arrangement of the bond orientations, both within the backbone, and any side-groups and branches. There are three specific orientations, called trans, +gauche and -gauche, as represented in the Newman projections below. The conformation can be changed by rotation about single bonds.
Explain how the dielectric constant of a polymer is affected by the transition to the glassy state.
Explain why the glass transition temperature is strain-rate dependent.
Below and above the Tg of a rubber ball it will rebound after impact. At Tg the ball will not rebound very much at all. Explain how the ball bounces in these three cases from an energetic point of view.