13.2: Crystalline and Amorphous Polymers
- Page ID
- 7865
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In ceramics or metals, a crystalline solid comprises repeating unit cells that contain each of the component atoms in the material. Each unit cell is composed of one or more molecular units. In a polymer this is not possible; the molecules are chains containing potentially millions of formula units. There is, however a repeating unit in a polymer - the monomer from which it was made. This must be the basis of both long and short-range order in a polymeric material.
For example, a short section of linear poly(ethylene) looks like this:
However, the conformation of the bonds around each carbon atom can be represented schematically as follows:
These diagrams are called Newman projections. The circle is a single C-H bond; and this diagram represents a projection along it. These two structures thus represent one half of the backbone continuing on either side of a C-C bond (trans), or both halves on the same side (gauche). Note that there are two possible gauche states, labelled gauche (-) and gauche (+).
Whilst the trans conformation has a lower energy (since it's easier to position the hydrogen atoms on the carbon backbone further apart), an all-trans conformation would be a considerably more ordered structure than a random one - that is, it has a much lower entropy.
Amorphous polymers are generally found in a random coil conformation and have a disordered chain structure. This is the most common structure of many polymers. Crystalline polymers are predominantly in the all-trans conformation, and the chains are arranged in lamellae, as below:
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The polymer crystal is made up from one-dimensional chain-folded sequences, shown on the above left, where the repeat distance is given by the chain spacing. To the above right is shown a schematic arrangement of folded chains into a two-dimensional lamella.
An amorphous polymer has the maximum entropy conformation (given by the Boltzmann distribution), and the chains are arrayed randomly throughout the material, making atomic positions quasi-random as in any other glassy material.
As a result of the difference between the amorphous and crystalline arrangements of polymer chains, the X-ray diffraction patterns of the two phases are very different. The amorphous phase contains no long-range order, meaning that there are no regular crystalline planes to diffract X-rays. Thus the incident X-rays are scattered randomly and there are no sharp peaks in the diffraction pattern. In the crystalline phase, the repeating lamellar chains provide a regular structure, thus the diffraction pattern will contain sharp, prominent signature peaks, the position of which depends on the exact spacing between chains.
As the degree of crystallinity of a polymer affects its properties, accurately determining it is important. X-ray diffraction can be used to determine the degree of crystallinity of a sample. Thermal analysis techniques such as differential scanning calorimetry (DSC) can also be used. The two determinations may not necessarily be in agreement, and the reasons for this are complex.