The density and associated percent crystallinity for two...

The density and associated percent crystallinity for two poly(ethylene terephthalate) materials are as follows: $$\begin{array}{cc} \hline \rho\left(g / c m^{3}\right) & \text { Crystallinity (\%) } \\ \hline 1.408 & 74.3 \\ 1.343 & 31.2 \\ \hline \end{array}$$ (a) Compute the densities of totally crystalline and totally amorphous poly(ethylene terephthalate). (b) Determine the percent crystallinity of a specimen having a density of $1.382 \mathrm{g} / \mathrm{cm}^{3}$

The density and associated percent crystallinity for two poly(ethylene terephthalate) materials are as follows: $$\begin{array}{cc}
\hline \rho\left(g / c m^{3}\right) & \text { Crystallinity (\%) } \\
\hline 1.408 & 74.3 \\
1.343 & 31.2 \\
\hline
\end{array}$$
(a) Compute the densities of totally crystalline and totally amorphous poly(ethylene terephthalate).
(b) Determine the percent crystallinity of a specimen having a density of $1.382 \mathrm{g} / \mathrm{cm}^{3}$

Key Concepts

Polymer Density

Polymer density is a fundamental physical property representing the mass per unit volume of the polymer. It provides insight into the molecular packing and arrangement within the material, reflecting how closely the polymer chains are arranged. Differences in density often indicate variations in the structural organization, such as between crystalline and amorphous regions.

Percent Crystallinity

Percent crystallinity measures the fraction of a polymer that is in a well-ordered, crystalline state compared to an amorphous, disordered state. This parameter is crucial because it influences many material properties, including mechanical strength, thermal behavior, and optical clarity. Higher percent crystallinity typically results in increased dimensional stability and stiffness.

Two-Phase Mixture Model

The two-phase mixture model treats semi-crystalline polymers as a composite of two distinct phases: the crystalline phase and the amorphous phase. It assumes that the overall density (or other properties) of the polymer can be represented as a weighted sum of the densities of each individual phase. This model is used to mathematically relate measured bulk properties to the volume fractions of the respective phases.

Linear Interpolation in Property Determination

Linear interpolation is a mathematical method used to estimate an unknown value that falls within the range of two known values. In the context of polymer crystallinity, it is applied to relate the measured density of a partially crystalline polymer to the known densities of 100% crystalline and 100% amorphous states, thereby calculating the percent crystallinity of the sample. This method relies on the assumption of a linear relationship between the property and the phase composition.

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