Question 4 of 8: Thermoplastic Molecular Mass and Crystallinity

Question 4: Thermoplastic Molecular Mass and Crystallinity (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Eight molecular-mass ranges with mass fractions $f_i$ (table above, $\sum f_i=1.00$).

Find. (a) Average (weight-average) molecular mass. (b) Effect of crystallinity on density and tensile strength. (c) Thermoplastic vs. thermosetting processing.

Approach

Because the given $f_i$ are mass fractions of the polymer in each range, weighting the midpoint molecular mass of each range by its mass fraction and summing directly gives the weight-average molecular mass $\bar M_w$ (this is the definition of $\bar M_w$, distinct from the number-average $\bar M_n$, which instead weights by mole fraction).

1. (a) Midpoint molecular mass of each range. 2,500; 7,500; 12,500; 17,500; 22,500; 27,500; 32,500; 37,500 g/mol.
2. Weighted sum. $$\bar M_w=\sum_i f_i\,\bar M_i=(0.02)(2500)+(0.11)(7500)+(0.18)(12500)+(0.22)(17500)$$ $$+(0.25)(22500)+(0.13)(27500)+(0.06)(32500)+(0.03)(37500)=\boxed{19{,}250\ \text{g/mol}}.$$
3. (b) Crystallinity vs. density and tensile strength. Increasing crystallinity increases density, because the ordered, tightly-folded chain-packing of a crystalline region is denser than the loose, random-coil packing of an amorphous region (the same reason crystalline polyethylene is measurably denser than amorphous/branched polyethylene). Increasing crystallinity also generally increases tensile strength and stiffness, since the ordered regions allow much stronger secondary (van der Waals/dipole) bonding between adjacent, well-aligned chain segments, resisting chain slippage under load — at the cost of reduced ductility/toughness, since the same ordered regions are also more resistant to the localized chain reorientation that gives amorphous polymers their flexibility.
4. (c) Thermoplastic vs. thermosetting processing. Thermoplastics are shaped by heating above their glass transition/melting range until they soften and flow (extrusion, injection molding, blow molding), then cooling to solidify in the new shape; because the long-chain molecules are held together only by physical (secondary) bonds, this heat–shape–cool cycle is fully reversible — the same part can be reground and reprocessed. Thermosets are shaped from a low-molecular-weight liquid or semi-solid precursor (compression molding, resin transfer molding, casting) while a chemical curing (cross-linking) reaction occurs during or after shaping, permanently locking the chains into a rigid, covalently cross-linked 3-D network; once cured, a thermoset cannot be re-melted or reshaped — heating it further only degrades/chars it.