Question 2 of 7: Polymer Molecular Weight, Crystallinity, and Thermoplastic vs. Thermoset Processing

Question 2: Polymer Molecular Weight, Crystallinity, and Thermoplastic vs. Thermoset Processing (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. Mass-fraction table for 8 molecular-mass ranges (midpoint $M_i$, weight fraction $f_i$):

($\sum f_i=1.00$, confirmed before computing.)

Find. (a) The average (weight-average) molecular mass $\overline{M}_w$. (b) Effect of crystallinity on density and tensile strength. (c) Processing differences, thermoplastic vs. thermoset.

Approach

Because the table gives the mass fraction of chains in each molecular-mass range (not the number fraction), the weighted sum $\sum f_iM_i$ directly yields the weight-average molecular mass $\overline{M}_w$. Parts (b) and (c) are conceptual and answered from structure–property reasoning.

1. (a) Weight-average molecular mass. $$\overline{M}_w=\sum_i f_iM_i=(0.02)(2500)+(0.11)(7500)+(0.18)(12500)+(0.22)(17500)$$ $$+(0.25)(22500)+(0.13)(27500)+(0.06)(32500)+(0.03)(37500)$$ $$\boxed{\overline{M}_w\approx19{,}250\ \text{g/mol}}$$
2. (b) Crystallinity vs. density and tensile strength. Crystalline regions pack polymer chains far more efficiently (tightly aligned, close-neighbour spacing set by van der Waals or secondary bonding) than the loosely tangled, open structure of amorphous regions, so increasing the volume fraction of crystallinity increases density in direct proportion — the standard two-phase density rule $1/\rho=X_c/\rho_c+(1-X_c)/\rho_a$ follows from this packing argument. Crystalline regions also act as physical cross-links and load-bearing domains that resist chain slippage under stress, so tensile strength (and stiffness/yield strength) generally increase with crystallinity as well, though ductility and impact toughness typically fall because the more rigid, tightly packed crystalline lamellae are more brittle and provide less capacity for the large-scale chain uncoiling that gives amorphous polymers their toughness.
3. (c) Thermoplastic vs. thermoset processing. Thermoplastics consist of linear or branched chains held together only by secondary (van der Waals/entanglement) bonds, so heating above $T_g$ (amorphous) or $T_m$ (semicrystalline) breaks down these secondary interactions and lets the material flow as a viscous melt; it can therefore be shaped by melt-processing methods — injection molding, extrusion, thermoforming, blow molding — and, critically, can be reheated and reshaped repeatedly (recyclable) because no permanent chemical bonds were broken or formed. Thermosetting plastics, by contrast, are shaped while still uncured (as a low-molecular-weight resin or partially polymerized prepolymer, often with a mold under heat and pressure — compression or transfer molding), and the shaping step itself triggers an irreversible chemical curing (cross-linking) reaction that locks the chains into a rigid, covalently bonded 3-D network. Once cured, a thermoset cannot be melted and reshaped — further heating only degrades (chars/decomposes) the network rather than softening it, so thermosets must be shaped once, during the single curing step, not repeatedly like thermoplastics.