Question 3 of 7: Selecting non-standard materials from their bonding

Question 3: Selecting non-standard materials from their bonding (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. Two property profiles that must both be met by non-metallic materials: (1) low density, electrically insulating and flexible; (2) low density, electrically insulating and extremely stiff. The justification is required in terms of bonding — that is, in terms of the primary bonds (ionic, covalent, metallic) and the secondary or molecular bonds (van der Waals, hydrogen) that hold the solid together.

Find. One named material for each application, with the choice argued from the bond type and bond architecture rather than from a datasheet.

Approach. All three requested properties are decided by bonding. Low density follows from light atoms and from open, directional packing; electrical insulation follows from localised electrons, that is, from the absence of the delocalised metallic bond; and stiffness follows from how much of the deformation has to be taken by stretching primary bonds rather than by rearranging weak ones. So the two applications are separated not by the type of primary bond — both answers are covalent — but by its architecture.

Part (1) — light, insulating and flexible: a linear thermoplastic polymer. The recommendation is a semi-crystalline linear thermoplastic such as polyethylene or polypropylene, or, where genuinely rubbery flexibility is wanted, a thermoplastic elastomer or a lightly cross-linked elastomer such as silicone rubber. Its density is of the order of 0.9 to 1.4 Mg/m³, roughly a third that of aluminium and an eighth that of steel, because the molecule is built almost entirely of the light elements carbon and hydrogen and because the chains pack loosely and inefficiently. It insulates because every valence electron is committed to a localised covalent bond in the backbone or in a C–H side bond; there is no partly filled band and no free electron gas, so the resistivity is of the order of 10¹⁴ Ω·m. And it is flexible because of the two-level bond structure that the left-hand figure shows. Along the chain the bonds are strong covalent bonds; between chains there are only weak secondary bonds — van der Waals attractions, or hydrogen bonds in a polyamide — whose energies are one to two orders of magnitude smaller. When the solid is loaded, the response is not stretching of the covalent backbone but uncoiling of the chains and sliding of one chain past another against those weak forces, together with rotation about the single bonds of the backbone. The modulus is therefore governed by the secondary bonds and lies in the range 0.01 to 3 GPa, and large recoverable strains are possible. That is exactly the behaviour the application asks for.

Part (2) — light, insulating and extremely stiff: an engineering ceramic. The recommendation is a covalent or mixed ionic–covalent engineering ceramic — silicon carbide or silicon nitride if stiffness per unit weight is the priority, alumina if cost and availability matter more. Density is 3.1 to 3.9 Mg/m³, well below steel, and again for a bonding reason: silicon, carbon, nitrogen, oxygen and aluminium are all light atoms, and the strongly directional covalent bonds force an open structure rather than the close packing a metal adopts. Electrical insulation follows from the same localisation of electrons in ionic and covalent bonds, with the additional point that the wide band gap of these compounds leaves no carriers available at room temperature. The stiffness comes from the architecture. As the right-hand figure shows, the primary bonds run continuously in three dimensions, so there is no weak interface anywhere in the structure and no mechanism of uncoiling or sliding available: any macroscopic strain must stretch and bend primary bonds directly. The result is a Young's modulus of 300 to 450 GPa for SiC and Si₃N₄, higher than steel at one half the density, and a specific modulus $E/\rho$ of about 120 GPa/(Mg/m³) against 26 for steel and 25 for aluminium.

If the second application also needs toughness or must be made in a large thin form, the honest alternative is a continuous carbon-fibre reinforced polymer, which reaches 100 to 200 GPa longitudinally at 1.6 Mg/m³. It is still bonding that carries the argument: the stiffness is supplied by the covalently bonded graphene sheets running along the fibre axis, and the polymer matrix contributes only the secondary-bonded medium that transfers load into them. Note, however, that carbon fibre is an electrical conductor along its axis, so it is disqualified by the insulation requirement unless glass or aramid fibre is substituted, at some cost in modulus.