Chemistry

Polymers and solids

Crystals and glasses, metal–ionic–covalent solids, polymer chains and the glass transition.

Basics

Crystals and unit cells

In a crystal, atoms repeat on a lattice with translational symmetry. The unit cell is the smallest box; simple cubic, body-centred cubic (BCC), face-centred cubic (FCC), and hexagonal close packing (HCP) are common in metals. FCC and HCP are close-packed; BCC is a little more open. Bragg’s law from X-ray diffraction measures spacing. Defects (vacancies, dislocations) change strength and diffusion.

Types of solid

Ionic solids are lattices of opposite ions (NaCl): high melting point, brittle. Metallic solids share a delocalised electron sea: conductive and ductile. Covalent networks (diamond, SiO₂) are directional and hard. Molecular solids (ice, iodine) are held only by intermolecular forces, so they are softer. Allotropes of one element (graphite vs diamond) can behave as different materials.

Polymers

A polymer is a long chain of repeating monomers. Polyethylene has a carbon–carbon backbone, nylon has amides, DNA has nucleotides. Average molar mass and its spread set melting point and viscosity. Cross-links make rubbery elasticity; branching lowers density. Thermoplastics can be melted again; thermosets lock into a network and are hard to reverse.

Glass transition and crystallinity

Warm an amorphous polymer and near the glass-transition temperature T_g it softens from a glass into a rubber. Crystalline polymers show a sharper melting point T_m. Folded chains can form crystallites mixed with amorphous regions, setting both strength and haze. Plasticizers lower T_g; a fast quench is more likely to leave a glass.

Formulas

Bragg’s law

n λ = 2 d sinθ

Constructive diffraction from spacing d.

Symbols

  • n integer order
  • λ wavelength
  • d interplanar spacing
  • θ Bragg angle

Degree of polymerisation

DP = M_n / M_monomer

Monomers per chain (number-average).

Symbols

  • M_n number-average molar mass
  • M_monomer monomer molar mass

Packing fraction (hard spheres)

η = V_atoms / V_cell

FCC/HCP ≈ 0.74, BCC ≈ 0.68, simple cubic ≈ 0.52.

Symbols

  • η volume packing fraction

Key table

PE vs PVC PE is C–H only. PVC carries Cl — stiffer, more flame-resistant
Cross-linked rubber sulfur vulcanisation ties chains so strain recovers
Radius ratio cation/anion radius ratio hints at coordination 4, 6, or 8

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