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
Constructive diffraction from spacing d.
Symbols
-
ninteger order -
λwavelength -
dinterplanar spacing -
θBragg angle
Degree of polymerisation
Monomers per chain (number-average).
Symbols
-
M_nnumber-average molar mass -
M_monomermonomer molar mass
Packing fraction (hard spheres)
FCC/HCP ≈ 0.74, BCC ≈ 0.68, simple cubic ≈ 0.52.
Symbols
-
ηvolume 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 |
In this field
Atoms and the periodic table
Atomic structure, nucleus and electrons, periods and groups.
Chemical bonding
Ionic, covalent, and metallic bonds, plus molecular shape.
The mole and stoichiometry
Moles, molar mass, empirical formulas, and yield.
Gases and acids–bases
Ideal gas, pH, and buffers.
Thermo, equilibrium, kinetics
Enthalpy, Gibbs energy, K, and rate laws.
Electrochemistry and organic basics
Oxidation numbers, cells, Nernst, functional groups.
Nuclear chemistry
Radioactivity, half-life, binding energy.
Solutions and kinetics
Concentration, colligative properties, rate laws.
Analytical chemistry
Titration, spectroscopy, and chromatography — measuring what is present and how much.
Coordination compounds
Ligands, coordination number, crystal field, colour, and an 18-electron sketch.
Electrochemical cells
Galvanic versus electrolytic, Nernst, Faraday, and a corrosion sketch.
Phase equilibria and diagrams
Gibbs phase rule, unary diagrams, eutectics, and the lever rule.