Macromolecular chemistry: monomers, polymerization mechanisms (step-growth, chain-growth), polymer-chain statistics, cross-linking, and the glass transition. Backbone of materials engineering and structural biopolymers.
polymer-chemistry
Monomer
A small molecule that can combine chemically with other monomers to form a polymer. Classified by polymerization mechanism compatibility:…
Polymerization
Reaction process by which monomers link to form polymer chains. Two canonical mechanisms: chain-growth (radical, cationic, anionic,…
Polymer chain
Long molecule made of repeating monomer units. Characterised by degree of polymerization, molar-mass distribution, configuration…
Cross-linking
Formation of covalent or ionic bridges between polymer chains, producing a three-dimensional network. Governs elastomer (vulcanised…
Glass transition (T_g)
Reversible kinetic transition in amorphous polymers between a hard, glassy state and a soft, rubbery state as temperature crosses T_g. Not…
Ziegler–Natta polymerization
Heterogeneous Ti(III)/Al-alkyl catalyst systems (or homogeneous metallocenes) polymerise α-olefins with high stereoregularity — producing…
Flory–Huggins theory of polymer solutions
Lattice-model free energy of mixing for a polymer of degree-of-polymerisation N in a solvent: ΔG_mix/k_BT = (φ₁/N) ln φ₁ + φ₂ ln φ₂ + χ φ₁…
Polymer MW (SEC/GPC, MALLS, viscometry)
Number-average Mn (colligative, end-group); weight-average Mw (scattering). Ð = Mw/Mn dispersity. SEC-MALLS gives absolute MW vs retention.…
Controlled radical polymerization (ATRP, RAFT)
Reversible-deactivation radical methods give narrow Đ + block copolymers. ATRP (Matyjaszewski) uses Cu-halide equilibrium; RAFT (Rizzardo)…
Block copolymer self-assembly
A-B diblocks microphase-separate into lamellae, gyroid, cylinders, spheres based on composition f + χN. Templates for lithography,…
Living polymerization
No termination/transfer: Mn = [M]/[I] × conv; Đ → 1. Anionic (styrene, dienes), cationic, ring-opening (lactide, caprolactone),…
Rubber elasticity (entropy spring)
Retraction force is entropic; f = (nkBT/L)(L/L₀ - L₀²/L²). Cross-links set modulus. Derived by Flory, Rivlin.
Flory–Huggins polymer solution theory
ΔG_mix = RT[(φ_1/N_1)ln φ_1 + (φ_2/N_2)ln φ_2 + χφ_1 φ_2]; predicts UCST/LCST; polymer-solvent interaction χ.
Reptation / tube model (de Gennes)
Entangled chains diffuse through effective tube; τ_rep ~ N³ molar-mass dependence; explains melt viscosity η ~ M^3.4.
Living/controlled polymerization (RAFT, ATRP, NMP)
Controlled chain growth with low dispersity; block copolymers; RAFT thiocarbonates, ATRP Cu catalysts; nanomaterials design.
Rouse model (unentangled)
Bead-spring chain with normal-mode relaxation times τ_p ~ N²/p²; applies below entanglement molar mass.
Flory–Stockmayer gel-point theory
Branching gel when pf=1/(f-1) for f-functional monomer; molecular-weight diverges; critical connectivity.
Block-copolymer microphase separation
AB diblocks order into lamellae, cylinders, gyroid, BCC spheres vs f, χN; Leibler theory; directed self-assembly lithography.
Polymer brushes (Alexander–de Gennes)
End-tethered chains stretched beyond R_g due to crowding; height H ~ Nσ^(1/3); used in colloid stabilization, lubrication.
WLF equation (T_g shift)
log a_T = -C₁(T-T_g)/(C₂+T-T_g); time-temperature superposition in viscoelastic regime; C₁≈17, C₂≈52 K universal.
Rubber elasticity (Gaussian)
σ = (ρRT/M_c)(λ-1/λ²) from entropic restoring force of Gaussian chains; modulus increases with T (anomalous).
Entanglement molar mass M_e
Critical M above which chains reptate; M_e ~ 10-20 kg/mol for polyethylene; G_N^0 = ρRT/M_e plateau modulus.
Polymer nanocomposites
Polymer + nanofillers (clay, CNT, graphene); percolation for conductivity; mechanical reinforcement via interfacial coupling.
Biodegradable polymers (PLA, PCL, PHB)
Hydrolysable esters; sustainable packaging; medical implants/sutures; drug-delivery microspheres.