Polymer Physics Chapter 1 1.6 Molar mass ・Low molar mass substances (oligomers) : m. p.↑ with MW↑. ・High molar mass substances (polymers) : m. p. constant with MW↑ but, rheological properties : (ex.) melt viscosity ↑ with MW↑ Molar mass distribution (3 ~ 4 지수 정도의 범위로 분포) ∙ Number average molecular weight ∑ N M ∑W 1 M = i i = ∑n M = i = n N i i W w ∑ i ∑ i ∑ i Mi Mi Ni = # of molecules ni = numerical fraction or number fraction ( = mole fraction xi) Wi = mass of Mi wi = weight fraction or mass fraction Polymer Physics Chapter 1 ∙ Weight average molecular weight 2 ∑ NiMi ∑WiMi M w = = = ∑ wiMi ∑ NiMi ∑Wi ∙ Viscosity average molecular weight 1/ a ⎛ ∑ N M 1+a ⎞ 1/ a M = ⎜ i i ⎟ = w M a , 0.5 ≤ a ≤ 0.8 v ⎜ ⎟ ()∑ i i ⎝ ∑ NiMi ⎠ ⎛η −η0 ⎞ []η = lim ⎜ ⎟ c→0⎝ cη0 ⎠ η0 : η of pure solvent [η] : intrinsic viscosity c : concentration of polymer in solution Polymer Physics Chapter 1 ∙ Mark-Houwink rule (relationship betw. [η ] and M v ) a []η = K M v K, a : Mark-Houwink parameters, Unique for the combination of polymer & solvent ∙ M n ≤ M v ≤ M w ≤ M z M w ∙ Polydispersity index, PI (or heterogeneity index) ≡ M n Polymer Physics Chapter 1 M n ≤ M w 의증명: 2 ∑ Ni ()Mi − M n ≥ 0 이 성립하므로 풀어 쓰면 2 2 이된다 이식을 N 로나누면 ∑ NiMi +∑∑NiM n − 2 NiMi Nn ≥ 0 . ∑ i 2 ∑ NiMi 2 2∑ NiMiM n + M n − ≥ 0 이므로 ∑ Ni ∑ Ni 2 ∑ NiMi 2 ≥ M n 이된다. 이를 다음과 같이 처리하면 ∑ Ni 2 2 ∑ NiMi 1 ∑ NiMi ∑ Ni × ≥ M n ⇒ × ≥ M n 이 되므로 ∑ Ni M n ∑ Ni ∑ NiMi M w ≥ M n 이 성립한다. Polymer Physics Chapter 1 Experimental techniques for MW determination Absolute methods (no calibration) Relative “ (calibration) Polymer Physics Chapter 1 • End group analysis (by IR, NMR, titration) → low molar mass polymers • Colligative properties Boiling point elevation (ebulliometry) Freezing point depression (cryoscopy) Osmotic pressure Polymer Physics Chapter 1 b. p. elevation & f. p. depression → M n for low molar mass ( ≤10000 g/mol ) 2 ⎛ ∆T ⎞ ⎛V RT ⎞ 1 V : molar volume of solvent ⎜ x ⎟ = ⎜ 1 0 ⎟ 1 ⎜ ⎟ T : b. p. or f. p. temperature for pure solvent ⎝ c ⎠c→0 ⎝ ∆H x ⎠ M n 0 △Tx : △T in f. p. or b. p. △Hx : transition enthalpy Osmometry ( M n ≤100,000 g/mol ) van't Hoff equation: ⎛π ⎞ RT ⎜ ⎟ = ⎝ c ⎠c→0 M n π ⎛ 1 ⎞ ← 2 = RT⎜ + A2c + A3c + L⎟ c ⎝ M n ⎠ Polymer Physics Chapter 1 → • Light scattering M w cf. small-angle neutron scattering(SANS) X-ray scattering • Viscometry → M v (relative method) • Size exclusion chromatography (SEC), or gel permeation chromatography (GPC) : relative method (∴ Calibration is necessary) porous gel을 지나는 시간이 다름. 농도를 굴절률이나 IR light absorption을측정. Polymer Physics Chapter 1 • Degree of polymerization ( X ) M X = Mrep ~ Molar mass of CRU M rep For step-growth polymerization : Most probable distribution (Schultz-Flory distribution) i−1 1 ⎛ 1 ⎞ ni = ⎜1− ⎟ X n ⎝ X n ⎠ ni : the number fraction of molecules of X = i M n : the number average of the degree of polymerization For chain radical polymerization : Schultz distribution i ⎛ ⎞ ⎜ ⎟ 4i 1 n = ⎜ ⎟ i 2 X −1 ⎜ 2 ⎟ ()n ⎜1+ ⎟ ⎝ X n −1⎠ Polymer Physics Chapter 1 1.7 Polymerization Flory scheme (based on polymerization mechanism) Criterion Step Chain Reaction proceeds by stepwise Repeating units are added Growth reaction intermolecular condensation one at a time Monomer Almost completely disappears Decreases steadily throughout concentration early in the reaction the reaction MW of high polymer Increases steadily Is formed at once Long reaction time is essential Long reaction time will Reaction time to achieve high MW increase the yield (not MW) Mixture contains high polymer, Reaction mixture All species are present monomer and small no. of growing chains Polymer Physics Chapter 1 • Step growth (ex: polyamide, polycarbonate, polyester, PPO, PPS, etc.) All reactions are reversible ∴ requires the removal of water for high MW. Number average degree of polymerization ⎛ N − N ⎞ 1 ⎜ 0 ⎟ X n = p : extent of rxn ⎜= ⎟ 1− p ⎝ N0 ⎠ no. of groups reacted = , 즉 conversion no. of groups present initially p 0.1 0.9 . 0.9999 M n 1.110. .10000 Polymer Physics Chapter 1 • Chain growth (ex: PE, PP, PS, PMMA, PVC, PVA etc.) Radical, anionic, cationic or coordination polymerizations Initiation, propagation, termination → Linear polymer → Branched polymer (by chain-transfer) HDPE (low-pressure PE) vs. LDPE (high-pressure PE) Anionic & cationic → Living polymerization → Molecular design Possible to prepare exact block copolymer Impurity (ex, water) leads chain transfer & termination of growing chains (고순도 필요) Polymer Physics Chapter 1 1.8 Thermal transitions and physical structures Fully amorphous ~ irregular chain structure Semicrystalline ~ lamella-shaped crystals & amorphous components Differences in crystallinity → differences in physical properties ⎛ stress ⎞ ex) relaxation modulus ≡ ⎜ ⎟ ⎝ strain ⎠ Polymer Physics Chapter 1 ※ Schematic diagram of stress relaxation modulus for isotactic PS and fully amorphous (atatic) PS I : glassy (below T g ) II : leather-like (at T g ) III : rubber-like (rubber plateau) IV, V : sliding motions of molecules Polymer Physics Chapter 1 1.9 Polymer materials Thermoplastics Thermosets (phenoxy, epoxy, melamines, etc.) Rubbers or elastomers (SBR, PBD, PI, etc.) Properties of a polymer material - by structure of polymers, additives, processing methods & conditions → cf. PE fibers 100 GPa (fibrous PE, longitudinal modulus) 1 GPa (conventionally processed).