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ACS: Polymer Chemistry

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Polymer Chemistry

Polymer Chemistry items cover molar-mass averages and distributions, step- versus chain-growth kinetics, the Carothers equation, thermal transitions, and how chain structure controls solid-state properties.

Molar mass and distribution

  • Number average Mn = ΣNiMi/ΣNi, weight average Mw = ΣNiMi²/ΣNiMi, and Mw ≥ Mn always, so PDI = Mw/Mn ≥ 1.
  • Mw is far more sensitive to the high-mass tail; a monodisperse standard has PDI = 1.0, while ideal step-growth approaches 2.0.
  • Degree of polymerization DP = Mn/M0, where M0 is the repeat-unit molar mass.

Step versus chain growth

  • Step-growth: monomers react at any conversion, but high molar mass appears only above p ≈ 0.99; Carothers gives Xn = 1/(1 − p).
  • With stoichiometric imbalance r = NA/NB ≤ 1, Xn = (1 + r)/(1 + r − 2rp); a few percent excess sharply caps chain length.
  • Chain-growth proceeds by initiation, propagation, and termination; chains grow long early and PDI is broad unless the polymerization is living (anionic, RAFT, ATRP).

Thermal transitions and structure

  • Tg rises with chain stiffness, bulky side groups, crystallinity, and crosslinking; plasticizers lower it.
  • Tacticity matters: isotactic and syndiotactic chains crystallize, atactic chains do not, so atactic polystyrene is amorphous and transparent while isotactic polystyrene is semicrystalline.
  • Crosslinking raises modulus and solvent resistance and prevents flow above Tg.

Worked example

Adipic acid (146 g/mol) plus 1,6-hexanediamine (116 g/mol) with 2.0% excess diamine gives a repeat unit of 226 g/mol and r = 1/1.02 = 0.980. At full conversion p = 1, Xn = (1 + r)/(1 + r − 2rp) = 1.980/(1.980 − 1.960) = 1.980/0.0196 ≈ 101. Then Mn ≈ 101 × 226 ≈ 2.3 × 10^4 g/mol, and adding more excess shortens the chains further.

Traps

  • Using Mw where the Carothers relation requires Mn.
  • Reporting a PDI below 1.
  • Forgetting to convert a percent excess into the ratio r.
  • Predicting Tg to rise after adding a plasticizer.
  • Assuming high conversion alone gives high molar mass despite stoichiometric imbalance.