Addition & Condensation Polymerization Reaction Mechanisms

Polymer synthesis is the foundation of modern materials science. Understanding addition (chain-growth) and condensation (step-growth) polymerization mechanisms enables polymer engineers to control molecular weight distributions, reaction kinetics, copolymer architectures, and material properties. Whether formulating high-density polyethylene (HDPE) pipes or producing Nylon 6,6 tire cords, controlling polymerization mechanisms determines yield, thermal stability, and mechanical strength.

By completing this lesson, you will be able to:

• Explain free-radical, ionic, and step-growth polymerization mechanisms.
• Calculate number-average degree of polymerization ((\bar{X}_n)) using Carothers equation for step-growth kinetics.
• Compare chain-growth vs step-growth mechanisms regarding monomer consumption, byproduct formation, and molecular weight buildup.
• Diagnose side reactions such as chain transfer to polymer leading to branching.

3.1 Addition (Chain-Growth) Polymerization

Chain-growth polymerization proceeds via three distinct, sequential elementary steps: Initiation, Propagation, and Termination. The active center can be a free radical, a carbocation, or a carbanion.

$$\text{Initiator (I)} \xrightarrow{k_d} 2\text{R}^\bullet$$ $$\text{R}^\bullet + \text{M} \xrightarrow{k_i} \text{RM}_1^\bullet$$ $$\text{RM}_n^\bullet + \text{M} \xrightarrow{k_p} \text{RM}_{n+1}^\bullet$$

Chain termination occurs by combination or disproportionation:

$$\text{RM}_n^\bullet + \text{RM}_m^\bullet \xrightarrow{k_{tc}} \text{P}_{n+m} \quad (\text{Combination})$$

graph TD
    A["Initiator Decomposition (I -> 2R*)"] --> B["Initiation (R* + Monomer -> M1*)"]
    B --> C["Propagation (Mn* + Monomer -> Mn+1*)"]
    C --> D["Termination (Combination or Disproportionation)"]
    C --> E["Chain Transfer (Branching / Retardation)"]

3.2 Condensation (Step-Growth) Polymerization & Carothers Equation Assumptions

Step-growth polymerization occurs through bi-functional or poly-functional monomers with the elimination of small molecule byproducts such as water ((\text{H}_2\text{O})), hydrochloric acid ((\text{HCl})), or methanol ((\text{CH}_3\text{OH})).

Nylon 6,6 synthesis from Hexamethylenediamine and Adipic Acid:

$$n\text{ H}_2\text{N-(CH}_2\text{)}_6\text{-NH}_2 + n\text{ HOOC-(CH}_2\text{)}_4\text{-COOH} \rightarrow \text{[-HN-(CH}_2\text{)}_6\text{-NH-CO-(CH}_2\text{)}_4\text{-CO-]}_n + (2n-1)\text{H}_2\text{O}$$

Carothers Equation for Step-Growth

The number-average degree of polymerization ((\bar{X}_n)) as a function of extent of reaction ((p)) is expressed as:

$$\bar{X}_n = \frac{1}{1 - p}$$

For non-stoichiometric monomer mixtures with stoichiometric ratio (r = \frac{N_A}{N_B} \le 1):

$$\bar{X}_n = \frac{1 + r}{1 + r - 2rp}$$

Worked Numerical Example:

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Problem: In an equimolar condensation polymerization of hexamethylenediamine and adipic acid, calculate the extent of reaction ((p)) required to reach a degree of polymerization ((\bar{X}_n)) of 200.

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Solution:

$$\bar{X}_n = \frac{1}{1 - p} = 200$$ $$1 - p = \frac{1}{200} = 0.005$$ $$p = 1 - 0.005 = 0.995 \quad (99.5\% \text{ Conversion})$$

Interpretation: High molecular weight in step-growth requires extremely high monomer purity and near-complete reaction conversion ((p > 99%)).

• Free Radical Chain Growth: Low-Density Polyethylene (LDPE) production in autoclave reactors operating at 2000–3000 bar pressure.
• Interfacial Condensation: Nylon 6,10 filament extrusion. (Illustrative Indian industry scenario based on standard synthetic fiber plant practices).

• Chain-growth produces high molecular weight polymer immediately at low monomer conversion.
• Step-growth requires (p > 99%) for structural engineering plastics.
• Carothers Equation: Relates degree of polymerization directly to extent of reaction.
• Disproportionation: Termination transfer of a hydrogen atom creating one saturated and one unsaturated polymer chain.

1. Odian, G. (2004). Principles of Polymerization, 4th Ed., Wiley-Interscience.
2. ISO 1628-1:2021 — Determination of the viscosity of polymers in dilute solution.