6.2 Reactivity ratios and copolymer composition

Reactivity ratios in copolymers determine how monomers combine, influencing the final structure and properties. These ratios help predict if the copolymer will be random, alternating, or form blocks, which affects its characteristics and applications.

Copolymer composition calculations use reactivity ratios to determine the ratio of monomers in the final product. This information is crucial for designing copolymers with specific properties, from rubber-like materials to thermoplastic elastomers.

Reactivity Ratios and Copolymer Composition

Reactivity ratios in copolymers

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• Reactivity ratios ($r_1$ and $r_2$) quantify the relative reactivity of two monomers (M1 and M2) in a copolymerization reaction determine the probability of a growing chain end (M1• or M2•) adding to its own monomer type or the other monomer
  • $r_1 = k_{11}/k_{12}$, $k_{11}$ is the rate constant for M1 adding to M1, $k_{12}$ is the rate constant for M1 adding to M2
  • $r_2 = k_{22}/k_{21}$, $k_{22}$ is the rate constant for M2 adding to M2, $k_{21}$ is the rate constant for M2 adding to M1
  • $r_1 > 1$, M1• prefers to add to M1; $r_1 < 1$, M1• prefers to add to M2
  • $r_2 > 1$, M2• prefers to add to M2; $r_2 < 1$, M2• prefers to add to M1
• The product of reactivity ratios ($r_1r_2$) indicates the tendency for the copolymer to form alternating, random, or block structures
  • $r_1r_2 = 1$, the copolymer is random (styrene-butadiene rubber)
  • $r_1r_2 < 1$, the copolymer tends to be alternating (maleic anhydride-styrene)
  • $r_1r_2 > 1$, the copolymer tends to form blocks or sequences of each monomer type (styrene-isoprene block copolymers)

Calculations of copolymer composition

• The instantaneous copolymer composition equation relates the mole fraction of M1 in the copolymer ($F_1$) to the mole fraction of M1 in the monomer feed ($f_1$) and the reactivity ratios ($r_1$ and $r_2$): $F_1 = \frac{r_1f_1^2 + f_1f_2}{r_1f_1^2 + 2f_1f_2 + r_2f_2^2}$
• The average copolymer composition can be calculated by integrating the instantaneous composition equation over the conversion range of interest
  • For low conversions (< 10%), the average composition is approximately equal to the instantaneous composition
  • At higher conversions, the average composition deviates from the instantaneous composition due to changes in the monomer feed composition as the reaction progresses (drift in composition)

Interpretation of composition diagrams

• Copolymer composition diagrams plot the instantaneous or average copolymer composition ($F_1$) against the monomer feed composition ($f_1$) the shape of the curve depends on the reactivity ratios ($r_1$ and $r_2$)
  • For an ideal random copolymer ($r_1 = r_2 = 1$), the composition diagram is a straight line with a slope of 1, indicating that the copolymer composition equals the feed composition
  • For a copolymer with $r_1 > 1$ and $r_2 < 1$, the composition diagram is above the diagonal line, indicating that the copolymer is enriched in M1 relative to the feed (acrylonitrile-butadiene copolymers)
  • For a copolymer with $r_1 < 1$ and $r_2 > 1$, the composition diagram is below the diagonal line, indicating that the copolymer is enriched in M2 relative to the feed (ethylene-propylene copolymers)
  • For an alternating copolymer ($r_1 \approx r_2 \approx 0$), the composition diagram is a sharp curve approaching the point (0.5, 0.5), indicating that the copolymer composition is always close to 50:50 regardless of the feed composition (maleic anhydride-vinyl acetate)

Effects on copolymer structure

• The monomer feed composition and reactivity ratios influence the distribution of monomer units along the copolymer chain, which affects the copolymer structure and properties
  1. Random copolymers ($r_1 \approx r_2 \approx 1$) have a statistical distribution of monomer units and properties intermediate between those of the homopolymers (styrene-acrylonitrile)
  2. Alternating copolymers ($r_1 \approx r_2 \approx 0$) have a regular alternation of monomer units and unique properties not found in the homopolymers (maleic anhydride-ethylene)
  3. Block or gradient copolymers ($r_1 > 1$ and $r_2 > 1$) have long sequences of each monomer type and can exhibit phase separation or microphase segregation (styrene-butadiene-styrene thermoplastic elastomers)
• The sequence distribution of monomer units affects the copolymer's thermal properties (glass transition temperature, melting point), mechanical properties (modulus, strength, elasticity), and solubility (hydrophobic-hydrophilic balance)
• By selecting monomers with appropriate reactivity ratios and adjusting the feed composition, copolymers can be designed with tailored structures and properties for specific applications (drug delivery, compatibilizers, adhesives)