Predicting the Chain: Copolymer Reactivity Ratios Quiz

The terminal model assumes the reactivity of a growing chain depends only on the identity of the last monomer unit added. There are four possible propagation steps: a type 1 radical adding monomer 1 or monomer 2, and a type 2 radical adding monomer 1 or monomer 2. These four distinct paths define the kinetics of the entire system.

The reactivity ratio r1 is defined as the ratio of the rate constant for homopolymerization to the rate constant for cross polymerization. A value of r1 greater than 1 means the radical prefers to add its own monomer type, while a value less than 1 means it prefers to react with the other monomer type.

To derive the equation, we assume a steady state where the rate of radical 1 changing to radical 2 equals the rate of radical 2 changing back to radical 1. We also assume the long chain approximation, meaning monomer consumption via initiation is negligible. High conversion is not assumed because the equation describes instantaneous composition at a specific moment.

If both ratios are zero, the rate constants for self addition must be zero. This means a radical cannot react with its own monomer type and is forced to react with the opposite monomer. This creates a strict 1-2-1-2 alternating sequence, regardless of the concentrations of monomers available in the reaction mixture.

Ideal copolymerization occurs when the product of the ratios is 1. This implies that the two types of radicals show the same relative preference for the two monomers. The resulting sequence is purely statistical or random, and the polymer composition is determined directly by the ratio of monomers in the feed.

When both radicals prefer cross addition, the composition curve crosses the diagonal line where polymer composition equals feed composition. At this azeotropic point, the polymer being formed has the exact same composition as the monomer feed. This is vital in industry because it prevents the feed ratio from changing as the polymer is produced.

The Fineman Ross and Kelen Tudos methods are mathematical rearrangements of the copolymer equation that allow the ratios to be found using the slope and intercept of a graph. The Mayo Lewis method uses intersecting lines from different experiments. The Carothers equation is used for molecular weight in step growth, not reactivity ratios.

Reactivity ratios are based on rate constants that follow the Arrhenius equation. Since different addition steps have different activation energies, temperature changes affect them. Typically, as temperature increases, the difference in activation energy becomes less significant, driving both reactivity ratios toward a value of 1.

In this scenario, radical 1 prefers monomer 1, and radical 2 also prefers monomer 1 because its ratio for self addition is so low. Consequently, monomer 1 is consumed rapidly at the start, forming what is essentially a homopolymer, until it is exhausted, at which point monomer 2 finally begins to incorporate.

The terminal model is often an oversimplification. In systems with bulky or highly polar side groups, the identity of the monomer unit immediately preceding the active center at the end of the chain can influence the electronic environment and steric hindrance, thereby changing the rate of the next monomer addition.

Monomer reactivity is governed by the stability of the resulting radical through resonance and the electronic attraction or repulsion between the radical and the monomer. Steric hindrance also plays a major role in 1,2-disubstituted monomers, where physical crowding makes self addition difficult and encourages alternation.

The Q e scheme is a semi-empirical method where Q represents resonance stabilization and e represents the polarity of a monomer. By comparing these values for two monomers, chemists can calculate predicted reactivity ratios using tabulated data without needing to perform time consuming laboratory trials.

r1 at 0.5 indicates that radical 1 is twice as likely to add monomer 2 as it is to add monomer 1. r2 at 2.0 indicates that radical 2 is twice as likely to add its own kind, monomer 2, than it is to add monomer 1. Since both radicals show a preference for monomer 2, it is the more reactive monomer.

When the product of the ratios is greater than 1, both radicals prefer self addition over cross addition. This results in the formation of long blocks of the same monomer within a single chain, or in extreme cases, the formation of two separate homopolymers rather than a combined copolymer.

The Mayo Lewis equation calculates the instantaneous ratio of monomers being incorporated into the polymer based on the current mole fractions of monomers in the feed and their respective reactivity ratios. While temperature affects the ratios themselves, it is not a direct variable inside the equation itself.