What is polymerization?

Polymerization is a chemical process in which one or more monomers combine to produce a very large chain-like molecule called a polymer. The functional groups present on the monomers and their steric effects are responsible for polymerization through a sequence of reactions that diverge in complexity. There exists a stable covalent chemical bond between monomers that sets apart polymerization from other processes. Polymerization is generally classified into step-growth and chain polymerization. Polymers are categorized into linear polymer and cross-linked polymers that are produced either by condensation or additional polymerization. 

Generally, all chain polymerization reactions involve initiation, propagation, and termination. Kinetics of polymerization differ based on the type of polymerization.

Step-growth polymerization kinetics

This gives an insight into how the reactions proceed over time, identifies the time taken to reach the optimum polymer chain length or molecular weight, the occurrence of polymerization, and the reactivity mechanism. Usually, condensation and the addition of polymers occur by step-growth polymerization. In condensation polymerization, substitution occurs at the carbon of the carboxylic acid group (COOH). For instance, the formation of polyester happens by substitution at carboxylic acid by an alcoholic group, thus forming an ester. For simple understanding, the reaction below depicts the formation of a polymer with ethylene glycol and oxalic acid.

An elementary reaction generally involves the mechanism steps where the first step is the rate-determining step. Taking stoichiometry into consideration, they follow the second-order rate law, known as the differential rate law.

$Rate= -d\left[M\right]/{\left[M\right]}^2 = k dt$

One would arrive at a straight line by measuring the inverse of concentration of monomer with time during polymerization. The rate constant is determined by the slope and the intercept corresponding to the inverse of monomer concentration with which the reaction was initiated.

Chain polymerization kinetics

They are characteristically demonstrated by a radical chain reaction and their kinetics are studied. Alkenes polymerize through a chain reaction, unlike monomers that usually undergo condensation. Radical polymerization is initiated with the thermal decomposition of the initiator to give two radicals. The rate constant of decomposition and the initiator concentration contributes to the rate of decomposition.

$I\stackrel{k_d}{\to }2R^{*}$

$\frac{-d\left[I\right]}{dT}=\frac{1d\left[R^{*}\right]}{2dT}=k_d\left[I\right]$

Generation of free-radical is followed by radical addition on a monomer double bond, which in turn produces a new radical. It is considered the first time a monomer was involved in the radical addition. Consequently, in regards to polymer science, it is an initial step; whereas theoretically, it is considered a propagation step. The radical chain length is extended when a monomer is consumed initially and new radical species is formed. Here, the rate of initiation depends on the concentration of both radical and monomer along with the rate constant of the chain initiator. The rate of free radical polymerization is,

$$\begin{gathered} R^{*}+M\stackrel{k_i}{\to }{M}^{*} \\ \frac{-d\left[M\right]}{dT}=\frac{d\left[M^{*}\right]}{\left(dT\right)}=k_i\left[R^{*}\right]\left[M\right] \end{gathered}$$

The rate law rests on the reactive intermediates. The slow step is considered a radical formation, as it involves bond breaking, which is energy consuming, after which the addition of monomer occurs faster, leading to chain growth. Essentially, the rate truly depends on the rate of decomposition step only.

$$\begin{gathered} k_i\gg k_d \\ \frac{d\left[M^{*}\right]}{dT}=\frac{d\left[R^{*}\right]}{dT}=2k_d\left[I\right] \end{gathered}$$

The principal propagation step is the one after the addition of monomer into the radical; it enchains with the next monomer forming another radical, and so on. The rate constant for the propagation step is the same for any number of monomers enchained but differs from k_i because the nature of the radical intermediates differs in each step.

The radicals produced with any number of styrenes look identical. The monomer consumption rate is identified by the rate constant of propagation, the concentration of monomer, and radical concentration propagation provided at any moment. Independent of the polymer chain length or molecular weight, the radical propagation is expressed as $M^{*}$.

$M^{*}+M\stackrel{k_p}{\to }M-M^{*}$

$\frac{-d\left[M\right]}{dT}=k_p\left[M\right]\left[M^{*}\right]$

Finally, during the termination step, the disproportion mode is carried over by the transfer of hydrogen from one radical to another. Kinetic chain length, which is represented by vee bar is utilized to establish the chain length of polymer theoretically.

Catalytic polymerization kinetics

The best example is the Ziegler-Natta polymerization of alkenes carried over the heterogeneous catalytic condition, where the reaction occurs on the surface of the solid. The kinetic features of catalytic reactions differ from other reactions and are interesting to explore. The metal catalyst is well-known for its capability to adsorb molecules on its surface. For instance, adsorption of alkenes and hydrogen in catalytic hydrogenation; adsorption of dinitrogen and hydrogen in Haber-Bosch process. The adsorption and desorption being the two important factors, the first one was considered as dynamic by the Langmuir. The rate of desorption and adsorption were equal at equilibrium condition and hence arrived at,

$\theta = k_a \left[M\right] / (k_d + k_a [M\left]\right)$

Now, Langmuir isotherm is introduced to express the portion of the covered surface by the substrate. Hence, the rate of the catalyzed reaction depends on the concentration of catalyst, enchainment rate constant, and the fraction of surface occupied by the monomer.

$Rat{e}_p = k_p{K}_{eq}\left[M\right]\left[Cat\right]x*/1+ K_{eq}\left[M\right]$

$x*$ denotes the inactive catalyst fraction.

It is also to be noted that the above equation resembles the Michaelis-Menten equation for an enzyme-catalyzed reaction.

Context and Application

This topic is important in the qualifying examination for undergraduate and postgraduate courses

• Bachelors in Science in Chemistry
• Masters in Science in Chemistry
• Bachelors in Science in Physics
• Masters in Science in Physics

Practice Problems

1. What kind of bond between monomers sets the polymerization process unique?

a. Stable ionic bond

b. Stable covalent chemical bond

c. Coordinate-covalent bond

d. Polar covalent bond

Answer- b

Explanation: There exists a stable covalent chemical bond between monomers that sets apart polymerization from other processes.

2. How many steps do a chain polymerization reaction generally involve?

a. Three

b. Five

c. Two

d. Four

Answer- a

Explanation: All chain polymerization reactions involve three steps: initiation, propagation, and termination.

3. At which group does substitution occur in the condensation polymerization?

a. Alcohol

b. Hydroxyl

c. Carboxyloid

d. Carbonyl

Answer- c

Explanation: In condensation polymerization, substitution occurs at the carboxyloid site.

4. Which step is considered the initiation step in radical polymerization that gives two radicals?

a. Combustion

b. Condensation

c. Redox reaction

d. Thermal decomposition

Answer- d

Explanation: Radical polymerization is initiated with the thermal decomposition of the initiator to give two radicals.

5. Which of these is the right example for a catalytic reaction driven by a metal catalyst?

a. Lane’s process

b. Dewar’s flask

c. Merck’s process

d. Haber-Bosch

Answer- d

Explanation: Adsorption of dinitrogen and hydrogen in the Haber-Bosch process is an example of a metal-catalyzed reaction. 

Common Mistakes

Students tend to get confused between adsorption and absorption. Adsorption refers to a surface phenomenon like the adhesion of molecules on a surface, an example is the action of water on silica gel. Absorption refers to the bulk phenomenon as the incorporation of molecules throughout the layers of a substrate. For instance, the soaking of water into a sponge.

Practice Problems

1. Which order of kinetics is followed by the polyesterification reaction catalyzed by a strong acid?

Answer: The polyesterification reaction is catalyzed by the addition of strong acid that does not participate in the reaction, as it is self-catalyzed. Hence, the reaction follows the second-order kinetics.  

2. Why in free radical polymerization the initiation step consists only of thermal decomposition?

Answer: After thermal decomposition of radical initiator in free radical polymerization, free radicals are generated. These free radicals undergo an addition reaction on a monomer double bond that also includes the initiation step since it is the first time that radical addition occurs with a monomer. Technically, it is a propagation step, but from the view of polymer science, it is still an initiation step.

3. What abnormal effects does the addition of solvents or additives reflect on polymerization?

Answer: The addition of solvents might tempt the initiator efficiency or the generation of radical to increase. This in turn increases the chain initiation’s rate as well as the polymerization rate.