Degree of polymerization
The degree of polymerization (DP) determines the length of a polymer chain. DP is the number of monomer units (repeating units) that make up this chain. The degree of polymerization of the polymer is directly proportional to the molar mass.
It is exceptional that a synthetic polymer consists of chains of the same degree of polymerization, but there is a distribution of chains of different lengths. More precisely, we are talking about the numerical average of the degree of polymerization, D p ¯ n {\displaystyle {\overline {DP}}_{n}}or X ¯ n {\displaystyle {\overline {X}}_{n }}. It is equal to the ratio of the number average molar mass of the polymer to the molar mass of the monomer unit, that is:
D p ¯ n = M ¯ n M 0 {\displaystyle {\overline {DP}}_{n} ={\frac {{\overline {M}}_{n}}{M_{0}}}}.
If the degree of polymerization is between 2 and several tens, the chains are called oligomers.
Effect on physical properties
Special properties of the macromolecular state (as opposed to the simple state) appear for high degrees of polymerization. In general, the viscosity, melting temperature, mechanical strength and glass transition temperature of a polymer material increase with DP up to a limited amount.
Therefore, the molar mass of most industrially produced linear polymers is in the range of tens of thousands of grams per mole, some of which are over a million.
Step by step polymerization
In the case of a stepwise polymerization reaction, if all molecules (monomers or polymers) are difunctional and divalent (of the type XAY, X and Y, which are opposite functions), the rate, p [to that degree (or rate) of progress They also say ], from the reaction at time t:
p = n 0 – n t n 0 {\displaystyle p={\frac {N_{0}-N_{t}}{N_{0}} }}
With :
n 0 N_{0}et N_t N_{t} the number of molecules (monomers or polymers) in the system, respectively, at the initial time and time t.
Or X ¯ n {\displaystyle {\overline {X}}_{n}} is defined :
X ¯ n = N 0 N t {\displaystyle {\overline {X}}_{n}={\frac {N_{0} }{ N_{t}}}}
In the sense that:
X ¯ n = 1 1 – p {\displaystyle {\overline {X}}_{n}={\frac {1}{1-p}}}
which is the Carothers equation to stoichiometry, relating X ¯ n {\displaystyle {\overline {X}}_{n }} to the reaction conversion rate at a given instant.
A high conversion rate is required to form polymers with a high degree of polymerization. In stepwise polymerization, if the reactions are balanced, they must be nearly complete, often with the removal of a secondary product (volatile such as H 2 O or HCl or insoluble) from the reaction as the reaction proceeds. its formation.
Free radical chain polymerization
In the case of radical chain polymerization, Carothers equation is not valid. On the other hand, long chains are formed from the very beginning of the reaction. Longer reaction times increase the polymer yield, but have little effect on the average molecular weight of the product. The degree of polymerization is related to the kinetic chain length, i.e. the average number of monomer molecules added to each initiated chain.
However, it can deviate from the kinetic chain length for various reasons:
Chain termination can be fully or partially accomplished by recombination of two chain radicals, which doubles the degree of polymerization.
Chain transfer to the monomer initiates a new macromolecule during a chain of kinetic steps that leads to a decrease in the degree of polymerization.
Transferring the chain to the solvent or to another solute (called regulator) also reduces the degree of polymerization.
