# Chain Length Distribution of Polymers after Degradation by Random Chain Scission

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows a simulation of the chain length distribution after the destruction of a polymer by random chain breaking. Move the slider "degree of destruction" to 0, set the initial distribution and observe the distribution change at different degrees of destruction.

Contributed by: A. A. Koledenkov (February 2019)

Open content licensed under CC BY-NC-SA

## Details

The kinetics of the process of random chain breaking for linear polymers is described by the equation:

,

where is the molar concentration of -mer and is the first-order rate constant for chain-breaking reaction.

For a monodisperse polymer with boundary condition , the general solution of this equation is:

,

where is the fraction of broken bonds, or the degree of destruction.

Normalization gives the numerical distribution function:

In case of complex initial distributions, the absence of mutual influence of the chains makes it possible to apply this distribution function to each polymer homolog, taking into account its concentration in the initial polymer.

A special solution for the initial Flory distribution, since the random chain breaking does not change the nature of the distribution:

,

where is the molar fraction of -mer and is the number-average degree of polymerization of the starting polymer.

For ladder polymers with monodisperse initial distribution:

,

where is the probability of double-stranded break at a degree of destruction .

Based on the chain length distribution, the number-average degree of polymerization , the weight-average degree of polymerization and the polydispersity index are calculated:

,

,

.

## Snapshots

## Permanent Citation