This Demonstration shows the number fraction (blue) and weight fraction (green) of polymer chains as functions of the number of monomer units for polymerization in a batch reactor. Select "step-growth" or "free-radical" polymerization with buttons, and use sliders to set reaction rate constants, initial concentrations and reaction time. The number average chain length , the weight average chain length and the polydispersity are shown. Distributions are calculated using the Flory–Schulz model. The and axes ranges change as the parameters change, and the thick red tick marks on the purple axes show the plot ranges used.

The number fraction and weight fraction of polymer chains for a polymer with monomer units are:

,

,

where is mole fraction and is the fraction of functional groups that have reacted:

.

For step-growth polymerization:

,

.

For free-radical polymerization:

,

,

where and are the initial monomer and initiator concentrations; is monomer concentration; , and are the rate constants for the reaction, initiation and termination; is time; is the terminator concentration and is fraction of chains initiated by initiator.

The number and weight average chain lengths are:

,

,

where is the polymer concentration.

The polydispersity is:

.

Reference

[1] H. S. Fogler, Elements of Chemical Reaction Engineering, 5th ed., Boston: Prentice Hall, 2016.