Chapter 5: Study Guide and Self-Assessment
Probability theory has a long and disreputable history having its origins in the desire to work out the odds in games of chance and thus get rich without having to work for a living. It has been applied to a whole range of problems in polymer science, although in this chapter our focus will be on the description of molecular weight and molecular weight distributions, where a young Paul Flory made his first contributions to the field. We start by examining molecular weight averages and distributions in step-growth polymerizations, as these are particularly well suited to a statistical treatment. The problems associated with the application of this approach to chain polymerizations are then considered and we conclude by returning to step-growth polymerizations to consider branching and gelation.
Objectives
Upon successfully completing this chapter you should be able to:
- Understand simple aspects of probability theory and be able to formulate equations for the probability of an event.
- Apply this theory to linear step-growth polymerization and obtain equations for the number and weight average molecular weights and molecular weight distributions.
- Account for the effect of a non-stoichiometric amount of monomers and the effect of monofunctional groups or chain stoppers”.
- Show how the use of the steady-state assumption allows the derivation of equations describing the rate of polymerization, conversion, the kinetic chain length and the effect of chain transfer.
- Show how this approach can be applied to chain polymerizations, but are less useful apart from the special case of living” polymerizations
- Understand how the polymerization of multifunctional monomers leads to network formation or hyperbranched polymers.
- Apply probability theory to a description of gelation and the incipient gel point.
Self-Assessment Questions