Abstract
The mathematical treatment of polymer modification systems, described by population balances containing convolution is discussed. The two-dimensional case (molecular weight vs. number of branch points) was considered by utilizing approximations of distributions, expanding them in terms of Gaussian basis functions. Three branching reactions were addressed: chain backbone to chain end point coupling; three-functional coupling of chain ends; and crosslinking. The results were compared to those of Monte Carlo (MC) simulations. Good agreement was observed, although the quality of a distribution as generated by the numerical approach is much better in view of the strong scatter in the MC data.
| Original language | English |
|---|---|
| Pages (from-to) | 89-106 |
| Number of pages | 18 |
| Journal | Macromolecular Theory and Simulations |
| Volume | 22 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Feb 2013 |
Keywords
- convolution
- Gaussian basis function
- molecular weight distribution
- population balance equation