Multivariate Composition Distribution in Free‐Radical Multicomponent Polymerization, 2

A shortcut approximate method is proposed for determining the multivariate composition distribution. It is found that the multivariate normal distribution can represent the major body of composition distribution for long chains reasonably well. The covariance of the multivariate composition distribution is obtained from the generating function proposed in Part 1 of this series. The covariance v ij changes with chain length r , however a simple relationship, rv ij  =  A  +  B / r , is found to exist, where A and B are the constants. These constants can be determined from the v ij values for rather small values of r , which reduces the required amount of calculation significantly, and the multivariate composition distribution for long chains can be estimated conveniently.Contour plot of the bivariate composition distribution for the three‐component system with r  = 100. The solid curves are the exact solution, while the dotted curve is the approximation using the multivariate normal distribution.