  We present a novel generating function (GF) method for the self-condensing
vinyl polymerization (SCVP) system with any initial distribution of preexisted
polymers. Such a method was proven to be especially useful to investigate the
semi-batch SCVP system allowing a sequence of feeding operations during the
polymerization. Consequently, the number-, weight-, and z-average molecular
weights as well as polydispersity index of hyperbranched polymers can be
explicitly given, which are determined by predetermined feeding details and
conversions in each polymerization step. These analytical results are further
confirmed by the corresponding Monte Carlo simulation. Therefore the present GF
method has provided a unified treatment on the semi-batch SCVP system.
Accordingly, hyperbranched polymers with desired properties can be prepared by
designing feeding details and presetting conversions at each step based on the
present GF method.
