and copolymerization with one or more different vinyl monomers, which is called self-condensing vinyl copolymerization (SCVCP). [5][6][7][8][9][10][11][12][13] Puskas and Grasmüller have developed a "one-pot" living carbocationic copolymerization of IM and isobutylene (IB) to produce arborescent polyisobutylene ( arb PIB), [ 14,15 ] which greatly reduced the labor required compared with previous multi-step processes. [16][17][18] This one-pot living copolymerization system is illustrated in Figure 2 , where there are two types of vinyl groups, i.e., V I and V M , and three types of chloride end groups, i.e., C I , C M , and C S . V I is the vinyl group on the IM and V M is the vinyl group on the IB monomer. C I is an unreacted chloride group on the IM; C M is a chloride group formed after a reaction with V M , and C S is a chloride group formed after a reaction with V I . Each type of chloride group can be uncapped to form an active carbocation that can react with either type of vinyl group. As a result, there are six different propagation rate constants, which are named k pII , k pIM , k pMI , k pMM , k pSI and k pSM . The fi rst subscript letter after k p is the type of chloride group that is uncapped to produce the reactive carbocation and the second subscript is the type of vinyl group that is consumed. The corresponding propagation reactions are summarized in Table 1 , along with estimated values of the corresponding apparent rate constants. The apparent rate constants in An advanced Monte Carlo (MC) method is developed, using weight-based selection of polymer chains, to predict the molecular weight distribution (MWD) and branching level for arborescent polyisobutylene ( arb PIB) at the end of a batch reaction. This new weight-based MC method uses differential equations and random numbers to determine the detailed structure of arb PIB molecules. Results agree with those from an advanced number-based MC method. The proposed weight-based algorithm requires approximately twice the computation time of the numberbased method, but produces more accurate results in the high-molecular-weight portion of the MWD when the same number of polymer chains is assembled.