Molecular parameters of hyperbranched polymers made by self-condensing vinyl polymerization. 1. Molecular weight distribution

The molecular weight distribution (MWD) and its moments are calculated for hyperbranched polymers formed by self-condensing vinyl polymerization (SCVP) of monomers (“inimers”) with the general structure AB*, where A is a vinyl group and B* is an initiating group. The calculated MWD is extremely broad, the polydispersity index (PDI) being equal to the number-average degree of polymerization:  Pw/Pn = Pn. It is twice as broad as that for the polycondensation of AB2 type monomers. If the fraction of unreacted monomer is not taken into account, the MWD becomes somewhat narrower, P‘w/P‘n ≈ 0.40P‘n. The kinetics of the polymerization process are first order with respect to the concentration of vi…

Kinetic Analysis of “Living” Polymerization Processes Exhibiting Slow Equilibria. 5. Effect of Monomer Transfer in Cationic Polymerization and Similar Living Processes

This work deals with the kinetics of polymerization processes with chain transfer to monomer and reversible formation of dormant species. Such a mechanism is typical for cationic polymerization in the presence of Lewis acids as co-initiators. The expressions of number- and weight-average degrees of polymerization and polydispersity index are derived rigorously for a mechanism with free ions as the active species, but it is also applied to other mechanisms, e.g., ion pairs as active species. Plots of polydispersity index versus monomer conversion can be easily computed on a PC computer even though the expressions for the weight-average degree of polymerization and the concentration of residu…

Kinetic analysis of "living" polymerization processes exhibiting slow equilibria. 6. Cationic polymerization involving covalent species, ion pairs, and free cations

The kinetics of cationic polymerization is studied theoretically in accordance with a three-state mechanism which consists of two successive equilibria:  the ionization/ion collapse equilibrium between covalent species and ion pairs, and the subsequent dissociation/association equilibrium between ion pairs and free ions. The number- and weight-average degrees of polymerization and the polydispersity index (PDI), Pw/Pn, are derived. The molecular weight distribution of the polymer generated from this mechanism is generally broader than that of polymers formed via a two-state mechanism, i.e. with only one equilibrium either between covalent species and ion pairs or between covalent species an…

Molecular Parameters of Hyperbranched Polymers Made by Self-Condensing Vinyl Polymerization. 2. Degree of Branching

Using a modified definition, the average degree of branching, , the fraction of branchpoints, , as well as the fractions of various structural units are calculated as a function of conversion of double bonds for hyperbranched polymers formed by self-condensing vinyl polymerization (SCVP) of monomers (or “inimers”) with the general structure AB*, where A is a vinyl group and B* is an initiating group. The results are compared to those for the polycondensation of AB2-type monomers. At full conversion, is somewhat smaller for SCVP ( ∞ ≈ 0.465) than for AB2 systems ( ∞ = 0.5). There are two kinds of linear groups in SCVP whereas there is only one kind in AB2 systems. Since there are two differe…

Promising Dendritic Materials: An Introduction to Hyperbranched Polymers

In nature and universe from living to nonliving things, branching occurs anywhere and anytime, such as the Crab Nebula, forked lightning, river basins, trees, nerves, veins, snow crystals, nervures, and proteoglycan ranging from light-years to kilometers, and to microscale and nanoscales (see Figure 1.1 for selected branching patterns). Hence, branching is a general and important phenomenon that could result in faster and more efficient transfer, dissipation, and distribution of energy and/or matter.

Kinetic Analysis of “Living” Polymerization Systems Exhibiting Slow Equilibria. 3. “Associative” Mechanism of Group Transfer Polymerization and Ion Pair Generation in Cationic Polymerization

The averages of the molecular weight distribution are derived for a “living” polymerization process which proceeds via active and “dormant” species and where the active species are formed by addition of a catalyst to a “dormant” species. Such a mechanism is applicable to group transfer and “living” cationic polymerizations (assuming that ion pairs are formed exclusively in the latter case). Both equilibrium and nonequilibrium initial conditions are used for the calculation. The results are very similar to those obtained for degenerative transfer (i.e., direct exchange of activity between active and “dormant” species). The dominating parameter is β = k2/(kpI0), where k2 and kp are the rate c…

Conclusions and Perspective: Toward Hyperbranched/Dendritic States