The theory of binary fragmentation and aggregation is of inhavior of the MWD or PSD for all times t Β’ 0, however, terest in numerous engineering applications, including polymer is fundamental to fragmentation-aggregation kinetics.
decomposition and addition. Particles can randomly aggregate
Numerous papers ( 9-13) discussed mathematical soluand simultaneously fragment to smaller sizes that may be distribtions for irreversible fragmentation processes. But many uted randomly or nonrandomly. When the initial particle-size systems that seem irreversible become reversible under apdistribution ( PSD ) is represented as a generalized g distribution, propriate conditions. For reversible polymerization with the time evolution of its parameters can be determined. We as-MW-independent rate coefficients and a monodisperse inisume the fragmentation rate coefficient depends on particle size, tial condition, Blatz and Tobolsky ( 14) applied discrete x , as x l , and the aggregation rate coefficient is independent of kinetics to derive an exponential MWD. Extending this treatparticle size. The type of fission ( e.g., random or midpoint ) is governed by the stoichiometric coefficient. Numerical solutions ment, Browarzik and Kehlen (15) applied continuous kinetshow the time evolution for general cases of fragmentation and ics to the problem of reversible polymerization with a genaggregation. We show that the PSD approaches similarity solueral initial distribution. Aizenman and Bak ( 16) pointed out tions for special cases of fragmentation -aggregation stoichiomethat the exponential distribution is a similarity solution of try and of l. α§ 1998 Academic Press the form of Flory's (17) most probable distribution. Saito Key Words: distribution kinetics; molecular-weight distribu-(18) used moment analysis for integrodifferential equations tions; particle-size distributions; similarity solutions; fragmentaproposed to describe simultaneous degradation and crosstion; aggregation; polymer degradation; addition reactions.
linking, as well as cyclization and branching, caused by irradiation. Cohen ( 19) presented a combinatorial approach to derive a similarity solution for reversible, random aggre-