Dynamics of Aggregate Growth Through Monomer Birth and Death

We investigate the kinetic behaviour of the growth of aggregates through monomer birth and death and propose a simple model with the rate kernels K(k) ∝ k^u and K'(k) ∝ k^v at which the aggregate A_k of size k respectively yields and loses a monomer. For the symmetrical system with K(k) = K'(k), the aggregate size distribution approaches the conventional scaling form in the case of u < 2, while the system may undergo a gelation-like transition in the u > 2 case. Moreover, the typical aggregate size S(t) grows as t^1/(2-u) in the u < 2 case and increases exponentially with time in the u = 2 case. We also investigate several solvable systems with asymmetrical rate kernels and find that the scaling of the aggregate size distribution may break down in most cases.