Kinetic model of two-monomer polymerization

Abstract

We propose a kinetic gelation model of polymer growth with two monomeric types that have distinct functionalities (reaction sites), and can polymerize using different reaction types. The heterotypic aggregation of two monomer types is modeled using a moment generating function approach by tracking the temporal evolution of a closed system of moment equations up until gelation. We investigate several scenarios of polymerization with two distinct monomers that differ in the types of reactions that can occur. We determine numerical and analytical conditions for finite time blow-up (the emergence of an oligomer of infinite size) that depend on initial conditions, reaction rates, and number of reaction sites per monomer.

Coalescense with arbitrary-parameter kernels and monodisperse initial conditions: A study within combinatorial framework

“…( 9) and ( 10) with x g specified by Eqs. ( 34) and (28). In effect, we obtain a set of self-contained expressions to calculate n s for the condensation kernel, K(i, j) = (A + i)(A + j).…”

“…Several technological applications are based on coagulation, including formation of polymers [22], food processing [23], material processing [24,25], and water treatment [26,27]. The aggregation formalism has recently started to play a significant role in modeling physiological processes [28,29]. Another interesting example of a broadly understood aggregation can be neurons accumulating into agglomerations observed in the neural network under specific conditions [30].…”

“…This area is still exhaustively researched [40][41][42][43][44]. On the basis of the Smoluchowski equation and the works of Ziff [33], a kinetic model of the gelling system consisting of two types of monomers was recently investigated [28]. The Smoluchowski equation was also used to describe the process of protein aggregation in living cells [29].…”

How initial condition impacts aggregation -- a systematic numerical study

“…In the last two decades, aggregation has * e-mail: lepek@if.pw.edu.pl been applied to a broad range of interdisciplinary topics, including percolation phenomena in random graphs and complex networks [7][8][9][10][11][12], pattern formation [14][15][16][17], and population genetics [13]. Recently, some physiological processes were modeled using aggregation formalism [18,19].…”

“…Further comment on that issue can be found in [26]. Nevertheless, classic approach is widely used and researched [18,19,21,22].…”