RAFT-mediated emulsion polymerization of styrene using a non-ionic surfactant

We report the successful RAFT-mediated emulsion polymerization of styrene using a non-ionic surfactant (Brij98), the highly reactive 1-phenylethyl phenyldithioacetate (PEPDTA) RAFT agent, and water-soluble initiator ammonium persulfate (APS). The molar ratio of RAFT agent to APS was identical in all experiments. Most of the monomer was contained within the micelles, analogous to microemulsion or miniemulsion systems but without the need of shear, sonication, cosurfactant, or a hydrophobe. The number-average molecular weight increased with conversion and the polydispersity index was below 1.2. This ideal 'living' behavior was only found when molecular weights of 9000 and below were targeted. It was postulated that the rapid transportation of RAFT agent from the monomer swollen micelles to the growing particles was fast on the polymerization timescale, and most if not all the RAFT agent is consumed within the first 10% conversion. In addition, it was postulated that the high nucleation rate from the high rate of exit ( of the R radical from the RAFT agent) and high entry rate from water-phase radicals ( high APS concentration) reduced the effects of 'superswelling' and therefore a similar molar ratio of RAFT agent to monomer was maintained in all growing particles. The high polydispersity indexes found when targeting molecular weights greater than 9000 were postulated to be due to the lower nucleation rate from the lower weight fractions of both APS and RAFT agent. In these cases, 'superswelling' played a dominant role leading to a heterogeneous distribution of RAFT to monomer ratios among the particles nucleated at different times.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.