Multiparticle brownian dynamics

The basic theoretical approach for the analysis of diffusion controlled reactions is due to Smoluchowski [9] who developed it for the analysis of diffusion limited aggregation of colloidal particles. We discuss the generalization of this approach to the case of rodlike molecules here. The computational method best suited for the simulation of the polymerization of rodlike molecules is Brownian dynamics. We discuss in this review both multiparticle Brownian dynamics and pairwise Brownian dynamics the latter is a hybrid method combining Smoluchowski s [9] theory and Brownian... 

The contents of the review are as follows. The dynamics of rodlike polymers are reviewed in Section 2 followed by a review of previous experimental results of the polymerization kinetics of rodlike molecules in Section 3. Theoretical analyses of the problem following Smoluchowski s approach are discussed next (Section 4), and this is followed by a review of computational studies based on multiparticle Brownian dynamics in Section 5. The pairwise Brownian dynamics method is discussed in some detail in Section 6, and the conclusions of the review are given in Section 7. 

Figure 8 Variation of the number average degree of polymerization (w ) with time (t) obtained from multiparticle Brownian dynamics. Results for different shear rates (/) are shown (Agarwal and Khakhar [57]).

The above results illustrate the utility of multiparticle Brownian dynamics for the analysis of diffusion controlled polymerizations. The results presented here are, however, qualitative because of the assumption of a two-dimensional system, neglect of polymer-polymer interactions and the infinitely fast kinetics in which every collision results in reaction. While the first two assumptions may be easily relaxed, incorporation of slower reaction kinetics by which only a small fraction of the collisions result in reaction may be computationally difficult. A more computationally efficient scheme may be to use Brownian dynamics to extract the rate constants as a function of polymer difflisivities, and to incorporate these in population balance models to predict the molecular weight distribution [48-50]. We discuss such a Brownian dynamics method in the next section. 

Brownian motion, multiparticle collision dynamics, hydrodynamic interactions, 118—121... 

We now assume that the wetting and disagglomeration stages are complete, and the particles are separated and uniformly distributed throughout the medium. The aim is to maintain this distribution and prevent flocculation, the process that reduces the number of particles due to collisions between particles, both under static (Brownian motion) and dynamic (under shear) conditions. In dilute dispersions it is sufficient to consider only the interaction between pairs of particles but in the very concentrated dispersions that one meets in practical systems it is necessary to take multiparticle interactions into account. Most of the published theoretical work has been concerned with pair interaction, relatively little has been written on multiparticle interactions. 

---