Brownian cluster dynamics with short range patchy interactions: Its application to polymers and step-growth polymerization

Abstract

We present a novel simulation technique derived from Brownian cluster dynamics used so far to study the isotropic colloidal aggregation. It now implements the classical KernFrenkel potential to describe patchy interactions between particles. This technique gives access to static properties, dynamics and kinetics of the system, even far from the equilibrium. Particle thermal motions are modeled using billions of independent small random translations and rotations, constrained by the excluded volume and the connectivity. This algorithm, applied to a single polymer chain leads to correct static and dynamic properties, in the framework where hydrodynamic interactions are ignored. By varying patch angles, various chain flexibilities can be obtained. We have used this new algorithm to model step-growth polymerization under various solvent qualities. The polymerization reaction is modeled by an irreversible aggregation between patches while an isotropic finite square-well potential is superimposed to mimic the solvent quality. In bad solvent conditions, a competition between a phase separation (due to the isotropic interaction) and polymerization (due to patches) occurs. Surprisingly, an arrested network with a very peculiar structure appears. It is made of strands and nodes. Strands gather few stretched chains that dip into entangled globular nodes. These nodes act as reticulation points between the strands. The system is kinetically driven and we observe a trapped arrested structure. That demonstrates one of the strengths of this new simulation technique. It can give valuable insights about mechanisms that could be involved in the formation of stranded gels.

Assembly of clathrates from tetrahedral patchy colloids with narrow patches

“…Collective motion can be mimicked using cluster moves designed to use in conjunction with MC or Brownian dynamics schemes but only approximately and at a considerable computational cost. [24][25][26] The most rigorous route to simulate the dynamics in out-of-equilibrium processes involves performing Brownian dynamics simulations in which hydrodynamic interactions within the clusters are taken into account, something that is beyond the scope of this work.…”

Mobile obstacles accelerate and inhibit the bundle formation in two-patch colloidal particle

“…It is either translated or rotated with equal probability only if this movement step doesn't lead to overlap or breakage of bond with any of the neighboring particles. In order to ensure correct diffusional behaviour, we have fixed our rotational step size s R = 0.018 and translational step size s T = 0.0132 41 . The cumulative effect of this step is the diffusion of center of mass of clusters.…”

“…When particles are in each other's interaction range but do not satisfy the conditions to form a Patchy bond, then a Non patchy isotropic(NPI) (see Fig. 1b) bond is formed with a probability α i and an existing bond is broken with a probability β i, such that α i α i +β i = 1−exp(−u i ) 41 . u i is given in terms of K B T and K B T is kept as unity.…”

“…In this study we have used range of B att values from 4 to 12 and quality of solvent deteriorates as we move from lower B att value towards higher B att value. In this study we have reported time in reduced units t/t 0 , where t 0 is defined as the time taken by a particle to travel a distance equal to it's own diameter 41 .…”

“…This technique has also been modified to study the binary system of a) Also at Department of physics, Indian Institute of Technology, Delhi-110016 colloidal particles 43,44 . This algorithm when applied to single polymer chain gave correct dynamic and static properties 41 .…”