Aggregation kinetics of irreversible patches coupled with reversible isotropic interaction leading to chains, bundles and globules

Abstract

In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern-Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined 3 different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effect of patch size on self-assembly under different solvent qualities for various volume fractions. We will show that at low volume fractions during aggregation process, we end up in a chain conformation for smaller patch size while in a globular conformation for bigger patch size. We also observed a chain to bundle transformation depending on the attractive interaction strength between the chains or in other words depending on the quality of the solvent. We will also show that bundling process is very similar to nucleation and growth phenomena observed in colloidal system with short range attraction. We have 1 arXiv:1710.09255v1 [cond-mat.soft] 27 Sep 2017 also studied the bond angle distribution for this system, where for small patches only 2 angles are more probable indicating chain formation, while for bundling at very low volume fraction a tail is developed in the distribution. While for the case of higher patch angle this distribution is broad compared to the case of low patch angles showing we have a more globular conformation. We are also proposing a model for the formation of bundles which are similar to amyloid fibers using two patch colloidal particles.

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

“…We observe that <Z NPI > value for ω ≤ 22.5 • after a plateau takes a sudden upturn at t/t 0 ≥ 100. This upturn is similar to nucleation and growth mechanism 42 and it indicates chain to bundle transition 38 . The snapshot of system formed at ω = 22.5 • is shown in Fig.…”

“…Patchy particles are also considered to be building blocks of various supracolloidal helices [35][36][37] . Two patch model along with isotropic interaction reproduced the chain to bundle transition usually seen in Lysozyme protein 38,39 . They also showed the coexistence of thermodynamically favored bundles along with equilibrium crystals 40 .…”

Phase diagram of two-patch colloids with competing anisotropic and isotropic interactions

“…Bundle formation is also observed in other biological systems like the actin filaments [19]. Chain to bundle transition was shown for a two patch particle where irreversible patchy interaction was coupled with reversible isotropic interaction [20]. Huisman et al [21] also observed the formation of bundles and they showed that transition is similar to sublimation transition of polymers.…”

“…u a is non zero only ifr i,j .v i > cos ωandr j,i .v j > cos ω, where ω is the semi solid angle of a cone having vertex at the center of a sphere which defines the patch size. In the present work we have used σ = 1, = 0.1 and ω = π/8 which ensures that only one bond per patch is possible [20]. In the present study, all quantities are reported in reduced units, hence bond strength is measured in units of u/k B T where k B T = 1.…”

“…In the present study, all quantities are reported in reduced units, hence bond strength is measured in units of u/k B T where k B T = 1. Reduced time is given by t/t 0 , where t 0 is the time taken by a particle to travel it's own diameter [20] and the volume fraction is defined as φ = π/6N tot /L 3 . We have kept φ = 0.02 which corresponds to a total number of N tot = 4774 particles.…”