Optimal number of linkers per monomer in linker-mediated aggregation

Phase behavior of a binary mixture of patchy colloids: Effect of particle size and gravity

We study theoretically the effect of size difference and that of gravity in the phase behavior of a binary mixture of patchy particles. The species, 2A and 3B, have two A and three B patches, respectively, and only bonds between patches A and B (AB bonds) are allowed. This model describes colloidal systems where the aggregation of particles (3B) is mediated and controlled by a second species, the linkers (2A) to which they bind strongly. Thermodynamic calculations are performed using Wertheim's perturbation theory with a hard sphere reference term that accounts for the difference in the size of the two species. Percolation lines are determined employing a generalized Flory-Stockmayer theory, and the effects of gravity are included through a local density approximation. The bulk phase diagrams are calculated, and all the stacking sequences generated in the presence of gravity are determined and classified in a stacking diagram. The relative size of the particles can be used to control the phase behavior of the mixture. An increase in the size of particles 3B, relative to the size of the linkers 2A, is found to promote mixing while keeping the percolating structures and, in certain cases, leads to changes in the stacking sequence under gravity.

Modeling of Cell-Mediated Self-Assembled Colloidal Scaffolds

A critical step in tissue engineering is the design and synthesis of 3D biocompatible matrices (scaffolds) to support and guide the proliferation of cells and tissue growth. The most existing techniques rely on the processing of scaffolds under controlled conditions and then implanting them in vivo, with questions related to biocompatibility and implantation that are still challenging. As an alternative, it was proposed to assemble the scaffolds in loco through the self-organization of colloidal particles mediated by cells. To overcome the difficulty to test experimentally all the relevant parameters, we propose the use of large-scale numerical simulation as a tool to reach useful predictive information and to interpret experimental results. Thus, in this study, we combine experiments, particle-based simulations, and mean-field calculations to show that, in general, the size of the self-assembled scaffold scales with the cell-to-particle ratio. However, we have found an optimal value of this ratio, for which the size of the scaffold is maximal when the cell-cell adhesion is suppressed. These results suggest that the size and structure of the self-assembled scaffolds may be designed by tuning the adhesion between cells in the colloidal suspension.

Smoluchowski equations for linker-mediated irreversible aggregation

We developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.