Rigidity-Induced Controlled Aggregation of Binary Colloids

Here, we report the proof-of-concept for controlled aggregation in a binary colloidal system. The binary systems are studied by varying bond flexibility of only one species, while the other species’ bonds remain fully flexible. By establishing the underlying relation between gelation and bond rigidity, we demonstrate how the interplay among bond flexibility, critical concentration, and packing volume fraction influenced the aggregation kinetics. Our result shows that rigidity in bonds increases the critical concentration for gels to be formed in the binary mixture. Furthermore, the average number of bonded neighbor analyses reveal the influence of bond rigidity both above and below critical concentrations and show that variation in bond flexibility in only one species alters the kinetics of aggregation of both species. This finding improves our understanding of colloidal aggregation in soft and biological systems.


Model and Method
Brownian cluster dynamics (BCD) is based on the Metropolis Monte Carlo method and inspired by the work of Meakin et al. 1,2 and Kolb et al.,. 3 It starts with the initial conguration of N tot randomly distributed hard-spheres in a 3-dimensional box of size L. The total volume fraction of the system is given as φ tot = π 6 N tot /L 3 .The composition of the binary system is dened by identifying a fraction of A monomers with the concentration c A = N A /N tot , where N A is the number of monomer of A species.Then the concentration of B monomers is given by c B = 1 − c A .For both the species, the monomers are considered to be bonded when they are within each other's interaction range, i.e., when the center-to-center distance between the same species of monomers is ≤ (1 + ), where is the interaction range.Thus, clusters are collections of bound monomers, and lone monomers are clusters of size 1, resulting in N c S1 number of clusters in the system.For the cluster construction, monomers are randomly chosen N tot times, and each monomer is displaced randomly with a step size s = 0.01, chosen to be at least 10 times smaller than the to mimic the Brownian motion . 4The movement step is rejected if it overlaps with another monomer or leads to a separation of bound monomers beyond interaction range.The center-of-mass displacement of the clusters is calculated, and the clusters move cooperatively in the same direction so that the total displacement is inversely proportional to their radius.Upon the cluster construction and the movement step, the time is incremented as t = ns 2 where n is the number of simulation steps.Thus, t = 1 is the time taken by a monomer to travel its own diameter, where the bare diusion coecient of monomer is dened as D 0 = 1/6. 4It is to underline that BCD is equivalent to Brownian Dynamics if the cooperative cluster displacement step is omitted, given that step size s should be suciently small.

Binary system
In Figure S1, the snapshots of the modeled system is shown for a composition of 20% and 80% of A and B monomers.The red and green represents A and B monomers, respectively.
A system with constant composition (c A = 0.2; c B = 0.8) is simulated for various values of exibility parameter p f lex and the snapshots are shown in Figure S1(a).In Figure S1(b) a binary system is simulated by swapping the composition of A and B, i.e., only 20% of monomers are of B species and remaining are A (c B = 0.2; c A = 0.8).In both Figure S1(a) and (b), the exibility is tuned only in A species, and bonds are fully exible in B. For both compositions, the snapshots are taken at t/t 0 = 1.496 × 10 3 when the cluster growth stagnates.It is important to note that c A = c B = 0.2 is below the critical concentration of percolation in binary system ; 5 therefore, the value of m w stagnates for A in Figure S1(   In the state diagram in the main text, the range of φ tot , c A and p f lex represent binary systems in which bigel start appearing at a particular p f lex for a given φ tot , c A .For example, at φ tot = 0.40, c A = 0.19±0.01 at p f lex < 0.3 system resulted into a 1 component gel but with the same composition of c A and p f lex ≥ 0.3 bigel appears in the system.The combination of S4 f lex for same c A and φ tot .Out of all simulations, in more than 50% systems, we observed bigels.With reduced bond exibility, it is observed that the critical concentration parameter (c A ) c for a bigel to appear increases.Which is higher than the previously reported c A values . 5or comparison the critical c A values ((c A ) c ) are tabulated in Table S1.Though the dierence in c A values is about 1% however, the number of monomers varies signicantly.In Table S1, the corresponding number of A monomers (N A ) are also tabulated along with critical c A .It is essential to note that the dierence of one monomer determines the percolated or non-percolated cluster in nite box size.
a) and B in Figure S1(b).

Figure S1 :
Figure S1: (a) Snapshots of the binary system are shown for varying bond exibility in A species, and bonds are fully exible for B. In the top row, A species is shown in the absence of B, and bottom row, A, and B both are shown.(b) The snapshots in the green box are shown by swapping the A and B compositions, but the bond exibility is tuned only in A.In the top row, only B species are shown, and in the bottom row, the snapshot of the full system is shown with A and B both.

Figure S2 :
Figure S2: The nearest neighbor of both A and B is shown to highlight the dierence in cluster growth with time at range of p f lex = 0.0(a), 0.01(b), 0.1(c) and 0.5(d), respectively.The Z c shown here corresponds to the Figure 1 (b) and (c) in the main text.

Table S1 :
Determined critical concentrations of A species ((c A ) c ) at 0.0 ≥ p f lex ≤ 1.0 .at p f lex < 1.0 at p f lex = 1.0A , φ tot and p f lex was further conrmed by performing 10 independent simulations at p f lex > p c