Self-Assembly of Miktoarm Star Polyelectrolytes in Solutions with Various Ionic Strengths

We studied the self-assembly of miktoarm star polyelectrolytes with different numbers of arms in solutions with various ionic strengths using coarse-grained molecular dynamic simulations. Spherical micelles are obtained for star polyelectrolytes with fewer arms, whereas wormlike clusters are obtained for star polyelectrolytes with more arms at a low ionic strength environment, with hydrophilic arms showing a stretched conformation. The number of clusters shows an overall decreasing tendency with increasing the number of arms in star polyelectrolytes due to strong electrostatic coupling between polycations and polyanions. The formation of wormlike clusters follows an overall stepwise pathway with an intermittent association–dissociation process for star polyelectrolytes with weak electrostatic coupling. These computational results can provide relevant physical insights to understand the self-assembly mechanism of star polyelectrolytes in solvents with various ionic strengths and to design star polyelectrolytes with functional groups that can fine-tune self-assembled structures for specific applications.


Cluster size and number of clusters
First of all, we divided the simulation box into a plenty of small cubic cells, the size of each cell is 1σ 3 .
Then we assigned the polymer beads on the corresponding cells, based on their coordinates. The first hydrophobic bead that we found by following the sequence of cells was set to the outset of a cluster.
Afterwards, we searched for the hydrophobic beads through the neighbor cells of the first hydrophobic bead, if they existed in neighbors, then we continued to search for the hydrophobic beads through the neighbor cells of the new hydrophobic beads we just found. The searching process would not stop until there were no hydrophobic beads in the adjacent cells. All the hydrophobic beads we found belonged to a cluster, and the MSPE molecules including these hydrophobic beads are distributed as a cluster. The above approach was repeated for counting other clusters in the system. Finally, the number of clusters (the parameter N c in the main article) and cluster sizes were obtained. The heat map for N c values in Figure 3C were plotted by setting 8 major levels (N c = 1 to 25, as shown in Figure 3C), each major level contains 8 minor levels, to estimate the intermediate values among the simulation system settings (white symbols in Figure 3C). In addition, smoothing is adopted in order to make the heat map to be viewed friendly. We worked on only hydrophobic beads in order to avoid the chain crossing between hydrophilic coronas belong to different clusters.

S2
Figure S1: Self-assembly structure formed by MSPEs with n arm = 16 under λ D = 1σ .    We also simulated the systems starting from an energy minimised full globular state with diameter d = 40σ , and we found that the spherical, wormlike micelles are also observed in the systems. Figure S7 shows the comparisons of self-assembly structures formed by MSPEs with the number of arms n arm =8, from randomly distributed initial configurations (in the manuscript) and globular initial state. The overall self-assembly morphologies do not depend on the initial configuration obviously, the spherical micelles S6 Figure S8: Self-assembly structures formed by MSPEs with n arm =16 at (A) λ D =1.5σ and (B) λ D =2σ , from the globular initial configuration.
are also observed at λ D =2.0σ , and the micelles with inter-connection are formed at λ D =4.0σ , from the snapshots shown in Figure S7A and B. We also calculated the cluster size distribution for the two systems with globular initial configuration, and the results are also similar as those shown in the manuscript ( Figure S7C and D).
In addition, we also checked the probability of wormlike micelle formation from globular initial state, and the representative self-assembly structures are shown in Figure S8, which are formed by the MSPEs with n arm =16 at λ D =1.5σ and λ D =2σ . The self-assembly structures are similar as Figure 3 and 6 in the manuscript. So we believe that the self-assembly structures like spherical or wormlike micelles are the results after the systems reach thermodynamical equilibrium state, and the results are independent on the initial configurations.