Figure 4

Percolation phase transition. (a–c) Several largest clusters in C₁₂, C₁₆ and C₂₂ systems, respectively, with the largest cluster colored blue. (a) The largest cluster in C₁₂ is very small and not well aligned. (b) The largest cluster in C₁₆ is larger and better aligned in parallel but still local with little orientation correlation between clusters. (c) The largest cluster in C₂₂ almost fills in the whole simulation box, indicating that the majority of the side chains are globally aligned in parallel and well connected. (d) Normalized sizes of the largest and second largest clusters for all systems. (e) Average cluster size versus side-chain length. After the percolation phase transition, the largest cluster is not counted in the calculation of the average cluster size. (f) Correlation length versus side-chain length. For a finite system, both the average cluster size and the correlation length reach their maxima at the phase transition point. The correlation length is actually directly related to the average cluster size.