Hoffmann Max, Lang Michael, Sommer Jens-Uwe
Leibniz Institute of Polymer Research Dresden e.V., Hohe Straße 6, D-01069 Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Feb;83(2 Pt 1):021803. doi: 10.1103/PhysRevE.83.021803. Epub 2011 Feb 23.
The cross-linking of polymer brushes is studied using the bond-fluctuation model. By mapping the cross-linking process into a two-dimensional (2D) percolation problem within the lattice of grafting points, we investigate the gelation transition in detail. We show that the particular properties of cross-linked polymer brushes can be reduced to the distribution of bonds which are formed between the grafted chains, and we propose scaling arguments to relate the gelation threshold to the chain length and the grafting density. The gelation threshold is lower than the percolation threshold for 2D bond percolation because of the longer range and broad distribution of bonds formed by the cross-linking process. We term this type of percolation problem star percolation. We observe a broad crossover from mean-field to critical percolation behavior by analyzing the cluster size distribution near the gelation threshold.
利用键涨落模型研究了聚合物刷的交联。通过将交联过程映射到接枝点晶格内的二维（2D）渗流问题，我们详细研究了凝胶化转变。我们表明，交联聚合物刷的特殊性质可归结为接枝链之间形成的键的分布，并且我们提出标度论证以将凝胶化阈值与链长和接枝密度联系起来。由于交联过程形成的键具有更长的范围和更广泛的分布，凝胶化阈值低于二维键渗流的渗流阈值。我们将这种类型的渗流问题称为星形渗流。通过分析凝胶化阈值附近的簇尺寸分布，我们观察到从平均场到临界渗流行为的广泛转变。
