Kartha Moses J, Tripathy Mukta
Department of Chemical Engineering, Indian Institute of Technology, Bombay, 400076, India.
Eur Phys J E Soft Matter. 2021 May 28;44(5):72. doi: 10.1140/epje/s10189-021-00064-3.
We have carried out Monte Carlo simulations to study the non-equilibrium aggregation of short patchy nanorods in two dimensions. Below a critical value of patch size ([Formula: see text]), the aggregates have finite sizes with small radii of gyration, [Formula: see text]. At [Formula: see text], the average radius of gyration shows a power law increase with time such that [Formula: see text], where [Formula: see text]. Above, [Formula: see text], the aggregates are fractal in nature and their fractal dimension depends on the value of patch size. These morphological differences are due to the fact that below the critical value of patch size ([Formula: see text]), the growth of the clusters is suppressed and the system reaches an 'absorbed state.' Above [Formula: see text], the system reaches an 'active state,' in which the cluster size keeps growing with a fixed rate at long times. Thus, the system encounters a non-equilibrium phase transition. Close to the transition, the growth rate scales as [Formula: see text], where [Formula: see text]. The long-time growth rate varies as [Formula: see text] where [Formula: see text]. These scaling exponents indicate that the transition belongs to the directed percolation universality class. The patchy nanorods also display a threshold patch size ([Formula: see text]), beyond which the long-time growth rate remains constant. We present geometric arguments for the existence of [Formula: see text]. The fractal dimension of the aggregates increases from 1.75, at [Formula: see text], to 1.81, at [Formula: see text]. It remains constant beyond [Formula: see text].
我们进行了蒙特卡罗模拟，以研究二维短补丁纳米棒的非平衡聚集。在补丁尺寸的临界值（[公式：见正文]）以下，聚集体具有有限尺寸且回转半径较小，[公式：见正文]。在[公式：见正文]时，平均回转半径随时间呈幂律增长，即[公式：见正文]，其中[公式：见正文]。在[公式：见正文]以上，聚集体本质上是分形的，其分形维数取决于补丁尺寸的值。这些形态差异是由于在补丁尺寸的临界值（[公式：见正文]）以下，团簇的生长受到抑制，系统达到“吸收态”。在[公式：见正文]以上，系统达到“活跃态”，其中团簇尺寸在长时间内以固定速率持续增长。因此，系统经历了非平衡相变。接近转变时，生长速率按[公式：见正文]缩放，其中[公式：见正文]。长时间生长速率随[公式：见正文]变化，其中[公式：见正文]。这些缩放指数表明该转变属于定向渗流普适类。补丁纳米棒还显示出一个阈值补丁尺寸（[公式：见正文]），超过该尺寸后，长时间生长速率保持恒定。我们给出了关于[公式：见正文]存在的几何论证。聚集体的分形维数从[公式：见正文]时的1.75增加到[公式：见正文]时的1.81。在[公式：见正文]以上它保持恒定。
