Abstract

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 (\(p_c = 0.31675\)), the aggregates have finite sizes with small radii of gyration, \(R_g\). At \(p_c\), the average radius of gyration shows a power law increase with time such that \(<R_g>\sim t^{\gamma }\), where \(\gamma =0.411 \pm 0.006\). Above, \(p_c\), 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 (\(p_{c}\)), the growth of the clusters is suppressed and the system reaches an ‘absorbed state.’ Above \(p_{c}\), 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 \(\varGamma (t) \sim t^{-\alpha }\), where \(\alpha = 0.160 \pm 0.030\). The long-time growth rate varies as \(\varGamma (\infty )\sim (p-p_c)^\beta \) where \(\beta = 0.279 \pm 0.034\). These scaling exponents indicate that the transition belongs to the directed percolation universality class. The patchy nanorods also display a threshold patch size (\(p_{t}\)), beyond which the long-time growth rate remains constant. We present geometric arguments for the existence of \(p_t\). The fractal dimension of the aggregates increases from 1.75, at \(p_c\), to 1.81, at \(p_t\). It remains constant beyond \(p_t\).

Graphic abstract

中文翻译：

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短片状纳米棒的非平衡聚集中的生长转变和临界行为

摘要

我们进行了蒙特卡罗模拟来研究二维短片状纳米棒的非平衡聚集。低于补丁大小的临界值（\(p_c = 0.31675\)），聚合体具有有限的大小，旋转半径很小，\(R_g\)。在\(p_c\) 处，平均回转半径显示幂律随时间增加，使得\(<R_g>\sim t^{\gamma }\)，其中\(\gamma =0.411 \pm 0.006\)。上面，\(p_c\)，聚合本质上是分形的，它们的分形维数取决于补丁大小的值。这些形态差异是由于低于补丁大小的临界值 ( \(p_{c}\)），群集的生长受到抑制，系统达到“吸收状态”。在\(p_{c}\)之上，系统达到“活动状态”，其中集群大小长时间以固定速率保持增长。因此，系统遇到非平衡相变。接近过渡时，增长率为\(\varGamma (t) \sim t^{-\alpha }\)，其中\(\alpha = 0.160 \pm 0.030\)。长期增长率为\(\varGamma (\infty )\sim (p-p_c)^\beta \)其中\(\beta = 0.279 \pm 0.034\)。这些缩放指数表明过渡属于有向渗透普遍性类。斑驳的纳米棒还显示阈值斑块大小 ( \(p_{t}\))，超过这个值，长期增长率保持不变。我们提出了\(p_t\)存在的几何参数。聚集体的分形维数从\(p_c\)处的 1.75 增加到\(p_t\)处的 1.81 。它在\(p_t\)之外保持不变。

图形摘要