We present a detailed study of the kinetic cluster growth process during gelation of weakly attractive colloidal particles by means of experiments on critical Casimir attractive colloidal systems, simulations, and analytical theory. In the experiments and simulations, we follow the mean coordination number of the particles during the growth of clusters to identify an attractive-strength independent cluster evolution as a function of mean coordination number. We relate this cluster evolution to the kinetic attachment and detachment rates of particles and particle clusters. We find that single-particle detachment dominates in the relevant weak attractive-strength regime, while association rates are almost independent of the cluster size. Using the limit of single-particle dissociation and size-independent association rates, we solve the master kinetic equation of cluster growth analytically to predict power-law cluster mass distributions with exponents $-3/2$ and $-5/2$ before and after gelation, respectively, which are consistent with the experimental and simulation data. These results suggest that the observed critical Casimir-induced gelation is a second-order nonequilibrium phase transition (with broken detailed balance). Consistent with this scenario, the size of the largest cluster is observed to diverge with power-law exponent according to three-dimensional percolation on approaching the critical mean coordination number.

中文翻译：

---

胶体凝胶非平衡主动力学方程建模。

我们通过对关键的卡西米尔吸引胶体系统进行实验，模拟和分析理论，对弱吸引胶体颗粒凝胶化过程中动力学簇生长过程的详细研究。在实验和模拟中，我们遵循簇生长过程中颗粒的平均配位数，以确定吸引力强度独立的簇演化与平均配位数的关系。我们将这种团簇演化与粒子和粒子团簇的动力学附着和脱离速率联系起来。我们发现，在相关的弱吸引力强度机制中，单颗粒脱离占主导地位，而缔合率几乎与簇大小无关。利用单粒子解离的极限和尺寸无关的缔合速率，$-3/2$ 和 $-5/2$凝胶化之前和之后，分别与实验和模拟数据一致。这些结果表明，观察到的关键的卡西米尔引起的胶凝是二阶非平衡相变（具有破坏的详细平衡）。与这种情况一致，根据接近临界平均配位数的三维渗流，观察到最大簇的大小与幂律指数有差异。