Rouwhorst Joep, Schall Peter, Ness Christopher, Blijdenstein Theo, Zaccone Alessio
Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge CB3 0AS, United Kingdom and School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, United Kingdom.
Phys Rev E. 2020 Aug;102(2-1):022602. doi: 10.1103/PhysRevE.102.022602.
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.
我们通过对临界卡西米尔吸引胶体系统进行实验、模拟以及运用解析理论，对弱吸引胶体颗粒凝胶化过程中的动力学团簇生长过程展开了详细研究。在实验和模拟中，我们追踪团簇生长过程中颗粒的平均配位数，以确定作为平均配位数函数的与吸引强度无关的团簇演化。我们将这种团簇演化与颗粒及颗粒团簇的动力学附着和脱离速率联系起来。我们发现，在相关的弱吸引强度区域，单颗粒脱离起主导作用，而缔合速率几乎与团簇大小无关。利用单颗粒解离极限和与大小无关的缔合速率，我们解析求解了团簇生长的主动力学方程，以预测凝胶化前后幂律团簇质量分布的指数分别为 -3/2 和 -5/2，这与实验和模拟数据一致。这些结果表明，所观察到的临界卡西米尔诱导凝胶化是一种二级非平衡相变（具有破缺的细致平衡）。与这种情况一致的是，在接近临界平均配位数时，观察到最大团簇的大小根据三维渗流以幂律指数发散。
