Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
J Chem Phys. 2013 Mar 14;138(10):104908. doi: 10.1063/1.4794695.
We present an approximation scheme to the master kinetic equations for aggregation and gelation with thermal breakup in colloidal systems with variable attraction energy. With the cluster fractal dimension df as the only phenomenological parameter, rich physical behavior is predicted. The viscosity, the gelation time, and the cluster size are predicted in closed form analytically as a function of time, initial volume fraction, and attraction energy by combining the reversible clustering kinetics with an approximate hydrodynamic model. The fractal dimension df modulates the time evolution of cluster size, lag time and gelation time, and of the viscosity. The gelation transition is strongly nonequilibrium and time-dependent in the unstable region of the state diagram of colloids where the association rate is larger than the dissociation rate. Only upon approaching conditions where the initial association and the dissociation rates are comparable for all species (which is a condition for the detailed balance to be satisfied) aggregation can occur with df = 3. In this limit, homogeneous nucleation followed by Lifshitz-Slyozov coarsening is recovered. In this limited region of the state diagram the macroscopic gelation process is likely to be driven by large spontaneous fluctuations associated with spinodal decomposition.
我们提出了一种用于胶体系统中聚合和胶凝的主动力学方程的逼近方案，该胶体系统具有可变的吸引能和热断裂。通过将可逆聚类动力学与近似流体力学模型相结合，以簇分形维数 df 作为唯一的唯象参数，预测了丰富的物理行为。通过将可逆聚类动力学与近似流体力学模型相结合，以簇分形维数 df 作为唯象参数，以封闭形式解析地预测了粘度、胶凝时间和簇大小作为时间、初始体积分数和吸引力的函数。分形维数 df 调节了簇大小、滞后时间和胶凝时间以及粘度的时间演化。在胶体状态图的不稳定区域中，聚集转变是强烈的非平衡和时变的，其中缔合速率大于离解速率。只有在接近初始缔合和离解速率对于所有物种都是可比的条件下（这是满足详细平衡的条件），聚集才能发生，并且 df = 3。在这个极限下，恢复了均相成核随后是 Lifshitz-Slyozov 粗化。在状态图的这个有限区域中，宏观胶凝过程可能由与旋节分解相关的大自发波动驱动。
