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The activation energy of particle aggregation in suspensions is a very important kinetic parameter in a wide range of science and engineering applications. At present, however, there is no theory that can theoretically predict the activation energy. Because the activation energy is often less than 10 kT (where k is the Boltzmann constant and T is the temperature), it is difficult to experimentally measure. In this study, a theory for calculating the activation energy is established. Experimental measurements of the activation energy of montmorillonite aggregation were performed with different electrolyte and particle concentrations using the dynamic light scattering (DLS) technique. The validity of the theory was verified by the experiments. This study confirmed that both the method for activation energy measurements by DLS and the theory for its calculation can be applied to suspensions of polydisperse nonspherical particles. The average kinetic energy at the moment of particle collision in the aggregation process was found to be 0.2 kT, which is less than the instantaneous kinetic energy of a Brownian particle (0.5 kT) because of the viscous resistance of the water medium. This study also shows that adsorbed Na+ is strongly polarized in the electric field near the particle surface, and the polarization increases the effective charge of Na+ from +1 to +1.18.

Cambial development in the stems of perennial woody species is rigorously regulated by phytohormones. Auxin and gibberellin (GA) play crucial roles in stimulating cambial activity in poplar (Populus spp.). In this study, we show that the DELLA protein REPRESSOR of ga1-3 Like 1 (RGL1), AUXIN RESPONSE FACTOR 7 (ARF7), and Aux/INDOLE-3-ACETIC ACID 9 (IAA9) form a ternary complex that mediates crosstalk between the auxin and GA signaling pathways in poplar stems during cambial development. Biochemical analysis revealed that ARF7 physically interacts with RGL1 and IAA9 through distinct domains. The arf7 loss-of-function mutant showed markedly attenuated responses to auxin and GA, whereas transgenic poplar plants overexpressing ARF7 displayed strongly improved cambial activity. ARF7 directly binds to the promoter region of the cambial stem cell regulator WOX4 to modulate its expression, thus integrating auxin and GA signaling to regulate cambial activity. Furthermore, the direct activation of PIN-FORMED 1 (PIN1) expression by ARF7 in the RGL1-ARF7-IAA9 module increased GA-dependent cambial activity via polar auxin transport. Collectively, these findings reveal that the crosstalk between auxin and GA signaling mediated by the RGL1-ARF7-IAA9 module is crucial for the precise regulation of cambial development in poplar.