A fast insight into the nonlinear oscillation of nano-electro mechanical resonators considering the size effect and the van der Waals force

Nano/micro actuators are widely used in micro/ nano electro mechanical systems (NEMS/MEMS) and the study on its nonlinear oscillation is of great significance. This paper begins with a wrong variational principle ([19] Appl Nanosci, 2016, 6: 309-317) of the reduced governing partial differential equation of the resonator which is used to describe the nonlinear oscillation of nano-electro mechanical resonators that takes into account the size effect and the van der Waals force. By using the Semi-inverse method, we establish the genuine variational principle. Then a simple method so called He’s frequency formulation is applied to solve the problem, where it only needs one-step to get the approximate amplitude-frequency relationship. Comparing with the existing method, it shows that the proposed method is simple but effective, which is helpful to be of significance to the study of the nonlinear oscillation in micro/nano electro mechanical systems.

Aggregation modeling of the influence of pH on the aggregation of variably charged nanoparticles

The aggregation of variably charged nanoparticles is usually induced by the changes in internal and external conditions, such as solution temperature, pH, particle size, van der Waals force, and electrostatic repulsion among particles. In order to explore the effect of pH on the aggregation of variable charge nanoparticles, this paper proposed an extended model based on the 3D on-lattice Cluster–Cluster Aggregation (CCA) model. The extended model successfully established the relationship between pH and sticking probability, and used Smoluchowski theory to calculate the aggregation rate of nanoparticles. The simulation results showed that: (1) the change of the aggregation rate of the variable charge nanoparticles with pH conforms to the Gaussian distribution, (2) the initial particle concentration has a significant effect on the aggregation rate of the nanoparticles, and (3) pH can affect the competition between van der Waals force and electrostatic repulsion between particles, thereby affecting the degree of openness of clusters. The research demonstrated the extended CCA model is valuable in studying the aggregation of the variably charged nanoparticles via transforming the corresponding influence factors into the influence on the sticking probability.