Electrical Repulsive Energy between Two Cylindrical Particles with Finite Length: Configuration Dependence

Abstract

The electrical repulsive energy between two model cylinders was calculated by solving nonlinear PoissionBoltzmann (P-B) equation under Derjaguin approximation. Effects of the surface potential, Debye screening length, and configuration of cylinders on the repulsive interaction energy were examined. Due to the anisotropy of the shape of cylinder, the interaction repulsive energy showed dependence to the configuration of particles; cylinders aligned in end-to-end configuration showed largest repulsive energy and crossed particles had lowest interaction energy. The configuration effect is originated from the curvature effect of the interacting surfaces. The curved surfaces showed less repulsive energy than flat surfaces at the same interacting surface area. The configuration dependency of interaction energy agreed with the previous analytical solution obtained under the linearized P-B equation. The approach and results present in this report would be applicable in predicting colloidal behavior of cylindrical particles.

Sulfate-Mediated End-to-End Assembly of Gold Nanorods

“…We developed a DLVO-based particle–particle interaction model that considers both van der Waals attractive forces as well as electrostatic repulsion (details are presented in the SI; pp 13–15). We note that more complicated models considering additional attractive or repulsive forces could have been considered; however, such models require assumptions with unknown applicability to elongated nanostructures. , DLVO modeling results for CTAB-GNRs in 2 mM CaSO 4 are shown in Figure .…”

Aggregation of Elongated Colloids in Water

“…The measured ζ potentials were used to calculate the interaction energy Δϕ between sphere–sphere and rod–rod configurations (see Materials and Methods); Figure A illustrates an example calculation of the energy profile as a function of distance at pH 5.0. Previous studies indicate that for elongated particles, h is dependent on the contact configuration and that the crossed configuration presents the lowest repulsive energy (Figure C); we choose this configuration to compute the theoretical aggregation time scale of silica rods (see Materials and Methods). The comparison of theoretical and experimental time scales of aggregation suggests that the classical DLVO theory provides a good estimate of aggregation kinetics under favorable conditions (low energy barrier and pH) but increasingly overestimates the interaction energy for both silica rods and silica spheres as the energy barrier (and pH) increases.…”