Analysis of the field-assisted permanent assembly of oppositely charged particles

We characterize experimentally and analyze analytically a novel electric-field-assisted process for the assembly of permanent chains of oppositely charged microparticles in an aqueous environment. Long chains of oppositely charged particles are rapidly formed when an external electric field is applied and break up into permanent linear fragments upon switching off the field. The resulting secondary chains are stabilized by attractive electrostatic and van der Waals interactions between the particles. We find that the length of the permanent chains is strongly dependent on the relative size (microsphere diameter D) of small and large particles and can be tuned by varying the particle size ratio s = Dsm/Dlg and particle number ratio r = Nsm/Nlg. Three latex microsphere systems of different particle size ratio, s = 0.9, 0.45, and 0.225, were characterized at different particle number ratios r by determining experimentally the length distribution of the permanent chains. The results are compared with statistical models based on a one-step or two-step process of forming the primary chains. We find that the one-step model is applicable to the system of similarly sized particles (s = 0.9) and the two-step chaining model is applicable to the system of dissimilarly sized particles (s = 0.225), where the large particles form chains first and the small ones serve as binders, which are later drawn in the junctions. Long permanent chains are formed only from particles of dissimilar size for which our model predicts a linear increase in the mean chain length with increasing r. On the basis of these results, we formulate a set of assembly rules for permanent colloidal chain formation by oppositely charged particles. The results make possible the precise large-scale formation of particle chains of any length, which can serve as components in new gels, biomaterials, and fluids with controlled rheology.