Films of colloidal particles, from the nanometer to micron scale, have a variety of materials applications, such as photonic devices, biosensors and high-density patterned magnetic memory. Precise control of the two- and three-dimensional architectures is critical for the function of these materials, and self-assembly of the particles in solution onto surfaces is a widely proposed method for their “bottom-up” construction. The synthetic conditions for the desired self-assembly, though, are difficult to know a priori, and experiments must be done to determine them. These experiments and subsequent characterization are expensive and time-consuming. Simulation of the synthesis of these films offers a means to understand the formation and properties of these materials and accelerate their development by testing synthetic strategies computationally.
With these simulations, several parametric studies have been performed to: 1) Evaluate strategies to form particulate films by varying particle sizes and translational freedom and patterning the surface; 2) Determine the kinetics of self-assembly and whether the structures are kinetic traps or thermodynamic equilibrium; and 3) Determine the mechanism and frequency of defect formation and how to minimize it.
Figure 1. Schematic of model system studied by us (Gray et al. 2000, 2001) for the adsorption of tethered nanoparticles. Steric stabilization prevents particle aggregation and irreversible “sticking” to the substrate. In the simulation van der Waals interactions keep the particles in contact with the substrate, forming a pseudo-two-dimensional system. Each particle has a tether with a functional group that can attach to the substrate and form an anchor. The tether restricts the particle mobility to within a circle of radius L.
In this theoretical study (Gray et al. 2000, 2001) we simulated the formation of two-dimensional films of nanoparticles that are attached to a surface via molecular tethers (figure 1), which might be derived from polypeptide chains, strands of DNA or semiconducting polymers. The particles are added to a random position on the surface one-by-one following random sequential addition (RSA). If a particle overlaps with other particles, the addition is rejected. In between attempts to add particles, the other attached particles on the surface are allowed to diffuse for a long-time to equilibrate on the surface.
Figure 2: Polydispersity/tether length (non-dimensionalized by the particle radius) phase diagram for adsorption of polydisperse tethered particles. The symbols represent liquid (cross), hexatic (triangle) and crystal (circle) phases. Dashed lines represent approximate phase boundaries, and hatched regions denote uncertain areas.
By tuning the length of the tethers relative to the radius of the particles (L/R), we found that the microstructure could be varied from a disordered liquid-like state (L/R < 1.5) to a hexatic crystal (1.5<L/R<4) to a triangular crystal (L/R > 4). The effect of particle-polydispersity was also studied, and a tether-length/polydispersity phase diagram was constructed as shown in Figure 2. As can seen particle polydispersity should not exceed about 5-7%, otherwise the ordering will be disrupted. In addition to the phase behavior, the kinetics of the process was also quantified. This computational study demonstrated the feasibility of using molecular tethers for controlling order-disorder in 2D nanoparticulate films and set targets for the tether-lengths and maximum polydispersity of the particles for order to help chemists and materials scientists synthesize these materials.