Impact of particle-size polydispersity on the quality of thin-film colloidal crystals

TL;DR

The paper addresses how particle-size polydispersity affects the quality of thin-film colloidal crystals produced by vertical drying. It employs a systematic experimental approach with silica batches spanning $PD$ from $6.3\%$ to $14.6\%$, using SEM, DLS, SLS, FIB-SEM, and UV-Vis to quantify 2D and 3D order via $g(r)$ and the local order parameter $\Psi_6$. Key findings show pronounced reductions in both long-range and local order as $PD$ increases, with two notable drops around $8\%$ and $12\%$, and evidence supporting an epitaxial-like growth mechanism in convective assembly. The work establishes empirical limits for crystallization in polydisperse systems and informs the feasibility of creating colloidal-crystal thin films from more polydisperse or sustainably synthesized particles.

Abstract

Size polydispersity in colloidal particles can disrupt order in their self-assembly, ultimately leading to a complete suppression of crystallization. In contrast to various computational studies, few experimental studies systematically address the effects of size polydispersity on the quality of colloidal crystals. We present an experimental study of structural order in thin films of crystals vertically dried from colloidal dispersions with a systematically varying polydispersity. As expected, an increase in polydispersity leads to a deterioration in order with significant drops in the local bond-orientational order at 8% and 12% polydispersity. Our results align with previously suggested models of epitaxial-like growth of 2D layers during convective assembly. Our results can offer critical insights into the permissible limits for achieving colloidal crystals from more polydisperse systems such as those synthesized through more sustainable methods.

Figures (5)

• Figure 1: SEM images of (a) 6.5% and (b) 10.8% polydispersity silica. The scale bars are 0.5 $\mu$m. (c), (d) The corresponding particle size distributions, from measuring 1000 particle diameters, fitted with normal distribution.
• Figure 2: (a) Schematic of vertical drying setup. (b) Photograph of vials containing low (6.3%, left) and high (14.6%, right) polydispersity colloidal assemblies on the interior, showing difference in appearance (iridescence) of samples. SEM images (top view) of self-assemblies of (c) 6.3%, (d) 9.1% and (e) 14.6% polydispersity silica batches. All scale bars are 1 $\mu$m.
• Figure 3: Characterization of 2D order in assemblies. (a) Radial distribution function ($g(r)$) computed from SEM images of assemblies of low (6.3%), intermediate (9.1%) and high (14.6%) polydispersity silica particles. The grey lines show the peak positions for a perfectly hexagonal system with the same (average) number of particles. The dashed line at $g(r)$=1 shows the convergence of the functions at larger radial distances. The horizontal axis has been scaled such that the position of the first peak is 2. (b) Average local six-fold bond-order parameter ($\left< \Psi_6 \right>$) for assemblies made from silica with polydispersities ranging from 6-15%. (c) A comparison of the polydispersity (in dried samples) from the starting dispersion, assembly and leftover dispersion (after vertical drying) for low, intermediate and high polydispersity silica batches. (d-f) $\psi_6$ of particles in 6.3%, 9.1% and 14.6% polydispersity silica assemblies computed from SEM images in Figure \ref{['fig:crystals']}(c-e).
• Figure 4: Characterization of 3D order in assemblies. (a), (b) SEM view of cross section of assemblies from low (6.3%) and high (14.6%) polydispersity silica with position of the substrate labeled. The scale bars are 1 $\mu$m. The faint vertical lines seen in (b) are an imaging artefact ('curtaining'), which is typical in FIB-SEM when encountering increased surface roughness giannuzzi2004introduction. (c) Transmission spectra of assemblies of low (6.3%), intermediate (9.1%) and high (14.6%) polydispersity silica. The transmission intensity has been normalized by incident intensity. The errors, shown as shaded regions, have been calculated from multiple runs, with each run performed on a different sample fabricated from the same particle batch. (d) Average local six-fold bond-order parameter ($\left <\Psi_6 \right>$) for layers in a low polydispersity (6.3%) assembly sample.
• Figure S1: Average particle diameter of silica batches vs. local six-fold bond-order parameter of their assemblies.