# Difference between revisions of "Patterned Colloidal Deposition Controlled by Electrostatic and Capillary Forces"

Figure 1. Deposition of charged colloidal particles controlled by micropatterned ionic self-assembled monolayers. (a) Positively charged spheres attach to negatively charged regions of a wet template. The inset shows a scanning electron micrograph of the substrate geometry. (b) The structures focus due to capillary forces as the template dries. (c) Positively charged colloids deposited from a 0.005M LiCl solution. (d) Negatively charged spheres attach to positively charged regions.

The deposition and self-assembly of charged colloidal particles can be controlled using substrates chemically micropatterned with either positively or negatively charged regions. In this process, electrostatic forces first cause colloids to be attracted to the region of the substrate of the opposite charge. Then additional ordering of the colloidal particles occurs as the suspension dries due to lateral capillary interactions. This technique enables the fabrication of complex two-dimensional arrays of colloidal particles.

## General Information

Authors: Joanna Aizenberg, Paul V. Braun, and Pierre Wiltzius.

Date: March 27, 2000.

Lucent Technologies, Bell Laboratories, Murray Hill, NJ 07974, USA

Physical Review Letters, vol. 84, no. 13, 2997-3000. [1]

## Summary

Self-assembly on its own produces close-packed 2D and 3D arrays of colloidal particles rather easily. More complex patterns can be produced by aiding self-assembly with electrostatic forces, using a substrate that has charged regions arranged in very specific and controlled patterns. Microcontact printing can be used to chemically pattern a surface at the micron scale. The deposition of colloidal particles onto a patterned surface is called colloidal epitaxy.

Here the authors used self-assembled monolayers (SAMs) with ionic regions as templates for the deposition of charged colloids. The authors found that, as expected, the charged colloidal particles preferred to interact with regions of oppositely charged SAMs (see Figures 1a, 1d). The preference was particularly apparent when the substrate consisted entirely of positively or negatively charged SAMs, without any neutrally-charged regions.

Within each circular ionic SAM region, the oppositely charged colloidal particles clustered within some radius less than the radius of the entire charged domain. This outer depletion region originates from the screened length in Coulomb interactions. The electrostatic interaction energy between the particles and surface can be estimated using a superposition approximation:

$\Delta V \approx \epsilon \Psi_1 \Psi_2 \frac{a_1 a_2}{L} e^{- \kappa (L - a_1 - a_2)}$

Here, $\epsilon$ is the dielectric constant, $\Psi$ is the surface potential of each particle, $a_1$ and $a_2$ are the particles' radii, $L = a_1 + a_2 + h$ is the distance between the particle centers, and $1/\kappa$ is the Debye-Hückel length. When LiCl solution was used with the colloids, the salt had the effect of suppressing Coulomb interactions, decreasing the screened length and enabling each circular charged region of the substrate to become more populated by colloidal particles (see Figure 1c).

Interestingly, as the template dried, the positively charged particles within each negatively charged region moved toward the centers of these regions, forming more dense clusters (see Figure 1b). The authors conclude that this is due to capillary forces that appear between the particles once they are only partially immersed in a layer of liquid. It can be shown that as the liquid surface descends, the energy of capillary attraction will at some point exceed that of the electrostatic interaction, and this is when the clusters should begin to focus.

Figure 2. Schematic of the proposed mechanism of particle ordering in the fabrication of ordered 2D arrays of single colloidal particles.

The authors also found that they could carefully manipulate the fabrication of ordered 2D patterns of single colloidal spheres with a combination of electrostatic and capillary forces. Of note is the fact that in this scenario, where the SAM regions are very small, the colloidal particles become quite focused at the centers of each circular region, and only one particle will occupy any given region. Only one sphere will occupy any given circular SAM region because of screened Coulomb interactions. The fact that they are particularly well centered in these domains is due to the fact that the last drops of water can be found in these circular regions. If a particle here is off-center, the contact line will be asymmetric, and a horizontal force will drive the sphere toward the center of the drop (see Figure 2).

## Connection to soft matter

In this paper, the authors report an experiment that utilizes two basic interactions in soft matter and uses them to control colloidal self-assembly. The fact that charged colloidal particles will prefer to interact with oppositely-charged SAM regions is not surprising. It is more interesting that the density with which they populate the SAM regions and the radius that they fill on these domains can be seen as a direct manifestation and function of the screened length in Coulomb interactions. In this sense, Coulomb interactions can be seen as driving self-assembly and, in particular, the salt concentration of the solution is a key parameter that determines the nature of the resulting self-assembled microstructures.

Also noteworthy here is the discovery that capillary forces affect the self-assembled colloidal particles as the template dries. Since the electrostatic interaction and the capillary interactions can be seen as separate stages of the self-assembly process in this system, the capillary interaction has the effect of focusing or refining the pattern initially formed due to Coulomb interactions. That this process can be used to produce 2D ordered patterns of microspheres with exceptional regularity and positional precision is particularly intriguing for its application potential to other research.