Self-Assembly in Confined Microgeometries

Self-Assembly in Confined Microgeometries

Confining geometries can have a significant effect on the self-assembly of particles and the structures that they form. This is especially true for paramagnetic beads and the chains that form when a magnetic field is imposed. In an open, unbounded system, the particles will form simple linear chains that continue to grow in length. In a microduct or a small pipe, when the field is transverse to the duct or pipe, the chains must fit within the cross-section. This limits the length of the chain and biases the final position the chain will take. For example in a micro-pipe, chains are formed across the diameter if the magnetic field is perpendicular to the axis of the pipe and the number of beads is relatively small. For a larger number of paramagnetic beads several shorter chains may be formed. These may ultimately join to form a single long chain if this can fit on a diameter, or else the chains may mutually repel and form an ordered array fitting within the pipe geometry.

We have simulated the formation of such chains in both pipes with circular cross-sections and microducts with triangular cross-sections. This is illustrated below in the figure that shows a time sequence for chain formation in a triangular duct for 10 beads. The beads are color-coded to show how their relative positions change and are initially at random locations.

A second time sequence is shown below with 16 beads in the triangular duct. The width of the duct is now too short to accommodate a single chain, even along the bottom edge where the width is greatest. Instead two shorter chains are eventually formed and these drift apart through a mutual magnetic repulsion force between the chains. The precise number of beads in each chain does vary with the initial seeding and defects in a chain can occur.

If there is also a flow in the pipe or duct, driven by an applied pressure difference at the two ends, the shear flow can affect the stability of the chains.

For further details see: D. Liu, M.R. Maxey and G.E. Karniadakis, 2005. Simulations of dynamic self-assembly of paramagnetic microspheres in confined microgeometries. J. Micromech. Microeng. 15, 2298-2306.