Dissipative self-assembly of colloidal suspensions

Abstract

Suspensions of paramagnetic colloids exhibit kinetic arrest in strong magnetic fields. Through a dissipative process of toggling the field on and off, suspensions self-assemble into dense and dynamic steady-state phases. Based on the domain elongation, alpha- and contour-shapes, and degree of phase separation, we construct a phase diagram using a k-means clustering analysis. We identify six characteristic structural regimes: a structureless phase, an arrested structure, sheets, ribbons, a spiky phase, and a transient fluid-fluid regime. We further report the distribution and alignment of domains and the generality of the results. We model self-assembled domain shapes using an equilibrium mean-field magnetostatic energy calculation, which predicts the surprising emergence of highly-anisotropic structures driven by the sample's confinement.

Figures (17)

• Figure 1: (A) Experimental apparatus for magnetically-guided self-assembly. Equipment housed in the microgravity glovebox on the International Space Station. (B) Schematic representation of key coil assembly components. (C) Field-parallel "ST" and field-perpendicular "RT" microscopy images. The field axis, denoted $H$, corresponds to the laboratory $x$-axis. The vertical dimension on the ST view is the laboratory $z$-axis, corresponding to the length of the 50 mm capillary. The horizontal dimension on the ST view corresponds to the laboratory $y$-axis. (D) Time evolution of the suspension structure at field strength $H_0 = 2276~\mathrm{A/m}$, frequency $\nu = 2~\mathrm{Hz}$, and duty ratio $\xi = 0.20$.
• Figure 2: (A--E) Sample kinetics of structure formation for various suspension steady states. Top halves show raw images, bottom halves are brightness- and contrast-equalized to highlight structure. The dark regions are two-dimensional projections of self-assembled colloidal aggregations, the bright regions are particle-dilute background. Steady states are differentiated by field conditions which are encoded into the symbols on the leftmost panel of each row; the legend for these symbols is given in Fig. \ref{['fig:kinetics']}.
• Figure 3: (A) Growth kinetics of the suspension are shown with the average transmitted light intensity through the sample cell ($\bar{I}$) versus experiment time. Average intensities are computed over one-minute intervals. (B) The collapsed curves where intensity is normalized and bound to $[0,1]$ through transformation to $\tilde{I}$ where $\tilde{I}=(\bar{I}-\bar{I}_\mathrm{min})/\max(\bar{I}-\bar{I}_\mathrm{min})$. Experiment time is made dimensionless as $t/t_{1/2}$ where $t_{1/2}$ is the time at which $\tilde{I}$ reaches half of its maximum.
• Figure 4: Video micrographs of the steady-state suspension structure. Toggle frequency ($\nu$) and duty ratio ($\xi$) are varied at a constant field strength $H_0 = 2276~\mathrm{A/m}$. Red, purple, orange, green, blue, and gray backgrounds denote the structure as being ribbons, spiky, sheets, arrested, fluid-fluid, and structureless phases, respectively, as identified in Section \ref{['sec:phasediagram']}. The dimensions of each image are $700~\upmu\mathrm{m}\times 700~\upmu\mathrm{m}$. The particle diameter is $2R = 1.05~\upmu\mathrm{m}$.
• Figure 5: (A) Area-weighted average dimensionless lengths ($\langle \tilde{L}\rangle$) and thicknesses ($\langle \tilde{T}\rangle$) of aggregates imaged with the field-parallel (ST) camera. These dimensions are nondimensionalized by the particle diameter, $2R=1.05~\upmu\mathrm{m}$. (B) Area-weighted average elongation, $\langle E\rangle$, as a function of aggregate number density in the micrograph. As $\langle E\rangle$ increases, the number of objects decreases, implying continued aggregation. (C) Schematic of the triaxial ellipsoid used to approximate aggregate geometry. The semi-axis $a$ always runs along the field axis, while $b$ and $c$ are the in-plane semi-axes; the measured in-plane thickness, $T$, is less than or equal to the measured length, $L$. The particle radius is given by $R$.