Dynamic stabilization of Janus sphere trans-dimers

We experimentally investigated the self-assembly of chemically active colloidal Janus spheres into dimers. The trans-dimer conformation, in which the two active sites are oriented roughly in opposite directions and the particles are osculated at their equators, becomes dominant as the hydrogen peroxide fuel concentration increases. Our observations suggest high spinning frequency combined with little translational motion is at least partially responsible for the stabilization of the trans-dimer as activity increases.

Figure 1

Top left: the conformation of a dimer is characterized by a pair of angles $(\alpha ,{\alpha }^{\prime })$. Top right: an example video frame of a single dimer; the dark section shows the location of the platinum (Pt) and the rest of the particle is silica. Bottom: in analogy with cis-trans isomers of alkenes, the cis-conformation $(\frac{\pi }{2},-\frac{\pi }{2})$ has a plane of symmetry and moves rectilinearly while the trans-conformation $(\frac{\pi }{2},\frac{\pi }{2})$ rotates in-place.

Figure 2

Symmetry operations of Janus sphere dimers and their effects on conformation and dynamical characteristics. (Left) Reflection $M_{\perp }$ through the vertical plane tangent to both spheres at the contact point, (middle) reflection $M_{\parallel }$ through the vertical plane containing both sphere centers and the contact point, and (right) ${180}^{\circ }$ rotation $R_{\pi }$ about the contact point.

Figure 3

(a) The density plot represents the intensity of the torque applied to the entire range of possible dimer conformations. The shaded regions show positive (counterclockwise - red) and negative (clockwise - purple) rotation primarily in the top right and bottom left regions of the density plot, respectively. Example dimer conformations are overlaid on the density plot. Physically, each of the four regions bordered by the diagonal lines (solid and dashed) contain identical dimers to each of the other three regions when only dynamics is considered (and chirality is disregarded). Thus, the dimers in the four regions can be mapped into a single triangular quadrant. We arbitrarily chose the quadrant marked as “I” for this mapping. (b) After mapping, the quadrant I is rotated by $\frac{\pi }{4}$ and the axes are adjusted to run from 0 to $\pi$. The dashed semicircles show the boundary for the region considered to be in the trans-conformation (top-left red region) and for the cis-conformation (bottom region) for the experimentally measured data points.

Figure 4

(a) Data points for different concentrations of hydrogen peroxide $C_{{\text{H}}_2{\text{O}}_2}$ are color-coded the following way: blue and green circles and squares represent low concentrations and red and yellow stars represent higher concentrations. The dashed blue rectangular section is magnified to the right of the plot in order to better resolve the data points in that region, and the values of hydrogen peroxide concentration are to the left of the inset. The data points that fall within the semicircles are considered to be in the “experimentally” trans-conformation (top left) or cis-conformation (bottom center). (b) The data points show the percentage of dimers which were found to be in the trans-conformation (black squares) or the cis-conformation (yellow circles with red outline) as a function of hydrogen peroxide concentration. The red (dashed) and black (dotted) lines show the linear fit for the percentage of cis- and trans-dimers, respectively; the blue (solid) line shows a Langmuir fit to the trans-dimer data.

Figure 5

(a) Interaction between two individual Janus spheres leads to a collapsing spiral ending in collision and dimer formation. (b) A dimer separates from an aggregate and the spheres slide over each other toward the trans conformation, but there does not seem to be rotation of the dimer as a whole as in (a), and the spheres eventually part ways. (c) A third particle fails to incorporate into a cluster for what appears to be a similar reason. The dimer is just spinning as it passes by. (d) A third particle (yellow dot) approaches a dimer, but is in an unfavorable position to be incorporated as it is pushed away by the particle marked by a blue square.