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Abstract
Clusters of spherical particles are called "colloidal molecules" because they adopt structures that resemble those of true molecules. In this analogy, the particles are the atoms, the attractive interactions between them are bonds, and the different structures that appear in equilibrium are isomers. We take this analogy a step further by doping colloidal molecules with colloidal "isotopes," particles that have the same size but different bonding energies from the other particles in the system. Our molecules are two-dimensional clusters consisting of polystyrene and silica microspheres held together by depletion interactions. Using a combination of optical microscopy and particle tracking, we examine an ensemble of 4- and 5-particle molecules at different isotope ratios. We find that the isotopes tend to segregate to particular positions in the various isomers. We explain these findings using a statistical mechanical model that accounts for the rotational entropy of the isomers and the different interaction potentials between the different types of particles. The model shows how to optimize the yield of any particular isomer, so as to put the isotopes in desired locations. Our experiments and models show that even in systems of particles with isotropic interactions, the structures of self-assembled molecules can in principle be controlled to a surprisingly high extent.
Highlights
We take this analogy a step further: we consider how “isotopes” are incorporated into equilibrium colloidal molecules
In even the smallest molecules, containing 4 particles, we find that certain isomers occur more frequently than others. 4-particle molecules containing three particles of one isotope and a single dopant of the other, P3S1 and P1S3, each have two isomers: the dopant can can be on the short axis or the long axis of the diamond-shaped ground state (Figure 3)
To independently verify the fitted values, we examine the homogeneous 3- and 4-particle molecules found in the same experimental data set, and we measure the absolute values of κ for P-P and S-S bonds by comparing the number of rigid molecules to the numbers of excited-state molecules with fewer than 2N − 3 bonds using the method of Holmes-Cerfon et al, 26 which we previously used in 6-particle homogeneous clusters
Summary
We take this analogy a step further: we consider how “isotopes” are incorporated into equilibrium colloidal molecules. In our colloidal system, isotopes are two different kinds of microspheres (silica and polystyrene) that have different masses (silica being twice as dense as polystyrene) and different bonding energies but the same sizes. In the presence of a depletion attraction, the particles attract one another to form two-dimensional (2D) colloidal molecules with networks of bonds composed of equilateral triangles (Figure 1). The reason we call these particles “isotopes” is that their identical sizes preserve the bond angles. If the two species had different sizes, the smaller species could be coordinated by more than 6 particles of the larger species, making it unlikely for the particles to form an equilaterial triangular bond network. Because our two types of particles have the same size, one can be substituted for another without changing the bond network, just as with true atomic isotopes
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