Boundary Mobility Controls Glassiness in Confined Colloidal Liquids

Gary L. Hunter, Kazem V. Edmond, and Eric R. Weeks

Phys. Rev. Lett. 112, 218302 – Published 27 May 2014

Abstract

We use colloidal suspensions encapsulated in emulsion droplets to model confined glass-forming liquids with tunable boundary mobility. We show that the dynamics in these idealized systems are governed by physical interactions with the boundary. Gradients in dynamics are present for more mobile boundaries, whereas for less mobile boundaries, gradients are almost entirely suppressed. The motions in a system are not isotropic but have a strong directional dependence with respect to the boundary. These findings bring into question the ability of conventional quantities to adequately describe confined glasses.

Received 12 March 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.218302

Authors & Affiliations

Gary L. Hunter^1,*,†, Kazem V. Edmond^1,†, and Eric R. Weeks¹

¹Department of Physics, Emory University, Atlanta, Georgia 30322, USA

^*GLHunter@gmail.com
^†Present address: Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003, USA.

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Vol. 112, Iss. 21 — 30 May 2014

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Images

Figure 1
Colloidal suspensions encapsulated within emulsion droplets. (a),(b) Raw confocal images of confined colloids at $ϕ = 46 %$ with (a) $η_{x} = 5.7 mPa s$ and $R = 14.4 μ m$ , and (b) $η_{x} = 15.2 mPa s$ and $R = 14.1 μ m$ . Movies of these data are included in the Supplemental Material [28]. Note that these data are from separate experiments and that droplets are not physically near one another. (c),(d) Two-dimensional trajectories of the larger species of particles from the data immediately above. Motions are shown over a period of 600 s. Voids apparent in (c),(d) are due to untracked particles slightly out of the focal plane of the microscope. Bulk translational motions are subtracted with standard particle tracking routines [26], and bulk rotational motions are subtracted with a modified version of the procedures described in Ref. [27]. (e) Mean-square displacements for the large particles in the droplets shown. Light symbols (orange in color) correspond to data in (a),(c). Dark symbols (purple in color) correspond to data in (b),(d). The solid line is the MSD for an unconfined suspension at $ϕ = 46 %$ , and the dashed line has a slope of unity for comparison to Brownian diffusion.
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Figure 2
MSDs at $Δ t = 30 s$ of particles in droplets of different $ϕ$ and different $η_{x}$ as a function of drop radius. Open symbols correspond to $ϕ = 33 %$ , and solid symbols are for $ϕ = 46 %$ . Light symbols (orange in color) are for $η_{x} = 5.7 mPa s$ , and dark symbols (purple in color) are for $η_{x} = 15.2 mPa s$ . Dashed horizontal lines are $⟨ Δ r^{2} (30 s) ⟩$ in unconfined samples at the same $ϕ$ . Data with $ϕ = 46 %$ are from two-dimensional confocal images at the equatorial plane of the droplets, whereas data with $ϕ = 33 %$ are from three-dimensional confocal images of the entire droplets. For meaningful comparison, we scale data for $ϕ = 33 %$ , such that $⟨ Δ r^{2} ⟩ = (2 / 3) ⟨ Δ x^{2} + Δ y^{2} + Δ z^{2} ⟩$ , whereas for data at higher $ϕ$ , $⟨ Δ r^{2} ⟩ = ⟨ Δ x^{2} + Δ y^{2} ⟩$ .
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Figure 3
Mobility as a function of interfacial distance. (a),(b) Particle mobility $Δ r = \sqrt{Δ r_{r}^{2} + Δ r_{θ}^{2}}$ as a function of distance $s$ from the fluid-fluid interface for systems with $ϕ = 46 %$ and at $Δ t = 30 s$ . Data are from two-dimensional confocal images at the equatorial plane of the droplets and so include only one angular direction tangential to the interface. Data in the left panels (a),(c),(e) have $η_{x} = 5.7 mPa s$ and right panels (b),(d),(f) have $η_{x} = 15.2 mPa s$ . Droplets decrease in size from light to dark (orange to black in color). Where the data terminate at larger distances is approximately the droplet radius. See Tables II and III in Ref. [28] for precise radii. (c),(d) Radial components $Δ r_{r}$ , and (e),(f) tangential components $Δ r_{θ}$ of particle mobility.
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