Liquid-Liquid Phase Separation in an Elastic Network

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Liquid-Liquid Phase Separation in an Elastic Network

Robert W. Style, Tianqi Sai, Nicoló Fanelli, Mahdiye Ijavi, Katrina Smith-Mannschott, Qin Xu, Lawrence A. Wilen, and Eric R. Dufresne

Phys. Rev. X 8, 011028 – Published 16 February 2018

Abstract

Living and engineered systems rely on the stable coexistence of two interspersed liquid phases. Yet, surface tension drives their complete separation. Here, we show that stable droplets of uniform and tunable size can be produced through arrested phase separation in an elastic matrix. Starting with a cross-linked, elastic polymer network swollen by a solvent mixture, we change the temperature or composition to drive demixing. Droplets nucleate and grow to a stable size that is tunable by the network cross-linking density, the cooling rate, and the composition of the solvent mixture. We discuss thermodynamic and mechanical constraints on the process. In particular, we show that the threshold for macroscopic phase separation is altered by the elasticity of the polymer network, and we highlight the role of correlations between nuclei positions in determining the droplet size and polydispersity. This phenomenon has potential applications ranging from colloid synthesis and structural color to phase separation in biological cells.

Received 5 October 2017
Revised 17 December 2017

DOI:https://doi.org/10.1103/PhysRevX.8.011028

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Phase separation

Colloids Gels

Polymers & Soft MatterPhysics of Living SystemsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Robert W. Style^1,*, Tianqi Sai¹, Nicoló Fanelli¹, Mahdiye Ijavi¹, Katrina Smith-Mannschott¹, Qin Xu¹, Lawrence A. Wilen², and Eric R. Dufresne¹

¹Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
²Center for Engineering Innovation and Design, School of Engineering and Applied Sciences, Yale University, New Haven, Connecticut 06520, USA

^*robert.style@mat.ethz.ch

Popular Summary

Clouds in the sky, vibrant colors in bird feathers, and tiny droplets that serve as mini chemical reactors within living cells all depend on phase separation, where two intermingled materials spontaneously separate. While ubiquitous in nature, it is very hard to artificially control phase separation to the point where researchers can precisely tune the structure of materials. Achieving such control could lead to the synthesis of microstructures with novel electrical or optical properties. Motivated by observations of phase separation inside cells, we study how liquids phase separate in the presence of a polymer network. We show that the network causes growing liquid droplets to stop growing at a uniform, controllable size, which allows us to easily make bulk polymeric materials with a well-defined microstructure.

We make gels by swelling a silicone gel with a mixture of two liquids. Upon cooling, these liquids phase separate and form uniform, micrometer-sized droplets. The size of the droplets can be tuned by varying parameters such as the gel stiffness, the cooling rate, and the total temperature change during cooling. We also demonstrate the generality of our technique by showing that it works for a selection of polymer gels and for different varieties of phase separation.

The resulting materials provide a new path toward making stretchable structural colors, nanoparticles, and flexible composites. Our results also have implications for the physiology of cells, which control multiple processes through the condensation of proteins in a viscoelastic environment.

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Vol. 8, Iss. 1 — January - March 2018

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Figure 1
Phase separation of a liquid mixture in a polymer network. (a)–(c) Schematic diagram of simple liquid-liquid phase separation in a system with an upper-critical solution temperature. Point (i) on the phase diagram indicates a marginally stable mixture where the majority component $B$ is saturated with a dilute component $A$ . Upon cooling to (ii), the system spontaneously separates into two phases, a continuous phase (iii) with a low concentration of $A$ and a droplet phase rich in $A$ (iii’). (d,e) Schematics of (d) a polymer network swollen by a mixture of $A$ and $B$ [at point (i) in the phase diagram], and (e) the same system after quenching to (ii) and phase separating. Note that the droplet must deform the network in order to grow beyond the mesh size.
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Figure 2
Droplets formed by phase separation of fluorinated oil in silicone gels. (a) Examples of droplets formed in a soft (top) and stiff (bottom) gels. Examples in the left column have a lower loading than the right column, as they are saturated at $37 / 44 ° C$ respectively, before being cooled at a rate of $1.5 ° C / \min$ to $23 ° C$ . Note that some of the droplets appear to have other droplets embedded within them, or some sort of substructure. In fact, this corresponds to the imaging of other droplets that lie behind the current plane of focus. (b) Examples of typical droplet distributions in different stiffness gels, each saturated at $44 ° C$ . (c) The dependence of droplet size on stiffness and saturation temperature. Data points are centered on the average value, and the error bars indicate the standard deviation. In each panel, $P$ is calculated using Eq. (1).
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Figure 3
Rate dependence of droplet size and polydispersity. (Top panel) The mean droplet radius reduces roughly logarithmically with the cooling rate. Here, the error bars are the standard deviation $σ$ of the droplet size distribution. (Bottom panel) The polydispersity ( $σ / μ$ ) is effectively independent of the cooling rate. Note that $E = 186 kPa$ , and the sample is saturated at $40 ° C$ . Thus, $c / c_{sat} = 1.37$ .
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Figure 4
Optical properties of self-assembled composites of uniform fluorinated-oil droplets in a silicone-gel matrix. (a) The light-scattering pattern of a helium-neon laser by a sample ( $E = 837 kPa$ silicone gel saturated with fluorinated oil at $40 ° C$ and cooled at $30 ° C / \min$ ) has a clear ring, indicating droplet uniformity. The center of the dark ring is at a scattering angle of 6.5°. The vertical, dark line is a beam stop. (b) Different wavelengths of light are scattered to different angles, leading to colorful rings when a sample (Sylgard 184, $E = 40 kPa$ , cooled from $42 ° C$ at $6 ° C / \min$ ) is illuminated from behind with a white-light LED. The scale bar is 10 mm long. (c,d) The color pattern is deformed upon stretching (Sylgard 184, $E = 412 kPa$ , cooled from $42 ° C$ at $6 ° C / \min$ ). Here, the direct light from the white-light LED source is blocked by a 2-mm-thick rod to better visualize the colors. See Video 2 in Ref. [37].
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Figure 5
Correlated nucleation and growth. (a) The number density of droplets depends on stiffness but not saturation. The dashed line is the line of best fit to the data. (b) The pair-correlation function $g (r)$ of droplet centers for a typical experiment (blue crosses) shows that nuclei do not form near each other. The range of internuclei repulsions is comparable to the interdroplet distance. The pink line shows the $g (r)$ for nuclei positions in our Monte Carlo growth simulation. Note that the experimental measurements of $g (r)$ are only accurate for $r ≳ 5 μ m$ because of the inaccuracy of out-of-plane tracking of droplet centers. (c) Droplet sizes are strongly correlated with the radius of their Voronoi cell. Blue: Data from the experiment in (b). Green and pink points show results of growth simulations with random and correlated nuclei positions. (d) Droplet size distributions for the experimental data in (b) (blue) and simulations with random (green) or correlated (pink) positions.
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Figure 6
Arrested isothermal phase separation in diverse hydrogels. Here, anise oil droplets nucleated and grew in an ethanol-water mixture (i.e., the Ouzo effect). Micrographs of dispersed droplets in (a) PDMA, a covalently cross-linked gel; (b) gellan gum, a thermally set, physically cross-linked gel; and (c) alginate, an ionically cross-linked physical gel. All droplets are stable against coalescence. Droplets in PDMA and gellan are reasonably monodisperse (see Ref. [37]). The scale bars are all $40 μ m$ wide.
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