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Phase Reentrances and Solid Deformations in Confined Colloidal Crystals

Xiaoxia Li, Huang Fang, Krongtum Sankaewtong, Minhuan Li, Yanshuang Chen, Jiping Huang, Ran Ni, Hajime Tanaka, and Peng Tan

Phys. Rev. Lett. 132, 018202 – Published 5 January 2024

Abstract

A simple geometric constraint often leads to novel, complex crystalline phases distinct from the bulk. Using thin-film charge colloidal crystals, a model system with tunable interactions, we study the effects of geometric constraints. Through a combination of experiments and simulations, we systematically explore phase reentrances and solid deformation modes concerning geometrical confinement strength, identifying two distinct categories of phase reentrances below a characteristic layer number, $N_{c}$ : one for $b c c$ bulk-stable and another for $f c c$ bulk-stable systems. We further verify that the dominant thermodynamic origin is the nonmonotonic dependence of solids’ free energy on the degree of spatial confinement. Moreover, we discover transitions in solid deformation modes between interface-energy and bulk-energy dominance: below a specific layer number, $N_{k}$ , geometric constraints generate unique soft deformation modes adaptive to confinement. These findings on the $N$ -dependent thermodynamic and kinetic behaviors offer fresh insights into understanding and manipulating thin-film crystal structures.

Received 13 July 2023
Revised 15 November 2023
Accepted 18 December 2023

DOI:https://doi.org/10.1103/PhysRevLett.132.018202

Physics Subject Headings (PhySH)

Phase transitions by order

Colloidal crystal Colloids

Polymers & Soft Matter

Authors & Affiliations

Xiaoxia Li ^1,2,*, Huang Fang ^1,*, Krongtum Sankaewtong ^3,*, Minhuan Li¹, Yanshuang Chen¹, Jiping Huang¹, Ran Ni^3,†, Hajime Tanaka ^4,5,‡, and Peng Tan ^1,2,§

¹State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
²Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China
³Chemical Engineering, School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459, Singapore
⁴Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
⁵Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan

^*These authors contributed equally to this work.
^†Corresponding author: [email protected]
^‡Corresponding author: [email protected]
^§Corresponding author: [email protected]

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Vol. 132, Iss. 1 — 5 January 2024

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Figure 1
Phase reentrance behaviors induced by confining low-density charged colloidal samples. (a)–(c) Illustration of typical layered structures parallel to the wall with an increase in the wall-wall separation $Z$ . These layered structures are categorized based on the rhombus angle $θ$ of the particle layer’s 2D lattice structure: $f c c$ type ( $θ = 60 °$ , $N △$ , or $N f c c$ with $(111)_{f c c} ∥ w a l l$ ), $b c c$ type ( $θ = 70 °$ , $N b c c$ with $(110)_{b c c} ∥ w a l l$ ), and rhombic type ( $80 ° < θ < 90 °$ and $W_{6} > 0$ , deformed $b c c$ type with $(100)_{b c c} ∥ w a l l$ ). Note that the particle positions fluctuate, and we draw white dashed rhombus with specified angle to facilitate comparison. Three types of reentrance behaviors are observed: $(N - 1) △ \to N rhombic \to N △$ when $2 \leq N \leq 3$ in (a), $N rhombic \to N b c c \to N f c c \to (N + 1) b c c$ when $N = 4$ in (b), and $N f c c \to (N + 1) b c c \to (N + 1) f c c$ when $5 \leq N < 13$ in (c). Simulation results (bottom panels) agree well with experiments (top panels). (d)–(f) $g (r)_{2 D}$ corresponding to each structure shown in (a)–(c), respectively. The simulation results (dashed lines) also agree well with the experiment ones (solid lines). (g) $Z$ -dependent reentrance behaviors in experiments at $κ σ \approx 2.0$ . Rhombic and $b c c$ -type structures have positive $W_{6}$ . $f c c$ -type structures have negative $W_{6}$ . Different symbols are used for $N$ and $N + 1$ layers due to the possible coexistence.
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Figure 2
Phase diagrams for the two categories of constraint-induced reentrances and the distinct 3D characters of reentrance structures. (a) The phase diagram for $b c c$ bulk-stable systems ( $κ σ \approx 2.0$ ) in the ( $Z / N$ , $N$ ) parameter space. (b) The phase diagram for $f c c$ bulk-stable systems ( $κ σ \approx 5.0$ ) in the ( $Z / N$ , $N$ ) parameter space. Experiments agree well with simulations in (a) and (b). (c) 3D view of the $b c c$ -type constrained structure and illustration of its geometric parameters, $D$ , $b$ , and $a$ . Note that $D = Z / N$ . $b$ and $a$ are the unit vector lengths of the rectangle cell regarding the deformed $(110)_{b c c}$ plane. (d)–(g) Illustration of the continuous structural transformation from $b c c$ type to $f c c$ type at $κ σ \approx 2.0$ and $N = 4$ . Scatter plots (gray clouds) are 2D projections of the solid phase’s 3D structure under thermal fluctuation. Note that the upper and lower layers deform in opposite directions. (h) 3D view of the $N □$ -type structures at $κ σ \approx 5.0$ . (i),(j) Illustration of the sharp structural transition from $N □$ to $N △$ .
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Figure 3
Illustration of the distinct modes of structure variation adaptive to the confinement. (a) Two different modes adaptive to the confinement operative when $N < 11$ and $N \geq 11$ in $b c c$ bulk-stable system ( $κ σ \approx 2.0$ ). We use the ( $b / a$ , $Z / N$ ) parameter space to illustrate the differences. Note the different trends of $b / a$ with an increase in $Z / N$ for the two modes are schematically illustrated by red-dashed and green-dashed arrows. (b) Another two modes adaptive to the confinement operative when $N \leq 12$ and $N > 12$ in $f c c$ bulk-stable system ( $κ σ \approx 5.0$ ). Besides the $Z / N a \propto Z / N$ response, we can see that a new $Z / N a \approx 0.84$ branch emerges when $N \geq 12$ .
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Physical Review Letters

Phase Reentrances and Solid Deformations in Confined Colloidal Crystals

Xiaoxia Li, Huang Fang, Krongtum Sankaewtong, Minhuan Li, Yanshuang Chen, Jiping Huang, Ran Ni, Hajime Tanaka, and Peng Tan

Phys. Rev. Lett. 132, 018202 – Published 5 January 2024

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