Adsorption superlattice stabilized by elastic interactions in a soft porous crystal

Letter
Open Access

Adsorption superlattice stabilized by elastic interactions in a soft porous crystal

Kota Mitsumoto and Kyohei Takae

Phys. Rev. Research 6, L012029 – Published 16 February 2024

Abstract

Elasticity is essential for organizing mesoscale patterns in condensed matter. Here, we numerically show that adsorbed molecules in soft porous crystals form a superlattice (SL) stabilized by elastic interactions. In a mechanically flexible honeycomb lattice model, a long-range ordered 1/3-filling SL state emerges during adsorption. The SL state is robust against thermal fluctuation when the elastic interactions between the next-nearest-neighboring lattice sites are strong. Our results provide a way to switch the functionalities of materials by controlling the distribution of adsorbed molecules.

Received 14 September 2023
Accepted 9 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.L012029

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)

Adsorption Classical statistical mechanics Elastic deformation

Metal-organic framework Porous media Superlattices

Lattice models in condensed matter Monte Carlo methods

Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsPolymers & Soft MatterInterdisciplinary Physics

Authors & Affiliations

Kota Mitsumoto ^* and Kyohei Takae^†

Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

^*kmitsu@iis.u-tokyo.ac.jp
^†takae@iis.u-tokyo.ac.jp

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 6, Iss. 1 — February - April 2024

Subject Areas

Materials Science

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic description of the proposed model. (a) Guest particles (dark blue spheres) are adsorbed into the host honeycomb matrix formed by the host particles (orange), inducing isotropic swelling of the host matrix locally. (b) An adsorbed particle strongly interacts with the host particles. (c) Mathematical representation of (a) and (b). Interaction potential $V_{2}$ arises from the filling of the guest particle in addition to the original host's potential $V_{1}$ .
Reuse & Permissions
Figure 2
Phase diagram of the model at $P = 0.5$ with $k = 3, α = 0.4$ , and the ratio of NNN interaction to the NN interaction, (a) $g = 1$ and (b) $g = 2$ . The solid curve represents the equilibrium phase boundary between the adsorbed and desorbed phases, determined from the specific-heat peaks obtained by the WL method. The transition point at $T = 0$ is analytically determined by comparing the minimum energy of the desorbed and adsorbed states. The boundaries between different colors are determined from the specific-heat peaks obtained by quasiequilibrium protocols: $T_{1 +}$ and $T_{2 +}$ represent transition points to the desorbed state and $\sqrt{3} \times \sqrt{3}$ (1/3-filling) SL state during a heating process, and $T_{1 -}$ and $T_{2 -}$ represent transition points to the adsorbed state and 1/3-filling SL state during a cooling process. The inset shows a zoom of the region where the SL state appears. (c) A snapshot of a 1/3-filling SL state at $(μ, T, P) = (4.8, 0.2, 0.5)$ with $k = 3, α = 0.4$ , and $g = 2$ . Light gray hexagons with circles and dark gray hexagons represent adsorbed and desorbed sites, respectively. Short-time averaging over 1000 MC steps with a fixed adsorbate distribution is performed to obtain the average lattice distortion. Red lines represent a unit cell of the SL.
Reuse & Permissions
Figure 3
(a) The enthalpy difference per adsorbed sites $Δ h = H / N_{ads}$ between the ground state at $(μ, P) = (0, 0.5)$ and the selected configurations [(i)–(vii)] for $k = 3, α = 0.4, g = 1$ , and $L = 24$ . The lattice sites are optimized by MC simulations at $T = 0$ for $10^{4}$ MC steps. Circles denote the adsorbates, and open hexagons denote the desorbed sites. (b) $Δ e_{NN}$ and (c) $Δ e_{NNN}$ represent the contributions of the NN and NNN elastic interactions to the enthalpy difference shown in (a), respectively.
Reuse & Permissions
Figure 4
Thermodynamic properties at $P = 0.5$ in the case of $k = 3, α = 0.4$ , and $g = 2$ . (a) Temperature dependency of the adsorption fraction $n_{ads}$ at $μ = 5.0$ , obtained by the WL simulation for $L = 12$ , and cooling ( $- T$ ) and heating ( $+ T$ ) simulations for $L = 48$ . (b) 1/3 plateau behaviors of $n_{ads}$ at $μ = 5.0$ –4.7 during the cooling protocols. Curves at $μ = 4.8, 4.9$ are simulated for $L = 72$ , otherwise $L = 48$ . (c) The osmotic grand potential $Δ Ω (n_{ads}) = Ω (n_{ads}) - Ω_{\min}$ at $T = 0.280 - 0.235$ and $μ = 4.9$ for $L = 12$ , where $Ω_{\min}$ is the minimum value at each $T$ . (d) Temperature dependency of $n_{ads}$ at $μ = 4.3$ , obtained by cooling ( $- T$ ) and heating ( $+ T$ ) simulations for $L = 48$ . The error bars in (a), (b), and (d) represents the standard error.
Reuse & Permissions

Physical Review Research