Designing Superselectivity in Linker-Mediated Multivalent Nanoparticle Adsorption

Xiuyang Xia and Ran Ni

Phys. Rev. Lett. 132, 118202 – Published 12 March 2024

Abstract

Using a statistical mechanical model and numerical simulations, we provide the design principle for the bridging strength ( $ξ$ ) and linker density ( $ρ$ ) dependent superselectivity in linker-mediated multivalent nanoparticle adsorption. When the bridges are insufficient, the formation of multiple bridges leads to both $ξ$ - and $ρ$ -dependent superselectivity. When the bridges are excessive, the system becomes insensitive to bridging strength due to entropy-induced self-saturation and shows a superselective desorption with respect to the linker density. Counterintuitively, lower linker density or stronger bridging strength enhances the superselectivity. These findings help the understanding of relevant biological processes and open up opportunities for applications in biosensing, drug delivery, and programmable self-assembly.

Received 25 October 2023
Revised 9 January 2024
Accepted 22 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.118202

Physics Subject Headings (PhySH)

Adsorption Biomimetic & bio-inspired materials

Grafted colloids Patchy particles

Monte Carlo methods

Polymers & Soft Matter

Authors & Affiliations

Xiuyang Xia ^* and Ran Ni ^†

School of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, 62 Nanyang Drive, 637459, Singapore

^*Present address: Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany.
^†r.ni@ntu.edu.sg

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Vol. 132, Iss. 11 — 15 March 2024

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Images

Figure 1
Linker-mediated adsorption of multivalent nanoparticles. (a) Schematic representation of multivalent nanoparticles adsorption composed of a guest-linker-host sandwich. (b) Illustration of the grand-canonical Monte Carlo simulation. The black dots are immobile receptors with gray circles being adsorbed nanoparticles. Receptors within blue regions can form bridges with the ligands on nanoparticles mediated by implicit linkers.
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Figure 2
$ξ$ -dependent superselectivity. (a) $θ$ , $α_{ξ}$ , and $α_{ξ, 0}$ as functions of $\log ξ$ at different $z_{g}$ . Symbols are simulation results with curves the theoretical prediction. Here $ρ = e^{- 2}$ , $ρ_{r} = 12.73$ , and $r_{eff} = 0.5$ . (b) Theoretical prediction of $⟨ q ⟩$ , $Γ$ (upper black solid line) and $α_{ξ, 0}$ as functions of $\log ξ$ at $ρ = e^{- 4}$ and various $⟨ n_{r} ⟩$ . Dots locate the self-saturation point $ξ^{*}$ , which is the cross point between the dashed black lines $Γ = ξ ξ_{cnf} ρ$ (lower $ξ$ ) and $Γ = ξ_{cnf} ρ^{- 1}$ (higher $ξ$ ). $\times$ indicate the crossover points $ξ^{ls}$ from linear to superlinear response. (c) Left: $ξ$ -dependent selectivity $α_{ξ}$ as a function of $\log ξ$ at different $\log ρ$ and $z_{g} = 10^{- 9}$ . Red, black, and blue curves indicate the location of $ξ^{ls}$ , $ξ^{*}$ , and $θ = 0.5$ , respectively. Right: at strong bridging limit, $b (ξ \to \infty)$ (yellow) and $Γ (ξ \to \infty)$ (green) as functions of $\log ρ$ . In all figures, unless otherwise specified, $⟨ n_{r} ⟩ = 10$ , $n_{l} = 4$ , and $Δ S_{cnf} = 0$ .
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Figure 3
$ρ$ -dependent superselectivity. (a) $θ$ and $α_{ρ}$ as functions of $\log ρ$ for monovalent and multivalent ligands with $⟨ n_{r} ⟩ = 1$ and 6. Gray area indicates no superselectivity. Here $ξ_{l} = ξ_{r} = e^{2}$ , $z_{g} = 10^{- 3}$ , and $r_{eff} = 0.5$ . (b) Theoretical prediction of $⟨ q ⟩$ , $Γ$ (upper black solid line), and $α_{ρ, 0}$ as functions of $\log ρ$ at $ξ_{l} = ξ_{r} = e^{- 2}$ with different $⟨ n_{r} ⟩$ . Black dot locates the adsorption-desorption transition point $ρ^{*}$ , the cross point between the lines $Γ = ξ ξ_{cnf} ρ$ (adsorption regime), and $Γ = ξ_{cnf} ρ^{- 1}$ (desorption regime). Other colored symbols indicates the crossover points $ρ_{ad}^{ls}$ and $ρ_{de}^{ls}$ from linear to superlinear responses in adsorption and desorption regimes, respectively. (c) Illustration of adsorption and desorption with increasing linker density where bridges are insufficient (upper) and excessive (lower). (d) Left: $ρ$ -dependent selectivity $α_{ρ}$ as a function of $\log ρ$ at different $\log ξ$ and $z_{g} = 10^{- 9}$ . Red, black, blue, and orange curves indicate the location of $ρ_{ad}^{ls}$ , $ρ^{*}$ , $ρ_{de}^{ls}$ , and $θ = 0.5$ , respectively. Right: at $ρ^{*}$ , $b (ρ^{*})$ (green) and $Γ (ρ^{*})$ (purple) as functions of $\log ξ$ .
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