The Buckling Spectra of Nanoparticle Surfactant Assemblies

Abstract

Fine control over the mechanical properties of thin sheets underpins transcytosis, cell shape, and morphogenesis. Applying these principles to artificial, liquid-based systems has led to reconfigurable materials for soft robotics, actuation, and chemical synthesis. However, progress is limited by a lack of synthetic two-dimensional membranes that exhibit tunable mechanical properties over a comparable range to that seen in nature. Here, we show that the bending modulus, B, of thin assemblies of nanoparticle surfactants (NPSs) at the oil–water interface can be varied continuously from sub-k B T to 106 k B T, by varying the ligands and particles that comprise the NPS. We find extensive departure from continuum behavior, including enormous mechanical anisotropy and a power law relation between B and the buckling spectrum width. Our findings provide a platform for shape-changing liquid devices and motivate new theories for the description of thin-film wrinkling.

A representation learning framework for detection and characterization of dead versus strain localization zones from pre- to post-failure

“…Methods that can effectively and efficiently characterize and model these ordered motions are of great importance in research and applications. Not only can they help advance fundamental knowledge of granular media, they offer a rational basis for practical strategies in: prediction and optimization of structure-granular interaction processes [16][17][18], mitigation of granular hazards [19,20], and discovery and design of novel granular materials with target properties [21,22], to name a few examples.…”

Bottlebrush Polymers at Liquid Interfaces: Assembly Dynamics, Mechanical Properties, and All-Liquid Printed Constructs

“…Even though the τ SR has similar values for PD3 to PD5 , the equilibrium ⟨ σ ⟩ false⟨ σ 0 false⟩ − 1 decreases from 0.5 ( PD3 ) to 0.3 ( PD5 ), showing the importance of packing efficiency on the stress relaxation (Figure E). The wavelength of the buckling pattern is related to the bending modulus ( B ) of the NPSs by λ = 2 π ( B Δ ρ g ) 1 / 4 where Δρ is density difference between the two liquid phases (0.13 g mL –1 ) and g is gravitational acceleration (9.8 m 2 s –1 ). , Since the resulting wrinkle patterns exhibited a distribution of wavelengths (Figure S24), we used the mean wavelength (λ̅) to determine B . Initially, B decreases with N BB (from 2 × 10 3 k B T for PD1 to 3 × 10 2 k B T for PD3 ), reaches a minimum at N BB = 100 ( PD3 ), and then apparently increases with N BB (5 × 10 3 k B T for PD5 , Figure F).…”

“…where Δρ is density difference between the two liquid phases (0.13 g mL −1 ) and g is gravitational acceleration (9.8 m 2 s −1 ). 8,49 Since the resulting wrinkle patterns exhibited a distribution of wavelengths (Figure S24), we used the mean wavelength (λ̅ ) to determine B. Initially, B decreases with N BB (from 2 × 10 3 k B T for PD1 to 3 × 10 2 k B T for PD3), reaches a minimum at N BB = 100 (PD3), and then apparently increases with N BB (5 × 10 3 k B T for PD5, Figure 5F).…”

“…As B is determined by both Young's modulus and the NPS structure, in NPS monolayers, the resistance toward bending of the individual NPs affects B. 8,49 Since BPSs with higher N BB have a greater capacity for multisite PAA/POSS-NH 2 complexation, when the BPSs are compressed, the tension caused by compression along the backbone of individual BP contributes to macroscopic bending rigidity and hence higher B (Figure 5F). Stability of All-Liquid Printed Constructs.…”

Direct Measurement of Surfactant-Mediated Picoforces among Nanoparticles in a Quasi-Two-Dimensional Environment

“…We also stress that, given the large separation between interfacial NPs, these monolayers are expected to be more sensitive to subtle variations in the interparticle forces induced by different environmental changes. Finally, the comprehension of forces acting between nanoparticles trapped at liquid interfaces is of paramount importance for the development of tailored low-dimensional structures, as liquid surfaces and interfaces provide a promising environment for the spontaneous assembly of molecules and nanomaterials into 2D or quasi-2D systems. − In fact, the finite contact angle at the nanoscale between NPs and the liquid subphase leads to the formation of three distinct interfaces, namely, the NP/subphase, NP/second fluid, and subphase/second fluid. Thus, NPs assembled at liquid interfaces represent a model system for the investigation of forces simultaneously propagating across two different media …”