Determining the layers’ Young’s moduli and thickness from the indentation of a bilayer structure

Zhang, Yin; Zhao, Yanru; Cheng, Zhihai

doi:10.1088/1361-6463/aaa55d

Cited by 9 publications

(7 citation statements)

References 47 publications

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“…While no analytical solution exists for the bilayer problem, some empirical expressions have been identified in the literature, where the decay has been described by a generalized form [ 53 ]: where the function decays from 1 to 0 over a range related to . In particular, it has been shown that either a trigonometric [ 54 ] or exponential [ 55 , 56 ] decay well approximates the experimental behavior.…”

Section: Resultsmentioning

confidence: 99%

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Elasticity spectra as a tool to investigate actin cortex mechanics

et al. 2020

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Background The mechanical properties of single living cells have proven to be a powerful marker of the cell physiological state. The use of nanoindentation-based single cell force spectroscopy provided a wealth of information on the elasticity of cells, which is still largely to be exploited. The simplest model to describe cell mechanics is to treat them as a homogeneous elastic material and describe it in terms of the Young’s modulus. Beside its simplicity, this approach proved to be extremely informative, allowing to assess the potential of this physical indicator towards high throughput phenotyping in diagnostic and prognostic applications. Results Here we propose an extension of this analysis to explicitly account for the properties of the actin cortex. We present a method, the Elasticity Spectra, to calculate the apparent stiffness of the cell as a function of the indentation depth and we suggest a simple phenomenological approach to measure the thickness and stiffness of the actin cortex, in addition to the standard Young’s modulus. Conclusions The Elasticity Spectra approach is tested and validated on a set of cells treated with cytoskeleton-affecting drugs, showing the potential to extend the current representation of cell mechanics, without introducing a detailed and complex description of the intracellular structure.

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Section: Resultsmentioning

confidence: 99%

“…Here we extended the same simulation approach to obtain a set of numerical F (δ) curves and exploited Eq. While no analytical solution exists for the bilayer problem, some empirical expressions have been identified in the literature, where the decay has been described by a generalized form [53]:…”

Section: Bilayer Modelmentioning

confidence: 99%

Elasticity spectra as a tool to investigate actin cortex mechanics

et al. 2020

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“…In the case where the indenter radius ( R ) is on the order of, or larger than, the foundation thickness ( h ), the thickness plays a role in the adhesion [ 34–36 ] and mechanical behavior. [ 37–40 ] Therefore, the total energy in the system ( U T ) is a summation of the surface energy U S = πR 2 G c , where G c is the critical strain energy release rate, and the elastic energy U E = F 2 h (Δ P )/2 πE (Δ P ) R 2 . [ 34 ] For a contact area ( A ), the adhesive capacity is determined when ∂ U T /∂ A = 0, where

F_{c} = {(\frac{2 π^{2} E false(normalΔ P false) G_{c} R^{4}}{h false(normalΔ P false)})}^{1 / 2}

which shows the dependence of F c on the applied pneumatic pressure in modulus and thickness.…”

Section: Figurementioning

confidence: 99%

Active Membranes on Rigidity Tunable Foundations for Programmable, Rapidly Switchable Adhesion

Swift

Haverkamp

Stabile

et al. 2020

Adv Materials Technologies

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Rapidly controlling and switching adhesion is necessary for applications in robotic gripping and locomotion, pick and place operations, and transfer printing. However, switchable adhesives often display a binary response (on or off) with a narrow adhesion range, lack post‐fabrication adhesion tunability, or switch slowly due to diffusion‐controlled processes. Here, pneumatically controlled shape and rigidity tuning is coupled to rapidly switch adhesion (≈0.1 s) across a wide range of programmable adhesion forces with measured switching ratios as high as 1300x. The switchable adhesion system introduces an active polydimethylsiloxane membrane supported on a compliant, foam foundation with pressure‐tunable rigidity where positive and negative pneumatic pressure synergistically control contact stiffness and geometry to activate and release adhesion. Energy‐based modeling and finite element computation demonstrate that high adhesion is achieved through a pressure‐dependent, nonlinear stiffness of the foundation, while an inflated shape at positive pressures enables easy release. This approach enables adhesion‐based gripping and material assembly, which is utilized to pick‐and‐release common objects, rough and porous materials, and arrays of elements with a greater than 14 000x range in mass. The robust assembly of diverse components (rigid, soft, flexible) is then demonstrated to create a soft and stretchable electronic device.

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“…Fig.3b highlights the expected decay of the elasticity from the cortex to the bulk, over an indentation depth comparable with d 0 . While no analytical solution exists for the bilayer problem, some empirical expressions have been identified in the literature, where the decay has been described by a generalized form [50]:…”

Section: Bilayer Modelmentioning

confidence: 99%

Elasticity Spectra as a Tool to Investigate Actin Cortex Mechanics

Lüchtefeld

Bartolozzi

Morales

et al. 2020

Preprint

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Background The mechanical properties of single living cells have proven to be a powerful marker of the cell physiological state. The use of nanoindentation-based single cell force spectroscopy provided a wealth of information on the elasticity of cells, which is still largely to be exploited. The simplest model to describe cell mechanics is to treat them as a homogeneous elastic material and describe it in terms of the Young's modulus. Beside its simplicity, this approach proved to be extremely informative, allowing to assess the potential of this physical indicator towards high throughput phenotyping in diagnostic and prognostic applications. Results Here we propose an extension of this analysis to explicitly account for the properties of the actin cortex. We present a method, the Elasticity Spectra, to calculate the apparent stiffness of the cell as a function of the indentation depth and we suggest a simple phenomenological approach to measure the thickness and stiffness of the actin cortex, in addition to the standard Young's modulus. Conclusions The Elasticity Spectra approach is tested and validated on a set of cells treated with cytoskeleton-affecting drugs, showing the potential to extend the current representation of cell mechanics, without introducing a detailed and complex description of the intracellular structure.

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Determining the layers’ Young’s moduli and thickness from the indentation of a bilayer structure

Cited by 9 publications

References 47 publications

Elasticity spectra as a tool to investigate actin cortex mechanics

Elasticity spectra as a tool to investigate actin cortex mechanics

Active Membranes on Rigidity Tunable Foundations for Programmable, Rapidly Switchable Adhesion

Elasticity Spectra as a Tool to Investigate Actin Cortex Mechanics

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