Size and shape dependent steady-state pull-off force in molecular adhesion between soft elastic materials

Wang, Jizeng; Gao, Huajian

doi:10.1007/s10704-010-9463-z

Cited by 20 publications

(16 citation statements)

References 18 publications

(16 reference statements)

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“…Qian et al 17,18 performed Monte-Carlo simulations to investigate the adhesion lifetime and strength of a single or periodic arrays of bond clusters between two elastic media. Wang and Gao 19 and Rizza et al 20 investigated the size-and shape-dependent pull-off force and adhesion lifetime of a bond cluster, and showed that strong and stable adhesion can be achieved by selecting an optimal surface shape, somewhat analogous to an earlier study of Gao and Yao 21 for non-specific van der Waals interaction between elastic solids.…”

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confidence: 84%

“…The relation between normal traction σ z along the interface and surface separation u = u 2 − u 1 + h can be Normalized interfacial traction distribution for different values of the stress concentration index α for an adhesion patch on a perfectly flat surface with all bonds closed. [17][18][19] The normalized pulling forceP is taken as 2.…”

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confidence: 99%

“…In our previous studies, [17][18][19] we have shown that the dimensionless parameter α acts as a stress concentration index which governs how the interfacial traction is distributed within the adhesion domain. For example, consider the special case of adhesion on a flat surface with all bonds closed, corresponding toρ = 1 andĥ = constant.…”

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Specific adhesion of a soft elastic body on a wavy surface

Wang

Yao

Gao

2012

Theoretical and Applied Mechanics Letters

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This paper aims at developing a stochastic-elastic model of a soft elastic body adhering on a wavy surface via a patch of molecular bonds. The elastic deformation of the system is modeled by using continuum contact mechanics, while the stochastic behavior of adhesive bonds is modeled by using Bell's type of exponential bond association/dissociation rates. It is found that for sufficiently small adhesion patch size or stress concentration index, the adhesion strength is insensitive to the wavelength but decreases with the amplitude of surface undulation, and that for large adhesion patch size or stress concentration index, there exist optimal values of the surface wavelength and amplitude for maximum adhesion strength.Most biological cells must adhere to an extracellular matrix (ECM) or other cells in order to perform normal physiological functions such as migration, spreading, differentiation, growth, and healing. 1 Cell adhesion involves coordinated actions of many biological molecules such as ECM proteins, cytoskeletal proteins and membrane receptors, and can be strongly influenced by the topographical structures of ECM and the basement membranes of many biological tissues. 2,3 Bozec and Horton 4 proposed that the topographic features of type I collagen monomers may enhance attachment and adhesion of mammalian cells. Bettinger et al. 5 found that nanogratings appear to enhance while nanoposts and nanopits tend to reduce cell adhesion strength. Sykaras et al. 6 showed that surface roughness can strongly affect the osseointegration of implants. Eisenbarth et al. 7 studied the adhesion of fibroblasts on Ti, Ti-6Al-4V, and Ti30Ta substrates, and found that cell alignment becomes more distinct as the surface roughness increases. These experimental findings suggest that surface topography may play important roles in cell adhesion.Cells usually adhere to a material surface through focal adhesions consisting of multiple transmembrane receptor-ligand bonds. 8-10 The random, discrete association/dissociation behaviors of these molecular bonds are an essential characteristic feature of cell adhesion. From a statistical point of view, a single molecular bond has only a finite lifetime, 11-14 but a cluster of bonds can survive for much longer time due to collective effects in a stochastical ensemble. Erdmann and Schwarz 15 showed that the lifetime of a cluster of bonds increases with the increase of cluster size. Wang and Gao 16 considered two elastic half-spaces joined together by diffusive molecular bonds and showed that a uniform bond disa) Corresponding author. tribution along the interface is intrinsically unstable. Qian et al. 17,18 performed Monte-Carlo simulations to investigate the adhesion lifetime and strength of a single or periodic arrays of bond clusters between two elastic media. Wang and Gao 19 and Rizza et al. 20 investigated the size-and shape-dependent pull-off force and adhesion lifetime of a bond cluster, and showed that strong and stable adhesion can be achieved by selecting an optimal surface shape, ...

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Specific adhesion of a soft elastic body on a wavy surface

Wang

Yao

Gao

2012

Theoretical and Applied Mechanics Letters

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“…Continuum contact mechanics is applied to model the deformation of elastic media. Then the relation between normal traction along the interface and the surface separation u = u 2 − u 1 + h can be written as 12,21 …”

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“…The relation starts to deviate significantly from the analytical relation when the stress concentration index α reaches 2.5. In our previous studies, 12 we have demonstrated that α can be viewed as an index to indicate how the interfacial traction is distributed. As shown in Fig.…”

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Wavelet method applied to specific adhesion of elastic solids via molecular bonds

Zhang

Wang

Zhou

2014

Theoretical and Applied Mechanics Letters

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We propose a wavelet method to analyze the stochastic-elastic problem of specific adhesion between two elastic solids via ligand-receptor bond clusters, which is governed by a nonlinear integro-differential equation with a singular Cauchy kernel to describe the mean-field coupling between deformation of elastic materials and stochastic behavior of the molecular bonds. To solve this problem, Galerkin method based on a wavelet approximation scheme is adopted, and special treatment which transforms the singular Cauchy kernel into a smooth one has been proposed to avoid the cumbersome calculation of singular integrals. Numerical results demonstrate that the method is fully capable of solving the specific adhesion problems with complex nonlinear and singular equations. Based on the proposed method, investigations are performed to reveal the relation between steady-state pulling force and mean surface separation under different stress concentration indexes, which is crucial for assembling the overall constitutive relations for multicellular tumor spheroids and polymer-matrix microcomposites.

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Structural Interfaces and Attachments in Biology

Thomopoulos¹,

Birman²,

Genin³

2013

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Size and shape dependent steady-state pull-off force in molecular adhesion between soft elastic materials

Cited by 20 publications

References 18 publications

Specific adhesion of a soft elastic body on a wavy surface

Specific adhesion of a soft elastic body on a wavy surface

Wavelet method applied to specific adhesion of elastic solids via molecular bonds

Structural Interfaces and Attachments in Biology

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