van der Waals interactions between nanostructures: Some analytic results from series expansions

Stedman, Troy; Drosdoff, D.; Woods, Lilia M.

doi:10.1103/physreva.89.012509

Cited by 12 publications

(9 citation statements)

References 35 publications

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“…r LJ,eq r 13 − r LJ,eq r 7 (9) are the minimal force value f LJ,min and corresponding distance r LJ,fmin f LJ,min ≈ 2.6899 Φ LJ,eq r LJ,eq and r LJ,fmin = 13 7…”

Section: Total Molecular Pair Potentials and Force Fieldsmentioning

confidence: 99%

“…The critical point is to transfer the first principles formulated for the interaction between atoms or single molecules to the interaction between macromolecules such as slender fibers. Here, the analytical approaches to be found in textbooks and also in recent contributions [7,8,9,10] from the field of theoretical biophysics are (naturally) restricted to undeformable, rigid bodies with primitive geometries such as spheres, half spaces or, most relevant in our case, cylinders. Some computational approaches can be found in the literature, but rather aim at including more complex phenomena such as retardation and solvent effects in vdW interactions [11], still limited to rigid bodies.…”

Section: Introductionmentioning

confidence: 99%

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A computational model for molecular interactions between curved slender fibers undergoing large 3D deformations with a focus on electrostatic, van der Waals, and repulsive steric forces

Grill

Wall

Meier

2020

Numerical Meth Engineering

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Summary This contribution proposes the first three‐dimensional (3D) beam‐beam interaction model for molecular interactions between curved slender fibers undergoing large deformations. While the general model is not restricted to a specific beam formulation, in the present work, it is combined with the geometrically exact beam theory and discretized via the finite element method. A direct evaluation of the total interaction potential for general 3D bodies requires the integration of contributions from molecule or charge distributions over the volumes of the interaction partners, leading to a six‐dimensional integral (two nested 3D integrals) that has to be solved numerically. Here, we propose a novel strategy to formulate reduced section‐section interaction laws for the resultant interaction potential between a pair of cross‐sections of two slender fibers such that only two one‐dimensional integrals along the fibers' length directions have to be solved numerically. This section‐section interaction potential (SSIP) approach yields a significant gain in efficiency, which is essential to enable the simulation of relevant time and length scales for many practical applications. In a first step, the generic structure of SSIP laws, which is suitable for the most general interaction scenario (eg, fibers with arbitrary cross‐section shape and inhomogeneous atomic/charge density within the cross‐section) is presented. Assuming circular, homogeneous cross‐sections, in a next step, specific analytical expressions for SSIP laws describing short‐range volume interactions (eg, van der Waals (vdW) or steric interactions) and long‐range surface interactions (eg, Coulomb interactions) are proposed. Besides ready‐to‐use expressions for the total interaction potential, also the resulting virtual work contributions, its finite element discretizations, as well as a suitable numerical regularization for the limit of zero separation are derived. The validity of the SSIP laws, as well as the accuracy and robustness of the general SSIP approach to beam‐beam interactions, is thoroughly verified by means of a set of numerical examples considering steric repulsion, electrostatic, or vdW adhesion.

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“…r LJ,eq r 13 − r LJ,eq r 7 (9) are the minimal force value f LJ,min and corresponding distance r LJ,fmin f LJ,min ≈ 2.6899 Φ LJ,eq r LJ,eq and r LJ,fmin = 13 7…”

Section: Total Molecular Pair Potentials and Force Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A computational model for molecular interactions between curved slender fibers undergoing large 3D deformations with a focus on electrostatic, van der Waals, and repulsive steric forces

Grill

Wall

Meier

2020

Numerical Meth Engineering

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“…If the applied electric potential difference gradually increases and exceeds a certain potential, the nanobeam would become unstable and collapse onto the substrate. Moreover, in nanoscale, the molecular interaction like van der Waals force and Casimir force present a significant contribution to the attraction between the nanobeam and the substrate [11,12]. Herein, the critical electric potential which causes the nanobeam to collapse onto the substrate is called the pull-in voltage and the correspondent maximum deflection of the structure before failure is called the pull-in deflection [13].…”

Section: Introductionmentioning

confidence: 99%

Pull-in instability of carbon nanotube-reinforced nano-switches considering scale, surface and thermal effects

Yang

Wang

Fang

2015

Composites Part B: Engineering

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“…Moreover, recent efforts have addressed orientation-dependent systems involving objects with finite size; however, this has not yet been extended to either the SEI or GSI techniques. 29,30 The ability to modify the SEI or GSI techniques to describe these types of interactions will enable the analysis of nontrivial systems. Here, we achieve this critical overarching objective by overlaying the interaction forces generated by multiple objects to form an adhesion force map.…”

Section: Introductionmentioning

confidence: 99%

Analyzing adhesion in microstructured systems through a robust computational approach

Hoss

Boudouris

Beaudoin

2017

Surface & Interface Analysis

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Analyzing surface forces for myriad geometric structures facilitates the design of properties in interacting interfacial systems. Along these lines, we demonstrate a generalized technique that can be utilized to evaluate the orientation dependence of a particle interacting with multiple finite or semi‐infinite objects. Specifically, the surface element integration technique is modified to account for surface elements of a particle not directly adjacent to the object with which it is interacting; this facilitates the analysis of objects with finite shape and with arbitrary orientations. Furthermore, as a technology‐relevant proof‐of‐concept demonstration, the influence of van der Waals (vdW) forces on the performance and reliability of microstructured systems used for the collection of trace particles is reported. The importance of the location of the particle contact with the microstructure and the independence of vdW forces generated by each microstructure is demonstrated using the developed computational approach. Thus, the methodology presented here can ultimately be utilized for a variety of interfacial forces generated by nontrivial systems with heterogeneous properties in order to provide design motifs in a low‐cost, high‐throughput manner.

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van der Waals interactions between nanostructures: Some analytic results from series expansions

Cited by 12 publications

References 35 publications

A computational model for molecular interactions between curved slender fibers undergoing large 3D deformations with a focus on electrostatic, van der Waals, and repulsive steric forces

A computational model for molecular interactions between curved slender fibers undergoing large 3D deformations with a focus on electrostatic, van der Waals, and repulsive steric forces

Pull-in instability of carbon nanotube-reinforced nano-switches considering scale, surface and thermal effects

Analyzing adhesion in microstructured systems through a robust computational approach

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