A scaling law for properties of nano-structured materials

2006 ◽  
Vol 462 (2069) ◽  
pp. 1355-1363 ◽  
Author(s):  
J Wang ◽  
H.L Duan ◽  
Z.P Huang ◽  
B.L Karihaloo
Keyword(s):  
Physical Properties ◽  
Size Dependence ◽  
Size Range ◽  
Scaling Law ◽  
Length Scales ◽  
Structured Materials ◽  
Nano Scale ◽  
Nano Structures ◽  
Simple Scaling ◽  
Intrinsic Length

In this brief communication, we identify intrinsic length scales of several physical properties at the nano-scale and show that, for nano-structures whose characteristic sizes are much larger than these scales, the properties obey a simple scaling law. The underlying cause of the size-dependence of these properties at the nano-scale is the competition between surface and bulk energies. This law provides a yardstick for checking the accuracy of experimentally measured or numerically computed properties of nano-structured materials over a broad size range and can thus help replace repeated and exhaustive testing by one or a few tests.

SIZE-DEPENDENT EFFECTS IN ATOMIC CLUSTERS

2020 ◽  
Author(s):  
A. S. Sharipov ◽  
◽  
B. I. Loukhovitski ◽  
Keyword(s):  
Binding Energy ◽  
Physical Properties ◽  
Size Dependence ◽  
Atomic Clusters ◽  
Energy Collision ◽  
Size Dependent

The size-dependence of different physical properties of atomic clusters (by the example of binding energy, collision diameter, and static isotropic polarizability) is discussed.

scholarly journals Hierarchy and extremes in selections from pools of randomized proteins

2016 ◽  
Vol 113 (13) ◽  
pp. 3482-3487 ◽  
Author(s):  
Sébastien Boyer ◽  
Dipanwita Biswas ◽  
Ananda Kumar Soshee ◽  
Natale Scaramozzino ◽  
Clément Nizak ◽  
...  
Keyword(s):  
High Throughput Sequencing ◽  
Scaling Law ◽  
Natural Populations ◽  
Value Theory ◽  
Darwinian Evolution ◽  
Future Evolution ◽  
Synthetic Protein ◽  
Simple Scaling ◽  
Protein Libraries

Variation and selection are the core principles of Darwinian evolution, but quantitatively relating the diversity of a population to its capacity to respond to selection is challenging. Here, we examine this problem at a molecular level in the context of populations of partially randomized proteins selected for binding to well-defined targets. We built several minimal protein libraries, screened them in vitro by phage display, and analyzed their response to selection by high-throughput sequencing. A statistical analysis of the results reveals two main findings. First, libraries with the same sequence diversity but built around different “frameworks” typically have vastly different responses; second, the distribution of responses of the best binders in a library follows a simple scaling law. We show how an elementary probabilistic model based on extreme value theory rationalizes the latter finding. Our results have implications for designing synthetic protein libraries, estimating the density of functional biomolecules in sequence space, characterizing diversity in natural populations, and experimentally investigating evolvability (i.e., the potential for future evolution).

scholarly journals Mechanics of spontaneously formed nanoblisters trapped by transferred 2D crystals

2018 ◽  
Vol 115 (31) ◽  
pp. 7884-7889 ◽  
Author(s):  
Daniel A. Sanchez ◽  
Zhaohe Dai ◽  
Peng Wang ◽  
Arturo Cantu-Chavez ◽  
Christopher J. Brennan ◽  
...  
Keyword(s):  
Scaling Law ◽  
New Physics ◽  
Adhesion Energy ◽  
Work Of Adhesion ◽  
Fourth Power ◽  
Layered Systems ◽  
Simple Scaling ◽  
Dynamics Simulations ◽  
2D Crystals ◽  
Good Agreement

Layered systems of 2D crystals and heterostructures are widely explored for new physics and devices. In many cases, monolayer or few-layer 2D crystals are transferred to a target substrate including other 2D crystals, and nanometer-scale blisters form spontaneously between the 2D crystal and its substrate. Such nanoblisters are often recognized as an indicator of good adhesion, but there is no consensus on the contents inside the blisters. While gas-filled blisters have been modeled and measured by bulge tests, applying such models to spontaneously formed nanoblisters yielded unrealistically low adhesion energy values between the 2D crystal and its substrate. Typically, gas-filled blisters are fully deflated within hours or days. In contrast, we found that the height of the spontaneously formed nanoblisters dropped only by 20–30% after 3 mo, indicating that probably liquid instead of gas is trapped in them. We therefore developed a simple scaling law and a rigorous theoretical model for liquid-filled nanoblisters, which predicts that the interfacial work of adhesion is related to the fourth power of the aspect ratio of the nanoblister and depends on the surface tension of the liquid. Our model was verified by molecular dynamics simulations, and the adhesion energy values obtained for the measured nanoblisters are in good agreement with those reported in the literature. This model can be applied to estimate the pressure inside the nanoblisters and the work of adhesion for a variety of 2D interfaces, which provides important implications for the fabrication and deformability of 2D heterostructures and devices.

Flow transitions and length scales of a channel-confined active nematic

Soft Matter ◽  
2021 ◽  
Author(s):  
Abhik Samui ◽  
Julia M. Yeomans ◽  
Sumesh P. Thampi
Keyword(s):  
Characteristic Length ◽  
Flow Regimes ◽  
Channel Width ◽  
Flow Structures ◽  
Length Scale ◽  
Length Scales ◽  
Turbulence Regime ◽  
Active Turbulence ◽  
Intrinsic Length ◽  
Flow Transitions

Different flow regimes realised by a channel-confined active nematic have a characteristic length same as channel width. Flow structures exhibit the intrinsic length scale of the fluid only in the fully developed active turbulence regime.

scholarly journals Three-dimensional numerical simulation of soft-tissue wound healing using constrained-mixture anisotropic hyperelasticity and gradient-enhanced damage mechanics

2020 ◽  
Vol 17 (162) ◽  
pp. 20190708 ◽  
Author(s):  
Di Zuo ◽  
Stéphane Avril ◽  
Haitian Yang ◽  
S. Jamaleddin Mousavi ◽  
Klaus Hackl ◽  
...  
Keyword(s):  
Wound Healing ◽  
Damage Mechanics ◽  
Healing Process ◽  
Three Dimensional ◽  
Biological Tissues ◽  
Collagen Fibres ◽  
Length Scales ◽  
Constrained Mixture ◽  
Proposed Model ◽  
Intrinsic Length

Healing of soft biological tissues is the process of self-recovery or self-repair after injury or damage to the extracellular matrix (ECM). In this work, we assume that healing is a stress-driven process, which works at recovering a homeostatic stress metric in the tissue by replacing the damaged ECM with a new undamaged one. For that, a gradient-enhanced continuum healing model is developed for three-dimensional anisotropic tissues using the modified anisotropic Holzapfel–Gasser–Ogden constitutive model. An adaptive stress-driven approach is proposed for the deposition of new collagen fibres during healing with orientations assigned depending on the principal stress direction. The intrinsic length scales of soft tissues are considered through the gradient-enhanced term, and growth and remodelling are simulated by a constrained-mixture model with temporal homogenization. The proposed model is implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three numerical examples have been achieved to illustrate the performance of the proposed model in simulating the healing process with various damage situations, converging towards stress homeostasis. The orientations of newly deposited collagen fibres and the sensitivity to intrinsic length scales are studied through these examples, showing that both have a significant impact on temporal evolutions of the stress distribution and on the size of the damage region. Applications of the approach to carry out in silico experiments of wound healing are promising and show good agreement with existing experiment results.

Bending of marble with intrinsic length scales : A gradient theory with surface energy and size effects

1998 ◽  
Vol 08 (PR8) ◽  
pp. Pr8-399-Pr8-406 ◽  
Author(s):  
I. Vardoulakis ◽  
G. Exadaktylos ◽  
S. K. Kourkoulis
Keyword(s):  
Surface Energy ◽  
Size Effects ◽  
Gradient Theory ◽  
Length Scales ◽  
Intrinsic Length

scholarly journals Determination of the Size of Irregular Particles Using Interferometric Out-of-Focus Imaging

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Marc Brunel ◽  
Huanhuan Shen ◽  
Sébastien Coëtmellec ◽  
Gérard Gréhan ◽  
Tony Delobel
Keyword(s):  
Physical Properties ◽  
Size Range ◽  
Central Peak ◽  
Mathematical Formalism ◽  
Focus Pattern

We present a mathematical formalism to predict speckle-like interferometric out-of-focus patterns created by irregular scattering objects. We describe the objects by an ensemble of Dirac emitters. We show that it is not necessary to describe rigorously the scattering properties of an elliptical irregular object to predict some physical properties of the interferometric out-of-focus pattern. The fit of the central peak of the 2D autocorrelation of the pattern allows the prediction of the size of the scattering element. The method can be applied to particles in a size range from a tenth of micrometers to the millimeter.

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