scholarly journals On selected aspects of space-fractional continuum mechanics model approximation

2020 ◽  
Vol 167 ◽  
pp. 105287 ◽  
Author(s):  
Krzysztof Szajek ◽  
Wojciech Sumelka ◽  
Tomasz Blaszczyk ◽  
Krzysztof Bekus
Keyword(s):  
Continuum Mechanics ◽  
Model Approximation ◽  
Mechanics Model ◽  
Fractional Continuum

Atomic Understanding of the Swelling and Phase Transition of Polyacrylamide Hydrogel

2016 ◽  
Vol 08 (07) ◽  
pp. 1640002 ◽  
Author(s):  
Shuai Xu ◽  
Ying Wang ◽  
Jianying Hu ◽  
Zishun Liu
Keyword(s):  
Phase Transition ◽  
Continuum Mechanics ◽  
Chemical Potential ◽  
Polymer Network ◽  
Point Of View ◽  
Dynamics Simulation ◽  
Mechanics Model ◽  
Basic Parameters ◽  
Solvent Molecules ◽  
And Diffusion

A polymer network can imbibe copious amounts of solvent (water) and swell, and the resulting state is known as a hydrogel. In this study, we have made the modification for the all-atom consistent valence force field (CVFF) to investigate the swelling property of polyacrylamide (PAM) hydrogel by molecular dynamics simulation. We have built 21 hydrogel models with different solvent contents and calculate the average chemical potential and diffusion coefficient of solvent molecules in PAM hydrogel. We find that when the mass fraction of solvent is about 90%, PAM hydrogel reaches its free swelling limitation and loses the motivation of absorbing solvent. Furthermore, it is also found that PAM hydrogel has a phase transition phenomenon when the values of solvent chemical potential are between [Formula: see text][Formula: see text]kcal/mol and [Formula: see text][Formula: see text]kcal/mol. This study will provide insight into the basic parameters which are widely used in continuum mechanics analysis of hydrogels from atomic point of view and help researchers to improve the continuum mechanics model for neutral hydrogel.

Prediction of chirality- and size-dependent elastic properties of single-walled carbon nanotubes via a molecular mechanics model

2006 ◽  
Vol 462 (2072) ◽  
pp. 2523-2540 ◽  
Author(s):  
Tienchong Chang ◽  
Jingyan Geng ◽  
Xingming Guo
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Molecular Mechanics ◽  
Elastic Properties ◽  
Continuum Mechanics ◽  
Governing Equations ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Mechanics Model ◽  
Molecular Mechanics Model

Molecular mechanics has been widely used to analytically study mechanical behaviour of carbon nanotubes. However, explicit expressions for elastic properties of carbon nanotubes are so far confined to some special cases due to the lack of fully constructed governing equations for the molecular mechanics model. In this paper, governing equations for an analytical molecular mechanics model are fully established. The explicit expressions for five in-plane elastic properties of a chiral single-walled carbon nanotube are derived, which make properties at different length-scales directly connected. The effects of tube chirality and tube diameter are investigated. In particular, the present results show that the classic relationship from the isotropic elastic theory of continuum mechanics between Young's modulus and shear modulus of a single-walled carbon nanotube is not retained. The present analytical results are helpful to the understanding of elastic properties of carbon nanotubes, and also useful to the topic of linking molecular mechanics with continuum mechanics.

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