Polymers multiscale modeling

The recent growth of multiscale modeling has permeated every material type known to mankind regarding structural members. Although most of the work has been focused on metal alloys as they have been used the most over time as reliable structural materials, multiscale modeling has also been employed for ceramics and polymer systems (both synthetic and biological). 

The use of multiscale modeling for polymers and polymer-based systems can be distinguished into synthetic (man-made) and biological (God-made) materials. Although synthetic polymers have been used as monolithic structural materials,... 

With the advent of nanomaterials, different types of polymer-based composites developed as multiple scale analysis down to the nanoscale became a trend for development of new materials with new properties. Multiscale materials modeling continue to play a role in these endeavors as well. For example, Qian et al. [257] developed multiscale, multiphysics numerical tools to address simulations of carbon nanotubes and their associated effects in composites, including the mechanical properties of Young s modulus, bending stiffness, buckling, and strength. Maiti [258] also used multiscale modeling of carbon nanotubes for microelectronics applications. Friesecke and James [259] developed a concurrent numerical scheme to evaluate nanotubes and nanorods in a continuum. 

Limbach, H.J., and Kremer, K. (2006) Multiscale modelling of polymers perspectives for food materials. Trends Food Sci. Technol. 17,215-219. 

As the structure, dynamics and properties are determined by phenomena on many length and time scales physical modelling is subdivided into the quantum mechanical, atomistic, mesoscale, microscale and continuum levels, while research into the way in which these levels are linked is known as hierarchical or multiscale modelling. The typical structural levels arising in the polymer field are shown Figure 1. 

Cagin, T. Wang, G Martin, R. Zamanakos, G. Vaidehi, N. Mainz, D. T. Goddard, W. A., Multiscale modeling and simulation methods with applications to dendritic polymers, Comp Theor. Polym. Sci. 2001, 11, 345-356... 

The relevant length scales in polymers span a range of at least four orders of magnitude, from Angstroms (see the forces in Fig. 1) up to at least a few micrometers. In soft matter and polymer theory the multiscale modeling approach, which attempts to simulate such systems in total including aU relevant interactions, has recently attracted a lot of attention [17], In experimental polymer research an analogous approach would be the combination of results from many techniques... 

Kiparissides C, Pladis P, Moen 0. From Polyethylene Rheology Curves to Molecular Weight Distributions. In Laso M, Perpete EA, editors. Multiscale Modelling of Polymer Properties, Computer-Aided Chemical Engineering. Volume... 

These are fields defined throughout space in the continuum theory. Thus, the total energy of the system is an integral of these quantities over the volume of the sample dt). The FEM has been incorporated in some commercial software packages and open source codes (e.g., ABAQUS, ANSYS, Palmyra, and OOF) and widely used to evaluate the mechanical properties of polymer composites. Some attempts have recently been made to apply the FEM to nanoparticle-reinforced polymer nanocomposites. In order to capture the multiscale material behaviors, efforts are also underway to combine the multiscale models spanning from molecular to macroscopic levels [51,52]. 

Li and Chou [73,74] have reported a multiscale modeling of the compressive behavior of CNT/polymer composites. The nanotube is modeled at the atomistic scale, and the matrix deformation is analyzed by the continuum FEM. The nanotube arrd polymer matrix are assttmed to be bonded by vdW interactions at the interface. The stress distributiorrs at the nanotube/polymer interface under isostrain and isostress loading conditiorrs have been examined. They have used beam elements for SWCNT using molectrlar structural mechanics, truss rod for vdW links and cubic elements for matrix. The rule of mixtrrre was used as for comparision in this research. The buckling forces of nanotube/polymer composites for different nanotube lengths and diameters are computed. The results indicate that continuous nanotubes can most effectively enhance the composite buckling resistance. 

Li, C. and Chou, X. W. Multiscale modeling of carbon nanotube reinforced polymer composites. J of Nanosci Nanotechnol., 3,423-430 (2003). 

Li, C. and Chou, T.W. Multiscale modeling of compressive behavior of carbon nanotube/ polymer composites. Comp Sci and Tech., 66,2409-2414 (2006). 

Wemik, J. M. and Meguid, S. A., Multiscale modeling of the nonlinear response of nano-reinforced polymers. Acta Mech., 217, 1-16 (2011). 

Yang, S., Yu, S., Kyoung, W., Han, D. S., and Cho, M. Multiscale modeling of size-dependent elastic properties of carbon nanotube/polymer nanocomposites with interfacial imperfections. Polymer, 53, 623-633 (2012). 

Franco AA (2013) Toward a bottom-up multiscale modeling framework for the transient analysis of PEM fuel cells operation. In Franco AA (ed) Polymer electrolyte fuel cells science, applications and challenges. CRC PressATaylor Francis Group, Boca Raton... 

Fermeglia, M. and Pricl, S. 2007. Multiscale modeling for polymer systems of industrial interest. Progress in Organic Coatings 58 187-199. 

Oleg Borodin works as a scientist at the Electrochemistry Branch of the Army Research Laboratory, Adelphi, MD since 2011. After obtained a Ph.D. degree in Chemical Engineering in 2000 he worked in the area of multiscale modeling of liquid, ionic liquid and polymer electrolytes for battery and double layer capacitor applications, modeling of energetic composite materials, polymers in solutions, and polymer nanocomposites. He coauthored more than a hundred publications and four book chapters. His modeling efforts focus on the scales from electronic to atomistic and mesoscale. 

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