Abstract
Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.
Highlights
The inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms
Every particle is practically “smoothed” over a finite volume with fixed mass. For this part of the paper, we focus our attention to two widely-used mathematical methods in macroscale calculations, i.e., finite element method (FEM) and finite volume method (FVM)
Depending on the number of atoms that are lumped into a single super atom, i.e., the degree of coarse-graining, the systemic coarse-graining methods are roughly divided into three major blocks; (i) low coarse-graining degrees where one or two monomers are coarse-grained into one super atom; for instance, in an iterative Boltzmann inversion (IBI) scheme; (ii) medium coarse-graining degrees where ten to twenty monomers are coarse-grained into one blob or bead, for instance, used in the so-called “blob model”; and (iii) high coarse-graining degrees where the whole chain is mapped to a single soft colloid in super coarse-graining methods
Summary
Polymeric materials display distinguished characteristics which range from the angstrom level of an individual bond, to tens of nanometers of the chain gyration radius, to micrometers, millimeters and larger in melts, blends, solutions and polymer nanocomposites (PNCs). The bridging of length and time scales via a combination of various methods in a multiscale simulation framework is considered to be one of the most important topics in computational materials research. The mesoscopic scale (~10−6 m, ~10−6–10−3 s): At mesoscopic scale, a molecule is usually described with a field or a microscopic particle generally known as a bead In this way the molecular details are introduced implicitly which provides the opportunity to simulate the phenomena on longer length and time scales hardly accessible by atomistic methods. We aim to emphasize different approaches, challenges, restrictions, and opportunities that models of each scale could generally possess Since such models are the building blocks for the multiscale methods, it is important to note how they convey their characteristics into a multiscale approach. The present review is meant to put forth the major directions in multiscale simulation strategies in polymer science
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