Grained Models

Coarse-grained polymer models neglect the chemical detail of a specific polymer chain and include only excluded volume and topology (chain connectivity) as the properties determining universal behavior of polymers. They can be formulated for the continuum (off-lattice) as well as for a lattice. For all coarse-grained models, the repeat unit or monomer unit represents a section of a chemically realistic chain. MD techniques are employed to study dynamics with off-lattice models, whereas MC techniques are used for the lattice models and for efficient equilibration of the continuum models.36 2 A tutorial on coarse-grained modeling can be found in this book series.43 

The literature on coarse graining is vast and cannot be treated in any detail here. There are many examples of coarse-graining strategies for bio-molecules and polymers, but there have not been as many studies for ionic liquids. A tutorial on coarse graining has been published in this book 

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Coarse-grained models have a longstanding history in polymer science. Long-chain molecules share many common mesoscopic characteristics which are independent of the atomistic stmcture of the chemical repeat units [4, 5 and 6]. The self-similar stmcture [7, 8, 9 and 10] on large length scales is only characterized by a single length scale, the chain extension R. 

Fig. 8.8 The bond fluctuation model. In this example three bcmds in the polymer arc incorporated into a singk effecti bond between effective moncmers . (Figure adapted from Baschnagel J, K Binder, W Paul, M Laso, U Sutcr, I Batouli [N ]ilge and T Burger 1991. On the Construction of Coarse-Grained Models for Linear Flexible Polymer-Chains -Distribution-Functions for Groups of Consecutive Monomers. Journal of Chemical Physics 93 6014-6025.)...

The bond fluctuation model (BFM) [51] has proved to be a very efficient computational method for Monte Carlo simulations of linear polymers during the last decade. This is a coarse-grained model of polymer chains, in which an effective monomer consists of an elementary cube whose eight sites on a hypothetical cubic lattice are blocked for further occupation (see... 

R. B. Pandey, A. Milchev, K. Binder. Semidilute and concentrated polymer solutions near attractive walls Dynamic Monte Carlo simulation of density and pressure profiles of a coarse-grained model. Macromolecules 50 1194-1204, 1997. 

Nevertheless, large-scale phenomena and complicated phase diagrams cannot be investigated within realistic models at the moment, and this is not very likely to change soon. Therefore, theorists have often resorted to coarse-grained models, which capture the features of the substances believed to be essential for the properties of interest. Such models can provide qualitative and semiquantitative insight into the physics of these materials, and hopefully establish general relationships between microscopic and thermodynamic quantities. 

The most complex and powerful coarse-grained models are those which retain the chain character of the amphiphile molecules. 

Sjoerdsma S.D., Bleijenberg A.C.A.M., and Heikens D., The Poisson ratio of polymer blend, effects of adhesion and correlation with the Kemer packed grain model. Polymer, 22, 619, 1981. 

Bridging the Gap Between Atomistic and Coarse-Grained Models of Polymers Status and Perspectives... 

Keywords. Atomistic models, Bridging, Coarse-grained models, Polymers, Simulations... 

A suitable approach to the equilibration of an amorphous polymer system at bulk density becomes much more likely when the fully atomistic model in continuous space is replaced by an equivalent coarse-grained model on a lattice with sufficient conformational flexibility. Different strategies, which seek results at different levels of detail, can be employed to create an appropriate coarse-grained model. Section 4 (Doruker, Mattice) describes an approach which attempts to retain a connection with the covalent bonds in the polymer. The rotational isomeric state (RIS) [35,36] model for the chain is mapped into... 

The mapping procedure provides an explicit connection between an atomistic model of a polymer chain and the corresponding coarse-grained model. For PE, we use an united atom description for the CH2 groups, resulting in a potential of the following type [146,182,183] ... 

Fig. 5.13. Relaxation time r3 plotted vs. temperature for the coarse-grained model of PE with N = 20, using the random hopping algorithm (upper set of data) or the slithering snake algorithm (lower set of data), respectively. The time r3 is of the same order as the Rouse relaxation time of the chains, and is defined in terms of a crossing criterion for the mean-square displacements [41], g3(t = r3) = g2(t = r3) [See Eqs. (5.2) and 5.3)]. From [32]...

In this review, the state of the art of the bridging of the gap between quantum chemical, atomistic, coarse-grained (and almost macroscopic) models of polymers has been discussed. Simulations with coarse-grained models provide the promise of the equilibration of models of dense amorphous polymers, whereas such equilibration is extremely difficult if the models are expressed in fully atomistic detail. The review presents the status of this rapidly developing field as of the beginning of 1998. A few minor additions were incorporated in the page proof, early in 2000, in response to suggestions from the reviewer. 

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