Polymer crystallization, computer modeling

Keywords Chain folding Computer modeling Crystal growth Crystal-melt interfaces Molecular dynamics Polymer crystallization... 

The modern availability of sensitive experimental techniques using synchrotron radiation and atomic force microscopy, and fast computers for molecular modeling, has spurred recent intense interest in following the mechanism of polymer crystallization. In spite of the heroic efforts by the... 

Readers interested in learning more about predicting Tm are also referred to a review article by Dearden [177]. Finally, direct simulations of polymer crystallization are of increasing interest as computers become more powerful, and were reviewed in 1994 by Goldbeck-Wood [178], The later work of Madkour and Mark [179-182], which employs Monte Carlo simulations to model the crystallization of polypropylene, is also of interest. 

Faso M, Muneta LM, Muller M, Alcazar V, Chinesta F, Ammar A. Hierarchical approach to flow calculations for polymeric liquid crystals. In Faso M, Perpete FA, editors. Multiscale Modelling of Polymer Properties, Computer-Aided Chemical Engineering. Volume 22. Amsterdam Elsevier 2006. 

Program Description. In order to determine polymer crystal structures, each of the participating Institutions uses computer programs that reflect different resources and abilities as well as philosophies. Models to be used for calculation of Intensities are constructed In various ways, and each has a different strategy for finding the best result. Each of the methods has some unique abilities and some disadvantages. 

Figure 6.3 shows crystal-shaped platinum deposits juxtaposed to the computer simulations. Note that the computer simulation were calculated for a minority phase volume fraction of 12%, while depending on the assumed polymer densities, the copolymer PLA volume fraction lies between 36 and 39 %. As discussed previously, for these high volume fractions the computer model predicts that the < 110> directions form vertices and tlius, increase the number of faces surrounding the < 100 > vertices by a factor of two to a total of 8 facets. 

Cheng SZD, Noid DW, Wunderlich B (1989) Molecular Segregation and Nucleation of Poly(elhylaie oxide) Crystallized from the Melt. IV. Computer Modeling. J Polymer Sd Part B Polymer Phys 27 1149-1160. 

Sumpter BG, Noid DW, Wunderlich B (1992) Computational Experiments on the Motion and Generation of Defects in Polymer Crystals. Macromolecules 25 7247-7255. Peterlin A (1971) Molecular Model of Drawing Polyethylene and Polypropylene. J Mater Sci 6 490-508. 

J-U. Sommer and G. Reiter, Polymer crystallization in quasi-two dimensions. II. Kinetic models and computer simulations, J. Chem. Phys. 112, 4384- 393 (2000). 

Most of the early proposed models satisfied only one or several of the above requirements, but not all Since deformation and relaxation involves the dynamics of the polymer chains, it is by using the molecular dynamics method, quantum dynamics, or variants thereof that one can begin to derive a clear and complete description of what is happening inside a polymer crystal. In this regard, we have performed a number of detailed, systematic dynamics computations on parafiin- and polyethylene-like crystals. 

Although secondary nucleation theory was, for a period, widely accepted, it is now coming under increasing pressure, from experimental data, from computer simulation, and from new approaches to the fundamental process of crystalhzation. It is not clear at this stage whether all that is required is a few adjustments to the theory, or whether the idea of a nucleation barrier is flawed, or even if the idea that the crystal thickness seen is the fastest growing is correct. With the development of new theoretical tools, and the increased integration of theory with computer simulation, it is hoped that a more complete model for polymer crystallization can be developed. 

A problem area that is not so amenable to mesoscale methods is polymer crystallization. This has proven to be one of the most difficult computational challenges in all of polymer science because the pertinent phenomena operate simultaneously over a wide range of length scales. The pol5uner crystallizes into a particular space group because of atomic detail, and the mechanical properties of the crystallites are determined by, and can only be calculated reliably with, atomic force fields with all atoms represented (126,127). Yet the size of the crystallites or spherulites is so large as to require mesoscopic methods for comprehension. But a crystalline polymer is almost never 100% crystalline. The interphases between crystalline and amorphous domains, with the possibilities for adjacent or nonadjacent reentry and tie-chain distributions, are critical to the properties of semicrystalline polymers. Only recently have models been developed (203) to rigorously address this problem area. 

A third, less obvious limitation of sampling methods is that, due to the heavy computational burden involved, simpler interatomic potential models are more prevalent in Monte Carlo and molecular dynamics simulations. For example, polarizability may be an important factor in some polymer crystals. Nevertheless, a model such as the shell model is difficult and time-consuming to implement in Monte Carlo or molecular dynamics simulations and is rarely used. United atom models are quite popular in simulations of amorphous phases due to the reduction in computational requirements for a simulation of a given size. However, united atom models must be used with caution in crystal phase simulations, as the neglect of structural detail in the model may be sufficient to alter completely the symmetry of the crystal phase itself. United atom polyethylene, for example, exhibits a hexagonal unit cell over all temperatures, rather than the experimentally observed orthorhombic unit cell [58,63] such a change of structure could be reflected in the dynamical properties as well. 

Rutledge G (2013) Chapter 6 computer modeling of polymer crystallization. In Piorkowska E, Rutledge GC (eds) Handbook of polymer crystallization. Wiley, Hoboken Sadler DM (1984) Chapter 4 structure of crystalline polymers. In Hall IH (ed) Elsevier Applied Science Publishers, London, p 125... 

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