Atomistic packing models

The quality of atomistic packing models is typically validated via comparisons between measured and simulated properties like wide-angle X-ray scattering (WAXS)... 

M. Heuchel, D. Fritsch, P. M. Budd, N. B. McKeown, D. Hofmann, Atomistic packing model and free volume distribution of a polymer with intrinsic microporosity (PIM-1), J. Membr. Sci., 318, 84-99 (2008). 

The construction of a correct model for the polymer structure is the prerequisite for obtaining accurate results and it is always the first step in the FV modelling. Nowadays several well established simulation methods exist for the preparation of atomistic packing models, both for high and for low free volume polymers [33]. In molecular modelling of amorphous polymers, usually a cubic characteristic volume element is filled with polymer... 

Figure 4.7 Representative slice of an atomistic packing model of ffyflon AD80X. The polymer chains are represented by the small sticks. The free volume elements are shown as the darker continuous regions, represented by a collection of neighbouring and overlapping spheres. Slice thickness ca. 5A...

Model systems can be, on the one hand, subjected to a static structure optimization. There, the fact is considered that the potential energy of a relaxed atomistic system (cf. Equation 1.1) should show a minimum value. Static optimization then means that by suited numeric procedures the geometry of the simulated system is changed as long as the potential energy reaches the next minimum value [16]. In the context of amorphous packing models, the main application for this kind of procedure is the reduction of unrealistic local tensions in a model as a prerequisite for later molecular dynamic (MD) simulations. 

Equation 1.3 represents a system of usually several thousand coupled differential equations of second order. It can be solved only numerically in small time steps At via finite-difference methods [16]. There always the situation at t + At is calculated from the situation at t. Considering the very fast oscillations of covalent bonds, At must not be longer than about 1 fs to avoid numerical breakdown connected with problems with energy conservation. This condition imposes a limit of the typical maximum simulation time that for the above-mentioned system sizes is of the order of several ns. The limited possible size of atomistic polymer packing models (cf. above) together with this simulation time limitation also set certain limits for the structures and processes that can be reasonably simulated. Furthermore, the limited model size demands the application of periodic boundary conditions to avoid extreme surface effects. 

The Insightll/MaterialsStudio/Discover software of Accelrys [18, 19] was utilized for the amorphous packing model construction, equilibration and the atomistic... 

Finally, Honeycutt" has applied blend PRISM theory at an atomistic RIS model level to study the effect of tacticity (stereochemical differences) on the phase behavior of a commercially important binary polymer mixture. Tacticity is found to result in significant changes of the computed spinodal boundaries, which serves to again emphasize the importance of monomer structure and local packing on the free energy of mixing. 

The amorphous packing model construction and the atomistic simulations of the shown polymers have been investigated using Accelrys Materials Studio (MS) Modeling... 

In summary, for Leukipp and Demokrit, the empty space between the atoms was a key assumption in their model, because, if particles were closely packed, they could not move and substances could not be mixed. When asking students to philosophise about the nature of matter, we indeed find parallels to the ancient Greek thinking, both to the so-called atomists and to the continuous ideas of Aristotle and others. For example, Leukipp s and Demokrit s explanation for the specific weight of substances corresponds to one student conception younger students especially tend to explain differences in the specific weight (but also hardness of substances) with differences in the closeness of particles (Fig. 10.6). They seldom take into account that the particles could have a different weight themselves. 

We can therefore conclude that differences in the structural relaxation between bead-spring and chemically realistic models can be attributed to either the differences in packing that we discussed above or the presence of barriers in the dihedral potential in atomistic models. To quantify the role of dihedral barriers in polymer melt dynamics, we now examine high-temperature relaxation in polymer melts. 

Yoon, Smith, and Matsuda, on the other hand, compared two approaches, using a united-atom model and a fully atomistic model.Stochastic dynamics and MD simulations of w-tridecane (C13H28) were used to study polyethylene. Besides studying the bulk melt, the authors examined confined melts between solid surfaces. Chain conformations, chain packing orientational correlations, and self-diffusion were among the properties studied. In regard to chain confer-... 

An alternative theoretical approach to exploring the limits of the tensile stress of fibres with perfectly oriented and packed polymer molecules was developed by Termonia et al. (1986 Termonia, 2000). The model bypasses details of the deformation on an atomistic scale and focuses instead on a length scale of the order of the distance... 

Detailed structural information can be obtained from experimental data for crystalline materials, often with exact knowledge of respective atomic positions within the material framework. For CMPs, which are mostly highly amorphous, we have little experimental data that can aid in the construction of a representative atomistic model. Even when there are some features of order, such as peaks in powder X-ray diffraction (PXRD) plots, it is very challenging to utilise this information to rationalise the structure in a meaningful way. As a result, very little is known about the atomistic structure and packing of the CMP framework. 

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