Amorphous cells packings

Fig. 1. A molecular model of a condensed phase polymer blend. The example shown is used to study a mixture containing atactic polystyrene 40-mer (2 chains) and atactic poly(methyl methacrylate) 40-mer (2 chains). Figure la shows the cell with the molecules configured as they are in space the parts of the molecules lying outside the cell occupy adjacent cells in the periodic structure. To convey the space filling nature of the construction, Figure lb shows the same molecules packed in the cell. The model system was constructed using the Amorphous Cell module in the Materials Studio software package distributed by Accelrys (103). The amorphous cell system was constructed at a density of 1.12 g/cm at 300 K and the subsequent 80 ps of NPT dynamics at the same temperature and zero pressure equilibrated the system to a density of 1.057 g/cm .

After construction of the amorphous cell using the method of Theodorou-Suter ° and geometric free volume analysis of the cell several (four to six) penetrant molecules to improve sampling are inserted at the free volume positions. The cell is further relaxed by 100 ps of a NPT-MD (constant particle number, temperature and pressure) simulation at 1 bar and room temperature before starting a longer (nanoseconds) NVT dynamics. The recorded trajectories of each penetrant gas molecule are analyzed and the diffusion coefficient is determined by means of relation (eqn (1.5)). In Figures 1.2 and 1.3 the packed cell model of polydimethylsiloxane (PDMS) and the trajectory of N2 molecules in the PDMS matrix are reported. The MD simulations show two types of motions of the N2 molecules jumps between cavities and local motion inside cavities. 

The comparison of modelled values of modified PEEK-WC with the experimental ones indicates that the new approach of packing produces amorphous cells show less scatter in predicted S and D values with respect to other previous published papers dealing with these membranes.The simulated values are more self-consistent showing less scatter than in recently reported papers dealing with modeling of alkylated PEEK-WC membranes. A relatively good agreement is obtained for O2 and N2 molecules for diffusion coefficient as well as the solubility. 

Reliable and reproducible results can only be obtained if the sample is prepared carefully. When a sample is packed in an X-ray holder, the distribution of crystal orientations can be non-random, and this condition is referred to as preferred orientation. Jenkins and Snyder have elegantly illustrated this point in Fig. 17. Atoms bond together, in a unique manner, to form unit cells. If the unit cells are grouped so as to have long-range order, a crystalline material is obtained. In the absence of long-range order, the material is amorphous (non-crystalline). A powder sample is composed of... 

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