Mean-square interfacial displacement

Figure 13. Average mean square particle displacement and Debye Waller factor of interfacial and crystal core atomic motion of a Ni nanoparticle. Filled circles denote the interfacial particles and the circles in the lower corner of the figure denote the crystal core particles. The size of the particle corresponds to N= 2899 atoms or a NP radius = 2.0 nm. Figure 13 was originally published in [71], ...

The permeability of small penetrant molecules through an organic matrix is determined by the solubility and diffusivity of the small molecule in the matrix as well as by the mean-square displacement (total path length traveled) divided by the sample thickness. In principle, the addition of a filler in the polymer matrix is expected to affect the solubility and diffusivity of a penetrant molecule, especially in the vicinity of the filler (i.e in the filler-polymer interfacial region and at least one polymer Rg away from the filler surface). Also, it is expected that fillers will affect the path tortuosity (mean-square displacement of penetrant versus film thickness) directly, when penetrants are forced to travel around impermeable fillers, and indirectly, when fillers induce polymer chain aUgnment or alignment and modification of polymer crystallites. ... 

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