Diffusion jumps of small molecules dispersed in chain molecules or other kinds of slow-moving matrices have already been observed in many previous simulations of such systems, and their treatment led to important qualitative conclusions. In the present work, a new, very simple yet effective method is described, allowing for both identification of individual penetrant jump events and their quantitative treatment in a statistical sense. The method is applied in equilibrium Molecular Dynamics simulations for systems of gaseous alkanes, methane through n-butane, including also a mixture of methane and n-butane, dispersed in n-decane or n-eicosane. Equilibration and attainment of a linear diffusion regime is confirmed by means of various criteria, and the jumps detection method is applied to all systems studied. The results obtained clearly show the existence of distinct jump events in all cases, although the average jump length is reduced with penetrant or liquid alkane molecular weight. The method allows one to determine the average jump length and the corresponding jumps frequency. On the basis of these results, it was possible to estimate a random walk type diffusion coefficient, D(s,jumps), of the penetrants, which was found to be substantially lower compared with the overall diffusion coefficient D(s,MSD) obtained by the mean square displacement method. This finding led us to assume that the overall penetrants' diffusion in the studied systems is a combination of longer jumps with a smoother and more gradual displacement, a result that confirms assumptions suggested in previous studies.

Microscopic mechanisms underlying the diffusion of particles in polymeric and other systems include 'jumps' that are said to provide for a substantial contribution to the overall particle displacement. Such jumps have been observed in molecular simulations and experimentally, leading to important qualitative conclusions. An efficient method has been proposed for the identification and quantitative processing of jumps, and successfully employed in simulations of gas-liquid alkane systems. In the present work, the same method is applied in equilibrium Molecular Dynamics simulations of methane-like molecules dispersed in polymer-like alkanes, at atmospheric pressure and temperature well above the polymer melting point. The systems studied were prepared and equilibrated and a linear diffusion regime was confirmed by means of various criteria. The occurrence of distinct jump events was clearly revealed and their average length and frequency were calculated. In this way, a random-walk-type diffusion coefficient, D s, jumps , of the penetrants, was obtained and found to be lower than the overall diffusion coefficient D s, MSD calculated by the mean square displacement method. This is a strong indication that the overall diffusion is a combination of longer jumps with other microscopic mechanisms such as smoother and more gradual displacements effected upon the diffusing particle by its surroundings.

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