Correlation single-file systems

For an estimate of the correlation between t he intracrystalline mean life time and the system properties, the exchange curve between the (labelled) molecules of a single-file system and the (unlabelled) surroundings ( tracer exchange curve ) may be assumed to be determined by a single dimensionless parameter... 

Molecular dynamics (MD) simulations in single-file systems are additionally comphcated by the requirement that in the absence of external forces the center of mass must be preserved. This comphcation results from the fact that, as a consequence of the correlated motion in a single-file system, the shift of a particular molecule must be accompanied by shifts of other molecules in the same direction. Depending on the total amoimt of molecules under consideration, the conservation of the center of mass therefore prohibits arbitrarily large molecular shifts. The maximum mean square displacement may be shown to obey the relation [22]... 

As soon as the movements of different species have to be distinguished from each other, however, the mutual correlation of the molecules in singlefile systems makes it impossible to predict the evolution of the particle distributions by differential equations. Eor this reason, the time dependence of the tracer exchange in single-file systems has thus far only been investigated by Monte Carlo simulations [1,55-57]. 

As in the case of tracer exchange, quantitative information about the correlated effect of transport and catalytic reactions in single-file systems has... 

Our understanding of diffusion and reaction in single-file systems is impaired by the lack of a comprehensive analytical theory. The traditional way of analytically treating the evolution of particle distributions by differential equations is prevented by the correlation of the movement of distant particles. One may respond to this restriction by considering joint probabilities covering the occupancy and further suitable quantities with respect to each individual site. These joint probabilities may be shown to be subject to master equations. 

A unique correlation in diffusional motion can occur in zeolites with one-dimensional micropores such as mordenite or ZSM-22 (TON). Single-file diffusion is defined as restricted mobility in one-dimensional pores, where molecules cannot pass each other. Indeed, dynamic Monte Carlo calculations that compute diffusion rates by considering them to be the result of the hopping of molecules between defined sites show a very steep decrease in the diffusion rate for a one-dimensional system compared with decreases found for three-dimensional systems. 

The difference between the correlation functions in a canonical and a grand canonical ensemble is largest for one-dimensional systems with hard core interactions. This occurs because in such a system the particles cannot pass each other. This also leads to a significantly different diffusion behavior (single file diffusion). In a grand canonical setting, however, particles can pass each other via the... 

The derivative at each point is obtained by a fourth order central difference equation, then an arbitrary but approximate value of n is chosen and all points other than very early and plateau points are correlated by a least-squares linear regression using Equation 3. The index n is incremented or decremented systematically until the best correlation coefficient is obtained. Data from a single experimental run can be reduced alone or combined with other data files of the same system. Employment of... 

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