Short-time and long-time dynamics of the zeolite films in the light of alternative diffusion models

Analysis of the dynamics of diffusion of two mixtures of hydrogen and heavier components through a flat zeolite film was carried out. The concepts of short-time and long-time dynamics were introduced. They derive from the observation of temporal trajectories obtained by applying abrupt perturbations of concentrations on one side of the membrane. An alternative description of the diffusion dynamics was proposed compared to the commonly accepted model that employs a matrix of thermodynamic factors Gamma. In this way, the difficulty of analytical determination of this matrix for more complex adsorption equilibria was eliminated. The model equations were expressed in a matrix form, which enables its easy extension to any number of components. The proposed research methodology was illustrated using an example of diffusion of two selected mixtures, i.e. {H-2, n-C4H10} and {H-2, CO2} in silicalite-1. These gaseous mixtures have applications in specific technological processes. The two models were used to perform quantitative benchmarking of short-time and long-time dynamics of flat zeolite membranes. The assumed boundary conditions correspond to a semi-batch Wicke-Kallenbach diffusion cell. It was demonstrated that the phenomena occurring in short-time and long-time diffusion represent two different dynamic features important from a scientific and practical point of view. A quantitative measure for degree of confinement was proposed based on dynamic adsorption-desorption hysteresis.