Reaction and particle distribution in networks of single-file systems

– A quadratic network of mutually intersecting channels with single-file confinement is considered as a host system for molecules A undergoing a unidirectional reaction A → B in the channel intersections. If each of the two sets of perpendicular channels is able to accommodate only one of the two types of molecular species, the overall particle concentration deviates significantly from being homogeneous. Under these conditions, the effective reactivity may substantially exceed that in an equivalent system without mutual particle exclusion. Introduction. – The invention of zeolite catalysts with networks of different channels like MFI-type zeolites (ZSM-5, silicalite [1]) has given rise to speculation about the possibility of reactivity enhancement by “molecular traffic control” [2]. This conception suffered from the fact that neither experimental evidence nor molecular simulations have so far been provided for the support of its feasibility. Thus, over many years, it has remained a subject of controversial discussion [3–8]. With the application of the concept of single-file diffusion —i.e. of onedimensional diffusion with the additional constraint that the individual diffusants are not allowed mutually to exchange their positions [9–11]— to zeolite science and technology [12–17], for the first time the analytical treatment of the transport behaviour in networks of zeolite catalysts, which have been claimed to give rise to an enhancement of the catalytic reactivity, has become possible [18]. It is the intention of this letter to demonstrate the interrelation between reactivity enhancement and the deviation from homogeneous site occupation. Reactive networks of uniform site occupancy. – Being subjected to constant boundary conditions, homogeneous host systems are well known to be homogeneously occupied by guest molecules. By assuming that the system may be represented by an entity of lattice sites with molecular diffusion proceeding by jumps between adjacent sites, this is an immediate consequence of the stationarity condition of the kinetic equation