Source of Reaction-Diffusion Coupling in Confined Systems due to Temperature Inhomogeneities A.V. Anil Kumar, 1 S. Yashonath, 1,2 and G. Ananthakrishna 3,2 1 Solid State and Structural and Chemistry Unit, Indian Institute of Science, Bangalore, India 560 012 2 Center for Condensed Matter Theory, Indian Institute of Science, Bangalore, India 560 012 3 Materials Research Center, Indian Institute of Science, Bangalore, India 560 012 Diffusion is often accompanied by a reaction or sorption which can induce temperature inhomo- geneities. Monte Carlo simulations of Lennard-Jones atoms in zeolite NaCaA are reported with a hot zone presumed to be created by a reaction. Our simulations show that localized hot regions can alter both the kinetic and transport properties. Further, enhancement of the diffusion constant is greater for larger barrier height, a surprising result of considerable significance to many chemical and biological processes. We find an unanticipated coupling between reaction and diffusion due to the presence of hot zone in addition to that which normally exists via concentration. Diffusion within porous materials or confined geom- etry is still poorly understood [1,2] despite increased attention in recent times [3,4]. Life sciences has a number of instances which relate to diffusion within confined regions — for example, ion diffusion across membranes and approach of a substrate towards an active site of an enzyme [5]. Hydrocarbon separation and catalysis within zeolites provide instances of processes in chemistry [6]. Problems involving fluid flow and excitonic transport through a porous medium are examples from physical sciences [2]. The richness of the subject partly arises from the geometry of confined systems (the fractal nature of the pores, for instance). Further, while nonuniformity of concentration has been dealt with in great detail, that of temperature has received little attention. In particular, when temperature is inhomogeneous, the very definition of diffusion as being an activated process needs a gen- eralization. Such nonuniformity in temperature arises routinely in biological, chemical, and physical systems for a variety of reasons. Here, we discuss issues relating to the possible sources of such hot spots and their influence on transport properties in the context of zeolites. Zeolites are porous solids with pore sizes comparable to molecular dimensions [7]. Because of its rich and di- verse catalytic as well as molecular sieve properties [8] it has attracted much attention. The existence of specific catalytic and physisorption sites coupled with their poor thermal conductivity could lead to local hot regions [8]. (Typically in 10 ps, the hot region decays less than a few percent.) This may affect both kinetic and diffusion prop- erties. Such a situation can arise in many biosystems as well. For instance, plasma membrane protein-encoding m-RNA IST2 is shown to have high asymmetry in con- centration between the mother cell and the bud [9]. One possible way of maintaining such an asymmetry against the concentration gradient is through localized hot or cold re- gions. In spite of the importance of such reaction induced hot spot and its influence on the diffusion of the species, this problem has not been addressed so far. Here, we study the effect of inhomogeneous temperature presumed to be created by a “reaction,” on the equilibration rate and self-diffusion coefficient of guest molecules in zeolites. Monte Carlo simulations on simple argon atoms in zeolite A are reported here. Our results show that self- diffusion coefficient D is increased substantially due to the presence of a hot zone. More significantly, at a conceptual level our analysis shows that local changes in temperature resulting from reactions can induce additional coupling between reaction and diffusion. Landauer [10], in a seminal paper, addressed the effect of a nonuniform temperature bath on the relative occu- pation of competing local energy minima. For the case of a bistable potential Ux (the curve ABCD in Fig. 1), he showed that the presence of a localized heating in a region (say BC ) lying between the lower energy mini- mum A and the potential barrier maximum C can raise the relative population of the higher energy minimum D over that given by the Boltzmann factor exp2DEk B T . This has come to be known as the “blowtorch” effect [10]. Since this effect is rather counterintuitive, following Lan- dauer, we convey the basic idea. Consider the motion of an overdamped particle in this potential (curve ABCD in Fig. 1) subject to a uniform temperature T 0 along the z U(z) A B C D C’ D’ Δ E FIG. 1. The effect of a hot zone at BC in the potential ABCD is to lower D to D 0 .