Interfacial Reaction Kinetics
نویسندگان
چکیده
We study A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. Coupled equations are derived for the hierarchy of many-body correlation functions. Postulating physically motivated bounds, closed equations result without the need for ad hoc decoupling approximations. We consider general dynamical exponent z, where xt ∼ t is the rms diffusion distance after time t. At short times the number of reactions per unit area, Rt, is 2nd order in the far-field reactant densities n ∞ A , n ∞ B . For spatial dimensions d above a critical value dc = z − 1, simple mean field (MF) kinetics pertain, Rt ∼ Qbtn∞A n∞B where Qb is the local reactivity. For low dimensions d < dc, this MF regime is followed by 2nd order diffusion controlled (DC) kinetics, Rt ≈ x t n∞A n∞B , provided Qb > Q∗b ∼ (n∞B ). Logarithmic corrections arise in marginal cases. At long times, a cross-over to 1st order DC kinetics occurs: Rt ≈ xtn∞A . A density depletion hole grows on the more dilute A side. In the symmetric case (n∞A = n ∞ B ), when d < dc the long time decay of the interfacial reactant density, nA, is determined by fluctuations in the initial reactant distribution, giving n s A ∼ t. Correspondingly, A-rich and B-rich regions develop at the interface analogously to the segregation effects established by other authors for the bulk reaction A + B → ∅. For d > dc fluctuations are unimportant: local mean field theory applies at the interface (joint density distribution approximating the product of A and B densities) and nA ∼ t. We apply our results to simple molecules (Fickian diffusion, z = 2) and to several models of short-time polymer diffusion (z > 2). PACS numbers: 05.40.+j, 68.45.Da, 82.35.+t
منابع مشابه
Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries
Solid state diffusion in a binary system, such as lithiation into crystalline silicon, often involves two symbiotic processes, namely, interfacial chemical reaction and bulk diffusion. Building upon our earlier work (Cui et al., 2012b, J. Mech. Phys. Solids, 60 (7), 1280–1295), we develop a mathematical framework in this study to investigate the interaction between bulk diffusion and interfacia...
متن کاملSize effect model on kinetics of interfacial reaction between Sn-xAg-yCu solders and Cu substrate
The downsizing of solder balls results in larger interfacial intermetallic compound (IMC) grains and less Cu substrate consumption in lead-free soldering on Cu substrates. This size effect on the interfacial reaction is experimentally demonstrated and theoretically analyzed using Sn-3.0Ag-0.5Cu and Sn-3.5Ag solder balls. The interfacial reaction between the Sn-xAg-yCu solders and Cu substrates ...
متن کاملA model for the interfacial kinetics of phospholipase D activity on long-chain lipids.
The membrane-active enzyme phospholipase D (PLD) catalyzes the hydrolysis of the phosphodiester bond in phospholipids and plays a critical role in cell signaling. This catalytic reaction proceeds on lipid-water interfaces and is an example of heterogeneous catalysis in biology. Recently we showed that planar lipid bilayers, a previously unexplored model membrane for these kinetic studies, can b...
متن کاملKinetic Modeling of Sunflower Oil Methanolysis Considering Effects of Interfacial Area of Reaction System
متن کامل
Interfacial kinetics of a model epoxy-amine addition reaction.
The kinetics of the addition reaction at a solid interface for a model epoxy-amine system composed of monofunctionalized phenyl glycidyl ether and hexylamine was examined. The chemical character for the reaction of this system at the interface was the same as that in the bulk, while the physical nature was significantly different. Slowing down of the diffusion for the reactants in close proximi...
متن کاملFormation of Chemical Compound Layer at the Interface of Initial Substances A and B with Dominance of Diffusion of the A Atoms
A theoretical approach to consider formation of chemical compound layer at the interface between initial substances A and B due to the interfacial interaction and diffusion is developed. It is considered situation when speed of interfacial interaction is large enough and diffusion of A-atoms through AB-layer is much more then diffusion of B-atoms. Atoms from A-layer diffuse toward B-atoms and f...
متن کامل