A KINETIC MODEL OF THE FIRST INTERCALATION OF GRAPHITE? K. K. BARDHAN Department of Physics, Carnegie-Mellon University. Pittsburgh, PA I521 3, U.S.A. and D. D. L. CHUNG Department of Metallurgy & Materials Science and Department of Electrical Engineering. Carnegie-Mellon University, Pittsburgh. PA 15213, U.S.A. (Received 8 Norrmher 1979) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON Abstract-A model of first rapid intercalation is presented to describe the kinetics of intercalation. The model applies to interface-controlled intercalation, as for the intercalation of Br, and other similar intercalates. In this model, intercalation proceeds by layer-by-layer nucleation and subsequent in-plane growth: a time gap is assumed between the nucleation of two successive intercalate layers. The model has been applied to analyze the variation of the surface and thickness profiles and mass increase during intercalation. Support of the model by relevant experimental results is discussed. 1. INTRODUCTION Graphite reacts with many chemical substances to form compounds [l]. One class of graphite com- pounds, known as the intercalation compounds [2], contains the reactant in the interstitial spaces between the planar hexagon layers of the graphite crystal and maintains the aromatic planar layer structure of the parent graphite. Such a reaction between graphite and the reactant is known as intercalation; the reactant is known as the intercalate. Graphite intercalation compounds have recently received considerable attention in the areas of the electronic, lattice and structural properties [2]. How- ever, relatively little attention has been given to the mechanism of intercalation, a process which results in the superlattice ordering of the intercalate layers with respect to the carbon layers. Bromine is the inter- calate species that has been most thoroughly studied, but little work has been done to rationalize the pub- lished experimental results on the kinetics of inter- calation. In this paper, we present a model of first rapid intercalation which allows for the first time a coherent explanation of many of the published results on the physiochemical effects of intercalation. How- ever, our model does not take into consideration crack formation, which often accompanies inter- tResearch sponsored by the Air Force Office of Scien- tific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-78-3536. The United States Govern- ment is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation hereon. calation [3] and which tends to enhance the effect of intercalate adsorption. The model rather. is directed toward an explanation of the elementary process involved in intercalation. Of the various methods of studying the kinetics of intercalation, those of our concern here are measure- ments of thickness [4-S], weight gain [4.6,9916], concentration profile [ 12,16,17] and surface pro- file [lS]. The first extensive measurements on thick- ness expansion were obtained by Saunders et u1.[4.5]. followed by Hooley et aI.[6,7]; both groups of workers advanced revealing arguments to explain their data. Gravimetric data have been obtained alone [6,9-12, 161 or simultaneously with other data such as thickness [4], electrical conductivity [ 13. 141 or magnetic susceptibility [IS]. Most of the attempts to explain the mass increase phenomenon during intercalation were based on Fick’s laws of diffusion, which require the existence of a concentration gradient of the diffusing species. On the other hand, consequences arising from Fick’s laws have not been applied to analyze the changing dimen- sions and the intercalate distribution during inter- calation. On a closer examination of the limited pub- lished data, we find that many of the difficulties with the diffusion model possibly arise from the failure to distinguish between two types of intercalation pro- cesses which are described below, along with the reasons behind the difficulties with the diffusion model. (i) Corrcentrntion zyxwvutsrqponmlkjihgfedcbaZYXWVUTS and surface topographical profiles An important test for the applicability of Fick’s law 303 CAR Vol. 18. No. LA