Kinetic Studies of Metal Hydroxide Intercalation (2) W. P. F. A. M. Omioo and F. Jeiiinek, J. Less-Common Metals, 20, 121 (1970). (3) R. B. Somoano and A. Rembaum, Phys. Rev. Lett., 27, 402 (1971); R. B. Somoano, V. Hadek, and A. Rembaum, J. Chem. Phys., 5 8 , 697 (1973); A. M. Hermann, R. B. Somoano, V. Hadek, and A. Rembaum, SolldStafe Commun., 13, 1068 (1973). (4) G. V. Subba Rao, M. W. Shafer, S. Kawarazaki, and A. M. Toxen, J. Solidstate Chem., 9, 323 (1974). (5) J. M. Van der Berg and P. Cossee, lnorg. Chem. Acta, 2, 143 (1968); F. Hulliger and E. Pobitschka, J. Solidstate Chem., I, 117 (1970). (6) F . R. Gamble, eta/., Science, 168, 568 (1970): 174, 493 (1971). (7) G. V. Subba Rao, M. W. Shafer, and L. J. Tao, AIP Conf. Proc., No. 10 (American Inst. of Phys.), 1973, p. 1173; M. W. Shafer, G. V. Subba Rao, and L. J. Tao, paper presented at the international Conference on Magnetism and Magnetic Materials, Moscow, Aug, 1973. (8) Looking along the c axis of the layered chalcogenide, we can picture the Ch-M-Ch slabs as being joined by long Ch-Ch bonds across the van der Waals gap akin to the case of graphite (Figure 1). (9) (a) See, for example. W. Eitel, Silicate Science," Voi. 1, Academic Press, New York, N.Y., 1964; (b) J. G. Hooiey, paper presented at the Conference on Layer Compounds, Calif., Aug, 1972 (unpublished). 10) A. R. Ubbeiohde, Carbon, I O , 201 (1972). 11) F. R. Gamble, etal., J. Chem. Phys., 55, 3525(1971). 12) G. Subba Rao and M. W. Shafer, J. Phys. Chem., following paper. 13) F. Kadijk, R. Huisman, and F. Jellinek, Rscl. Trav. Chim. Pays-Bas, 83,
557 768 (1964). (14) J. F. Revelii, Ph.D. Dissertation, Stanford University, 1973. (15) (a) For starting mole ratios TaS2:KOH of 1: 0.5) are allowed to intercalate into TaS2, can be explained on the assumption that, in these cases, t’ 2 t and partial intercalation results until all the OH- ions in the bulk of the solution are consumed. A t this point, the driving force for the intercalation ceases to exist and the ions in The Journal of Physical Chemistry, Vol. 79, No. 6, 1975
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the intercalated regions slowly diffuse into the unintercalated regions. However, this diffusion is not random but occurs in a specific fashion to give rise to a second stage intercalation (where the intercalate is present in every second TaS2 layer1). KOH concentrations of y < 0.1 do not produce noticeable intercalation in TaS2, thereby indicating that the number of OH- ions available in solution is too low to satisfy the criterion demanded for the formation of an activated complex. As discussed in an earlier paper,l the intercalate ions go to occupy the empty octahedral interstices in the host chalcogenide lattice. 2s TaS2 has one octahedral hole per T a atom (two holes in the unit cell). In the initial stages of the intercalation reaction the OH- ions occupy the first available octahedral sites dragging K+ ions and the polarized HzO molecules (hydration sphere) along with them. Since it is experimentally observed that stage I intercalation is reached a t time t’, this should mean that some of the octahedral sites (assuming each particle of TaS2 has, e.g., -IO4 unit cells) are occupied by HzO molecules instead of Kf and OH- ions to give the compositions we find by analyses, T ~ S ~ ( K O H ) ~ / ~ ( H this Z O )is~ plausible /~;~ since the polarized H20 molecules associated with an OH- ion can effectively act as intercalate species. Continuation of intercalation reaction after t’ must then be a replacement of the intercalated H2O molecules by the OH- and K+ ions at the octahedral sites to give the limiting composition TaS2(KOH)1,2. This argument was tested experimentally as follows. One run of TaS2-KOH reaction was stopped a t t’ and the product was removed and X-rayed; it showed complete stage I intercalation. Then the sample was kept in high vacuum for 12 hr a t 25’ after which X-rays showed evidence of partial intercalation indicating that the loosely bound H2O molecules (possibly, also some KOH) were expelled and the lattice collapsed to the pure TaS2 phase in certain regions. Unfortunately it is not possible to replace all the HzO molecules by K+ and OH- ions since TaS2 decomposes chemically after prolonged treatment (-12 hr) with concentrated alkali hydroxides. The observed first-order rate constants ( t = t’; y = 2; TaS2-KOH system) at various temperatures (2-100’) were found to roughly obey the Arrhenius equation. The observed value of energy of activation (-3 kcal/mol) was in the range of values encountered for adsorption reactions but far below the values for typical homogeneous reactions in solution (-30 kcal/m01).~k 1 is seen to be slightly higher for lower initial concentrations (y S 0.5 KOH) compared to concentrations where y > 1.0. It is thus possible, that the reaction is inhibited to a small extent at times less than t’ as well, at the high initial concentrations (Table I). The effect of particle size is not at all considered in the above discussion even though, for the temperature variation studies, TaS2 particles of same size have been employed. No doubt an increase of particle surface area will enhance the initial reaction velocity which may also depend on the relative ratio of the basal plane us. edge areas if these were to act differently toward the formation of the activated complex.* One point is worth mentioning regarding the temperature variation of the first-order rate constants. Although the increase of k 1 with temperature is not
The Journal of Physical Chemistry, Vol. 79, No. 6, 7975
very great in the temperature range 2-loo’, data on a particular system (of same particle size, starting composition, etc.) are probably significant and real. The low measured activation energy of -3 kcal/mol is probably inherent to the TaS2-MOH system, where MOH intercalates with ease and rapidity compared to, for example, pyridine which requires drastic conditions of temperature and pressure.2 Summary
For low initial alkali hydroxide concentrations (KOH; y
< 0.5), the rate of intercalation of TaS2 follows a first-order
rate law but the product is a mixture of different intercalation stages as identified by X-rays. Pure stage I intercalation product is obtained for y > 0.5 but the first-order rate law with respect to the alkali concentration (NaOH or KOH) is obeyed only up to t’ of the total time (t’ < t ) and thereafter the rate decreases. This falling off of the rate is interpreted as due to the “poisoning” effect of the intercalated product at the surface of TaSz and due to the slowness of diffusion of the intercalate species into the host lattice. The significance of t’ is that, from a structural point of view, the intercalation reaction is essentially complete at t’ where all the available octahedral interstices in TaSz are filled by M+, OH- ions, and H20 molecules to give a composition TaS~(MOH)1/3(H20)1/3for the complex. Continuation of the reaction above t > t’ is presumed to be the replacement of the intercalated HzO by fresh M+ and OHions to give the composition TaSZ(MOH)l/z. This limiting composition could not be achieved experimentally. Metal hydroxide intercalation into TaS2 is an endothermic process with a low energy of activation (-3 kcal/mol).
Acknowledgments. We wish to acknowledge valuable discussions and helpful suggestions on the kinetic aspects with R. A. Ghez. Thanks are also due to R. A. Figat for technical assistance and to C. Aliotta for electron micrographs of TaS2 powders. References and Notes G. V. Subba Rao, M. W. Shafer, and J. C. Tsang, J. Phys. Chern., preceding paper. F. R. Gamble, eta/., Science, 174, 493 (1971). When the intercalate species are inserted between every two layers of the host TaS2, the complex is of stage I; when it is inserted between aiternate sets of layers, the complex is of stage ii, etc. Different stages of intercalation are characterized by varying c lattice parameters.’ K. J. Laidler, “Chemical Kinetics,” McGraw-Hill, New York, N.Y., 1950. E. S. Amis, “Kinetics of Chemical Change in Solution,” Macmillan, New York, N.Y., 1949. Data exist in the literature5 where eq 3 is obeyed by the adsorptlon rate of benzoic acid and iodine by charcoal in solution. We have considered other forms of rate expressions including the Eiovic equation.’ It is possible to fit the observed data at high t values to the Elovic equation, x = (I/@) In (1 t c a t ) where c and a are constants and x the amount adsorbed (intercalated) at time t. Even though the Elovic equation is best understood in the light of a constant site generation and decay in the course of adsorption, it does not give insight into the mechanism of the intercalation process. C. Aharoni and F. C. Tompkins in “Advances in Catalysis,” Vol. 21, D. D. Eley, H. Pines, and P. 6.Weisz, Ed., Academic Press, New York, N.Y., 1970. We have one set of data at 25O with TaSp:NaOH of the same initial concentration but of two different particle sizes (
