摘要:

GENERAL DISCUSSION Prof. P. Meares ( University of Aberdeen) said: ( 1 ) In his paper Prof.‘Dickel has indicated that the contribution to the flux of Donnan co-ions causing a flux of solvent corresponds to complete coupling to the co-ions with the solvent, whereas the flux of counter-ions so produced is equal to the concentration of counter-ions multiplied by one half of the average velocity of solvent. The solvent drag coefficient for the sodium counter-ions in the cation exchanger Zeo-Karb 3 15 was found to lie between 0.5 and 0.6 over the concentration range up to and just beyond that at which the concentrations of Donnan ions and fixed charges are equal.’ The solvent drag coefficient of the Donnan ions lies between 1.3 and 1.4 over most of this concentration range. The value is believed to exceed unity because of the non-uniform distribution of the water stream in the polymer network of the membrane.The coupling coefficients qik of non-equilibrium thermodynamics’ have also been evaluated for the system. In the case of counter-ions and water the values lie between 0.5 and 0.6 but for Donnan ions the range is 0.2-0.4 over most of the concentration range and lower still in more dilute solutions. This anomalous behaviour of the co-ion coefficient is not readily interpreted. Prof. Dickel’s theory of isotonic osmosis leads to the expectation that the electro-osmotic flow of solvent will vanish when the concentrations of Donnan ions and counter-ions are equal. He has shown this to be so in a system he has studied. With Zeo-Karb 315 in NaBr solutions at this point of equal concentrations an electro-osmotic transfer of ca.12mol water/F takes place and in SrBr, solutions the transfer is ca. 6 mol water/E3 ( 2 ) In his eqn (37) Prof. Dickel expresses the vanishing of forces on the mem- brane during steady flow. This, of course, is true when the membrane is at rest but it appears possible that the sum of forces should include a contribution from the flange of the transport cell in which the membrane is clamped since in unrestrained stationary flow one expects the centre of mass of the whole system of membrane + solutions to remain at rest. ’ P. Meares, J. Membr. Sci., 1981, 8, 295. ’ S. R. Caplan, J. Phys. Chem., 1965, 69, 3801. Prof. G. Dickel (Universitiit Miinchen, West Germany) said: From eqn (35) and W.J. McHardy, P. Meares, A. H. Sutton and J. F. Thain, J. Colloid Znrerface Sci., 1969, 29, 116. (36) of my paper results for the Donnan ions and the counter-ions J D = J:, + (c,/ cL)JL and V , = VO, + V, J,= J:+ 1/2(cc/c,)J, and V,+ V:+iV, where Jb and J: represent the fluxes in absence of a flux of solvent. From these equations we conclude that the action resulting from the flux of the solvent on the counter-ions equals half the action on the Donnan ions. Whilst this is the effect of reverse osmosis, the osmosis itself follows from eqn (45). For this reason we transform the latter into p = (-;c,+ c ~ ) F d q 217218 GENERAL DISCUSSION and state that the action on the solvent (i.e. the electro-osmotic pressure) resulting from the flux of the counter-ions equals half the action resulting from the Donnan ions.This statement concerning the reciprocal relation reveals further that the factor $ gives rise to a retardation resulting from an intrinsic interfacial equilibrium between the matrix of the membrane and the pore solution. Replacing the factor f by 1 we get the equation discussed by Schlogl. This represents a Galilean transformation which does not yield the observed effect of the inversion of isotonic osmosis. Concerning the condition of the sum of all forces vanishing, this is a necessary condition, first being valid only for the total system membrane + adjacent solutions. The postulate that the sum of all forces in the membrane itself must vanish is a good approximation. Indeed, we have observed in the course of our experiments alternating deflections of the membrane, indicating such forces.As the latter, however, are small with respect to the osmotic forces these can be disregarded. I now direct attention to the following paper, by Prof. Sanfeld and Dr. Steinchen. The effect of isotonic osmosis is a special case of the electrokinetic effects well founded on non-equilibrium thermodynamics. Thus eqn (45) in our paper is also valid in the case of a single electrolyte, if an outside electric field is applied to a membrane. Therefore the coefficient i(cF-cD) is identical to the coefficient = L2, in the general structure of irreversible thermodynamics. In the numerous representations of this effect, however, we could find no indication of the variation and vanishing of this effect.My question is thus as follows: is it possible to give simple and useful criteria concerning the existence of such or similar effects, in order to avoid the application of the extensive method of least dissipation of energy. Prof. H. Linde (Academy of Sciences of the G.D.R., Berlin, East Germany) (communicated): I would like Prof. Dupeyrat and Dr. Nakache to comment on the following remarks. In your paper, the movements at the interface are characterized as pseudoperiodic oscillations. In Marangoni instability there occurs amplification of classical waves (longitudinal capillary waves) as well as of autowaves (the spatial and temporal synchronization of typical relaxation oscillations, for Marangoni instability has recently been recognized in our laboratory also).Classical waves show interference and reflexion at a wall, whereas autowaves show evidence of collision between two waves or between a wave and a wall. Can you connect your pseudoperiodic oscillations with the behaviour of classical waves or with autowaves? Prof. M. Dupeyrat, Dr. E. Nakache and Dr. M. Vignes-Adler (Universite' Pierre et Marie Curie, Paris, France) (communicated): We have to note that the experimental procedure used up to now does not allow us to obtain homogeneous concentration gradients. Consequently it is not possible to obtain regular patterns such as those described by Linde and thus to develop a theoretical model which may be compared with the differential equations proposed for capillary and autowaves. Experimentally we observed that the relaxation oscillations and cells depend on the size of the interface, and therefore on the reflexion at a wall, and on the deformation of the interface bound to the presence of a stirrup during the measure- ment of the interfacial tension.It is likely that these relaxation oscillations are enhanced by the curvature of the interface imposed by the measurement method. We also remark that if HPi is not present, or if KPi replaces HPi (that is to say if there is no chemical reaction), these instabilities are not observed. Thus some chemical autowaves must also be important.GENERAL DISCUSSION 219 The phenomenon seems to be related to a coupling between capillary and auto w aves . Dr. C . Tondre (University of Nancy, France) said: May I ask Dr.Nakache to give some more details on a technical point of her work, the measurement of the time dependence of the interfacial tension y (fig. 1 of the paper): could she explain how the measurement of y using the detachment of a stirrup can be made fast enough to obtain the recordings shown in fig. I ? Is there no perturbation of the interface due to the measurement itself? Would not the optical methods using the intensity of the light scattered by liquid interfaces’ be particularly appropriate for such measurements? ’ J. Lachaise, A. Graciaa, A. Martinez and A. Rousset, J. Phys. Lett., 1979, 40, L-599. Dr. E. Nakache (Universite‘ Pierre et Marie Curie, Paris, France) replied: The measurement of the interfacial tension, y, with a stirrup can be made in two ways: (1) detaching the stirrup after its elevation and (2) elevating the stirrup to the maximum of the traction curve, as Guastalla’ proposed. This author has shown that, under these conditions, there is a relation between the force measured and the interfacial tension.This method was used in this work because it permitted the measurement of y as a function of time. Preliminary experiments have shown that the influence of the curvature of the interface along the wall of the beaker was very important, probably because the convection process is enhanced.* Consequently the presence of the stirrup at the interface probably disturbs it by the two menisci created. It would be interesting to measure y without disturbing the interface, for instance with the optical methods used by Lachaise et al.Unfortunately these methods are now too slow: according to Dr Langevin-Wallon’ the time to obtain a measurement of y is, at present, between one and several minutes. * J. Guastalla, J. Chim. Phys., 1971, 68, 822. ’ J. C. Berg and C . R. Morig, Chem. Efig., 1969, 24, 937. D. Langevin-Wallon, personal communication. Dr. M. Spiro (Imperial College, London) said: There are certain aspects of the experimental arrangements used by Samec and coworkers that I do not understand. In the first place, how were they able to achieve a stable flat interface over a circular area > 5 mm in diameter with the heavier nitrobenzene layer (density 1.20 g cm-’) lying above the lighter aqueous layer (density 1.00 g ~ m - ~ ) ? My second set of questions concerns their method of placing an isolated metallic wire inside the Luggin capillary for the nitrobenzene phase.(a) What was the wire made of? (6) Since the wire is connected to the silver of the reference electrode RE2, does it not introduce an extra potential into cell I so that the potentials of the two reference electrodes no longei cancel each other out? ( c ) Does ‘isolated’ mean that the wire was insulated from both aqueous and the nitrobenzene solutions inside the Luggin capillary? ( d ) In what respect did the introduction of this wire achieve a ‘remarkable improvement’ in the cell’s response? It would be helpful if Dr. Samec could give more details of the arrangement used. Dr. 2. Samec (J. Heyrovsky’ Institute, Prague, Czechoslovakia) said: The stable location of the water/nitrobenzene boundary in the round hole of the glass barrier B (see our fig.1) was ensured both by the low surface tension between water and220 GENERAL DISCUSSION glass and by the liquid's incompressibility. In fact the inner space of the glass cell was made as hydrophilic as possible by washing with acetone, doubly distilled water and drying at a temperature of 120 "C in a dry-box. Eventually, the surface of the glass was treated by a concentrated solution of sodium hydroxide. Referring to fig. 1, the bottom space of the cell was filled completely with the aqueous phase. Concerning the reference electrode RE2 for the nitrobenzene phase, the copper wire of 0.4 mm in diameter was placed inside the Luggin capillary down to its tip. This wire was insulated from both the aqueous solution of TBABr and the nitrobenzene solution of TBATPB, and only the metallic disc of geometric area 0.13 mm2 was exposed to the nitrobenzene solution just at the capillary tip.Since this wire was connected to the silver Ag' of the reference electrode RE2, a galvanic cell (11) c"(TBABr) 1 c"(TBATPB) I Cu I Ag' (0) must be considered in addition to cell (I) of the paper. It can be assumed that the copper electrode is ideally polarizable and hence the short circuit in cell (11) has no effect on the potential of the AglAgBr reference electrode. However, even if a faradaic process occurs at the copper/nitrobenzene interface, e.g. copper disso- lution or nitrobenzene reduction, the potential of the Agl Ag Br reference electrode can hardly change.This is because the area of the Cu/o interface is at least two orders of magnitude smaller than the areas of the Ag'/w' and w'/o interfaces; the latter two interfaces are practically non-polarizable. On the other hand the introduc- tion of the metallic wire had a remarkable effect on the response time of the cell. Referring to fig. 6 of our paper it is seen that the ohmic potential drop appears as a step in the galvanostatic transient, and in an ideal case the time necessary for its completion would be zero. However, it is apparent that the transient has a finite slope at t = to, which corresponds to a delay of ca. 0.1 ms for a potential change from 10 to 90% of the final value. Without the metallic wire inside the Luggin capillary, this delay was ca.1 ms. Dr. M. Spiro (Imperial College, London) said: Since the wire used was a copper one, and since pulses passed along the wire, there is surely the danger that a Cu2+/Cu or Cu'/Cu potential would be set up at the end of the wire. This would have affected the measured e.m.f. of cell (I). A platinum wire would have been better in this respect. However, a faradaic pulse passing through the tip of any wire would generate ions that could contaminate the nearby nitrobenzene/water interface. Moreover, even with a platinum wire the potential difference between the nitroben- zene solution and the platinum metal will not be identical to that between the nitrobenzene solution and the AglAgBrlBr-( aq) electrode because only the latter includes a physical nitrobenzene/water interface with its ionic double layers.Dr. 2. Samec (J. Heyrovskj Institute, Prague, Czechoslovakia) said: Both reference electrodes were connected to the high-impedance inputs of the FET operational amplifiers (the voltage followers) and practically no current can flow through them during the change in the potential drop between the tips of the Luggin capillaries. However, Cu2+/Cu or Cu'/Cu potentials could be set up at the end of the wire owing to the short-circuit current in cell (11). As explained above, this would have only a small effect on the measured e.m.f. of the cell. In any case tetramethylam- monium was always used as the inner standard for the evaluation of the interfacial potential difference. However, I agree with Dr Spiro that a platinum wire wouldGENERAL DISCUSSION 22 1 be better in most respects, including the less probable contamination of the nitro- benzene phase by the metal ions. Dr. E. Nakache ( Universite' Pierre et Marie Curie, Paris, France) said: I would like to ask Prof. Koryta if he could provide more information about the adsorption of the different monensins at the nitrobenzene/ water interface? Prof. J. Koryta ( J . Heyrovsky Institute, Prague, Czechoslovalia) replied: We have no information on monensin adsorption at the water/nitrobenzene interface. The only paper dealing with the influence of adsorption on ion transfer studied by voltammetry at TTTES is concerned with phospholipid adsorption.' ' J. Koryta, Le Q. Hung and A. Hofmanova, Stud. Biophys., 1982, 90, 2 5 .

ISSN:0301-7249    

DOI:10.1039/DC9847700217

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 223-234 Ion-exchange Dynamics at the Zeolite/ Solution Interface Studied by the Chemical-relaxation Method BY TETSUYA TKEDA, MINORU SASAKI AND TATSUYA YASUNAGA" Department of Chemistry, Faculty of Science, Hiroshima University, Hiroshima 730, Japan Received 17 th November, 1983 The kinetics of the hydrolysis of surface hydroxyl groups on the aluminosilicate framework and ion exchange of NH4+, CH3NH3+, C2H,NH3+, n-C3H7NH3+, i-C3H7NH3+, (CH3)2NH2+, (CH3)3NH+ and (CH3)4N+ for Na+ at the zeolite/solution interface have been studied by using the pressure-jump relaxation method with electric-conductivity detection. Above pH I 1.5 a single relaxation was found and was attributed to the hydrolysis of surface hydroxyl groups. Below this pH value two relaxations were found in aqueous suspensions of the systems comprising zeolite 4A with NH4+, CH3h d3+, C2H5NH3+, n-C3H,NH3+ and (CH3)2NH2+, but no relaxation was observed in the systems involving zeolite 4A and i- C3H,NH3+, (CH3)3NH+ and (CH&N+.The fast and slow relaxations observed were attributed to diffusion of the alkylammonium ion on the surface of the particles, followed by adsorption of the alkylammonium ion on a site in the zeolite cage. From the kinetic and static experimental results it was found that the affinity of zeolite 4A for exchangeable cations is limited by the available intracrystalline space in the cage with larger cations unable to diffuse into the cage because of a lack of available intracrystalline space. The difference in the values of the rate constants associated with the alkylammonium ion entering the cage is interpreted in terms of a steric factor.Crystalline zeolites having anionic aluminosilicate framework structures give rise to molecular-sieve action for adsorbing molecules as a shape-selective catalyst.' Such molecular-sieve materials have recently been synthesized in increasing quan- tities for use in adsorptive and catalytic applications because of their unique shape-selectivity and their framework The aluminosilicate framework of zeolites, which is terminated by surface hydroxyl is a major factor in the determination of their acidic properties.' In order to understand the dynamic properties of acid sites at the zeolite/solution interface, the chemical-relaxation method has been applied to the hydrolysis of surface hydroxyl groups on zeolite surfaces' and to acetate-ion adsorption on amorphous silica-alumina surfaces.'* Another interesting property of zeolites is the existence of Na' in the cage structures, in which the exchange of organic and inorganic cations for Na+ in the cage accompanies an ion-sieve effect or ion selectivity for exchangeable cations.' '-I7 However, the mechanism of ion exchange, which includes the ion-sieve action, has not been well established on the basis of the kinetics because the ion-exchange reaction is too fast to be observed by ordinary methods, e.g.using radioactive tracers.14 In the insertion process of the guest organic cation into the host cage through the channels of the zeolite, the diffusion rate is governed by a steric factor of the entering cation which may depend on both the aperture of the host cage and the size of the entering guest cation.In order to clarify size and shape correlations between the host cage and the guest molecule in the ion-exchange reaction, one must study the ion-exchange kinetics of various organic cations for Na+ in the zeolite. 223224 ION-EXCHANGE DYNAMICS AT THE ZEOLITE/SOLUTION INTERFACE In this paper we present the results of pressure-jump relaxation experiments on the kinetics of the hydrolysis of surface hydroxyl groups on the aluminosilicate framework and of ion exchange of the various alkylammonium ions for Na+ at the zeolite/aqueous-solution interface, and discuss the influence of ion size and shape on the ion-exchange properties. EXPERIMENTAL The details of the pressure-jump apparatus have been described previously.'8 The time constant of the pressure jump is 80 ps.Zeolite 4A ( Na,O. Al,03 - 2Si02. n H 2 0 ) was supplied by the Toyo Soda Co. X-ray diffrac- tion patterns were identical with those of zeolite 4A reported by Broussard et a/." Micro- scopic examination confirmed that the mean diameters of the dispersed zeolite 4A particles were < 1 pm. Such small particles formed very stable suspensions with no sign of sedimenta- tion during the kinetic measurements. The amount of alkylammonium ion adsorbed was determined indirectly from the con- centration change in the supernatant solution by means of colorimetric analysis with 2,4- dinitrofluorobenzene" for CH3NH3+, C2HSNH3+, n-C3H7NH3+ and (CH3),NH2', and with ninhydrin2' for NH,+.Prior to the measurements, samples of zeolite 4A suspensions containing each alkylamine hydrochloride were centrifuged for 30 min at 10 OOOg to-settle the particles completely. The particle concentration of all samples was 30 g dm-3, and the samples were equilibrated for 72 h after preparation. All preparatiohs and experimentation were done in a nitrogen atmosphere, and the temperature was controlled at 25.0 f 0.1 "C. RESULTS AND DISCUSSION CHEMICAL RELAXATION I N AQUEOUS SUSPENSIONS OF ZEOLITE 4A A single relaxation process of decreasing conductivity having a characteristic duration of the order of seconds was observed in basic aqueous suspensions of the system zeolite 4A-NaOH only above pH 1 1.5 by using the pressure-jump relaxation method.Values of the relaxation time were obtained from a semilogarithmic plot of the relaxation curveland the dependence of the reciprocal relaxation time T - * on OH- concentration in aqueous suspensions of the zeolite 4A is shown in table 1. The experimental results show that the value of T-' increases with increasing OH- concentration. Since Na' can enter the cage of the zeolite 4A as mentioned above, a plausible mechanism for the relaxation phenomenon observed may be the base-catalysed adsorption-desorption of Na+. However, when tetramethylam- monium hydroxide was added as the base in the same manner, the same relaxation phenomenon was observed, even though the.tetramethylammonium ion cannot enter the cage. Therefore it is suggested that the single relaxation observed may originate in the interaction between OH- and the active site on the zeolite surface, i e .the hydrolysis of surface hydroxyl groups on the aluminosilicate framework. Below pH 11.1 another relaxation phenomenon shown in fig. l(a) was observed in aqueous suspensions of systems comprising zeolite 4A with NH4+, CH3NH3+, C2H5NH3+, n-C3H,NH3+ and (CH&NH,+ by using the pressure-jump method, where the relaxation signal again shows a decrease in the conductivity of the suspension during relaxation. No relaxation was observed in a zeolite 4A suspension of the same pH (pH < 11 .I) in the supernatant solutions of the above systems and in aqueous suspensions of zeolite 4A with i-C3H7NH3+, (CH3),NH+ or (CH3)4N+C.Furthermore, measurements of the change in concentration of Na+ in the bulk phaseT. IKEDA, M. SASAKI AND T. YASUNAGA 225 Table 1. Kinetic and static data for aqueous suspensions of zeolite 4A at 25 "C [OH-] [SOHI [so-I r-I/s-l / mol dmP3 / lov3 rnol dm-3 / low2 rnol drn-3 0.88 * 0.10 2.63 1.06 * 0.13 4.57 1.47 * 0.09 6.76 1.80 * 0.1 3 9.12 1.91 k0.12 11.8 3. I 2.2 1.1 1 .o 0.8 1.54 I .63 1.74 1.75 1.77 I 1 I I 1 b, 50 0.5 1 1.5 2 t 0 1 2 3 4 5 time/s Fig. 1. Typical relaxation curves observed by using the pressure-jump relaxation method below pH 11.1 at a particle concentration of 30 g dm-3 and 25 "C for zeolite 4A with the following ( a ) NH,+, CH3NH3+, C2H,NH3+, n-C3H,NH3+ and (CH3),NH2+; ( b ) i-C3H,NH3+, (CH3)3NH+ and (CH,),N+. confirmed that release of Na' from the zeolite cage requires 48-72 h in the systems of zeolite 4A with NH4+, CH3NH3+, C2H5NH3+, n-C3H7NH3+ and (CH3)2NH2+ as shown in fig.l(b). These results suggest that for the alkylammonium ions relaxation reflects the difference in the size and shape correlations between the guest ion and the host cage. From the semilogarithmic plot of the relaxation curve it is seen that relaxation consists of two processes. The dependences of the fast and slow reciprocal relaxation times, 71' and T T ' , on the concentrations of added ammonium chloride, methylamine hydrochloride, ethylamine hydrochloride, n-propylamine hydro- chloride and dimethylamine hydrochloride in aqueous suspensions of zeolite 4A are shown in fig. 2 and 3, respectively. The value of 7;' shows a steep increase, while the value of 72' shows an increase and then approaches a constant value.From a comparison of the values of the relaxation times for each alkylammonium ion in fig. 2 and 3 it can be seen that the values of both 7;' and 72' decrease with226 ION-EXCHANGE DYNAMICS AT THE ZEOLITE/SOLUTION INTERFACE added alkylammonium ion/ I 0-3 mol dmp3 Fig. 2. Dependence of the fast reciprocal relaxation time on the added concentrations of ammonium chIoride, methylamine hydrochloride, ethylamine hydrochloride, n-propylamine hydrochloride and dimethylamine hydrochloride in aqueous suspensions of zeolite 4A at a particle concentration of 30 g dmV3 and 25 "C. 1 I I 1 0 5 10 added alkylammonium ion/ lo-' mol dmP3 Fig. 3. Dependence of the slow reciprocal relaxation time on the added concentrations of ammonium chloride, methylamine hydrochloride, ethylamine hydrochloride, n-propylamine hydrochloride and dimethylamine hydrochloride in aqueous suspensions of zeolite 4A at a particle concentration of 30 g dm-3 and 25 "C.T.IKEDA, M. SASAKI AND T. YASUNAGA 227 increasing alkyl chain length. Taking into account the absence of relaxation in the supernatant solution, the concentration dependences of the relaxation times and the existence of an Na+-release process, the results suggest that the relaxation observed may be due to ion exchange of the alkylammonium ion in the bulk phase for Na+ in the cages on the zeolite surface. Furthermore, it appears from the above kinetic measurements that the ion exchange may consist of at least 'three elementary processes.In order to clarify the mechanism of the two kinds of the reactions in aqueous suspensions of zeolite 4A, the kinetics of fast reactions were studied in detail, taking full account of both kinetic and static data. HYDROLYSIS O F SURFACE HYDROXYL GROUPS ON THE ALUMINOSILICATE FRAMEWORK For the single relaxation observed above pH 1 1.5, the mechanism of the hydrolysis of the hydroxyl groups on the aluminosilicate framework of zeolite 4A can be written as \ ' \ -' +OH- ,A]\ /Si, + *;O] (I) H I 0 0 0 0 O\ /O\ 1 /A1\ ,S1\ SOH so- where SOH and SO- denote the surface hydroxyl group and the dissociated hydroxyl group on the aluminosilicate framework, respectively, and k f and kb are the forward and backward rate constants, respectively. For the above mechanism 7-l is given by T - ' = kX[SOH] +[OH-]) + k(, (1) with In order to plot eqn (1) one must measure the equilibrium concentration of SOH.The concentrations of SOH together with SO- were determined from the adsorption isotherm of OH- and are listed in table 1. The plot of 7-' against the concentration term in eqn ( I ) yields a straight line, as shown in fig. 4. The linearity of this plot confirms the plausibility of mechanism (I). The values of the rate constants kf and kl, were determined from the slope and the intercept of the straight line and are listed in table 2. The value of the kinetic equilibrium constant K L was calculated from the ratio of the obtained rate constants and is given in table 2. The values of tde static equilibrium constant calculated from K L = [SO-]/([SOH][OH-I) are also listed in table 2.As can be seen from a comparison of the kinetic and static equilibrium constants obtained, the kinetic equilibrium constant is in good agreement with the static equilibrium constant. Consequently, both the linearity in fig. 4 and the agreement of the equilibrium constants obtained from different sources lead to the conclusion that the single relaxation observed can be attributed to mechanism ( I ) . Kinetic parameters in the systems comprising zeolite X and zeolite Y with hydroxyl groups obtained previously are also given in table 2. Comparison of the three K L values in table 2 shows that the variation of K L with aluminosilicate228 ION-EXCHANGE DYNAMICS AT THE ZEOLITE/SOLUTION INTERFACE 0 5 10 [SOH] +[OH-]/ lo-' mol dmP3 Fig.4. Plot of T - ' as a function of [SOH]+[OH-] in eqn (1). Table 2. Rate constants for the hydrolysis of hydroxyl groups on the surface of zeolites A, X and Y at 25 "C K El /mol-' dm3 k f k;, zeolite /mol-' dm3 s-' /s-' kinetic static A 1.6 X lo2 8.7 x 2.0 x 103 2.0 x 103 X" 2.0 x lo2 2.0 x 1 0 - ~ 1.0 x 104 1.3 x lo4 Y" 8.1 X 10 7.3 x lo-' 1.0 x lo2 1.3 x lo2 ~ Typical formulae of zeolites X and Y are Na20.AI2O3+2.5SiO2 and Na20.Al2O3.4.8SiO2, respectively. The values of k f , kf, and K b have been reported in ref. (9). framework structure is representative of the composition difference of the zeolites and that the difference in acid strength is mainly reflected in the values of the backward rate constant, since the values of the forward rate constant arefnearly equal in all cases studies.ION EXCHANGE OF ALKYLAMMONIUM ION FOR Na+ Consider the following mechanism of ion exchange of alkylammonium ion A' for Na' in zeolite 4A: Interfacial reactionT. IKEDA, M. SASAKI AND T. YASUNAGA Bulk reaction K , A+HzO * r A’+OH- very fast with 229 where S(Na), S-, S - A and S(A) denote the bound site of Na+ in the zeolite cage, the vacant site, the bound state on the surface and the bound site of the alkylam- monium ion which has entered the cage by intracrystalline diffusion, respectively. k+1,2,3 are the rate constants of each step. Under the assumption that step ( a ) is much slower than steps ( b ) and ( c ) , and that hydrolysis of the alkylamine in the bulk phase is a very fast reaction, the fast and slow reciprocal relaxation times are given by 6,: = S h +a”f[(all + ~ 2 ’ ~ 2 - - 4 ( ~ , 1 ~ 2 , - ~ 1 2 ~ ’ , ) 1 1 ’ 2 ~ (4) with ~ 1 2 ~ k-l (6) a21 = k2 (7) aZ2 = k, + k-2.(8) Eqn (4) cannot be solved explicitly for the general case. However, there is a procedure based on the following relationship which allows the evaluation of all four rate constants with good precision:” 71’ +7y1 = k l C + k - l + k z + k - 2 (9) (10) T Y ’ T ~ ’ = kl(k2 + k-2)C + k-1 k-2 with KB +LA’] Kg +[A+] +[OH-]’ C =[A’] +[S-] In order to plot eqn (9) and (lo), one must measure the equilibrium concentrations of S- and A+. Fig. 5(a) shows the adsorption isotherms of NH4+, CH3NH3’, C2HI,NH3+, n-C3H,NH3’ and (CH3)2NH2t in aqueous suspensions of zeolite 4A, where the concentration of each alkylammonium ion was estimated by using the pH value of each suspension and the dissociation constant Ka of each alkylammonium ion.23 Furthermore, the amounts of i-C3H7NH3+ and (CH3)3NH+ in aqueous suspensions of zeolite 4A were measured, but proved to be negligibly small.Since the lack of adsorption of i-C3H7NH3+ and (CH&NH+ corresponds to a lack of relaxation as described above, it is clear that a size effect for the exchangeable cation is revealed in both the kinetic and static experimental results in the present study. The variation of pH accompanied by addition of each alkylamine hydrochloride in the bulk phase is in the range 10.5-1 1.1. This may be explained by the hydrolysis of the alkylamine230 ION-EXCHANGE DYNAMICS AT THE ZEOLITE/SOLUTION INTERFACE 0 1 2 3 [A']/ mol dmP3 1 3 0 1 2 [A']/ I O r 3 mol dm-3 Fig.5. ( a ) Adsorption isotherms of NH4+, CH3NH3+, C2H5NH,+, n-C,H,NH,+ and (CH,),NH,'. ( b ) The amounts of Na' released by the adsorption of each cation. C/ lo-' mol dm--3 Fig. 6. Plots of 7;' +T;' against C in eqn (9). and is nor necessarily indicative of increased adsorption of OH- caused by alkylam- monium ion adsorption. The amounts of Na+ released by the adsorption of each alkylammonium ion were measured by using a sodium electrode, and the results are also shown in fig. 5(b). For each system, a variation profile of the amount of Na+ released is similar to that of the amount of alkylammonium ion adsorbed. The plots of 71' + 72' against C and ~ 1 ' 7 2 ' also against C for NH4+, CH3NH3+, C2H5NH3+, n-C3H,NH,+ and (CH3)2NH2+ are shown in fig.6 and 7. They yieldT. IKEDA, M. SASAKI AND T. YASUNAGA 23 1 C / 10 -3 mol dm-3 Fig. 7. Plots of ~1'7;' against C in eqn (10). Table 3. Rate constants of steps ( b ) and ( c ) and the overall equilibrium constant of ion exchange of organic cations for Na+ in zeolite 4A at 25 "C kl k- 1 k2 k-2 cation /mol-' dm3 s-' / S - l /s-I /s-I K ' NH,+ 1.8 x lo4 28 3.7 3.7 48 25 9 17 - CH3NH3' 1.2 x lo4 1 .a 2.3 C2H,NH3+ 2.8 x lo3 0.42 1.3 - I (CH3)2NH2: 2.1 x 103 0.73 1.8 n-C3H,NH, 1.6 x lo3 1.3 0.28 0.48 0.5 straight lines for each cation. These straight lines lead to the conclusion that the fast and slow relaxations can be attributed to steps ( b ) and ( c ) in mechanism (111, respectively.The four rate constants were evaluated from the slope and intercept of these straight lines. The values of the four rate constants obtained are listed in table 3. However, since the plots for CH3NH3+, C2H5NH3+ and (CH&NH2+ in fig. 7 yield straight lines through the origin, the value of k-, could not be evaluated. With respect to step ( a ) in mechanism (II), equilibration for the release of Na' in the present study required 48-72 h. This result is in agreement with that reported by Sherry et al." and Barrer et Moreover, since the concentration dependences of the two relaxation times cannot be interpreted except for the case that step ( a ) is much slower than steps (6) and ( c ) , the rate-determining step in the present ion-exchange reaction can be attributed to step ( a ) .This result suggests that the affinity of the site in the cage for the small ion Na' may be stronger than that for the alkylammonium ion.232 ION-EXCHANGE DYNAMICS AT THE ZEOLITE/SOLUTION INTERFACE K ' volume of cation/nm3 Fig. 8. (a) Plot of K ' as a function of the volume of the cation. (b) Plots of 0, kl ; e, k-l and a, k2 as a function of the volume of the cation. EQUILI@RIUM PROPERTIES OF STERIC AND ION-SIEVE FACTORS The static equilibrium constant K ' of the overall reaction in mechanism (11) is given by (amount of A' adsorbed) "a'] K'=- [ W a ) l [ ~ + I The values of K ' calculated by using the static data for systems of zeolite 4A with NH4+, CH3NH3*, C2H5NH3+, n-C3H7NH3+ and (CH3)2NH2+ are also listed in table 3. Fig. $ ( a ) shows a plot of K ' as a function of cation volume in which the volumes of the alkylammonium ions were estimated from their van der Waals dimensions. The value of K ' decreases with increasing volume of the entering alkylammonium ion.From fig. 8(a), since the upper limit of the volume of the exchangeable alkylammonium ion is ca. 0.12 nm3, the affinity series suggests that the values of K ' for i-C3H7NH3+, (CH3)3NH' and (CH3)4N+ would be zero. In the light of the space requirement of the cations in the cage, such larger alkylammonium ions cannot be exchanged with Na' in the cage for the lack of available intracrystalline space. Consequently, the kinetic and static results for zeolite 4A with i-C3H7NH3+, (CH3)3NH+ and (CH3)JV+, i.e. no relaxation and no exchange of cations, can be reasonably interpreted in terms of space requirements.This may indicate that the volume steric effect described by Theng et al. can limit the overall equilibrium constant of the ion exchange. In ion exchange in zeolites water molecules together with Na' in the cage are displaced by adsorbed organic cations as described by Barrer et al.25 If the alkylam- monium ion exchange for Na' requires the release of 4 water molecules, the volumeT. IKEDA, M. SASAKI AND T. YASUNAGA 233 Fig. 9. Plot of log k - , against pK,- of the displaced space of the Na+. 4H20 complex would be ca. 0.12 nm3. From a comparison of the estimated volumes of the organic cations and the upper lim-it in fig. 8( a ) , one can consider that rejection of a guest ion from the available intracrystal- line space of the host cage causes an ion-sieve effect for the larger cations.Further- more, from the relation found between K ' and the cation volume, it can be seen that the extent' of exchange of the organic cation for Na+ in zeolite 4A may be governed mainly by the available intracrystalline space of the cage. This leads to the conclusion that the space requirement of the exchangeable alkylammonium ion is the major factor determining the extent of ion exchange in the present experimental conditions. DYNAMIC PROPERTIES OF STERIC AND ION-SIEVE FACTORS Fig. 8(6) shows the dependence of the rate constants obtained on the volume of the cation for NH4+, CH3NH3+, C2H5NH3+, n-C3H7NH3+ and (CH3)*NH2+. The values of k , and k2, which are the rate constants for the process of insertion of the alkylammonium ion, decrease linearly with the volume of cation and become zero at a cation volume of nearly 0.12 nm'.This result confirms that the rates of adsorption and intracrystalline diffusion may be controlled by a steric factor of the entering cation. As can be seen from fig. 8(b), however, only the behaviour of the value of k- I differs essentially from those of k , and k2. As is shown in fig. 9, a plot of log k- , against pK, yields a straight line. This linear relationship indicates that the values of k - , may reflect the difference in the chemical properties of the exchangeable cations rather than the steric factor. ' D. W. Breck, Zeolite Molecular Sieves (Wiley-Interscience, New York, 1974).E. M. Flanigen, J. M. Bennet, R. W. Grose, J. P. Cohen, R. L. Patton and R. M. Kirchner, Nature (London), 1978, 271, 512. G. T. Kokotailo, S. L. Lawton, D. H. Olson and W. M. Meier, Nature (London), 1978,272,437. S. T. Wilson, B. M. Lok, C. A. Messian, T. R. Cannan and E. M. Flanigen, J. Am. Chern. SOC., 1982, 104, 1146. ' G . T. Kerr, E. Dempsey and R. J. Mikovsky, J. Phys. Chem., 1965, 69, 4050. ' J. Wytterhoeven, L. G. Christner and W. K. Hall, J. Phys. Chem., 1976, 69, 2177. L. V. C. Rees and C. J. Williams, Trans. Faraday SOC., 1965, 61, 1481. * K. Tanabe, Solid Acids and Bases (Kodansha, Tokyo, 1970). 'I T. Ikeda, M. Sasaki and T. Yasunaga, J. Phys. Chem., 1982, 86, 1678.234 ION-EXCHANGE DYNAMICS AT THE ZEOLITE/SOLUTION INTERFACE T. Ikeda, M. Sasaki,'K. Hachiya, R. D. Astumina, T. Yasunaga and Z. A. Schelly, J. Phys. Chem., 1982,86, 3861. D. W. Breck, W. C. Eversole, R. M. Milton, T. B. Reed and T. L. Thomas, J. Am. Chem. SOC., 1956, 78, 5963. 10 I ' l 2 H. S. Sherry and H. F. Walton, J. Phys. Chem., 1967, 71, 1457. l 3 R. M. Barrer and J. Klinowski, J. Chem. SOC., Faraday Trans. I, 1972, 68, 1956. l4 L. M. Brown and H. S. Sherry, J. Phys. Chem., 1971, 75, 3855. l 5 R. M. Barrer and W. M. Meier, Trans. Faraday SOC., 1958, 54, 1074. R. M. Barrer, R. Papadopoulos and L. V. C. Rees, J. Inorg. Nucl. Chem., 1967, 29, 2047. l 7 B. K. G. Theng, E. Vansant and J. B. Uytterhoeven, Trans. Faraduy Soc., 1968, 64, 3370. '' K. Hachiya, M. Ashida, M. Sasaki, H. Kan, T. Inoue and T. Yasunaga, J. Phys. Chem., 1979,83, 1866. L. Broussard alld D. P. Shoemaker, J. Am. Chem. SOC., 1960, 82, 1041. D. T. Dubin, J. Biol. Chem., 1960, 235, 783. 19 2o W. Troll and R. K. Cannan, J. Biol. Chem., 1953, 200, 803. 22 C. F. Bernasconi, Relaxarion Kinerics (Academic Press, New York, 1976). 23 R. P. Bell, The Proton in Chemistry (Cornell University Press, Ithaca, 1959). 25 R. M. Barrer and R. M. Gibbons, Trans. Faraday SOC., 1963, 59, 2569. R. M. Barrer and R. P. Townsend, J. Chem. SOC., Faraday Trans. I, 1978, 74, 745. 24

ISSN:0301-7249    

DOI:10.1039/DC9847700223

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1984, 77, 235-242 Kinetics of Dissolution of Calcium Hydroxyapatite BY JQ~RGEN CHRISTOFFERSEN" AND MARGARET R. CHRISTOFFERSEN Department of Chemistry, Panum Institute, University of Copenhagen, Blegdamsvej 3 , DK-2200 Copenhagen N, Denmark Received 5 th December, 1983 The rate of dissolution of calcium hydroxyapatite microcrystals [Ca,o(P04)6(OH)2, HAP] in aqueous suspension is controlled by a surface reaction, the diffusion of dissolved substance away from the crystal/liquid interface not influencing the rate. The rate can be described by a polynuclear mechanism. The rate cannot be expressed purely in terms of thermodynamic expressions ; kinetic effects are important. The rate constant for the polynuclear mechanism depends on pH. This can be explained by hydrogen-ion catalysis of the linear rate of growth of the dissolution nuclei.Application of the model leads to a value of the Gibbs surface energy of 47 f 3 mJ m-2 for HAP in the range 5.0 S pH S 7.2. The acidity constant for the HPOi- surface complex is found to be 10-6-10-7 mol dm-3, depending on the electrical potential difference between the crystal surface and the solution. Inhibition of the rate of dissolution of calcium hydroxyapatite owing to adsorption of foreign ions or molecules can often be described by a simple Langmuir adsorption isotherm. SURFACE PROCESSES AND TRANSPORT PROCESSES IN DISSOLUTION KINETICS When crystals dissolve in an aqueous medium two consecutive reactions take place, a surface process and a transport (diffusion or convective diffusion) process.The surface process involves transfer of substance from the crystalline phase to the solution adjacent to the crystal. This region is for simplicity called the interface region. The transport process involves the transfer of dissolved substance from the interface region to the bulk. The rate may be controlled by either of these two types of processes or by combinations thereof. For sufficiently large unsuspended crystals, gravity causes the crystals to move relative to the medium, and description of the transport process is complicated.' As this complication does not occur for dissolution of microcrystals of HAP, this effect will not be discussed any further here. When the transport process affects the rate of dissolution, a concentration gradient is set up between the interface region and the bulk.In the simple case where the rate is controlled by the diffusion of substance from the interface region to the bulk, the rate of dissolution, J, of a spherical crystal is, in the steady-state approximation, given by (1) dr/dt=-DV,(C,- C ) / r (2) J = -dn,,/dt = 4rD(Cs - C)r and the rate of change of r, the radius of the crystal, is given by in which ncr is the amount of undissolved substance in the crystal, D is the diffusion coefficient, V, is the molar volume of the crystalline phase, C, is the solubility of the crystalline phase and C is the bulk concentration of dissolved substance in solution.2 If the surface processes are not fast enough to keep the concentration, 23 5236 KINETICS OF DISSOLUTION OF CALCIUM HYDROXYAPATITE C', of dissolved substance in the interface layer close to C,, the rate of transport can still be described by eqn (1) and (2), but with Cs replaced by C'.If the surface process is so slow that C' is close to C, we may neglect the concentration gradient and describe the rate by an expression for the surface process in terms of C. The natural surroundings of biominerals normally contain inhibitors for growth and dissolution of the mineral. To describe or explain the interaction between the mineral surface and the medium, information about the surface reactions of the pure mineral is most essential. For HAP microcrystals the only method for obtaining such information is to work with a large number of crystals, of the order of For a polydisperse sample of crystals, all dissolving, one can measure the overall rate of dissolution (3) J = -dn,,/dt = - C dn,,(i)/dt I where index i runs over all crystals, ncr is the amount of undissolved substance and ncr(i) is the amount of substance in the ith crystal.The aim of studying the overall rate of dissolution of HAP was to find the kinetic law followed by the individual crystals. This is, in principle, impossible unless some auxiliary assumptions are introduced. The linear rate of growth or dissolution perpendicular to the various crystal faces can in general be described by an expression of the type in which g ( C ) represents the influence of Concentration on the rate and f(r) represents the influence of size and of surface structure, including density of dislocations and types of dislocations.3y4 With f(r) independent of the concentration history and g ( c ) being the same for all crystal faces, the overall rate of dissolution or growth of a polydisperse sample of polyhedral crystals may to a good approxima- tion be expressed as in which k is a rate constant, mo the initial mass of seed crystals, F( m/ mo) represents the influence of size distribution, etc., of crystals and g ( C ) represents the influence of concentration on the rate. A pH-stat technique was used to study the rate of dissolution of HAP microcrys- tals at constant values of pH in the pH range 5.0-7.2.4-6 For dissolution into solutions with a calcium-to-phosphate ratio of 1.67, the rate, for a constant value of m/mo, was found to be proportional to (1 - C/QP, with p in the range 3-6.The rate constant, k, was found to increase with the hydrogen ion concentration (see fig. 1 ) . From electron micrographs a size distribution of the crystals was obtained. From the size distribution the number of crystals per unit mass, N/mo, was estimated. Assuming the rate of dissolution to be diffusion controlled, an apparent diffusion coefficient Dapp - cm2 s-' was obtained. As diffusion coefficients of small inor- ganic ions in water are ofthe order of lop5 cm2 s-', the rate of dissolution is ca. lop4 times the rate corresponding to diffusion. Similarly it was shown that the rate of diffusion of H' from the bulk to the crystal surface cannot be the rate-controlling process. From the above observations it can be concluded that the rate of dissolution of HAP microcrystals in aqueous solution with 5.0 s pH s 7.2 is controlled by a surface reaction.The dependence of the absolute value of the rate constant on pH indicates that the hydrogen ion plays an important role for the dissolution of HAP.J. CHRISTOFFERSEN AND M. R. CHRISTOFFERSEN 237 I -1.0 - 0.5 In ( I - C/CJ Fig. 1. Plots of ln(Jm,’) against l n ( l -C/C,) for five constant v.alues of pH: 0, 5.03; A, 5.51; 0, 6.31; A, 6.76; X, 7.15. The rates were measured when 30% of the initial mass of crystals had dissolved, i.e. m/ m, = 0.7. The slopes of the lines vary from 4 to 6, indicating that the rate is not controlled by a transport process or by a surface spiral process, for which slopes of 1 and 2, respectively, would be expected.SURFACE NUCLEATION, A POSSIBLE MECHANISM FOR DISSOLUTION OF HAP Based on the theory of surface nucleation for growth described by Hillig’ and on the computer calculation of crystal growth (Gilmer and Bennema,8’9 De Haan et ~ 1 . ’ ~ and Bennema and Van der Eerden”), we have developed a similar mechanism, but for dissolution of crystal^.^ This mechanism can explain the main features of the rate of dissolution of HAP. In all nucleation theories for growth and in the present theory for dissolution, nuclei are treated as continuous in size and no distinction is made between the various lattice ions. This is not a severe limitation as the nucleation phenomenon is of a statistical nature. For dissolution a nucleus is a microscopic hole in the crystal surface, whereas for growth a nucleus is a small hill of material stacked on the crystal surface.Nuclei of different sizes have different energies of formation. The distribution of nuclei according to their energy of formation is assumed to be given by a Boltzmann distribution. AG for formation of a cylindrical nucleus, radius r, one mean ionic diameter, a, deep can be expressed as AG = -xkTP + 2 ~ r a c r ( 6 ) in which x is the number of missing ions in the nucleus, x = m2/ a*, kT is Boltzmann’s constant times the absolute temperature, p is the dimensionless dissolution affinity23 8 KINETICS OF DISSOLUTION OF CALCIUM HYDROXYAPATITE for a single ion or growth unit, a is the edge length of the volume-equivalent cube of a growth unit and (T is the Gibbs surface energy, assumed constant, despite the small size of the nuclei. For a critical nucleus dAG/dr is zero.This leads to the following expression for the radius, r*, of a critical nucleus: r* = a3u/ kTp. (7) Hillig7 derived the following expression for the rate of surface nucleation I = k”C(l)P’/2v+ exp [-.rra4~’//3(kT)’] (8) where I is the rate of nucleation per unit surface area and p = -Ap/kT, with A p equal to the average increase in chemical potential for one growth unit (ion) in the actual reaction. v , is the linear rate of growth of a nucleus in the case where no back reaction occurs. For growth, C(1) is the concentration of single growth unit adsorbed in the crystal surface. For dissolution, C( 1) is the concentration of holes formed by the loss of a single growth unit.C(1) is assumed to vary relatively little with concentration and may be included in the rate constant, k”. For a polynuclear mechanism, the rate of nucleation is so fast that nuclei intergrow. Assuming the linear rate of growth, v, of a nucleus to be constant during the lifetime of the nucleus, the nuclei per unit area created in the time interval to, to +dt have an area I d t m 2 ( t - to)2 at a later time t. If the nuclei formed in the time interval to, to + r cover one unit of area, we have I.rrv2(t - to)’ d t = In-v2r3/3. (9) The frequency of removing one atomic layer from the crystal face is thus u = 1/r and the linear rate of dissolution perpendicular to a crystal face is d r l d t = -ua = - a ( I ~ v ~ / 3 ) ’ / ~ (10) which leads to the following expression for the overall rate of dissolution of a polydisperse sample of polyhedral crystals J = kJmoF(m/mo)v2~3v:/3~1~6 exp ( - a / p ) with a = 7ra4a2/3(kT)’.(12) The mechanism determining the rate, u, of lateral growth of a nucleus is not known. Gilmer and Bennema9 expressed v in terms of p ; such an expression for v cannot be used to account for specific ion effects. We have suggested4 a simple kinetic expression for v which has been used in connection with specific ion effects.6’12 This expression is v = kaC,(C/C,- 11 which leads to v’=kaC and v’=kaC, (14) for growth and for dissolution, respectively. as The overall rate of dissolution for the polynuclear mechanism can be expressed J = kJmOF(m/mo)(l - c/cs)2/3p1/6 exp ( - a l p ) (1 5 ) with kJ proportional to C,, and with a given by eqn (12).J.CHRISTOFFERSEN AND M. R. CHRISTOFFERSEN 239 c/ c, - 0.7 - 0.5 - 0.2 I I I - 2 - 1 J -3 +-' Fig. 2. The experimental results shown in fig. I are plotted here according to a polynuclear dissolution mechanism, for which Jm,' (1 - C / Cs)-2/3/3-'/6 should be proportional to p-'. The slopes of these lines lead to a value of 47 f 3 mJ m-2 for the surface free energy, and the intercepts of the lines give the values of kJ plotted in fig. 3. In fig. 1 In (hi') is plotted against In (1 - C / C , ) for dissolution of HAP in solutions with Ca/ P = 1.67 and for several values of pH. From this plot it is seen that the rate is controlled by a surface process and not by a diffusion process, which would require that the slopes of the lines in fig.1 should be close to unity. Fig. 2 shows plots of In [Jm,' (1 - C / Cs)-2'3p-1'6] against -p-' for the same experimental results as shown in fig. 1. The rate constants, kJ, can be determined as the intercepts of the lines with p-' = 0. kJ is found to increase with decreasing pH. As the slopes of the lines are nearly identical, the values of the Gibbs surface energy, u = 47 f 3 mJ m-2, determined from these slopes are nearly independent of pH in the range 5 s p H G 7 . This indicates that the specific effect of hydrogen ions can be explained by the lateral rate of growth of dissolution nucleus being catalysed by hydrogen ions. The aqueous solution calcium phosphate ion pairs are much more stable than calcium hydrogen phosphate ion pairs.We may similarly expect hydro- gen phosphate ions in the crystal surface to be more weakly bonded to surrounding calcium ions than phosphate ions. Assuming the lateral rate of growth of the dissolution nuclei to be proportional to xHp, the mole fraction of the crystal surface phosphate groups in the form of hydrogen phosphate ions, leads to k, = kXHp = k/[ 1 + k,,/(H+)] (16) in which (H+) is the activity of hydrogen ions in the solution, k is a rate constant, which may depend on A+, the electrical potential difference between the crystal240 KINETICS OF DISSOLUTION OF CALCIUM HYDROXYAPATITE O O 1.5 - I 0 c 2 1.0 v1 M --. h 222 : v 0.5 5 10 3 Fig. 3. k,' plotted against (H+)-' for the results shown in fig. 1 and 2. From line 1 we obtain k = 2 . 3 ~ 1 O - ~ m o l g - ' s - ' and pK,,=_6.7, when A+ =O.From line 2 we find that k = 1.3 x mol g-' s-' and pK,, = 5.7, giving A 4 = 60 mV around pH 5-6. surface and the solution, and k,, is an acidity constant for the hydrogen phosphate surface complex, defined by K,,= K,, exp (FA#/RT> = (H+)x,/x,, (17) with K,, being the acidity constant for A+ = 0 and F Faradafs constant. In fig. 3 k;' is plotted against (H+)-' for m/m, = 0.7. If Kc, and k were proper constants, a straight line would be obtained. The deviation from a straight line can be explained by A+ increasing as pH decreases. As an approximation, in fig. 3 we have drawn two straight 'lines crossing at l/(H+) = 4.8 dm3 pmol-' (pH 6.7). HAP crystals are not significantly charged at ca. pH 7. From line 1 in fig. 3 we obtain k = 2.3 x mol s-I g;' and K,, = 2 x lop7 mol dmA3, i.e.pK,, = 6.7, where k . and K,, are the va!ues of k and K,, for A 4 = 0, From line 2 in fig. 3 we obtain, for 5 s pH s 6.3, k = 1.3 x 10z5 mol s-' g-' and Kc, = 2 x mol dm-3, i.e. pK,, = 5.7. These values of K,, and K,, are only approximate. As the crystals become charged, the acidity constant of HP0;- surface ions will gradually change from a value close to lo-' mol dm-3 to a value ca. 10 times larger. From eqn (17) we obtain A# = ( R T / F ) In (icr/Kc,) == 60 mV. (18) Assuming that HP0;- ions leave the crystal surface relatively easily compared with calcium ions, the actkation energy for removing a calcium ion, calculated by inserting the value of k or k in Eyring's formula, is ca. 1.4 x J. In HAP, calcium ions are surrounded by 6-8 oxygens from hydroxyl or phosphate groups, half of which are missing in the edge of a nucleus.The activation energy therefore corre- sponds to breaking 3-4 oxygen-calcium bonds in connection with removal of a calcium ion. The activation energy found is also close to three times the energyJ. CHRISTOFFERSEN AND M. R. CHRISTOFFERSEN 24 1 required to remove a water molecule from a hydrated calcium ion in solution.12 Note that knowledge of absolute rate constants for surface-reaction-controlled dissolution processes gives information about the energy needed to break bonds in the crystalline phase, whereas knowledge of absolute rate constants for surface-reaction-controlled crystal-growth processes13 gives information about the interaction between the solvent and the ions in solution. INHIBITION OF THE DISSOLUTION PROCESS OF HAP The effect of an inhibitor for surface nucleation may be described as prevention, or strong retardation, of the nucleation process in areas around the adsorbed inhibitor molecules or ions.Each inhibitor unit in the crystal surface is surrounded by a neighbouring ions, all having the same sign of charge. Owing to interaction with the inhibitor such ions are strongly attached to the crystal surface. These ions, including the inhibitor, occupy an area T&= ( a + l)d2, in which d is the diameter of a mean ion. The area around an inhibitor unit in which nucleation is strongly retarded is of the order of T ( ro+ T * ) ~ , r* being the radius of the critical nucleus.This means that the fraction of the crystal surface area in which nucleation is prevented, AL/A, is larger than the mole fraction, x, of the adsorption sites occupied by the inhibitor, i.e. AJA = #x, with # > 1. For a Langmuir adsorption isotherm, we have, for low degrees of surface covering, in which Jo and JL are the rates of dissolution without and with the inhibitor present, respectively, both rates being determined for the same values of the parameters influencing Jo. As the solution composition approaches an equilibrium value, r* increases and so does #. This causes an increase in the effect of the inhibitor. This effect has been dem0n~trated.l~ CONCLUSION The rate of dissolution of HAP can be described by a surface nucleation process, but not purely in thermodynamic terms, kinetic effects being important.This demonstrates the importance of analysing empirical data for growth and dissolution of crystals in terms of models in which chemical reactions in the crystal/solution interface are taken into account. We are grateful to the Danish Medical Research Council for grants for laboratory assistance (1 2-0323, 12-22 15, 12-36 17). ’ A. E. Nielsen, J. Phys. Chem., 1961, 65, 46. ’ A. E. Nielsen, in Kinetics ofPrecipitation (Pergamon Press, Oxford, 1964), p. 34. J. Christoffersen and M. R. Christoffersen, J. Crysf. Growth, 1976, 35, 79. J. Christoffersen, J. Cryst. Growth, 1980, 49, 29. J. Christoffersen and M. R. Christoffersen, J. Cryst. Growth, 1982, 57, 21. G. H. Gilmer and P. Bennema, J. Cryst. Growth, 1972, 13/14, 148. G. H. Gilmer and P. Bennema, J. Appl. Phys., 1972, 43, 1347. ’ J. Christoffersen, M. R. Christoffersen and N. Kjaergaard, J. Cryst. Growth, 1978, 43, 501. ’ W. B. Hillig, Acra Metallurg., 1966, 14, 1868.242 KINETICS OF DISSOLUTION OF CALCIUM HYDROXYAPATITE S. W. H. de Haan, V. J. A. Meeusen, B. P. Veltman, P. Bennema, C. van Leeuwen and G. H. Gilmer, J. Cryst. Growth, 1974, 24/25, 491. 10 ” P. Bennema and J . P. van der Eerden, J. Cryst. Growth, 1977, 42, 201. ‘* S. Petrucci, in Ionic Interactions, ZI. Kinetics and Structure, e d . 3 . Petrucci (Academic Press, New l 3 A. E. Nielsen, in Industrial Crystallization 81, ed. S. J. JanEic and E. J. de Jong (North-Holland, York, 1971). Amsterdam, 1982), pp. 35-44. J. Christoffersen and M. R. Christoffersen, J. Cryst. Growth, 1981, 53, 42. 14

ISSN:0301-7249    

DOI:10.1039/DC9847700235

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 243-256 Kinetics and Simulation of Dissolution of Barium Sulphate BY VINCENT K. CHENG, BRUCE A. W. COLLER" AND JOHN L. POWELL? Department of Chemistry, Monash University, Clayton, 3 I68 Victoria, Australia Received 16th December, 1983 Rates of dissolution of a natural barite single crystal mounted in a rotating disc have been found to be proportional to the square of undersaturation in terms of concentration, depressed by added common ion, enhanced by foreign bivalent metal ions and unaffected by monovalent ions. Activation energies for dissolution of barium sulphate microcrystals of three types show variation from 20 to 80 kJ mol-' and are inversely correlated with energies of dissolution calculated from kinetic solubilities, these energies varying from AHo to near zero.Monte Carlo simulation of dissolution of crystals with stress fields such as would a&e from screw, edge and plane dislocations and from edges and apices gave a corresponding variation of simulated activation energy, depending on the degree of stress and on the initial configuration of the surface. Effects of foreign ions were simulated by introducing next-nearest-neighbour repulsions in the Monte Carlo treatment of adsorption on an initially flat surface with a 4 ~4 columnar hole. The kinetics of growth and dissolution of barium sulphate have been the subject of a number of previous studies.'-6 The processes are surface controlled and provide a test case for theories of growth and dissolution of ionic crystals. The rates of growth and dissolution of microcrystalline suspensions were reported to be propor- tional to the square of supersaturation or undersaturation in terms of concentration R = k(A)( C,, - C)2.Similar behaviour was reported for strontium and lead sulphates7'* but runs counter to the naive expectation that rates of dissolution or growth of solid salts might be proportional to the distance from equilibrium in terms of ionic product, PI: R = k( A)( K , - PI) which for stoichiometric solution would take the form R = k(A)( C& - C') reducing, when close to equilibrium, to the linear form R == 2k(A)C,,( Ceq - C). (4) Davies and Jones9 intuitively identified the observed proportionality of the rate ofgrowth of silver chloride to the square of supersaturation with the binary ionic nature of the salt in an adsorbed monolayer of mobile hydrated ions, but they had no sound physical basis for their model.However, later workers have reported rates of dissolution depending on the cube of undersaturation for the ternary ionic compounds Ba( 103)2 l o and Ag,(CrO,). I ' t Present address: Oil and Gas Division, BHP Ltd, 35 Collins Street, Melbourne, 3000Victoria, Australia. 243244 KINETICS OF DISSOLUTION The kinetic solubilities of certain barium sulphate preparations have been found to be significantly greater than the accepted equilibrium ~olubility.~ The extent of solubility enhancement is dependent on the conditions of nucleation and growth and thus on the regularity of the crystals. Successive dissolution runs using one batch of crushed crystals showed progressive decreases in both kinetic solubility and dissolution rate c o n ~ t a n t .~ Our earlier finding of the elevation of kinetic and saturation solubilities for barium sulphate depending on crystal type and on radioactive labelling were attributed to submicrometre crystallites on the surfaces of the crystal and as grains within the bodies of the crystal^.^ We would now also give weight to the effect of preferential dissolution at dislocation centres and lines of dislocation (grain boun- daries). Nancollas et al.4 found that rate constants for growth and dissolution of different crystal types are not proportional to their specific surface areas and suggested the involvement of active sites yet to be identified. Similar observations were recently reported by Christoffersen in which the rate constants for growth and dissolution of calcium sulphate dihydrate were found to depend on the initial growth conditions and on the washing and aging treatment.'* The cause of such variation in rate constant was given in terms of the dislocation density and grain boundary structure at the surface.The topography of a crystal surface can be modified as a result of preferential dissolution at stressed regions. The extent of changes in surface activity will therefore be determined by the perfection of the crystals, the solvent undersaturation and also by the initial mass and the duration of dissolution. The initial perfection is affected by the method of preparation; microscopic and X-ray examination of barium sulphate crystals l 3 , I 4 reveals that crystals grown under vigorous conditions contain extensive imperfections, such as dislocations and mosaic and grain boun- daries within both the surface and bulk of the crystal.Well aged crystals appear to have smooth surface^.^ In accordance with the Kossel-Stranski model for crystal growth,15 the majority of growth events may be considered in terms of a three-dimensional lattice (B,) with steps terminated by kink units (K) to which free units (F) from the solution become attached after one or two stages of diffusion, desolvation and adsorption. Each such event adds one unit to the lattice: B,K+F r* 7* B,+IK. ( 5 ) The rate of growth is often interpreted in terms of equilibrium between free units (F) and terrace units (T), with terrace diffusion-controlled rates of attachment of units to steps (ledges, L) in equilibrium with kinks.The rate of growth should then depend on the number of available kinks (NK) and the oversaturation in terms of concentration: growth rate = kN,( C - C,,). (4) Screw dislocations are widely held to be necessary for the growth of crystals, both ionic and molecular. Burton, Cabrera and Frank (B.C.F)I6 showed that the screw-dislocation mechanism can provide a continuous supply of step and kink sites with a steady-state area density such that growth rate/area = k In ( Ceq/ C)-'( C - Ceq). (7) A similar expression would apply to dissolution if this were dominated by reverse spirals developing around screw dislocations, and would tend toward proportionality to the square of undersaturation in terms of concentration when close to equilibriumV.K. CHENG, B. A. W. COLLER AND J. L. POWELL 245 for simple crystals. Such an approximation may also apply for ionic crystals dissolving into stoichiometric solutions by the mechanism controlled by terrace diffusion and screw dislocation. With a more generalised rate law, van Rosmalen17 showed that the rate of growth of calcium sulphate dihydrate close to equilibrium is consistent with the B.C.F. process. We have studied dissolution rates with a cleaved surface of barite which was mounted in a rotating disc to compare the applicability of the B.C.F. equation with the square-of-undersaturation equation given above. The surfaces of similar barite samples were examined by scanning electron microscopy before and after dissolu- tion.The activation energy for the dissolution of barium sulphate, reported by Jones ( E , = 24 kJ mol-1),2 is comparable to the activation energy of diffusion, despite the clear demonstration of surface-controlled kinetics. Our studies are now extended to values of the activation energy determined from the temperature dependence of the initial rate using microcrystalline suspensions prepared by different methods. Apparent enthalpies of dissolution are also evaluated from kinetic solubilities. The dependence of the activation energy on crystal surface stress was simulated by calculating rates at different simulated temperatures using Bennema’s Monte Carlo model incorporating a cylindrical stress field.” Reductions of crystal growth and dissolution rates in the presence of added impurities are commonly reported.Small quantities of polyelectrolytes, or other high-molecular-weight material, are commonly inhibitors of the growth and dissolu- tion of barium ~ u l p h a t e ~ ” ” ~ ~ and calcium sulphate.” Simon reported that addition of cadmium chloride retarded the dissolution of sodium chloride.22 The blocking of movement of surface steps by the adsorption of high-molecular-weight impurities has been used to account for the inhibition e f f e ~ t . ~ ’ , ~ ’ , ~ ~ However, traces of sodium chloride enhanced the growth of calcium ~ u l p h a t e , ~ ~ and potassium dichromate and potassium ferrocyanide were found to enhance the growth of barium ~ u l p h a t e .~ that traces of impurities which form strong impurity-host bonds at the surface may cause enhancement of the growth rate through nucleation. Impurities that form surface clusters cause enhancement of the growth rate by providing a large number of step sites. Thus the effectiveness of impurities in altering crystal growth rates will depend on their adsorption characteris- tics.26 The dissolution rate can be expected to be enhanced if adsorbed impurities can reduce the binding energy of the nearby surface lattice ions. At low solution concentrations simple ionic compounds are adsorbed on the surface of barium ~ u l p h a t e ~ ~ in electroneutral amounts. Their characteristic adsorption isotherms indicate that the adsorbate ions are well isolated from one another. Under these conditions lattice ions which are next-nearest neighbours to an adsorbed ion will experience repulsion.Such weakening of the binding energy of surface ions provides the potential for enhancement of the dissolution rate. We have added trace quantities (< l 0-4 mol dm-3) of simple ionic additives such as chlorides of potassium, strontium, calcium and barium and sodium sulphate to the dissolving barite to investigate the alteration of the dissolution rate. The results are compared with those obtained from a simulation model which incorporates next-nearest-neighbour lattice-adsorbed ion repulsions in the manner described by Bennema et aL2* Computer simulation studies have EXPERIMENTAL DISSOLUTION STUDIES Three types of barium sulphate microcrystals were prepared as previously de~cribed.~ mol dmP3 reactant Type I crystals were made by slow mixing (with paddle stirring) of246 KINETICS OF DISSOLUTION solutions. Type I1 crystals were prepared by rapid mixing of 0.1 mol dmP3 reactant solutions.Type 111 crystals were prepared from solutions in methanol, which were mixed rapidly at room temperature. The colloid was allowed to coagulate and settle before washing and storage. The precipitates were aged for an initial period of 4 h at 90 "C. At weekly intervals during subsequent storage the overlying solutions were gently decanted and replenished with doubly distilled water. The crystals were crushed and mounted onto polythene plates as described previ~usly.~ Dissolution of barium sulphate was monitored conductimetrically. Rate coefficients and kinetic solubilities were obtained from a plot of (rate)"2 against concentration and initial rates calculated therefrom.Arrhenius activation energies were calculated from ratios of rate coefficients determined before and after changing the temperature from 25 to 35 "C in mid run. Plates with a given type of crystals were re-used in several runs. The composition and crystallographic characteristics of the natural barite used were determined by AAS, X-ray fluorescence and X-ray diffraction. The barite contains over 96% barium sulphate and the other impurity detectable by X-ray fluorescence was strontium. Its unit-cell dimensions (5.3 x 7.2 x 8.4 A') were compatible with the literature values.29 A single crystal was cleaved at an existing plane of weakness (100) and mounted in an Araldite disc to enable rotation in a dissolution medium.The barite surface was not polished. Conduc- timetric measurements were used to determine the rate of dissolution into doubly distilled water and into diluted samples of solution that had become saturated (12.4 pmol dmP3) in contact with a microcrystal suspension. Effects of added salts were determined by adding measured amounts of the salts after a period of dissolution (ca. 3 h) into distilled water and continuing the run for a similar period of time. Linear conductance-time relations were observed and each dissolution run corresponded to an increase of ca. lo-' mol dmP3 in the concentration of barium sulphate. MONTE CARL0 SIMULATION METHODS Monte Carlo simulation of the dissolution of a stressed surface was carried out by means of a computer program kindly supplied by P.Bennema.'* The model incorporates an effective nearest-neighbour attraction energy, 4. The cylindrical stress field located around the centre of the surface is given by where r is the distance from the dislocation centre, U(0) is the stress energy density at the dislocation centre, rh is the Hooke radius [rf4/ U(O)] and rf is the Frank radius, which effectively measures the size of the stress field or dislocation region. Surface diffusion is not included, and the microscopic reversibility condition for the ratio of deposition and detachment probability at each site depends on the number of lateral nearest neighbours, n: __- k - exp {[(4-2n)@+ U ( r ) ] / k T } k+ - c/ c e , (9) The program has been extended to allow initial surface configurations that are not flat.On an unstressed lattice surface the absolute energy required to remove one kink unit and thus create one less bulk unit is 64. This corresponds to the enthalpy (AH") of dissolution of the stress-free crystal. In a real crystal activation barriers in-the elementary deposition and detachment events are to be expected. It has been shown that activation barriers can be factorised into pre-exponential frequency factors in the attachment and detachment probability expression^.'^V. K. CHENG, B. A. W. COLLER AND J. L. POWELL 241 The reference conditions chosen were +/ kT = 2 and C / C,, = 0.135. Rate calcu- lations were then carried out assuming constant 4 and C with selected values of U(0) and initial configurations.Changes of temperature of 2.5%, up and down, were imposed. The new C/Ceq inputs were calculated by allowing for the change in equilibrium concentration due to temperature change Simulations were carried out for an initially stress-free surface, for one starting with a 4 ~4 columnar hole25 at its centre and for surfaces with different stress fields and initial configurations. The rate of dissolution was calculated from the change in the number of lattice units per unit area over a period of time sufficient to obtain a steady average rate and root-mean-square deviation. Monte Carlo simulation of the effects of the foreign bivalent metal ions on the kinetics of dissolution of barium sulphate was achieved by means of a newly developed program based on Bennema’s previous work referring to a two-component solid.28 The initial crystal lattice was assigned a flat surface with a 4 ~4 columnar hole without specific recognition of its binary nature.Foreign ions were assumed to attach to the surface, on top of lattice ions of opposite charge, with the attractive interaction energy equal to the lattice-ion interaction energy &. Next-nearest neighbours in the lattice surface adjacent to the adsorbed ion, being of l i h charge, were then assigned an interaction energy to replace the stress function in eqn (9) above, using negative values of (Y to represent the repulsive character of the interaction. The foreign ions in solution were assigned a potential p, (solution) such that the average fractional coverage (0,) of the surface by adsorbed ions would tend with time to an equilibrium value such that kT In [&/( 1 - 6,)] = p l (solution).RESULTS KINETIC DATA Rates of dissolution of barium sulphate into partly saturated solutions from a single crystal barite surface are represented in fig. 1. The observations conform to the square of distance from a kinetic solubility C, [eqn(l)]: R = k(A)C2(1- C/C,)* rather than to the B.C.F. theory [eqn (7)]. The corresponding dissolution rate constant k(A) was found to be 190 dm3 mol-’ min-’. If this is divided by the area it is compatible with that reported for the type A crystals used by Liu et aL4 Extrapolation of fig. 1 to zero of (rate)”’ gives the kinetic solubility of barite as 1 1.5 f 0.9 pmol dmP3, intermediate between the saturation solubility of the barium sulphate suspension (12.4 pmol dmP3) and the accepted equilibrium solubility (10.4 pmol dm-3).3 SEM STUDIES Plate 1 shows the barite disc used in the kinetic studies.Slight dulling of the surface as a result of the dissolution is evident. However, it appears that dissolution has occurred to a greater degree near natural cracks and edges. Plate 2 shows a low-magnification micrograph of a similar barite surface obtained by cleavage along planes of weakness. Flat and smooth areas were separated by multiple step features (plate 3) originating from fracture between mismatched planes of weakness. A third248 0 20 40 60 80 100 saturated solution(%) (12.4 pmol d ~ n - ~ ) Fig.1. Square root of rate of dissolution from rotated single barite crystal face plotted against percentage of solution saturated by microcrystals ( 12.4 pmol dm-3) 0, Stoichiometric solu- tion; 0, with added SrC12 (10 pmol drnv3). sample (plate 4), after standing in water for several days, showed smooth areas that were largely unaffected, together with clear indications of dissolution and roughening along fracture steps and in other areas, presumably of surface imperfections such as emergent dislocations and grain structure. Plate 5, at high magnification, shows the erratic etching that occurs in such areas. Thus it is evident that dissolution occurs preferentially in the vicinity of steps, edges, cracks and other lattice defects. EX PER1 M ENTAL ACTIVATION EN ERG1 ES Table 1 shows the ranges of kinetic solubilities at 25 and 35 "C, and the corre- sponding energy changes (enthalpies) of dissolution, together with activation ener- gies based on calculated initial rates [ k(A)C&], for several microcrystalline barium sulphate preparations mounted on polythene plates.An inverse correlation (fig.2) exists between the activation energies and the energy changes (enthalpies) of dissolu- tion, while both of these properties are roughly correlated with kinetic solubilities at 25 "C, the more soluble crystals showing less positive energies of dissolution, as would normally be expected, However, the variation in Gibbs free energy of dissolution (see table 1) is small while the energy change varies from approximately the calorimetric value (19.2 kJ mol-I)" to near zero.The activation energies vary from 20 up to 80 kJmol-I, the crystals having the less positive energy changes requiring the higher activation energies for dissolution. Variability is also seen for crystals of each type. This is likely to be due to use of each plated specimen in several successive dissolution-and-storage cycles. Such variation may also be expected to occur in wash-and-age cycles during storage of seed crystal^.^ Specimens prepared with radioactive tracer (35S, 20 and 50 mCi)3 showed behaviour patterns similar to those of the corresponding inactive preparations and will not be discussed separately.Plate 1. Barite disc (area 131 mm2) used in the experiment, showing surface texture after dissolution.[To face page 248Plate 2. Scanning electron micrograph of a mechanically cleaved surface (100) before disso- lution. Regular microsteps are evident. 50 x magnification. Bar represents 200 pm.Plate 3. Specimen of plate 2 at 1000 x magnification, showing the topography of fractured microsteps. Bar represents S pm.Plate 4. Scanning electron micrograph of a similarly cleaved surface ( 1 00) after dissolution. Roughening of edges, steps and patches is evident. 50 x magnification. Bar represents 200 pm.Plate 5. Specimen of plate 4 at 5000 xmagnification, showing the irregular pits in the roughened patch. Bar represents 2 pm.V. K. CHENG, B. A. W. COLLER AND J. L. POWELL 249 Table 1. Characteristics and dissolution behaviour of three types of microcrystalline barium sulphate" crystal type parameter I I1 111 size3/ p m shape precipitation nucleation (inferred) defect structure (inferred) kinetic solubility pmol dm-3 (suspension) /pmol dm-' (suspension) kinetic solubility /pmol dm-3 (from plates)' - i A c / k J mol-' -iAH/kJ mol-.' E,/ kJ mol-' dissolution rate law saturation solubility3 (kinetic solubilities) 5-1 5 rectangular [4] slow, heterogeneous central region of stress/ dislocation [4,131 lo-' mol dmP3 10.4' 12.5 10.5-ll.ld 0.03-0.16 19-11 AHO-AH k( c, - q2 20-50 <5 irregular rapid, homogeneous high surface energy near edges and apices stars [4] lo-' mol dm-. 11.0 10.9 12.5-15.2 0.42-0.94 16-0 A H O ~ AH k'( c, - q2 40-80 (0.2 aggregated colloids from methanol homogeneous grain boundaries, high surface energy 3 13.5 13.0 1 4.6- 1 7 .O 0.85- 1.20 11-2 40-70 AHO>AH>O k"( c, - q2 a Accepted equilibrium solubility, 10.4 pmol dm-3.3 Calorimetric energy (enthalpy) of 1 1 .1 to dissolution, AHo = 19.2 kJ m01-I.~~ 13.0 pmol dm-3 for radioactive specimens. 11.0 for radioactive specimen. ' This work. SIMULATED DISSOLUTION OF CRYSTALS WITH STRESS FIELD Simulated dissolution of an unstressed initial flat surface showed the establish- ment of a more or less steady surface configuration with a small number of pits (1 or 2) of depth one lattice unit. The rates of dissolution showed oscillations corre- sponding to initiation, propagation and completion in the removal of surface layers. Table 2 shows that with increasing intensity of stress at the centre [ U(O)] and with greater radius over which stress is present (rf), average rates of dissolution become higher and root-mean-square deviations in the oscillations become smaller.The steady-state surface configurations are marked by deeper pits centred on the stressed region. Arrhenius activation energies, based on rates obtained at three simulated temperatures for a fixed small concentration (ca. 0.135 Ceq) of dissolved units, were seen to decrease with increasing intensity and increasing extension of the stress field, as intuitively expected. For a given stress field, an initial surface configuration, which had previously been obtained from extensive simulated etching, led to a higher steady average dissolution rate and a lower activation energy. This result may correspond to the250 KINETICS OF DISSOLUTION E I I I + - %* + t ' ' ' I * ' # ' + a I 0 5 10 15 20 energy of dissolution, $AH/kJ mol-' Fig.2. Activation energies and energy changes for dissolution for three types of microcrystal- line barium sulphate: ., type I ; +, type 11; e, type 111. Star points'on symbols indicate radioactive labelling (20 or 50 mCi). Table 2. Simulated activation energy at various stress field strengths and initial surface configurations" rate and r.m.s. dev. pit depthh initial - final U(O)/kT at 4/kT=2.0 Ea/ 4 rf = 10.0 0 2.5 4.5 open core rf = 2.5 4.5 -0.0069 (f0.003 5) -0.033 7 ( f 0.008 0) -0.0326 (f 0.007 5) -0.1 102 (h0.003 9) -0.0689 (f0.0030) 20.0 -0.0489 (f0.0103) -0.1574 (k0.0058) 9.0 f 0.1 0 4 1 9.0 f 0.3 0 - 4 4.7 f 0.1 29 - 5' 3.4f0.2 0 ---+ 29d 3.8 f 0.4 0 ---* 14 5.3f0.1 0 - 5 2.4 f 0.4 0 - 50d # / k T = 2.05,2.00, 1.95.C / C,, = 0.182,0.135,0.100 (AH" = 6#). Pit depth is defined as the difference between the maximum and minimum height of the steady-state surface configuration. Initial pit depth 29 units (reduced by dissolu- tion of upper layers). Pit depth increases with temperature. The value given is at #/ kT = 2.0.V. K. CHENG, B. A. W. COLLER A N D J. L. POWELL 25 1 Table 3. Relative initial rate of dissolution of barite with added salts in solution final solution relative initial salt added concentration/pmol dmP3 dissolution ratea KC1 Na2S04 BaC1, CaCl, SrCl, 100 10 20 9 10 54 100 10 20 10 10 1.01 0.60 0.34 0.68 1.18 1.25 1.45 1.13 1.41 1.33' 2.03' ~ ~~ Relative rate=rate in salt solution/rate in distilled water.When SrCl, was added to a 10% saturated BaSO, solution. ' When SrCl, was added to a 35% saturated BaSO, solution. variation in activation energy of dissolution for successive runs with a given type of barium sulphate crystals, as described above. For the system with a 4 x 4 open core, simulating a case where deep etch- pit formation has led to removal of a stressed region around a dislocation, the dissolution rate and activation energy were intermediate between those for high stress [ U(O)/kT = 4-51 and low stress [ U(O)/kT = 2-51. This again shows how vari- ability of behaviour can arise from differences in the initial surface configuration. An otherwise perfect lattice can be expected to dissolve more rapidly when an etch pit is present.Simulation, with a columnar core present at the start, also models the effects of outer crystal edges, but not apices, on rates of dissolution. EFFECTS OF ADDED SALTS ON RATES OF DISSOLUTION The effects of added salts on the rate of dissolution of barium sulphate from the single crystal are shown in fig. 1 and table 3. The simple univalent ions K+ and C1- had no significant effect on the rate of dissolution and should have a negligible effect on the position of equilibrium. On the other hand, addition of either barium chloride or sodium sulphate reduced the rate of dissolution. Since these salts involve the common ions Ba2+ and SO:-, the distance from equilibrium in terms of concentra- tion and ionic product is also reduced. Addition of foreign alkaline-earth ions to the solution, either Sr" or Ca2', enhanced the dissolution rate but will hardly have altered the distance from equilibrium.SIMULATED EFFECTS OF ADSORBED IONS Results obtained by Monte Carlo simulation of dissolution in the presence of foreign ions which can be adsorbed with various strengths of the next-nearest- neighbour (NNN) repulsions are represented in fig 3. Rates of simulated dissolution were found to increase with the magnitude of the NNN repulsion.252 6 - KINETICS OF DISSOLUTION 1 L I I I I I I I -1- ATTRACT I ON REPULSION I I a I I - ' e e ' I t I 0 I I I I I I I I 0.4 0 -0.4 - 0 . 8 -1.2 next-nearest-neighbour parameter, a Fig. 3. Dependence of simulated dissolution rate (dimensionless) on the next-nearest-neigh- bour (NNN) parameter, a.c$/ kT = 2.0, ApL/ kT = - 1 .O, pI/ kT = -6.0. I I I I f. NO A DSO R BAT E 0 . e NO ADSORBATE @ 0 a a -6 -5 - 4 - 3 - 2 adsorbate deposition potential, p , / k T Fig. 4. Simulated dissolution rate (dimensionless) at various adsorbate deposition potentials, 0, ApJkT=-2.0; 0, ApJkT=-1.0. # / L T = 2 , (Y =-0.7. The effectiveness of the NNN repulsion in the enhancement of dissolution rate is evident even at low fractional coverage of foreign ions on the surface (In O1 == p , / k T = -6.0). Extensive chstering of the adsorbate was evident at high p,/ kT (0, = 0.5), but this will only be realistic for ions if counter-ions are taken into account. None of the foreign entities was found to be incorporated into the lattice. The dissolution rates at various simulated undersaturations and foreign-ion concentrations are plotted in fig.4. At low impurity deposition potential ( p I / k T < -3.0, 8, < 0.05) and moderate undersaturation the isolated adsorbate ions did notV. K. CHENG, B. A. W. COLLER AND J. L. POWELL 253 affect the dissolution rate to any considerable degree. Otherwise the presence of adsorbed ions tended to increase the dissolution rate. For every 2.7-fold increase in adsorbate-ion concentration in the solution the rate enhancement at high under- saturation (C/C,,= 0.135, fig. 4, ApL = -2.0) was found to be ca. lo%, whereas at moderate undersaturation ( C / C,, = 0.37) the higher value of ca. 30% was found. Thus we can explain why the observed degree of enhancement of dissolution rate for barium sulphate was greater when strontium chloride was added to a partially saturated solution.Overall, the simulation results show that non-nearest-neighbour repulsive effects of adsorbed ions can lead to enhancement of dissolution rate of the kind found when Sr2+ or Ca2' ions are added to a solution into which barium sulphate is dissolving. DISCUSSION OF RESULTS The present results show that the rate of dissolution of barium sulphate from a single-crystal face is proportional to the square of distance from equilibrium in terms of concentration. Such a rate law can be expected if the mechanism is one in which the rate of reaction of certain active units (in this case kink units) is proportional to the distance from equilibrium while the number of active units [eqn (6)J is also proportional to the distance from equilibrium.Preferentially dissolved regions were found on the barite surface at steps, edges and cracks and other regions of structural imperfection. The pits generated as a result of dissolution at imperfect regions may serve as a ready-made supply of layer openings, so that only step openings are required to sustain dissolution. This can be expected to give rise to a higher order than simple proportionality to undersatur- ation. However, the consistent proportionality of rates to the square of undersatur- ation in terms of concentration remains to be explained quantitatively in terms of mechanism. Table 1 lists observed and inferred characteristics of the three types of microcrys- talline barium sulphate used in the present study.For microcrystalline barium sulphate of type I, with kinetic solubility close to the accepted equilibrium solubility, Arrhenius activation energies based on rates of dissolution were found to be similar to, or more than, the calorimetric energy of dissolution. The energies (enthalpies) of dissolution based on temperature coefficients of kinetic solubilities were similar to or less than this quantity. Crystals of types I1 and I11 showed considerably higher activation energies and considerably lower energy changes for dissolution. The above observations are explicable insofar as the conditions of nucleation and growth of the crystals determine their defect structure and dictate the mechanism of dissolution. The inverse correlation between energy of dissolution and activation energy can be explained at least partly by reference to surface topographies and inferred internal stresses as indicated below.Type I crystals grown from dilute neutral solutions after heterogeneous nucleation appear to have large flat faces with line defects (possibly screw disloca- tions) at their centres, as evidenced by the flower-like growths4 and dissolution pits13 that develop around these points. The energy of dissolution would be high and the activation energy low if the dissolution process was dominated by detachment of kink units from steps between the flat terrace areas with the steps emanating from an etch pit formed in a more labile stressed area around the central line defect. The above proposals can also be used to explain why the saturation solubility of type I crystals3 exceeds both the kinetic and equilibrium solubilities. From the254 KINETICS OF DISSOLUTION rate law, which involves higher order than simple proportionality to undersaturation, it is clear that the number of active dissolution units (kink or step units) decreases as saturation is approached.The units exposed at the central etch pit will be subjected to residual stress and will continue to dissolve, while those on the outer unstressed areas have passed their point of equilibrium and may slowly take up units from the solution. Type I1 crystals, grown from more concentrated media with homogeneous nucleation, show more erratic or dendritic surface topography and are likely to be affected by plane dislocations (grain or crystallite or dendrite boundaries) as well as by axes of stress (screw or edge dislocations). Plane dislocations, being more extensive in their areas of influence, may thus be expected to affect both solubilities and rates of dissolution.The dissolution process, on a crystal lattice plane without emergent screw dislocations, requires initiation of layer opening for each new layer dissolved. Smaller crystallites, having more edge or apex units and thus having higher average molar surface energies, may have higher solubilities and lower energies of dissolution, and yet require higher energies of activation to initiate layer opening by detachment of units from edges or apices, because of the absence of adjacent steps. Kinetic and saturation solubilities for type I1 crystals are equal to one another, but significantly higher than the accepted equilibrium solubility of barium sulphate.This can be explained if detachment of units from apices, edges and corners has a major role in determining rates and remains important in the exchange between surfaces and solution when saturation is reached. Type I11 crystals, being aggregrates of crystallites of colloidal dimensions and thus having a high proportion of edges and apices, can also be expected to display high solubilities, low energies of dissolution and high activation energies for dissolu- tion. The saturation solubility for type I11 crystals appears to be less than the kinetic solubility. Variability for a given type of barium sulphate crystal appears to arise from the crushing of samples to increase their surface areas before mounting them on the polythene plates.The initial sample will thus involve many crystals of smaller sizes which give higher kinetic solubilities, lower energies of dissolution and higher activation energies. After several trials of dissolution the smaller crystals will be dissolved away and the size distribution restored more nearly to the normal for the particular crystal type. Variation of activation energy and rate of dissolution with surface stress has been demonstrated by the present simulation studies. Both the real and the simulated dissolution must consist of the coupling of initiation of dissolution (nucleation) and its propagation by detachment of kink units in succession along steps.Thus the activation energy is a combination of the energies required to execute the two types of events. At low stress-field strength the energy for initiation is large and layer opening is less frequent. High activation energy is a result of this factor in the rate of dissolution. At high stress field, initiation of layer opening at the stress centres becomes energetically favourable and step opening becomes more frequent. The activation energy may thus approach a lower value, corresponding more nearly to that for kink-unit detachment. If the stress field is of larger radius the simulated activation energy is found to be smaller because the region of easy step opening is more extended. The weekly age-and-wash cycle previously used in extended storage of seed crystals is likely to lead to periodic removal of stressed material to an extent determined by the fraction of mass dissolved and the strength of the stress field.V.K. CHENG. B. A. W. COLLER AND J. L. POWELL 255 Although topographically imperfect, such crystals will be energetically more stable. Ageing in saturated solution will partially refill pits and smoothen surfaces but the stress is also likely to be restored insofar as it arises from long-range and permanent mismatching of crystal lattice regions. Further dissolution of already pitted surfaces may give rise to progressively higher energies of dissolution because of the reduction in stress, while the development of more steps around the pit may lead to lowering of the activation energy. The effectiveness of foreign bivalent ions, Ca2+ and Sr2+, in the enhancement of the dissolution rate of barium sulphate is attributed to their double ionic charge.The monovalent K+ and C1-, which would exert weaker repulsions on next-nearest- neighbour ions in BaSO,, did not perceptibly change the dissolution rate. Simulation indicates that ionic adsorbates with weak NNN repulsions should have little effect on the dissolution rate, while those with stronger NNN repulsions lead to marked enhancement of simulated dissolution rates even at average coverage as little as Low surface coverage by adsorbate ensures that the impurities are well isolated and the NNN repulsions exerted by the adsorbed ions are not cancelled by the presence of nearby ions of opposite charge. A reduction rather than an enhancement of dissolution rate when sodium chloride was dissolved into 0.07 mol dm-' cadmium chloride, reported by Simon,22 may be associated with clustering of ions at the higher surface coverage to be expected with adsorption from this more concentrated solution of bivalent metal ion. Dissolution-rate enhancement in the presence of added Sr2' was found to be greater when closer to equilibrium.The simulation study gives a similar result. This appears to arise from the frequency of initiation of layer opening around adsorbed ions being higher relative to the rate of kink-unit detachment at lower undersatur- ation. Such an explanation is similar to that given by GilmerZ6 for impurity- enhanced nucleation of crystal growth due to strong impurity-host interaction.0.1 O/O (fig. 3). CONCLUSIONS This work shows that the sensitivity of rate coefficient, activation energy and solubility to the origin and history of crystals may cause confusion in understanding the mechanisms of growth and dissolution, although concentration-dependent terms in the rate laws may remain unaffected. The surface-activity hysteresis found in successive dissolution trials with a given batch of microcrystals limits their usefulness for studying the effects of concentration variables, as when common ions or foreign species are added. The reproducible results obtained from the barite rotating-disc assembly simplifies this problem. The experimental results on the variation of the activation energy of dissolution and enhancement of dissolution rate by foreign divalent metal ions indicates that the common cause for such observations is the weakening of the binding energy of the surface ions.Dislocations displace ions from their equilibrium positions while the NNN repulsion exerted by adsorbed but isolated simple ionic species is a manifestation of the long-range electrostatic repulsion between ions of like charge. Because of the higher ionic charge in these sparingly soluble salts, a given perturba- tion to the ion-ion distances inside a dislocation is likely to cause a large change in binding energy of lat-tice ions and also in the dissolution activation energy. The specific effectiveness of dissolved impurities on crystal growth and dissolution rates will be related to their surface coverage by adsorption and consequently to their solution concentrations.256 KINETICS OF DISSOLUTION The asymmetry between crystal growth and d i s s o l ~ t i o n ~ ~ suggests that the activa- tion energy for growth will behave differently.We have not found significant variations of activation energies reported in studies of growth rates of ionic crystals.33 We thank Prof. P. Bennema of the University of Nijrnegen for his generosity in supplying a copy of the stress-field simulation program. ' G. H. Nancollas and N. Purdie, Trans. Faraday SOC., 1963, 59, 735. C . H. Bovington and A. L. Jones, Trans. Faraday SOC., 1970, 66, 764. J. L. Powell, B. A. W. Coller and A. L. Jones, J. Cryst. Growth, 1978, 43, 185. S. T. Liu, G. H. Nancollas and E. A. Gasiecki, J. Cryst. Growrh, 1976, 33, 11. G. M. van Rosmalen, M. C. van der Leeden and J. Gouman, Krist. Tech, 1980, 15, 1213. J. R. Campbell and G. H. Nancollas, J. Phys. Chem., 1969, 73, 1375. C. W. Davies and A. L. Jones, Trans. Faraday SOC., 1955, 51, 812. ' E. N. Rizkalla, J. Chem. SOC., Faraday Trans. 1, 1983, 79, 1857. ' D. M. S. Little and G. H. Nancollas, Trans. Faraday SOC., 1970, 66, 3103. l o A. L. Jones, G. A. Madigan and I. R. Wilson, J. Cryst. Growth, 1973, 20, 93; 99. I ' A. L. Jones, H. G. Linge and I. R. Wilson, J. Cryst. Growrh, 1974, 26, 37; 1975, 28, 254. l 2 M. R. Christoffersen, J. Christoffersen, M. P. C. Weijnen and G . M. van Rosmalen, J. Cryst. l 3 K. Takiyama, Bull. Chem. SOC. Jpn, 1959, 32, 68. l 4 I. V. Melikhov and Z . Vukovic, J. Chem. SOC., Faraday Trans. 1, 1975, 71, 2017 l 5 I. N. Stranski, 2. Phvs. Chem., 1928, 136, 259. l 6 W. K. Burton, N. Cabrera and F. C. Frank, Philos. Trans. R. SOC. London, Ser. A, 1951, 243, 299. Growth, 1982, 58, 585. G. M. van Rosmalen, P. J. Daudey and M. G. J. Marchee, J. Cryst. Growth, 1981, 52, 801. G. Z. Liu, J. P. van der Eerden and P. Bennema, J. Cryst. Growth, 1982, 58, 152. G. M. van Rosmalen, M. C. van der Leeden and J. Gouman, Krist. Tech., 1980, 15, 1269; 1982, 17, 627. S. T. Liu and G. H. Nancollas, J. Colloid Znterface Sci., 1975, 52, 602. *' S. T. Liu and G. H. Nancollas, J. Colloid Interface Sci., 1975, 52, 593. 22 B. Simon, 1 Cryst. Growth, 52, 1981, 789. 23 R. J. Davey, J. Cryst. Growth, 1976, 34, 109. 24 W. P. Brandse, G. M. van Rosmalen and G. Brouwer, J. Inorg. Nucl. Chem., 1977, 39, 2007. 25 G. H. Gilmer, J. Cryst. Growth, 1977, 42, 3. 26 G. H. Gilmer, Science, 1980, 208, 355. *' L. de Brouckere, Ann. Chirn., 1933, XIX, 86. 29 DANA Handbook of Minerology (1954), p. 407. 30 T. A. Cherepanova, in Industrial Crystallisation, ed. J. W. Mullin (Plenum Press, New York, 1976), p. 113. 31 Nut1 Bur. Stand. (U.S.) Circ., 1952, 500. 32 J. W. Mullin, Crystallisation (Butterworths, London, 1972) p. 199. 33 G. E. Cassford, W. A. House and A. D. Pethybridge, J. Chem. SOC., Faraday Trans. I , 1983,79,1617. 17 18 19 2 0 T. A. Cherepanova, J. P. van der Eerden and P. Bennema, J. Cryst. Growth, 1978, 44, 537. 28

ISSN:0301-7249    

DOI:10.1039/DC9847700243

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faruduy Discuss. Chem. SOC., 1984, 77, 257-263 Study of the Dynamic Equilibrium in the CaFJAqueous Solution System using Y a 2 + as Radiotracer BY JOHANNES J. M. BINSMA* AND ZVONIMIK KOLAR Interuniversity Reactor Institute, Mekelweg 15, 2629 JB Delft, The Netherlands Received 9th January, 1984 The transport of Ca" ions at the interface between CaF, crystals and an aqueous solution of CaF, has been studied under equilibrium conditions with the aid of "Ca*+ as a radioactive tracer. The kinetics of the isotopic exchange between CaF, and its saturated solution appears to consist of a fast and a slow component with rate constants of ca. 2 x and 1 X s-', respectively. Total fluxes of Ca" from the solution to individual crystal faces of the order of lo-'" mol m-, s-' were found. The exchange was retarded by the presence of some foreign ions in the solution, but eventually the same number of Ca'+ ions were transported as for pure solutions.The crystallographic orientation ({ 100) or { 1 1 I}) of the faces did not have a large influence on the exchange rate, but the relative amount of transported Ca2+ ions (compared with the amount present in the first crystal layer) was lower for the (100) faces than for the { 1 1 1) faces. Also, it has been demonstrated that some 30%) of the 45Ca2' remains inside the crystal when re-exchange with a saturated CaF, solution which initially does not contain tracer ions is attempted, probably by diffusion into the crystal. In recent years many studies have been undertaken concerning the kinetics at crystal/ solution interfaces under non-equilibrium conditions, i.e.during growth or dissolution [see ref. (1)-(3) for example]. Under such circumstances a driving force is present which results in a net transport of material towards or from the crystal. This means that attention is focussed on the dependence of the net transport during growth or dissolution on the various relevant parameters (e.g. supersaturation or undersaturation, temperature, interface properties). In performing this kind of investigation, however, it should be kept in mind that the net transport is the result of oppositely directed fluxes of material. The absolute value of these fluxes is a very important parameter for the phenomenon of 'interfacial instability'. In addition, the fluxes provide for the attainment of the dynamic equilibrium between crystal and solution under equilibrium conditions.In the latter case the interfacial instability will be entirely determined by the inward and outward fluxes. In practice, interfacial instability is found in a wide variety of systems, e.g. at the surface of ion-selective electrodes, in ion exchange in soils and in bone formation. Transport kinetics (exchange) in equilibrium have been the subject of many experimental studies in which radiotracers are used to follow the material in one of the subsystems (solution or crystal)."' With the aid of so-called tracer kinetics' the tracer experiments may lead to a description of the exchange in terms of compartments and transport rates between these compartments. The term compart- ment has also been used in a more physical sense in the description of the crystal/sol- ution interface, namely as a region with a specific environment for the building unir(s) (e.g.ions or molecules) of the crystal. For instance, the Gouy-Chapman layer, the Stern layer, the outer crystal layer and the inner (bulk) crystal might be considered as such compartments. l o Also, the different positions (surface, step and 257258 DYNAMIC EQUILIBRIUM CaF2/AQUEOUS SOLUTION Fig. 1. Crystal/solution interface with various possible positions for a building unit: (1) in solution, (2) at a flat surface, (3) at a step and (4) at a kink site. solution surface step kink Fig. 2. Different possible routes for transport from solution to the crystal in terms of compartment models.kink) for building units at a crystal interface (see fig. l), often used in describing crystal growth processes, may be thought to constitute different compartments. Such an interpretation of the results obtained for tracer experiments in a crystal/solution system has not yet been attempted. Different possible routes for transport from the solution to surface, step or kink sites are shown in fig. 2. The compartments are distinguished by the different amounts of building units which they contain and by their specific bond strengths for the building units, and will thus have different exchange rates.' The building units may diffuse from their position at the interface to the inner crystal layers. These layers can also be included in the compartment models and then form a fifth compartment. Whether a compartment really comes to the fore in an experiment depends on the magnitude of the exchange rate constants and on the amount of material in each compartment (the compartment size).The exchange rates and thus the interfacial instability may be influenced by various factors such as the crystallographic structure of the outer solid layer, theJ. J. M. BINSMA AND 2. KOLAR 259 surface morphology (roughness) and the presence of impurities which can be preferentially adsorbed at the interface. The aim of this study is to gain more insight into the relevant influencing factors in the system CaF,/aqueous solution. For the solid CaF2 phase, larger single crystals (centimetre size) were taken because the characterization of the surface is much more easily performed on such crystals than for a population of small crystals in suspension. In addition, recrystallization effects have to be expected because of Ostwald ripening for suspensions which are not completely monodisperse." CaF, has been chosen as a model compound because it possesses a simple crystal structure (fluorite), making the surface structures simple too, and because a suitable radiotracer is available (45Ca2').Moreover, from a comparison with the behaviour of SrF, and BaF, (which have the same structure) the influence of the solid phase on the exchange rate might be deduced. In the present study the exchange between CaF, crystals and the saturated solution is followed by measuring the uptake of 45Ca from the tracer-containing solution onto the individual CaF, crystal faces.EXPERIMENTAL Synthetic CaF, single crystals were obtained from Dr K. Korth (Monokristalle-Kristall- optik oHG, 'K-crystals') and from Dr H. W. den Hartog of the University of Groningen ('H-crystals'). Natural CaF, crystals were also employed. The synthetic crystals were colour- less, while the natural ones had slight yellow colouring. By neutron activation analysis it was found that the most important impurities were Sr (3.1 x 10, ppm) and Ba (1.9 x 10' ppm) in the K-crystals and Sr (1.2 x lo2 ppm) in the H-crystals. The dominant impurities in the natural crystals were found to be Ti (7.4 x lo3 ppm) and As (2.7 x lo2 ppm). CaF, crystals of typical size 10 x 10 x 5 mm3 which were to be used in the exchange experiments were cleaved ({ 1 1 1) faces) or cut ({ 100) faces) from the specimens mentioned above.The { 100) faces were polished up to optical quality. The orientation of the faces was checked by X-ray diffraction. Some of the synthetic H-crystals and of the natural crystals were used to prepare saturated CaF, solutions. The concentration of impurities introduced by the solid was CQ. 2 X lo-* and 2 x lop6 mol dm-3 for the two types of solutions, respectively, as can be calculated on the basis of the results of the chemical analysis of the crystals. After equilibration at 25 "C for some days in doubly distilled water, the concentrations of Ca2+ and F- were checked using calcium and fluoride ion-selective electrodes, respectively. If the concentrations corresponded to the equilibrium values, the liquid was separated by filtration.The crystal was then added to this liquid in a polyethylene vessel, and after several days of equilibration a few mm3 of an aqueous solution of 45CaC1, (Amersham, 2.16 mCi ~ m - ~ , 2.9 x mol dmP3 Ca2+) was added. The crystal was taken out of the solution after a time t (varying from 1 min at the beginning of the experiment to several days at the end of the experiment). All experiments were carried out at 25 "C. In order to remove the adherent solution, the crystal was washed once with water and twice with ethanol. The activity present at the various faces was counted by means of a Geiger-Muller counter. Because of the rather low p energy of 45Ca (E,,, = 0.252 MeV) it is possible to measure the activity at one face without contributions of other faces if the crystal is not too thin (thicker than ca.0.3 mm) and the edges of the crystal are not included in the counting. This is achieved by using a stainless-steel diaphragm with an opening of 2 x 5 mm2 and by counting only the central part of a face. Calibration was carried out by measuring the activity of the solution in the same geometry as that used for the crystals. This was achieved by attaching a drop of 1 mm3 of the solution to a glass plate and measuring the activity after all water had evaporated. In this way it was possible to determine the fraction of the activity present at the crystal faces. By autoradiography using electron-sensitive film (Agfa-Gevaert Scientia) we checked whether the activity was distributed homogeneously over the crystal faces.260 DYNAMIC EQUILIBRIUM CaF2/AQUEOUS SOLUTION RESULTS AND DISCUSSION For some natural crystals which manifested small cracks, preferred accumulation of activity along the intersecting lines of the cracks with the surface was observed by means of autoradiography.Also, relatively high activities were found at the crystal edges and for faces which had no specific crystallographic orientation (rounded faces). These inhomogeneous distributions of activity point to recrystal- lization processes. For quantitative determinations of the activity only those crystals were taken into consideration which showed no inhomogeneous distributions of activity. In addition, the edges and rounded (side) faces were excluded from the measurements (see previous section).Fig. 3 shows the relative activity (the ratio of the count rate at time t, R,, and the final equilibrium count rate, R,) as a function of time for different crystal faces of the CaF, crystals S, and N I in solutions obtained from synthetic and natural CaF, crystals ('pure' and 'impure' solutions, see previous section). The influence of impurities present in the solution on the exchange rate is obvious. The impurities retard the exchange processes appreciably, possibly by preferential adsorption at the CaF,/solution interface. The influence of crystallographic orientation ({ 100) or { 11 I}) is much smaller under the present conditions. In contrast to the exchange rate the final activity does not show significant differences for crystals in pure and impure solutions.The total flux of Ca" ions from solution to a crystal face can be evaluated from the initial uptake of activity, Aq, by that face after a very short time At, according to where qs and Q, are the activity and the amount of Ca2' in the solution, respectively. Fluxes of 1 . I x lo-'' mol rn-, s-' ({ 100)) and 3.7 x lo-'' rnol rn-, s-' ({ 1 1 I}) were calculated for crystal N, and 7.3 x lo-" mol rn-, s-' ((100)) and 5.6 x lo-" mol m-* s-' ({ 1 1 1)) for crystal S , . Thus, the fluxes appear to be smaller in the impure solution than in the pure solution. If In ( R , - R,) is plotted against t, a curve is obtained in which two linear parts with slopes g , and g , can be discerned, as illustrated in fig. 4 for crystal S , (impure solution).This means that three different compartments are involved, one of which must be the saturated solution. Because only the activity incorporated in the crystal is measured, the two other compartments should correspond to Ca2' ions at different types of position in the crystal. Only if these two compartments have no exchange between each other and are both connected to the very large central solution compartment individually can the slopes g , and g , be assumed to be equal to the rate constants ( k , and k,) for transport between the central compartment and the two peripheral ones. The residence times of the Ca2+ ions in the peripheral compart- ments can then be calculated according to 7, = k i ' = g i ' (i = I , 2). Other compart- ment models do not give such a simple relation between T~ and g , and require a different type of evaluation which is still in progress.In table 1 the g values and the residence times calculated on the basis of the assumption given above are listed for different natural (N) and synthetic (S) CaF, crystals in pure and impure solutions. The residence times appear to lie in the range (3.0-6.7) x lo4 s for the fast exchange and in the range (0.37-1.7) x lo6 s for the slow exchange. The number of exchangeable Ca2+ ions per cm2 in the crystal can be determined from the final count rate, R,, because the specific activity of Ca in the compartments of the crystal which are taking part in the exchange will be equal then to the specificJ . J. M. BINSMA AND 2. KOLAR 26 1 I V A 1 -7 01 I , A L I r/ h Fig.3. Relative activity plotted as a function of immersion time for CaF2 crystals in saturated solutions of different degrees of purity (see text). Crystal N1 (pure solution): 0, { 100) face; 0, { 1 1 1) face; crystal S1 (impure solution): 0, { 100) face; El, { 11 1) face. 0 I00 200 300 800 900 , V 5.0 2.0 0 100 200 300 400 500 t l h Fig. 4. Plot of In (Rm- R,) against t for CaF, crystal S,: El, (1 11) face; 0, (100) face. Table 1. gi values and residence times T~ ( T ~ = l/gi) for different crystal faces of various CaF2 crystals under equilibrium conditions crystal solution face gl/ s-' g2/ s-' 7,/1o4s 7,/106s I .5 1.7 3.3 2.8 2.0 1.6 2.3 1.9 0.58 0.67 1.81 2.69 0.97 0.97 1.92 1 .oo 6.7 1.7 5.9 1.5 3 .O 0.55 3.5 0.37 5.0 1 .o 6.3 1 .o 4.3 0.52 5.3 1 .o262 DYNAMIC EQUILIBRIUM CaFJAQUEOUS SOLUTION Table 2.Number of exchangeable Ca2+ ions Q, and f values for different crystal faces of various CaF, crystals under equilibrium conditions crystal solution face Q,/nmolcm-2 f 0.35 0.40 0.23 0.30 0.32 0.40 0.24 0.2 1 0.63 0.93 0.4 1 0.70 0.57 0.93 0.56 0.49 activity of Ca2' in the solution. We can then write: where 9, and Qc are, respectively, the activity of the crystal face under consideration and the amount of Ca2' ions present at the crystal face. The activity q is related to the measured count rate R by q = R / E , where E is the overall efficiency of the counting technique. Because the activity of the solution and of the crystal faces is measured with the same efficiency, we can substitute count rates for activities in eqn (2), which leads to The numbers of exchangeable ions Q, which are obtained on the basis of eqn (3) for the (100) and (111) faces of the same crystals as listed in table 1 are given in table 2, together with the ratio f, which is defined as f = Qc/Qt where Qt is the theoretical number of Ca2' ions present at the crystal face as calculated from the crystallographic structure.For the { 100) and { 11 l} faces Qt takes the values 0.557 and 0.429 nmol ern-,, respectively. It appears that only a very small amount of material (0.2 to 0.4nmol cm-') takes part in the exchange. In fact less than one lattice layer is involved in the exchange as f ranges from 0.41 to 0.63 for the { 100) face and from 0.49 to 0.93 for the { 11 1) face.For each crystal the value o f f for the { 100) face is smaller than that for the { 11 l} face, but whether the differences found are significant is not yet clear. For the growth of CaF, crystals (and also SrF, and BaF,) from aqueous solutions it is k n ~ w n ' ~ ' ~ ~ that the (100) faces are the slowest growing. This might be in accordance with the rather small f values found for the (100) faces in this study; however, one should be careful in comparing the observations made for non-equilibrium systems (growth) with those of an equilibrium system in which no net transport of material takes place. The so-called 're-exchange' was studied by measuring the decrease in activity at the faces of a crystal which had reached equilibrium activity and which was immersed in an initially inactive saturated aqueous solution of CaF,. It appears that the exchange is not entirely reversible; some 30% of the 45Ca2' ions remain in the crystal.A similar effect was found for CaCO, by Moller and Sastri: who ascribed it to diffusion into the inner parts of the crystal. These Ca2+ ions are thenJ . J. M. BINSMA AND 2. KOLAR 263 no longer available for the exchange processes and do not play a role in maintaining the dynamic equilibrium. The present study has shown that there are at least two different types of bonding for Ca2' ions within the crystal or at its surface. Different rate constants are found for these two types of Ca2' ions, which if they are considered to belong to compart- ments that are only connected with the solution compartment correspond to residence times of ca.5 x lo4 and ca. 1 x lo6 s, respectively. This different behaviour of one type of ion could be explained by the fact that the Ca2' ions differ in type of bonding at the crystal surface, e.g. Ca2+ in kink- and step-like positions. The real { 100) and { 1 1 1) faces of CaF, differ from the face represented in fig. 1, but in analogy with the latter, ions in the kink positions possess half the number of bonds of ions inside the crystal and ions in step positions one bond less. Another explanation of the existence of two different compartments for the Ca2+ ions would be that the ions having the larger rate constants are situated in the first crystal layer and those having the smaller rate constants correspond to ions in the bulk of the crystal.The first explanation is sustained by the fact that the equivalent of approximately one monolayer (probably the first layer at the surface) takes part in the exchange processes. The second explanation is sustained, however, by the re-exchange experi- ment, which showed that some (ca. 30%) of the 45Ca2+ ions remain inside the crystal. Further studies will be performed in order to identify the correct explanation. The influence of impurities present in the solution is reflected in the exchange rates, which are reduced if impurities are present. The impurities do not influence the number of exchangeable ions, however. By means of tracer experiments useful information can thus be obtained with respect to rate constants and the attainment of dynamic equilibrium in a crys- tal/aqueous solution system.From the rate constants residence times may be deduced; these are a measure of interfacial instability. This information can be obtained on the basis of very small fluxes of material by means of tracer experiments. Further studies on the influence of impurities and surface morphology on the exchange are under way. We thank Mr J. F. van Lent and Dr Th. H. de Keyser (both of the Metallurgy Laboratory, University of Technology, Delft) for performing the X-ray diffraction experiments. I Proc. 7th Symp. on Industrial Crystallization, ed. E. J. de Jong and S. J. JanEiC Amsterdam, 1979). Proc. 8th Symp. on Industrial Crystallization, ed. S . J. JanEiC and E. J. de Jong Amsterdam, 1982). W. J. P. van Enckevort, Thesis (Nijmegen, 1982). K. E. Zimens, Ark. Kemi, Mineral. Geol., 1945, 21A, no. 16. G. Lang and K. H. Lieser, Z. Phys. Chem. N.F., 1973, 86, 143. P. Moller and C. S. Sastri, Inorg. Nucl. Chem. Lett., 1973, 9, 759. North Holland, North Holland, ' T. C. Huang, K. Y. Li and S. C. Hoo, J. Inorg. Nucl. Chem., 1972, 34, 47. ' Y. Inoue and Y. Yamada, Bull. Chem. SOC. Jpn, 1983, 56, 705. R. A. Shipley and R. E. Clark, Tracer Methods for In Vivo Kinetics (Academic ?re,,, New York, 1972). W. E. Brown and L. C. Chow, Colloids SurJ, 1983, 7 , 67. 10 ' I T. Sugimoto and G. Yamaguchi, J. Cryst. Growth, 1976, 34, 253. I 2 P. Hartman, Mineral Genesis (Bulgarian Academy of Sciences, Sofia, 1974), p. 1 1 1. l 3 Z. Kolar, J. J. M. Binsma and B. SubotiC, J. Cryst. Growth, accepted for publication.

ISSN:0301-7249    

DOI:10.1039/DC9847700257

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 265-274 High-temperature Dissolution of Nickel Chromium Ferrites by Oxalic Acid and Nitrilotriacetic Acid BY ROBIN M. SELLERS* AND WILLIAM J. WILLIAMS Central Electricity Generating Board, Berkeley N-uclear Laboratories, Berkeley, Gloucestershire GL13 9PB Received 14th December. 1983 A study of the dissolution of a number of spinel-type oxides containing iron(II1) ions by oxalic acid and nitrilotriacetic acid (NTA) is reported. Increasing the chromium content of oxides of general composition Nio.6Cr,Fe, 4--x04 (x = 0.3-1.5) brought about a marked reduc- tion in dissolution rate, and it is suggested that this arises by a mechanism involving a change from kink-site attack to ledge-site attack as the former become ‘blocked’ by less reactive chromium(II1) ions.The Ni,,,Cr,,,Fe, oxide was investigated in more detail. The con- centration dependences determined suggest that both oxalic acid and NTA are adsorbed at surface sites prior to dissolution. NTA brings about dissolution simply by ‘complexing’ attack, but with oxalic acid it was not possible to distinguish directly between complexing and reductive attack. The divalent cation also plays a role, for in the dissolution of a number of ferrites, AFe204 (A = Co, Fe, Mn, Ni), in oxalic acid appreciable differences in dissolution rate were found, the order of reactivity being Fe > Mn> Co > Ni. The reasons for this are discussed. Oxalic acid and strong complexants such as nitrilotriacetic acid (NTA) have been widely used to remove oxide deposits in power lants or to decontaminate pipework surfaces in water-cooled nuclear reactors.’-’ Despite the considerable practical experience with these reagents there is still only a poor understanding of how they bring about dissolution and the factors which influence their reactivity. ‘76 In practice the oxides to be dissolved are often of the spinel type (AB204), usually either magnetite or magnetite substituted by nickel(II), zinc(rI), chromium(rr1) etc., although goethite or haematite may be significant under certain circumstance^.^*^ Complexants bring about the dissolution of the oxide lattice at the site of adsorption. Such processes tend to be slow, but if the oxide contains iron(r1) and iron(rI1) ions an autocatalytic process may occur as a result of a reductive dissolution rea~tion:~”’ (1) Fe2++nL + Fe”L,.(2) Fe”L, + > Fe3+ + Fe”!L, + Fe2+ Oxalic acid may also bring about dissolution by complexing attack (certainly this is what happens with materials such as chrysotile which contain no variable- valency metal ions’ ’), but reductive dissolution is possible with oxides rich in iron(m). Here again autocatalytic processes have been observed due to the formation of ferrous ~ x a l a t e . ~ ” ~ ” ~ Although oxalic acid tends to be more reactive than strong complexants such as NTA, even more rapid dissolution can be achieved with one-electron reductants such as tris(picolinato)vanadium(~~). 1 4 , 1 5 Detailed studies of this reagent have been made in our laboratory; amongst other things, these have shown that increasing the chromium content of a series of nickel chromium ferrites dramatically reduced the dissolution In this paper we describe what happens when dissolution of the same oxides is induced by oxalic acid and NTA.265266 HIG H-TEM PERATURE DISSOLUTION KINETICS EXPERIMENTAL MATERIALS All solutions were prepared using triply distilled water and analytical-reagent-grade chemicals, except nitrilotriacetic acid, which was B.D.H. general-purpose-reagent grade. The pH was adjusted by addition of H,SO, or NaOH. The oxides were prepared by coprecipitation of the appropriate hydroxides by addition of Na,C03 to solutions of the metal nitrates (the 'carbonate' methodI5), washing, drying and calcining under argon for 6 h at 1400 "C. Finally the oxides were ground and sieved, the fraction passing through a 53 pm sieve being retained for use.Mean particle diameters were measured using a model TAII Coulter counter and were typically ca. 6 um. The composition of the oxides was checked by chemical analysis, infrared spectroscopy and X-ray crystallography. Further details of these measurements will be given in a separate publication. One of the oxides used, NiohCr0.6Fel.80,, showed some ageing between the initial series of experiments (carried out in late 1981/early 1982) and the final part of the work (summer 1983). Several of the earlier runs were repeated in the latter period, and there appeared to be a constant relation between the two sets of data. For convenience we treat the oxide before and after ageing as two different batches, referred to here as batches A and B.respectively. APPARATUS AND PROCEDURE Neither oxalic acid nor nitrilotriacetic acid dissolve the spinel oxides under consideration here sufficiently rapidly at temperatures below 100 "C for convenient measurement. We therefore carried o.ut most of our measurements at 140°C using an apparatus consisting of a 50cm3 round-bottommed flask of specially thickened glass, a Gyrolok adapter, a Pierce and Warriner septum swinger and a frame to restrain the flask. A seal was obtained by compression of a rubber O-ring onto the glass neck of the flask. Solutions could be injected into the flask at temperature through the septum (using a Precision Sampling Corp. hypodermic syringe), but for reasons of safety we did not attempt to remove solution under these conditions. Heating was achieved by immersion of the flask (but not the septum assembly) in a bath of water-soluble oil.Solutions were stirred continuously by magnetic stirrer. Various safety devices were incorporated into the design to prevent overheating and overpressurisation of the apparatus. Only modest pressure rises were required to keep the bulk of the water in the liquid state, and in our experience the apparatus could be operated quite safely at temperatures up to ca. 150 "C. Solutions plus ca. 3 mg oxide were degassed at room temperature by bubbling with high-purity argon for ca. h. The septum swinger was then closed and the apparatus heated. The pressure was relieved periodically at temperatures up to ca. 80 "C by opening the swinger.When the apparatus had reached the desired temperature the reaction was initiated by injection of oxalic acid and/or nitrilotriacetic acid as appropriate. The solution injected was at room temperature, so some small decrease in temperature in the first few minutes of reaction was inevitable, but we do not believe that this will have materially affected the results obtained. Reaction was terminated by removal of the whole assembly from the oil bath; the temperature fell rapidly, and so the dissolution reaction was quickly inhibited. When sufficiently cool the solution was removed, filtered through a 0.22 pm filter (Millipore Millex GS) to remove unreacted oxide, diluted x1Q with 0.1 mol dm-3 HCl (B.D.H., C.V.S. reagent) and analysed for iron, nickel, chromium etc.by atomic absorption using a Baird A5100 instrument. Ferrous ion was estimated spectrophotometrically as the 1,lO-phenanthioline complex.'6 Oxalic acid interferes strongly with the estimation of Fe3+ by this method, so this was calculated as the difference between the total iron (from atomic absorption measurements) and iron(I1). Oxalate reduces the tris( 1,lO-phenanthroline)iron(m) complex over a period of hours, so all spectrometric measurements were made on freshly prepared solutions. The pH was measured on the cooled, but undiluted, solution at the end of each run using an EIL type 7050 meter.R. M. SELLERS AND W. J. WILLIAMS 267 12 10 7 8 E E 6 .- N M I 0 m Z L 2 0 0 ' 1 I I 0.5 1.0 1.5 0 0.5 1 .o 1.5 Fig. 1. Effect of chromium content on the dissolution of Nio,6Cr,Fe2,,-x0, by (a) oxalic acid (0) and NTA (A) and (b) oxalic acid + NTA (0).The measurements were made in solutions containing: 0 , 5 . 3 x 1 0-3 rnol dm-3 oxalic acid, pH25 2.4, 140 "C ; A, 5.2 x 1 OP3 mol dm-3 NTA, pHZS 5.0, 140 "C and El, 2.6 x lop3 rnol dm-3 oxalic acid +5.2 x loP3 rnol dmP3 NTA, pH25 3.0, 140 "C. Some difficulty was experienced in preliminary runs with leaks. We found that this could readily be overcome by careful attention to detail during assembly, but as a cross-check the flask and its contents were weighed before and after each experiment. If >3 cm3 (lO0/o of the solution) had been lost the run was rejected; if smaller than this, appropriate corrections were made to the concentrations of species in solution deduced from the atomic absorption measurements.RESULTS EFFECT OF CHROMIUM CONTENT ON THE DISSOLUTION OF NICKEL CHROMIUM FERRITES BY OXALIC ACID AND NITRILOTRIACETIC ACID The effect of increasing chromium content on the dissolution of nickel chromium ferrites of general formula Nio.6CrxFe2,4-x04 by oxalic acid, NTA and their mixtures is shown in fig. 1. Four different oxides were employed in the experiments, with chromium contents corresponding to x = 0.3, 0.6, 1 .O and 1.5. With a fifth oxide, NiCr,04, there was < 1 O h dissolution in 4 h in oxalic acid + NTA mixtures. Values of a were calculated from the amounts of iron dissolved after 4 h at 140°C. The corresponding figures for nickel dissolution were a few percent smaller, whilst those based on chromium were consistently 15% or more smaller, indicating some specific leaching of both iron and nickel by both reagents.The concentrations of the reagents in the three series of experiments were, respectively, ( a ) 5.3 x mol dm-3 oxalic acid, pHzs 2.4, ( b ) 5.2 X lop3 rnol dm-3 NTA, pHzs 5.0 and ( c ) 2.7 x rnol dm-3 oxalic acid + 5.2 x l 0-3 mol dm-3 NTA, pHZ5 3.0. DISSOLUTION OF Nio.,Cr,.,Fe 1 . g o 4 BY OXALIC ACID An appreciable fraction of the Ni0.6Cr0,6Fe1,804 oxide dissolved in the 4 h of the experiments described above, and so this oxide was selected for more detailed study.268 HIGH-TEMPERATURE DISSOLUTION KINETICS 0 2 4 6 8 10 time/h Fig. 2. Time dependence of the dissolution of Ni0.6Cr0,6Fe,.804 by 5.3 x mol dmP3 oxalic acid at pHzs 2.5 and 140 "C. Line calculated from eqn (3) taking kobs = 1.25 x min-'.The rate law for its dissolution by oxalic acid at 140 "C was determined by carrying out a series of runs of varying duration. The fraction of the oxide dissolved varied with time as shown in fig. 2. Some curvature is apparent, but when (1 - was plotted against time a linear dependence was obtained. This corresponds to the shrinking-core model of diss0lution,6~~~ for which the rate law is of the form where kobs = k / rop with ro the initial particle radius and p the oxide density. The curve in fig. 2 has been calculated according to eqn (3). There was no evidence for an autocatalytic pathway. Even when ferrous ions were injected at the commence- ment of a run to give a solution containing 9 x mol dmP3 ferrous oxalate only a slight increase in dissolution rate could be detected.Since this ferrous ion concentration is at least a factor of five higher than produced in oxalic acid solutions at a < 0.2, it is clear that the ferrous oxalate pathway plays only a minor part under our conditions. In the remaining work described in this section the validity of eqn (3) has been assumed, and it has been used to calculate values of kobs from 'single-point' dissolution measurements. The rate of dissolution of Nio.6Cr0.6Fe,.S04 at 140 " c increased as the oxalic acid concentration increased. The dependence was not linear, but showed a tendency to level off at oxalic concentrations above ca. 0.1 mol dmP3, as shown in fig. 3. Decreasing the pH from 6 to 1.5 brought about a marked increase in dissolution rate (fig.4). At very low pH it seemed probable that some dissolution was being brought about by proton attack at the oxide lattice. This was checked using sulphuric acid solutions of varying concentration, and was shown to be significant below pH ca. 2.5. Increasing the temperature also brought about an increase in dissolution rate. A plot of log (kobs) against T-I was linear (temperature range 1O5-16O0C), and from this the value for the activation energy given in table 1 was calculated.R. M. SELLERS AND W. J. WILLIAMS 269 15 - 10 r: 2 "E MI I 0 Y M c5 0 5 10 I5 [oxalic acid]/ lop3 mol dm-3 Fig. 3. Effect of oxalic acid concentration on the dissolution of Nio.,Cr,,,Fe,.804 at 140 "C. Measurements made at pH15 2.5 and using oxide batch A.10 0 - 1 f 6 E 2 4 N bn I .-. -Y m 2 0 1 2 3 4 5 6 7 pH at 25 "C Fig. 4. Effect of pH on the dissolution of Ni0.6Cr0,6Fe,~,0, by oxalic acid at 140 "C (0); dashed line after correction for proton-induced dissolution. Measurements made in 5.3 x mol dm-3 oxalic acid and using oxide batch A; A, dissolution by sulphuric acid. Practically all the iron dissolved by oxalic acid with this oxide was found to be iron(i1). Other experiments showed that iron(rr1) was rapidly reduced by oxalic acid, so any iron dissolved as iron(rI1) would be rapidly reduced in the bulk solution to iron(I1) and be indistinguishable from iron dissolved reductively.270 HIGH-TEMPERATURE DISSOLUTION KINETICS Table 1. Activation energies for the dissolution of Ni0.6Cr0.6Fe1.804 by oxalic acid and nitrilotriacetic acid system EJkJ mol-I 5.3 x 5.2 x mol dm-3 oxalic acid, pH25 2.5, mol dmP3 NTA, pH2, 4.9, oxide batch A 42*6 oxide batch B 18*3 I .o 0.8 0.2 0 5 to 15 [NTA]/ rnol dm-3 Fig.5. Effect of nitdotriacetic acid concentration on the dissolution of Nio.6Cro.6Fe, at 140 "C. Measurements made at pH25 3.1 and using oxide batch B. DISSOLUTION OF Ni,&r0.&,.@4 BY NITRILOTRIACETIC ACID Dissolution of Ni0,6Cr0,6Fe,,@4 by NTA at 140 "C was in general considerably slower than with oxalic acid. Unfortunately this resulted in large errors in the estimated rate constants (particularly with the batch B oxide), and in part masked the details of the dependences. For NTA concentrations above ca. 2 x mol dmP4 at pH 3.0 the dissolution rate was practically independent of complex concentration (fig.5 ) and increased with decreasing pH at 5.0X10-3 NTA (fig. 6). Increasing temperature caused an increase in rate consistent with the Arrhenius law and from which the activation energy shown in table 1 was calculated. In an experiment in which ferrous ions were added at the start of the reaction to give 9 x lo-' mol dm-3 nitrilotriacetatoiron(r1) a factor of ca. 3 increase in dissolution rate was found. At the concentrations of iron(r1) formed in solutions containing initially only NTA this pathway will not have been significant. DISSOLUTION OF OTHER FERRITES BY OXALIC ACID To investigate the effect of the divalent cation on the dissolution kinetics, the ability of oxalic acid to dissolve four different ferrites (AFe,04 with A = Co, Fe,R.M. SELLERS AND W. J. WILLIAMS 27 1 10 8 72 6 E 2 N m" L 1 -Y 2 0 1 2 3 L 5 6 7 8 9 pH at 25 "C Fig. 6. Effect of pH on the dissolution of Nio~6Cro,6Fel,804 by nitrilotriacetic acid at 140 "C. Measurements made in 5.2 x lop3 mol dm-3 NTA and using oxide batch B (0); dashed line after correction for acid-induced dissolution (cJ fig. 4). Table 2. Rate constants for the dissolution of some ferrites by oxalic acid at 140 "C" oxide k/gm2min-' log K , solubility'/g dm-3 NiFe2O4 0.01 1 5.2 CoFe,O, ca. 0.04d 4.7 MnFe,O, 0.087 3.7 Fe304 0.35 3 .O 1 i 0.03 1 0.022 5.3 x mol dm-3 oxalic acid, pH2, 2.5. is the equilibrium constant for M2++ C2042- from ref. (18)]. water at 25 "C (i = insoluble) [from ref. (23)]. K , (in units of dm3 mol-I) MC2H402 [values taken Solubility of the oxalate complexes (MCi04.2H20) in ro = 2.5 p m (assumed).Mn, Ni) was studied under otherwise identical conditions. The measurements were made in solutions containing 5.3 X mof dm-3 oxalic acid at pH 2.5 and 140 "C. The runs were terminated after 4 or 1 h depending on the reactivity of the oxide. The results obtained are shown in table 2. The rate constants have been corrected for both differences in initial particle size and density (calculated from X-ray crystallographic data) and are therefore directly comparable. They show a marked dependence on the nature of the divalent cation, the order of reactivity being Fe > Mn > Co> Ni. DISCUSSION DISSOLUTION BY OXALIC ACID The cubic rate law, eqn (3), clearly establishes that the dissolution process involves reaction at the oxide particle surface as the rate-determining step.The oxalic acid concentration dependence we interpret in terms of adsorption of the oxalic acid at the surface prior to reaction according to the Langmuir adsorption272 HIGH-TEMPERATURE DISSOLUTION KINETICS isotherm, reaction (4): c ~ o ~ ~ - + > s > S- - .c204*-. (4) We have no direct information on the nature of the adsorbed complex, but there is evidence from infrared measurements that adsorption of oxalic acid on goethite gives a binuclear complex,*7 and this may well occur with the ferrites under consider- ation here. The rate-determining step may involve either electron transfer from the adsorbed complex to Fe3' ions at the surface: > s. - .c2042-- + > s-.* .c,o,- ( 5 ) ( 6 ) followed by dissolution of the site as Fei,': > S-"*c204- -+ siq +c02 +ic2042- > s. * *c*o:- +. s(c*o:-)aq. or desorption of the adsorbed complex without change in valency state: (7) The very rapid reduction of F e / l by oxalic acid under our experimental conditions, and hence the failure to detect any iron(1rr) in the solutions following dissolution, prevents us from distinguishing directly between the reductive and complexing pathways. A mechanism consisting of reaction (4) followed by either reaction ( 5 ) or (7) as the rate-determining step predicts an oxalic acid concentration dependence of the form where k = k5 or k,, and [C20:-]T represents the total oxalic acid concentration. This describes the data in fig.2(a) well. The solid line in fig. 2(a) is calculated from eqn (8) taking k = 0.020 min-' and K4 = 70 dm3 mol-l. The pH dependence (fig. 3) arises from both the acid-base properties of oxalic acid (pK, = 3.6, pK2 = 1.2 at 25 "C and I = 1 mol dmP3 I s ) and the oxide (pK =: 3.5 for NiFe,04 at 80°C 15). There are no acid dissociation constants available for oxalic acid at high temperatures. Taking into account the six possible parallel pathways, a very complicated rate expression can be derived. In view of the large number of adjustable parameters (6 rate constants and 3 equilibrium constants) and the uncertainties in the experimental data (It20%) we have not attempted to obtain a best fit to the data. Nickel, chromium and ferrous ions are presumably dissolved by a complexing mechanism, or pass into solution as the hexa-aquo ions.The specific leaching of iron and nickel suggest that the surface becomes slightly enriched in chromium, but this did not appear to limit the reaction rate under our conditions (typically <20% dissolution). Surface enrichment has also been observed in the reductive dissolution of magnetite'' [enriched in iron(rr)] and franklinite" [enriched in zinc(rr)] by tris( picolinato)vanadium( II), and in the oxalic-acid-induced dissolution of chry- sotile'' (enriched in silicon). It may be that the chromium(r~~) ions only dissolve after the neighbouring ions have been removed, i.e. by an 'undercutting' mechanism. A similar suggestion has been made for the dissolution of the nickel ion in NiFe20, induced by tris(picolinato)vanadium(rI). The marked effect of the chromium content on the dissolution rate parallels the situation with NTA, bis(histidinato)vanadium(~r)'~ and tris(picolinat0)-R.M. SELLERS A N D W. J. WILLIAMS 273 vanadiurn(~i),'~ and it seems likely that some common factor 'is responsible. Since these reagents unquestionably bring about dissolution in different ways [complexing attack by NTA, reductive attack by the vanadium(1r) complexes] it is probable that some physical, rather than chemical, characteristic of the surface is involved. We suggest that this can be understood in terms of a 'surface-blocking' mechanism. We envisage that dissolution occurs primarily by the sequential dissolution of iron( 111) ions in kink (the dissolution of a kink site will in general result in the formation of a new kink site).When a chromium(1Ir) ion occupies a kink site dissolution can only proceed via the dissolution of an iron(II1) in a ledge site (which in general gives rise to two kink sites). Thus as the chromium content of the oxide increases the dissolution of iron(r1r) in ledge sites becomes progressively more important. If the ledge sites are more difficult to dissolve than the kink sites, as seems reasonable since they have more nearest neighbours, the overall dissolution rate will fall as the chromium content increases. A diagrammatic representation of this in terms of a simple 'building-block' model has been given by Segal and Sellers.6 These arguments neglect some of the complexities of the spinel structure (for instance only half the octahedral holes and a quarter of the tetrahedral holes are occupied), and it has not proved possible to account quantitatively for the results obtained. Nevertheless these suggestions do, we believe, provide a framework within which the observations can be rationalised.The effect of changing the divalent cation in simple ferrites (AFe204) is in marked contrast to the behaviour of the same oxides with tris(picolinato)vanadium(~~),'~ where only a factor of two or so separate the fastest and the slowest. The dissolution rate constants are inversely correlated with the stability constants for the formation of the 1 : 1 metal-ion-oxalate complexes in aqueous solutions (table 2). This probably arises because of binding by oxalate at divalent cation sites (or by bridging between a divalent site and a neighbouring ferric ion), which may inhibit dissolution either by slowing down the rate at which the site passes into solution or by hindering the mobility of the divalent cations on the surface.Dissolution is presumably favoured by adsorption at iron(n1) sites alone. The values may also reflect (at least in part) the differences in the solubility of the oxalate complexes ( c j table 2). Two other factors may also play some part in the varying reactivity of these oxides. First, small differences in the fault density, surface morphology etc. due to slight variations in the preparation and calcining history of the samples may affect the reactivity. [Every attempt was made to keep these to a minimum; the results of dissolution in tris(picolinato)vanadium(II) suggest that such differences are quite minor.] Secondly, we note that the divalent cations in these oxides do not occupy identical sites in the oxide lattice.Magnetite, nickel ferrite and cobalt ferrite are inverse spinels, in which the divalent cations occupy octahedral holes [the iron(1rr) ions are equally divided between octahedral and tetrahedral holes], whilst manganese ferrite (which has very nearly a normal spinel structure) has 80% of the manganese(r1) ions in tetrahedral holes.22 DISSOLUTION BY N ITRI LOTRI ACETIC ACID The concentration dependences in the dissolution of Ni0.6Cr0.6Fel by NTA parallel those in the oxalate system and can be understood in similar terms to those described above. Not surprisingly NTA appears to be much more strongly adsorbed than oxalate, and at the concentrations employed in this work the oxide particles appear to be more or less completely covered.This accounts for the much smaller activation energy measured in these solutions in comparison with those containing274 HIGH-TEMPERATURE DISSOLUTION KINETICS oxalic acid (table 1). In NTA solutions eqn (8) simplifies to kobs = k, and so the activation energy refers only to reaction (5) or (7), whereas with oxalic acid the activation energy relates to reaction (5) or (7) and reaction (4). The acid dependence again reflects both protonation of surface sites and the acid-base behaviour of the complex itself, for which pK, = 9.7, pK2 = 2.5 and pK3 = 1.9 at 20 OC.18 The effect of increasing the chromium content of the oxides can be understood in terms of the surface blocking mechanism described above.That iron and nickel are leached in preference to chromium is no doubt related to the substitution inertness of the chromium( III) ion. We are indebted to Dr D. Bradbury, who first suggested and set up the high- temperature reaction cell used in this work. We also thank Drs T. Swan and M. G. Segal for their advice and encouragement. This paper is published by permission of the Central Electricity Generating Board. M. A. Blesa and A. J. G. Maroto, in Decontamination of Nuclear Facilities, Keynote Addresses (American Nuclear Society), p. 1. Decontamination of Nuclear Reactors and Equipment, ed. J. A. Ayres (Ronald Press, New York, 1970). G. R.Choppin, R. L. Dillon, B. Griggs, A. B. Johnson, J. F. Remark and A. E. Martell, Electric Power Research Institute Report, no. EPRI NP-1033 (1979). A. B. Johnson, B. Griggs, R. L. Dillon and R. A. Shaw, in Decontamination and Decommissioning of Nuclear Facilities, ed. M. Osterhout (Plenum Press, New York, 1980), p. 65. C. S. Lacy and B. Montford, in Decontamination and Decommissioning of Nuclear Facilities, ed. M. Osterhout (Plenum Press, New York, 1980), p. 93. M. G. Segal and R. M. Sellers, Adv. Inorg. Bioinorg. Mech., in press. Y. L. Sandier, Corrosion, 1979, 35, 205. A. B. Johnson, B. Griggs, F. M. Kustas and R. A. Shaw, in Water Chemistry of Nuclear Reactor Systems 2 (British Nuclear Energy Society, London, 1981), p. 389. G. V. Buxton, T. Rhodes and R. M. Sellers, Nature (London), 1982,295, 538. lo G. V. Buxton, T. Rhodes and R. M. Sellers, J. Chem. SOC., Faraday Trans. I , 1983, 79, 2961. ‘ I J. H. Thomassin, J. Goni, P. Baillif, J. C. Touray and M. C. Jaurand, Phys. Chem. Miner., 1977, 1, 385. E. Baumgartner, M. A. Blesa, H. A. Marinovich and A. J. G. Maroto, Inorg. Chem. 1983,22,2226. I 3 R. M. Sellers, unpublished data. l4 M. G. Segal and R. M. Sellers, J. Chem. SOC., Chem. Commun., 1980,991. l6 A. E. Harvey, J. A. Smart and E. S. Amis, Anal. Chem., 1955,27, 26. ” R. L. Parfitt, V. C. Farmer and J. D. Russell, J. Soil Sci., 1977, 28, 29. M. G. Segal and R. M. Sellers, J. Chem. SOC., Faraday Trans. I , 1982, 78, 1149. ( a ) ChemicalSociety Special Publication No. 17 (The Chemical Society, London, 1964); ( b ) Chernicd Society Special Publication No. 25 (The Chemical Society, London, 197 1). l 9 G. C. Allen, R. M. Sellers and P. M. Tucker, Philos. Mag., 1983,48, L5. 2o G. C. Allen, C. Kirby, R. M. Sellers and P. M. Tucker, unpublished work. 2’ G. M. Rosenblatt, in Treatise on Solid State Chemistry, ed. N. B. Hannay (Plenum Press, New 22 A. F. Wells, Structural Inorganic Chemistry (Clarendon Press, Oxford, 4th edn, 1976), p. 492. ’’ Handbook of Chemistry and Physics, ed. R. C. Weast (C.R.C. Press, Boca Raton, Florida, 62nd York, 1976), vol. 6A, p. 165. ed, 1981/82), pp. B95, B109, B118 and B124.

ISSN:0301-7249    

DOI:10.1039/DC9847700265

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1984, 77, 275-286 Interfacial Kinetics in Solution Linear Free-energy Relationships Applicable to Heterogeneously Catalysed Reactions in Solution BY MICHAEL SPIRO Department of Chemistry, Imperial College of Science and Technology, London SW7 2AY Received 6 t h December, 1983 The Bronsted and Hammett linear free-energy relations (LFER), widely used for homogeneous reactions, are applicable also to heterogeneously catalysed reactions in solution. When the reaction at the surface is sufficiently fast the kinetics become diffusion controlled. An analysis of this situation reveals a new LFER in which a ( = d In k/d In K, where k is the rate constant and K the equilibrium constant) depends only on the stoichiometric coefficients of the reaction, as do the kinetic orders.Redox reactions catalysed by metals exhibit a different kind of diffusion control when the formal electrode potentials are far apart. If the two interacting redox couples are electrochemically reversible, the In k against In K diagram resembles the shape of a Bronsted-Eigen plot, although both the rising section and the plateau region are now controlled by diffusion processes. THE BRONSTED AND HAMMETT RELATIONS It has long been recognised that relationships exist between the rate constants ( k ) and the equilibrium constants ( K ) of groups of closely related reactions. Sixty years ago Bronsted and Pedersen’ proposed an equation of the type log k = a log K +constant (1) to describe the way in which the rate of a base-catalysed reaction depends on the dissociation constant K of the conjugate acid of the catalysing base; cy here is negative.A similar Bronsted relation with positive a values connects the rate constants of acid-catalysed reactions with the dissociation constants of the catalysing acids.* The correlation is improved by taking statistical factors into account.2 Bronsted and Pedersen akeady recognised in this first paper that the rates of simple base- (acid-) catalysed reactions would become independent of the dissociation constant of the relevant acid for bases (acids) so strong that every collision with the substrate resulted in reaction. Plots of In k against In K were therefore expected to take the form of the curve in fig. 1. Their prediction was confirmed after experimental techniques had been developed for measuring fast reaction rates.Eigen3 then showed that many plots of In k against In (Kdonor/Kacceptor) were in fact gentle curves that tended to diffusion-controlled plateau values ( a = 0). The initial value of the slope cy was unity because here the back reaction became sufficiently fast to be diffusion controlled. In between, and over a range of several pK units, data points of In k against In K scatter about a reasonable straight line. Such a plot is equivalent to the existence of a linear relation between the Gibbs free energies of activation and the ‘standard’ Gibbs free-energy changes for the acid dissociations 275276 INTERFACIAL KINETICS I N SOLUTION In K Fig. 1. Schematic Bronsted-Eigen plot for homogeneous acid-base reactions.(in the prevailing medium), as follows from the introduction of transition-state theory: A G' = a A Ge + constant'. A low value of the Bronsted exponent a indicates a similarity in structure between the transition state and the reactants while a value approaching unity suggests structural similarity between the transition state and the p r o d ~ c t s . ~ A more explicit analysis of a has been given by Marcus.' For fairly strong overlap reactions such as proton transfers he showed that where AG; is the Gibbs free-energy barrier for proton transfer within the encounter complex when AG*=O. The effects of two work terms have been omitted in eqn (3). The same equation has been derived by a different route by Murdoch.6 For a series of structurally similar acids AGA is probably constant4 and its value can be calculated from the curvature of the Bronsted plot since Thus proton transfers to and from 0 and N atoms, which are intrinsically fast because AGA is small, will show significant curvature in their Bronsted plots. Proton transfers to and from most carbon atoms, on the other hand, involve large energy barriers and therefore display good LFER over a wide range of AGQ.7.8 In the diffusion-controlled plateau region the Marcus analysis is no longer appropriate.Here a will be zero and independent of AGe. Since the rate constant is now given by the Smoluchowski equation,2 AG' will be a function of the activation energies of diffusion of the two reacting species.' One finds similar diff usion-limited plateaux in homogeneous reactions that involve fast electron transfer in the encounter complex, as in certain fluorescence quenching reactions." Fendler et al." have correlated the rates of hydrolysis of 2,4-dinitrophenyl sulphate with various amines in the presence of micellar catalysts by means of the Bronsted relation, and they found that a varied according to the surfactant used.This example illustrates the value of linear free-energy relationships in micro- heterogeneous catalysis. Catalyses of this kind exhibit many features in common with true heterogeneous catalysis in solution. l 2 The Bronsted relation has also been introduced by Gold et all3 to help in understanding the catalytic effect of weak-acid ion-exchange resins on a hydrolysis reaction subject to general acid catalysis.(2) Q = i ( l +AGe/4AGi) (lAGeIS4AGi) (3) da/dAGe= 1/8AG;. (4) The most numerous LFER are forms of the Hammett e q ~ a t i o n ' ~ ' ' ~ log (kJ k0J = PJ*, ( 5 ) where k, is the rate (or equilibrium) constant of a given reaction j when one of tfie reactants bears a substituent i and ko, is the corresponding constant in the absenceM. SPIRO 277 of any substituent. The primary value of the substituent parameter ai, characteristic of the type and position of the substituent i and independent of the reaction, is given by ( 6 ) where KO and K j are the dissociation constants of the unsubstituted and of the correspondingly substituted benzoic acids, respectively. The reaction constant pj, on the other hand, depends only upon the reaction and the experimental conditions (medium, temperature).Combination of eqn (5) and (6) and introduction of transition-state theory shows that for any reaction ai = log ( K i / KO) AG* = p j ~ ~ e +constant. (7) The Hammett relations work well for a wide range of meta- and para-substituted aromatic compounds.16 To make this type of equation applicable also to ortho- substituted aromatics and to substituted aliphatic compounds, Taft" proposed the modified form log ( k , / k o j ) = p r a ? +sjESj where ESj is a steric substituent parameter18 and a: is a polar substituent parameter calculated from the experimental rates of acidic and alkaline hydrolysis of the appropriate esters. Its use has recently been criticised, however." Several other variants of eqn (5) are k n ~ w n . ' ~ , ~ ' The reaction parameters p and p* are not infrequently > 1 or < - I , in contrast to Bronsted LY values which rarely stray outside the bounds of 0 and Literature discussions about the Hammett and Taft equations regularly omit mention of diffusion control.This is easily understood. The homogeneous organic reactions involved are relatively slow: on the Marcus model, they involve sizeable intrinsic energy barriers.' These lead to the long linear free-energy relations observed and would require huge values of log ( Ki/ KO) before a diff usion-limited plateau region can be reached.' Kraus has shown in two reviews21y22 that the rates of many gas-phase and some liquid-phase heterogeneously catalysed reactions can also be correlated by means of a, E, or, most frequently, a* parameters.It is quite surprising to find that these parameters, derived from homogeneous liquid-phase equilibria at 25 "C, are capable of relating the catalytic rates of gas reactions at temperatures from 100 to 500 "C. The slopes p or p * , respectively, are generally high and in a few cases lie outside the limits f 10. The processes studied were predominantly eliminations and hydro- genations, as well as some dehydrogenations, hydrogenolyses, esterifications and miscellaneous organic reactions ; the catalysts employed were metals or metal oxides. It should be borne in mind, however, that several of these correlations refer not to relative rate constants but to relative rates. These are the products of heterogeneous rate constants and (Langmuir) adsorption coefficients which do not always change in the same direction on substitution.Nor has it been established in every case that the catalytic mechanism remains the same when one of the reagents is progressively substituted. Nevertheless, the fact that so many correlations have been observed points to the usefulness of LFER in heterogeneous as in homogeneous reactions. To allay any remaining doubts it might be as well to test the applicability of the LFER with a simpler reaction that can be more thoroughly studied. A good candidate would be the unimolecular solvolysis of a series of substituted t-butyl halides. These reactions are heterogeneously catalysed by silver salts, silver metal and other solids incorporating soft acid sites on which the halide end of the substrate278 INTERFACIAL KINETICS IN SOLUTION Because the interaction here is of the soft-acid-soft-base type, the Bronsted relation is inapplicable. More appropriate would be the Hammett equation or a variant of it such as that suggested by Swain and for nucleophile-electrophile interac- tions and subsequently applied to inorganic as well as organic reactions in solution.26 In view of the way in which Hammett or Taft parameters have been found to fit both homogeneous and heterogeneous rates, one would expect that catalytic rates at micellar surfaces in solution would also lend themselves to this type of correlation.Little seems to have been done along these lines. However, LFER of the Hammett type have been used for some to correlate the biological activity of drugs and are known as QSAR (quantitative structure-activity relationship^).^^ DIFFUSION-CONTROLLED REACTIONS We have seen that in homogeneous solution, fast proton transfers with small intrinsic energy barriers AGi show curved In k against In K plots which also display diff usion-limited plateaux.In contrast, slow proton transfers to and from carbons that obey the Bronsted relation, as well as organic reactions that follow the Hammett or Taft equations, involve quite large intrinsic energy barriers. These barriers will be lower when the reactions are heterogeneously catalysed. If they are speeded up sufficiently, one would again expect diffusion to play a role in the kinetics. In this section we shall derive the kinetics for a catalysed reaction that is fully diffusion controlled.Consider a general chemical reaction taking place at the surface of a catalyst with a net velocity v, (mol m-2 s-') given by v, = V l s - V - l S . (9) These velocities are functions of the concentrations of the species i (molm-3) at the surface, cis. We may visualise these species as present in a thin layer at the surface3' or as physically or chemically adsorbed, but no assumption about its exact state is needed in the present treatment. If the catalyst is sufficiently powerful v l , = v-~, >> v, so that the surface reaction is virtually at equilibrium. Of course the species in the bulk solution will not be in equilibrium for a long time because the reactants must diffuse to the catalyst surface before they can react there and the products must diffuse away.The disappearance of A, B etc. from the bulk solution and/or the gradual appearance of X, Y etc. are the very phenomena monitored by the experimenter, who will interpret them in terms of the stoichiometric reaction (I). He will therefore write for the observed rate of reaction ?Jobs (mol mP3 s-'1 It follows from dimensional analysis that where S is the area of the catalyst surface and V is the volume of the solution. Should reaction (I) also proceed to an appreciable extent in the bulk solution, theM. SPIRO 279 vobs value in the present treatment must be corrected for the homogeneous contri- b ~ t i o n . ~ ' In the steady state, the flux of reactant A (mol s-l) diffusing towards unit area of catalyst must equal the net rate at which A disappears by chemical reaction at the surface.By Fick's first law where DA is the diffusion coefficient of A and SA is the effective thickness of the (Nernst) diffusion layer for this species. Hence cAS = cA- V,YASA/ D A . (13) In the case of a product such as X, its net steady-state rate of formation by the catalytic reaction equals the rate at which it diffuses away into the bulk solution. Thus Dx(cxs - cx)/ ax = 21, vx exs = CX + V,YXSX/ Dx. (14) (15) When the catalytic reaction is so fast that the surface reaction is effectively at equilibrium n (cx + wxSx/DX)YX Il (c, - V S YASA/ D A ) vA (16) prod c w x c v Y . . . c z c z * - * xs Y s - K , = - react Initially cx = cy = - - - = 0 and cA, cB, . . . are large. Hence whence The summation function in eqn (1 8) is likely to be of the order of 1/ lov4 mol m-* s-l, whereas typical values of v, are of the order3' of mol m-* s-'.We may therefore reasonably adopt the more severe approximation to v, = v;. (20) An experimental test of these equations is discussed in the final section. Certain conclusions can now be drawn about these heterogeneously catalysed reactions. First, they are sufficiently fast to become wholly transport controlled. The product of the (DX/ax) terms in eqn (19) is essentially a mean ( D / S ) raised to280 INTERFACIAL KINETICS IN SOLUTION the first power, and the summation term in eqn (18) contains a corresponding parameter. Thus if the catalyst is present in the form of a rotating disc (see below), the overall rate will be directly proportional to the square root of its rotation speed.Secondly, the catalytic rate is of fractional order in the various reactants A, B etc. but independent of the concentrations of the products. The magnitudes of these orders depend solely on the stoichiometry of the reaction. Because of the general model used, the fact that the orders are fractional does not imply Freundlich or any other particular kind of adsorption of the reactants on the catalyst surface. It also follows from eqn (16) that addition of either product to the initial reaction mixture will considerably decrease the catalytic rate and also change the kinetic orders of the reactants. Thirdly, the catalytic rate constant k,,, is given by the terms preceding the final product sign in eqn (1 9).Taking logarithms ( vx + vy + - * a ) In k,,, = In K , + C [ vx In Dx - vx In ( V , ~ ~ ) J . (21) prod The relationship between the catalytic rate constant and the equilibrium constant is therefore given by a In k,,, 1 ff =-- - aln K u,+Y,+ - . a and also depends only on the stoichiometry of the reaction. Two comments are required here. First, K in eqn (22) is the equilibrium constant of the reaction under study and not that of some related process such as the dissociation of an acid. Secondly, the equation shows that a significant degree of thermodynamic control is retained even in the diffusion region. If vx = v y = 1, an LFER with a slope a of is obtained. This stands in strong contrast to homogeneous reactions in which diffusion control manifests itself by a horizontal plateau region in the In k against In K plots,3 i.e.by a = 0. It is possible, therefore, that experimen- ters have studied heterogeneous reactions in this region and not been aware of it, especially if the reactions were carried out under constant-stirring conditions. It is by changing the conditions of hydrodynamic flow, and thus the thickness of the Nernst layer, that one can best test whether diffusion is playing a role in heterogeneous processes at smooth surfaces or even at moderately rough ones.32 Application of the transition-state equations’ for both k and D leads to ( V , + Y ~ + - * -)AG,?,,=AGe+ 2 vxhG&diffn +RT 1 vxln(vX&/A2) (23) prod prod where R is the gas constant, T is the absolute temperature and A is the distance between successive equilibrium positions in diffusion.The first term on the right- hand side of eqn (23) represents the thermodynamic contribution to the Gibbs free energy of activation of the catalysed reaction while the subsequent terms constitute the kinetic or flow contributions. The corresponding enthalpy relationship can be derived by inserting the transition-state equations into eqn (2 1) and differentiating with respect to 1/ T : ( v x + y , + - - A AH:,^ =AH-+ 1 v X ~ ~ : d i f f n . (24) prod In deriving eqn (24) it was assumed that A and 6 were independent of the temperature. The value of 6 is essentially fixed by the hydrodynamic regime in the reaction vessel, whether this is streamline or turbulent, and will depend upon the size and shape of the catalyst, the diffusion coefficient of the speciesM.SPIRO 28 1 involved and the properties of the solvent. If, for example, the catalyst is introduced in the form of a rotating disc, the Levich equation tells us that under conditions of streamline Si = 1.613Df/3~1/6w-1/2 (25) where Y is the kinematic viscosity of the medium and o is the angular velocity of the disc. The situation is quite different for a rapidly swirled suspension of spherical catalyst particles. If their radius r exceeds an eddy length given approximately by u/U, where U is the velocity of the liquid in the reaction vessel, then it follows from an analysis by L e v i ~ h ~ ~ ~ that ai = D ~ L ~ / ~ / ( ~ ~ ) ~ / ~ u (26) where L is the scale of motion of the agitated fluid as a whole. Values of Si calculated from eqn (26) are typically 100-1000 times smaller than those given by eqn (25).Diffusion through the Nernst layer can become rate-determining in other inter- facial processes, as the papers on liquid-liquid extraction in this Discussion testify. It also plays an important role in interfacial drug transfer.29 REDOX REACTIONS CATALYSED BY METALS Metals and carbons often catalyse oxidation-reduction reactions of the type ~0X2OX2 + Vred,red, - %d,red, + ~ O X , O X l (11) where the stoichiometric coefficients Y are such as to refer to the transfer of one electron. Particular attention has been paid to the aqueous redox reaction Fe(CN);- +$I- -+ Fe(CN):- +;I; (111) which is strongly catalysed at the surfaces of several noble metals34 as well as by carbons.35 By combining kinetic and electrochemical measurements at the same anodically pretreated platinum surface it has been dern~nstrated~~,~’that the catalysis takes place by a purely electrochemical mechanism.In the reacting solution the platinum automatically adopts a so-called mixture (or mixed) potential Emix such that no net current passes, the anodic current caused by the oxidation of iodide at its surface being exactly equal in magnitude to the cathodic current produced by the surface reduction of ferricyanide. This is illustrated in fig. 2 and 3. These show the current-potential curves of the individual redox couples oxl/red, (e.g. Ii/I-) and ox,/red, [ e.g. Fe(CN):-/ Fe(CN):-]. When both couples are present together, their curves are usually treated as additive according to a principle enunciated by Wagner and T r a ~ d .~ * At any given potential, therefore, the net current in the mixture equals the algebraic sum of the contributing currents. At the mixture potential the net current is zero. The two contributing currents, equal in magnitude, are designated Imix, and by Faraday’s law are proportional to the catalytic rate vS = Imix/ FS (27) where F is the Faraday constant. The values of 21, calculated by eqn (27) from electrochemical experiments on the separate I;/ I- and Fe(CN)i-/ Fe(CN);- couples were found to be equal, within experimental error, to the catalytic rates obtained from kinetic runs with reaction ( III).36737 Also equal were the electrochemically determined mixture potentials Emix and the potentials E,,, taken up by the catalysing platinum disc in the reaction mixtures.These sets of experiments clearly establish282 INTERFACIAL KINETICS IN SOLUTION red, +ox, I / ! I I / 1 I r n i x l I ' L , I I . I = . I I I I I I I L r n t x I E, I ox2 --+ red, Fig. 2. Schematic plots of current against potential for sets of electrochemically irreversible couples. Couple 1 is paired successively with three different couples 2 of increasing formal potential. 0 '0 C .- I V 5 5 0 red, -+ oxI ox2 - red, Fig. 3. Schematic plots of current against potential for sets of electrochemically reversible couples. Couple 1 is paired successively with three different couples 2 of increasing formal potential.M. SPIRO 283 the electrochemical mechanism. Evidence in the literature makes it likely that numerous other redox reactions of type (11) are catalysed at the surfaces of noble metals39 and carbons35 by the same mechanism of electron transfer through the solid.We shall defer to the next section the equations that apply to the regions of the gradually rising curves in fig. 2 (electrochemically irreversible couples) or the steeply rising curves in fig. 3 (electrochemically reversible couples).4o Here we shall treat the situations that arise in both cases when the formal electrode potentials are sufficiently far apart. This is shown in both diagrams where couple 1 is successively paired with three other couples of increasing formal potential. In each case condi- tions are so arranged as to make the limiting current L, for the oxidation of red, less than the limiting currents L2 for the reduction of the various oxidants ox2.It can be seen that above a certain value of EmiX, the mixture current for the two couples is simply equal to L , , so that4' The reaction therefore remains wholly diffusion controlled through the inverse dependence on 8, and has become first order in one of the reactants (red,) and zero order in the other (ox2). This kind of diffusion control can occur even with couples whose formal potentials are close together if the concentration of one of the reactants (red,) is very low, for its limiting current region will then begin very near its formal potential. Two very early catalytic studies in the literature appear to fall into this category: that of Jablc~ynski~~ of the reaction Cr" +H+ -+ CrlI1 +$H2 (IV) Ti3++H+ -P Ti4'+iH2 (V) and that of Denham43 of the reaction both catalysed by platinised platinum.More recently the same interpretation has been applied to the catalysis by noble-metal colloids of the reaction (VI) in a scheme for photocatalytic water reduction.44 The electrochemical model under- lying eqn (28) has also been to interpret previously puzzling corrosion data in the literature and is generally accepted in metal-dissolution theory.46 Certain corollaries follow from eqn (28). If one inserts the transition-state equations for the rate constant 2),/c,ed, and for & . d , , and assumes as before that 8 remains constant, then one obtains MV+ + H' ---+ MV2+ +$ H2 (MV = methyl viologen) AG&t = AG:edI(diffn) +RT In (vred18redl/A2)- (29) Thermodynamic control has thus vanished completely.The same point is made by the equation where EP is the formal electrode potential of couple i in the medium employed. This kind of diffusion control therefore differs radically from that given in eqn (18)-(23). Indeed, it bears a resemblance to the type of diffusion control found in homogeneous reactions except that AG:at in eqn (29) depends on the activation energy of diffusion of only one of the reacting species instead of on both and also depends on the stirring conditions.284 INTERFACIAL KINETICS IN SOLUTION METAL-CATALYSED REDOX REACTIONS INVOLVING TWO IRREVERSIBLE COUPLES OR TWO REVERSIBLE COUPLES We now return to the value of the catalytic rate when Emix lies within the rising sections of the current-potential curves.Consider fig. 2, in which the curves for both couples possess the shapes typical of redox systems that are electrochemically irreversible? i.e. couples whose electrochemical rate constants and exchange current densities are small. The exponentially rising parts of the curves are described by Tafel equations, and from these and the additivity principle38 it is possible to calculate the potential Emix at which the anodic and cathodic currents are equal, as well as the currents themselves (Imix) and hence us. Wher, the anodic process of couple 1 is just first order in red, and the cathodic reaction of couple 2 first order in ox,, the resulting equation is4' us = kpk;l exp [a,z,r,F(E; - E ~ ) / R T ] C ~ : , , C & ~ (31) where ki is the electrochemical rate constant of the couple ox,/red,, a, is its cathodic transfer coefficient, zi is the charge-transfer valence and the r, values are given by If the electrode kinetics are not both first order, the concentration terms are more complex.41 The fractional kinetic orders of red, and ox2 are a natural consequence of the electrochemical mechanism and do not signal Freundlich adsorption.By collecting all the non-concentration terms into a catalytic rate constant kc,,, and remembering that the equilibrium constant of reaction (11) is given by (33) K = exp [ F ( E z - E:)/RT] we obtain another LFER In k,,, = r2 In kl + rI In k, + a2z2rI In K . (34) Since k , and k, vary with the couples in question, and depend upon the respective free-energy changes of solvent reorgani~ation~,~' as well as the energies needed to break chemical bonds, the linearity condition should be tested by plotting In ( kc,,/ kpk;l) against In K .Commonly a = 4 and z = 1, which makes r l =: 4 and the slope cy2z2rI = (1 - aI)zI r2 = t. Let us now turn to pairs of electrochemically reversible couples whose elec- trochemical rate constants and exchange current densities are large. Fig. 3 shows the shapes of their current-potential curves. From the known equations of the steeply rising sections and the additivity principle, Freund and S p i r ~ ~ ~ have calculated the mixture potentials and currents when the two couples are present together at the metal surface. The resulting equation [eqn (33) in ref. (48)] is the exact electrochemical analogue of eqn (18) and (19).This equation was rigorously tested in the laboratory for reaction (111) at an anodically pretreated platinum rotating-disc ~ a t a l y s t . ~ ' All the theoretical predictions were verified including the proportionality of the rate to the square root of the disc rotation speed, the kinetic orders of I-(l) and of Fe(CN)2-(2/3), the effect on those orders of adding one of the products to the mixture, the value of the initial rate constant and the value of the activation energy. One may therefore have confidence in the validity of eqn (18) and corollaries based on it. This applies specifically to the resulting linear free-energy relations (21) and (22). For reaction (111) the value of the slope LY equals 1/(1 +,')=$M. SPIRO 285 In K (or EP-E?) Fig.4. Schematic plots of In k,,, against In K (or E ; - Ey). Full curves represent conditions of slow stirring, dashed curves conditions of fast stirring. See the text for other conditions. We are now in a position to compare the behaviour of different metal-catalysed redox reactions when the various reactants are present in similar concentrations. Plots of In k,,, against In K (or E ; - E T ) will exhibit the shapes sketched in fig. 4. The initial linear portion possesses a slope of (x2z2r1 for pairs of irreversible couples [if we plot In (kcat/ k;.-k;l)] and of l/(vx + uy + - - -) for pairs of reversible couples. For the latter type, we should compare only reactions of the same stoichiometry or else make an appropriate correction to the data according to eqn (19).With irreversible couples the linear section will be unaffected by faster stirring, with reversible ones it will rise to a parallel position. When ( E ; - Ey) is sufficiently large the rate constants of both types of catalysed reaction will reach a diffusion- controlled limit. According to eqn (28), this limit too will increase with faster stirring because this decreases the thickness of the Nernst layer. It is apparent that the shapes of all these curves resemble that of the Bronsted-Eigen plot in fig. 1. Whereas, however, only the plateau region is diffusion controlled in homogeneous reactions and in catalysed reactions between irreversible redox couples, the whole curve is diffusion controlled for metal-catalysed reactions between reversible redox couples.In the linearly rising region the rate of the latter depends upon the diffusion of the reactants towards the catalyst and, particularly in the early stages, on the diffusion away of the products. In the plateau region only the diffusion towards the catalyst of one of the reactants (generally the one of smallest concentration) is of kinetic significance. Over the whole potential range, then, k,,, for reversible couples will be a function of the hydrodynamic regime and will be directly proportional to the square root of the rotation speed with a rotating-disc catalyst. This kind of plot represents an extension of the traditional Bronsted-Eigen or Hammett picture. J . H. Bronsted and K. Pedersen, Z. Phys. Chem., 1924, 108, 185. ' R. P. Bell, The Proton in Chemistry (Chapman and Hall, London, 2nd edn, 1973), chap.7 and 10. ' M. Eigen, Angew. Chem., Int. Ed., 1964, 3, 1. J. E. Crooks, in Proton-transfer Reactions, ed. E. F. Caldin and V. Gold (Chapman and Hall, London, 1975), chap. 6. R. A. Marcus, J. Phvs. Chem., 1968,72,891; A. 0. Cohen and R. A. Marcus, J. Phys. Chem., 1968, 72, 4249. J. R. Murdoch, J. Am. Chem. SOC., 1972, 94, 4410. A. J. Kresge, Chem. SOC. Rev., 1973, 2, 475. * W. J. Albery, Annu. Reu. Phvs. Chem., 1980. 31, 227.286 INTERFACIAL KINETICS I N SOLUTION ' S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941), chap. IX. D. Rehm and A. Weller, Isr. J. Chem., 1970, 8, 259; F. Scandola, V. Balzani and G. B. Schuster, J. Am. Chem. SOC., 1981, 103, 2519.M. Spiro, in Essays in Chemistry, ed. J. N. Bradley, R. D. Gillard and R. F. Hudson (Academic Press, London, 1973), vol. 5, p. 63. 10 ' I J. H. Fendler, E. J. Fendler and L. W. Smith, J. Chem. SOC., Perkin Trans. 2, 1972, 2097. I2 l 3 V. Gold, C. J. Liddiard with J. L. Martin, J. Chem. SOC., Faraday Trans. 1, 1977, 73, 1128. l4 L. P. Hammett, J. Am. Chem. SOC., 1937, 59, 96. l 5 L. P. Hammett, Physical Organic Chemistry (McGraw-Hill Kogakusha, Tokyo, 2nd edn, 1970), l 6 P. R. Wells, Chem. Rev., 1963, 63, 171. l 7 R. W. Taft Jr, J. Am. Chem. SOC., 1952, 74, 3120; 1953, 75, 4231. chap. 1 1 . R. Gallo, in Progress in Physical Organic Chemistry, ed. R. W. Taft (Wiley-Interscience, New York, 1983), vol. 14, p. 115. M. Charton, in Progress in Physical Organic Chemistry, ed.R. W. Taft (Wiley-Interscience, New York, 1981), vol. 13, p. 119. 2o J. Shorter, in Advances in Linear Free Energy Relationships, ed. N. B. Chapman and J. Shorter (Plenum Press, London, 1972), chap. 2. 2 1 M. Kraus, in Advances in Catalysis, ed. D. D. Eley, H. Pines and P. B. Weisz (Academic Press, New York, 1967), vol. 17, p. 75. 22 M. Kraus, in Advances in Catalysis, ed. D. D. Eley, H. Pines and P. B. Weisz (Academic Press, New York, 1980), vol. 29, p. 151. 23 E. F. G. Barbosa, R. J. Mortimer and M. Spiro, J. Chem. SOC., Faraday Trans. 1, 1981, 77, 1 1 1. 24 R. J. Mortimer and M. Spiro, J. Chem. SOC., Perkin Trans. 2, 1982, 1031. 25 C. G. Swain and C. B. Scott, J. Am. Cbem. SOC., 1953, 75, 141. 26 R. G. Pearson, in Advances in Linear Free Energy Relationships, ed.N. B. Chapman and J. Shorter (Plenum Press, London, 1972), chap. 6. 27 C. Hansch, R. M. Muir, T. Fujita, P. P. Maloney, F. Geiger and M. Streich, J. Am. Chem. SOC., 1963,85, 2817. 28 A. Cammarata and K. S. Rogers, in Advances in Linear Free Energy Relationships, ed. N. B. Chapman and J. Shorter (Plenum Press, London, 1972), chap. 9. 29 J. T. M. van de Waterbeemd, Doctoral Thesis (University of Leiden, 1980); H. van de Waterbeemd, in Quantitative Approaches to Drug Design, ed. J. C . Dearden (Elsevier, Amsterdam, 1983), p. 183. 30 P. D. Totterdell and M. Spiro, J. Chem. SOC., Faraday Trans. 1, 1976, 72, 1477. 31 P. L. Freund and M. Spiro, J. Chem. Soc,, Faraday Trans. I , 1983, 79, 491. 32 M. Spiro and D. S. Jago, J. Chem. SOC., Faraday Trans. I , 1982, 78, 295. 33 V. G. Levich, Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, N.J., 1962), ( a ) 34 M. Spiro, J. Chem. Soc,, 1960, 3678. 35 J. M. Austin, T. Groenewald, and M. Spiro, J. Chern. SOC., Dalton Trans., 1980, 854. 36 M. Spiro and P. W. Griffin, Cbem. Commun., 1969, 262. 37 M. Spiro and P. L. Freund, J. Electroanal. Chem., 1983, 144, 293. 38 C. Wagner and W. Traud, 2. Elektrochem., 1938,44, 391. 39 M. Spiro and A. B. Ravno, J. Chem. Soc., 1965, 78. 4 1 M. Spiro, J. Chem. SOC., Faraday Trans. 1, 1979, 75, 1507. 42 K. Jablczynski, 2. Phys. Chem., 1908, 64, 748. 43 H. G. Denham, 2. Pbys. Chem., 1910, 72, 641. 44 D. S. Miller, A. J. Bard, G. McLendon and J. Ferguson, J. Am. Chem. SOC., 1981, 103, 5336. 45 T. P. Hoar, in Modern Aspects of Electrochemistry, ed. J. O'M. Bockris (Butterworths, London, 1959), no. 2, chap. 4. M. Spiro, in The Physical Chemistry of Solutions, ed. D. V. Fenby and I. D. Watson (Massey University Press, New Zealand, in press). 19 p. 69, (b) sections 4, 25 and 33. A. J. Bard and L. R. Faulkner, Electrochemical Methods (Wiley, New York, 1980), chap. 3. 40 47 R. A. Marcus, J. Chem. Pbys. 1965, 43, 679; Electrochim. Acta, 1968, 13, 995. 48 P. L. Freund and M. Spiro, J. Chem. SOC., Faraday Trans. 1, 1983, 79, 481.

ISSN:0301-7249    

DOI:10.1039/DC9847700275

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. B. H. Robinson (University of Kent) said: I wish to put three questions to Prof. Yasunaga. ( 1 ) The rate constant of the hydrolysis of hydroxyl groups at the zeolite/solution interface in table 2 of your paper was determined to be the order of lo2 dm3 mol".' s-'. If this rate is governed by a diffusion-controlled reaction, why is the value of the rate constant not of the same order ( 108-10'o dm3 mol-* s-l) as in homogeneous systems? (2) Did YOU determine the temperature dependence for the rate constants shown in table 3 of your paper? (3) How did the relaxation amplitudes vary for the series of alkylammonium ions? Prof. T. Yasunaga (Hiroshima University, Japan) said: For the first question, the following two reasons may be proposed to explain the smaller value of the rate constant.First, in the adsorption-desorption of ions at the solid/liquid interface, since the reaction occurs at a two-dimensional interface, it may be argued that the reduction of a degree of freedom lowers the rate constant by ca. lo2- lo4 dm3 mol-' s-I.' The extent of this reduction is thought to be affected by differen- ces in the site density and particle size. Another possible explanation is that there is a higher activation energy for surface hydrolysis owing to the strongly bound water molecule formed during hydrolysis. It is well known that metal oxides strongly adsorb water molecules on particle surfaces. Taking this fact into account, mech- anism ( I ) in our paper can be rewritten as H H- steady state diff usion-controlled where SO---aH=O is in the steady state.If the second step, Le. the step involving H the release of the bound water molecule, is the rate-determining step in the above mechanism, then the reduction of the rate constant can reasonably be explained by the higher activation energy of the rate-determining desorption of water from the steady-state intermediate. With regard to the second question, we did not carry out additional experiments on the temperature dependence for the rate constants obtained. In our paper the effect of molecular size of the adsorbing molecule in the ion-exchange reaction of the alkylammonium ion for Na+ in the cage was studied only at 25 "C. A temperature- dependence experiment and the determination of activation parameters would be useful and are under consideration for future work.For the third question, the amplitude of the relaxation signal decreased and diminished with increasing alkyl chain length (the volume of the cation). ' R. D. Astumian and Z. A. Schelly, J. Am. Chem. Soc., 1984, 106, 304. 287288 GENERAL DISCUSSION Dr. G . Sartori (Exxon, Annandale, N.J.) said: I would like to address a question to Prof. Yasunaga regarding the molecular size of the ion-exchanging molecules. You have shown that a bulky alkyl group, e.g. isopropyl, directly attached to the nitrogen atom greatly reduces the ability of the ammonium ion to exchange with Na+ in the cage of zeolite 4A. What would happen if the bulky substituents were not directly attached to the nitrogen atom, but removed from it by one carbon, such as in C C I I I C C-C-C-NH,' and C-C-C-NH:? Prof.T. Yasunaga (Hiroshima University, Japan) said: We did not argue the basis of heterogeneities of the hydrocarbon and the charge density of the penetrat- ing alkylammonium ions. We have studied the ion-exchange kinetics of the alkylam- monium ion, in which a bulky alkyl group is attached directly to the nitrogen atom in order to avoid the hydrophobic effect due to the alkyl chain length of the entering alkyiammonium ion. Several investigators have reported that larger molecules having long hydrocarbon chains are difficult to exchange in zeolite 4A'.2 and that for higher concentrations of the larger cations (25 mol dm-3) some cations identified by Dr. Sartori can exchange slightly. Under the present circumstances, as pointed out by Dr.Sartori, it is considered that the conclusion in our paper may be applicable for the alkylammonium ions having homogeneous distributions of both the charge density and the hydrophobicity of the cation itself. Kinetic studies of the hydro- phobic effect in the ion-exchange reaction are now in progress3 and the results will be reported in the near future. D. W. Breck, Zeolite Molecular Sieves (Wiley-Interscience, New York, 1974). T. Ikeda and T. Yasunaga, J. Phys. Chem., in press. * R. M. Barrer and W. M. Meier, Trans. Faraday Soc., 1958, 54, 1074. Dr. B. A. W. Coller (Monash University, Australia) said: I address my remarks (1) How was p, the scaled potential, calculated in this work? (2) The formulation of the polynuclear mechanism, leading to eqn (15) of the paper, does not explicitly deal with the components of the ionic product.Have you investigated the dependence of rate of dissolution on the concentrations of calcium and phosphate ions varied separately? (3) Added inert electrolyte can be expected to alter the electric potential at the interface. Has the effect of a salt such as potassium chloride been investigated? to Prof. Christoff ersen. Prof. J. and Dr. M. R. Christoffersen (University of Copenhagen, Denmark) replied: We define the dimensionless affinity. of dissolution, P, as the difference between the chemical potential of one mole of substance in the solid phase, per, and the chemical potential of one mole of substance in solution, paq, divided by the number of ions in one mole of substance and divided by kT, i.e. P = (pu,r-pu,q)/18kT=ln (Ks/ Y)/18 where Y = [Ca2~]'o[PO~-]6[OH-]2 and Ks is the corresponding ionic product at equilibrium, for which we have used the value 10-"6.4 mol" dm-54.More details of the calculation are given in Appendix 2, ref. (4) of our paper.GENERAL DISCUSSION 289 It is correct that eqn (15) in our paper does not deal specifically with the components of the ionic product. This equation should only be applied for solutions with a Ca/P ratio of 1.67. We have investigated the dependence of the rate of dissolution on variations in the Ca/P ratio. Far from equilibrium a constant rate is obtained for constant values of the product [CaIa[P], with a = 3 ; as equilibrium is approached a approaches 1.67. For further details see ref.(1). We have not found any large change in the rate due to increased concentrations of inert electrolytes, such as potassium nitrate. We have avoided the presence of chloride ions in our experiments because these ions may enter the crystal lattice. Increasing the concentration of inert electrolyte will reduce the magnitude of the zeta potential, but is not expected to change the charge on the crystal surface. J. Christoffersen and M. R. Christoffersen, J. Cryst. Growth, 1979, 47, 671 Dr. W. A. House (Freshwater Biological Association, Dorset) said: I also turn to Prof. Christoff ersen. (1) Could you explain in a little more detail how you obtained an apparent diffusion coefficient, Dapp== lop9 cm2 s-', from your dissolution data? Does your calculation involve an implicit assumption about the effective diffusion layer boun- dary thickness for the particles.(2) Do you know of any other evidence that is available concerning the proposed change in A+ with pH? The microelectrophoresis work of Foxall et al.' for a precipitated Ca3( PO& solid indicated that the mobility of these particles was essentially independent of pi-I in the region pH 8-1 1. ' T. Foxall, G. C . Peterson, H. M. Rendall and A. L. Smith, J. Chem. SOC., Faraday Trans. I , 1979, 75, 1034. Prof. J. and Dr. M. R. Christoffersen (University of Copenhagen, Denmark) answered: For the estimation of an apparent diffusion coefficient we have assumed the crystals to be spherical and so small that they can be treated as stagnant in the medium.Assuming the amount of substance, K, which per unit time diffuses through a set of concentric spheres, with the crystal situated in the centre, to be independent of the radius of these spheres, r, leads to 4 n r ? D ( 3 r = r , =47v2lJ(%) r=rz . . . = K in which D is a diffusion coefficient and rl, r 2 , . . . are the radii of the spheres. Integrating this equation gives from which we obtain K = 4nDr( C, - C ) . Combining eqn (1) and (3) gives290 GENERAL DISCUSSION The overall rate per unit mass, J / m , can thus be expressed as J / m = AspDapp( c s - C>/ rcr ( 5 ) with Dapp being an apparent diffusion coefficient. For pH ca. 7 the solubility of HAP is ca. mol s-' g-', ' the specific surface area of our HAP crystals is CQ. 30 m2 g-' and the linear dimension of the crystals, rcr, is ca.0.03 pm. Inserting these values in eqn (5) leads to Dapp = an2 s-', which is of the order of lop4 times the diffusion coefficient of small ions in aqueous solution. The above derivation of eqn (4) is not original.233 The electrophoretic mobility of HAP is pH-dependent and is zero around pH 7.66 mol dm-3, the experimentally determined rate is < ' J. Christoffersen, M. R. Christoffersen and N. Kjaergaard, J. Cryst. Growth, 1978, 43, 501. * A. E. Nielsen, J. ColZoid Sci., 1955, 10, 576. M. V. Smoluchowski, Z. Phys. Chem., 1918, 92, 129. F. Z. Saleeb and P. L. de Bruyn, J. Electroanal. Chem., 1972, 37, 99. P. Somasundaran and G. E. Agar, Trans. SOC. Mining Eng., 1972, 252, 348. S. K. Doss, J. Dental Res., 1976, 55, 1067. Mr. V. K.Cheng (Monash Uniuersity, Australia) said: Nucleation mechanisms, in general, are well known for their ineffectiveness close to equilibrium. In fact the B.C.F. theory for spiral growth was proposed to overcome such difficulties.' Does the polynuclear model show such a property and how does the dissolution rate of HAP compare with theory close to saturation? The factor C( 1) in eqn (8) of Prof. Christoffersen's paper for the rate of surface nucleation is described, for dissolution, as the concentration of holes formed by the loss of a single growth unit, earlier indicated as being one ion. Electroneutrality must apply unless the numbers of missing charges are small, and so also should the principles of equilibrium. Therefore C( 1);:2+C( l)&-C( l)&- should be proportional to the corresponding ionic pro- duct, [Ca2']'o[PO-]6[OH-]2, for the solution.The values of C(1) for each ion should thus vary more or less in proportion to the lattice ions in solution and also with pH. In the polynuclear mechanism for dissolution, what would be the effects of undersaturation and pH on C ( l ) ? The removal of the first dissolution unit during nucleation of holes requires a large activation energy, and consequently there is a slower dissolution rate. Crystal edges and apices have been proposed to be viable alternative sites for the initiation of dissolution.2 What are the roles of crystal edges and apices and perhaps, spiral steps which may be present on the surface, in determining the dissolution rate of HAP? The activation energy for solvent exchange in the vicinity of alkaline-earth ions has not been r e p ~ r t e d .~ How can the proposal that the calculated activation energy for the detachment of a calcium ion during nucleation is three times larger than that for dehydration, which has been suggested to be equivalent to solvent e ~ c h a n g e , ~ be established? Recent work by N i e l ~ e n ~ . ~ indicates that the latter corresponds to the growth activation energy. Solvent exchange in the vicinity of most alkaline- earth ions is known to be very fast.3 Does it mean that the incorporation of growth units into kinks by dehydration becomes rate-determining and the activation energy of this step determines the growth activation energy? Furthermore, would it be correct to infer that the activation energy for dissolution for HAP is larger than that for crystal growth? If not, why not?GENERAL DISCUSSION 29 1 The asymmetry between interfacial controlled crystal growth and dissolution lies in the faster dissolution rate coefficient (for a given type of ~rystal).~?’ How can my inference from the suggestion of Christoff ersen and Christoff ersen, if correct, be consistent with this well established experimental observation? The overall dissolution is an electroneutral process with no net charge transfer.How can variations of electric potential difference between the crystal surface and the solution have a major effect on the rate of dpsolution? Previous workers8y9 have often used m2’3 ( i e . surface area) as the variable representing the activity of the interface. A number of recent however, have suggested that such a relationship may hold for only a given type of crystal, regarding their history of preparation and storage. This raises two questions.(1) What is the reason for selecting a fixed value of m/ m, at which to compare the rate of dissolution whilst the ‘surface activity’ of the different crystal samples used in the large number of runs was not explicitly considered? (2) What is the variation of rate with concentration over the course of a single dissolution run with HAP? ’ W. K. Burton, N. Cabrera and F. C. Frank, Philos. Trans. R. SOC. London, Ser. A, 1951,243, 299. N. Cabrera and V. Coleman, in Art and Science of Crystal Growth, ed. J. J. Gilman (Wiley, New York, 1963), p. 3. S. Petrucci, in Ionic Interactions, II.Kinetics and Structure, ed. S. Petrucci (Academic Press, New York, 1971). A. E. Nielsen, Pure Appl. Chem., 1981, 53, 2025. A. E. Nielsen, in Industrial Crystallisation 81, ed. S. J. Jancic and E. J. de Jong (North Holland, Amsterdam, 1982). J. W. Mullin, Crystallisation (Butterworths, London, 1972), p. 199. ’ S. T. Liu, G. H. Nancollas and E. A. Gasiecki, J. Cryst. Growth, 1976, 33, 1 1 . * C. W. Davies and A. L. Jones, Trans. Faraday Soc., 1955, 51, 812. l o M. R. Christoffersen, J. Christoffersen, M. P. C. Weijnen and G. M. van Rosmalen, J. Cryst. D. M. S. Little and G. H. Nancollas, Trans. Faraday SOC., 1970, 66, 3103. Growth, 1982, 58, 585. Prof. J. Christoffersen and Dr. M. R. Christoffersen (University of Copenhagen, Denmark) replied: We agree with you that spiral growth and dissolution can be expected to be faster than nucleation-controlled rates close to saturation.In our experiments the rates become too low to be measured using our present technique when C / C, > 0.7. The factor C ( 1) in eqn (8) is not simple to determine accurately. We have estimated C ( l ) in the following way. With C(1) being the density (mole fraction) of surface sites from which an ion is missing, but where none of the lateral neighbours is missing, and C ( 0 ) being the corresponding density of sites where the ion is not missing, we may estimate C(l)/C(O) =exp ( - 4 a ’ a l k ~ ) -0.02 using a = 0.3 nm, a == 0.045 J m-* and kT = 4 X lo-*’ J. Using C(0) =. 1 we have C ( 1) = 0.02. For a polynuclear mechanism the linear rate of growth is proportional to C ( 1)1’3, = 0.25.This factor is not very important. As a has been found to be nearly independent of pH, we do not expect C(l)/C(O) to vary much with pH or with C/C,. The rate of dissolution of HAP can be explained by quite a normal polynuclear mechanism. Edges and apices do not seem to play a special role. As the rate is controlled by a nucleation process, the density of kink sites on the crystal surface is also controlled by the nucleation process. Steps associated with spirals are thus unimportant.292 GENERAL DISC US S I 0 N Mr. Cheng's statement about ref. (3) in his question is quite correct, but one may calculate the activation energies from dehydration frequencies using Eyring's formula. The only answers we can suggest to the question why the calculated activation energy for dissolution of HAP is about three times t,he activation energy for removing one water molecule from a dehydrated calcium ion is either that more calcium-oxygen bonds in the crystal surface have to be broken in order to remove a calcium ion, or that the calcium-oxygen bonds in the crystal surface are stronger than the calcium-oxygen bond in the aqueous solution.We agree that the activation energy for growth of crystals of simple salts containing alkaline-earth cations according to Nielson's work is less than the activation energy for dissolution of HAP. This may be due to the frequency of detachment being lower than the frequency of complete incorporation in the crystal surface, once a cation like Ca2' is partly dehydrated and has formed at least one bond to an anion in the crystal surface.The rate of growth of HAP is not well known to us, neither are accurate rate constants for growth and dissolution of other crystals with a complex structure like apatites. For crystals of simple electrolytes the rate of growth is normally less than the rate of dissolution, both rates being determined for the same value of the affinity. The question concerning the effect on the rate of the electrical potential difference between the crystal and the solution touches a very important problem. If we do not distinguish between cations and anions, imagining crystals to be made of identical charge-less building units, this effect cannot be understood. On the other hand, if the density of hydrogen phosphate groups in the cqstal surface increases, bonds to Ca2' are weakened and these ions may leave the crystal surface faster than if no hydrogen phosphates were present in the crystal surface. In the model used for HAP dissolution one may think of hydrogen ions as catalysing the rate of dissolution.The last few questions about the difference between ( m / m0)2/3 and the expression F(m/rn,) in eqn (5) of our paper can be answered quite simply. If the crystals used in an experiment are not identical, the surface area can in general not be represented accurately by (m/m0)2/3, but the area can be expressed as an unknown function of ( m / rn,) if the linear rate can be expressed by an equation of the type given in eqn (4) of our paper.As far as we know, the rate of growth or dissolution of crystals can only be separated into a concentration term and an area term, if the above eqn (4) can be applied. In order to obtain an accurate expression for the influence of solution composition, we have determined rates, J/mo, for the same values of pH and m/m,, but for different values of the dissolution affinity. The rate varies by a factor of ca. 10 from the start to the point where an experiment is terminated, see for example fig. 1 in ref. ( 6 ) of our paper. Dr. R. M. Sellers (C.E.G.B., Berkeley) said: The dissolution of ionic crystals generally takes place with a rate law given by R d = kA( C,, - C,)" where A is the surface area, C,, is the salt solubility and C, is the concentration of salt in solution at time t.n is a constant which apparently takes integral values. Table 1 summarises some of the measured values. Linge' comments that n = 2 for 1 : 1 electrolytes and n = 3 for 2 : 1 electrolytes, but the results of Simon2 seem to run counter to this. There seems to be some underlying order here, but it is not clear what these results mean at a fundamental level. Perhaps Prof. Christoffersen, Dr. Coller or Mr. Cheng would care to comment.GENERAL DISCUSSION 293 Table 1. Experimentally determined values of n in eqn (1)" n crystal dissolving 1 NaC1,KCl 2 PbS04, SrS04, CaS04, BaSO,, TlBr, CaCO, Ag2Cr04, MgF2, Ba(103)2. ~ ~~ ~~ ~ a Data from Linge' and Simon.2 I should also like to hear their comments on whether in the systems they have studied there is any evidence for migration on the surface (say from kink sites to adatoms) prior to dissolution.There is some evidence for this in the work of Jones et aL3 on the dissolution of MgO crystals in HCl, but little other information seems to be available. ' H. G. Linge, Adv. Colloid Interface Sci,, 1981, 14, 239. B. Simon, J. Cryst. Growth, 1981, 52, 789. C. F. Jones, R. L. Segall, R. St. C. Smart and P. S. Tucker, Prbc. R. Soc. London, Ser. A, 1981, 374A, 141. Prof. J. Christoffersen ( University of Copenhagen, Denmark) replied: As far as I know, there exists no sound theory for crystal growth or dissolution relating the power n to the stoichiometry of the crystals. In general, a simple diff usion-controlled rate will lead to n = 1, whereas spiral growth (and dissolution) will show n =s 2.For nucleation-controlled rates the power of n increases as saturation is approached.'92 In regard to Dr. Sellers' question about surface migration, the rate of dissolution of HAP can be accounted for without taking such migration into account. This indicates that we have equilibrium between the solution and adatoms in an adsorbed layer. ' A. E. Nielsen, J. Cryst. Growth, 1984, in press. A. E. Nielsen and J. M. Toft, J. Cryst. Growth, 1984, in press. Mr. V. K. Cheng (Monash University, Australia) said: Dr. Sellers' first question is of particular relevance to our understanding of the growth and dissolution of ionic crystals at the fundamental level.'92 The rate law given is an empirical one. Its concentration factor is expressed as the distance from saturation raised to the nth power (the order) and is distinct from those commonly encountered in homogeneous kinetics or the 'reaction controlled' interfacial kinetics reported by Dr.Sellers and others in this meeting. The parameters in the rate law, among which n is of particular interest, are determined from the fitting of experimental data, and our fundamental objective is to establish the meaning of n in terms of mechanisms. We highlighted the disagreement between the BCF theory involving a one- component solid/vapour interface and the second order ( n = 2) dependence of the rate on the distance from equilibrium observed for the growth and dissolution of bivalent metal sulphates. A number of modified BCF theories have been proposed in the past374 which appeared to be capable of providing agreement between theory and experiment.Linge's view2 is an alternative mechanism which considers the transfer of ions across the 'double layer' region of the interface as equivalent to that of electron transfer. The electroneutrality and/ or stoichiometric composition of ions in this region and the double-layer potential are necessarily involved in the description of growth and dissolution kinetics. This idea was initiated by Davies and Jones' and we have294 GENERAL DISCUSSION also raised its lack of rational physical basis in our paper. In particular, it cannot account for the asymmetry between growth and dissolution. Basic chemistry remind us of the general absence of relationship between the stoichiometry and the empirical rate order of a reaction. I have raised the issue of preservation of electroneutrality at the interface in discussion with Prof.Chris- toffersen. Under such conditions I am doubtful of any involvement of the double- layer potential in determining the growth and dissolution of ionic crystals. We must note the apparent regularity of the data given in the table and ‘the usefulness of the Davies-Jones model” ( i e . the rate equation with n = 2). After all, the equation is empirical and its usefulness is self-assured. The agreement between stoichiometry and order for binary salts is perhaps a coincidence and can be accounted for in terms of more adequately formulated theories based on step movement. In my opinion, the third-order law reported for the given group of 2 : 1 crystals and its relation to stoichiometry is disputable.The dissolution of Ag2Cr04 is largely controlled by volume diffusion.’ The third-order kinetics was established from the data measured at C / C, over 96%. Inspection of the published ‘interfacial- controlled’ data suggests to me that they can be fitted over a range of n. The published data for Ba(103)210 are not conclusive in support of the third-order law and can also be fitted with a second-order law.” Perhaps observed orders higher than 2 can be accounted for in terms of the process reported by Christoffersen in this Discussion which gives rise to a very complicated theoretical rate expression. However, nucleation is not a plausible process near equilibrium except with the aid of lattice imperfections I 2 , l 3 during dissolution. The second order for 2 : 1 ionic crystals was established a long time ago for K2S0414 and very recently for SrF2.” Despite the choice of a Nernst-volume diffusion model unfamiliar to me and the mix up of enthalpy and activation enthalpy in Simon’s paper,16 the first-order law together with the small (activation) enthalpy found for the dissolution of KCl and NaCl was accounted for in terms of volume diffusion.G. H. Nancollas, Adv. Colloid Interface Sci., 1979, 10, 215. R. Reich and M, Kahlweit, Ber. Bunsenges. Phys. Chem., 1968, 72, 66; 75. A. E. Neilsen, Pure Appl. Chem., 1981, 53, 2025. C. W. Davies and A. L. Jones, Trans. Faraday SOC., 1955, 51, 812. G. I. Brown, Introduction to Physical Chemistry (Longmans, London, 1972), p.336. B. H. Mahan, University Chemistry (Addison-Wesley, 2nd edn, 1969), p. 356. W. A. House, J. Chem. SOC., Faraday Trans. I , 1981, 77, 341. A. L. Jones, H. G. Linge and I. R. Wilson, J. Cryst. Growth, 1974, 26, 37; 1975, 28, 254. A. L. Jones, G. A. Madigan and I. R. Wilson, J. Cryst. Growth, 1973, 20, 93, 99. ’ H. G. Linge, Adv. Colloid Interface Sci., 1981, 14, 239. 10 I ’ G. A. Madigan,’ Ph.D. Thesis (Monash University, Melbourne, 1969). l 2 B. van der Hoek, J. P. van der Eerden and P. Bennema, J. Cryst. Growth, 1982, 56, 621. l 3 G. Z. Liu, J. P. van der Eerden and P. Bennema, J. Crysf. Growth, 1982, 58, 152. l4 R. Marc, 2. Phys. Chem., 1908, 61, 385; 1909, 67, 470. l 5 R. A. Bochner, A. Abdeul-Raman and G. H. Nancollas, J. Chem. SOC., Faraday Trans.I , 1984, l6 B. Simon, J. Cryst. Growth, 1981, 52, 789. 80, 217. Dr. R. M. Sellers (C.E.G.B., Berkeley) said: In much of our work on the dissolution of mixed oxides we have found that one or more components (often iron) dissolves slightly more rapidly than the others. There must therefore be some enrichment of the surface in the other components, and we have demonstrated this with crystals of magnetite or franklinite using surface-sensitive techniques such as X-ray photoelectron spectroscopy’ or chemically.2 In general these effects do notGENERAL D 1 SC U SS I 0 N 295 cause a dramatic change in kinetics, and the shrinking-core model describes the data to upwards of 75% dissolution.' There are exceptions, for instance in the oxidative dissolution of nickel chromium ferrites, where an outer barrier of increasing thickness is formed.Here the Crank, Ginstling and Brounshtein equation: 1 -%a - (1 - = 1 - kt holds.4 Does either Prof. Christoffersen or Mr. Cheng have any evidence that the surfaces of his crystals become enriched in one or other of the components during dissolution, and if so, how does this evolve with time? ' G. C. Allen, R. M. Sellers and P. Tucker, Philos. Mag., 1983, 48, L5. * G. V. Buxton, T. Rhodes and R. M. Sellers, J. Chem. SOC., Faraday Trans. I , 1983, 79, 2961. M. G. Segal and R. M. Sellers, J. Chem. SOC., Faraday Trans. I , 1982, 78, 1149. F. Habashi, Extractive Metallurgy (Gordon and Breach, New York, 1969), vol. 1. Prof. J. and Dr. M. R. Christoffersen (University of Copenhagen, Denmark) said: In the case of the dissolution of calcium hydroxyapatite (HAP) we have avoided such effects by studying the rate of dissolution at constant pH and constant calcium to phosphate ratio.We have found that the rate constant increases with increasing concentration of hydrogen ions in solution. In our experiments we have equilibrium between hydrogen ions in solution and on the crystal surface. If this was not the case it would be most difficult to analyse the data. Dissolution of HAP with some of the hydroxy groups substituted by fluoride ions in solutions unsaturated with respect to HAP and FAP (calcium fluorapatite) will cause a surface enrichment with respect to fluoride ions.' ' M. R. Christoffersen, J. Christoffersen and J. Arends, J. Cryst. Growth, 1984, 67, 107.Mr. V. K. Cheng (Monash University, Australia) said: Continuing my response to Dr. Sellers, I wish to remark that our paper did not consider the problem of surface diffusion. However, the involvement of surface diffusion in crystal growth has been inferred from the fitting of growth data (first-order growth-rate law) for NaClO, and potash alum with the B.C.F.*,2 Alternatively it is possible to decide the involvement of surface diffusion in crystal growth and dissolution from the ratio of direct detachment to surface diffusion probabilities of surface units. For example, in the SOS model for the solid/fluid interfa~e,~ the evaporation probability of a site with n lateral neighbours is given by k , = v exp ( z ( 2 - n ) ) where y = 441 kT. From eqn (12), (14) and (15) in ref.(3) of this comment, the probability of surface migration from a site with n lateral neighbours to a neighbouring site with m neighbours is given by k,, can be calculated from eqn (12) of ref. (3) and the B.C.F. t h e ~ r y . ~ k,, = Y exp (- UJkT).296 GENERAL DISCUSSION The migration along sites which does not result in any change in coordination number gives Us = 0. Thus koo = v. Substitution of eqn (1) into (2) with the appropriate choice of n leads to kn0 = Y exp ( - n y / 2 ) . Therefore k , -=exp ( 7 ) . kn0 A decrease in temperature or an surface diffusion for less soluble increase in y would make the ratio larger and crvstals less favourable. However. simulations involving surface diffusion carried out so far395 consider the surface migration frequency as an independent input variable.Such choice would have been effective for the examination of the role of surface diffusion on crystal growth at a given 4 / k T . The estimate given above is very useful for describing the growth and dissolution of (non-polar) ionic crystals far from edges and apices. It has been shown7 that because of the partial cancellation of contributions from lattice ions of opposite charges, adsorbed ions experience short-ranged attraction from the rest of the lattice. The movement of solvent molecules during an elementary event of incorporation or detachment is more complicated to describe, but the assumption given in ref. (3) that the solvent can be treated as a continuum with defined average interactions is probably valid because of the short lifetime of the solvated water.The short-ranged electrostatic repulsion between ad-ions and lattice ions of like charge, however, would probably limit the number of available surface diffusion paths. The ad-ions move like a bishop on a chess board! ’ P. Bennema, J. Cryst. Growth, 1967, 1, 287. ’ P. Bennema, J. Cryst. Growth, 1969, 5, 29. G. H. Gilmer and P. Bennema, J. Appl. Phys., 1972, 13, 1347. W. K. Burton, N. Cabrera and F. C. Frank, Philos. Trans. R. SOC. London, Part A, 1951,243,299. J. D. Weeks and G. H. Gilmer, Adv. Chem. Phys., 1979, 40, 157. J. E. Lennard-Jones and B. M. Dent, Trans. Faraday SOC., 1928, 24, 92. Prof. J. Christoffersen ( University of Copenhagen, Denmark) said: The rates of dissolution of different preparations of BaSO, are described as proportional to ( C , - C)2, but in order to obtain this power law a different solubility, C,, is assigned to each preparation.A plot of log rate against log (C, - C ) of Mr. Cheng’s data given by the points marked in his fig. 1, taking C, to be the accepted equilibrium value of the solubility of BaSO,, 10.4 pmol dmP3, leads to the rate being proportional to ( C , - C)’.6. Could this indicate that some diffusion process has to be taken into account? That the adsorption of Sr2’ and Ca2+ onto BaSO, crystals causes an increase in the rate of dissolution is interesting. Has this also been found for the rate of dissolution of microcrystals of BaSO, in aqueous suspension? Has Mr. Cheng an explanation for the order of effectiveness of CaCl; and SrC12 given in table 3: 10 pmol dm-3 SrC12 < 10 pmol dm-3 CaC12 < 54 pmol dmV3 CaC12 < 20 pmol dmP3 SrC12? Dr.B. A. W. Coller and Mr. V. K. Cheng (Monash University, Australia) said: The exponent n in crystal growth and dissolution kinetics can be obtained by means of a number of apparently equivalent presentations of experimental data.”’ TheGENERAL DISCUSSION 297 solubility of a crystal is involved in all presentations. We have shown3 that choice of a smaller solubility will lead to a decrease in the value of the exponent in the log-log plot. The ‘accepted’ equilibrium solubility used by Prof. Christoff ersen is smaller than the kinetic solubility obtained in our work. Therefore the exponent of 1.6 is not surprising. By using an exponent of 2 we obtain a kinetic solubility; a parameter that we interpret in terms of energies of dissolution affected by regions of stress and discontinuity at the surfaces of the crystals.Prof. Christoffersen’s use of the accepted equilibrium solubility would lead to exponents depending on the nature of the crystal which could be interpreted in terms of energies of initiation of dissolution, possibly by formation of dissolution nuclei, in stressed or unstressed regions. The ambiguity highlights the lack of a single agreed theoretical model and empirical presentation of rate data for the dissolution of ionic crystals found in the literature at present. We are confident that the dissolution of barium sulphate is controlled by transfer at the interface because the rates found with the single crystal did not vary with rotation speed and with microcrystalline samples did not depend on stirring speed.We have not yet studied the effects of additives on the dissolution of microcrystal- line samples, nor do we yet have an explanation for the large effect of SrC1, at 20 pmol dm-3 with the single crystal. ’ G. H. Nancollas, J. Cryst. Growth, 1968, 34, 335. * J. L. Powell, B. A. W. Coller and A. L. Jones, J. Cryst. Growth, 1978, 43, 185. V. K. Cheng, Ph.D. Thesis (Monash University, Australia), to be submitted. Dr. W. A. House (Freshwater BiologicaZ Association, Dorset) asked Dr. Coller if there was any systematic trend in the activation energies E, and enthalpies of dissolution shown in table 1 with ageing and use of the crystals? Could one foresee a situation when after prolonged ageing and allowing the surface to reform that this variability was reduced? Dr.B. A. W. Coller (Monash University, Australia) replied: Activation energies and enthalpies of dissolution, shown in fig. 2 of our paper refer to seven different preparations of barium sulphate crystals mounted on polythene plates. For a given sample, successive values of E, and An obtained in dissolution trials at intervals of one to three days did not show a systematic trend along the correlation line. This could be the effect of variation in the periods of dissolution (‘washing’) and storage in contact with saturated solution (‘ageing’). However, it is not clear that the slow processes of growth and dissolution during extended ageing will remove the effects of rapid dissolution during washing, particularly in regions of localized stress associated with dislocations, grain boundaries and crystal edges.There is need for further study of the effects of wash-and-age cycles on crystal morphology. Dr. J. J. M. Binsma (IRI, Delft, The Netherlands) said: I would like to ask Dr. Coller whether the barium sulphate crystals of type I1 and I11 are still facetted? For dendritic or aggregated crystals it is to be expected that they are bounded by faces which do not have a specific crystallographic orientation and which are rough on an atomic scale. Such faces will have a very low activation energy for dissolution, because almost all atoms (ions) are found in kink or less strongly bound positions and no ‘dissolution nuclei’ need to be formed.298 GENERAL DISCUSSION Dr. B.A. W. Coller (Monash University, Australia) replied: Type I1 crystals of barium sulphate appear to retain many small facets of low Miller index but bounded by edges and multiple steps (see, for example, electron micrographs published by Liu et ul.'). In qualitative terms, the surfaces of these crystals dissolve more rapidly than those of type I and appear to have lower energies of dissolution, but our experiments indicate that their activation energies for dissolution tend to be higher. We suggest that the rhombohedra1 type I crystals are produced by growth around screw dislocations which are centres of stress and serve as ready-made dissolution nuclei. Such crystals appear to dissolve from the central areas of their faces.If dendritic type I1 crystals grown from more concentrated solutions are relatively free of dislocations, then dissolution of layers on facets will begin at apices and along edges. Kink units on faces, kink units on edges and kink units at apices may have similar energies of total detachment. However, displacement of a crystal unit from an apex kink or edge kink onto a terrace will involve passage through a transition state in which the unit is more exposed than when an intrafacial kink unit is moved out onto an adjacent terrace. For molecular crystals, where non-neighbour interactions may be neglected, the two processes can be expected to have similar activation energies.' However, with ionic crystal units, next-to-nearest neighbour electrostatic interactions that can affect the potential-energy surface and make a difference between the activation energies.Simple models of movement of ion pairs lead us to expect a higher activation energy for displacement from edge kink to terrace than for displacement from intrafacial kink to terrace. There is need for more detailed calculations. Type 111 crystals of barium sulphate have not yet been subjected to scanning electron microscopy to investigate the surface topography, although transmission and diffraction studies by Takiyama' indicate a well developed crystal structure even in very small crystals. S. T. Liu, H. Nancollas and E. A. Gasiecki, J. Cryst. Growth, 1976, 33, 11. K. Takiyama, Bull. Chem. SOC. Jpn, 1959, 32, 68. Mr. V. K. Cheng (Monush University, Australia) added: The roughening of surfaces depends on the temperature and interaction ($/ kT).' The roughening transition occurs at $/kT== 1.75.I would expect sparingly soluble salts to have high 4/ kT, i.e. they have low-temperature surfaces. The absence of macroscopic facets is a characteristic of a roughened crystal. Arrangement of ions at this type of crystal surface will create local polarity, as reflected by the non-zero surface unit-cell dipole moment. The electrostatic energy of such a crystal is known to be enormous and makes formation of roughened ionic crystal very unfavourable.* The formation of polar habits, such as the (1 11) face of KC1, requires the stabilisation provided by added impurities. The surfaces of ionic crystals are therefore likely to be flat.Furthermore the growth and dissolution kinetics of ionic crystals in general do not conform to those of a roughened s ~ r f a c e . ~ ' H. J. Leamy, G. H. Gilmer and K. A. Jackson, in Surface Physics of Materials, ed. C . Blakely (Academic Press, New York, 1975), p. 121. E. R. Smith, Proc. R. Soc. London, Ser. A, 1982, 381, 241. J. D. Weeks, G. H. Gilmer and K. A. Jackson, J. Chem. Phys., 1976, 65, 712.GENERAL DISCUSSION 299 Dr. B. A. W. Coller (Monash University, Australia) said: (1) Binsma and Kolar's compartment model allows for exchange between sol- ution, surface (terrace), steps and kinks. The numbers of sites available for adsorp- tion in each of these compartments could be very different from one another. Have the capacities of the compartments been estimated from the exchange data? (2) According to the hard-sphere model of an ipnic crystal, the transition states for diffusion of ions across the surface occur at points of zero electrostatic potential, i.e.the energy of the transition state in a diffusion step would be equal to the energy of the completely detached ion. However, the presence of solvent at the interface could make a considerable difference. Is Dr. Binsma able to assess the ease of diffusion on the crystal surface, by comparison with the ease of detachment? (3) Dr. Binsma drew attention to the seemingly irreversible incorporation of some labelled ions into the crystal and supposed them to be contained in layers that had been overlain by several others. It seems to us that dissolution can be as different from the simple reversal of growth as the unravelling of a knitted garment can be different from reversing the sequence of the original knitting.With exchange under equilibrium conditions, the changes of surface configuration should be at their most nearly reversible, but should still be subject to statistical fluctuations in which ions are taken up in surface layer sites and surrounded by other surface units laid down in rows to form patches. Has Dr. Binsma considered the statistics of incorporation and release of labelled ions, in terms of rows rather than layers? Dr. J. J. M. Binsma (IRI, Delft, The Netherlands) said: The answers to Dr. Coller's questions can be summarized as follows. (1) The activity against time curves have been fitted to a three-compartment model made up of a central compartment (the solution) and two peripheral ones which are not connected to each other.Within this model it appears that the compartment sizes do not differ very much from each other and are each equal to about half the total amount of exchangeable Ca2+ ions. (2) As an upper limit for the activation energy of surface diffusion one can take the activation energy for detachment of an adatom from the underlying crystal lattice.' The jumping frequency for surface diffusion, which can be calculated from the activation energy via the Eyring equation, will then be equal to or lower than the real value. For the calculation of the surface-diff usion jumping frequency along this line the required data concerning the dissolution of CaF, are lacking, however.(3) I agree that the kinetics of dissolution may be entirely different from the kinetics of growth. With regard to the seemingly irreversible incorporation of labelled ions it should be kept in mind that the number of relatively weakly bonded ions (e.g. in kink or step-like positions) will be very small under equilibrium conditions.' Most ions will be more strongly bonded, making the crystal surface very flat. These more strongly bonded ions nevertheless take part in the exchange since the experiments showed that ca. one lattice layer of CaF, participates in the exchange. The exchange of these ions may proceed via one of two alternative pathways, namely either by direct transitions out of the surface into the solution or via the fluctuation of kink-like positions. If, starting at a kink position, rows of ions go into the solution, the kink position travels along the surface giving all ions the opportunity to detach from a relatively weakly bonded state.With regard to the statistics it remains in the latter case that the exchange of ions should be reversible. ' G . H. Gilmer and P. Bennema, f. Appl. Phys., 1972, 43, 1347.300 GENERAL DISCUSSION Prof. J. Christoffersen (University of Copenhagen, Denmark) said: Could Dr. Binsma explain why the different rate constants obtained cannot be explained by two of the three compartments involved being the adsorbed layer and the more solid surface of the crystals? Dr. J. J. M. Binsma ( I N , Delft, The Netherlands) said: Prof.Christoffersen suggested that two of the three compartments involved in the exchange processes may correspond to the adsorption layer and the more solid surface of the crystals. If this were so, the measured rate constants should be of the same order of magnitude as the frequency of adsorption of Ca2+ ions from the solution, fad, and the frequency of integration, fin. The frequency for adsorption is related to the flux of ions F by where Qa is the amount of Ca2+ ions in the solution which are available for adsorption, V, the volume of the solution from which adsorption in one 'jump' is possible, c, the solubility of CaF,, A the surface area of the crystal in contact with the solution and a the so-called molecular diameter (0.3 nm according to Nielsen'). It is thus supposed that adsorption in one jump is possible from a layer of thickness a adjacent to the crystal surface.For a flux of ions of 1 x 10-'omol m-, s-l (see our paper), the adsorption frequency should be 1.7 s-', which is much larger than the rate constants found in our experiments. The integration frequency, An, for incorporation into the more solid surface (kink sites) appears to be related to the cation dehydration frequency fdh by An = 10-3fdh, as checked for CaF, by Nielsen.' For CaF, (fdh = 1.6 x lo8 s-l) Ln should be 1.6 x lo5 s-l, which is again much higher than the experimentally observed rate constants. ' A. E. Nielsen, J. Cryst. Growth, to be published. Dr. A. R. Flambard (Free University of Berlin, West Germany) said: I address my remarks to Dr Binsma.My questions concern your re-exchange studies. In accordance with similar observations by Moller and Sastri you ascribe a loss in exchangability of some 30% of the total amount of the 45Ca2' ions as being due to diffusion into the bulk of the crystal. Do you have any evidence for this from other types of measurements? Have you considered any statistical analyses of the partition of 45Ca2+ between the solid (surface) and solution phases? Rather than diffusion into the bulk of the crystal, is it not also possible that your observation of at least two different types of bonding for Ca2' within the solid phase could be explainable if one considers an exchange of Ca2' between the first and second, or possibly third, layers of the crystal's surface? (Then in simple terms one would expect the properties of these layers at, or close to the surface to differ from those in the bulk.) Finally, during your re-exchange experiments, after the system had reached equilibrium again, did you try replacing the saturated CaF, solution with fresh solution and if so, were there any changes in observed activities? Dr.J. J. M. Binsma ( I N , Delft, The Netherlands) said: The following comments (1) The diffusion of Ca2' from the surface into the bulk of the crystal has not can be made regarding Dr. Flambard's questions. yet been measured independently.GENERAL DISCUSSION 301 (2) The amounts of 45Ca2+ in the solid (surface) and in the solution are correlated with the size of the respective compartments. When the solid has gathered its final (equilibrium) amount of activity, the relation between the amounts of 45Ca2+ and the total amounts of Ca2+ in the solid and in the solution is given by eqn (2) of our paper.(3) It is certainly possible that exchange occurs between the solution and a number of layers of the crystal. More refined experiments are needed in order to be able to draw conclusions in this respect. (4) The saturated aqueous solution of CaF, has not been renewed in the re- exchange experiment. This will not have had any influence on the results because the specific activity of the solution after the system had reached equilibrium was ca. 1000 times lower than that of the solution used in the exchange experiments, whereas the specific activity of the solid had decreased by only 70%.Dr. W. A. House (Freshwater Biological Association, Dorset) asked: Does Dr. Binsma think the 45Ca isotopic exchange method is at all suitable for measuring the specific surface areas of calcium carbonate minerals? The range o f f values shown in table 2 of the paper indicates that for (100) face of CaF, only part of the surface takes part in the exchange and models based on the entire lattice taking part in the exchange would lead to erroneous estimates of the extent of surface. I raise this point because the 45Ca exchange method' is used to estimate specific surface areas. C. G. Inks and R. B. Hahn, Anal. Chem., 1967, 39, 625. Dr. J. J. M. Binsma (IRI, Delft, The Netherlands) said: In reply to Dr. House it should be stressed that the so-called isotopic exchange method for determining specific surface areas as used for instance by Inks and Hahn' can only be applied to steady-state systems and if a correlation exists between the final value of the activity of the solid phase and its geometrical surface area. The method is carried out generally for populations of small particles of micrometre size or smaller having rather rough surfaces.In that case a relatively fast and complete exchange with the first surface layer can be expected. It should not be excluded, however, that deeper layers are also taking part in the exchange, especially if the surface is very rough. Whether the isotopic-exchange method can be used should therefore be checked for each compound and even for each type of sample because of the influence of the surface properties.' C. G. Inks and R. B. Hahn, Anal. Chem., 1967, 39, 625. Mr. V. K. Cheng (Monash University, Australia) said: I address my question to Drs. Sellers and Williams. What is the variable k in fig. 1 of your paper? Its unit apparently involves an area factor. How did you characterise the surface area of the crystals? I am not able to find an explicit description on the rate measurement. Presumably, in each dissolution run, a known amount of solid was dissolved over a fixed duration and is determined thereafter. Thus each data point in fig. 1-6 is obtained with different initial solid samples. Over a period of many hours of dissolution, as indicated in fig. 2, the large (ca. 20%) amount of solid dissolved would change the surface activity significantly through the decrease in both surface area and mass of crystals.302 GENERAL DISCUSSION What is the variation of the initial amount of solid in each run and what would be the relative contributions of the variation of initial crystal mass and crystal imperfections to the rate measured? How was aging characterised? How many Fe" ions are there in the solids? Can the absence of autocatalytic paths be related to the Fe3+ content in the solid? At 140 "C pH values of the acids different from that at 25 "C would be expected.Has the variation of pH due to temperature been considered and if so what would be the effect of the variation of pH of the individual acids in the solution at different temperatures on the dissolution rate? The rate law in general expresses the rate in terms of the concentration of reactants or products raised to the nth power, where n is the rate order. In crystal growth and dissolution, the concentration factor is expressed as the supersaturation or undersaturation and the order for the dissolution of barium sulphate and HAP, as presented in this Discussion, was found to be, respectively, 2 and 4-6.(The order varies over a wide range of values as you have commented earlier.) However, your rate equation [eqn (3)] does not express rate and the concentration variables in the form used by us and Prof. Christoffersen, nor is the index in your rate equation equal to 3. How can a third-order or cubic law be justifiably declared? Furthermore does the rate law, as derived from the 'shrinking-core model' which is not described in your paper, contain any mechanistic information such as the time evolution of the surface topography? What is the binuclear complex mentioned in the dissolution involving oxalic acid? Do you suggest that a small molecule like the oxalate ion can become a bridging ligand to two neighbouring cation sites and, as a result, the dissolution depend on the electron transfer from the complex to Fe3+ ions at the surface? What is the origin of the values for the variables k and K4 used in eqn (8)? The cause of reduction of the dissolution rate of crystals was related to the increasing Cr3' content and the substitutional inertness of the Cr3+ ions. Is it true that the Cr3+ ions are more difficult to remove by complex formation, compared with Fe3+ and other divalent ions in the crystal? Have you proved this point by investigating the stability constants of the complexes between Cr3+ and the ligands? How do you know that NTA is more adsorbable than oxalic acid and that NTA completely covers the oxide particles (or do you mean microcrystals)? Dr.R. M. Sellers (C.E.G.B., Berkeley) said: The variable k in fig. 1 of our paper is a rate constant, and is related to the kobs of eqn ( 3 ) by kobs = k / rop, where ro is the initial particle radius and p the density. As described in the Experimental section the mean initial radii of the various oxides were determined using a Coulter counter. The oxides have low surface roughness, so the mean radius is a reasonable measure of the surface area. In fact the oxides had nearly the same sizes, and did not appear to differ significantly in surface roughness, so the corrections for differences in size were small.The rate measurements were carried out as described in the Experimental section. Cu. 3 mg of oxide were used in each run. Small differences in this amount are taken into account in calculating kobs from the shrinking-core model. It is important only that the other reagents are present in sufficient excess that their concentrations do not vary appreciably during a particular run. We assume that faults are distributed evenly throughout the particles. The ageing of the Ni0.6Cr0,6Fe,.804 oxide manifested itself through a reduction in dissolution rate between the initial and final phases of the work. We do not know for certain what the cause of this was, but changes in the nature of the fault structure of the oxide are probably implicated.GENERAL DISCUSSION 303 The surface area undoubtedly increases in the initial phases of the dissolution, but there appears to be no concomitant increase in rate.We believe the reason for this is that the number of reactive sites does not vary in parallel with the surface area, but rather decreases with time in a manner mathematically the same as the shrinking-core model. The spinel oxides have a general composition AB204 where A is a divalent cation and B trivalent. The mixed oxides used in our work have a composition Nio,,Cr,Fe2.4-,04. The divalent ions are therefore Ni0.6 + Fee-4, and the trivalent Cr, and Fe2,0-n. The absence of autocatalytic pathways is related to ( a ) failure to dissolve ferric ions reductively and ( b ) a rate constant for reaction (1) comparable with that for reaction (2): FeI'L, + >Fe3+ -+ FelllL, + Fe2+ (1) L,+=Fe3+ + Fe"*L,.(2) The pK, values of both oxalic acid and NTA at 140 "C are undoubtedly different from the values at room temperature. No data appear to be available on these, however. In view of this we have been unable to calculate the pH values in the solutions at 140"C, and so throughout this paper pH values are quoted at 25°C. This introduces some bias to the data (e.g. in fig. 6), but will not alter the general conclusions, for instance, that with oxalic acid the dissolution rate increases as the pH decreases. Eqn (3) in the paper is an integrated form of the rate equation.Its derivation is given, for instance, by Segal and Sellers' or Habashi2 but starts with the assumption that the rate is proportional to the instantaneous surface area. The shrinking-core model is relatively crude, and does not take into account, for instance, the evolution of surface topography as the reaction proceeds. Nevertheless, we have found it useful in this and previous work on spinel diss~lution.'~~ It seems that the number of active surface sites (kinks?) is the most important factor, and as noted above, the variation of this with time parallels the change in surface area of a dissolving sphere. The description of eqn (3) as a 'cubic' rate law is misleading; the 'shrinking- core' equation is to be preferred. Small molecules such as oxalic acid can indeed bind simultaneously at two neighbouring sites, as indicated by i.r.measurement^.^ Other species such as picolinic acid,3 selenious acid, orthophosphoric acid and sulphuric acid5-'' behave similarly on iron-rich oxides such as haematite or goethite. In the case of oxalic acid electron transfer can be envisaged as occurring from such a 'complex' as follows: - 9 O 0 \c-c -&- 'Fern FeK \ / \ / \ I 0 0 0 0 0 c c 0 0 Fen Fen \ / / - II II - I/\/\/ 0 0 0 2 co* + 2 Fe:q The values quoted for k and K4 in eqn (8) were deduced from the slope and intercept of plots of kObs-' against [C~O:-]~*. Cr3+ ions in these mixed spinel oxides are difficult to dissolve by any means.'' They can be dissolved by oxidative processes but these are inhibited by iron,'2 or304 GENERAL DISCUSSION with Cr,03 by reductive means if the reductant is sufficiently p0werfu1.l~ The stability constants for many Cr3+ complexes in aqueous solution have been m e a s ~ r e d ' ~ but the problem is not one of thermodynamics; rather it is the kinetics that are limiting.The well known substitution inertness of Cr3+ is unquestionably a key factor. That NTA is more strongly adsorbed than oxalic acid is inferred from the results (compare fig. 3 and 5 ) . It is also the expected result since NTA is tetradentate, whilst oxalic acid is bidentate. For NTA to be removed from the surface requires that four bonds are broken, a statistically improbable, and therefore slow, process. Other aminocarboxylate ligands, such as EDTA, are known for their ability to bind strongly to oxide ~urfaces.'~ I 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 M.G. Segal and R. M. Sellers, J. Chem. Soc., Faraday Trans. I , 1982, 78, 1149. F. Habashi, Extractive Metallurgy (Gordon and Breach, New York, 1969), vol. 1. D. Bradbury, M. G. Segal, R. M. Sellers, T. Swan and C. J. Wood, Electric Power Research Institute Report No. EPRI NP-3177 (1983). R L. Parfitt, V. C. Farmer and J. D. Russell, J. Soil Sci., 1977, 28, 29. J. D. Russell, R. L. Parfitt, A. R. Fraser and V. C. Farmer, Nature (London), 1974, 248, 220. R. J. Atkinson, R. L. Parfitt and R. St. C. Smart, J. Chem. Soc., Faraday Trans. I , 1974,70, 1472. R. L. Parfitt, R. J. Atkinson and R. St. C. Smart, Soil. Sci. SOC. Am. Roc., 1975, 39, 837. J. D. Russell, E. Paterson, A. R. Fraser and V.C. Farmer, J. Chem. Soc., Faraday Trans. I , 1975, 71, 1623. R. L. Parfitt, J. D. Russell and V. C. Farmer, J. Chem. Soc., Faraday Trans. I , 1976, 72, 1082. R. L. Parfitt and R. St. C. Smart, J. Chem. SOC., Faraday Trans. I , 1977, 73, 796. M. G. Segal and T. Swan, in Water Chemistry of Nuclear Reactor Systems 3 (British Nuclear Energy Society, London, 1983), p. 187. W. J. Williams, unpublished data. S. Bennett, D. Bradbury, B. Daniel, R. M. Sellers, M. G. Segal and T. Swan, in Water Chemistry of Nuclear Reactor Systems 3 (British Nuclear Energy Society, London, 1983), p. 36 1. ( a ) ChemicaZ Society SpeciaZ Publication No. 17 (The Chemical Society, London, 1964); ( b ) Chemical Society Special Publication No. 25 (The Chemical Society, London, 1971).E.g. H-C. Chang, T. W. Healy and E. MatijeviC, .I. Colloid Interface Sci., 1982, 92, 469. Prof. J. Christoffersen ( University of Copenhagen, Denmark) said: Integrated rate laws are in general not very accurate in use. Could the authors, despite the complexity of their system, apply the differential rate law corresponding to their eqn (3), i.e. d(l - a ) - 3 kobs( 1 - dt or is this not possible for their system? The term (1 - a)2/3 in the above equation indicates that the rate of dissolution is proportional to the surface area of the remaining solid; the rate constant kobs includes a term representing the solution composition. The above equation can hardly be used to take into account that the surface of the solid may become richer in Ni during the dissolution process.Could one apply a rate expression of the type in our paper? eqn ( 5 ) ? If so, do Drs. Sellers and Williams agree that the possible effect of surface enrichment with Ni can to a first approximation be included in the term F( m/ mo)? Dr. R. M. Sellers (C.E.G.B., Berkeley) said: No doubt the differential form of the rate equation could be used, but it does not offer any particular advantages over the more simply applied integrated form. Similarly eqn ( 5 ) in Prof. Chris- toffersen's paper could also be used. His suggestion that surface enrichment in Ni could, to a first approximation, be included in the term F(rn/rno) is a good one and deserves further investigation.GENERAL DISCUSSION 305 Dr. W. J. Williams (C.E.G. B., Berkeley) said: In addition to Dr.Sellers' com- ments on eqn (3), it is also worthwhile re-emphasising the possible stages involved in heterogeneous reactions, uiz.: (i) diffusion of reactants to the surface, (ii) adsorption of reactants on the surface, (iii) reaction at the surface to yield adsorbed product, (iv) desorption of product from the surface and (v) diffusion of product away from the surface. Any one of these steps may be rate controlling. We have found in most of our systems the reaction rate is consistent with a control step under category (iii). Thus, provided the reactant concentrations are kept in excess and thus essentially constant, the rate will be directly proportional to the instan- taneous surface area of the particle provided also that the concentration of reactive sites per unit area of surface remains constant as the particle dissolves; hence dR --- - kA.dt Eqn (3) follows directly from this expression if the loss of mass by dissolution is translated into the increase of product concentration in the dissolving media. The 1/3 order is independent of the shape of the particles; it is a natural corollary of solid volume being dissolved through a surface-controlled process. Presumably in the systems studied by Dr. Coller, Mr. Cheng and Prof. Chris- toffersen, steps (iv) and (v) play an increasingly important role as implied by the incorporation of the (C, - C)" term. Mr. A. M. Creeth (Imperial College, London) said: This contribution links the ideas of Dr. Spiro's paper with the kinetics of dissolution of solids, discussed in previous papers.Linear free-energy relationships (LFER) can be derived for the diffusion- controlled dissolution of solids. The situation is depicted in fig. 1, where cs is the concentration of A at the surface, cB that in the bulk and xD is the diffusion-layer thickness. ' A X Fig. 1. Concentration profile of solute for the diff usion-controlled dissolution of solids.306 GENERAL DISCUSSION If the solid A is dissolving so quickly that, at the surface, solid A is in equilibrium with dissolved A, then cs is the solubility of A and we may write k, A(s) Ft: A(aq) - A(aq). Applying Fick's first law for the flux J (mol m-2 s-') of A(aq) away from the surface J = D( Cs - C , ) / X , . Initially cB = 0, whereupon dCB ADc, - d t x,V where A is here the area of the solid surface exposed to the liquid, V is the volume of the liquid phase and D is the diffusion coefficient of A in solution.For a molecular solid cs= K,; thus dc, ADK, ---- - kobs - d t x,V where k&s is the initial observed zero-order rate constant. Despite being diffusion- controlled, the rate is proportional to the concentration of A at the surface and hence to the equilibrium constant. Taking logarithms This is an LFER with slope a = 1. A plot of log kobs against log K, will yield a straight line with intercept log (AD/xD V). For fixed hydrodynamic conditions comparisons between compounds may be made. These are meaningful because diffusion coefficients vary by at most a factor of 10, whereas the solubility constants vary by several powers of 10. An electrolyte produces slightly more complicated equations.Consider the following salt, which is completely dissociated in solution: AaBb aAzA+bBzB This leads to In this case the slope a equals I/( a + b). controlled are Examples of solids for which dissolution has been found to be diffusion- (1) AgC1,'.2 K, = 1.77 x lo-'' mo12 dm-6 (2) CaSO, in the gypsum (3) Ca( H2P04)2.H20,4 K , = 9 x K , = 4 x lop5 mo12 drn-6 and mo13 dm-9. The experimental results are not sufficiently detailed to allow a graph to be plotted.307 GENERAL DISCUSSION 1% Ks Fig. 2. Plot of log k against log K,. One interesting aspect of this situation is the absence of a plateau region in the plot of log k against log K , (fig. 2). This is unlike the cases mentioned by Dr. Spiro because here there is only one type of diffusion control.‘ A. L. Jones, Trans. Faraday SOC., 1963, 59, 2355. ’ Stability Constants ofMetal Ion Complexes, ed. L. G. Sillkn and A. E. Martell (Special Publication, The Chemical Society, London, 1964). A. F. M. Barton and N . M. Wilde, Trans. Faraday SOC., 1971, 67, 3590. A. F. M. Barton and S. R. McConnel, J. Chem. SOC., Faraday Trans. I , 1974,70,2355. Dr. D. Leahy ( I C I Pharmaceuticals, MacclesJield) said: I would like to make a few comments as an addendum to Dr. Spiro’s interesting discussion of LFER in interfacial kinetics. Exactly the same kind of Bronsted-Eigen relationship described by Dr. Spiro (fig. 1 in his paper) exists between the partitioning rates and equilibria of organic molecules between water and organic solvents. Similarly, the diffusion-controlled rate plateau can be raised by stirring (fig.4). More interestingly, work by Brodin in which diffusion across unstirred layers is eliminated has shown a linear log-log relationship between intrinsic water/ oil partitioning rate and equilibrium with slopes around 0.9. This suggests that the solute has lost most of its aqueous solvation shell at the transition state, a quite reasonable and predictable result. ’ J T. M. van de Waterbeemd, in Quantitative Approaches to Drug Design, ed. J. C . Dearden (Elsevier, ’ ( a ) A. Brodin and M. I. Nilsson, Acta Pharm. Suecica, 1973, 10, 187; ( b ) A. Brodin, Acta Pharm. Amsterdam, 1983), p. 183. Suecica, 1974, 11, 141. Dr. M. Spiro (Imperial College, London) (partly communicated): I am grateful to Dr.Leahy and to Mi-. Creeth for pointing out further applications of linear free-energy relationships to interfacial reactions in solution. I had in fact referred briefly in my paper to van de Waterbeemd’s work on interfacial drug transfer for which, as Dr. Leahy has pointed out, the plots of log(rate) against log(partition coefficient, P ) correspond in shape to those for the heterogeneous catalysis of redox308 GENERAL DISCUSSION reactions between irreversible couples in my fig. 4. The work of Brodin, however, is new to me: it illustrates how LFER can provide structural insights into interfacial processes. It might be worth adding that the log P values themselves possess an additive-constitutive nature and can be correlated with Hammett and Taft para- meters.' Mr. Creeth's interesting contribution concerning the dissolution rates of solids that dissolve rapidly has brought to light another set of diffusion-controlled inter- facial processes whose LFER is of finite slope. In fact, perusal of several of the papers in this Discussion shows that analogous LFER can be written for certain other types of interfacial process. Thus it follows from eqn (20) of Savage et al. and eqn (12) of House et al. that for transport-controlled gas dissolution in liquids In J = l n (Dp/S) +In H where J is the initial mass-transfer flux (mol m-* s-'), p the partial pressure of the gas over the liquid, S the effective thickness of the boundary layer and H the Henry's law constant or solubility coefficient. For different gases under similar flow condi- tions, plots of In J should therefore vary linearly with In H, the slope a being unity. The term In (Dp/ S) should remain relatively constant because, following Mr. Creeth's argument, the values of D will vary much less than will the values of H. The kinetics of various transport-controlled chemical reactions at liquid/liquid interfaces can also lead to LFER with a = 1. For example, by an extension of eqn (10) in the paper by Crooks and Chisholm, one can obtain In J=ln(Dc/S)+ln P. In this situation the rate-determining step is the diffusion through the Nernst layer of the reactant (toluene) from the organic phase, where its concentration is c, into the aqueous phase where it reacts (is nitrated); P is the partition coefficient caq/corg. The rates of different organic substrates reacting under similar physical conditions should therefore again fit a LFER. Although this linear log(rate) against log P relation formally resembles that for surface-controlled drug transfer between phases, the different underlying mechanisms are revealed experimentally by the effect of stirring and numerically by the value of the slope a. It is now clear that the rates of many types of interfacial process will fit LFER with finite slopes. These processes may be catalytic, chemical or transfer in nature. Provided they are fast enough to have become diffusion-controlled, the values of a are determined by the stoichiometry of the process and are frequently unity. This behaviour may be contrasted with that of diff usion-controlled homogeneous reac- tions, which exhibit log(rate) against log K plots of zero slope. ' T. Fujita, in Progress in Physical Organic Chemistry, ed. R. W. Taft (Wiley-Interscience, New York, 1983), vol. 14, p. 75.

ISSN:0301-7249    

DOI:10.1039/DC9847700287

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1984, 77, 309-3 12 Closing Remarks BY M. SPIRO Department of Chemistry, Imperial College of Science and Technology, London SW7 2AY Scientists working on liquid/liquid extraction processes normally gather together in little groups of their own, as do those concerned with drug transfer, those studying the dissolution of gases, those whose interests lie in the crystallisation and dissolution of solids or in ion exchange and those involved with various catalytic phenomena. It was the aim of the organisers of this Discussion to bring them together. We hoped that this would highlight the common ground and also allow new experimental techniques and new theoretical ideas to be more freely disseminated. One criterion by which we can judge the success of this aim is by the institutions from which the 52 authors have come.Fewer than half worked in departments of chemistry; the others came from industry, various kinds of research institute, departments of pharmacy and departments of chemical engineering or chemical technology. The participants at the meeting have equally varied backgrounds, with over 36% from overseas. I believe that the resulting interactions have been both stimulating and fruitful, not only at the formal discussion sessions but also in the informal gatherings in between. Turning to the scientific content of the papers, we have seen that reactions occurring at or through interfaces may be kinetically controlled by one of three steps: transport through the diffusion layer or layers, reaction in one of the bulk phases or in a reaction layer, or reaction at the interface itself. Examples of all three types have been given in this Discussion, with frequent observations of intermediate control.Since diffusion is always to be reckoned with, it must be either identified as the rate-controlling step or else extrapolated out to yield surface or bulk rate constants. Several different designs of cell have been employed for this purpose and, as someone who does not work in this field, I have been struck by the close resemblance between them and the standard methods of determining diffusion coefficients. Thus cells in which the bulk phases on each side of the interface are stirred, such as the Lewis cell and its variants, bear a likeness to the Stokes diaphragm cell.’ The Albery rotating diffusion cell is clearly based on two rotating discs to which the Levich equation applies.The rising- or falling-drop method2 shows a superficial similarity to the dropping mercury electrode, although the hydrodynamics of the former are far less well under~tood.~ Laminar jets,too, have been employed both to study interfacial reactions4 and to measure diffusion coefficient^.^ In this meeting Dr. Guy has described a radiotracer capillary technique which is modelled on the idea of Anderson and Saddington6 for measuring self- diffusion coefficients. This line of thought suggests the possibility of applying other diffusion methods (recently described in considerable detail by Tyrrell and Harris’) to interfacial kinetics. Optical methods involving interference patterns, for example, appear not to have been tried except in the study of Marangoni effects.Moreover, I believe the time has come for us to heed Prof. Nitsch’s plea for a proper comparison between different types of apparatus, particularly between those employing free and those employing supported interfaces. He has suggested the zinc/dithizone system as a suitable one for normalising procedures because it exhibits both transport and 3093 10 CLOSING REMARKS chemical steps and shows no interfacial instabilities. Certainly the few comparisons available so far do not all agree with the *lo% claimed by the proponents of the various techniques, and I therefore hope that his proposal will be taken up. In many practical situations, transport processes at interfaces are speeded up by mechanical instabilities-the Marangoni effects.We have all been impressed by the beautiful pictures of these in several of the papers and especially by the remarkable phenomena in the film shown by Dr. Nakache. Prof. Meares has rightly urged experimenters to be aware of these effects and drawn attention to the theories of Drs. Sanfeld and Steinchen which should allow us to predict under what conditions such instabilities can be avoided or encouraged. However, it is still not clear to what extent Marangoni effects will manifest themselves in various kinds of supported liquid/liquid interface, and experiments designed to test this point would be wel- come. It is a pity that Marangoni phenomena are rarely treated in standard courses of chemistry although chemical engineers do learn about them.One chemical engineer who has made significant contributions in this area is Prof. Sawistowski, who was also a member of our organising committee. You will all share our regret that due to illness he was unable to be present with us. Reactions become completely transport controlled when the chemical or surface step is sufficiently fast. This can occur when the interfacial reaction has come to equilibrium (as in some heterogeneously catalysed reactions) or when the surface concentrations in one phase are in equilibrium with the bulk concentrations in the other phase (which we have learnt happens with C 0 2 transfer into certain solutions, or the dissolution of soluble solids). The resulting rates of reaction then exhibit the interesting property of being a function of thermodynamic and hydrodynamic parameters only.These rates can therefore be completely calculated from ancillary data provided the flow conditions are sufficiently well defined. All the relevant examples at this meeting have referred to transport control in the liquid phase, but this is not a necessary restriction. Liquid/solid systems showing transport control in the solid phase are met with in extraction processes. Here it has been shown that the rate-determining step is frequently the diffusion of the soluble material from the interior of the plant product to its periphery, as in the extraction of caffeine from swollen coffee beans to make decaffeinated coffee.' The rate then depends only on the diffusion coefficient within the bean and on geometrical and thermody- namic properties.' Several authors have reported rates which are completely surface-controlled or else they were able to determine such rates by suitably extrapolating out the transport contributions. These rates exhibit the expected sensitivity to steric factors.This aspect was beautifully illustrated in the pioneering work of Alexander and coworkers" for reactions taking place at the water/air interface. Compression of films of substrate (e.g. ethyl palmitate) at the surface forced the molecules to pack more tightly, and their changed orientations produced a decrease in the rate of attack by ions (e.g. OH-) in the water phase. The deliberate introduction of chemi- cally inert surfactant species into the films also affected the rates markedly, especially if these species were charged." In several of the papers presented at this Discussion we have seen similar features.The important effect of surfactants at liquid/liquid interfaces has been mentioned a number of times and this aspect deserves further study, Adsorption of foreign ions or molecules was also found to affect the kinetics of exchange and dissolution processes at solid/liquid interfaces, and Cheng, Coller and Powell have made progress in understanding this phenomenon by carrying our Monte Carlo simulations. There can be no doubt, either, that spatial requirements both on and within the structure of the solid play an important role, as severalM. SPIRO 31 1 contributors have pointed out.We must remember that as yet we cannot predict the rate constants of surface-controlled reactions although we do understand trans- port processes sufficiently well to predict diff usion-controlled rates in an appropri- ately designed cell. This brings me to the question of specialist physicochemical techniques that have been applied in these researches. Take electrochemical ones. The electroanalytical methods employed include conductance, ion-selective electrodes and the pH-stat, as well as an ingenious arc-ring electrode affixed onto the disc of a rotating diffusion cell. The structure of the liquid/liquid interface itself has been probed by cyclic voltammetry and electrical pulse methods, an activity in which the Prague school has been prominent.Interfacial potentials will particularly affect the rates of ionic interfacial reactions. Current-voltage curves at metal electrodes, moreover, have allowed us to predict the catalytic effect of the metal on redox reactions in solution. However, if electrochemical techniques, and also radiochemical ones, have been widely used, the same cannot be said for spectroscopic ones. This is rather surprising. Nowadays more and more spectroscopic probes are being turned on to catalyst and electrode surfaces to study their own structure and that of species adsorbed on them, yet in this Discussion such investigative means have rarely been mentioned except in connection with Marangoni studies. Perhaps there is a lesson here for us. Moving from techniques to systems one cannot help noticing the emphasis in this Discussion on geochemical and mineral systems.Metal extraction, sa!f and gas dissolution, and to a lesser extent drug transfer, have clearly been the majur processes of interest. Only one paper, that of Crooks and Chisholm, deals with an organic chemical reaction. Nevertheless, the experimental methods and theories so lucidly described by various contributors should apply also to other types of interfacial process, such as interfacial polymerisation and phase-transfer catalysis. The last mentioned, in particular, has proved of increasing utility to practical synthetic chemists but has received less than its fair share of attention from physical chemists. Finally, I would like to draw your attention to some other broader aspects. Interfacial reactions, whether transfer or chemical in nature, display many features in common with catalytic processes that are either truly heterogeneous or micro- heterogeneous.By the latter I mean reactions at dissolved entities like enzymes or micelles, which are so large in comparison with substrate molecules that they act as if they were part of another phase. All these processes, transfer or chemical or catalytic, occur at or through an interface of limited area and therefore display saturation phenomena. These have several times been mentioned here. Moreover, the reacting species must compete for sites at the interface with other reactants, with products, with solvent molecules and with impurity species. The presence of the latter may render reproducibility more difficult and can lead to poisoning or blocking of the interface.The effect of surfactants, already referred to, is particularly important in this respect. Another consequence of the physical resemblance between all interfacial processes is the strikingly similar form of many of the resulting rate equations. Once any transport contributions have been extrapolated out or removed by use of sufficiently strong forced convection, we find repeatedly equations of the Langmuir type: 1 1 6 - +- vat where v is the rate or flux and c the concentration of a reactant. Such equations are found not only in the heterogeneous catalysis of gas reactions but also with micellar and enzyme catalysis, and indeed a derivative of the Michaelis-Menten _-_312 GENERAL DISCUSSION equation was specifically named by Hadgraft et al.in their analysis of the flux of dye transferred across a liquid membrane. At every session the discussion has been lively, frequently illuminating, and at times controversial. The question as to what is meant by an interfacial reaction provoked particularly vigorous comment. Since at one stage the argument was described as one of semantics, it reminded me of an apt little verse by my favourite poet, Ogden Nash: I give you now Professor Twist, A conscientious scientist. Trustees exclaimed, ‘He never bungles!’ And sent him off to distant jungles. Camped on a tropic riverside, One day he missed his loving bride. She had, the guide informed him later, Been eaten by an alligator. Professor Twist could not but smile. ‘You mean,’ he said ‘a crocodile’. This seems a fitting point on which to end, for we shall all now be swallowed up by the outside world on leaving this comfortable conference centre. Dr. Aveyard and his helpers at Hull University deserve our grateful thanks for their hospitality; their efforts have played a significant role in making this Discussion such a successful one. ’ R. H. Stokes, J. Am. Chem. SOC., 1950, 72, 763. ’ W. Nitsch, Ber. Bunsenges. Phys. Chem., 1965, 69, 884. R. J. Whewell, M. A. Hughes and C . Hanson, J. Inorg. Nucl. Chem., 1975, 37, 2303. C . Hanson and H. A. M. Ismail, Chem. Eng. Sci., 1977,32, 775. C . Hanson and H. A. M. Ismail, J. Appl. Chem. Biochem., 1976, 26, I 1 1 . J. S. Anderson and K. Saddington, J. Chem. SOC., 1949, S 381. H. J. V. Tyrrell and K. R. Harris, Diffusion in Liquids (Butterworths, London, 1984), chap. 5. B. Bichsel, Food Chem., 1979,4, 53. M. Spiro and R. M. Selwood, J. Sci. Food Agric., 1984, 35, 915. and E. K. Rideal, Proc. R. SOC. London, Ser. A , 1937, 163, 70. l o A. E. Alexander and J. H. Schulman, Proc. R. SOC. London, Ser. A, 1937,161, 115; A. E. Alexander ‘ I J. T. Davies, Ado. Catal., 1954, 6, 1.

ISSN:0301-7249    

DOI:10.1039/DC9847700309

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

INDEX OF NAMES* Albery, W. J., 53, 139, 144, 148, 151 Amantea, M., 127 Astarita, G., 17, 48 Barker, N., 97 Binsma, J. J. M., 257, 297, 299, 300, 301 Cheng, V. K., 51,243,290,293,295,296,298,301 Chisholm, J. M., 105 'Christoff ersen, J., 235,288,289,29 1,293,295,296, Christoffersen, M. R., 235, 288, 289, 291, 295 Choudhery, R. A., 53 Coller, B. A. W., 243, 288, 296, 297, 298, 299 Creeth, A. M., 305 Crooks, J. E., 105, 151 Dickel, G., 157, 217 Du, G., 209 Dupeyrat, M., 189, 218 Fisk, P. R., 53, 151 Flambard, A. R., 300 Gu, Z. M., 67 Guy, R. H., 127 Hadgraft, J., 97, 149, 150 Hinz, R. S., 127 Homolka, D., 197 House, W. A., 33, 47, 49, 50, 51, 289, 297, 301 Howard, J. R., 33 Hughes, M. A., 75, 139, 146, 147, 148 Ikeda, T., 223 Kolar, Z., 257 Koryta, J., 209, 221 300, 304 Kreevoy, M. M., 140, 147, 148 Li, N. N., 67 Leahy, D., 149, 307 Linde, H., 47, 181, 218 MareEek, V., 197 Meares, P., 7, 139, 217 Nitsch, W., 85, 147 Nakache, E., 189, 218, 219, 221 Noble, R. D., 143, 146 Powell, J. L., 243 Robinson, B. H., 140, 149, 155, 287 Rod, V., 75 Ruth, W., 209 Samec, Z., 197, 219, 220 Sanfeld, A., 140, 169 Sartori, G., 17, 288 Sasaki, M., 223 Savage, D. W., 17 Sellers, R. M., 265, 292, 294, 302, 304 Skirrow, G., 33 Spiro, M., 50, 150, 219, 220, 275, 307, 309 Steinchen, A., 140, 148, 169 Tondre, C., 47, 115, 143, 151, 155, 219 Vanisek, P., 209 Vignes-Adler, M., 189, 2 18 Wasan, D. T., 67 Williams, W. J., 265, 305 Wotton, P. K., 97 Xenakis, A., 115 Yasunaga, T., 223, 287, 288 * The page numbers in heavy type indicate papers submitted for discussion. 313

ISSN:0301-7249    

DOI:10.1039/DC9847700313

出版商:RSC    

年代:1984

数据来源: RSC