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ION-EXCHANGE PROPERTIES OF KAOLINITE SLURRIES
From the last two equations, by usingf as a parameter, the rate dM/dt can be found as a function of conversion. The most interesting case arises for r>>l, Le., short zips occurring in long chains. We obtain the following solutions, now valid for both monomer radical disproportionation and evaporation, by making the appropriate approximations in equations 57 and > 1 f = f(0)exp ( - k i ” t / 2 ) (60) ki‘ = 0 In A!l =: 2f(O)(exp ( - k i ” t / 4 )
- l)/r
(61)
The last equation implies that the polymer never degrades completely, but asymptotically approaches a fractional weiglht of
M , = exp(-2f(O)/r)
29
1 - [2f(O)/r]
(62)
While equation 60 shows that the fraction f of double-bonded ends decays with first-order kinetics, the mass decay implied by (61) obeys a remarkable law, probably new to chemical kinetics. Here In M instead of 211 decays exponentially with time, ie., the process behaves like a first-order reaction in which the rate “constant” itself decreases with time according to firsborder kinetics. Nevertheless, the plot according to (61) of dM/dt against M mould still be practically a straight line (joining the points M = 1, dM/dt = (dM/dt)o and M = exp(-2f(O)/r), dM/dt = 0.)11i12 (11) N. Graesie, “Chemistry of High Polymer Degradation Pmceases,” Butterwortha, London, 1956, p. 45.
(12) M. H. Mackay and H. 323 (1949).
W. Melville,
Trans. Fatadag SOC.,46,
ION-:EXCHAKGE PROPERTIES OF KAOLINITE SLURRIES’ BY MURRYA. T A M E RAXD P HEKRYC. THO MAS^^ Contrihtion from the Department of Chemistry, Yak University Received M a y IS, 1969
The ion-exchange properties of kaolinite have been studied by use of isotopic exchange reactions on continuously stirred slurries of the material in a fluidized bed type of arrangement. The results show that the cation and anion exchange capacities of the clay vary with the concentration and type of electrolyte used. An isotherm is presented which illustrates the specificity of kaolinite for cesium over sodium exchange. The slow attainment of ion-exchange capacity equilibrium and other unusual roperties are explained by the changing state of aggregation of the clay particles. Flocculation removes both anion a n f cation exchange sites from availability and thus reduces the observed ion-exchange capacity in the more dilute solutions.
In earlier work:’ we have been concerned with the ion-exchange behavior of clay minerals in which lattice replacements produce the sites against which the ions are held. In such minerals the composition of the silicate “backbone” is correspondingly complex, as in the minerals montmorillonite and attapulgite. Kaolinite, however, is a very nearly pure aluminosilicate. Its relatively stable 1-1 structure favors the survival of crystals, large for clay minerals, which expose a relatively small surface. The cation exchange capacity of kaolinite is a factor of fifty or a hundred lower than that of montmorillonite. It is not far from equal to the anion-exchange capacity and is certainly not primarily due to substitutions in the lattice. Perhaps the principal result of the present work is a demonstration of conditions under which there are relations between the amounts of anion and cation sorbed on kaolin. The low values of the exchange capacities of kaolinite make entirely impractical the technique
of the “equilibrium column” for investigating these quantities. Batch equilibrations in the study of ion-exchange equilibria are quite successful with materials of high capacity which are easily separated from the solutions by simple drainage or centrifugation. However, errors increase rapidly as capacity decreases; and with kaolin, which forms difficultly dispersible masses on centrifugation, the batch method is quite unsatisfactory. Either of these methods must necessarily give results obscured by the uncertain state of aggregation of the clay. We have therefore turned to a method of the “fluidized bed” in which we measure the effluent composition of solutions passing through a continuously stirred suspension of the clay mineral. It was found possible to maintain the clay in a constant or only slowly varying state of aggregation and so to study rapid ion-exchange effects as very slow changes in aggregation took place. Experimental
(1) Contribution No. 1581 from the Sterling Chemistry Laboratory of Yale University, based on the dissertation submitted t o the Faculty of the Graduate School b y Murry A. Tamers in partial fulfillment of the requirementa for the dejzree of Doctor of Philoaophy. (2) (a) Department of Chemistry, University of Texas, Austin. Texas. (h) Department, of Chemistry, University of North Carolina, Chapel Hill, North Carolina. (3) C. N. Merriam and H. C. Thomas, J . Chem. Phys., 24, 993 (1956).
The apparatus finally adopted consisted of cylindrical Pyrex reaction vessels two inches in diameter and having hold-up volumes of approximately one hundred ml. The reactors have short necks about one-half inch in diameter. The solution enters the bottom of a vessel through a one-way glass ball valve, passes a magnetic stirrer and is mixed with the suspension of clay. The stirring speed and the rate of flow of the solution are adjusted to maintain the level of the suspension not far below the neck of the container. The
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MURRYA. TAMERS AND HEHRY c. THOMAS
Vol. 64
ml. Thus only large deviations in the measured values of Q from final equilibrium values would manifest themselves as . 1.8 changes in the slopes of these lines. Actually values of Q .-8a were not determined from slopes of these lines; rather the contents of the reaction vessel were brought to the desired 3 1.6 composition by passing 2 liters of labeled solution over the d clay during a period of about 8 hr. and the total retention, A 1.4 bb vh Q/c, of the reaction vessel then determined after a 0 similar elution of the tracer with 2 liters of untraced solution E: 1.2 and by a measurement of the activity of the entire eluate. -2 In all cases approximately twenty times the equivalent v 1.0 volume of the reactor was passed before making measurements, and the clay was treated with a t least 10 liters of solu$ 0.8 tion of the same concentration before the actual runs were started. Ideally the exchanges should have been within 0.1% of completion. In an experiment designed t o confirm 6 12 18 24 30 36 42 48 54 this point, a sample was equilibrated with a total of 4 liters of 0.001 N Cs( 137)Cl. The isotopic exchange was carried out Days. Fig. 1.-Approach to cation-exchange capacity equilibrium with 1.8 liters 0.001 N CsC1. The eluate showed an activity corresponding to 2.6 meq. Cs/100 g. clay. An additional 2 of an agitated kaolinite suspension in 0.0005 X CsC1. liters of 0.001 A- CsCl was passed, and after evaporation to small volume, an activity corresponding to 0.008 meq./100 g. was found. The clay then was boiled for 2 hr. with 0.05 N CsC1. The activity found in this solution corresponded to less than 0.001 meq./100 g. clay. It seems safe to suppose that these elutions actually went to within 0.4% of completion. Standard counting procedures with glass jacketed solution counters were employed, all significant corrections being applied. The isotopes used were C136,NaZ2and Cs137. In the cme of the cesium tracer the Geiger tubes were filled and allowed to stand for 20 minutes before counting t o ensure radioactive equilibrium with Ba137m. The C136 as obtained was of high specific activity but contained some inactive chloride, corrections for which were made in preparing the 1 2 3 4 5 6 7 8 9 1 0 solutions. Kaolinite from the Lamar Pit, Bath, South Carolina,4 was l o 3 C (moles salt/l.). Fig. 2.-Dependence of the cation-exchange capacity of used in all the work. The clay was prrpared merely by kaolinite suspensions on the concentration of the equilibrat- grinding to pass a 100 mesh screen and drying a t room temperature under reduced pressure. This particularly pure ing solution: curve A, SaCl; curve B, CsC1. clay mineral has been characterized by the American Petrosolution passes out through a compact glass wool filter filling leum Institute under Research Project KO.49 and denoted the neck of the vessel. It is possible with this e uipment to as Sample 5. Undoubtedly the principal error in these experiments maintain a relatively sharp slurry level, the J a y settling against the flow of the solution. A small amount of kaolinite stems from the necessity of subtracting the relatively large gradually collects in the filter and increasingly obstructs the hold-up volume of the reaction vessel from the total retenflow of the solution. From time to time this obstruction is tion. The effects of errors in counting and in measuring Vh depend on the conditions of the experiments and amount washed out by a brief forced backward flow of the eluate. In this operation the ball valve maintains the slurry in the to 5-10y0 in Q. All other errors are negligible by comparireactor; the liquid level momentarily rises in a small air son. Cation- and Anion-exchange Capacities of Kaolinite.reservoir provided a t the top of the vessel. On return to normal operation the liquid content of the apparatus returns The most significant advantage of the method of investigato its original volume (to f O.l%), a necessity in the treat- tion just described is exhibited in the direct confirmation that with kaolinite the approach to true chemical equilibment of the results. By a sufficiently long preliminary elution, the clay in the rium vith a solution is very slow. We have shown that reaction vessel is brought to ionic equilibrium with the flow- isotopic equilibration between a solution and a suspension of ing solution. This equilibrium is studied by measurements the clay (in its "momentary" state) is relatively rapid. of the distribution of isotopic (radioactive) tracers between JThen, however, a sample of the clay is maintained in a nearly steady state of suspension in a given solution over a solution and clay. If we suppose that isotopic exchange between the solution long period and intermittently subjected to isotopic rxand the suspended solid is rapid, i . e . , complete in a time short change, the result illustrated in Fig. 1 is obtained. Hrre it compared to the residence time of the solution in the reaction is seen that the cesium content of the clay, continuously in contact with a 0.0005 S solution of CsC1, steadily decreases vessels, then for a solution carrying tracer into an initially over a period of nearly two months and finally approaches a full reaction vessel a t chemical equilibrium we have constant value for a given state of suspension in the solution. - log ( I - s/e,) = 2.30v/(vh - Q / C ) In Fig. 2 are given the final equilibrium values, based on two In this equation 6/60 is the ratio of effluent to input counting months suspension with intermittent elutions, of the total rate when a volume V of effluent has been passed in; Vh is cation capacity of kaolinite in solutions of cesium chloride the hold-up volume of the reaction vessel; Q the number of and of sodium chloride of different concentrations. It apmilliequivalents of exchange capacity associated with thc pears that thrre are relations between the cation caparitics clay in the vessel, and c is the concentration of the solution. and the ronccntr:ttions of the ions in solution, differrnt for The value of Vih was determined by weighing after the reitc- the two ionb. In these experiments the anion raparitirs wn' liken ibc tion vessel had been filled to marks on the inlet and outlet tubes. Evidently for small values of Q and relatively higl? measured. The ion capacities for a partirular sample were values of c, errors in the determinations of Vh have significant measured within two days of each other by making three isoeffects on the determination of Q. Many of these isotopic topic exchanges, one with the radioactive cation, one with elutions were carried out and the activity of the effluents radioactive rhloride, the third again with traced cation. followed up to0/Oo as high as0.85. Plots of -log(l - 6/61) In this short time the total exchange capacities changed but 2)s. V give excellent straight lines. Such results cannot, hcm- little, and v e assume that n-e get nenrlr corresponding value.. ever, be taken as proof that we actually have an equilibrium of the tmo cnpacitics. In the case of the experiments nith single stage reactor. Vh generally was higher than Q/c: (4) From Ward's Xatural Science Establiqhment. Rochester, Kew v h was always near 100 ml. and Q/c varied widely according to the conditions of the experiment, from about 30 mi. to 90 York.
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ION-EXCHANGE PROPERTIES OF KAOLIXITE SLURRIES
sodium solutions, curve A in Fig. 3, five out of six of the experiments were done at true equilibrium, as evidenced by unchanging exchange capacity. I n the following we shall refer t o this condition as one of “capacity equilibrium.” The single point lying off the curve was determined before capacity equilibrium had been reached. Curve B in Fig. 3 gives the results with solutions of cesium chloride, the points marked by flagged symbols referring t o capacity equilibrium. For the cesium solution the data suggest that the relation between anion and cation content is independent of the degree of approach t o full equilibrium. I n the sodium solutions it appears that this may not be true. The point, however, cannot be considered as established by these data. Cesium-Sodium Exchange Isotherms.-Several series of experiments were made to investigate the nature of the cationexchange isotherms for cesium and sodium, the procedure being essentially the same a$ that outlined above. The clay suspension was eluted with a mixed solution of the desired compositions t o bring it into ionic equilibrium with this solution. In each series of compositions the total concentration was maintained constant (O.QO1, 0.002, 0.003 N ) . In the series a t concentration 0.002 N the clay was also in rapacity equilibrium. The composition of the clay was determined by isotopic exchange with cesium, followed by isotopic exchange with sodium. The procedure thus measured both composition and total cation capacity. In some cases the results were checked by a repetition of the cesium exchange. In most of these cases very little change in cesium content was found, and these checks were not carried out in the series a t capacity equilibrium. Although the results of all these experiments show qualitatively the high selectivity of the clay for cesium, especially a t low cesium content, only in the case done at total capacity equilibrium is there discernible a smooth relation between the total cation capacity and the ceaium content of the clay. This relation is shown as curve A in Fig. 4; the single point which lies well off the curve belongs to the only experiment in this series in which the clay Waf3 not a t capacity equilibrium. Curve B in Fig. 4 gives the exchange isotherm for this case. The isotherms for those series not a t capacity equilibrium lie close to curve B, Fig. 4; their quantitative meaning is, however, obscured by the lack of full equilibrium, and we omit the results.
I
I
I
31 I
I
I
I
1 2 3 4 5 Meq. cation/100 g. kaolinite. Fig. 3.-Relations between cation- and anion-exchange capacity of kaolinite in suspension: curve A, NaC1; curve B, CsCl. cationic capacity (meq./100 g. kaolinite).
Discussion The unusual ion-exchange properties of kaolinite can be explained on the supposition that the exchange behavior depends upon the degree of flocculation of the clay. According to van 01phen6 the edges of the crystallites of kaolin are I positively charged and open three-dimensional 0.2 0.4 0.6 0.8 networks are formed when these sites are asSoln. fraction of Cs. sociated with negative sites on other particles. Fig. 4.-Exchange sorption Cs-Na on kaolinite: curve Schofield and E;amson6 advance this idea by sug- A, Cs content us. total cation-exchange capacity; curve B, gesting that the flocculation is due to association Cs-Na exchange isotherm. between positive edges and negative cleavage faces. These authors go further and suggest that the edge- more rapidly with concentration. (An analogous to-face flocculation occurs only in dilute solutions, effect is observed in precipitation titrations.) that the effect of higher concentrations of elec- Additional confirmation of this interpretation is trolyte is to decrease this type of flocculation, and, found in the character of the relations between with some electrolytes, to produce another type of cation and anion capacity, Fig. 3. The capacities aggregation in which the crystallites are associated rise together, corresponding to a simultaneous face-to-face. release by deflocculation of positive and negative Our results are in complete qualitative agreement sites. The fact that neither with cesium nor with with these ideas. The slow approach to capacity sodium is a simple 1-1 relation obtained requires equilibrium, Fig. 1, is easily understandable in further explanation. The linear relation obtained terms of a slow adjustment in the degree of floc- for cesium would indeed be the result of the deculation. The Lncrease in cation capacity with con- flocculation of edge-to-face aggregates if some centration, Fig 2, corresponds to a decrease in chloride ion sorbed on the edges were effectively degree of flocculation in which a larger proportion shielded from the solution in the aggregate. The of the sites are made available to exchange. Fur- splitting of such a combination would then inthermore, since cesium is selectively sorbed in pref- crease the anion capacity both by making more erence to sodium the cesium capacity increases sites available and by offering more anions for exchange. We have only to suppose that a con(5) H. van Olphen Disc. Faraday Soe.. 11. 82 (1951). stant proportion of the anions is thus shielded in (6) R. K. Schofield and H. R. Samson, abzd , 18, 135 (1954). t
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MARKP. FREEMAN
the aggregate to obtain the observed relation. I n the case of the sodium chloride solutions the situation is not so simple; a t least two types of shielding would be necessary to explain the results. Some independent evidence for such an explanation is to be found in the work of Schofield and Samson7 who found viscosities of kaolinite suspensions in sodium chloride solution lower than those for potassium chloride, the effect being very large
VOl. 64
indeed. This may be interpreted to mean that a large part of the flocculation in NaCl is face-toface even a t the low concentrations measured (less than 0.01 hf),while the greater viscosity of the KC1 suspensions is due to the bulky edge-to-face aggregates. We may certainly suppose that cesium behaves like potassium, so that the more complex relation between anion and cation uptake in sodium solutions parallels the viscous behavior.
THE QUAKTURI MECHAKICAL CORRECTION FOR THE HIGH TEMPERATURE V A S DER WAALS INTERACTION OF LIGHT GASES AKD SURFACES. A NEW METHOD OF DETERMINING SURFACE AREA BY MARKP. FREEMAN’ Contribution from the Department of Chemzstry, University of California,Berkeley, California Recetved Mau i6, 1969
An experiment is reported in which the exact magnitude of the effect of negative discrete energy levels in the potential energy well for gas-surface interaction is determined. The experiment involves the surface interaction of two kinds of gas molecules differing only in mass (Hz and DI with about 1700 m.* of a low ash charcoal surface) and the interpretation of the data with the high temperature e uation of state for gas-surface interaction as properly modified for an “almost classical” quantum mechanical assembly. auantitative agreement of certain independently obtained parameters indicates that the quantum mechanical equation of state for these light gases is at least as good as the classical equation has been for interpreting data for the heavier gases. Unexpect,ed verification of the 9-3 potential model is apparently found and a new unambiguously defined surface area is discussed.
Introduction The theory of the high temperature interaction2 of gases and solids seems to be surprisingly well supported by experiment. That is, it has been found possible to derive an equation of state for the interaction of gas and surface (after the manner in which one derives the virial equation of state in gas-gas interaction) assuming spherical gas systems (molecules or atoms) and a uniform structureless surface. This equation has been successful in reconciling theory and experiment to within the experimental error for a large number of assemblies, including some that depart rather far from the model.3 At the same time, it is true that the detailed description obtained for the theoretical gas-surface behavior is remarkably indifferent to the exact shape of the assumed potential model, especially the repulsive portion. Furthermore, although the treatment yields a capacity factor Aso (the product of the area A and a collision parameter), there has been no way consistent within the model of obtaining the area. Again, although something can be inferred about the nature of the surface from the classical interpretation, the amount of information one obtains is relatively small. Finally, a very deep potential energy well exists between the individual gas systems and the surface. The very depth of the well ensures a spacing of energy levels that might very well cause a light molecule to interact peculiarly even a t high temperatures which would complicate the interpretation of the parameters obtained by (1) Amrrican Cyanrtmid Company, Rcsearoh Dhision, Stamford, Connecticut. (2) For summary of references see: h1. P. rreeman, THISJOURNAL, 62,723,729 (1958). (3) J. F. IIanlan and M. P. Freeman, Can. J. Chsrn.,Ill, 1575 (1959).
fitting the data to the classical model. That this could be so becomes apparent when one realizes that most of the time that a gas system is interacting with a surface it will simply be oscillat>ingback and forth in the potential well as it travels over the surface. If the gas system is light, only certain amplitudes of this oscillation will be allowed and this could clearly affect the gas-containing capacity of the surface. This quantum effect was first considered by who developed the quantum DeMarcus, et mechanical configuration integral for the 9-3 potential model and fitted some data of Steele and Halsey6 for helium interacting with carbon black to their model. Unfortunately, the temperature dependence for the quantum mechanical configuration integral is not different enough from that for the classical integral to distinguish the better fit by curve fitting. Furthermore, although their theory claimed that a large difference in surface capacity should exist a t any temperature for He interpreted classically or quantum mechanically, when they used the respective parameters Aso together with so obtained through use of the Kirkwood-Mueller formula2 to get the area, they found a difference in surface areas of only 5%. It is clear now that this was because of a cancellation of effects, but it was primarily this fact that first directed the attention of the present author toward exploring this quantum effect. An examination of the equations obtained by DeMarcus, et al., showed that one should be able to obtain some or all of the following advantages (4) W.C. DeMarcas, E. 13. Hopper and A . hl. Allcn, A.E.C. 13111letin K-1222 (1955). (5) W.A. Steele and G. I). Halsey, Jr., J . Chern. P h y s . , 22, 979 (1954).
