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J. Phys. Chem. 1980, 84, 268-272
Heat Capacity Changes in Glass-Forming Aqueous Solutions and the Glass Transltion in Vitreous Water C. A. Angell” and J. C. Tucker Department of Chemistry, Purdue University, West Lafayette, Indlana 47907 (Recelved January 8, 1979; Revised Manuscript Received October 18, 1979) Publication costs asslsted by the Natlonal Science Foundation
The heat capacities of supercooled liquid and glassy states of several aqueous electrolyte systems have been measured by differential scanning calorimetry over a range of compositions and temperatures. The partial molal heat capacity of water in the glass-forming composition range is constant. In the glassy state it is the same as that of ice within experimentaluncertainty. The partial molal heat capacity change at the glass transition for water in these solutions falls in the range 19-25 J mol-’ deg-’ which is much smaller than that observed for vapor-depositedvitreous water. It is suggested that the latter value is possibly in error due to a relaxational contribution, and that the lower heat capacity indicated for water, under conditions in which anomalous fluctuationsare frozen out, permits a thermodynamicconnection between supercooled water and vapor-deposited glassy states of water without requiring improbable or counter-intuitive entropy states.
There is gathering e~idencel-~ that simple liquids become mechanically unstable to specific microscopic fluctuations at temperatures of some tens of degrees below their equilibrium freezing temperatures, and that the impending instabilities are reflected in the (kinetic) homogeneous nucleation phenomenon. In the specific case of water the latter occurs at -42 OC, (TH) and various macroscopic studies have suggested the instability falls a t -45 OC (T,).416.7It is therefore perplexing that studies of glass formation in binary aqueous solution^^*^^^ should predict by extrapolation the existence of a glass transition for water molecule assemfar below the putative instablages at a temperature, Tg, bility point, T,, i.e., at temperatures at which, mechanically as well as thermodynamically,the amorphous phase should be incapable of existing. Even more disturbing, the temperature of this (extrapolated) glass transition, which is almost independent of the type of binary system (ionic or molecular solutes) examined, is identical with the glass transition temperature observedl0V1lfor the “vitreous” or “amorphous solid” water, ASW,12which is obtained via a vapor deposition procedure. It is natural to ask what significance can be attached to the meaning of the term “transition” applied to the behavior of an unstable phase, and it is this question which, at root, is addressed in this paper. However, a preliminary but more immediate question which we address by a plausibility argument concerns the relation of ASW to supercooling liquid water. Both Rice and co-workers12and Angell and co-workers have assumed13that there is a close, essentially continuity-of-states,relationship, while Johari14 has made a contrary suggestion by use of a quantitative argument based on an apparently large increase in heat capacity of ASW observed at 135 K during heating of the deposit.ll The at-first-sight convincing argument is repeated here in the Discussion section where the data presented in this paper will be used to show that the same extrapolations which correctly predict the Tgof ASW, predict a ACp considerably smaller than that one on which the argument is based. While this does not disprove Johari’s contention, it leaves the question of continuity of states open for the time being, and encourages further work on this interesting question. ,6i6
0022-3654/80/2oa4-0268$0 i.oo/o
Experimental Section Materials. The following substances were used as second components in the aqueous solutions of this study: AlC13, Al(N03)3, MgC12, Ca(N0J2, and three acetates (OAc-) NH40Ac, LiOAc, and Mg(OAc)* The salts were all reagent grade hydrates. These were used without further purification because the limits of accuracy for the experiments reported here are determined overwhelmingly by the uncertainties in the differential scanning calorimetry heat capacity measurements. Solutions were made by weighing and spanned the known glass-forming composition range.s Compositions are conveniently specified, for solutions of the present high concentrations, by the water/salt mole ratio, R (molality, m = 55.5/R). Differential Scanning Calorimetry. Heat capacities were determined on approximately 20-mg samples hermetically sealed in aluminum pans. The heat capacities were determined by scans conducted in all cases at 10 deg min-l, using the Perkin-Elmer Model 2 differential scanning calorimeter. Calibration was made with reference to sapphire by standard DSC techniques. Repetitive scans were made in most cases, and reproducibility to f3W in final heat capacities was established. Results Typical results are shown in Figure 1 for the cases of solutions in the aqueous calcium nitrate and magnesium acetate systems. For these systems, which were studied more extensively than the others because of the wealth of other data available, measurements were made from as low as 140 K up to crystallization or room temperature. In other systems the extent of measurements was limited to and in no case higher temperatures in the vicinity of Tp., than that at which recrystallizatlon of the supercooled liquid occurred during heating. The glass transition temperature and the change in heat capacity at the glass transition were defined as shown in Figure 1 for the R = 20 Mg(OAc), solution. Data from Figure 1 have been utilized to construct Figure 2 which contains plots of the isothermal solution heat capacities at 140 K (which in all cases lies below the glass transition temperature) and at 238 and 213 K, temperatures which lie partially in the liquid state. The 140-K 0 1980 American Chemical Society
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The Journal of Physical Chemlstty, Vol. 84, No.
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R Flgure 3. Plots of AC,, per mole of {salt-RH20)at T, vs. composition in R units for various salt water systems.
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Figure 1. Heat capacity-temperatwe relation for solutions in the systems H20, showlng the definition of T,, Ca(N0J2 t H20 and Mg(OAc), and of AC; at Tv C,,values shown are for 1 mol of (s~~.RH,O]where
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R values iare marked on the respective curves.
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Figure 2. Isothermal plots of the normal molar heat capacity [Le., ( C , of Figure 'l)/(l R)]for Ca(NO,), HzO and M ~ ( O A C ) ~H20 liquid and glassy solutions, showlng extrapolations to pure water values.
+
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isotherm, which is dominated in all cases by contributions from vibrational degrees of freedom, extrapolates smoothly to the hieat capacity of ice at vanishing salt content. As expectedl, the extrapolations for the liquid solutions at -35 "C yield values of C, for water far below the observed quantity1, because of the absence, from the glass-forming solutions, of any anomalous component due to fluctuations anticipating crystalli~ation.~J~ Changes in heat capacity at the glass transition for all seven systems of the study are shown as a function of the water/salt ratio, R , in Figure 3. It is observed that, for R > 2, the relationships are in all cases linear implying that each additional mole of water added to the solution increases the heat capacity of a fixed amount. Although essentially constant for each system this quantity varies
+
Flgure 4. (a) T vs. R-',for the salt water systems of thls study, and of L i l H28solutiis, showing extrapolations to pure water value. Small solid points are data from previous studies.' (b) AC,,vs. R-' for solutions of this study showlng extrapolations to pure water value. 'he inset shows C,, Increases at T, observed for different ASW samples by adnbatic calorlmetry studies (from ref 11). The relatively low value of Tocompared to the 139 K directly observed by DTA In ref 10, and also extrapolated in Figure 4a, is due to the long time scale of the adnbatic experiment compared with that of DTA or DSC experiments.
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somewhat from system to system, being greatest for .Al(NO,), and least for LiOAc.
Discussion The implications of Figure 3 are brought out more forcefully if the data are plotted in such a way as to pennit easy extrapolation to zero salt content. This is done in Figure 4 in which both the changes in heat capacities per mole of water at Tgand the temperature Tgat which the change occurs are plotted as a function of R-I. Figure 4a shows that, despite the very different character of the ions interacting with the water molecules in the different solutions, the systems are rather consistent in their prediction of the temperature at which the glass
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transition tends to occur as the salt content is reduced to zero. Excluding the magnesium and aluminum chloride solutions,l6 the value is 139 f 2 K, which is the same as that observed for the vapor-deposited ASW when observed at the same heating rate.1° More striking, however, is the implication of Figure 4b that the change in heat capacity at the glass transition for water is in the range 19-25 J mol-’ deg-l. The same range is obtained by using a plot of AC,/mole of solution vs. mole fraction of salt. In view of the coincidence of the established glass transition temperature with that detected in studies of vapor-deposited vitreous water, it seems reasonable to conclude that Figure 4b is predicting the increase in heat capacity for ASW at its glass transition. There are, however, two alternative possibilities, each of which demands acceptance of a coincidence which we consider improbable. These are (i) the extrapolation correctly predicts the AC, of a successfully vitrified liquid water but not that of the amorphous vapor deposit which in this view would be a structurally distinct form having, by coincidence, the same glass transition temperature; (ii) the extrapolation does not predict the AC, of either the amorphous vapor deposit or the vitrified liquid but, rather, the AC, of a special completely disordered non-network form of water, which coincidentally has the same glass transition temperature as the vapor deposit (and possibly also as the vitrified pure liquid). If we deny these coincidences and accept that the Figure 4b extrapolation should give the AC, for ASW, then it is important to note that the change in heat capacity is considerably less than those reported for ASW samples in the study of Sugisaki et al.ll These are reproduced in the inset to Figure 4b. The Sugisaki et al. values suffer from an uncertainty due to the instability of the deposits in the region of Tgand the fact that different deposits gave different C, increases, apparently due to partial crystallinity. No sample gave a clear “supercooled liquid”, i.e., post-transformation value, like the plateaus above Tgin Figure 1. Because of the evidence for partial crystallinity in some of Sugisaki et al. samples, and of the incompleteness of the transition, it has been felt14that the maximum C, observed represents a minimum value for the “supercooled liquid” phase, i.e., the opposite implication from that of our extrapolations. However, there is evidence from another Sugisaki et al. study17that the data for ASW may in fact be falsely high due to the presence of a sharp relaxation overshoot effect perhaps peculiar to certain vapor deposits. We refer here to data published for the marginally glassforming substance methanol, which has been obtained and studied in normal liquid,17J8vitrified liquid,lg and vapor-deposited glass forms.17 The Sugisaki measurements on methanol, reproduced in the inset to Figure 5, show clearly that the vapor-deposited material exhibits a major “overshoot” at Tgwhich is well in excess of that expected for the relaxation peak of a normally vitrified material during warm-up. In the first series for this sample the overshoot was twice as great as that shown in the figure.17 In differential scanning calorimetry studies such as sharp overshoot in heat capacities measured during warm-up is characteristic of glasses formed at cooling rates much slower than the heating rate of the measuring scan,2obehavior which can be quantitatively accounted for with current relaxation theoryaZ1Its presence in the results of the (effectively)very slow heating rate adiabatic calorimetry measurements is at first sight paradoxical since the vapor deposition is generally thought to be in many ways equivalent to an extremely fast quench after all it can be used to produce
Angeli and Tucker
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Log(T/ K ) Flgure 5. C, vs. log Tfor supercooled water and ice comparing the difference in liquid and ice I entropy losses, during hypothetical fast cooling process, wlth the entropy of fusion of ice (shaded area). The
dotted line shows approximate temperatwe dependence of the “normal” component of C,,for water, obtained from extrapolations of Figure 2 Isotherms. Thin dashed line shows the C, vs. Tfunction suggested by Rice et at., ref 29.
vitreous materials which cannot be produced in the vitreous state from the liquid even with the fastest available quenching rates. On the other hand there are occasional instances among classical adiabatic calorimetry studies on liquid-formed glassesz2of similar sharp peaks immediately above Tg, and it may be an accidental by-product feature of the incremental heat-wait-measure sequence of the adiabatic method. Without seeking to elaborate on this issue, we must stress that if the same 20% overshoot observed for deposited methanol is assigned to deposited water, then the resulting AC, for water, 27 J mol-’ deg-l, is close to that yielded by the extrapolations of Figure 5. Clearly a new study of the vapor deposit by differential scanning calorimetry is needed to confirm or deny the latter value. We can now proceed to one of the main points of this paper which is to consider the plausibility of linking the vapor-deposited vitreous material with liquid water through some continuous sequence of structural changes within the amorphous phase. The essence of Johari’s refutation of this possibility lies in his demonstration, reproduced in Figure 5 that, if the Sugisaki et al. heat capacity for the supercooled liquid near Tgis accepted, then it is not easy to account for the implied entropy loss during cooling and between 0 “C and Tgwith the available excess entropy at 0 OC (which latter is A&). Essentially he argued that the entropy loss diagrammgiven by Angell et al.13was inconsistent with the magnitude of ACp found by Sugisaki et at.ll Johari’s diagram neatly illustrates the problem by placing an area equal to the entropy of fusion adjacent to the ice C, curve (log T scale) and challenges the reader to connect the supercooled water high and low temperature C, end values in a plausible way such that there will remain some excess entropy in the amorphous phase at Tr Johari’s diagram is reproduced in Figure 5. The dashed line we have added to Figure 5 shows our response to the above challenge. Our response is based essentially on the assertion that Sugasaki et al. AC, is probably too high for
The Journal of Physical Chemistry, Vol. 84, No. 3, 1980 271
AC, of Glass-Forming Solutions
reasons cited above and should be replaced by the AC, (T,) value obtained from Figure 4b. Our construction leaves some 15% of the entropy of fusion residual at Tg. Our construction, which is intended to represent the heat capacity of a sample of water during cooling at a rate sufficiently high to elude the homogeneous nucleation phenomenon at -40 “C, hence also the instability at -45 “C, has three features which require comment and explanation. 1. I t is assumed to depart from the metastable equilibrium ‘heat capacity at a value somewhat below the maximum observed value (which has been recorded at T = -38 O C = TFt3v2*) on the basis that the anomalous increases are due to long-range reconstructive entropy fluctuations which should have long growth and decay times relative to those for “normal” fluctuations, and which therefore should “freeze out” first (Le., at higher T ) during cooling. Once these fluctuations are frozen, crystal nucleation, which apparently depends on them?15 would no longer be able to occur. Associated with the “freezing out” of the “iznomalous” degree of freedom, C, must drop (almost vertically on t,he log T scale), and it is assumed here to fall to a value of 57 J deg-’ mo1-I indicated in Figure 5 by the dashed line for “anomalous fluctuation-free”water obtained by the extrapolations of Figure 2. (Parenthetically, WE! note that the value of 51 J deg-l mol-‘ at -60 “ C should probably be regarded as a lower limit since it is based on extrapolations of data from compositions where most of the water present is in the first or second coordinatioii shells of a divalent cation where it would be more restricted than in a purely molecular milieu. Both larger and smaller values are indicated by current results on H20-H202and H20-NzH4mixtures.z5 This whole quegtion warrants detailed study with a variety of molecular second components and if possible some “fast” measurement to distinguish specific anomalous fluctuatilons from nondescript contributions to merely nonideal mixing behavior. 2. On reaching -57 J deg-l mol-l, C, is assumed to move monotonically toward the slightly lower value at T indicated by the sum of AC, for vitreous water (from fiigure 4b) and the C, of ASW just below Tg.ll Again we should recognize this as a probable lower limit. 3. Finally, C, is assumed to drop smoothlyz6to a value somewhat above that of ice. Due to the very high cooling rate being considered, this drop will occur at a temperature considerably above 139 K. This is because internal equilibrium for the “normal” configurational degrees of freedom ?willbe lost at a temperature where the structural relaxation time is very much shorter ( lo4 s assuming a cooling rate of lo8 degls) than that (-100 s) characterizing relaxation near the “normal” Tgobserved during heating at about 10 deg min-1.27 Clearly Figure 5, which is based minimal data and also on an unsubstantiated supposition concerning the separabiliityof an “anomalous” degree of freedom, is highly speculative, and may mot withstand the weight of further investigations. Nevertheless, in view of the (i) (admittedly inconcluaive) evidence that water can be vitrified in sufficiently fast quenching experiments28 and (ii) the importance of establishing the relation of ASW to ordinary water, we believe such speculations are warranted. The tools for establishing the validity or otherwise of the degrees of freedom separability postulate are already available (dielectric and hypersonic relaxation techniques), so some tests of the concepts, if not the specific thermodynamic quantities involved, are feasible in the immediate future.
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We should note here the existence of another heat capacity vs. temperature plot suggested recently by Rice and co-workersBwhich preserves the possibility of a continuity of states between ASW and supercooled water, but with which we must take exception. It is indicated by the dash-dot line in Figure 5, and was suggested following the observation that it was possible to obtain Raman spectra on the vapor-deposited amorphous phase up to temperatures as high as 160 K. The latter implies a substantial lifetime in the supercooled liquid state above T , which is not evident in the measurements of Sugasaki et The problem with C, vs. T suggested by Rice et aLZ9is that it appears to deny the existence of any heat capacity change associated with the transition from amorphous solid to supercooled liquid. This is implausible in principle, arid, in practice, is in conflict with the DTA observations, reported long ago by McMillan and Los for warm-up characteristics of ASW. These authors observed a glass tramsition followed by a short supercooled liquid region before crystallization to ice I, occurred. The Rice et al. conjecture therefore stands as an extreme possibility on the opposite side of our suggested C,-T function from that of Johari. The second point to be made follows the problem posed in the introduction and concerns the significance of the concept “glass transition” in a phase which may be mechanically unstable at the temperature of the transition. Evidently the glass transition can be directly observed in amorphous water and it probably can be characterized by definite changes in the derivative thermodynamic properties by means of the appropriate (fairly rapid) measurements. The problem then is to rationalize this observation if we, at some time, assert the possibility of a continuous progression of liquid states between this glass transition and supercooled water. Clearly the question of significance hinges on the distinction or otherwise between the time scales on which the transition, on one hand, and the instability, on the other hand, can be manifested. If, as we have speculated above, the putative instability is not absolute but requires for its manifestation the exercise of some degree of freedom which is slow with respect to the fluctuations determining the glass transition, then the concept of glass transition is acceptable. A critical test would, of course, be the observability or otherwise of the glass transition in a vitreous phase resulting from the successful splat-quenching off a liquid water sample. In the meantime it is important to emphasize the current evidence given in the previous paragraphs for the existence, over a reasonable length of time, of a metastable liquid phase derived from the vapor deposited solid material by passage through the glass transition. It would be rather surprising if this supercooled liquid should exist, at 1 atm pressure, in a free-energy minimum totally disconnected from that in which ordinary water exists.
Acknowledgment. This work was supported by t:he National Science Foundation under Grants GH40717 and DMR 77-04318A1, and the office of Water Resources Research, US.Department of the Interior under Water Resources Research Act 1964, Project No. B-051-IND (Agreement No. 14-31-0001-3883). References and Notes (1) L. Bosio and C. G. Windsor, Phys. Rev. Lett., 35, 1652 (1975). (2) (a) T. Schnebr, R. Bout, H. Thomas, arid J. Feder, phys. Rev. Leg., 25, 1423 (1970); (b) T. Schneider, Phys. Rev. A , 3, 2145 (1971). (3) S. Alexander and J. McTague, Phys. Rev. Lett., 41, 702 (1978). (4) R. J. Speedy and C. A. Angell, J. Chem. Phys., 65, 851 (1976). (5) B. J. Mason, “Clouds, Rain and Rainmaking”, Cambridge University Press,London, 1962.
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(6) C. A. Angeii, "Supercoded Water" in "Treatise on Water", F. Franks, Ed., Vol. 7, to be published. (7) J . 4 . Bacri and R. Rajaonarison, J . Phys. Lett., 40, L-403 (1979). (8) C. A. Angeli and E. J. Sare, J . Chem. Phys., 52, 1058 (1970). (9) D. H. Rasmussen and A. P. MacKenzie, J . Phys. Chem., 75, 967 (1971). (10) J. A. McMiiian and S. C. Los, Nature (London), 206, 806 (1965). (1 1) M. Sugisaki, H. Suga, and S. Seki, Bull. Chem. SOC.Jpn., 41, 2591 (1968). (12) (a) C. G. Venkatesh, S. A. Rice, and A. H. Narten, Science, 186, 927 (1975); (b) J. Wenzel, C. Linderstromlang, and S. A. Rice, ibM., 187, 428 (1975); (c) C. G. Venkatesh, S. A. Rice, and J. B. Bates, ibid., 68, 1065 (1975); (d) S. A. Rice, Curr. Top. Chem. (1976). (13) C. A. Angeil, J. Shuppert, and J. C. Tucker, J. Phys. Chem., 77, 3092 (1973). (14) G. P. Johari, Phi/. Mag., 35, 1077 (1977). (15) H. Kanno and C. A. Angeli, J . Chem. Phys., 65, 851 (1976). (16) These two chlorides show a sudden flattening out at 139 K in the To vs. composition plot like that observed over a wider range of composition by LiCl solutions. There is some evidence that this may be associated with a separation of the solution into immiscibleaqueous and salt-rich Dhases (C. A. Anaeil and E. J. Sare. J. Chem. Phvs.. 49, 4713 (1968); S. Y . Hsich,k. W. Gammon, P. B. Macedo, land C. J. Montrose, ibid., 56, 1663 (1972)). (17) M. Sugisaki, H. Suga, and S. Seki, Bull. Chem. SOC.Jpn., 41, 2586 (1968). (18) K. K. Kelley, J. Am. Chem. SOC.,57, 180 (1929).
( 19) J. A. Faucher and J. V. Koieske, phys. Chem. G/asses, 7, 202 (1 966). (20) S. M. Wolpert, A. WeRz, and 8. Wunderlich, J. Polym. Sci. A 2 , 9 ,
1887 (1971). (21) M. A. DeBoit, A. J. Easteai, P. B. Macedo, and C. T. Moynihan, J. Am. Ceram. SOC.,59 [l-21, 16-21 (1976). (22) E.g., 2-methyipentane glass in the study of D. R. Dousiin and J. A. Huffman, J . Phys. Chem., 68, 1704 (1946). (23) C. A. Angeil, J. Chem. Educ., 47, 583 (1970). (24) D. H. Rasmussen, A. P. Mackenzie, J. C. Tucker, and C. A. Angeil, Science, 181, 4079 (1973). (25) M. Oguni and C. A. Angeil, to be published. (26) Heat capacity always changes more gaduaily near Toduring a cooling half cycle than during a heating haif cycle (e.g., as in Figure 1). The differences are quantitatively accounted for by nonlinear relaxation theory (see ref 21). (27) Glass transitions during cooling which occur at much higher temperatures than those detected during reheating are routine in the splat-quenched metal alloy glasses on whlch so much attention Is currently being focussed. The frozen-in structure in such glasses is characteristlcaily a rather "loose" one in which a considerable amount of iocailzed relaxational motion is permitted, and in which C, is somewhat greater than in the corresponding crystalline solid near To. (28) B. J. Luyet, J. Phys. Chem., 43, 881 (1939); also footnote 16 in ref 13. (29) S. A. Rice, M. S. Bergren, and L. Swingie, Chem. Phys. Lett., 59, 14 (1978).
Association of Anions to Cationic Micelles Daniel Bartet, Consuelo Gamboa, and LUISSepQlveda" Depatfment of Chemistry, Faculty of Sciences, University of Chile, Las Paimeras 3425, Santiago, Chile (Received July 5, 1979) Publication cost assisted Servicio de Desarrolio Cientifico, Atfktico y de Cooperaci6n Internaclonai de la Universidad de Chile
The relative association degrees of different anions to micelles of hexadecyltrimethylammonium bromide (CTA) were measured by spectrophotometrically determining the amounb of p-toluenesulfonate (TOS) or benzenesulfonate (BS) anions desorbed from the micelles by addition of increasing amounts of NaN03, NaBr, NaC1, NaOH, NaF, NaOAc, Na2S04,Na2HP04,Na2C03,and Na2B407.A simple ion-exchangemodel was used for interpreting the results in a quantitative way and values for the ion-exchange constants were calculated. These values are discussed in terms of the hard and soft acid-base principle.
Introduction It is well known that micellar catalysis can be inhibited or practically suppressed by the addition of salts to the reaction m e d i ~ m . l -Bunton ~ et al.lr3have demonstrated that this inhibition can be satisfactorily explained in terms of a competition between salts and substrates for binding to micelles. Larsen and Magid4 measured the binding of Br-, NO,, TOS-, and OH- to CTA micelles but it was later recognized that their measurements for competitive counterion binding were incorrect in the case of OH-.5 The association of protons and hydroxyl anions to micelles is of great importance in the interpretation of reaction rates occurring in the presence of micelles where H+or OH- can act as reagents or when acid-base equilibria of the reactive species are involved.6 In addition, most measurements of the rate of reactions in the presence of micelles are carried out in buffered solutions and buffer ions are considered inert species only acting as bulk pH controllers. There is no reason to believe that buffer ions do not interact with the micellar surface. Their competitive binding to micelles could affect the amount of bound ionic substrate as well as the pH at the Stern layer due to the different distribution of acid and base buffer species between water and the micellar phase. 0022-3654/80/2084-0272$0 1.OO/O
The binding of protons to anionic micelles of sodium dodecyl sulfate has been satisfactorily measured7 but attempts to measure the binding of OH- to CTA micelles have failed.5*6 We report here a simple method which allows the quantitative determination of relative binding strengths of some anions to cationic micelles including OH- and buffer anions.
Method Our method is based on the observation that the UV spectra of aqueous solutions of some aromatic anions (S) experience a shift in the presence of CTA micelles.8 By increasing the CTA concentration the absorbance of S at a given wavelength changes gradually until it reaches a constant value. The interpretation given to this phenomenon is that a constant absorbance occurs when the CTA concentration is large enough to bind all existing S.8 At lower concentrations of CTA, S exists bound to micelles as well as free in the water phase. The change in absorbance of such a solution upon addition of a salt whose anion C competes with S for its place in the micelle is a measure of the amount of S displaced. The total amount of bound C can be obtained with the assumptions that, for 0 1980 American Chemlcal Society
