J . Phys. Chem. 1990, 94, 6781-6785
6781
Ion Binding and Selectivity in Zwitterionic Micelles Sergio Brochsztain,t Pedro Berci Filho,t Vicente G. Toscano,l Hernan Chaimovich,? and Mario J. Politi*vt*' ,
Departamento de Bioquimica and Laboratorio Interdepartamental de Cinetica Rapida, Instituto de Quimica, Unicersidade de Sao Paulo, Caixa Postal 20780, Sao Paulo, S.P., CEP 01498, Brazil (Received: October 4, 1989; In Final Form: April 3, 1990)
Micelles of 3-(N-hexadecyl-N,N-dimethylammonio)propanesulfonate (HPS) incorporate N-butyl-2,3-naphthalimide(NBN), N-decyl- (DeCP), and N-dodecyl-4-cyanopyridinium(DoCP) ion. Upon incorporation in HPS micelles, the NBN fluorescence emission spectra was comparable to that of the same probe in methanol. The fluorescence of micelle-incorporated NBN was quenched by chloride and bromide ions, suggesting specific ion binding to HPS micelles. HPS micelles increased the rate of alkaline hydrolysis of DoCP and DeCP and decreased the rate of hydrolysis of NBN. Added salts inhibited the micellar modified OH- attack on the three substrates. Salt inhibition, analyzed by using a competitive inhibition scheme, demonstrated that HPS micelles bind bromide better than chloride ion and that both ions can displace OH- from the micellar surface. These data show that both charged and zwitterionic micelles can selectively concentrate ions at the micelle-water interface.
SCHEME I
Introduction
The distribution of ions between bulk solution and micelles determines several fundamental features of charged micellar solutions. Different theoretical approaches have been used for the description of such ion distribution. It is generally accepted that charged micelles bind counterions specifically, that ions can be displaced from the surface by similarly charged species, and that the concentration of co-ions at the surface increases upon addition of salt.' Zwitterionic micelles have been less explored than charged systems. Specific ion binding in zwitterionic micelles is supported by some evidence.2 Betaine-type micelles adsorb anions preferentially.2 Detailed description of ion binding is a prerequisite for the further understanding (and utility) of zwitterionic micelles. Several micellar properties have been unveiled analyzing the effect of micelles on chemical reactivity. Here we have used base-sensitive substrates, namely, N-butyl-2,3-naphthalimide (NBN) and N-alkyl-4-cyanopyridinium(XCP) ions (Scheme I), to analyze ion-binding properties of zwitterionic micelles. Kinetic effects and variations of fluorescence quenching were utilized to demonstrate that sulfobetaine micelles can specifically adsorb ions and that bound ions can be displaced from the interface by added electrolytes. Materials and Methods
3-(N-Hexadecyl-N,N-dimethylammonio)propanesulfonate (HPS) was prepared a s described.j The starting N-hexadecylamine (Aldrich) was distilled (0.13 mmHg, 138 "C) and was pure by GLC. The crude product was recrystallized (X3) from acetone/methanol (90/10 v/v) and shown to be pure by elemental analysis and N M R . N-Butyl-2,3-naphthalimide(NBN) was prepared and purified as d e ~ c r i b e d . ~The N-alkyl-4-cyanopyridinium halides (XCP) were prepared from 4-cyanopyridine (Aldrich) and the corresponding bromoalkanes (Aldrich).6 Melting points, elemental analyses, and spectra of X C P were in accord with structures.6 All other reagents were of analytical grade: water was deionized and twice distilled (glass). Spectra were obtained at 30 "C in a Beckman DU-7 spectrophotometer or a Perkin-Elmer LS-5 spectrofluorometer (fixed 2.5-mm slits for both emission and excitation monochromators). The rates of alkaline hydrolysis of X C P and N B N were followed a t 275 and 362 nm, re~pectively.~.' Some of the hydrolysis of X C P was followed at 265 nm with results identical with those obtained at 275 nm. Reported rate constants are averages of at least three separate experiments, differing by no more than 5%. 'Address correspondence to this author at the Departamento de Bioquimica. Departamento de Bioquimica.
'* Laboratorio lnterdepartamental de Cinetica Rapida.
0022-3654/90/2094-678 1$02.50/0
6 r;
R = CIO H ~= D I eCP
NBN
R=C~~H~~=DOCP
TABLE I: Medium Effect on the Spectra of N-Butyl-8-naphthalimide X of max e,' M-'
medium CH3CN CH3CHZOH H20 0.024 M HPS
abs, nm
cm-' (XlO-')
354 356.0 362 357.5
2.31 2.81 2.96 3.60
Ab of max
em, nm 394.0 395.0 415.0 395.0
Molar extinction coefficients. *Obtained by excitation at the absorption maximum. Rate constants were obtained by linear regression under pseudo-first-order conditions. Reactions were followed for at least four half-lives. ( I ) (a) Fendler, J. H. Membrane Mimetic Chemistry; Wiley-Interscience; New York, 1982. (b) Romsted, L. S. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1977;p 509. (c) Romsted, L. S. J . Phys. Chem. 1985,89, 5107. (d) Lissi, E.;Abuin, E.; Bianchi, N.; Miola, L.; Quina, F. H. J . Phys. Chem. 1983,87, 5166. (e) Lissi, E.; Abuin, E.; Ribot, G.; Valenzuela, E.; Chaimovich, H.; Araujo; Aleixo, R. M. V.; Cuccovia, I. M. J . Colloid Interface Sci. 1985, 103, 139. ( f ) Quina, F. H.; Chaimovich, H. J . Phys. Chem. 1979,83, 1844. (g) Chaimovich, H.;Bonilha, J. B. S.; Politi, M. J.; Quina, F. H. J . Phys. Chem. 1979,83, 1851. (h) Bunton, C. A.; Moffatt, J. R. J . Phys. Chem. 1986,90, 538. (i) Bunton, C. A.; Moffatt, J. R. J . Phys. Chem. 1988, 92, 2896. (j) Hall, D. G.J . Phys. Chem. 1987, 91, 4287. (2) (a) Bunton, C. A.; Mhala, M. M.; Moffatt, J. R. J . Phys. Chem. 1989, 93,856. (b) Bunton, C. A.; Mhala, M. M.; Moffatt, J. R. J . Org. Chem. 1987, 52, 3832. (c) Pillersdorf, A.; Katzhendler, J. Isr. J . Chem. 1979, 18, 330. (d) Pottel, R.; Kaatze, U.; Muller, S. Ber. Bunsen-Ges. Phys. Chem. 1978, 82, 1086. (e) Clunie, J. S.;Corkill, J. M.; Goodman, J. F.; Ogden, C. P. J. Chem. Soc., Trans. Faraday Soc. 1967,63, 505. ( f ) Bunton, C. A.; Mhala, M. M.; Moffatt, J. R. J . Org. Chem. 1987, 52, 3832. (3) (a) Fendler, E. J.; Day, C. L.; Fendler, J. H. J . Phys. Chem. 1972, 76, 1460. (b) Lucassen, J. J . Chem. Soc., Faraday Discuss. 1975, 59, 76. (4) (a) Schroeder, H.R.; Boguslaski, R. L.;Carrico, R. J.; Buckler, R. T. Methods Enzymol. 1979, 57, 425. (b) Campbell, A. D.; Grimmett, M. R. Aust. J . Chem. 1963, 16, 854. (5) Landquist, J. K. J . Chem. SOC.,Perkin Trans. I 1976, 454. (6) (a) Politi, M. J.; Chaimovich, H. Submitted for publication. (b) Politi, M. J. Masters Thesis, Universidade de Sao Paulo, Instituto de Quimica, 1980. (c) Politi, M. J.; Cuccovia, I. M.; Chaimovich, H.; Almeida, M. L. C.; Bonilha, J. B. S.; Quina, F. H. Tetrahedron Lett. 1978, 115. (7) (a) Berci-Filho, P.; Toscano, V. G.; Politi, M. J. J . Photochem. Photobiol. A: Chem. 1988, 43, 51, and references therein. (b) Pardo, A,; Poyato, J . M. L.; Martin, E.; Camacho, J. J.; Reyman, D.; BraAa, M. F.; Castellano, J. M. J . Photochem. Photobiol. A : Chem. 1989, 46, 323.
0 1990 American Chemical Society
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Brochsztain et ai.
The Journal of Physical Chemistry, Vol. 94, No. 1 7 , 1990 01
02
3 O
5
7 8 00
O6
o
4
0
09
IOdb" dl2 013 14al5
016
017 WAVELENGTH ( n m )
Figure 1. Absorption and emission spectra of NBN in aqueous solution. [NBN] = 7.2 X IO" M (absorbance), 3.6 X IO" M (emission). Excitation X = 362 nm. Noncorrected spectra, intensity in arbitrary units.
I
I
/
018 0.2 K O S O W E R PARAMETER
0
Figure 3. Kosower plot for NBN. [NBN] = 7.7 X 10" M. Excitation X from 350 to 363 nm. Solvent scale: I , hexane; 2, carbon tetrachloride; 3, ethyl ether; 4, chloroform; 5, ethyl acetate; 6, dichloromethane; 7, acetone; 8, acetonitrile; 9, dimethylformamide; IO, ethanol; 1 1, methanol; 12-17, ethanol/water scale (w/w. %) 85.3, 76.0, 62.7, 54.2, 34.5, 16.9; 18, water; 0 , HPS, 0.024 M.
d
4w
390 0
0 0 05
4
r - , o
1.0 5 HPS ( m M )
,
01
10
Figure 2. Effect of H P S on emission wavelength of NBN. Excitation A from 350 to 358 nm. [NBN] = 3.6 X IO" M. Inset shows a plot of the data according to a two-state association model (see textlo).
Results
N-Butyl-2,3-naphthalimide (NBN), a butyl derivative of a series of fluorescent solvent-sensitive interfacial probes,' exhibits a number of interesting spectral properties.* Typical spectra (absorption and emission in water) of NBN are shown in Figure 1 . The fluorescence emission spectra of NBN were red-shifted with increasing polarity and hydrogen-bonding character of the solvent (Table I). Addition of H P S to aqueous NBN decreased the wavelength of the emission maximum, reaching a plateau with increasing HPS concentration (Figure 2). This behavior was attributed to incorporation of NBN into micellar HPS,Iaq9and the spectral shifts were used to calculate a value of 7960 M-l for the incorporation constant (K,).'O Bulklike properties of solubilization sites can be estimated from comparison of spectral properties of a micelle-incorporated probe with an appropriate reference scale obtained with the same probe in different solvents." From the data shown in Figure 3 it is apparent that the solubilization site of NBN in HPS micelles has methanol-like properties. This result suggests that NBN resides at the surface of HPS micelles.7J1 Chloride and bromide ions quenched the emission of NBN with different efficiencies (Figure 4). The values of the Stern-Volmer quenching constant (&), calculated from the (linear) plots relating the ratio of the fluorescence intensities in the absence of quencher to that in the presence of added quencher (lo/[) with quencher
0.4
24 I0
0.I
0.2
0.3
M X(M1
Figure 4. Stern-Volmer plot for quenching of NBN fluorescence by chloride or bromide ion. [NBN] = 3.6 X IO" M. Excitation and emission h 362 and 415 nm, respectively. M = Na+ or K+, X = CI- or Br- (0,NaBr; 0 , KBr; A, NaCI; A, KCI). A 0
0
1.5 0 -
0
1.1
0 O
I
-
0
0 H
;1.0
U
1000
0
20
40 60
~
(8) Almeida, F. C. L.; Santos, 0. A,; Berci-Filho, P.; Toscano, V. G.; Politi, M. J Submitted for publication. (9) Kalyanasundaran, K. Photochemistry in Microheterogeneous System; Academic Press: Orlando, FL, 1987. (IO) Taking the limiting emission wavelength values (absence of surfactant and high surfactant concentration) as a measure of the totally free and bound probe, respectively, and assuming a two-state partition equilibrium, the reciprocal of the bound fraction (Fr) is given by 1/Fr = 1 + I/(K&). K, is and C, is the analytical concenthe substrate distribution constant (M-'), tration of micellized surfactant. ( I I ) Zachariasse, A. K.; Phuc, N . V.; Kozankiewicz, B. J Phys. Chem. 1981,85. 2676
0
1000 0 20 KBr(mM)
40 6 0
Figure 5. Stern-Volmer plot for quenching of micelle-incorporated NBN by chloride or bromide ion. [ H E ] = 0.023 (A) or 0.019 M (B); [NBN] = 4.3 X IOd M. Excitation and emission X 358 and 392 nm, respectively. Insets show expansion at the lower salt concentrations.
Ion Binding and Selectivity in Zwitterionic Micelles
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 6783 TABLE 11: Calculated Parameters for the Alkaline Hydrolysis of XCP Ions and NBN in HPS Micelles substrate k,, s-I ko, s-’ Ks,M-’ ( X 10-j)
DoCP DeCP
0.125 0.139
NBN
4.8 X IO4
0.014’
1.64
0.0 14’ 0.010b
0.12 6.63
‘pH = 11.63. b p H = 11.10.
I 0
30
60 MBr ( m M )
90
120
Figure 6. Stern-Volmer plot for quenching of micelle-NBN by bromide with added chloride ion. [NaCI] = 0.1 ( 0 )or 1.0 (0)M. [HPS] = 0.02 M. [NBN] = 3.6 X lod M. Excitation and emission X 358 and 392 nm,
respectively. M = Na’ or K+.
K X (MI 0
1
N :
0
r
I
0
5
P I
0
0
0
-
o v l-
I / C n .10-3
50 HPSlmM)
0 0
O 0 0.5 KX(M)
1.0
@I
Figure 8. Salt effect on HPS-catalyzed alkaline hydrolysis of dodecylcyanopyridinium ions. pH = 11.63. (0)KBr; ( 0 )KCI. [HPS] = 0.02 M. [DoCP] = 3.8 X IO” M. Inset shows data treatment using competitive inhibition model (see text).
I 100
Figure 7. Effect of HPS on the alkaline hydrolysis of cyanopyridinium M. [DeCP] ( 0 )= 4.2 X ions. pH = 11.63. [DoCP] (0) = 3.8 X IOd5 M . Inset shows data treatment using distribution model (see text) ( 0 )DoCP; (0)DeCP.
concentration (Figure 1 ), were 1 and 40 M-l for CI- and Br- ions, respectively. Identical values of K,, were obtained for the K+ and Na’ salts. Upon addition of micellar HPS the quenching of NBN by Bror CI- ions gave curved Stern-Volmer plots (Figure 5). The quenching of micelle-incorporated N B N exhibited an apparent saturation limit (Figure 5). It should be noted that curvature arose at ca. 0.025 M with Br- and at 0.14 M with CI- (Figure 5), suggesting that HPS micelles bind Br- better than CI- ion. The slope of the initial (linear) portion of the quenching plots (Figure 5) was higher in micelles than in water, suggesting that the quenching efficiencies of the halides were higher in the presence of micelles. Linear Stern-Volmer plots for the quenching of micellar-incorporated N B N by Br- were obtained in solutions initially containing CI- (Figure 6). Values of the apparent K,, were 20 and 30 M-’ for 1.O and 0.1 M initial NaCI, respectively. Taken together these results suggest ion binding and ion displacements in micellar HPS. Direct evidence for these latter phenomena was obtained by analyzing the effect of salts on the alkaline hydrolysis of XCP and NBN. N-Alkyl-4-cyanopyridiniumions undergo OH- attack, and the reaction rate is modified by charged micelles.6 Micellar HPS produced marked rate enhancements of the rate of alkaline hydrolysis of N-decyl- (DeCP) and N-dodecyl-4-cyanopyridinium (DoCP) ions (Figure 7). The rate constant vs [HPS] profile (Figure 7 ) was similar to other micelle-modified effects on bimolecular reactions between a micelle-incorporated substrate and a bound reactive ion.’.12 The maximum rate enhancements (ca. (12) (a) Fendler, J . H.; Fendler, E. J . Catalysis in Micellar and Macromolecular Systems; Academic Press: New York, 1975. (b) Berezin, 1. V.; Martinek, K.; Yatsimirskii, A. K . Russ. Chem. Reo. (Engf.Trans!.) 1973, 42, 487.
IO-fold) were the same for both substrates. The micellar effects on the rates of alkaline hydrolysis of XCP were analyzed according to an “enzyme model”I3 (Figure 7, inset). This model permits and pseudo-first-order rate the calculation of incorporation (K,) constants in the micelle ( k , ) (Table 11). The absolute value of K, is model-dependent;I4however, a comparison of the K, of related substrates can be used to estimate the relative applicability of the method. In the present case the standard free energy of transfer for a methylene group (AGo(CH,)) from water to the micelle, calculated from the difference in K, of DeCP and DoCP, was -0.79 kcal/mol, well within the expected range.I5 The rate enhancement produced by HPS was reduced by added salts, Br- being more effective than CI- ion (Figure 8). Quantitative analysis of salt effects in ionic micelles requires the use of parameters such as ion dissociation or electrostatic potentials,1*2*’6 not presently available for zwitterionic micelles. In order to have an estimate of the relative inhibitory efficiencies of salts in this reaction, we analyzed the effect of salts using a competitive inhibition formalism.” The inhibition can be described by
In eq 1, K , is the substrate incorporation constant, C, the concentration of micellized surfactant, I the analytical concentration of added salt, and K I the dissociation constant of the inhibitormicelle-like complex. k , and ko are the observed rate constants in the presence and absence of I, respectively. The inhibition of the alkaline hydrolysis of DoCP by salts was well described by the model (Figure 8). The calculated values for the Kl’s were (13) Menger, F. M.; Portnoy, C. E. J. Am. Chem. SOC.1967,89, 4698. (14) Sepulveda, L.; Lissi, E.; Quina, F. H. Adu. Colloid Interfuce Sci. 1986, 25, 11. (15) Tanford, C. The Hydrophobic Effect; Wiley: New York, 1980. (16) (a) Nome, F.; Rubira, A. F.; Franco, C.; lonescu, L. J. J . Phys. Chem. 1982, 86, 1881. (b) Neves, M. F. S.; Zanette, D.; Quina, F. H.; Moretti, M. T.; Nome, F. J. Phys. Chem. 1989, 93, 1502. (17) (a) Metzler, D. E. Biochemistry: The Chemical Reactions ofLiuing Cells; Academic Press: New York, 1977. (b) Marshall, A. G. Biophysical Chemistry: Principles, Techniques and Applications; Wiley: New York, 1978.
I
-loot
s
-13b
-
‘ 1
3 1 s
51i
p3l o
{ - 1 0 5- l
I.o I / C D 10-3
0
0
0
q
20
0
2.0
0,
1
i
oi 40
HPS(mM)
Figure 9. Effect of H P S on alkaline hydrolysis of NBN. (NBN] = 9.4 X 10“ M. [KOH] = 0.002 M. Inset shows data treatment using distribution model (see text).
p ..
0 ’ X
7 . x 3
Brochsztain et al.
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990
6784
5 -
0
O O
0
*. 0.2
K X (MI
0.4 KX (M)
Figure 10. Salt effects on HPS-modified alkaline hydrolysis of N B N . (e) KBr; (0)KCI. (NBN] = 9.2 X IOd M. [HPS] = 0.02 M. [KOH] = 0.03 M. Inset shows data treatment using competitive inhibition model (see text).
3.3 X and 1.54 X M for Br- (Kler) and CI- ion (KIcl). respectively. A KI calculated with such a model lacks a clear physical significance. However, if both salts inhibit the reaction by the same mechanism, the KI ratio gives a quantitative measure of the relative affinity of each ion for the HPS micelle. In the was 4.5. hydrolysis of DoCP KIC1/KlBr The alkaline hydrolysis of NBN was inhibited by HPS (Figure 9). Inhibition of the alkaline hydrolysis of hydrophobic substrates by detergents (including HPS) has been The effect of HPS on the hydrolysis of NBN was analyzed as described above for the XCP’s. The corresponding values of k , and K,, derived from the data shown in Figure 9, are presented in Table 11. The inhibition by the detergent was increased by added salts (Figure IO). The competitive inhibitor model (see above) gave a value of 4.0 for KIC’/KlBrfor the reaction of N B N hydrolysis in HPS micelles. Discussion
HPS aggregates adsorb anions preferentially from aqueous solutions.2 HPS foams, formed in aqueous NaBr, are enriched in bromide by (up to) 20-fold above the bulk salt concentration.2e HPS micelles adsorb anions and exhibit selectivity with affinity decreasing in the order Br- = CI- > F > OH- > SO,2-. Thus, selective ion binding appears to be a property shared by charged] and zwitterionic2 micelles. Here we will argue that our results support selective ion binding and can also be analyzed qualitatively (18) Quina, F. H.; Politi, M. J.; Cuccovia, I . M.; Franchetti, S. M . M . ; Chaimovich, H. In Solurion Chemistry ofSurfactants; Mittal, K., Fendler, E. J., Eds.; Plenum Press: New York. 19x2.
within the framework of ion-exchange descriptions of the micellar pseudophase. Quenching of the fluorescence of micellar-bound NBN was to be expected on the basis of probe l o ~ a l i z a t i o n . ~ ~A” higher ~~~~’~ quenching efficiency by Br- or CI- ions, relative to that in water, can be rationalized by proposing surface enrichment of these ions. However, different quenching mechanisms could equally well account for these observations. Since the surface quenching rate constants (k,) were not determined, we cannot distinguish between the two alternatives. The deviations from linearity in the Stern-Volmer plots for CI- and Br- occur at different concentrations and are consistent with different micellar affinities for the two ions. At high salt concentration the quenching by chloride and bromide levels off, strongly suggesting a saturation of the ion-binding compartment. The value of K,, obtained for Br- ion with 0.1 M added CI- ion was smaller than, but near, that obtained for Br- ion in water. With 1.0 M added NaCl the value of K,, for Br- ion was 20 M-’ and there was no curvature in the Stern-Volmer plot (Figure 6). Taken together, these data can be rationalized by proposing a preferential surface enrichment of Br- ion even in the presence of added CI-. The effect of HPS on the alkaline hydrolysis of XCP was fitted with a simple two-phase distribution model.12 The values of k , for both DoCP and DeCP were similar to those found with CTAB micelles,6 suggesting that both XCP and OH- ion are located in similar environments. We have shown that the second-order rate constants for the reaction of DoCP and DeCP with OH- ion in water, as well as in CTAB micelles, are identicaL6 Moreover, the pH dependence of the observed rate constant in water ( k , ) for the alkaline hydrolysis of XCP can be described by6 log k , = 1.072pH - 14.30 (2) The local pH at the micellar reaction site can be calculated from eq 2 by replacing k , by the mean value of k , (0.132; Table 11). When compared with the bulk pH (1 1.63; Table II), the calculated surface pH (1 2 . 5 ) indicates a 10-fold enrichment of the HPS micellar surface with OH- ion. Our results demonstrate unambiguously that X C P incorporation in HPS micelles leads to a IO-fold rate enhancement (Table 11; Figure 7 ) . However, a 10-fold enrichment in surface OH-, although not unprecedented,ls constitutes an upper limit, calculated on the basis of equal reactivity of OH- in water and in the micellar surface. An increase in the OH- reactivity would lead to a decrease in the calculated surface enrichment of OH-. In CTAB, the second-order rate constant for the alkaline hydrolysis of XCP (in the micellar pseudophase) is 8-fold higher than that in the aqueous phase.6 Thus, our data are compatible with the 2-fold OH- concentration at the surface of HPS micelles, as reported by Bunton and co-workers.2a Chloride ion and bromide ion inhibited the alkaline hydrolysis of XCP and NBN, Br- being more effective. Salt inhibition of dephosphorylation in zwitterionic micelles has been described.2f In this latter system there is little salt selectivity in the inhibition and the results were not analyzed quantitatively.2f Salt inhibition of micelle-modified reactions has been generally ascribed to ion exchange between the reactive and the added inert salt.’ Ion exchange in ionic micelles has been analyzed by use of using different models.’a,b.f.hjThe inhibition data were well described using the competitive inhibition approach. Moreover, the K, ratios, calculated by use of the competitive ion approach, are the same within experimental error for two different substrates reacting with OH-. Moreover, it should be noted that the Br-/CI- selectivity found here (ca. 4) approaches closely that found for the same ions in positively charged alkyltrimethylammonium micelles.’ With the data at hand we cannot define the extent of the anion-binding region of the zwitterionic micelle. Any ion binding must be finite, and thus the limit for the growth of the “bound-ion” compartment is given by the intermicellar ion concentration where bulk equals “bound”. The fact that bromide is more effective than (19) (a) Schmehl, R. H.; Whitten, D. G . J . Am. Chem. SOC.1980, 102, 1983. (b) Foreman, T. K.; Sobol, W. N . ; Whitten, D. G. J . Am. Chem. SOC. 1981. 103, 5339. (c) Dill, K A,; Flory, P J. Pror. Natl. Arad. Sri. U.S.A. 1981, 78. 6 7 6 .
J . Phys. Chem. 1990, 94, 6785-6791 chloride suggests that, as for charged micelles, the differential binding affinity, observed in our fluorescence experiments, is also reflected in selective displacement. In conclusion we have demonstrated that zwitterionic micelles can concentrate anions at the interface, ion adsorption was selective, and added ions displaced reactive ions from the surface
6785
of HPS micelles. The physical description of the binding process is a subject of current interest in our laboratory. Acknowledgment. This work was supported in part by grants from CNPq, FINEP, PADCT, and FAPESP. We are grateful to Dr. I. M. Cuccovia for helpful discussions.
Localized Adsorption with Lateral Interaction on Random and Patchwise Heterogeneous Surfaces James A. Ritter,* Akhilesh Kapoor, and Ralph T. Yang Department of Chemical Engineering, State University of New York at Buffalo. Buffalo, New York 14260 (Received: October 1 1 , 1989; In Final Form: March 14, 1990)
An analytical expression for an overall adsorption isotherm was derived which accounts for both lateral interaction of the
Bragg-Williams kind and surface heterogeneity via a random distribution of sites described by a uniform distribution of energies. The isotherm reduces to the Langmuir, Fowler and Guggenheim, and Langmuir uniform distribution isotherms when the appropriate limits are taken. In addition, a parametric study was made which reveals the following features of localized monolayer adsorption with lateral interaction on both random and patchwise heterogeneous surfaces: (1) Adsorption with favorable lateral interaction on a patchwise heterogeneous surface, compared to a random heterogeneous surface, results in higher fractional surface coverages but only at low pressures, whereas at high pressures or for unfavorable lateral interaction, there is little difference between the isotherms. For the case of no lateral interaction, random and patchwise heteroeneous surfaces are indistinguishable. (2) Irrespective of heterogeneity, unfavorable and no lateral interaction result in concave isotherms, whereas favorable lateral interaction results in sigmoidal isotherms with the convex region occurring at low pressures. (3) Irrespective of lateral interaction and heterogeneity, all the isotherms intersect at 0 = 0.5. Furthermore, as lateral interaction varies from unfavorable to none to favorable. the characteristic pressure at which the isotherms intersect decreases exponentially.
Introduction It is widely accepted that most surfaces of solid adsorbents are energetically heterogeneous and that lateral interaction between adsorbate molecules becomes appreciable at high surface coverages. The recent monograph by Jaroniec and Madey’ presents a comprehensive review of the studies that have examined simultaneously energetic heterogeneity and lateral interaction. It is clear from the monograph that significant contributions to this area came from Hill,2 Steele,3 Ross and O l i ~ e rand , ~ Jaroniec and P a t r y k i e j e ~ among ,~ many others. In these studies, energetic heterogeneity has been treated in two ways: the surface has been considered to be composed of sites distributed r a n d ~ m l y , ~or, ~ * ~ a patchwise distribution of sites has been con~idered.~.~ Also, three approaches have been adopted to account for lateral interaction which were all based on the work by Fowler and G u g g e n h e i d for a homogeneous surface: the Bragg-Williams approximation,2,3,4*5 the quasi-chemical approximation,2 or the two-dimensional van der Waals equation of state.4 Hill2 extended the treatment of Fowler and Guggenheim6 for localized monolayer adsorption with lateral interaction on a homogeneous surface to that on a random heterogeneous surface. He discussed the configurational entropy and demonstrated a unique phase change associated with such a surface. Steele3 derived a general theory of adsorption based on rigorous statistical mechanics which described mobile or localized monolayer adsorption with lateral interaction on a heterogeneous surface and included in his model site distribution functions for both random and patchwise heterogeneous surfaces. It is worth noting that Pierotti and Thomas’ extended the work by Steele3 to include gas-phase imperfections. They also presented methods to evaluate the second and third adsorption virial coefficients from experimental data. However, the application of these models to situ-
* To whom correspondence should be addressed. Permanent address: Westinghouse Savannah River Co., Savannah River Laboratory, Aiken, SC 29802. 0022-3654/90/2094-6785$02.50/0
ations other than low-coverage physical adsorption requires a great deal of experimental information. An alternative approach was adopted by Ross and Oliver4 where various isotherms derived for mobile or localized adsorption on a homogeneous surface (with or without lateral interaction) were employed to describe adsorption on each patch of a heterogeneous surface. The overall adsorption isotherm was obtained numerically by summing the local contributions from the adsorption on each patch weighted by an assumed Gaussian energy distribution function. Their study revealed some interesting features of both mobile and localized monolayer adsorption with lateral interaction on a patchwise heterogeneous surface. Jaroniec and P a t r y k i e j e ~ on , ~ the other hand, proposed a method based on a random heterogeneous surface which made use of the fact that when, for example, the Fowler and Guggenheim (FG) isotherm is applied locally to describe adsorption on each kind of site of a random heterogeneous surface, the lateral interaction is accounted for globally over the whole surface, i.e., independent of the distribution of site energies2 Thus, for a random distribution of sftes the form of the FG isotherm becomes identical with the Langmuir isotherm and can thus be treated as such. The simplicity of this approach is made clear later. The primary purpose of this paper is to derive an analytical expression for an overall adsorption isotherm which describes localized monolayer adsorption with lateral interaction on a random heterogeneous surface. The lateral interaction is based (1) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (2) Hill, T. L. J . Chem. Phys. 1949, 17, 762. (3) Steele. W. A. J . Phys. Chem. 1963, 67, 2016. (4) Ross, S.; Oliver, J. P. On Physical Adsorption: Interscience Publishers: New York, 1964. ( 5 ) Jaroniec. M.: Patrvkieiew, A. Phvs. Lett. 1978, 67A. 309. (6) Fowler, R. H.; Giggknheim, E: A. Statistical Thermodynamics; Cambridge University Press: London, 1939. (7) Pierotti, R. A,; Thomas, H. E. J . Chem. Soc., Faraday Trans. 1 1974, 70, 1725.
0 1990 American Chemical Society
