J. Phys. Chem. 1081, 85, 1429-1434
1429
Free Energies of Transfer of Anions from Water to Cationic Micelles from Ionic Exchange Measurements Consuelo Gamboa, Luls SepClveda,’ and Ramdn Soto Department of Chemistry. Facutty of Sciences, University of Chile, Las Palnmras 3425, Casllk 853, Santhgo, Chile (Receiveil: October 2, 1980)
Ionic exchanges for several anions in hexadecyltrimethylammonium (CTA) have been measured by ultrafiltration and by the shift in the concentration of ferric thiocyanate complex by CTA addition. The results are compared with those previously reported using an absorbance method. The agreement between the three methods is good, and they allow one to calculate the free energies of transfer from water to CTA micelles for the anions studied. The values are discussed in terms of several properties of the anions. It is concluded that both entropic and enthalpic effects are responsible for the specificity of binding of the anions to CTA micelles. Introduction In a recent paper’ a method for measuring the ionic exchange constants of several anions on micelles of hexadecyltrimethylammonium bromide (CTABr) was presented. The method is based on the removal of the amphiphilic anion, tosylate or benzenesulfonate (BS), from CTABr by the addition of a salt whose anion is exchanged with the amphiphilic anion. However, it is known that the benzene ring interacts strongly with CTABr micelles.24 Therefore, the ionic exchange constants measured by this method may be affected by the hydrophobic contribution, since it is expected that a simple anion would not displace an amphiphilic anion on account of only electrostatic interactions. In order to test this effect, we have chosen a system in which the hydrophobic contribution is absent and the measured species is present only in the water phase. The chosen system deals with the effects of CTA micelles on the equilibrium Fe3+ + SCN- e Fe(SCN)2+ All species involved in this equilibrium are hydrophilic, and only thiocyanate ion, SCN-, will interact with the cationic micelles. Thus, the concentration of the bulky colored complex Fe(SCN)2+will depend on the micellarbound SCN- which in turn would be controlled by the competition of any other counterion present in the solution. Therefore, by looking at the changes of the complex concentration, one can measure the ionic exchange equilibrium from the bulk phase and not from the micellar one, and any hydrophobic contribution would be absent. On the other hand, the binding constants obtained previously by the method of absorbances1were rechecked by using ultrafiltration as an alternative method. It is felt that any attempt to throw light on the validity of the ionic exchange model in micellar systems and on the reliability of the values found would be welcome. Finally, we were able to calculate the free energies of tranfers for all of the anions studied, and the results are discussed in terms of several properties of the anions. Experimental Section Ultrafiltration Method. The experiments were performed in an Amicon cell of 50 mL fitted with a PM-10 membrane able to retain particles of molecular weights ~
~~~~
(1) Bartet, D.; Gamboa C.; SepGlveda, L. J. Phys. Chem. 1980,84,272. ( 2 ) Bunton, C. A.; SepBlveda, L. J. Phys. Chem. 1979,83, 680. (3) Septilveda, L.; Soto, R. Makrornol. Chem. 1978,179, 765. (4) Mukerjee, P. In “Solution Chemistry of Surfactants”;Mittal, K., Ed.; Plenum Press: New York, 1979; Part 1, Vol. 1. 0022-3654/81/2085-1429$01.25/0
greater than lo4. Solutions containing a constant concentration of CTABr and BS (4.0 X and 1.0 X M, respectively) and a variable concentration of added salt were prepared and ultrafiitrated through the cell. Samples of filtrate (5 mL) were collected, and their absorbances read in a Beckman DU-2 spectrophotometer at 262 nm, where BS has a molar absorbtivity of 395. The absorbances of all solutions were also measured before ultrafiltration. Using these two values, we calculated the fraction f of BS bound at any given concentration of added salt acccording to eq 1,where subindexes m and t denote f = BS,/BSt = (filtrand adsorbance filtrate absorbance) /filtrand absorbance (1) micellar and total species, respectively. No adsorption of BS by the membrane was detected. Ferric Thiocyanate Method, The formation constant of the complex in the absence of micelles was measured by preparing different solutions containing a constant concentration of 2 X loA2M FeCla and increasing conM. These concencentrations of KSCN up to 2.0 X trations assure that all existing SCN- was in the complex form which was measured at 560 nm and 25 f 0.1 OC. The formation constant of the complex is defined as
Kf = [Fe(SCN)z+]/([Fe3+][SCN-1)
(2)
and as [Feat] >> [SCN-1 >> [Fe(SCN)2+] the following relation can be obtained Kf[Fe3+]e A= [SCN-] 1 Kf[Fe3+]
+
(3)
in which A is the absorbance of the solution and E is the molar absorbtivity of the complex whose value was 780 mol-* (obtained under conditions in which the excess of FeC13assured that the known concentration of KSCN was entirely present in the complex form). In this way and according to eq 3, Kf may be calculated from the slope of the straight lines obtained by plotting A vs. [SCN-] provided that [Fea+]and e are known. The value obtained for Kf was 220 mol/L, in good agreement with previously reported value.6 The micellar effect upon the complexformation equilibrium was measured by recording the absorbances of solutions of constant concentration of FeBra or FeC13and KSCN and variable concentrations of CTABr (5) SillBn, L. G.; Marteil, A. E. Spec. Pub1.-Chem. SOC.1971, 25.
0 1981 American Chemical Society
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c
The Journal of Physical Chemistry, Vol. 85, No. 10, 1981
A
Gamboa et ai.
/
I
8
16
21
32
40
Figure 1. Absorbances ( A ) of the filtrate of solutions of 1 X M BS and 4 X lom3M CTABr as a function of the molarity of the corresponding salts.
and CTAC1, respectively. The concentrations of FeBr3 and 0.78 X M in the presence of 2.0 were 1.6 X X lo-, and 1.0 X lo-, M KSCN, respectively. The concentration of FeCl, was 2.0 X M in the presence of 2.0 X lo-, M KSCN. In order to avoid complications due to the presence of more than two counterions,we used CTACl in conjunction with FeCl,, whereas CTABr was used in conjuction with FeBr,. This last salt was prepared from a solution of Fe2(S04),treated with an equivalent amount of B a r z and followed by filtration in order to separate the insoluble BaS04. All solutions containing Fe3+ were standardized by the sulfosalicylic-complexmethod. Reagents. All reagents were Merck p.a. CTACl was a sample kindly supplied by Dr. C. A. Bunton from the University of California at Santa Barbara and which did not show a minimum in surface tension vs. concentration plot. CTABr from Matheson C. B. was recrystallized from ethanol-ether mixtures. Results and Discussion The experimental results show that addition of salts to solutions of CTABr containing BS results in the release of micellar-bound BS (detected as an increase in the absorbance of the filtrate as the salt concentration goes up). Some typical results are shown in Figure 1. These data can be interpreted in terms of ionic exchange between BS, the bromide coming from CTABr, and the anion of the added salt. Two cases can be clearly distinguished. In the first case the added salt carries bromide, i.e., the same counterion already present in CTABr. In this case, the only ion exchange would be between BS and Br- anions, and eq 10 of ref 1can be applied. This implies that a plot of ((1-f)/f)((la)[Dml- f[BSt]) (called Y) against [Brad] + f[BSt] (called X)should result in a straight line with a slope equal to the ionic exchange constant between BS and Br- (KBSIBr-). [D,] is the detergent concentration in micellar form, a is the micellar ionization degree taken as 0.2,196J and f is the fraction of BS bound to micelles at any concentration of detergent. Subindexes ad and t mean added and total,respectively. In the second case the added salt carries an anion different from Br- (eq 7 of ref 1must be used), which means that a plot of ((1- f ) / f l ( la)[D,] - f[BS,] - [CTAt]KBS/Brf-/(l - f + KBs/Br-))) (called Y? vs. (6) Quina, F. H.; Chaimovich, H. J. Phys. Chem. 1979, 83, 1844. (7) Romsted, L. S. Ph.D. Theis, Indiana University, Bloomington, IN, 1975.
1 2 3 4 Figure 2. Parameters of eq 10 of ref 1 obtained for NaBr by ultrafiltration. [BS] = 1 X lo3 M and [CTABr] = 4 X M.
Figure 3. Parameters of eq 7 of ref 1 obtalned by ultrafiltration for added NO3- and SO,'-. [BS] = 1 X lo3 M and [CTABr] = 4 X lo4 M.
[Ctl + f[BStl + [CTA#WBrr/(l - f + KmIBp)(called X? should result in a straight line with slope equal to the ionic exchange constant between BS and the added anion. Figures 2 and 3 show the plots of the equations described above for some anions. The ionic exchange constants
Free Energies of Transfer of Anions
The Journal of Physlcal Chemlstty, Vol. 85, No. 10, 198 1 1431
TABLE I: Ionic Exchange Constants for Different Anions Relative to BS Obtained by Ultrafiltration (UF) and by Absorbance Methods’ (A) anion 10zKK,BS/C (UF) P 10ZKeBSIC(A) 0.995 10.1 NO,10.7 Br9.6 0.997 9.2 so,5.0 0.996 5.7 c12.3 0.998 1.8 HP0,Z1.3 0.980 1.4 B,O,’0.8 0.979 1.4 F 0.5 0.968 0.4 a
r is the correlation coefficient for the UF method.
0.5
1.0
1.5
2.0
2.5
Flgure 5. Parameters of e 9 (see text): (A) [Fe(Br),] = 0.775 X lo-, M, [KSCN] = 1 X IO- M, and CTABr; (0) [Fe(Br),] = 1.55 X io-* M, [KSCN] = 2 X lo3 M, and CTABr; (0)Fe(CI), = 2.00 X lo-* M, [KSCN] = 2 X M, and CTACI.
9
\cm
9
to the following mathematical model. The exchange between thiocyanate, T, and the halide, H (chloride or bromide), can be expressed as H, + T, e Ha + T, (4) and the equilibrium constant, neglecting activity coefficients is KeT/H = [HJ [T,I/([H~I[T~I) (5) If a is assumed to be constant, the following condition might be obeyed:
L 8 12 1G Figure 4. Absorbances of solutions of (A) 1.55 X lo-* M Fe(Brb and (0) 2 X IO-* M Fe(Ci), at a constant concentration of 2 X M KSCN as a function of CTAB and CTACI molarities, respectively.
calculated from the slope of the corresponding straight lines are presented in Table I and are compared with those obtained in ref 1. The agreement between both methods is satisfactory although the correlation coefficient r is still poor for the weakly bound anions like HP042-and F-. Unfortunately the ultrafiltration method cannot be used to measure the OH- exchange constant since the membrane is not alkali resistant. In spite of the fact that both methods are based on the displacement of BS from the micelles by the added salts, the good agreement serves to confirm that the change in absorbances of a CTABr-BS solution when a salt is added is really due to the transfer of BS from the micellar phase to the water phase and not due to changes in micellar configuration. Thiocyanate-Complex Method As mentioned in the Introduction, the addition of CTA micelles to a system containing Fe(SCN)2+complex is expected to displace the equilibrium of reaction 1toward the left since the thiocyanate anions will be removed by micelles as a consequence of the exchange of these anions by the counterions accompaning the CTA micelles. This fact is indeed observed, as shown in Figure 4, where the absorbances of either KSCN-FeBr3 or KSCN-FeC1, solutions containing constant concentrations of both salts are plotted against the concentration of CTAl3r or CTAC1. The decrease in absorbances, which is proportional to the concentration of the complex, is more pronounced for chloride than for bromide, indicating that chloride is more weakly bound than bromide anion, as may be expected. The behavior discussed above can be analyzed according
[Hml + [ T m l = (1- a)[Drnl Mass balance of H and T results in [H,] = [H,]
(6)
+ [Ha] = 3[Fe3+]+ [CTAH]
(7)
[Ttl = [Tml + [Tal + [ F e ( s W 2 + 1 (8) where subindex t denotes total molar concentration. By using eq 3-8 and the reasonable aproximation that 3[Fe3+]+ [T,] >> a[D,] + CMC [Fe(SCN)2+](l+ 1/(Kf[Fe3+1)] one obtains the following linear expression (1- a)[Dml + A/e{l + 1/(Kf[Fe3+l)l= [T,] + 3[Fe3+]Kf[Tt][Fe3+] keTIHA (1+ 1/(Kf[Fe3+]))[Tt]+ 3[Fe3+]Kf[Fe3+] KeTiH
+ [Ttl
(9)
from which a plot of the first member (Y”j against 1/A should result in a strai ht line from whose slope the exchange constants KeTISican be calculated by using the known parameters occurring in the equation. The plots are shown in Figure 5, where Y” has been plotted against 1/A. In this way, the values obtained for the ionic exchange constants relative to SCN- were 122 for KtCNIC1 and 22.3 and 21.0 for KtCNIBr at a total [KSCN] of 2.0 X and 1.0 X lo-, M, respectively. The ratio of the K t C N and K 5CN/CI values corresponds to the exchange constant KeBrICtandgives a value of 0.18 as compared with 0.20 obtained from the absorbance meth0d.l The agreement between these two different methods is quite good in spite of the approximations made, especially that related to the constancy in a. In this respect we have tried to explore the influence of the a value upon the exchange Constants. Thus we calculated the ionic exchange constants in the
1432
Qamboa et al.
The Journal of Physical Chemistry, Vol. 85, No. 10, 1981
12t
TABLE 11: Total Free Energies of Transfer (Ap",) for Different Anions and Specific Free Energies of Transfer Apex Obtained After Subtracting the Electrostatic Contribution Apoe from Ap"c)
A
anion
\-
-4J0c,
kcal/mol
4.10 4.14 3.84 3.17 3.03 3.02 2.77 2.72 2.34 2.29
-0.736 -0.68 -0.39 0.28 0.43 0.43 0.68 0.74 1.12 1.17
NO;
Br-
s0,z-
ClB,O,'-
HPO,*-
4
+APOX,
kcal/mol
AcOcos*-
OHF
anc. ,.e standard free-energy change AGO, involved in this equilibrium is then given by (12) -RT In K, = AGO, = pot; poem- (pot,, p0$
+
+
On the other hand, the transfer free energy from water to micelles for C and C' taken separately is defined as AP0c
I
cy t
I
0.2
I
I
0.4
I
0.G
Flgure 6. Calculated Ionic exchange constants of NO3-, SO,", and
CI- relative to BS as a function of assumed values for the micellar ionlzation degree, a.
same manner as above for three different anions (NO3-, SO?-,and C1-) as a function of different values arbitrarily assigned to a. The results are presented in Figure 6. It can be seen that a clear linear relation exists between and a. The resulting negative slopes are -0.154, -0.0714, and -0.0357 for NO3-, SO?-,and C1-, respectively, and thus are higher for the more strongly bound anions. However, the percentage variation of K,BSIc for a equal to 0.1 and 0.4 relative to a = 0.2 (used in this work) is not big considering the experimental error. For example, for a = 0.1 the increase in is 15,10, and 14% for NO3-, Sod2-,and C1-, respectively, while an a value of 0.4 decreases K,BSIc 31,22, and 32% for the same sequence of anions. We feel that these numbers reflect the fact that the constancy in a is not crucial for the application of the ionic exchange model, since a variation of 100% in a is not to be expected for most of the anions studied here. The situation, however, is not so clear for weakly bound anions like F- or OH-, since some evidence has been found that a for this last anion could be as high as 0.5 or morea8
Free Energies of Transfer of Anions from Water to Micelles
Thermodynamically, the ionic exchange may be considered as a transfer free energy from water to micelles for all of the anions involved in the exchange, in the following manner. The ionic exchange equilibrium can be expressed as c, + Cm' P c,' + cm (10) in which C and C' denote the counterions present in the solution and subindexes a and m refer to aqueous and micellar phases as above. The corresponding ionic exchange constant is Ke = [Ca'l[Cml/([CJ[Cm'l) (11) (8) Sepiilveda, L., unpublished results.
e:
poem - pot.
APocf = Pocmt-
Pot:
(13)
From the above equations, eq 14 is easily obtained. Thus Apoct = Apoc + RT In K, (14) if a particular value for Ap0c and the corresponding value for K , are known, Apoct can be obtained from eq 14. In order to calculate Ap0c we insert the values of A p 0 ~ o a reported by Larsen and Magidg into eq 15 but express them in terms of molar fractions of total micellar volume rather than in terms of molarities in the Stern volume. All of the calculations may also be done in terms of the concentration in the Stern layer which could have a volume of -0.14 L/mol,lo but we believe that this approach leads to a more confusing understanding of the problem by introducing a parameter not completely well-defined. In this way Ap0~oais expressed by eq 15, which gives a value of AP0NOa- =
R T In ([NO3-.]/55.5)
X
([CTAmI
+ [NO~-mI)/[NO3-mI (15)
-4192 cal/mol. This value, together with the K, values reported here, is now introduced into eq 14 to obtain the values for all of the rest of the anions. The results are shown in Table 11. As expected, Ap0c for all of the anions studied is less than zero, indicating that the transfer process from water to cationic micelles is always spontaneous. The table also illustrates the dependence of Ap0c on the nature of the anions. Up to now, this difference has been expressed qualitatively in terms of lyotropic series, and Stigter defines it as the specific adsorption potential." The dependence of Ap0c on the nature of the anions can be analyzed by splitting Ap°C into two contributions: Apoc = Apoe Apox (16)
+
where Apoe is the electrostatic contribution and Apo, is an unknown contribution responsible for the differences in behavior of the anions. If the location of the anions in the micellar surface is the same, i.e., they are located at a distance or in a place (9) Larsen, J. W.; Magid, L. J. J. Am. Chem. SOC.1974, 96,6774. (10) Bunton, C. A.; Cerichelli, G.; Ihara, Y.; SepGlveda L. J. Am. Chem. SOC.1979,101,2429. (11) Stigter, D.J. Phys. Chem. 1964,68,3603.
The Journal of Physlcal Chemistry, Vol. 85, No. 10, 1981 1433
Free Energies of Transfer of Anions
5t
- _ _ _ - - -Ani I
1
1.2
1.G
1
2.0
S t o k e s ' t a w Hydrated Radius
2-4
i
Flgure 7. Transfer total free energies Apoc (0)and specific transfer free energies Ap", (A) as a function of the hydrated radius of the given anions.
where the surface potential is the same, Apoe must be a constant, and any specificity must be attributed to the extra term Apex. On the other hand, it might be possible that anions penetrate the micellar surface at a different depth, which would mean that the specificity could be entirely included in the Apoe term, and thus the potential at which the anion is located may be calculated according to eq 17. = Apoc/(ze) (17) Proceeding this way, it is possible to compare the experimental values of Ap0c with those calculated from eq 17 by assuming different values for the surface potential. The Apoc values calculated in this manner go from -920 to -4610 cal/mol for a surface potential going from 40 to 200 mV, respectively. A surface potential of -100 mV corresponds to the transfer free energy of the most weakly bound anions like F- or OH-, and a surface potential of -180 mV would be necessary for strongly bound anions like NO3-. It can be seen that the calculated surface potentials are reasonable and in the range of reported value~.~*-~~ On the other hand, if one attempts to interpret the specificity through Aho, by maintaining Apoe constant, the value of 150 mV may be chosen (some sort of average of the reported values) and the specific factor Apox can be calculated. The values obtained are included in Table 11. If the chosen value for the surface potential of CTA micelles is correct, it is found that alJ of the weakly bound anions have a positive contribution to the specific factor, which may be explained, by following Stigter," as due to disarrangement of water molecules around the ions in the Stern layer. This effect would add a positive or repulsive term to Ap"0 In other words, it would suggest that the specific factor is related to a repulsive potential rather than to an attractive potential. This repulsive free-energy contribution is exhibited by the more hydrated anions like F- or OH-. The above discussion is based on the assumption that the anions are located at a distance from the micellar surface at which the potential is 150 mV. The situation lead to a certain degree of compromise between the dehydration and the closer approximation of the anions to the micellar surface. In this way the nonhydrated anions like N03- would be bound exclusively by electrostatic forces in contrast to the weakly bound anions which are also very hydrated and therefore may remain a t a distance where the surface potential would be less than 150 mV, or they may enter the Stern layer, losing water of hydration, which (12) Hartley, G.S.;Roe, M. Trans. Faraday SOC.1940,36, 101. (13) Stigter, D.;Mysels, K. L. J. Phys. Chern. 1966, 59, 45. (14) Fernlndez, M. S.;Fromherz, P. J. Phys. Chern. 1977,81, 1755.
-ash L.U.
NO
