Dissociation of acids in aqueous micellar systems

Analytica Chimica Acta. 140 (1982) Elsevier Scientific

DISSOCIATION

Pubhshing

89-97 Company, Amsterdam

OF ACIDS IN AQUEOUS

-

Printed

in The Netherlands

MICELLAR

SYSTEMS

A. L. UNDERWOOD

Department of Chemistry. Emory (Received

23rd

November

University. Atlanta, GA 30322

(U.S.A.)

1981)

SUMMARY Incorporation

in charged

varying type. Analysis reasonably satisfactory and the exact character

micelles

induces

large

pKa shifts

for

a number

of acids of

of the measurements in terms of simple electrostatic theory is in view of uncertainties regarding the net charge on the micelle of its surface. The behavior of the long-chain fatty acids, whose

mode of incorporation in micelles that the effective dielectric constant

is least uncertain, confirms the suggestion at the micellar surface is quite low.

of others

Several workers have measured pK values of dissociable amphiphiles above their critical micelle concentrations [l-3] _ The observed shifts from intrinsic values were satisfactorily interpreted in terms of micellar charge by using the electrostatic treatment developed by Katchalsky and Gillis [4] and Arnold and Overbeek [5] for monomeric polyelectrolytes. A similar approach was successful in rationalizing the pK values of dissociable amino acid side-chains in terms of the charge on the globular protein ribonuclease [6,7] _ In a like manner, the charge on an ionic surfactant micelle influences the pK value of an incorporated guest molecule_ This was first observed by Hartley with acid-base indicators [8], and similar examples have been reported more recently [9-13]_ These pK shifts for solubilized indicators have been ascribed partly to the low dielectric constant at the micellar surface and partly to the surface potential [12, 13]_ Information regarding micellar effects on the pK values of a wider variety of acids and bases is of interest in connection with the increasing use of aqueous micellar systems as solvents in analytical chemistry [ 141 as well as in other areas such as micellar catalysis [15]. Such studies may also suggest the possibility of analogous pK shifts for biologically active compounds induced by their incorporation in membranes, liposomes, or surfactant micelles. EXPERIMENTAL

Apparatus

and reagents

The pH values were measured with a Leeds and Northrup Model 7401 pH meter using a standard L&N 1199-30 glass and 1199-31 calomel electrode pair. The excessive drift which was found to be associated with tile fiber

90

junctions of certain calomel electrodes in surfactant solutions was not encountered. Sodium dodecyl sulfate (SDS; U.S.P.; Fisher Scientific) was leached four times with ether, recrystallized twice from ethanol, and dried in vacua over silica gel at 60°C (m-p. 179”C, dec.). Dodecyltrimethylammonium chloride (DTAC; General Mills Chemicals) was obtained as an aqueous 50% solution called Aliquat 4; the solution was lyophilized and the solid residue was recrystallized twice from acetone and dried in vacua over phosphorus pentoxide at 40°C (m-p_ 252-255”C, dec_). (As reported earlier [IS], this material is very hygroscopic; weighings were done in a dry box.) Dodecylammonium chloride (DAC; Eastman Kodak) was recrystallized from an ethanol-acetone mixture and dried in vacua over silica gel at 40°C (m-p_ 178-179”C, dec.). Hexadecylpyridinium chloride (HPC; Aldrich Chemical) was recrystallized twice from an ethanol-acetone mixture (with a charcoal treatment during the first recrystallization to remove a yellow impurityj and dried in vacua over silica gel at 40°C (m-p. 82.5”C). Hexadecyltrimethylammonium bromide (HTAB; Baker, Analyzed Reagent) was used as obtained_ Dodecanoic (Eastman Kodak), hexadecanoic (Matheson), and octadecanoic (Fisher Scientific) acids were specially purified via their molecular compounds with acetamide by the method of Magne et al. [17] ; they were finally recrystallized from aqueous ethanol and dried in vacua over silica gel at 40°C The respective melting points were 44.5-45_5”C, 62.0-62_5”C, and 68.5-69.5”C (lit., 44”C, 63-64”C, and 69-70°C [IS] ). Other compounds were recrystallized from suitable solvents until melting points were satisfactory. Procedure Solutions were protected against carbon dioxide. Typically, an 8 X 10e3 M standard solution of the guest acid or base in aqueous 1 X 10-l M surfactant was prepared, sometimes with gentle warming to speed solution. To an aliquot of this solution were added measured quantities of standard sodium chloride and either sodium hydroxide or hydrochloric acid solutions, and the solution was diluted to 50 ml. The pH value was determined at 22.0 + 0.5”C. The final solution was generally 4.00 X 10” M in guest, 5.00 X lo1 M in surfactant, and either 2.00 X 10-i or 4.00 X 10-l M in sodium chloride_ Each reported pK, is the mean of four values obtained with solutions which were 20,40,60, and 80% titrated to the appropriate equivalence point. RESULTSAND DISCUSSION Fatty acids in SDS In order to relate the pK, shift for a solubilized guest to the micellar charge, an intrinsic value, pK&ti~, is required as a reference. Ideally, this would be the pK, displayed by the guest in a hypothetical micelle identical in other respects to the one in question but bearing no charge. _4 reasonable

91

choice which can be estimated from the literature is the pK, which the acid would exhibit as a free solute in a solution of the same overall composition as the one in which it is, in fact, solubilized. Thermodynamic K, values for the homologous series from acetic to nonoic acid at 25°C are available [ 19]_ (This temperature is close enough to the one used here; for esample, in one study the pK, for acetic acid changed from 4.7562 at 20°C to 4.7560 at 25°C [20] _) Of various plots involvin g K, or pK, and the length of the alkyl chain, the one which appeared to be linear was K, vs. t.he logarithm of the number of carbon atoms, provided that the point for propionic acid, which was peculiar in all of the plots, was excluded. Extrapolation of the leastsquares straight line for the remaining seven points as shown in Fig_ 1 yielded hypothetical thermodynamic pK, values for dodecanoic, hexadecanoic, and octadecanoic acids of 4.98, 5.03, and 5.05, respectively. Corrections for solution conditions were then applied_ The pK, values for acetic acid at the same concentration as that of the solubilized guests were determined in appropriate surfactant-sodium chloride solutions. For example, at alevelof4.00 X 10e3Min 5.00 X 10-'&lSDS and 2.00X 10-Ihl sodium chioride, the pK, for acetic acid was 4.62. Subtraction from the thermodynamic value of 4.76 [19] gave a correction of 0.14 which was applied to the long-chain acids to give the pK,,,,, values in Table 1. This procedure is based on the assumption that acetic acid is not incorporated in the micelles but rather is subject to only general electrolyte effects in surfactant solutions. Apparently this is valid, because 4.62 is close to a reported value of 4.64 for acetic acid in 2 X 10-I M potassium chloride [21] . In some cases, the location and orientations of the dissociable groups of the guest compounds are uncertain, but for the solubilized long-chain fatty acids it is difficult to imagine anything other than mixed micelle formation, with hydrocarbon chains mingling with surfactant tails in the interior and carboxyl groups in the Stem layer, as suggested schematically in Fig. 2.

1.6 -

1

I I I I 0.8 1.0 1.2 0.6 0.4 logarithm of the number of carbon atoms

Fig. 1. Estimation of thermodynamic Ka values for dodecanoic, hexadecanoic, and octadecanoic acids. The solid circles show the data of Dippy [ 19]_

92

TABLE pl;,

1

shifts and micellar

charge values for 4.00

2.00

Acid

x 10-l

Pl(,(int)

x 10e3 M fatty

4.00

M NaCI L

P&(,X,)

acids in 5.00 x 10-l

P%irh)

x 10-r M SDS

M NaCl PKw,)

z

Dodecanoic

4.85

7.40

-25

4.81

7.38

-28

Hesadecanoic Octadecanoic

4.89 4.91

7.62 7.59

-27 -26

4.86 4.88

7.55 7.45

-29 -28

Hence

these acids should

plicability

provide

of simple electrostatic

well-behaved

systems

for testing the ap-

theory to this type of guest-host

interaction

and for interpreting observations on guest molecules whose mode of incorporation in micelles is less obvious. Thus mice&r charges calculated from the pli, shifts for solubilized fatty acids will be compared with values obtained by other methods. The charge is z = an, where CYis a degree of counterion dissociation and n is the aggregation number. Unfortunately, literature values for both Q and n scatter rather badly. Romsted has compiled CYvalues for a number of ionic micelles [ 223. For SDS, these range from 0.14 to 0.70. After two extreme values are dropped, the average of the remaining twenty-

eight is. 0.22 with a relative average deviation of 21% [ 221. Variation of a with electrolyte concentration is buried within the uncertainty 1231. A value of CY= 0.22 is used here. For SDS in 2 X 10-l M sodium chloride, the smallest n value reported seems to be 101 [24] ; excluding this and the highest value of 169 [ 251, which seems aberrant because the next highest is 123 1261, one

Fig. 2. Schematic section of an SDS micelle containing hydrocarbon interior, polar head groups, and bound depicted_

solubilized long-chain fatty acid; and dissociated counterions are

93

obtains a mean literature value of 113. This gives z = -25 micellar charge in 2 X 10-l M sodium chloride. The equation can be written [ 6,7, 271 pKa(exp) = PK,,,,,

- O-868Wz

for the SDS

(1)

The term 0.868~2 represents the work required to remove a proton from the surface of a sphere of uniformly-distributed charge z. The electrostatic interaction factor w is given by w = [e*/2DkTb]

-

[&/(2D’kT)

(1 + ~a)]

(2)

where E is the unit of charge, D and D’ are dielectric constants (see below), k is the Boltzmann constant, T is the temperature, b is the radius of the sphere, and (I is the distance of closest approach_ The Debye-Hiickel constant, K, depends on the square root of the ionic strength, 1-1 K * = 8iie*Nd~/lOOOD’kT

(3)

where N is Avogadro’s number and d is the density. It is not totally clear how to evaluate the contribution of a micellized surfactant to the ionic strength of a solution; here, sodium chloride became the major contributor. The value 19-7 9, recommended by Emerson and Holtzer [28] was selected for b, the micellar radius. The distance of closest approach, a, is the sum of radius b and the radius of the hydrated hydrogen ion. In the absence of a firm recommendation fcr the latter term, the distance across a pair of water molecules separated by a “hydrogen bond” H atom, was measured using CPK models: this gave 3.4 a for the radius and hence 23.1 .r\ for a. This is perhaps little better than a guess in regard to a proton darting from one site to another in a fluctuating cluster of water molecules, but it yields a reasonable number for a term in which a small error does not have a large impact. Now, if the bulk solvent dielectric constant is inserted for both D and D’ in Eqns. (2) and (3), then the charge z calculated for the SDS micelle from Eqn. (1) using the pK, shifts for the fatty acids is of the correct order of magnitude but probably too large. For example, in 2.00 X 10-l M sodium chloride, u from Eqn. (2) is 0.056, and Eqn. (1) then gives z = -52 from the pK, shift for dodecanoic acid. In order to obtain the desired charge of -25, w must be 0.118. This value can be used to obtain the dielectric constant at the micellar surface and the result can be compared with the estimates of others. Different values are required for D and D’ in Eqn. (2): D’ is the bulk solvent value (for which 79 is used here) and D should be a “suitable” average between the bulk value and a Stem layer value. Equation (2) yields D = 56 for this average. If, for want of a better formula, this value is viewed as the arithmetic mean of 79 and the Stem layer value, then the latter is 33, not far from the dielectric constant of a fairly polar organic solvent such as methanol or nitrobenzene. Despite the approximations, this result agrees well with the conclusions of others. As examples, the study of highly solvent-

94

dependent charge-transfer absorption bands led to an estimate of 36 for the effective dielectric constant at the surface of a dodecylpyridinium iodide micelle [29], and the value of 32 has been given for SDS and HTAB from a study of micelle-bound pH indicators [12]. Additional references can be found in a recent discussion [ 301. The value w = 0.118 was used to calculate values of z based on pK, shifts for the other two fatty acids from Eqn. (1); the results are shown in Table 1. The same approach with dodecanoic acid for solutions which were 4.00 X 10-l M in sodium chloride, based on (Y = 0.22 and n = 126 1161, gave w = O-106 and a dielectric constant for the micellar surface of 35. Using this value for w in Eqn. (1) gave about the same value for z from the pK, shifts of the other fatty acids, as seen in the table. The agreement among the z values for the three acids suggests that the micellar interior is sufficiently fluid to accommodate 15- and 17-carbon chains as easily as 11. The C,7 chain of octadecanoic acid, which is over 40% longer than that of the host, does not prevent the carboxyl group from nestling in the Stem layer in the same manner as that of dodecanoic acid. The SDS concentration ir, these experiments is below the so-called “second c.m.c.” where large, rod-like micelles are thought to form [31], and the assumption of sphericity is reasonably valid, although the micelles may be somewhat ellipsoidal [ 32]_ It is assumed that incorporation of the guest molecules does not alter the parameters Q and n and that these remain COP.star& as the guest is titrzited. From the c.m.c. value of 9.0 X lo* M for SDS in 2 X 10-I M sodium chloride [ 331, retaining n = 113 and assuming that the guest acid is distributed uniformly in a monodisperse micelle system, one calculates for 4.00 X 10e3 M guest in 5.00 X 10” M SDS that there are nine guest molecules per micelle, i-e., that about 7% of the molecules in the micelle are guests. Because, within experimental error, the measured p.K, of the guest is unchanged during the titration, the micellar charge remains about the same; perhaps the effect of the guest’s carboxyl ionization is countered by the binding of additional sodium ions as the titration proceeds_ Because of the uncertainty in literature values for LYand n, there is little point in attempting to evaluate possible changes caused by the insertion of the guest. It would be interesting to observe the influence of cationic micelles on the pK, values of solubilized fatty acids, but this was impossible for DAC, DTAC, HPC, or HTAB_ Although the free acids are solubilized in such systems, the solutions become cloudy on titration with sodium hydroxide and heavy precipitates form on standing, i.e., insoluble salts are formed by the alkyl carboxylate and cationic surfactant ions in preference to soluble mixed micelles at room temperature. (For 4.00 X 10e3 M dodecanoic acid in 5.00 X lo-’ M DAC and 2.00 X lo-’ M sodium chloride, the turbidity disappeared on warming, and the pK, was shifted in the expected direction to about 4.1 at 38°C; for quantitative purposes, the warm surfactant solutions provide an escellent titration medium [ 34]_)

95 TABLE

2

pl(, shifts and calculated micellar charges with some surfactant solutions at 2.00 x 10-l EVINaCl Acid

PKzi(int)

SDS P”a(exp)

Z-Naphthoic 1-Naphthaleneacetic s-Quinolinol (PI&,) (PR,,) Bmcine

Quinine Sulfathizzole

(PK&

(PKa,) (PK,,)

(ph’,,) (PKa,)

4.03 1351 4.10 1361 5.02 1371 9.67 1371 8.28 [381 4.13 [391 8.52 I391 2.1 [401 7.27 IllI

Approximate micelIar charge. z. estimated from the literature

5.59 5.14 5.72 10.29 9.31 5.35 9.79 2.90 7.61

3.00 x lo-’

DTAC = -15 -10 -7 -6 -10 -12 -12 -8 -3 -25

HPC

PKa(exp) 4.13 4.06 4.26 9.35

-1

4.20 7.57 1.46

-1

6.12

M acids in 5.00 X 10.’ IU

z

PKa(exp)

0 7 3

4.28 4.18 9.03

9 6

4.03 7.26 1.06

11 11

5.96

HTAB z

-

Ph’,(,,P)

-2

12 9

=

4.40 3.98 9.44

-4 14 9

1 18 14

3.89 7.37

3 15

StrOIlE

-

18

acid 6.12

15

20

20-30

Other acids in SDS Table 2 shows intrinsic and experimental pK, values for a variety of acids different in structure from those of the fatty acid series. Where the charge type was the same as that of the fatty acids, the corrections obtained from acetic acid as described above were applied in estimating pk’,,,,, values based on the literature; in other cases, the literature values indicated in the table were used directly. In any event, these values probably vary in reliability and should be viewed as approximate. The z values in the table were calculated from Eqn. (1) using w = 0.118 as obtained above with the fatty acids. It is seen that the resultfng micellar charges are much smaller than those from the fatty acid study. It is unlikely that the guest molecules, at the low level studied, actually change the charge to the extent indicated in the table, nor can the values be esplained by errors in pKacinrj_ For esample, to obtain z = -25 using pK,, for quinine, an intrinsic value of 2.8 would be required instead of 4.1; an error of this magnitude in the literature value is unlikely. The charge calculation is biased toward z = -25, provided that the microenvironment of the dissociable groups is similar to that provided by the micelle for the fatty acid carbosyl group. Although it is not realistic to propose a model in which the position of the guest is explicit based upon approximate calculations, it seems reasonable to suggest that the solubilization of the acids in Table 2 is a surface phenomenon different from the mode of incorporation of the fatty acids. Whereas the hydrocarbon chains of the latter experience a strong hydrophobic interaction in the micellar core, the molecules in Table 2 not only possess polar groups but are highly polarizable as well. It may be supposed, then, that interaction of these molecules is restricted to the micellar surface, placing their dissociable groups near but not totally within the Stern region. The calculated charge of -3 based upon may be taken as virtually zero; perhaps the cationic PK,: of sulfathiazole

96 diacid, H:B ÷, interacts appreciably with the anionic micelle, leading to the calculated charge of --8, while the neutral HB form experiences a very weak interaction, or possibly none. However, in most case, the observed pKa shifts are not trivial and a pronounced influence of micellar charge on the work of proton removal from the guest is indicated. Other acids in cationic rnicelles The acids in Table 2 exhibited interesting behavior in the cationic micelles of DTAC, HPC, and HTAB. (In DAC, turbid viscous solutions were obtained in several cases which were unsuitable for measurement except at temperatures above about 35°C, and this system was not studied carefully.) The z values in the table were obtained from PKa shifts using Eqn. ( 1 ) w i t h values of w calculated from Eqns. (2) and (3) with D = 56 and D' = 79. Values of radius b were obtained from the literature value employed above for SDS [ 28] by comparing molecular models of the cationic surfactants and an SDS model, with the following results: DTAC, 19.3 £; HPC, 25.7 £; and HTAB, 24.4 3,. The w values were then as follows: DTAC, 0.119; HPC, 0.083; and HTAB, 0.089. The z values on the b o t t o m line of the table are based on estimates of ~ and n obtained by admittedly crude interpolations and extrapolations to the present conditions, using literature values from a large number of sources, and represent only rough guides. It is seen that micellar charges calculated from the pKa' shifts are probably too low in several cases, suggesting again that the dissociable groups find themselves in a microenvironment quite different from those of the fatty acid carboxyl groups. In the case of PKa, for quinine, it is probable that the dication is sufficiently water-soluble to preclude appreciable interaction with cationic micelles, leading to calculated z values near zero. With sulfathiazole, it is seen that the cationic micelles influence PKa~ much more than does SDS; one may suspect that the anionic dissociation product forsakes the SDS micelle, facilitating the dissociation nearly as much as the negative micellar charge hampers it. In summary, incorporation in miceUes induces significant pK shifts in a n u m b e r of guest molecules of varying types. These shifts can generally be rationalized by means of simple electrostatic theory; calculated micellar charges are of the proper magnitude, and, in some cases, reasonable assumptions lead to close agreement with independent estimates from the literature. The pK shifts are too large to be ignored by analytical chemists and by other workers encountering such systems in their several fields.

Helpful conversations with Profs. H. L. Clever, F. M. Menger, and C. G. Trowbridge and a grant-in-aid from the Emory University Research Committee are gratefully scknowledged. REFERENCES 1 F. Tokiwa and K. Ohki, J. Phys. Chem., 70 (1966) 3437. 2 F. Tokiwa and K. Ohki, J. Phys. Chem., 71 (1967) 1827. 3 S. H. Yalkowsky and G. Zografi, J. Colloid Interface Sci., 34 (1970) 525. 4 A. Katchalsky and J. Gillis, Recl. Tray. Chim., 68 (1949) 879.

97

5 6 7 8 9 10 11 12 13

14

15

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

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