FUMIKATSU TOKIWA AND KENJIOHKI
1824
Potentiometric Titration of Amphoteric Surfactants in Micellar Solutions
by Fumikatsu Tokiwa and Kenji Ohki Research Laboratories, Kao Soap Company, Wakayamu-ahi, Japan
(Received December 9 , 1066)
Potentiometric titration curves have been obtained for micellar solutions of amphoteric surfactants, N-dodecyl-P-aminopropionic acid (DAPA) and N-dodecyl-8-iminodipropionic acid (DIPA), in the presence of 0.10 M sodium chloride. The potentiometric equation for surfactant micelles, proposed in the previous paper, has been developed to describe the electrochemical behavior of these amphoteric surfactants. The surface potential, evaluated from the titration curves, of the DAPA micelle is higher than that of the DIPA micelle, and their potentiometric behavior was discussed on the basis of a Gouy-Chapman model for a uniformly charged plane. The different potentiometric behavior between DAPA and DIPA micelles may be accounted for by different structural features of the micelles, probably the DIPA micelle having a looser structure.
such high concentrations as a test solution, the experimentally measurable P can be used as PM. In the previous paper' the general potentiometric The purpose of the present paper is to extend the titration equation for polyelectrolyte^^^^ has been above potentiometric equation for micelles to the insuccessfully applied to the interpretation of potentioterpretation of the electrochemical behavior of ammetric titration data of a nonionic-cationic surfactant, photeric surfactants. The micelles of amphoteric dimethyldodecylamine oxide ( C I ~ H ~ ~ N ( C H S+) ~ O H surfactants composed of acidic and basic groups are of CI2Hz&(CH&0 Hf), by taking into account the interest as a model of amphoteric colloids. The electromicelles formed in the solution above its critical micelle chemical behavior of these micelles resembles that of concentration (cmc). An expression for the potentioproteins, while their chemical structure relates them metric behavior of the micelle of this surfactant can to the common surfactants. be written' The amphoteric surfactants studied are N-dodecylP-aminopropionic acid (abbreviated as DAPA) and N-dodecyl-p-iminodipropionic acid (abbreviated as DIPA) which can exist in both anionic and cationic where p K o , is ~ the negative logarithm of the intrinsic forms depending upon the pH of the solutions. With dissociation constant of the micelle and Gel is the elecDAPA, these two forms are related by the equilibrium trostatic free energy of the micelle carrying t positive (whereR = C12H25) ~ eq 1 can be expressed as1 charges. Here, the / 3 in CH2CHzCOOH + z = C O / C PM = (P - xPrn)/(l - 2); (2) I R-N+-HZ where p is the observed degree of ionization of the surCH2CH2COOCH&HzCOOfactant, &, and BM are the degrees of ionization of the + I I monomer and of the micelle, respectively, c is the total R-N-H R-N +-H2 concentration of the surfactant, and co is the monomer concentration which can be assumed to be nearly (1) F. Tokiwa and K. Ohki, J . Phya. Chem., 70, 3437 (1966). equal to the C M C . ~ , ~ For sufficiently concentrated (2) A. Katchalsky and J. Gillis, Rec. Trav. Chim., 68, 879 (1949). (3) R. Arnold and J. Th. G. Overbeek, ibid., 69, 192 (1950). solutions where c is very large compared to cot 2 ap(4) E. Hutchinson, Z.Phy8ik. Chem. (Frankfurt), 21, 38 (1959); proaches zero and then PM also approaches p, as deE. Hutchinson, V. E. Sheaffer, and F. Tokiwa, J . Phya. Chem., 68, scribed in eq 2. Thus, when we choose a solution of 2818 (1964).
Introduction
+
=
The Journal of Physical Chemistry
POTENTIOMETRIC TITRATION OF AMPHOTERIC SURFACTANTS
With DIPA, the equilibrium is
-
CH&H&OOH
I
CHzCH2C00-
I
R-N+-H
R-N +-H
G I
I
CH&H&OO-
CH&H&OO-
5R-NII
I I
R-N+-H
CH&H&OO-
CHaCH2COO-
Expressing the degree of ionization of the carboxyl group as (Y and that of the amino (or imino) group as p, we may write the forms of the potentiometric equations for the micelles of these surfactants &s pH
&M
- log l-(yy =
+
pK(’)o,~
-(
0.434 bG,l({, bv
kT
”’>
(3)
(4) where p K ( a ) oand , ~ P K ( ~ ) ~are . Mthe intrinsic dissociation constants of the acidic and of the basic group, respectively, and the subscript, M, refers to the micelles. The state of ionization of the amphoteric micelles is given by the number of positive (S) and negative ( v ) ionized groups carried by each micelle, and the net charge (f - v) substantially contributes to the electrostatic free energy of the micelle.
Experimental Section Materials. N-Dodecyl-p-aminopropionic acid (DAPA) was prepared by the reaction of dodecyl amine with P-propiolactone in acetonitrile at 25-30’ for 4 hr, according to Gresham, et aL8 (The dodecylamine used was shown to be more than 99.5% pure by gas chromatography.) The crude product was purified by repeated recrystallization from a mixture of acetone and water and then dried under vacuum. Thin layer chromatography showed that the purified sample was free of the unreacted amine but contained a very small amourit of N-dodecyl-p-iminodipropionic acid (less than 1 .O% by mass spectroscopy). N-Dodecyl-p-iminodipropionic acid (DIPA) was prepared by the reaction of the dodecylamine with methyl acrylate in methanol at 70-75” for 15 hr, followed by saponification of the methyl ester of DIPA with sodium hydroxide.7 The product obtained was
1825
in the form of the sodium salt of DIPA. It was repeatedly recrystallized from a mixture of acetone and water and then dried under vacuum. The presence of DAPA could not be detected by thin layer chromatography and mass spectroscopy. Preparation of Solutione. Stock solutions were prepared on a weight per volume basis and diluted volumetrically to the desired concentrations. Glass-redistilled water was used to make up all solutions. pH Measurements. A Potentiograph E-336 pH meter (Metrohm Herisau Co.), accurate to 0.01 pH unit, was used with Beckman standard buffers. The titrations were carried out in an atmosphere of purified nitrogen a t 25”, using standardized hydrochloric acid and sodium hydroxide solutions containing sodium chloride of a concentration equal to that in the sample solutions, the procedure described in the previous paper being employed.‘ The concentration- of free acid is deduced from the measured pH assuming that the activity coefficient of hydrogen ion in the surfactant solution is the same as that in a corresponding hydrochloric acid or sodium hydroxide solution containing no surfactant. The forward titration curve, i.e., from the acid to the alkaline side, waa compared with the backward curve to check the titration process. They were almost coincident with each other. In the present experiment, the titration on the acid side of the pH which the sample solution exhibited was carried out by using the acid titer, and the titration on the alkaline side was done by the alkaline titer to minimize a change in surfactant concentration during the course of the titration. With DAPA, the solution was viscous and turbid in the region of pH 3.0-4.5. With DIPA, the solution was also in the similar state in the region of pH2.3-4.2. Determination of Critical Micelle Concentrations. The cmc values of DAPA and DIPA at different pH were determined by the solubilization method described elsewhere.8
Results Figure 1 shows the modified potentiometric titration curves for the carboxyl group of DAPA, pH log [a/(l - a)] vs. a, at different concentrations in 0.10 M NaCl solution. While the quantities of pH ~~~
(5) K. Shinoda, “Colloidal Surfactants,” Academic Press Inc., New York, N . Y.,1963,p 25. (6) T. L. Gresham, J. E. Jansen, F. W. Shaver, R. A. Bankert, and F. T. Fiedorek, J . Am. Chem. SOC.,73, 3168 (1951). (7) E. H.Riddle, “Monomeric Acrylic Esters,” Reinhold Publishing Corp., New York, N. Y., 1954,p 153. (8) F. Tokiwa, Bull. Chem. Soc. Japan, 36, 222 (1963). ~
Volume 71, Number 6 May 1967
FUMIKATSU TOKIWA AND KENJI OHKI
1826
4.0
r-----l t
q
I
.
Q
I 10.0
-
9.5
0
+
% 0
0.5
9.01
1.0
a.
Figure 1. The modified potentiometric titration curves for the carboxyl group of DAPA a t different concentrations in 0.10 M NaCl solution. The part indicated by a broken line denotes the region where the solution was turbid and viscous.
log [a/(1 - a)] are practically independent of a below the cmc, they are markedly dependent on a a t concentrations higher than the cmc. The crnc of DAPA in M in the 0.10 M NaCl solution lies a t (0.3-3.5) X range of pH 2.3-11.0, although it changes with pH. At high concentrations where c is very large compared to co, L e . , z ( = c o / c ) is near zero, CYM approaches a since LYM = (CY- zam)/(l- 2). In fact, the pH log [ a / ( l - a)]us. a curves at concentrations higher than 0.03-0.05 M converges to a single curve. The curve a t such high concentrations thus represents the pH - log [ a ~ / (-l a ~ )us. ] CYM relation for the micelle, which is shown by a thick line in Figure 1. Figure 2 shows the titration curves for the amino group of DAPA a t different concentrations. The thick line also represents the pH log [&/(l - PM)] VS.@M curve for the micelle. Figure 3 shows the titration curves for the second carboxyl group of DIPA, where a‘ is the degree of ionization of the second carboxyl group. Unfortunately, the curves for the first carboxyl group could not be obtained because of formation of insoluble material and high viscosity in the region of interest. The cmc values of DIPA in 0.10 M NaC1 solution were found to 111in the range of pH 4.8-11.0. be (0.7-1.8) X Figure 4 shows the titration curves for the imino log [P/(l - p ) ] group of DIPA. Variation of pH with p is rather small even at high concentrations.
+
0
0.5
1 .o
8.
Figure 2. The titration curves for the amino group of DAPA at different concentrations in 0.10 M NaCl solution.
6.0
1
0.030
0.01 0
I 4.5
- 0.0050
0
0.5
1.0
a’.
Figure 3. The titration curves for the second carboxyl group of DIPA a t different concentrations in 0.10 M NaCl solutions.
sentially governed by the degrees of ionization of the acidic and basic gro~ps.~JOIn the first instance, let us consider the surface potential of the DAPA micelle on the acid side of the isoelectric point. Since the last term of eq 3, bG,l({, Y ) / ~ Y represents , the electrical work necessary to remove a hydrogen ion from the micelle with ({ - Y ) charges, eq 3 can be rewritten
+
Discussion The electrostatic potential a t the surface of the amphoteric micelle carrying ({ - Y) charges is related to the electrostatic free energy of the micelle which is esThe Journal of Physical Chemistry
~
(9) A. Katchalsky and I. R. Miller, J. Polymer Sci., 13, 57 (1954). (10) A. Katchalsky, N. Shavit, and H. Eisenbery, ibid., 13, 69 (1954).
POTENTIOMETRIC TITRATION OF AMPHOTERIC SURFACTANTS
1
a I
1827
4.0
i
0.050H
*. X
E
9.5
2.0
0 .-(
0.0I 0 0.0050
+
1
I
0
5 -2.0
t
-4.0
0.5
0
t
1
Figure 5. The +O u8. p curves for the micelles of DAPA and DIPA, where p is (cry - BY) for DAPA and (QM a’y - BY) for DIPA.
1.0
B.
+
Figure 4. The titration curves for the imino group of DIPA at different concentrations in 0.10 M NaCl solution.
4.0
7
where tLo is the electrostatic potential at the surface of the micelle and 4 is the elementary charge. In the present case, pK ( B ) o , ~ and pK‘b’~ ,M are separate enough to consider the ionization of the carboxyl group and of the amino group to be independent of each other. Namely, under the condition where the ionization of the carboxyl group takes place, it remains that BY = 1and then the potential in eq 5 is reduced to
~LO(CYM,PM) = ~ L o , ~ M - I ( c Y M )
(6)
Figure 6. The dependence of micelles of DAPA and DIPA.
As is easily understood from eq 5 and 6, a difference between the quantities of pH - log [ c Y M / ( ~ - (YY)] at CYM = 1 and at a certain CYM corresponds to 0.434(qbO/ IcT). Using Figure 1, the surface potential a t each CYM can be obtained from this difference.‘ From a similar consideration, we obtain the following expression for evaluating the surface potential of the DAPA micelle on the alkaline side-the eleotrical work in this case, however, is the one required in combining a hydrogen ion with the micelle carrying (C - u ) charges.
The surface potential a t each PM can be evaluated from log [&/(1 - P M ) ] vs. BY curve shown in the pH Figure 2. Combining the surface potential thus obtained on the acidic side with that on the basic side, we can construct Figure 5 in which $to is plotted against p, where p = am - &. For reference, the $0 vs. pH curve for the DAPA micelle is illustrated in Figure 6, together with the curve for the DIPA micelle, to show how the surface potential depends on pH. On the other hand, the construction of the surface potential curve for the DIPA micelle is somewhat com-
on pH for the
-coo-
coo-
(:;;$)
p= 1
p-0
2
(7)
+O
4
6
8
p=2
10
12
PH.
Figure 7. The schematic titration behavior of the DIPA micelle.
+
plicated. For the sake of understanding, the titration behavior of the DIPA micelle is schematically shown in Figure 7. In the region indicated by a broken line in Figure 7, the observed pH values were unreliable because of the reason already described, and therefore the potential on the acid side of the isoelectric point could not be estimated. Now let us turn our attention to the surface potential of the DIPA micelle on the alkaline side. In order to Volume 71, Number 6 M o y 1867
FUMIKATSU TOKIWA AND KENJI OHKI
1828
evaluate the potential, the point where LYM = 1, CY’M = 1, and PM = 1 was taken as an arbitrary base point of the potential (indicated by an arrow in Figure 7), because it is inadequate in the present case to take the isoelectric point ($o = 0) as a base point. Since the ionizations of the second carboxyl group and of the imino group take place independently of each other, as in the case of DAPA, the potentiometric equation for the second carboxyl group of the DIPA micelle may be written in the form pH - log ____ 1 - Ql’M Ql‘M
a t the surface and the charge density u are related by the expression1’J2 $0
=
2kT
7sinh-l
U
42NoDkTl K
where D is the dielectric constant and No is the bulk concentration of ionic species which can be assumed to be constant in the present case. The charge density on the micellar surface is given by u = -nep/A = - t p / ( A / n )
(11)
where n is the number of surfactant molecules per micelle, A is the surface area of the micelle, and therefore A / n represents the surface area occupied by one molecule. Putting A / n = s, then eq 11 is (12)
u = -ep/s
Substituting this expression into eq 10, we obtain $o =
2kT
sinh-’ B!
(13)13
S
where B = -e/d2NODkT/r. The potential $0 depends on both p and s. The total change in $0 when p and s are varied is where $O,rel is the potential relative to that at the base point, pK“”bp ,M is the ionization constant of the micelle a t the base point, and the superscript a’ refers to the second carboxyl group. Similarly, the equation for the imino group of the micelle is given by
(9)
where
s)?(
2kT
=
1
e ~ ( S / B +) ~
p2
2kT
(g),,- 7 =
According to eq 8 and 9, the surface potential at each QI’M and @M can be obtained from Figures 3 and 4, respectively. Here, it should be remembered that the potential thus obtained is the one between at the base point and at a certain Q’M (or OM); that is, it is not “absolute” but “relative” potential. An extrapolation to the point where $’, = 0, Le., to the point where CYM = 1, (Z’M = 0, and PM = 1, is required to obtain the absolute potential. In Figure 5 the $o of the DIPA micelle is plotted against p , where p represents the value of
(LYM
+
Ql’M
- PM).
A characteristic feature of the surface potential curves shown in Figure 5 , especially, of the curve for DIPA, is a decrease in the slope with increasing magnitude of p at high charges. If we assume a uniformly charged plane for the micelle, the potential The Journal of Physical Chemistry
1
+
2 / ( ~ ~ / B p ) ~s2
From eq 15 it can be seen that the slope, b $ o / b p , decreases as the magnitude of p increases a t a constant value of s. The value of s tends in general to increase with increasing lpI owing to the electrical repulsion between charged groups; this effect results in lowering the potential according to eq 16. Thus, eq 14-16 explain the characteristic feature of the $o vs. p curves shown in Figure 5 . As seen in Figure 5 , the surface potential of the DIPA micelle is relatively low as compared with that of the DAPA micelle. It is expected from eq 16 that the micelle with a looser structure will have lower poten(11) E. J. W.Verwey and J. Th. G . Overbeek, “Theory of the Stability of Lyophobic Colloids,” Elsevier Publishing Co., Inc., New York, N. Y.,1948, pp 22-50. (12) D.J. Shaw, “Introduction t o Colloid and Surface Chemistry,” Butterworth and Co. Ltd., London, 1966, pp 117-125. (13) At low charge where p
