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Equimolar surface films of cationic and anionic surfactant solutions
Equimolar Surface Films of Cationic and Anionic Surfactant Solutions JANINA RODAKIEWlCZ-NOWAK Department of Physical Chemistry and Electrochemistry, Institute of Chemistry, Jagiellonian University, 3, Karasia St., 30 060 Krak6w, Poland Received April 10, 1980; accepted May 6, 1981 Parameters of the Butler-type adsorption isotherm for some alkylammonium salts, sodium alkylsulfonates, and AOT (at the air-water interface) were estimated. The bulk mixing ratios of cationic ad anionic surfactants corresponding to their equimolar surface mixtures were then calculated both for the absence and the presence of inorganic salt. The surface mixing ratios of the components for three equimolar bulk mixtures in the excess of NaBr were also presented. 1. INTRODUCTION
Thermodynamic parameters of anioniccationic surfactants adsorption may be found by measuring the surface tension of equimolar mixtures of the respective cationic and anionic surfactants, when both surfactants do not differ in their hydrocarbon chain length (then both the bulk and the Surface of the solution are practically equimolar in respect to both organic ions). In other cases the surface of equimolar bulk mixture contains more ions of higher surface activity (1-3). The asymmetry of the surface depends on the difference in surface activity of the components and it is enhanced by the presence of inorganic salts in the solution (1, 3). The purpose of this work is a quantitive estimation of the bulk mixing ratio of anionic and cationic surfactants, needed to make the surface equimolar in both organic ions. 2. BASIC EQUATIONS
The application of Butler's equation to the description of ionic surfactants' adsorption from multicomponent solutions was presented by Lucassen-Reynders (4-6). Let R+A- be a cationic surfactant, R-Me + an anionic surfactant, Me+A - an inorganic
salt composed of ions common with both surfactants. The surface mole fractions are interrelated by x~20 + 2(x~+'xX-) 1/2 = 1
[11
for a cationic surfactant dissolved in water, X~2o +
s . XMe+) s 1/~ = 1 2(xR-
[2]
for an anionic surfactant dissolved in water, and: X~2o + 2(x~+.xX- + x~+'x~s . s --~ X R - XMe+ ~-
s s XMe+ "XA) 112
=
1 [3]
for a solution containing both surfactants and the inorganic salt. Each of the surface mole fraction x? is given by the Butler equation: x~ = fp "xb"exp(- AGJRT)
× exp(-zctoJRT),
[4]
where by x~, f~, AGi, and to~--the bulk mole fraction, the bulk activity coefficient (calculated from the Debye-Htickel formula), the free enthalpy of adsorption (including the surface activity coefficient term), and the partial molar area for the component i are denoted: 7r--denotes the surface pressure of a solution. In particular
586
0021-9797/82/020586-06502.00/0 Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 85, No. 2, Febrllary 1982
CATIONIC-ANIONIC SURFACE FILMS
587
x~+'x~- = (f+_) b ~.XR+'XAb b
ride was repeatedly purified by crystallization from acetone and extraction with × exp(-AGR+A-/RT) petroleum ether, while octyltrimethylam× exp(-zrtOR+A-/RT) [5] monium bromide was first extracted with and petroleum ether for 15 hr and with diethyl ether for 20 hr. Then it was precipitated s . s b 2. b . b xa- XMe+= (f_+) Xa- X M e + with diethyl ether from the acetone solution and again extracted with petroleum ether. × exp(-AGR-Me+/RT) n-Dodecyltrimethylammonium perchlo× exp(--ZrOJR-Me+/RT). [6] rate was precipitated from the aqueous soluLet us consider the mixtures containing no tion of the purified specimen of dodecylinorganic electrolyte first. From the electro- trimethylammonium chloride, by the addineutrality condition for the surface: x~+ tion of KC104 p.a. Next, it was three times + x~+ = x~- + x~-, it follows that when crystallized from water. Sodium n-octylsulfonate (Schuchardt) x~+ is equal to x~-, then also x%- equals to x~+. Dividing Eq. [5] by [6] we obtain was heated in the acetone solution with an Eq, [7]: activated charcoal, and repeatedly extracted with petroleum ether and crystallized from ( CR+/Ca-) 2 exp((AGR-M~+ -- AGR+A-)/RT) ethanol. Sodium n-decylsulfonate was obtained by × exp(Tr(tOa-M~+ -- O~+A-)/RT) = 1. [7] the syntfiesis from n-decylbromide and Let the bulk mixing ratio of ionic surfactants thiourea, crystallized from methanol and be CR-/CR+ = X . When both surfactants are extracted with petroleum ether. characterized by the comparable values of All surfactants mentioned were purified (.Osurf, then so as to obtain constant values of the surX = exp((AGR-Me+ -- AGR+A-)/2RT). [8] face tension of their aqueous solutions. The values of CMC were consistent with literaIn the case of the presence of an excess of ture data and no minimum was found in the inorganic electrolyte sufficient to maintain curves y vs log C~urf near the CMC. concentration of inorganic ions in the soluAOT, di(2-ethylhexyl) sodium sulfosuction constant, C M e + = C A - and the division cinate (Merck) was not purified. of Eq. [5] by Eq. [6] leads to the formula The surface tension of the solutions was X = exp((AGR-Me+ -- AGR+A-)/RT). [9] measured stalagmometrically by a dropweight method, within an accuracy of 0.1 raN/m, at a temperature 25.0 + 0.2°C. 3. MATERIALS Sodium n-hexylsulfonate and sodium n-butylsulfonate were described elsen-Tetradecyltrimethylammonium bromide where (7). (Schuchardt) was four times crystallized from acetone. 4. RESULTS n-Dodecyltrimethylammonium bromide, 4a. Equimolar Surface Films n-dodecyltrimethylammonium chloride, and n-octyltrimethylammonium bromide were The results of surface tension measureobtained by the synthesis of the respective ments are shown in Fig. 1 and Fig. 2 as the akylhalides and trimethylamine and crystal- circles. The continuous lines represent the lized from an acetone-methanol mixture results of fitting Eq. [1] or Eq. [2] to the ex(2:1). Then, dodecyltrimethylammonium perimental data, for cationic and anionic bromide was three times crystallized from surfactants respectively. acetone, dodecyltrimethylammonium chloTwo of four parameters of Eq. [1] and [2] Journal of Colloid and Interface Science, Vol. 85, No. 2, February 1982
588
JANINA
RODAKIEWICZ-NOWAK
7oi 6O
613
T ~z 50 E
i,° -5
1
l (3
log C =
FIG. I. The surface tension of aqueous solutions of cationic surfactants (1) n-octyltrimethylammonium bromide, (2) n-dodecyltrimethylammonium chloride, (3) n-tetradecyltrimethylammonium bromide, (4) ndodecyltrimethylammonium perchiorate.
were fixed. They were oJmo = 9 . 7 / ~ per molecule (3, 6) and O.)surf = 30 /~2/molecule (3). The latter was chosen constant for all the surfactants studied e x c e p t AOT, so as to enable applying Eq. [8] or [9]. The other two parameters AGH~o and AGsu~f were fitted. To simplify the computations they were taken as concentration independent. The function F = Y~=I (X~2o + 2X~ua- 1)2 was minimized for n experimental points, using the p r o c e d u r e M I N U I T S from the C E R N LIBRARY. ~ Then the values 3'int corresponding to the values obtained for the AGH2o and AQurf were computed and the lines in Fig. 1 and 2 were drawn. The results of fitting are shown in Table I. The first column of the table contains the standard deviation of 3'~nt from the experimental points. In most cases it is within the range o f the accuracy o f experiments. Assuming ~0~urf equal to 20 AS/molecule results in moving AG~u~f by 0.38 kcal/mole for cationic surfactants and by 0.30 kcal/ mole for anionic ones. Such replacement improves the results of fitting for alkylsulfonates considerably, but at the same time it makes the deviations of 3"for cationic surfactant greater. It does not significantly change X however, as the values of X become 1.14 times lower. x~f~ = x~+ = x~- in [1] and x~ua = x~- = x~+ in [2]. Journal of Colloid and Interface Science, Vol. 85, No. 2, February 1982
50
-5
-4
-5
-2
-1
0
log
FIG. 2. The surface tension of aqueous solutions of anionic surfactants: (1) sodium n-butylsulfonate, (2) sodium n-hexylsulfonate, (3) sodium n-octylsulfonate, (4) sodium n-decylsulfonate, (5) AOT. AGn2o values presented in Table I do not vary significantly, thus the errors made by neglecting variations of f~ with surface composition should be comparable for anionic and cationic surfactants and they should cancel more or less within the difference AGMe+R-- AG~+A-, for equimolar surface films (in Eq. [8] or [9]). Table I shows both the influence of hydrocarbon chain length and the effect of inorganic counterion (anions) nature on the surface activity of ionic surfactants (2). The values of X for the possible combinations of the surfactants in the presence and the absence of the respective inorganic salt are presented in Table II. The prediction of X for mixtures o f alkyltrimethylammonium salts with A O T is not possible on the basis o f Eq. [8] or [9] due to the difference in values of o~. In such cases the values of X depend on the range of components concentrations, as the term exp(Tr(¢On-Me+ -- ogn+A-)/RT) of Eq. [7] does not vanish. The validity of predicted values of X for the mixed anionic/cationic films on the surface of water, may be easily confirmed by superposition of the curves in Fig. 2 on the respective curves in Fig. 1. By reading values log Cn-Me+ and log CR+A- corresponding to a similar slope o f the curves 3' vs log Csurf(Frt+ = Fn-) one may find X. It may be seen that values of X are far
589
C A T I O N I C - A N I O N I C SURFACE FILMS TABLE I Results of the Fitting: ~0mo = 9.7 AZ/molecule, COsurf= 30 A2/molecule
Compound n-Octyltrimethylammonium bromide n -Decyltrimethylammonium bromide a n-Dodecyltrimethylammonium bromide n-Tetradecyltrimethylammonium bromide n-Dodecyltrimethylammonium chloride n-Dodecyltrimethylammoniumperchlorate Sodium n-decylsulfonate Sodium n-octylsulfonate Sodium n-hexylsulfonate Sodium n-butylsulfonate AOT b
T (mN/m)
AGmo (kcal/mol¢)
0.16
0.001 ± 3 × 10-4
0.16 0.07 0.08 0.27 0.33 0.20 0.13 0.34 0.07
0.025 0.06 0.006 0.04 0.016 0.04 0.02 0.04 0.004
+ ± ± ± ± ± ± ±
AGsua
(kcal/mole) -6.27 -8.04 -9.80 -11.50 -8.99 -12.05 -8.39 -7.04 -5.40 -4.53 -14.24
0.003 1 x 10-4 1 × 10-5 0.001 0.002 0.001 2 × 10-4 0.002 0.01
± 0.001 ± 0.001 __ 1 × 10-4 ± 0.003 ± 0.007 ± 0.02 ± 0.002 ± 0.001 ± 0.02 ± 0.02
a The value was estimated from the fitted values AG for n-dodecyl and n-octyltrimethylammonium bromide. b For AOT the value of C0surfwas also fitted. It is equal to 61.01 _+ 0.07 A2/molecule.
from unity. The presence of inorganic salt excess moves X away even for surfactants of relatively similar surface activity. Hence in most of the presented pairs of surfactants the surface of equimolar bulk solutions, containing inorganic salt is not equimolar with respect to organic ions. Then the term X~+'X~A (when a cationic surfactant is s .s (when more surface active), or xR-Xue+ an anionic surfactant is more surface active)
cannot be neglected under the square root of Eq. [3]. In the first case the surface contains a considerable amount of inorganic anions, in the latter, inorganic cations.
4b. The Surface of Equimolar Bulk Solutions Nonequimolarity in the organic ions of the mixed anionic/cationic films on the surface
T A B L E II The Bulk Mixing Ratio X of Surfactants; in Water (the lower value) and in the Excess of Inorganic Salt (the upper value) Akylsulfonatc n-Decyl
n-Octyl
n-Hexyl
n-Butyl
n-Octyltrimethylammonium bromide
0.028 0.167
0.27 0.52
4.35 2.09
18.9 4.35
n-Decyltrimethylammonium bromide
0.55 0.74
5.41 2.33
n-Dodecyltrimethylammonium bromide
n-Tetradecyltrimethylammonium bromide
n -Dodecyltrimethylammoniu m chloride
n -Dodecyltrimethylammoniu m perchlorate
10.8 3.3 191 13.8 2.76 1.66 484 22
106 10.3 1870 43 27 5.2 4735 69
86 9.3 1690 41 3.104 173 430 21 7,5-104 275
375 19 7345 86 1" lOs 360 1870 43 3.3.105 573
Journal of Colloid and Interface Science, Vol. 85, No. 2, February 1982
590
JANINA RODAKIEWICZ-NOWAK
of equimolar bulk solutions containing excess o f inorganic salt m a y be visualized on the plots of log Ca+ against the value o f log CR- required to r e a c h a constant surface pressure (8). Equimolarity of the surface is reflected in a slope - 1 in such plots (5, 8). The Gibbs law for the mixture of anionic and cationic surfactants takes the form
log CR*
50 4 6
-4
-5
drr/RT = Fa+d In aR+ + FA-d In aA-
o
+ FR-d In aR- + FMe+d In aue+
[10]
leading to
-4
-5
tog c R-
109 CR*
d~r/RT = FR+d In CR+ + FR-d In CR-
[10a]
~44
-3-
4"0
50
~,6 -,
32
"
in the presence o f Me+A - excess, and to
drr/RT = (FR+ + FA-)d In aR+ -4
+ (FR- + Fu~+)d In art-
[10b]
in the absence of inorganic salt. At constant rr, Eq. [10a] simplifies to
-5
-4
d log Ca+/d log CR=-Fn-/FR+=-Y.
[lla]
As one of the inorganic F ' s should b e c o m e negligible and the other may be found f r o m the electroneutrality condition, hence at constant 7r Eq. [10b] leads (9) either to
-~
-~ Iog%-
-~
-~ Jogc._
log CR*
4O
-3
d log aR-/d log aR+ = 1 - 2/Y, if
-4.
FMe+ ~ 0
[lib]
or to
c
-4
d log aR-/d log aR+ = I -- 2Y, if FA- ~ 0.
[llc]
The a s y m m e t r y of the mixed dodecylt r i m e t h y l a m m o n i u m bromide/sodium alkylsulfonate films on the surface of 0.1 M N a B r solutions is illustrated in Figs. 3 and 4. Nonequimolarity of the surface m a y be o b s e r v e d even for the mixtures of dodecyltrimethyla m m o n i u m bromide with sodium decylsulfonate (Fig. 3a). It m a y be seen that, in the studied range of concentrations, the values o f Y remain constant for particular lines. Nevertheless, the slopes o f experiJournal of Colloid and Interface Science, Vol. 85, N o . 2, Fe bruary 1982
FIG. 3. Plots of log CR+ against the value of log CRrequired to reach a constant surface tension, given next to the curves. The slope corresponding to equimolar surface of equimolar bulk solutions is shown by the dotted lines. (a) The mixtures of dodecyltrimethylammoniumbromide with sodium decylsulfonate in 0.1 M NaBr. (b) The mixtures of dodecyltrimethylammonium bromide with sodium octylsulfonate in 0.1 M NaBr. (c) The mixtures of dodecyltrimethylammonium bromide with sodium hexylsulfonate in 0.1 M NaBr.
mental lines deviate from - 1, and the lower is the surface pressure, the more they deviate. The same tendency m a y be o b s e r v e d in
CATIONIC-ANIONIC SURFACE FILMS
o:
YI~ I -5
]
2
-4
-3
log C
FIG. 4. The mixing ratio Y of ionic surfactants at the surface of their equimolar mixtures in 0.1 M NaBr: (1) dodecyltrimethylammonium bromide and sodium decylsulfonate; (2) dodecyltrimethylammonium bromide and sodium octylsulfonate; (3) dodecyltrimethylammonium bromide and sodium hexylsulfonate.
591
ing ratios X, down from the values given in Table II, for the mixtures of dodecyltrimethylammonium bromide with sodium decyl- and octylsulfonates and for about one decade for the mixtures of dodecyltrimethylammonium bromide with sodium hexylsulfonate (cf. (5, 6)). The exact limit of X, corresponding to a given range of Y deviations changes obviously with the range of surfactants concentrations. Nevertheless, all the results indicate, that for the surfactants differing in surface activity, the equimolarity of the surface may be safely assumed for the equimolar bulk solutions only when these solutions do not contain a considerable amount of inorganic salt.
the other studied systems. Figure 4 presents the values of Y for the equimolar bulk mixtures of surfactants, shown in Fig. 3. Surface tension measurements for solutions of ACKNOWLEDGMENTS dodecyltrimethylammonium bromide with The author would like to express her gratitude to sodium alkylsulfonates (in 0.1 M NaBr) Dr. E. H. Lucassen-Reynders for helpful suggestions were carried out so as to enable the use of and to Dr. M. Paluch for the data on the surface tenEq. [10a] for determining FR÷ and FR- by sion values for the sodium n-hexylsulfonate and sodium polynomial evaluation of derivatives [(07/ n-butylsulfonate aqueous solutions. 0 log COcj] (2). Namely, the mixtures inREFERENCES vestigated consisted of series of varying content of only one of the surfactants 1. CorkiU, J. M., Goodman, J. F., Harrold, S. P., and (either dodecyltrimethylammonium broTate, J. R., Trans. Faraday Soc. 63,247 (1967). 2. Rodakiewicz, J., Walig6ra, B., and Pomianowmide, or one of sodium alkylsulfonates). To ski, A., "Trudy VII Miezhdun. Kongressa po avoid double interpolation (one to obtain the Poverkhnostno-Aktivnym Wieszczestvarn, curves, the other to find the slope d log CR+/ Moscov, 1976," Vol. B, p. 174. Publ. 1978. d log CR-) the values of Y presented in 3. Rodakiewicz, J., Ph.D. Thesis, Cracov, 1976. Fig. 4 were calculated directly from the [Polish] 4. Lucassen-Reynders, E. H., J. Phys. Chem. 70, experimental data. 1977 (1966). Based on the data presented here and 5. Lucassen-Reynders, E. H., Kolloid Z. Z. Polym. earlier (2) one may state that such strong 250, 356 (1972). asymmetry of the surface as in Fig. 4 does 6. Lucassen-Reynders, E. H., Prog. Surf. Membr. Sci. 10, 253 (1976). not appear for equimolar mixtures of the 7. Paluch, M., Pol. J. Chem. 53, 2139 (1979). surfactants in water. The rough estimation 8. Pomianowski, A., Rodakiewicz-Nowak, J., Pol. J. shows that deviation from surface equimoChem. 54, 267 (1980). larity lower than 1% (1 ~< x~÷/x~- <. 1.01) 9. Lucassen-Reynders, E. H., Lucassen, J., Giles, D., holds for about ten decades of the bulk mixJ. Colloid Interface Sci. 81, 150 (1981).
Journal of Colloid and Interface Science, Vol. 85, No. 2, February 1982
Thermodynamic parameters of anioniccationic surfactants adsorption may be found by measuring the surface tension of equimolar mixtures of the respective cationic and anionic surfactants, when both surfactants do not differ in their hydrocarbon chain length (then both the bulk and the Surface of the solution are practically equimolar in respect to both organic ions). In other cases the surface of equimolar bulk mixture contains more ions of higher surface activity (1-3). The asymmetry of the surface depends on the difference in surface activity of the components and it is enhanced by the presence of inorganic salts in the solution (1, 3). The purpose of this work is a quantitive estimation of the bulk mixing ratio of anionic and cationic surfactants, needed to make the surface equimolar in both organic ions. 2. BASIC EQUATIONS
The application of Butler's equation to the description of ionic surfactants' adsorption from multicomponent solutions was presented by Lucassen-Reynders (4-6). Let R+A- be a cationic surfactant, R-Me + an anionic surfactant, Me+A - an inorganic
salt composed of ions common with both surfactants. The surface mole fractions are interrelated by x~20 + 2(x~+'xX-) 1/2 = 1
[11
for a cationic surfactant dissolved in water, X~2o +
s . XMe+) s 1/~ = 1 2(xR-
[2]
for an anionic surfactant dissolved in water, and: X~2o + 2(x~+.xX- + x~+'x~s . s --~ X R - XMe+ ~-
s s XMe+ "XA) 112
=
1 [3]
for a solution containing both surfactants and the inorganic salt. Each of the surface mole fraction x? is given by the Butler equation: x~ = fp "xb"exp(- AGJRT)
× exp(-zctoJRT),
[4]
where by x~, f~, AGi, and to~--the bulk mole fraction, the bulk activity coefficient (calculated from the Debye-Htickel formula), the free enthalpy of adsorption (including the surface activity coefficient term), and the partial molar area for the component i are denoted: 7r--denotes the surface pressure of a solution. In particular
586
0021-9797/82/020586-06502.00/0 Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 85, No. 2, Febrllary 1982
CATIONIC-ANIONIC SURFACE FILMS
587
x~+'x~- = (f+_) b ~.XR+'XAb b
ride was repeatedly purified by crystallization from acetone and extraction with × exp(-AGR+A-/RT) petroleum ether, while octyltrimethylam× exp(-zrtOR+A-/RT) [5] monium bromide was first extracted with and petroleum ether for 15 hr and with diethyl ether for 20 hr. Then it was precipitated s . s b 2. b . b xa- XMe+= (f_+) Xa- X M e + with diethyl ether from the acetone solution and again extracted with petroleum ether. × exp(-AGR-Me+/RT) n-Dodecyltrimethylammonium perchlo× exp(--ZrOJR-Me+/RT). [6] rate was precipitated from the aqueous soluLet us consider the mixtures containing no tion of the purified specimen of dodecylinorganic electrolyte first. From the electro- trimethylammonium chloride, by the addineutrality condition for the surface: x~+ tion of KC104 p.a. Next, it was three times + x~+ = x~- + x~-, it follows that when crystallized from water. Sodium n-octylsulfonate (Schuchardt) x~+ is equal to x~-, then also x%- equals to x~+. Dividing Eq. [5] by [6] we obtain was heated in the acetone solution with an Eq, [7]: activated charcoal, and repeatedly extracted with petroleum ether and crystallized from ( CR+/Ca-) 2 exp((AGR-M~+ -- AGR+A-)/RT) ethanol. Sodium n-decylsulfonate was obtained by × exp(Tr(tOa-M~+ -- O~+A-)/RT) = 1. [7] the syntfiesis from n-decylbromide and Let the bulk mixing ratio of ionic surfactants thiourea, crystallized from methanol and be CR-/CR+ = X . When both surfactants are extracted with petroleum ether. characterized by the comparable values of All surfactants mentioned were purified (.Osurf, then so as to obtain constant values of the surX = exp((AGR-Me+ -- AGR+A-)/2RT). [8] face tension of their aqueous solutions. The values of CMC were consistent with literaIn the case of the presence of an excess of ture data and no minimum was found in the inorganic electrolyte sufficient to maintain curves y vs log C~urf near the CMC. concentration of inorganic ions in the soluAOT, di(2-ethylhexyl) sodium sulfosuction constant, C M e + = C A - and the division cinate (Merck) was not purified. of Eq. [5] by Eq. [6] leads to the formula The surface tension of the solutions was X = exp((AGR-Me+ -- AGR+A-)/RT). [9] measured stalagmometrically by a dropweight method, within an accuracy of 0.1 raN/m, at a temperature 25.0 + 0.2°C. 3. MATERIALS Sodium n-hexylsulfonate and sodium n-butylsulfonate were described elsen-Tetradecyltrimethylammonium bromide where (7). (Schuchardt) was four times crystallized from acetone. 4. RESULTS n-Dodecyltrimethylammonium bromide, 4a. Equimolar Surface Films n-dodecyltrimethylammonium chloride, and n-octyltrimethylammonium bromide were The results of surface tension measureobtained by the synthesis of the respective ments are shown in Fig. 1 and Fig. 2 as the akylhalides and trimethylamine and crystal- circles. The continuous lines represent the lized from an acetone-methanol mixture results of fitting Eq. [1] or Eq. [2] to the ex(2:1). Then, dodecyltrimethylammonium perimental data, for cationic and anionic bromide was three times crystallized from surfactants respectively. acetone, dodecyltrimethylammonium chloTwo of four parameters of Eq. [1] and [2] Journal of Colloid and Interface Science, Vol. 85, No. 2, February 1982
588
JANINA
RODAKIEWICZ-NOWAK
7oi 6O
613
T ~z 50 E
i,° -5
1
l (3
log C =
FIG. I. The surface tension of aqueous solutions of cationic surfactants (1) n-octyltrimethylammonium bromide, (2) n-dodecyltrimethylammonium chloride, (3) n-tetradecyltrimethylammonium bromide, (4) ndodecyltrimethylammonium perchiorate.
were fixed. They were oJmo = 9 . 7 / ~ per molecule (3, 6) and O.)surf = 30 /~2/molecule (3). The latter was chosen constant for all the surfactants studied e x c e p t AOT, so as to enable applying Eq. [8] or [9]. The other two parameters AGH~o and AGsu~f were fitted. To simplify the computations they were taken as concentration independent. The function F = Y~=I (X~2o + 2X~ua- 1)2 was minimized for n experimental points, using the p r o c e d u r e M I N U I T S from the C E R N LIBRARY. ~ Then the values 3'int corresponding to the values obtained for the AGH2o and AQurf were computed and the lines in Fig. 1 and 2 were drawn. The results of fitting are shown in Table I. The first column of the table contains the standard deviation of 3'~nt from the experimental points. In most cases it is within the range o f the accuracy o f experiments. Assuming ~0~urf equal to 20 AS/molecule results in moving AG~u~f by 0.38 kcal/mole for cationic surfactants and by 0.30 kcal/ mole for anionic ones. Such replacement improves the results of fitting for alkylsulfonates considerably, but at the same time it makes the deviations of 3"for cationic surfactant greater. It does not significantly change X however, as the values of X become 1.14 times lower. x~f~ = x~+ = x~- in [1] and x~ua = x~- = x~+ in [2]. Journal of Colloid and Interface Science, Vol. 85, No. 2, February 1982
50
-5
-4
-5
-2
-1
0
log
FIG. 2. The surface tension of aqueous solutions of anionic surfactants: (1) sodium n-butylsulfonate, (2) sodium n-hexylsulfonate, (3) sodium n-octylsulfonate, (4) sodium n-decylsulfonate, (5) AOT. AGn2o values presented in Table I do not vary significantly, thus the errors made by neglecting variations of f~ with surface composition should be comparable for anionic and cationic surfactants and they should cancel more or less within the difference AGMe+R-- AG~+A-, for equimolar surface films (in Eq. [8] or [9]). Table I shows both the influence of hydrocarbon chain length and the effect of inorganic counterion (anions) nature on the surface activity of ionic surfactants (2). The values of X for the possible combinations of the surfactants in the presence and the absence of the respective inorganic salt are presented in Table II. The prediction of X for mixtures o f alkyltrimethylammonium salts with A O T is not possible on the basis o f Eq. [8] or [9] due to the difference in values of o~. In such cases the values of X depend on the range of components concentrations, as the term exp(Tr(¢On-Me+ -- ogn+A-)/RT) of Eq. [7] does not vanish. The validity of predicted values of X for the mixed anionic/cationic films on the surface of water, may be easily confirmed by superposition of the curves in Fig. 2 on the respective curves in Fig. 1. By reading values log Cn-Me+ and log CR+A- corresponding to a similar slope o f the curves 3' vs log Csurf(Frt+ = Fn-) one may find X. It may be seen that values of X are far
589
C A T I O N I C - A N I O N I C SURFACE FILMS TABLE I Results of the Fitting: ~0mo = 9.7 AZ/molecule, COsurf= 30 A2/molecule
Compound n-Octyltrimethylammonium bromide n -Decyltrimethylammonium bromide a n-Dodecyltrimethylammonium bromide n-Tetradecyltrimethylammonium bromide n-Dodecyltrimethylammonium chloride n-Dodecyltrimethylammoniumperchlorate Sodium n-decylsulfonate Sodium n-octylsulfonate Sodium n-hexylsulfonate Sodium n-butylsulfonate AOT b
T (mN/m)
AGmo (kcal/mol¢)
0.16
0.001 ± 3 × 10-4
0.16 0.07 0.08 0.27 0.33 0.20 0.13 0.34 0.07
0.025 0.06 0.006 0.04 0.016 0.04 0.02 0.04 0.004
+ ± ± ± ± ± ± ±
AGsua
(kcal/mole) -6.27 -8.04 -9.80 -11.50 -8.99 -12.05 -8.39 -7.04 -5.40 -4.53 -14.24
0.003 1 x 10-4 1 × 10-5 0.001 0.002 0.001 2 × 10-4 0.002 0.01
± 0.001 ± 0.001 __ 1 × 10-4 ± 0.003 ± 0.007 ± 0.02 ± 0.002 ± 0.001 ± 0.02 ± 0.02
a The value was estimated from the fitted values AG for n-dodecyl and n-octyltrimethylammonium bromide. b For AOT the value of C0surfwas also fitted. It is equal to 61.01 _+ 0.07 A2/molecule.
from unity. The presence of inorganic salt excess moves X away even for surfactants of relatively similar surface activity. Hence in most of the presented pairs of surfactants the surface of equimolar bulk solutions, containing inorganic salt is not equimolar with respect to organic ions. Then the term X~+'X~A (when a cationic surfactant is s .s (when more surface active), or xR-Xue+ an anionic surfactant is more surface active)
cannot be neglected under the square root of Eq. [3]. In the first case the surface contains a considerable amount of inorganic anions, in the latter, inorganic cations.
4b. The Surface of Equimolar Bulk Solutions Nonequimolarity in the organic ions of the mixed anionic/cationic films on the surface
T A B L E II The Bulk Mixing Ratio X of Surfactants; in Water (the lower value) and in the Excess of Inorganic Salt (the upper value) Akylsulfonatc n-Decyl
n-Octyl
n-Hexyl
n-Butyl
n-Octyltrimethylammonium bromide
0.028 0.167
0.27 0.52
4.35 2.09
18.9 4.35
n-Decyltrimethylammonium bromide
0.55 0.74
5.41 2.33
n-Dodecyltrimethylammonium bromide
n-Tetradecyltrimethylammonium bromide
n -Dodecyltrimethylammoniu m chloride
n -Dodecyltrimethylammoniu m perchlorate
10.8 3.3 191 13.8 2.76 1.66 484 22
106 10.3 1870 43 27 5.2 4735 69
86 9.3 1690 41 3.104 173 430 21 7,5-104 275
375 19 7345 86 1" lOs 360 1870 43 3.3.105 573
Journal of Colloid and Interface Science, Vol. 85, No. 2, February 1982
590
JANINA RODAKIEWICZ-NOWAK
of equimolar bulk solutions containing excess o f inorganic salt m a y be visualized on the plots of log Ca+ against the value o f log CR- required to r e a c h a constant surface pressure (8). Equimolarity of the surface is reflected in a slope - 1 in such plots (5, 8). The Gibbs law for the mixture of anionic and cationic surfactants takes the form
log CR*
50 4 6
-4
-5
drr/RT = Fa+d In aR+ + FA-d In aA-
o
+ FR-d In aR- + FMe+d In aue+
[10]
leading to
-4
-5
tog c R-
109 CR*
d~r/RT = FR+d In CR+ + FR-d In CR-
[10a]
~44
-3-
4"0
50
~,6 -,
32
"
in the presence o f Me+A - excess, and to
drr/RT = (FR+ + FA-)d In aR+ -4
+ (FR- + Fu~+)d In art-
[10b]
in the absence of inorganic salt. At constant rr, Eq. [10a] simplifies to
-5
-4
d log Ca+/d log CR=-Fn-/FR+=-Y.
[lla]
As one of the inorganic F ' s should b e c o m e negligible and the other may be found f r o m the electroneutrality condition, hence at constant 7r Eq. [10b] leads (9) either to
-~
-~ Iog%-
-~
-~ Jogc._
log CR*
4O
-3
d log aR-/d log aR+ = 1 - 2/Y, if
-4.
FMe+ ~ 0
[lib]
or to
c
-4
d log aR-/d log aR+ = I -- 2Y, if FA- ~ 0.
[llc]
The a s y m m e t r y of the mixed dodecylt r i m e t h y l a m m o n i u m bromide/sodium alkylsulfonate films on the surface of 0.1 M N a B r solutions is illustrated in Figs. 3 and 4. Nonequimolarity of the surface m a y be o b s e r v e d even for the mixtures of dodecyltrimethyla m m o n i u m bromide with sodium decylsulfonate (Fig. 3a). It m a y be seen that, in the studied range of concentrations, the values o f Y remain constant for particular lines. Nevertheless, the slopes o f experiJournal of Colloid and Interface Science, Vol. 85, N o . 2, Fe bruary 1982
FIG. 3. Plots of log CR+ against the value of log CRrequired to reach a constant surface tension, given next to the curves. The slope corresponding to equimolar surface of equimolar bulk solutions is shown by the dotted lines. (a) The mixtures of dodecyltrimethylammoniumbromide with sodium decylsulfonate in 0.1 M NaBr. (b) The mixtures of dodecyltrimethylammonium bromide with sodium octylsulfonate in 0.1 M NaBr. (c) The mixtures of dodecyltrimethylammonium bromide with sodium hexylsulfonate in 0.1 M NaBr.
mental lines deviate from - 1, and the lower is the surface pressure, the more they deviate. The same tendency m a y be o b s e r v e d in
CATIONIC-ANIONIC SURFACE FILMS
o:
YI~ I -5
]
2
-4
-3
log C
FIG. 4. The mixing ratio Y of ionic surfactants at the surface of their equimolar mixtures in 0.1 M NaBr: (1) dodecyltrimethylammonium bromide and sodium decylsulfonate; (2) dodecyltrimethylammonium bromide and sodium octylsulfonate; (3) dodecyltrimethylammonium bromide and sodium hexylsulfonate.
591
ing ratios X, down from the values given in Table II, for the mixtures of dodecyltrimethylammonium bromide with sodium decyl- and octylsulfonates and for about one decade for the mixtures of dodecyltrimethylammonium bromide with sodium hexylsulfonate (cf. (5, 6)). The exact limit of X, corresponding to a given range of Y deviations changes obviously with the range of surfactants concentrations. Nevertheless, all the results indicate, that for the surfactants differing in surface activity, the equimolarity of the surface may be safely assumed for the equimolar bulk solutions only when these solutions do not contain a considerable amount of inorganic salt.
the other studied systems. Figure 4 presents the values of Y for the equimolar bulk mixtures of surfactants, shown in Fig. 3. Surface tension measurements for solutions of ACKNOWLEDGMENTS dodecyltrimethylammonium bromide with The author would like to express her gratitude to sodium alkylsulfonates (in 0.1 M NaBr) Dr. E. H. Lucassen-Reynders for helpful suggestions were carried out so as to enable the use of and to Dr. M. Paluch for the data on the surface tenEq. [10a] for determining FR÷ and FR- by sion values for the sodium n-hexylsulfonate and sodium polynomial evaluation of derivatives [(07/ n-butylsulfonate aqueous solutions. 0 log COcj] (2). Namely, the mixtures inREFERENCES vestigated consisted of series of varying content of only one of the surfactants 1. CorkiU, J. M., Goodman, J. F., Harrold, S. P., and (either dodecyltrimethylammonium broTate, J. R., Trans. Faraday Soc. 63,247 (1967). 2. Rodakiewicz, J., Walig6ra, B., and Pomianowmide, or one of sodium alkylsulfonates). To ski, A., "Trudy VII Miezhdun. Kongressa po avoid double interpolation (one to obtain the Poverkhnostno-Aktivnym Wieszczestvarn, curves, the other to find the slope d log CR+/ Moscov, 1976," Vol. B, p. 174. Publ. 1978. d log CR-) the values of Y presented in 3. Rodakiewicz, J., Ph.D. Thesis, Cracov, 1976. Fig. 4 were calculated directly from the [Polish] 4. Lucassen-Reynders, E. H., J. Phys. Chem. 70, experimental data. 1977 (1966). Based on the data presented here and 5. Lucassen-Reynders, E. H., Kolloid Z. Z. Polym. earlier (2) one may state that such strong 250, 356 (1972). asymmetry of the surface as in Fig. 4 does 6. Lucassen-Reynders, E. H., Prog. Surf. Membr. Sci. 10, 253 (1976). not appear for equimolar mixtures of the 7. Paluch, M., Pol. J. Chem. 53, 2139 (1979). surfactants in water. The rough estimation 8. Pomianowski, A., Rodakiewicz-Nowak, J., Pol. J. shows that deviation from surface equimoChem. 54, 267 (1980). larity lower than 1% (1 ~< x~÷/x~- <. 1.01) 9. Lucassen-Reynders, E. H., Lucassen, J., Giles, D., holds for about ten decades of the bulk mixJ. Colloid Interface Sci. 81, 150 (1981).
Journal of Colloid and Interface Science, Vol. 85, No. 2, February 1982