J . Phys. Chem. 1990, 94, 3675-3681
3675
Physicochemical Properties of Aqueous Mixtures of Tetrabutyiammonium Bromide and Anionic Surfactants. 3. Effects of Surfactant Chain Length and Salinity Zhi-Jian Yu,* Xingkang Zhang, Guangzhi Xu, National Laboratory for Structure Chemistry of Unstable and Stable Species, Institute of Chemistry, Academia Sinica, Beijing 100080, China
and Guo-xi Zhao Chemistry Department, Peking University, Beijing 100871, China (Received: March 17, 1989; I n Final Form: November 10, 1989)
The solution behaviors of equimolar mixtures of tetrabutylammonium bromide and sodium alkyl sulfate (B,NC,,S, n = 8-18) have been studied. The surface tension measurement shows that the ratios of tetrabutylammonium to alkyl sulfate both in micelles at the cmc and in surface adsorption layers obtained by using the Gibbs-Duhem equation are less than unity and decrease with increasing surfactant chain length. The Krafft point of B4NC$ in 0.2 M NaBr decreases with increasing surfactant concentration and is considerably lower than that of the corresponding alkyl sulfate salt without tetrabutylammonium. The cloud point phenomenon is observed in all surfactant systems. The cloud point increases with increasing surfactant chain length except for n > 16 below 56 mM surfactant concentration. This behavior is interpreted in terms of the variation of tetrabutylammonium content in the micelles by using our previously proposed model for the cloud point phenomenon. The addition of NaBr increases the cloud point initially, passing through a maximum, and then decreases again. The possible causes for the phenomenon of a maximum in the cloud point are discussed. B4NC18Smay form a stable homogeneous micellar solution at room temperature, the micellar size of which increases with temperature in the presence of a comparable amount of NaBr to the surfactant or in the absence of NaBr and decreases in excess NaBr. An Arrhenius type of equation cannot be used in calculating the activation energy of viscous flow of micellar solutions without considering the effect of micellar size change with temperature.
Introduction The physicochemical properties of surfactants are greatly affected by the surfactant molecular size. Generally, the micellization surface activity for lowering the surface or interface tension of a surfactant solution: washing a b i l i t ~micellar ,~ size,6 and solubilizing power' increase systematically with increasing hydrophobic chain length of surfactants. Unfortunately, however, the Krafft point of surfactants becomes higher with increasing hydrophobic chain length as well as concentration of co~nterions.8,~For example, sodium octadecyl sulfate is insoluble in water below 50 "C. This greatly restricts the use of long-chain surfactant. Hence, a study of the depression of the Krafft point and the increase of the solubility of long hydrophobic chain surfactants is of both practical and theoretical importance. Previously, we have investigated some unusual behaviors of ionic surfactants, Le., cloud point phenomenon, temperature-induced micellar growth, and critical-like behaviors of the tetrabutylammonium tetradecyl sulfate system.I0 In the present study we have systematically investigated the influence of chain length and salinity on the solution properties for equimolar mixtures of tetrabutylammonium bromide and a homologous series of sodium alkyl sulfates with the number of carbons per chain ranging from 8 to 18. The motivations for the present work were 3-fold. First, we show that the Krafft point of the surfactants is depressed considerably in the presence of tetrabutylammonium ion; hence, homogeneous micellar solutions could be obtained at ambient temperature even for sodium octadecyl sulfate. Second, we previously observed that tetrabutylammonium tetradecyl sulfate has a cloud point property and that the cloud point increases with increasing salinity. Thus, it is appealing to investigate whether such phenomena are universal for other surfactant systems and for other salt concentrations. Third, the present study is relevant to the examination of the unusual micellar growth behaviors. Experimental Section Sodium hexadecyl sulfate (C16SNa) and sodium octadecyl sulfate (C,,SNa) were commercial research grade products from To whom correspondence should be addressed. Present address: Department of Chemical Engineering, Auburn University, Auburn, AL 36849.
Beijing Chemical Co. and were recrystallized from ethanol four times. Tetrabutylammonium octadecyl sulfate (B4NC18S)was obtained by the following procedure: mixing the equimolar amounts of tetrabutylammonium bromide (B4NBr) and C18SNa in water, extracting the B4NCI8Sfrom water by chloroform, washing the chloroform phase by water five times, evaporating off the chloroform, and drying the final product under vacuum for 1 day. B4NC18Sobtained was a white crystal product at room temperature. The sodium alkyl sulfates (C,SNa, n = 8, 10, 12, and 14), B4NBr, NaBr, and water used were the same as used previously.lOJI Surface tensions were measured by the drop volume method. The viscosity and the cloud point measurements were the same as previously.I0 Krafft points were obtained by placing several cells, each filled at a different amphiphile concentration equilibrated with surfactant crystals, into a temperature-controlled water bath whose temperature was increased at a constant rate (typically 0.5 OC h-I near the Krafft point). The phase transition temperature was determined by the naked eye within 0.3 OC.
Results and Discussion Micelle Compositions at cmc. The surface tension y of all solutions was measured at 25 OC in 0.2 M ionic strength by adding NaBr. Figure 1 contains the plots of y vs logarithm of concentration of dodecyl sulfate (C12S)at various molar ratios of tetrabutylammonium (B4N) to C I 2 Sand of single B4N. The break (1) Klevens, H. B. J . Am. Oil Chem. SOC.1953, 30, 74; J . Phys. Chem. 1948, 52, 130.
(2) Evans, H. C. J . Chem. SOC.1956, 579. (3) Kreshek, G. In Water. A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1975; Vol. 4, Chapter 2. (4) Rosen, M. J. Surfactants and Interfacial Phenomena; Wiley: New York, 1978. (5) Preston, W. C. J . Phys. Chem. 1948, 52, 84. (6) Missel, P. J.; Mazer, N . A.; Benedek, G. B.; Carey, M. C. J . Phys. Chem. 1983, 87, 1264. (7) Sataka, I.; Matuura, R. Bull. Chem. SOC.Jpn. 1963, 36, 813. (8) Shincda, K . Pure Appl. Chem. 1980, 52, 1195. (9) Shinoda, K.; Hato, M.; Hayashi, T. J . Phys. Chem. 1972, 76, 9C9. (10) Yu, Z.-J.;Xu, G. J . Phys. Chem. 1989, 93, 7441. Yu, Z.-J.; Zhou, Z . ; Xu, G . J . Phys. Chem. 1989, 93, 7446. ( 1 I ) (a) Yu, Z.-J.;Zhao, G.-X. J . Colloid Interface Sci. 1989, 130, 414, 421. (b) Yu, Z.-J. Doctoral Thesis, Peking University, 1987.
Q022-3654/9Q/2094-3675$02.50/0 0 1990 American Chemical Society
3676 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
Yu et al.
TABLE I: Experimental Data of B,NC,,S for Micelles at the cmc and the Surface Adsorption Layer at 0.2 M Ionic Strength at 25 C (y = 42 m N m-l), system cmc, mM Pm mM Ycmo m N m-' P, r+ rr+ 41.4 0 83.2 93.3 0 CSS 0 6.10 36.2 0 CIOS 10.5 0 0.348 33.0 0 Cl2S 0.805 BdNCBS 24.5 0.682 8.41 32.0 0.75 3.75 1.61 31.6 1.47 0.41 4.03 1.18 4.17 0.373 B"0S 31.2 0.155 0.198 0.16 4.47 0.62 B4NC12S 0.525
+
a
r+and r- values are in
O c a
r1.78 2.13 2.10 2.14 2.85 3.85
mol cm-2.
-2
-1.5
I
I
-1
-1
55
I
--k \ 50
3 -2 E & 4: d n r
&-
40 -3
2-
30
-3
-2
-1
log [B4X]
-3.5
-4
Figure 2. Relation between logarithm of concentrations of B 4 N and C,$ at the cmc: (e), n = 8; (0) n = IO; ( 0 )n = 12.
-3
log C (M)
Figure 1. Surface tension of the mixtures of B4NBr/C12SNaat 0.2 M ionic strength at 25 OC: (). single B,N; (Q)single CI2S; (0, 0 , 8, 0 , 0 , and 0 ) the molar ratios of B4Nto CI2Sare 0.5, I , 2, 3.2, 6.5, and 8,
respectively.
ai in eq 2 can be replaced by the bulk concentration of the corresponding species Ci Cni d In Ci = 0 (3) i
point in the curve corresponds to the cmc. The surface tensions of the mixed systems of B4NBr/C8SNaand B4NBr/CI$Na were also measured in the same experimental conditions. The appearance of these curves was very similar to Figure 1. It is difficult to determine y of the surfactant solutions with chain lengths larger than tetradecyl in the above ionic strength condition because of the low cmc and high Krafft point. It can be seen from Figure 1 that the addition of B4NBr to the solutions of ClzSNa reduces the cmc value of C12SNadrastically while B4N itself cannot form micelles even at very high concentrations. Table I lists the cmc values of the equimolar mixtures together with that of single C,$Na. It is seen that although the micellization ability increases with the increase of surfactant chain length, the shorter the chain length is, the larger the extent of reduction of the cmc by B,N. According to the pseudophase separation model for micelles,lh the Gibbs-Duhem equation can be expressed as
Eni dwim= 0
(1)
I
where ni and w,, are the molar number and the chemical potential of the ith component in the micelle phase, respectively. From the equilibrium condition we have
Eni d In ai = 0 i
(2)
where ai is the activitv of the ith component in the aqueous phase. As the activity coefficients of all the components in the systems shown in Figure 1 were constant due to the constant ionic strength, (12) (a) Shinoda, K . In Colloidal Surfactants; Academic Press: New York, 1963. (b) Mazer, N. A.; et al. In Micellization, Solubilization and Microemulsions; Mittal, K.L. Ed.;Plenum Press: New York, 1977; Vol. I, p 359.
The adsorption of Br- on the negatively charged micelles may be neglected. The term of the Na+ component in eq 3 may also be neglected since the amount of NaBr in the solution is excessive and the adsorption of BIN on the micellar surface is far more effective than that of Na+ due to the hydrophobicity of B4N. Thus nB4N d In CB,N ncS d In cc, = 0 (4)
+
or
pm
~B,N = - E -
d log Cca (5)
d log G,N Figure 2 is the relationship between the logarithm of concentrations of C,,S and BIN at the cmc taken from Figure 1. From the slope of these curves and eq 5, we obtained the molar ratios of B4N to C,S in the micellar phase, P,. P, values of the equimolar mixtures are listed in Table I. It shows that P, < 1 for all three systems, which indicates that the micelles are negatively charged. Table I also shows a decrease of P, with increasing surfactant chain length. Several factors, such as size, shape, and structure of the micelles, the hydrophobicity of the surfactants, and the difference of the hydrophobicity between B4N and the surfactant, may be responsible for the chain length dependence of P,. But of these factors the most important one is the hydrophobicity difference of the two organic ions. The larger the hydrophobicity difference is, the smaller the P, value. It will be further discussed in the following section. Surface Adsorption. From Figure 1 it is evident that the surface tension at the cmc (ycmc),which describes the surface activity of a surfactant,4J1 is reduced largely on the addition of even a small amount of B4N. The ycmcvalues of the equimolar mixtures and of the single surfactants are listed in Table I. It is seen that the shorter the chain length is, the larger the ycmcvalue is reduced. The slope of the surface tension curves below the cmc changes
nca
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
Properties of B4NBr-Surfactant Mixtures
3677
m-
-4
-3
-2
108 IB4N]
Figure 3. Relation between logarithm of concentrations of B4N and C,,S at y = 42 m N m-l: (a) n = 8; (0) n = 10; ( 0 )n = 12.
very little with the variation of mixing ratio of BIN to C,,S. The total amount of the surface excess per area, r+ r-, can thus be calculated from these slopes,1owhere I’+ and l’- are the surface excesses of BIN and C,S per area, respectively. The results for equimolar mixtures and single surfactants are listed in Table I. Applying the Gibbs-Duhem equation to the surface adsorption phase at constant surface tension, and following a similar procedure to that of the micellar phase, we obtain
+
I
Figure 4. Phase diagram of B4NCI4Sat various salinities: (0 and 0 ) the Krafft point curves for 0.2 and 0.5 M NaBr, respectively; (e,0, @, and a) the cloud point curves for 0.5, 0.2, 0.05, and 0 M NaBr, respectively. 60
where [C,S] and [B4N] are the concentrations of the corresponding species in bulk phase at constant surface tension and P,is the molar ratio of B4N to C,$ at the surface adsorption layer. Figure 3 shows the relationship between log [C,S] and log [B,N] at y = 42 mN m-l obtained from the data in Figure 1. Table I lists the P, values deduced from the slopes of these curves by using eq 6,from which the surface excess of individual components can be obtained. For this homology, both the total amount of the surface excess and the surface excess of C,S are seen to increase whereas the content of B4N in the surface adsorption layer decreases with increasing surfactant chain length. That both P, and P, decrease with increasing surfactant chain length is very much consistent with the two phenomena observed above that the shorter the chain length is, the larger the extents of reduction of cmc and of ycmcby BIN. Table I also shows an increase in the surface adsorption of the surfactant on adding B4N, which indicates a synergistic effect existing between B4N and C,S. One can easily see that the factors of micellar size and shape no longer exist in the case of surface adsorption layers, yet the chain length dependence of P, is almost the same as that in micelles. This strongly suggests that the relationships between P, as well as P, and the surfactant chain length are affected by the surfactant chain length. We have studied mixed systems of cationic/anionic surfactants with different surfactant chain lengths and found that both P, and P, are dependent on the symmetry of the chain lengths rather than on the single or total chain length.Iib Since the hydrophobic cation is the same in the present systems, one may see that P, and P, decrease with increasing hydrophobicity difference between BIN and the surfactants. Further discussions are seen elsewhere.Iib Krafff Point. Figure 4 shows the Krafft point T fas a function of the concentration of Cl4S for the equimolar mixture of B4N and C I 4 Sat two different NaBr concentrations. The Krafft point is below 0 OC for the mixture without NaBr. It can be seen from
I
I
50
0
150
100
[C,S]
200
(mM)
Figure 5. Krafft point as a function of surfactant concentration for B4NC,,S at 0.2 M NaBr: (a,0, and 0)n = 14, 16, and 18, respectively.
Figure 4 that T f increases with increasing salinity. This result is consistent with that of an ordinary ~ u r f a c t a n t . ~ * ~ ~ ~ Figure 5 is a relationship between rfand the concentration of B4NC,,S (the equimolar mixtures of B4NBr and C,,SNa, n = 14, 16, 18) at 0.2 M NaBr. It is evident from Figure 5 that the Krafft point is depressed with increasing surfactant concentration, which indicates an increase in the content of B4N in the hydrated crystals of the surfactant. The depressing rate of Tf with increasing concentration, as can be seen from Figure 5, is more rapid in the low concentration range. This result is different from other or~~~~
~
(13) Zhou, Z.: Yu,Z.-J. Acta Phys.-Chim. Sin. 1985, 1, 141.
3678 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 dinary ionic surfactant systems where Tfslightly shifts to a higher temperature with increasing stoichiometric concentration of geg e n i ~ n s ' ~and , ' ~may be considered as the result of the nonstoichiometric precipitation of B4N to C,S owing to the competing of B4N in the hydrated surfactant crystals by Na+. The competing ability of Na+ is progressively weakened with increasing surfactant concentration from an accumulation of B4N in the solution and the consequent enhancement of the chemical potential of BIN relative to that of Na+. Such a competing effect of Na+ on raising T, may also be seen from Figure 4 where T f is higher in 0.5 M NaBr than in 0.2 M NaBr. It is clear from Figure 5 that Tfdecreases with decreasing surfactant chain length from n = 18 to n = 14, and Tr is below ambient temperature when the chain length is further shortened. Our experiments have shown that the Krafft point of B4NC,,S without NaBr is below 23 OC. It is interesting to note that the solubility of CI8SNa,which is often used as a material for insoluble film because of its extremely low solubility in water ( T fis about 5 3 OC in pure water), increases enormously and forms micelles at room temperature in the presence of B4N. A surfactant with such long hydrophobic chain length has not been reported in the literature to form stable micelles at ambient temperature. Cloud Point. The cloud point Td as a function of the concentration of B4NCI4Sat various salinities is shown in Figure 4. It can be seen that Td decreases with increasing B4NC14Sconcentration for all concentrations of NaBr from 0.05 to 0.5 M and the addition of NaBr to the pure B4NCI4Ssolution invariably increases Td.I0 A striking feature of Figure 4 is that Td is not a monotonous function of salinity. It increases at the initial range of salinity, Le., from pure water up to 0.2 M NaBr, and decreases again at high salinity with a maximum located at 0.2 M NaBr. This phenomenon suggests that the temperature range in which the homogeneous micellar solution may exist will be shrunk at high salinity due to the increase of the Krafft point and the reduction of the cloud point. We have suggestedI0that there are four kinds of forces between micelles of B4NC14S:the van der Waals attraction, the electrostatic repulsion, the hydrophobic effect of the butyl chains on one micelle to penetrate into another, and the structured water layer around the ionic head groups of the micelles. We also have statedlo that initial salt addition reduces the B4N content of the micelles since more Na+ ions are present to compete for sites on the micellar surface, thus opposing phase separation. Further salt additions increase the micellar size as will be shown below, which favors the increase of van der Waals attraction force between micelles, meanwhile reducing the electrostatic repulsion between the micelles. These two effects promote phase separation, Le., decrease Td,
Figure 6 shows Td as a function of surfactant concentration of B4NC,S with n from 8 to 18 at 0.2 M NaBr. The cloud point phenomenon is also observed in the mixtures of B4N with other types of anionic surfactant. Thus, it may be said that the cloud point is a universal phenomenon for the mixtures of B4N and anionic surfactants. From Figure 6 one can see an increase of Td with the chain length of the surfactants from n = 8 to 14 at the same surfactant concentration in the whole concentration range studied. Such a phenomenon still occurs for n = 16 and 18 in the surfactant concentration range above 56 mM. In the surfactant concentrations below 56 mM, however, Tddecreases with increasing chain length from n = 14 to 18. Td at 56 mM is nearly unchanged with the chain length. It is shown above that the BIN content in micelles at the cmc increases with decreasing surfactant chain length. Such a phenomenon very likely holds at high micelle concentrations from a thermodynamical consideration. Hence, the behavior of the cloud point decrease with chain length may be understood by our intuitive model:1° the hydrophobic effect of the butyl chains on one micelle to penetrate into another, which favors the cloud point to occur, is strengthened by increasing the amount of BIN on the micelles. The behaviors of the cloud point in the concentration range below 56 mM for n > 14 are complex. We have measured the
Yu et al. 100
100
80
80
60
-
0
0
v
e
v
P
a
-
E-
60
40
40
20
50
100
150
200
[CnS] (dfi)
Figure 6. Cloud point as a function of surfactant concentration for B,NC,S at 0.2 M NaBr: (e,O , O , 0 , 0 ,and 0 ) n = 8 , 10, 12, 14, 16, and I S , respectively.
ratios of the reduced viscosity of B4NCI8Sto that of B4NC14S at 0.2 M NaBr. They are 4.8 at 52 "C and 4.6 at 40 OC for surfactant concentrations of 50 and 100 mM, respectively, and 9.2 at 65 OC for 20 mM. It may be considered from this result that the ratio of micelle size of the longer chain surfactant to that of the shorter one changes little at the high concentration range and increases rapidly on dilution at low concentration range. The larger the micelle size is, the greater the van der Waals attraction and the greater the amount of B4N on one micelle. These two factors favor the reduction of Td for a long-chain surfactant. Rheological Measurements. Figure 7 shows the relationship between the relative viscosity qr and temperature at various salinities for an equimolar mixture of B4N and C14Sat 50 mM C I S concentration. The viscosities were measured by a Ubbelohde viscometer and were examined by a Controvers 30 low-shear viscometer at 25 "C. The results showed that there was no shear rate dependence, which indicates a Newtonian flow of the solution. The dashed lines at the right side of the curves indicate the cloud point temperatures of the corresponding solutions. The appearance of the qr vs temperature curves at other surfactant concentrations is similar to that in Figure 7. An interesting feature can be seen from Figure 7 that the dependence of qr on temperature is different from low to high salinity. For salinities above 0.2 M NaBr, qr decreases with temperture, while for those below 0.05 M NaBr, qr increases with temperature. We have discussed the influence of excess amount of NaBr on the micellar properties in terms of the competing effect of Na+ to the adsorption of B4N on the micellar surface.1° The present result indicates that a comparable amount of Na' to that of B4N has no such effect as to induce a reversed dependence of micellar size with temperture. Nevertheless, the effect of NaBr on the micellar properties does exist, since the curves of 0.05 M NaBr are concave downward which is different from the concave upward curves in the solutions without NaBr. Another feature of Figure 7 is that qr increases with addition of NaBr. Since the micelles are charged due to the different
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3679
Properties of B4NBr-Surfactant Mixtures 12
1101
10
\
E
$
6
4
2
I 20
I 30
I
I
40
50
T ('C)
30
Figure 7. Plot of relative viscosity vs temperature at 50 mM B4NCI4S concentration. @,a,0 , and 0 denote NaBr concentrations of 0.5,0.2, 0.05, and 0 M, respectively. The dashed lines indicate the cloud points
of the solutions.
TABLE 11: Viscosity Data of Micellar Solutions of B,NC,& at 0.2 M NaBr
C, mM
'Ir
M-l
30.00 40.00 50.00 100.0
48.74 40.23 34.34 23.73
40 OC 1591 98 1 667 227
5.000 10.00 20.00 30.00 40.00 50.00 100.0
7.29 15.06 25.72 20.53 18.24 16.99 17.42
45 OC 1258 1406 1236 65 1 43 1 3 20 164
L, A
Lja
910 754 650 417
1.73 1.69 1.64 1.54
1670 1320 1000 780 654 572 394
1.43 1.54 1.61 1.57 1.53 1.51 1.48
hydrophobicities of B4N from that of C,$ as is seen at the cmc, it may be considered that when the salinity increases, the electrostatic repulsion between surfactant head groups is weakened, which decreases the area per surfactant molecule occupied and consequently increases the micelle size.14 Representative examples of the dependence of qr upon the temperature are shown in Figure 8 for B4NCI8Swithout NaBr and with 0.2 M NaBr. The surfactant concentrations were all at 50 mM. The appearance of the curves at other surfactant concentrations is essentially the same as that in Figure 8. Table I1 lists the dependence of qr with the surfactant concentrations at two different temperatures at 0.2 M NaBr. The viscosities measured by the Ubbelohde viscometer were also examined by the Controvers 30 low-shear viscometer at 40 OC. No shear rate dependence of the viscosities was found, which again indicates a Newtonian flow of the solutions. As can be seen from Figure 8, qr increases with increasing temperature and the curve is concave upward for B4NCI8Swithout NaBr. Such temperature-induced micellar growth behavior is similar to that of B4NCI4Swithout NaBr.l0 The difference between the two surfactant systems is that vr is about l order of magnitude larger in the former than in the latter. For a solution of B4NC18Swith 0.2 M NaBr, qr decreases with increasing temperature rapidly. This type of change in micellar size is also (14) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J . Chem. SOC., Faraday Trans. 2 1976, 72, 1525.
40
50
60
T ('C)
Figure 8. Relative viscosity of 50 mM B4NC18Sas a function of temperature: ( 0 and 0)with 0.2 M and without NaBr, respectively.
observed in the systems of B4NCI4Swith 0.2 M NaBr. However, the specific viscosity of the former is larger than that of the latter by 29-fold at 35 O C and 5-fold at 52 OC. It is puzzling to note that qr of the solution without NaBr is larger than that with 0.2 M NaBr in the temperature range from 43 to 45.4 OC (the cloud point of the former solution). Such a phenomenon was not observed in the systems of B4NCI4S. Table I1 shows that qr decreases with increasing surfactant concentration in the concentration range above 20 mM. Such a phenomenon strongly suggests that the micellar size decreases with the concentration. Previously,Io we have drawn a similar conclusion from the intrinsic viscosity for the mixtures of B4NBr/C14SNaat 0.2 M NaBr, which is not so apparent as shown presently. It can be seen from the reduced viscosity data, vrd, that the surfactant concentration range in which micelles grow with dilution is larger than that deduced from qr. If one takes the effect of intermicellar interaction into account, this concentration range may be further widened as will be seen below in the case of micellar length. For concentrated solutions of rodlike molecules which are overlapping each other, the relative viscosity at zero shear rate qr(0) is related to the length of rod L'5J6by
(7)
e
where r is the radius of the rod and is the number of rods per ;nit volume. The condition for overlapping rods is C >> l/L3. C can be calculated from
e = (c - cmc)NAu/(7rr2L)
(8)
with u the volume of the micelle one monomer surfactant occupies and NA the Avogadro constant. In the case of L >> 2(r - l), we have (9)
where I, is the radius of micellar core and we here take it as the length of the fully extended alkyl chain; u, is the volume of the (15) Doi, M.; Edwards, S . F. J . Chem. SOC.,Faraday Trans. 2 1978, 74, 918. (16) Hoffmann, H.; Rehage, H.; Platz, G . ; Schorr, W.; Trurn, H.; UIbricht, W. Colloid Polym. Sci. 1982, 260, 1042.
3680 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 6OC
Yu et al. 2 .o
900
B 1.5
500
700
h
m
-4
O
v
b
v
c7
ci
c
1 .o
bo o
r(
400
500
0.5
I
J
30
40
I 50
I
3.1
? (*C)
Figure 9. Micellar length as a function of temperature for 50 mM B,NC,S: (@ and 0 ) B4NC18S,with 0.2 M and without NaBr: (0 and 0)B4NCI4S,with 0.2 and 0.5 M NaBr, respectively.
monomer in the micellar core. They can be calculated by using Tanford’s formula1’ I, = 1.5 1.265nC (10) V, = 27.4 + 26.9nC (11)
+
where n, is the number of carbons in a hydrophobic chain. Since the micellar core consists of the hydrocarbons of B4N and C,S, V, must be taken as the average value of the two kinds of hydrocarbon chains. It is difficult to calculate this average value. So, as a first approximation, we assume that the number of butyl chains in the micellar core is equal to that of the hydrophobic chain of the surfactant. From the fact that the viscosity of the B4NC1,S solution is greater than that of B4NCI4S,we assume in the following that the micellar shape of B4NClBSis rodlike as in the case of B4NCl4S. Figure 9 shows the length of the rodlike micelles as a function of temperature calculated from the viscosity data in Figure 8 by using eqs 7-1 1. The r value is chosen as 30 A which is the fully extended length of the surfactant plus a binding layer of water and counterions of approximately 2 A. A small change of r value has no significant effect on the L values. It is seen that the length of the micelles increases linearly with the temperature from 421 A at 25 OC to 610 8, at 45 OC for the solution without NaBr. The length of the micelles in the solution with 0.2 M NaBr decreases from 782 A at 35 OC (1 OC above the Krafft point) to 520 A at 5 3 OC (0.3 OC below the cloud point). Table 11 lists the length of the micelles as a function of surfactant concentration. For the concentrations above 30 mM the ratio of length to diameter of the rods is less than 15; thus, the assumption of stiff rods in eq 7 seems reasonable. In the dilute concentration range, however, this ratio may reach about 30, and consequently some degree of bending of rods may probably occur. The overlap ratio L/u,where a is the mean distance between rods, calculated from eqs 8-1 1 is tabulated in Table 11. It is seen that the length of the micelles shortens with increasing surfactant concentration in the whole concentration range studied and that the L / u value (the degree of overlap of the micelles) reduces in the high concentration range. This result suggests that the decrease of the micellar size is not due to the overlap of the micelles. Such a conclusion is consistent with our earlier resultll that the overlapping of micelles cannot prevent the micelles from growing. The phenomenon of micelle shortening was previously interpreted in terms of the conformation energy of the micellar core.I0J1 In order to compare the effect of surfactant chain length on the micellar size, Figure 9 also plots the micelle length of 50 mM B4NC14Ssolutions at 0.5 and 0.2 M NaBr as a function of tem-
I 3.2
I
I
3.3
>.4
1CLG/T
(b-’)
Figure 10. Plot of logarithm of viscosity vs 1/T for 50 mM B,NC, S : (e and 0 ) B4NC18S,with 0.2 M and without NaBr: (0, 0 , and 0 ) B4NCI4S,with 0.5, 0.2, and 0.05 M NaBr, respectively.
pertaure. The r value is estimated as 25 A. It is evident from Figure 9 that the micellar length of B4NCIBSis greater than that of B4NCI4Sat the same NaBr concentration by nearly 2-fold. According to Missel’s ladder model for the sphere-to-rod transition for single-surfactant systems18 and for the mixtures of cationic/anionic surfactants,” the thermodynamic parameter K,which measures the tendency for no moles of surface active ions to transfer from a spherical state to a cylindrical state, increases with no and follows a power law. The minimum aggregation number of spherical micelles no calculated is 93 and 55 for B4NC18Sand B4NCI4S,respectively. Thus, the larger tendency of the micellar growth for longer surfactant chain system can be understood from this point of view. Activation Energy for Viscous Flow. The activation energy E for viscous flow of micellar solution has been calculated by several a u t h o r ~ ~ from ~ J ~ the 9 ~ equation ~ 11 = A exp(E/RT) (12) where A is a constant and 7 the viscosity of the solution. These authors found that the curves of log 7 vs 1 / T were not entirely linear throughout the relevant temperature range, and E was calculated separately for several segments of temperature. We plotted in Figure 10 the log 7 vs 1 / T curves from the viscosity data in Figures 7 and 8 where the surfactant concentrations were kept at 50 mM. The E value obtained from eq 12 is proportional to the slope of the curves. It can be seen from Figure 10 that the slope of the curves of B4NC14Swith 0.05 M NaBr decreases with increasing 1/ T and becomes zero in the low temperature range. For the solution of B4NC14Swith 0.2 M NaBr, the curve is linear over the entire temperature range, indicating a constant value of E. As the concentration of NaBr increases further, the curve is concave upward resulting in an increase of E with 1/T. The curve of B4NC18Swith 0.2 M NaBr is similar to that of B4NC14Swith 0.5 M NaBr in appearance except for a greater value of E in the former curve. A striking feature of the curve of B4NC18Swithout NaBr is a linear dependence of log 7 on 1 / T with a negative slope. It is meaningless for the activation energy to take a negative value. Clearly, the nonpositive value of E is induced by the growth of micelles with temperature which runs counter to the effect of the activation energy on the viscosity. In the systems with positive E, the micelle size decreases with increase of temperature, which has the same effect on the activation energy on the measured viscosity. Hence in this case, the activation energy of micellar solution deduced by eq 12 is overestimated. From the above analysis we conclude
~~~
(17) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley: New York, 1980.
(18) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Carey, M. C . J . Phys. Chem. 1980, 84, 1040.
J . Phys. Chem. 1990, 94, 3681-3689 that eq 12 cannot be used to calculate the activation energy of viscous flow for our present micellar systems, and the effect of micellar size change should be taken into account in applying this equation to other micellar solutions, which, unfortunately, was overlooked in the l i t e r a t ~ r e . ' ~ J ~ - * ~
Conclusions 1. A method for calculating the content of organic ions in micelles at the cmc using the Gibbs-Duhem equation is proposed. The results show that the content of B4N in the alkyl sulfate micelles at the cmc and in surface adsorption layer decreases with increasing alkyl sulfate chain length, which arises from the increase of the hydrophobicity asymmetry between BIN and the surfactants with the surfactant chain length. 2. The Krafft point of alkyl sulfate salt is reduced considerably in the presence of B4N, which enables a practical use of the micellar solutions with a hydrophobic chain length as long as octadecyl at room temperature. The Krafft point decreases with increasing micellar concentration in the presence of inorganic salt and increases with increasing inorganic salt concentration and chain length of the surfactant. (19) Ekwall, P.; Mandell, L.; Solyom, P. J . Colloid Interface Sci. 1971, 35, 519. (20) Hoffmann, H.;Platz, G.; Rehage, H.; Schorr, W. Adu. Colloid Interface Sci. 1982, 17, 275.
3681
3. The cloud point of B4NC,,S increases with increasing surfactant chain length except for that of the hexadecyl and octadecyl chains at concentrations below 56 mM. It is interpreted in terms of the variation of the B4N content in the micelles with the surfactant chain length by using our previously proposed model for the occurrence of the cloud point phenomenon. The addition of NaBr raises the cloud point initially, passing through a maximum, and then decreases again. The decrease of the cloud point may be relevant to the micellar growth and the reduction of electrostatic repulsion between micelles with inorganic salt. 4. B4NCI8Sforms homogeneous micellar solutions in the temperature range from the Krafft point to the cloud point. The micellar size decreases with increasing surfactant concentration at 0.2 M NaBr in the concentration range studied and is not likely due to an overlap of the micelles. The temperature dependence of the micellar growth varies with the salinity. The micellar size increases with increasing temperature in the presence of a comparable amount of NaBr to the surfactants or in the absence of NaBr and decreases on adding excess NaBr. The micellar size increases with increasing surfactant chain length. 5 . An Arrhenius type of equation cannot be used to calculate the activation energy of viscous flow of micellar solutions without considering the effect of micellar size change with temperature. Registry No. Bu4NBr, 1643-19-2; Bu4NC8S, 88815-10-5; Bu4NCl&, 125829-45-0; B u ~ N C ~ ~32783-22-5; S, B u ~ N C ~ ~122271-88-9; S, B u ~ N C I ~ 125829-46-1; S, B u ~ N C ~ 125829-47-2. ~S,
Molecular Second Harmonic Generation Studies of Methylene Blue Chemisorbed onto a Sulfur-Modified Polycrystalline Platinum Electrode Deborah J. Campbell, Daniel A. Higgins, and Robert M. Corn* Department of Chemistry, University of Wisconsin-Madison, Madison. Wisconsin 53706 (Received: March 28, 1989; In Final Form: November 20, 1989)
The resonant molecular second harmonic generation (SHG) response of a monolayer of adsorbed methylene blue is studied in situ on a polycrystalline platinum electrode modified by the deposition of a monolayer of chemisorbed sulfur. The sulfur monolayer prevents the irreversible decomposition of the dye molecules on the platinum electrode and ensures that the contributions to the surface nonlinear susceptibility from the metal and from the methylene blue remain separable. At an incident angle of 40°, the resonant molecular SHG signal from the methylene blue monolayer dominates the nonlinear optical response of the interface, and the potential dependence of the resonant SHG signal matches that expected during the electrochemical reduction and reoxidation of the chemisorbed methylene blue. The polarization dependence of SHG signal provides a picture of the average molecular orientation of the dye molecules as a function of surface coverage; this calculation of the average molecule orientation must include the complex Fresnel coefficients for the metal-electrolyte interface at the fundamental and second harmonic wavelengths and a full accounting of the various molecular nonlinear polarizability tensor elements.
Introduction A number of research groups are currently exploring the use of the nonlinear optical process of second harmonic generation (SHG) as an in situ probe of chemisorption and structure at metal electrodes.'-9 The sensitivity of S H G to the interfacial region ( I ) Campbell, D. J.; Corn, R. M. J. Phys. Chem. 1988, 92,5796. (2) Campbell, D. J.; Corn, R. M. J. Phys. Chem. 1987, 91,5668.
when the adjacent bulk media are both centrosymmetric has led to its extensive implementation as a probe of surfaces.1° At electrochemical interfaces, the SHG process is particularly useful due to its ability to discriminate between surface and solution species. In a recent paper' we used changes in the nonresonant optical response of the metal surface to indirectly monitor the chemisorption of species (e.g., monatomic hydrogen, bisulfate ions)
(3)(a) Corn, R. M.; Romagnoli, M.; Levenson, M. D.; Philpott, M. R.
Chem. Phys. Lett. 1984,106,30.(b) Corn, R. M.; Romagnoli, M.; Levenson, M. D.; Philptt, M. R. J . Chem. Phys. 1984,8J,4127. (4) Richmond, G. L.; Robinson, J. M.; Shannon, V. L. Prog. Surf Sci.
1988,28, I , and references therein. ( 5 ) Biwer, B. M.; Pellin, M. J.; Schauer, M. W.; Gruen, D. M. Langmuir 1988,4 , 121. (6) Furtak, T. E.; Miragliotta, J.; Korenowski, G. M. Phys. Reu. B 1987, 35,2569.
(7) Heskett, D.; Urbach, L. E.; Song, K. J.; Plummer, E. W.;Dai, H. L.
Surf Sci. 1988,197, 225.
(8) Heuer, W.; SchrBter, L.; Zacharias, H. Chem. Phys. Lett. 1987,135, 299. (9) Grubb, S. G.; DeSantolo, A. M.; Hall, R. B. J . Phys. Chem. 1988,92, 1419. (10) Shen, Y.R. The Principles of Nonlinear Optics; Wiley: New York, 1984.
0022-3654/90/2094-368 1 $02.50/0 0 1990 American Chemical Society
