Langmuir 1990,6, 1596-1600
1596
Determination of Partition Coefficient of Alkanols between Bulk Water and Micelles of an Ionic Surfactant by a Novel Method Based on Surfactant Counterion Concentration Masahiro Manabe,. Hideo Kawamura, Susumu Kondo, Morikazu Kojima, and Susumu Tokunaga Department of Industrial Chemistry, Niihama National College of Technology, Niihama, Ehime 792, Japan Received January 5, 1989. In Final Form: January 17, 1990 A novel method is proposed for the determination of the partition coefficient of 1-alkanols(C4-G) between bulk water and micelles of the ionic surfactant, sodium dodecyl sulfate (SDS).In the method, the counterion concentration (CN,) at a given concentration of SDS (C,) was measured as a function of the concentration of added alkanol (CJ in order to estimate the limiting slope, dCN,/dC,, at C, 0. A theoretical equation has been derived which well explains the dependence of dCN,/dC, on C, at infinite dilution of the alkanols. By fitting the parameters in the equation to experimental data, we obtained the following three characteristic quantities: (1)The partition coefficient, K,, has little dependence on both C, and C, and is in good agreement with a literature value for each alkanol. (2) The effect of alkanol incorporated into micelles at the mole fraction xnm on the degree of ionization of micelles (a),denoted da/dx,m, is 0.17, independent of the carbon number of the alkanol molecule. (3) The effect of free monomer alkanol (concentration Cnf) on the free monomer surfactant (concentration CSf) in the micellar solution, dCSf/dC,f,is numerically identical with the well-known rate of cmc decrease on the addition of alkanol, d(cmc)/dC,. The determinations were carried out lower than xamby about 0.1.
-
Introduction When an organic substance is added to a micellar solution of a surfactant, the additive is considered to be distributed between the bulk water phase and the micellar one, on the basis of the pseudo phase separation model of micelle formation.' So far, some methods for the determination of the partition coefficient have been devisedU2-*l In a previous paper,12 a new method, the "differential conductivity method", was proposed which is applicable to nonionic additive dissolved in the micellar solution of ionic surfactants. There, the conductometric behavior of sodium dodecyl sulfate solutions on the addition of 1alkanols was explained by the two competitive factors. One is a conductivity-decreasing factor: the alkanol dissolved monomerically in the bulk water causes the free monomer surfactant (completely ionized) to form micelles (partially ionized). The other is a conductivity-increasing factor: the alkanol solubilized in micelles promotes micelle ionization. Namely, the former factor participates in the decrease of the concentration of free counterion of surfactant and the latter in the increase of the concentration of free counterion on the addition of alkanols. Conductivity
is physically a complex quantity which is a function of some variables such as the concentration, size, and valence of each ion. Thus, the validity of the consideration of the conductometric behavior may be justified by measuring the concentration of the counterion itself. This is one of the purposes of the present study. Consequently, when it is verified, the data of the counterion concentration may lead to the partition coefficient in addition to other important parameters representing the monomer surfactant concentration and the degree of ionization of micelles which characterize the solubilization equilibria. Moreover, the parameters allow us to evaluate t h e concentration of each species existing in solubilization systems a t any composition. For simplicity of the theoretical analysis, the present study has been carried out only in a low-concentration region of alkanols.
(9) Hoiland, H.; Ljosland, E.; Backlund, S. J. Colloid Interface Sci. 1984.101.467. ~.~~ (10) Christian, S. D.; Tucker, E. E.; Smith, G. A,; Bushong, D. S. J . Colloid Interface Sci. 1986, 213, 439.
Experimental Section Materials. Sodium dodecyl sulfate (SDS) was prepared by the same procedure as in a previous study.'3 It gave no minimum around its critical micelle concentration (cmc) in the plot of the surface tension vs concentration. Sodium chloride was commercially available (extra pure grade, Wako). 1-Alkanols (C4-C7) (G.R. Grade, Tokyo Kasei) were purified by fractional distillation under reduced pressure. Water deionized through ion-exchange resin was used after distillation. Electromotive Force (emf) Measurements. The concentration of Na+ ion in NaCl solution and in SDS solution in the absence and presence of the alkanols was measured by using a Na+ ion selective electrode (Orion, 97-11 type) and a doublejunction reference electrode (Orion,90-02 type). The construction of the electrical cell was as follows: reference electrode/ KCI solution (Orion, 90.00.02 type)/NH,NO, solution (1 mol kg-')/sample solution/Na+ ion electrode. The cell was immersed in a water bath controlled at 25 f 0.05 "C and covered with glass plates. A concentrated stock solution was added in small portions to an amount of solvent placed in the cell. The solution in the cell was stirred with a magnetic stirrer during each run. The emf measurements were carried
1988, 30,335. (12) Manabe, M.; Kawamura, H.; Yamashita, A,; Tokunaga, S. J . Colloid Interface Scc. 1987, 125, 147.
(13) Manabe, M.; Tanizaki, U.; Watanabe, H.; Tokunaga, S.; Koda, M. Niihama Kogyo Koto Senmon Gakko Kiyo, Rikogaku-hen 1983,19,50.
(1) Shinoda, K.; Nakagawa, T.; Tamamushi, B.; Isemura, T. Colloidal Surfactants; Academic Press: New York, 1963; p 25. (2) Dougherty, S. J.; Berg, J. C. J . Colloid Interface Sci. 1974,48,110. (3) Hayase, K.; Hayano, S. Bull. Chem. SOC.J p n . 1977,50, 83. (4) Manabe, M.; Shirahama, K.; Koda, M. Bull. Chem. SOC.Jpn. 1976, 49, 2904.
( 5 ) Almgren, M.; Grieser, F.; Thomas, J. K. J . Chem. SOC.,Faraday Trans. I 1979, 75, 1674. ( 6 )Goto, A.; Nihei, M.; Endo, F. J. Phys. Chem. 1980, 84, 2268. (7) Kaneshina, S.; Kamaya, H.; Ueda, I. J. Colloid Interface Sci. 1981, 83, 589. (8) Abuin, E. B.; Lissi, E. A. J . Colloid Interface Sci. 1983, 95, 198.
(11)Nguyen, C. M.; Scamehorn, J. F.; Christian, S. D. Colloids Surf.
0743-7463/90/2406-1596$02.50/0
0 1990 American Chemical Society
Langmuir, Vol. 6, No. 10, 1990 1597
Determination of Partition Coefficient of Alkanols 2
0
20
40
200
20
>
, 150 w
1, 100
0
10
20
c,
/
"01
30
k9-1
Figure 2. Dependence of emf on the concentration of 1hexanol added to nonmicellar solutions of SDS. C, (mmol kg-l): A (4.954), B (5.996), C (7.115), D (9.033). The arrow indicates C, at cmc, taken from ref 13.
1
0 104 I C
/
mol
kg-'
1
Figure 1. Dependence of emf or CN, on the concentration of NaCl (open circle) and SDS (closed circle). out with an accuracy of 0.1 mV on the meter (Orion, 701 type). A stable reading was obtained 20-30 min after each addition of the stock solution. For the preparation of the SDS solution containing the alkanol, a SDS solution with a given concentration was first prepared. A half portion of it was moved into the cell, and the other portion was used as the solvent of the stock solution of alkanol. Solutions were prepared by weight. In order to correct the reading for the drift of the electronic circuit, the emf value (represented by Eh) of a standard solution (NaCl solution a t 10 mmol k g l ) was measured just before each experimental run.
Results and Discussion In respective experimental runs for NaCl solutions, distinct linear relations between the emf reading and the logarithm of the NaCl concentration were obtained, and the lines were parallel to each other. The distance between the lines is due to the drift in the electronic circuit. Then, the emf reading was corrected by subtracting the difference of Eh between experimental runs. The correction leads to the single linear relation shown in Figure 1, which is expressed as
E = E*
-k
fl log CN,
(1)
where fl, CN,, and E * stand for t h e slope (56.0 mV/ decade), concentration of free Na+ ion, and E (corrected emf value) at CN, equal to unity, respectively. The emf data for SDS solutions are also plotted in Figure 1. The curve is found to consist of a straight line extending up to a break point and a monotonically increasing line above the point. It is obvious that the straight line is in good agreement with t h a t of NaCl. The agreement ~ suggests that eq 1 is available for estimating C N Then CN, in the SDS solutions in the absence and presence of alkanols mentioned below was calculated not by eq 1but, as a matter of convenience, by eq 2
where E - E h corresponds to the difference between the emf reading of the sample solutions and that of the standard solution with t h e concentration c h . T h e calculated CN, value of the SDS solution is plotted in Figure 1 against the SDS concentration (C,). The plots reflect that after a linear increase with slope equal to unity (indicating complete ionization) to the break point, CNa increases linearly with a less steep slope (0.22) which is,
on the basis of Botre's approach,14 regarded to be the degree of ionization of micelles and is represented by a. The linearity indicates little dependence of a on C,. The concentration a t the break point is taken to be the critical micelle concentration (cmc) of SDS alone (8.0 mmol kg-l), which is denoted cmco to distinguish it from the cmc in the presence of alkanols mentioned below. On the addition of alkanol to a SDS solution with a given C,, t h e emf changes as follows. Figure 2 shows t h e dependence of emf (AE:difference of E from the value in alkanol-free solution) on the concentration (C,) of alkanol added to nonmicellar solution (C, < cmco). During the initial addition of alkanol, the emf remains constant up to a break point and then decreases with increasing C,. It is noticed that the higher the C, the lower the C, a t the break point and that just above cmq, (e.g., 9.033 mmol k g l in Figure 2) the emf decreases without remaining constant. The emf behavior is explained in terms of t h e wellknown fact that the cmc of a surfactant is reduced by the addition of organic substances such as alkanols.13-15 T h e value of Ca at the break point of each curve in Figure 2 agrees with the concentration of alkanol (indicated by the arrow) existing a t the cmc (corresponding to the present C, value), determined in a previous study.13 Therefore, the decrease in emf, i.e., the decrease in C N ~above , the break point in Figure 2 can be attributed to the micellization of free monomer surfactant, caused by the added alkanol. In addition, the constancy below the break point suggests that there exists little interaction between free monomer species of surfactant and alkanol. The result for SDS solutions above the cmco is shown in Figure 3, where, instead of the emf difference as in Figure 2, the difference of CNa, denoted by ACN, (calculated by eq 2), is plotted against Ca, since CN, is physically more understandable than E. Just above cmco, the added alkanol most effectively reduces CN,, and the decreasing tendency becomes less remarkable with increasing C,. CNa then tends to increase a t high C,. The dependence of emf or CNa on C, in Figures 2 and 3 is in line with t h a t determined in the emf study by Backlund and Rundt in SDS-pentanol and SDS-hexanol system@ and also with the conductometric results in the previous study.12 As long as C, is low, each curve in Figure 3 can be regarded as linear and gives the limiting slope at C, 0, represented by dCN,/dC,. In Figure 4, this quantity is plotted against C, above cmco. It is apparent that dCNa/ dC, for each alkanol increases from a negative value at cmq
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(14) Botre, C.; Crescenz, V. L.; Meie, A. J. J. Phys. Chem. 1956, 63, 650. (15) Manabe, M.; Koda, M. Bull. Chem. SOC.Jpn. 1978,51, 1599. (16) Backlund, S.;Rundt, K. Acta Chem. Stand. A 1980,34, 433.
1598 Langmuir, Vol. 6, No. 10, 1990 I
Manabe et al.
t
A
l
0.2
I
1
I
I
E
I
O
5
0
0
10 Co
/
I
t -0.4
mol k4-I
Figure 3. Dependence of CN. on the concentration of 1hexanol added to micellar solutions of SDS. C, (mmol kg-l): A (10.49), B (14.00), C (18.97), D (24.66), E (44.94).
,
I
1
A /
15
I
I
O
0, i
1
Figure 5. Dependence of dCN,/dC, on j . The number indicates the carbon number of alkanol.
I
solution with a given C,, some portion of the alkanol is considered to be dissolved monomerically (concentration Ca3 and the other located in micelles (Cam). That is
c, = C,f + cam
(5)
The quantity dCN,/dC, corresponding to the limiting slope determined in Figure 3 can be derived by differentiating eq 4 with C, under the condition of C, being constant dCN,/dC, = (dC,'/dC,f)(dC,f/dC,) + a(dC,"/ d C,? (dC /: d C,) 8
30
C,
/
50 mol kg"
CSm(da/dxam)(dxam/dCam)(dCam/dC,) (6) = Cam/(Cam + Csm),the mole fraction of al-
70
Figure 4. Dependence of dCN,/dC, on the concentration of SDS. The number indicates the carbon number of alkanol.
to positive ones at higher C, values, and the longer the chain length of the alkanol molecule, the more remarkable the increasing tendency. I t is possible to explain qualitatively the dependence of dCN,/dC, in terms of the following two competitive effects. The one is the CNadecreasing effect: the free monomer alkanol dissolved in the bulk water leads the free monomer surfactant (ionized completely) to the micellar one (ionized restrictively),owing to the hydrophobic interaction between alkanol and surfactant. The other is the CN,-increasing effect: the alkanol solubilized in micelles enhances the ionization of micelles because of the reduction of the surface charge density of micelles. As for the former effect, the relationship between concentrations of respective monomer species is well-known just at the cmc;15 however, it is not known above the cmc, i.e., for micellar solutions. The latter effect has often been adopted when discussing solubilization systems. However, no quantitative study on the CNaincreasing effect has been made until now; therefore, both effects will be quantitatively analyzed in the following manner. For surfactant species, their concentrations (C,f for the free monomer species and C," for the micellar one) are related as
c, = C,f + c,m
+
(3)
For the counterion, CN, is represented as (4)
When a small amount of alkanol is added to a micellar
where x a m kanol in the micellar phase. When C, is extremely low as in the present experimental condition, eq 6 can be approximated in the same manner as described elsewhere12 dC,,/dC,
=k(l -a)
+ [(da/dxam)- k ( 1 - a ) ] j
(7)
where j and k are the quantities defined as
j = dCam/dC,; k = dC,f/dC,f
(8)
The physical meaning of j is the fraction of solubilized alkanol in the amount of the added alkanol, and that of k is the effect of monomerically dissolving alkanol on the concentration of free monomer surfactant dissolved in the intermicellar region of the bulk phase. The partition coefficient of alkanols between the bulk water and micelles, K,, is defined (in mole fraction) as K, = xam/xaf,where Xaf refers to the mole fraction of alkanol in the bulk phase, and it can be approximated to be Caf/nw (n, represents the molar number of 1 kg of water). As described previously,12j can be related to the partition coefficient, with C, being very small: where K , is another partition coefficient defined as K,/ n,. I t is perceived that in eq 7 dCN,/dC, is a linear function of j if both k and da/dxam are independent of C, as well as C,, as long as C, is very low. In other words, eq 7 can be solved by linear regression taking the K,value which minimizes the standard deviation for the predicted linear plots. Resultant linear relation obtained in the regressive analysis for each alkanol is shown in Figure 5. It is clear that the longer the alkyl chain of the alkanol the steeper the slope, and all these straight lines are regarded as having a common intercept a t j = 1.
Langmuir, Vol. 6, No. 10, 1990 1599
Determination of Partition Coefficient of Alkanols
~
Table I. K,,k,and da/dxp in l-Alkanol-SDS Systems at 25 O C CNa K, K2 -k -d(cmc)/dCac da/dxam 4 5 6 7 0
3.46 X 1.03 X 2.39 X 4.88 X
lo2 lo3 lo3 lo3
3.00 X 7.22 X 2.25 X 6.02 X
lo2 lo2 lo3 lo3
0.0299 0.0712 0.205 0.545
0.028 0.078 0.21 0.53
0.162 0.164 0.170 0.187 avg 0.170
Number of carbon atoms of alkanol. From ref 3. From ref
15.
-
.P z 0 u
c
t./
I
r.
0
5
IO
'.,
The determined values of K, are listed in Table I. It is found that K, for each alkanol is in agreement with that determined by the vapor pressure m e t h ~ d .Accordingly, ~ it is claimed that the present method is satisfactory for the partition coefficient determination: in other words, a t infinite dilution of alkanol both k and da/dxam are independent of C,. Respective intercepts at j = 0 and j = 1 of each line in Figure 5 allow us to evaluate, from eq 7 , k and da/dxam: = (dCNa/dCa)j=o/(l- a)
da/dxam = (dCNa/dCa)jil
(10)
These values are listed in Table I. The value of a (=0.22) determined in Figure 1is used in the calculation for k. For all alkanols studied, k is found to be negative; i.e., C,', which was called the "intermicellar concentration of surfactant" by Sasaki et al.,17J8at a given C, tends to decrease on the addition of alkanol. Further, k becomes larger in magnitude with increasing chain length of alkanol molecule. Since k is the quantity concerning concentrations of monomer species of both surfactant and alkanol in equilibrium with their mixed micelles, it is significant to compare k with the well-known quantity d(cmc)/dC,, which is the cmc-decreasing rate of a surfactant on the addition of a l k a n ~ l s . ~It~ Jis~noticed that k is defined "above cmc", whereas d(cmc)/dCa is defined "at cmc". Table I indicates that k and d(cmc)/dC, for each alkanol are numerically in good agreement with each other. Therefore
k = d(cmc)/dC,
(11)
as described in the previous conductometric study.12 As mentioned below, this relation is very important and useful for estimating the intermicellar concentrations of surfactant and alkanol since the value of d(cmc)/dC, is determined more easily than k. It is found that the values of da/dxamlisted in Table I are in accordance with each other, as also seen from the common intercept a t j = 1in Figure 5. Little dependence of dn/dxam on the alkyl chain length of alkanol suggests that only the hydrophilic moiety, the OH group with some neighboring methylene groups in the alkanol molecule, is located in the surface region of micelles, and the moieties reduce the surface charge density of micelles to enhance ionization of micelles. Manabe et al.19 derived the equation of da/dxamwhich is a function of molecular cross sectional areas of the surfactant and solubilizate in their mixed micelles. Assuming the respective areas are identical, the equation gives 0.13 for d a / x a m , taking a to be 0.22 determined above. The mean value of da/dxam,0.17, in (17)Sasaki, T.; Hattori, M.; Sasaki, J.; Nukina, K. Bull. Chem. SOC. Jpn. 1975,48, 1397. (18) Sasaki, T.: Yasuda. M.: Suzuki. H. Bull. Chem. SOC.Jon. 1977. 50, 2538.
Co
/
0
ml k 9 - I
Figure 6. Dependence of Na+ concentration and xamon C. of l-hexanol. C. = 10.49 mmol kg'. Circle, experimental A C Nthin ~ solid line, the same line as in Figure 3 for limiting slope; thick solid line, ACN. calculated by eq 15; broken line, C,' - C,ro calculated by eq 13; chain line, calculated xam (see text). Table I is in reasonable agreement with the calculated value -and also with 0.18 evaluated by the differential conductivity method.12 Christian et al. studied the relationship between K,and X,m over its complete region in some solubilization systems, and they found that in every case K, is a strong function of xama t least when values of xem are greater than 0.1 or 0.2.10J1 Abuin and Lissi8 also determined such a dependence for hexanol and heptanol in the SDS solution: K , tends to decrease suddenly around 0.5 xem with increasing Xam, In the present results, the constancy of K, as well as k and da/dxam must remain due to the condition of low C, in which region the cmc decreases linearly with increasing C,.15 The region of xamfor the determination of the parameters will be estimated below. From the equations and parameters described above, it is possible to estimate C,' and C N at~ any composition of the micellar SDS solution as long as the amount of alkanols contained in the solution is small. The definition of k suggests the relation C,f = C,fo + kC,f
(12) where CSmstands for C,f in alkanol-free solution, and it can be regarded to be identical with cmco since the dependence of CSmon C, is very From eqs 3, 5,8,9, and 12 a quadratic equation of C,' is derived. The equation can be solved for C,f: C,f = c,fo+ [(C, + c, - c,fo+ l / K J + ((C, + c, - c,fo+ 1/K,)2 - 4(k + l)Ca/Kc)1'2]/[2(l+ l / k ) ] (13) This provides C,f a t any C, and Ca when K,, k, and cmco are known. Besides, CNa a t the C,' can be calculated as follows. If a is expressed as a = a.
+ (da/dxam)xam
(14) the equation of C N is~ derived by using eq 4 and the definitions of both K, and k as C,, = C,'+ [ao+ (da/dxam)(Kc/k)(C,'- C:)](C,
(15) where a0 (=0.22 mentioned above) indicates a for alkanolfree micelles. In Figure 6, the values calculated by eq 15 a t a certain C,are illustratively shown as a function of Ca and compared with experimental CNa values. The C, value (10.49 mmol kg-l) chosen here is just above cmco because a t a given Ca
(19) Manabe, M.; Koda, M.; Shirahama, K. J. Colloid Interface Sci.
1980, 77, 189.
- C,f)
(20) Vikingstad, E. J. Colloid Interface Sci. 1979, 72, 68.
1600 Langmuir, Vol. 6, No. 10, 1990
at cmc is supposed to be higher than any other Xam values a t C, higher than cmc. I t is obvious that the calculated values of ACNa (the difference of CNa from that of alkanol-free solution) are coincident with the experimental values in a low-C, region in which the limiting slope of the straight line, dCNa/dCa, is estimated. However, these values are not coincident a t higher Ca in which the equations mentioned above do not hold since the alkanol even in micelles is not in a limiting dilution. The higher the C,, the wider the C, region a t which the coincidence is recognized, although no curve for higher C, is drawn here. The free Na+ ion is considered to be from both the free monomer surfactant and the micellar one. Therefore, ACNa can be divided into two contributions: C,' - CSm(=AC,? from monomer species and a(C, - C,9 - ao(C,- CSm)( = A (aC,m)) from micellar species. The curves shown in Figure 6, calculated by eqs 14 and 15, indicate that the value of hC,' is lower than 3 . c a~t any ~ C,, which is also observed at any other C,. The difference between the curves, AC,f - XN,, corresponds to the increment of CNa due to the enhancement of ionization of micelles, i.e., A(aCSm), caused by the alkanol located in micelles. Finally, x,m is calculated, by using C,f in eq 13 and from its definition, as (Ca - Ca?/(C, - C,f + Ca - Ca9 where Caf = (CBf- CSm)/kfrom eq 12. The xamvalue for hexanol calculated a t C, = 10.49 mmol kg-I is shown as a function of C, (Figure 6). By comparing the Xam curve with the ACNa curve, the xam value above which the calculated ACNa deviates from the experimental one or from the linear x,m
Manabe et al.
relation providing the limiting slope can be estimated to be around 0.1 (at C, N 3 mmol kg-I). As a result, the determination of K, as well as other parameters in the present study has been carried out below about 0.1 Xam. This value is close to the value (xam = 0.1 or 0.2) pointed out by Christian et al.lOJ1 Therefore, no dependence of K , on Ca in the present study is acceptable. So far, in such solubilization systems, the a-increasing effect has been noticed21-22in addition to the cmcdecreasing one participating in the quantity d(cmc) / dC,.15 However, the quantity k has been ignored in most studies. It is claimed that k is essential in order to estimate the concentration of each species in the micellar solutions containing organic additives. The recent study supports the significance of k. T h e partition coefficient of homologous w-phenylalkanols in micellar solutions of SDS was determined by a spectroscopic methodaZ3When k was taken into account in the analysis, the partition coefficient had little dependence on C, over a wide C, region from just above cmco, although it tends to increase with increasing C, without consideration of k. Registry NO. SDS, 151-21-3; CIHBOH, 71-36-3; C S H ~ ~ O 71H, 41-0; C6H130H, 111-27-3; C7HlSOH, 111-70-6; Na, 7440-23-5. (21)Tominaga, T.; Stem, T. B.; Evans, D. F. Bull. Chem. SOC.Jpn. 1980,53,795. (22)Hall, D.G.;Price, T. J. J. Chem. Soc., Faraday Trans. 1 1984, 80,1193. (23)Kawamura, H.; Manabe, M.; Miyamoto, Y.; Fujita, Y.; Tokunaga, S. J. Phys. Chem. 1989,93,5536.
