J. Phys. Chem. 1985, 89, 2311-2384
2377
Strengthening of Hydrophobic Bonding and the Increase In the Degree of Micellar Ionization by Amphiphiles and the Micelle-Water Distribution Coefficient as a Function of the Surfactant Chain Length in Sodium Alkyl Sulfates Mohammed Abu-Hamdiyyah* and Ibrahim A. Rahman Department of Chemistry, University of Kuwait, Kuwait (Received: May 23, 1984; In Final Form: January 3, 1985)
We have investigated the effect of amphiphiles on the critical micelle concentration (cmc) and on the slope of the conductance-concentration line above the cmc, Sz (which is proportional to the micellar degree of ionization a),of sodium decyl, dodecyl, tetradecyl, and hexadecyl sulfates in aqueous solutions at 43.8 OC and confirmed the linear relationship between the initial rate of decrease of the cmc with additive concentration and the corresponding initial increase in S2(and hence in a ) , which was recently found for sodium dodecyl sulfate at 25 OC,for each of these surfactants. The empirical linear relations are summarized by (4In (xf)i/dyf)vro = bi(d In Sz/dyf)yro = bi(d In (a)i/dyf),ro, where i signifies the surfactant, xf and yf are the free monomer and free additive mole fraction concentrations, respectively, with bi a constant equal to 0.84, 1.10, 2.00, and 3.94 for the decyl, dodecyl, tetradecyl, and hexadecyl surfactants, respectively. On substituting each of these relations in the equation relating the distribution coefficient K to the ability of the additive to depress the cmc and its ability to increase the micellar degree of ionization, we obtain (-d In (xf)i/dyf)yd = O,K with Oi a constant having the value 0.59, 0.71, 1-00,and 1.33 for decyl, dodecyl, tetradecyl, and hexadecyl sulfates, respectively. The outstanding features emerging from these results are the following: (1) the nonspecificity of amphiphilic action in each of these ionic surfactants when the additives are compared at the same mole fraction concentration in the micelle, (2) the ability of an amphiphile to strengthen hydrophobic bonding and its ability to increase the micellar degree of ionization at a given mole fraction in the micelle increase with decreasing surfactant chain length, (3) for a given surfactant and for all the additives used the increase in the value of K with increasing size of the hydrophobic group of the additive, and (4) the important finding that the K value for a given amphiphilic additive decreases with increasing surfactant chain length. The results are interpreted in terms of a micellar structure having a rough outer region consisting of the ionic heads plus portions of the surfactant hydrocarbon chains in contact with water, the reduction of which provides a driving force for amphiphilic coaggregation, and an interior region composed of the remaining portions of the hydrocarbon chains not in contact with water and where inert nonpolar additives tend to be coaggregated, with the latter region growing at the expense of the former as the surfactant chain length increases. Finally, we estimated the values of the distribution coefficient suggested by Treiner and discussed its relation to that obtained by us.
Introduction The critical concentration at which surfactant monomers aggregate to form micelles in water is lowered in the presence of amphiphilic additives at low concentrations as both the nonpolar moieties of the surfactant monomer and those of the additive tend to be expelled from bulk water and coaggregate together,' resulting in the distribution of the amphiphile between the aggregates and the surrounding aqueous solution and the concomitant dilution of the micellar surface charge density and the increase in the micellar degree of i o n i ~ a t i o n . ~ The , ~ dependence of the cmc lowering ability on the hydrophobicity of the additive and of the surfactant chain has been known for some time.4*5 It is only recently6 that the cmc lowering ability was explicitly linked to the distribution coefficient of the amphiphile between the micelle and water. Hayase and Hayano6 determined experimentally the effect of several 1-alkanols on the cmc of sodium dodecyl sulfate as well as the distribution coefficient of the alkanol between the micellar phase and the aqueous phase and found for the first time an empirical relation between these two important parameters, the cmc lowering ability of an additive with its distribution coefficient K (mole fraction units), namely (-d In xf/dyf),& = OK (1) where xf and yf are the free monomer and free additive mole fraction concentrations in bulk water, respectively, with 0 a constant independent of the number of carbon atoms in the alcohol molecule. They called -8 the interaction of surfactant and the (1) Abu-Hamdiyyah, M.; Al-Mansour, L. J. Phys. Chem.1979,83,2236. (2) Abu-Hamdiyyah, M.; El-Danab, C. J. Phys. Chem.1983,87, 5443. (3) Almgren, M.; Swarup, S. J. Colloid Interface Sci. 1983, 91, 256. (4) Herzfeld, S. H.; Corrin, M. L.; Harkins, W. D. J. Phys. Chem.1950, 54, 271. (5) Shinoda, K. J. Phys. Chem. 1954, 58, 1136. (6) (a) Hayase, K.; Hayano, S . Bull. Chem.Soc.Jpn. 1977, 50,83. (b) k y a s e , K.; Hayano, S. J. Colloid Interface Sci. 1978, 63. 446.
additive coefficient. Manabe et ale7verified the above relation, and the physical meaning of 0 was extensively discussed. This was taken a step forward by Treiner,* who derived an equation in which the distribution coefficient (termed q ) is calculated from the additive's ability to lower the cmc and a salting-out effect, namely 2.3 X 1000 (2KM - Kg) '= 18 where KM is the initial slope of log cmco/cmc vs. Cadline, cmco is the cmc in the absence of the additive, and Kg is the salting-out constant. This equation treats additives that lower or raise the cmc such as propanol or urea, respectively. More recently2 an equation was derived in which the distribution coefficient K (mole fraction units) has two contributions, one from the ability of the additive to lower the cmc of an ionic surfactant and the other from the additive's ability to reduce the electrostatic interaction between the micelle and counterions as reflected in the additive's ability to increase the micellar degree of ionization, namely
K = -%(d In Xf/dYf)ypo + (d In a/dyr),po (3) It was also shown experimentally that the last two terms in eq 3 are related and the relation is obtainable from conductance measurements.2 It was found for sodium dodecyl sulfate and a large number of amphiphiles at 25 OC that (4In xf/dyf)yd is approximately equal to (d In a/dyf),+, so eq 3 reduces to eq 1 with 8 = 2 - 2(d In a/dy,),m,o (4) where y, is the mole fraction concentration of the additive in the micelle and 0 was found to be constant, approximately 0.67, for (7) Manabe, M.; Koda, M.; Shirahama, K. J. Colloid Interface Sci.1980, 77, 189.
(8)Tteiner, J. Colloid Interface Sci.1982, 90,44.
0022-3654/85/2089-2377%01.50/0 , 0 1985 American Chemical Society I
,
2378 The Journal of Physical Chemistry, Vol. 89, No. 11, 1985
Abu-Hamdiyyah and Rahman
all 17 amphiphiles examined which varied in length and shape of nonpolar moieties and type of polar head. The value 0.67 obtained for 8 was not significantly different from the value 0.69 obtained empirically by Hayase and Hayano using 1-alkanols. This method was applied also to CTAB9 using a large number of amphiphilic additives, resulting in an equation equivalent to (1) with 0 = 0.8. K values obtained by this method in sodium dodecyl sulfate and in cetyltrimethylammonium bromide are in reasonable agreement with values directly measured by gas chromatography6,l0or by solubility." The fact that 8 is essentially constant for a given ionic surfactant regardless of the amphiphilic additive is indicative of the nonspecificity of strengthening of hydrophobic bonding in the aqueous solution of the surfactant at low concentration of the additive. In terms of eq 3 and 4 the nonspecificity is given by (&f/dy,,,)ym+ = exofand (da/dy,),m, = (1 - 8/2)a0, respectively. Nonspecificity was also recently noted by Almgren and Swarup3 regarding the effect of amphiphiles on the decrease of the micellar surface charge density in sodium dodecyl sulfate aqueous solutions. The knowledge of how 0 varies with surfactant chain length and how the distribution coefficient for a given amphiphile behaves as a function of surfactant chain length is of paramount importance and basic to the understanding of the physical chemistry of solubilization and its application especially in biological systems as micelles are increasingly being used as models for biological membranes.I2 In this study we report our experimental results on the relation between the ability of an amphiphile to depress by cmc and the corresponding ability to increase the slope of the conductanceconcentration line above the cmc (and hence the micellar degree of ionization) as a function of the surfactant chain length in sodium alkyl sulfates. It will be shown that linear relations between the cmc lowering and the micellar ionization increasing abilities are obtained for sodium decyl, dodecyl, tetradecyl, and hexadecyl sulfates. The empirical relations will be used with eq 3 to provide us with equations similar to eq 1 for each of the surfactants which will give us values of 0 and values of K for a given amphiphile as a function of surfactant chain length. The resulting pattern that emerges and its implications to micellar structure will be discussed. We shall also obtain the values of q according to Treiner's method and discuss the relationship of q to K. Experimental Section
Chemicals. Benzocaine (purum), ethyl 4-hydroxybenzoate (purum), urethane (purum), 6-caprolactam (purum), and 6valerolactam (purum) were from Fluka; phenol was a laboratory reagent from British Drug Houses; butanol (proanalysis) and sodium decyl sulfate were from Merck; octanol (99%) and decanol (99%) were from Sigma. All compounds were used as received; 4-ethylphenol was described previously. Propionamide (pure) and butyramide (pure) from Koch-Light laboratories were recrystallized from chloroform and benzene, respectively, and valeramide (pure) from Eastman Kodak was recrystallized from benzene. The surfactants sodium dodecyl sulfate (from British Drug Houses) and sodium tetradecyl and hexadecyl sulfates (from Merck) showed minima in the surface tension-concentration plots, and each was recrystallized three times from absolute ethanol until no minimum was evident. All the recrystallized chemicals were dried in a vacuum oven before they were used. Water was distilled from an all-glass apparatus (Corning megapure) and deionized by passing it through an ion exchanger. Apparatus and Procedure. We have used the same apparatus and procedure described previously for the measurement of the electrical conductance of the various surfactant solutions.' The solutions which were preequilibrated were injected into the cell (9) Abu-Hamdiyyah, M.; El-Danab, C., paper presented to the 5th International Symposium on Surfactants in Solution, Bordeaux, France, July 1984, Abstract 3OCl. (10) Miyashita, Y.; Hayano, S . J. Colloid Interface Sci. 1982, 86, 344. (1 1) Gettins, J.; Hall, D.; Jobling, P. L.; Rassing, J. E.; Wyn-Jones, E. J . Chem. Soc., Faraday Trans. 1 1979, 75, 1951. (12) Treiner, C. J . Chem. Soc., Faraday Trans. 1 1983,93, 33.
(13) Evans, H. C. J. Chem. SOC.1956, 585. (14) Goddard, E. D.; Benson, G. C. Can. J. Chem. 1957, 35, 986.
Sodium Alkyl Sulfates
The Journal of Physical Chemistry, Vol. 89, No. 11, 1985 2379 1
62
SODIUM HEXADECYL S l i t F A i E
1
I. I 15
\\
5.2t
SODIUM DECYL SULFATE
--
Y
u 0 001
0049 0 005 Additive Concentration IHI
0 001
0 01
Figure 2. The variation of the cmc of sodium hexadecyl sulfate in the
presence of the additives which are numbered according to their serial numbers in Table I.
0 01 Additive Concentration IMI
0 015
Figure 5. The variation of S1,the slope of the conductance line above the cmc of sodium decyl sulfate in the presence of the additives numbered according to their serial numbers in Table I.
2.0
t
0.0
-
SODIUM DECYL SULFATE 4.0 3.L
3.3
- 3.2
-
i-2.0 -
L:
$I-J
3
-
-
U r*.r
3.0
Y
-6.0 -
2.9
1
1
0.Wl
I
0.W5
I
I
0.01
0 OS
I
Addltivc Cocwmtratii (MI
6
F w e 3. The variation of the cmc of sodium decyl sulfate in the presence
of the additives which are numbered according to their serial numbers in Table I.
I f
SODIUM HEXADECYL SULFATE
I
8
10
12
n in Na ,C, I+
14
16
SO4
Figure 6. The variation of initial slopes of cmc-Cad lines as a function
of surfactant chain length for the additives which are numbered according to their serial number in Table I.
0 055
0 054
4.0
0 053
0052
2
001.f
2.0
t
I
I
0050
0
jI 0.0
-9
-2.0
Additive Concentration IHl
Figure 4. The variation of S2,the slope of the conductance line above
the cmc of sodium hexadecyl sulfate in the presence of the additives which are numbered according to their serial numbers in Table I.
-
-1.0
I
6
These illustrations and the table show that for a given surfactant the ability of an additive to depress the cmc and to increase S2 increases with the hydrophobic character of the additive. This order is essentially preserved among the additives that differ significantly in hydrophobicity for all the surfactants investigated. However, for a given additive the ability to depress the cmc increases with decreasing surfactant chain length as seen in Figure 6 where we plotted In (-d(cmc)/dC.&,+, against the number
I
1
I
I
I
8
10
12
14
16
n in Na C,
%.l
I
SO4
Figure 7. The variation of initial slopes of S2-Cad lines as a function of
surfactant chain length for the additives which are numbered according to their serial numbers in Table I. of carbon atoms in the surfactant chain and obtained lines similar to those obtained by S h i n ~ d awho , ~ studied the effect of alkanols on the cmc of potassium alkanoates in the presence of 0.02 M
Abu-Hamdiyyah and Rahman
2380 The Journal of Physical Chemistry, Vol. 89, No. 11, 1985
TABLE I: The Initial Slopes of the Lines cmc = a - bCd and S2 = a' + b'Cd Obtained by the Least-Squares Method for the Variation of the cmc's of the Various Sodium Alkyl Sulfates Investigated and of the Corresponding Slopes of the Conductance-Concentration Lines above the cmc with Additive Concentration in the Low-Concentration Range at 43.8 "C c10 c12 C14 C16 additive b b' b b' 102b lob' 103b 102b' 2 f 1.5 0.072 f 0.007 0.11 f 0.03 0.020 f 0.001 0.10 f 0.01 0.32 f 0.02 0.24 0.09 0.70 f 0.04 1. propionamide 1.2 f 0.4 2.2 f 0.6 4.5 f 0.4 0.100 f 0.006 0.17 f 0.05 0.030 f 0.001 0.14 f 0.02 0.8 f 0.1 2. butyramide 4.2 f 0.6 10 f 3 0.190 f 0.004 0.38 f 0.03 0.060 f 0.001 0.26 f 0.01 1.67 f 0.08 1.7 f 0.3 3. valeramide 0.6 f 0.1 0.39 f 0.03 4. n-butanol 120f 1 2.9 f 0.3 20.8 f 0.3 15 f 2 54 f 3 3.1 f 0.3 5.3 f 0.3 0.74 f 0.02 5. benzocain
*
3.6 f 0.3 6. octanol 10.1 f 0.3 7. decanoi 8. 6-valerolactam 9. phenol 10. 4-ethylphenol 1 1. ethylparaben 12. urethane 13. caprolactam
6f1 18 f 2
2.73 f 0.06 0.03 f 0.001 0.074 f 0.003 0.321 f 0.006 0.80 f 0.04 0.024 f 0.002 0.059 f 0.02
KOH by the dye titration method. The lines in Figure 6 are practically parallel with a slope of -0.63 compared with -0.69 obtained by Shinoda. The initial rate of variation of S2 with additive concentration as a function of the surfactant chain length is shown in Figure 7 . It shows the ability of an amphiphile to increase S2 increases also with decreasing surfactant chain length, with the rate of this increase approximately constant in going from the C16 to C10 surfactant. The scatter in curve 1 for propionamide is most likely due to experimental error. It also occurs in Figure 6. Strengthening of Hydrophobic Bonding and the Increase in Sz in Solutions of the Various Surfactants. We have plotted the ability of an amphiphile to depress the cmc, In (-d(cmc)/ dC,d)c,d--o, against its ability to increase S2,In (dS2/dCad)c,d,o, and obtained a linear relation between these two quantities for each of the surfactants. The amphiphiles used with a given surfactant (seven amphiphiles with C10, eleven with C12, eight with C14, and ten with C16) are all shown in Table I. These results confirm the validity of the linear relation and the nonspecificity of amphiphilic action previously obtained2 for sodium dodecyl sulfate at 25 OC, for surfactants of various chain lengths. We obtain with the slope, intercept, and correlation coefficient (1 .OO f 0.06, -3.08 f 0.15, 0.985), (1.05 f 0.07, -2.12 f 0.14, 0.987), (0.99 f 0.05, -1.41 f 0.07, 0.990), and (0.99 f 0.02, -0.53 f 0.04, 0.999) for hexadecyl, tetradecyl, dodecyl, and decyl sulfates, respectively. We shall assume that all the lines in Figure 8 have same slope, and this is equal to unity. Converting to mole fraction concentrations and assuming2yf, the free additive concentration, is equal to cad/55.4,x o f = cmc0/55.4, (1 /S02)(dS2/dYf),,0 = (d In S*/dYf),,O, (l/Xof)(-d(cmc)/dCad)C.d,o = (-d In Xf/dYf)ypO,and (d In s2/ dyf),,, = (d In a/dyf),,o (see next section), we obtain (-d In Xf/dYf),pO = bi(d In CY/dYf)y,O
7.9 f 0.8 0.88 f 0.04 0.9 f 0.2 0.30 f 0.04 1.45 f 0.05 1.6 f 0.1 1.0 f 0.2 10.0 f 0.1 4.7 f 0.8 23 f 2 25.3 f 0.5 3.0 f 0.3 0.08 f 0.02 0.21 f 0.04
2-
I
(15) (a) Stigter, D.; Mysels, K. J . Phys. Chem. 1955, 59, 45. (b) Stigter, D.Ibid. 1975, 79, 1015.
I
-4
I
-3
I
I
-2
In
{*}
I
I
-1
0
[ad-
1
1
2
I
I
3
0
Figure 8. Ability of amphiphilic additives to depress the cmc of sodium
decyl (ClO), dodecyl (C12), tetradecyl (C14), and hexadecyl (C16) sulfate, at 43.8 OC, vs. the corresponding ability to increase the slope of the specific conductance curve above the cmc for each of the above surfactants. The additives used with each surfactant are shown in Table I.
Although each of these methods weigh the ionic distribution around the micelle between bound and free to some extent differently, theoretical expressions for the degree of ion binding corresponding to each of these methods have recently been derived,Is giving values which are in agreement with experiment. For example, the degree of ion binding to an anionic micelle measured through a transport property such as conductance is give byI8 1 - CY = ~ ~ " C + 4 7 r dr r2
(6)
with bi equal to 0.84, 1.10, 2.00, and 3.94 for decyl, dodecyl, tetradecyl, and hexadecyl sulfates, respectively. The coefficient bi gives the ratio of the relative ability of an additive to depress the cmc of surfactant i to the corresponding relative ability to increase the micellar degree of ionization. The Micellar Degree of Ionization, CY,and Its Relationship to S,. The association of monomeric ions into a micelle results in the concentration of charge at the aggregate surface which leads to the binding of a fraction (1 - a ) of counterions between and close to the ionic heads15 such that this fraction of bound counterions move as part of the kinetic micelle and only a fraction CY of the counterions are free as revealed by several experimental (thermodynamic, transport, and spectroscopic) method^.'^-'^
S f l 2.6 f 0.2 4.8 f 0.3 11 f 2 40 f 4 31 f 3 180 f 30 66 f 3 6f5 3.49 f 0.08 5.00 f 0.01 15 f 4
0.11 f 0.01
n
b
(7)
where C+ is the concentration of counterions in the region r
