J. Phys. Chem. 1003, 8 7 , 5443-5448
It is not surprising that the cross section for rotational diffusion is less than that for thermodynamic excluded volume, since one might expect the short, extended side chains to be free draining and thus not contribute significantly to the hydrodynamic cross section. In helicogenic solvents, the side chains are undergoing fast reorie n t a t i ~ n . ~ Therefore, ' the side chains are certain to be less than fully extended but, because of steric constraints, more extended than independent, free rotators. If one takes the excluded volume cross section as the mean extension, over half of the space is occupied by solvent. A true Yhard-corendiameter of 6.5 A compared to a rotational equivalent hard-core diameter of up to 10 A from sidechain contributions to drag suggests a very porous cylinder (57) A. Allerhand and E. Oldfield, Biochemistry, 12, 3428 (1973).
5443
as the proper hydrodynamic model. A description of porous sphere hydrodynamics has been given.58 The small thickness of the porous zone and the possibility of specific solvent-side chain interaction appears to preclude meaningful modeling by a similar approach to our rods of illdefined cross section. Acknowledgment. This work was supported by the National Institutes of Health, and the Department of Energy. Registry No. Poly(y-benzyl glutamate) (homopolymer), 25014-27-1; poly(y-benzyl glutamate) (SRU),25036-48-0; 2,2,6,6-tetramethyl-4-aminopiperidinyl-l-oxy, 14691-88-4. (58) P. F. Mijnlieff and F. W. Wiegel, J. Polym. Sci., Polym. Phys. Ed., 16, 245 (1978).
Strengthening of Hydrophobic Bonding and the Increase in the Degree of Ionization of Sodium Lauryl Sulfate Micelles by Amphlphlles and the Micelle-Water Distribution Coefficient Mohammad Abu-Hamdlyyah' and Chrlstlane M. El-Danab
,
Chemistry Department, Kuwalt Unlversl~,Kuwait (Received: August 13, 1982; I n Final Form: May 10, 1983)
The effect of the amphiphiles ethylene glycol, propane-l,3-diol, butane-l,4-diol, hexane-2,5-dio17hexane-1,6-diol, decane-1,lO-diol,ethylene glycol monomethyl ether, allylthiourea, butyramide, n-butylurea, propylene oxide, propylene carbonate, 6-valerolactam,6-caprolactam, phenol, benzyl alcohol, 2-phenylethanol,3-phenylpropanol, and 4-ethylphenol, as well as of benzene, cyclohexane, and n-hexane on the critical micelle concentration (cmc) and the micellar degree of ionization ( a ) of sodium lauryl sulfate (NaLS) in aqueous solutions at 25 O C , has been determined experimentally by the conductance method. The results show that for the amphiphiles that decrease the cmc the initial rate of decrease with additive concentration (d(CmC)/dC,dd}Cadd+is linearly related to the corresponding initial increase of the slope of the conductance-concentration curve above the cmc, (bS2/dCadd}C,dd4, and that, when mole fraction concentrationsare used, the results approximate to (-d In xf/dyf),+ = (d In S2/dyfIYfl = (d In a/dyfIYfl where xf and yf are the mole fractions of free surfactant ions and free amphiphiles in aqueous solution, respectively. We also derived the equation (-d In xf/dyf)v+ = -2(d In a/dyfIYd + 2K relating the effects of the amphiphillic additive on the cmc and on a with the distribution coefficient of the additive between the aqueous phase and the micelles ( K ) . For the nonpolar additives benzene, cyclohexane, and n-hexane, which decreased the cmc but did not significantly affect S2,the general equation reduces to (-d In xf/dyf)y+, = 2K. For the amphiphilic additives used in this investigation except for the ethylene glycol, which did not effect the cmc nor S2,the data lead to the relation (-d In xf/dyf}y+,= 2/3K= 8K. These relations allow the estimation of K and the standard free energy of coaggregation of an additive with an ionic surfactant. For example, we obtain -2.5, -4.3, and -5.5 kcal mol-l for the standard free energy of coaggregation of benzene, cyclohexane, and n-hexane, respectively, and -0.35 and -0.59 kcal for the standard free energy of coaggregation per mole of methylene groups in the phenol and alkanediol homologues, respectively. According to our analysis fl = 2 - 2(d In oc/dym)y,-.owhere ymis the mole fraction of the additive in the micelle. Introduction It is now well established that amphiphilic additives at low concentrations strengthen hydrophobic bonding tendency in aqueous surfactant The ability of an additive to strengthen hydrophobic bonding in the surfactant solution depends among other things on the size and nature of the nonpolar moiety of the additive. Two indices have been used to measure and compare this (1) Shinoda, K. J. Phys. Chem. 1954,58, 1136. (2) Shirahama, K.; Kashiwabara, T. J. Colloid Interface Sci. 1971,36, 65. (3) Manabe, M.; Koda, M. Bull. Chem. SOC.Jpn. 1979,51, 1599. (4) Abu-Hamdiyyah, M.; Al-Mansour, L. J . Phys. Chem. 1979, 83, 2236.
0022-3654/83/2087-5443$0 1.5010
strengthening of hydrophobic bonding: (a) the initial rate of decrease of the cmc with additive c~ncentrationl-~ (d(cmc)/dcadd]Cad,,+-, and (b) the distribution coefficient of the additive between the bulk aqueous solution and the m i ~ e l l e , K. ~ - ~It was recently suggested4 that the initial rate of increase of the slope of the specific conductanceconcentration curve above the cmc with additive concentration {dS2/dCadd)cdd+may also be useful as an index for (5) Dougherty, S. J.; Berg, J. C. J. Colloid Interface Sci. 1974,48,110. (6) Goto, A.; Endo, F. J. Colloid Interface Sci. 1978, 66, 26. (7) Hayase, M.; Hayano, S. Bull. Chem. SOC.Jpn. 1977, 50, 83. (8) Hayase, K.; Hayano, S. J. Colloid Interface Sci. 1978, 63, 446. (9) Goto, A.; Nihei, M.; Endo, F. J. Phys. Chem. 1980, 81, 2268. (10) Mukerjee, P.; Mysels, K. J.; Kapauan, P. J. Phys. Chem. 1976, 71, 4166.
0 1983 American Chemical Society
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The Journal of Physical Chemlstry, Vol. 87, No. 26, 1983
comparing the ability of an amphiphilic additive to strengthen hydrophobic bonding in ionic surfactant solutions. An empirical relation between the first two indices was recently reported by Hayase and Hayano8 for alkanols in NaLS-H20 systems (-d In xf/dyf)y4 = OK, with 0 being independent of the number of carbon atoms in the alcohol molecule and equal to 0.82. They called -0 the interaction of surfactant and additive coefficient. Manabe at al.ll confirmed the validity of the above empirical relation obtaining 0 equal to 0.69. They analyzed in detail the various factors involved (0, K , and cmc, the degree of ionization of the micelle, the surface charge density, and the electrical potential on the surface of the micelle) arriving at a physical meaning of 0, namely, 0 = (1 + a ) / & where a is the degree of ionization of the micelle and q5f (g2) the osmotic coefficient of the ionic surfactant below the cmc. In this study we present the results on the effect of a number of amphiphilic additives and of benzene, cyclohexane, and n-hexane on the cmc of NaLS at 25 "C as well as on S2, the slope of the specific conductance-concentration curve above the cmc (which is directly related to the degree of ionization of the micellelO a). It will be shown that a simple quantitative relationship exists between the ability of an amphiphilic additive to lower the cmc and ita ability to increase Sz. We shall also extend the analysis of Manabe et a1.l1 and derive an equation relating the ability of an amphiphilic additive to decrease the cmc of an ionic surfactant and to increase a, the degree of micelle ionization, with K , the distribution coefficient of the additive between the aqueous solution and the micelle. This is then used with the experimentally obtained relationship between the effects of the amphiphilicadditives on the cmc and on a of NaLS to obtain the empirical equation relating the cmc depression with K , with 0 = 0.67, a relationship which allows the estimation of K and thence the standard free energy of coaggreation directly from the measurements of the initial depression of the cmc or the corresponding increase in S2(a)with additive concentration. Our analysis leads also to a physical meaning of 0 related to the rate of change of degree of ionization of the micelle with additive concentration.
Experimental Section Chemicals. Butyramide (BA) (pure) and propylene carbonate (PC) (puriss) were from Koch and Light; hexane-1,6-diol (1,6-HD),benzene, and phenol were laboratory reagents from British Drug House; allylthiourea (ATU) (purum), propylene oxide (PO) (puriss), propane-1,3-diol @-1,3-D) (purum), hexane-2,5-diol (2,5-HD) (purum), decane-1,lO-diol (1,lO-DD)(purum), benzyl alcohol (puriss), 2-phenylethanol (purum), 3-phenylpropanol (purum), valerolactam (purum), and 6-caprolactam (purum) were from Fluka; butane-1,4-diol (B-1,4-D) and cyclohexane (99.5%) were from Riedel de Haen; and ethylene glycol (pro analysis) and n-hexane (pro analysis) were from Merck. All compounds were used as received without further purification. 4-Ethylphenol (purum) was recrystallized twice from chloroform and dried under vacuum. Sodium lauryl sulfate and n-butylurea (BU) were described in a previous paper? Water was distilled from an all-glass apparatus (Corning megapure). Apparatus and Procedure. We have used the same apparatus and procedure described previously4 for the measurement of the electrical conductance of the various (11)Manabe, M.; Koda, M.; Shirahama, K. J. Colloid Interface Sci. 1980, 77, 189.
Abu-Hamdiyyah and El-Danab
0 EG
0
6
I
I
01
I
1
0.2 0 3 Additive Concentrotion ( M )
Figure 1. Effect of alkanediols on the cmc of NaLS at 25
0 4
OC.
li \ 0 6 L
0
5
I
I
I
I
01
0 2
0.3
04
Additive Concentration ( M I
Figure 2. Effect of ethylene glycol monomethyl ether, propylene oxide, propylene carbonate, butyramide, allylthiourea, 6-valeroiactam, and butylurea on the cmc of NaLS at 25 O C .
solutions. The solutions which were made up volumetrically were injected into the cell which was completely immersed in a covered water bath kept at 25 f 0.01 "C.
Results and Discussion The cmc value for each NaLS solution was determined from the intersection of the two straight lines obtained on plotting specific conductance against concentration of NaLS. The cmc of NaLS in the absence of the additive was checked periodically during the investigation and was found to fall in the range (8.30 f 0.05) X M in good agreement with the literature.12 SZ0and Sl0,the slopes above the below the cmc in the absence of the additive, were around 0.0241 f 0.0003 and 0.064 0.002 0-1cm-l mol-l, respectively. The variations of the cmc and of S2with additive concentration are linear in the low concentration range. The coefficients of these lines as well as their standard deviations and the correlation coefficients are given in Table I. These relations are illustrated in Figures 1-5. Figure 1 shows that the initial rate of decrease of the cmc with additive concentration for the alkanediols is practically zero for ethylene glycol and this rate increases as the number of methylene groups increases. The results show that hexane-2,5-diol is less effective than hexane1,6-diol in decreasing the cmc. This is in line with the expectation that the hydroxyl groups would be in the aqueous phase and the methylene groups directed toward the center of the micelle. Moving the hydoxyl groups from 1,6 to 2,5 positions is equivalent to shortening of the length of the hydrocarbon portion maneuverable toward the in-
*
(12) Mukerjee, P.; Mysels, K. J. Natl. Stand. Ref. Data Ser. (US'., Natl. Bur. Stand.) 1971, No. 36.
The Journal of Physical Chemistry, Vol. 87,No. 26, 1983 5445
Strengthening of Hydrophobic Bonding
t .I E
Benzyl Alcohol
I
I
1
Addilivs
I
0 01
1 0.02
I
I
0 03
Additive Concentration
0.04
(M)
I
0 02
0 01
Elbonol
I
I
a04
0 03
0 05
Concentration I M I
Figure 5. Effect of benzene and of phenol homologues on the value of the slope of the specific conductance curve above the cmc of NaLS at 25 O C .
Figure 3. Effect of benzene and of phenol homologues on the cmc of NaLS at 25 OC.
/
3'00/ .40
?
4
0
'v V
-2.20
V r\
A
-10.00 01
1
I
0 2
03
Additive
Concentrotion
1 Q 4
-5.33
-0.70
. e3
-2.33
400
It41
Figure 4. Effect of alkanedlols and of ethylene glycol monomethyl ether on the value of the slope of specific conductance curve above the cmc of NaLS at 25 OC.
terior of the micelle. It is also seen in Figure 2 that the ability to decrease the cmc is greater in propylene carbonate than that in propylene oxide. This is probably due to the larger strain in the ring in PO than in PC, making the latter more hydrophobic. It is also observed that 6valerolactam has a slightly weaker effect than n-butylurea, despite the larger hydrophilic group in the latter indicating that the effective hydrophobic size in 6-valerolactam is smaller than in n-butylurea. Figure 3 summarizes the results of benzene, phenol, benzyl alcohol 2-phenylethanol, 3-phenylpropanol, and 4-ethylphenol. The ability to decrease the cmc increases as the number of methylene groups between the hydroxyl group and the benzene ring increases. The cmc-lowering ability of 4-ethylphenol is greater than that of 3-phenylpropanol, indicating that an ethyl group in the para position to OH on the benzene ring is more hydrophobic than three methylene groups positioned between the benzene ring and the hydroxyl group. Moreover, the presence of OH in the benzene ring enhances the hydrophobic effect. The results for benzene, cyclohexane, and n-hexane show that the ability to strengthen hydrophobic bonding increases in going from benzene to cyclohexaneto n-hexane in agreement with the trend obtained by Rehfeld13 using surface tension measurements. However, our values for (-d(CmC)/dC,dd)c, -, are consistently lower than those obtained from Rexfeld's data. Figures 4 and 5 show the variation of S2 with additive (13) Rehfeld, S. J. J.Phys. Chern. 1967, 71, 745. (14) Kaneshina, S.;Kamaya, H.; Ueda, I. J. Colloid Interface Sci. 1981, 83, 589.
(
In
dS dC:dd
Figure 6. Ability of an amphiphilic additive to depress the cmc of NaLS at 25 OC vs. the corresponding ability to increase the slope of the specific conductance curve above the cmc.
-51
I
I
I
I
I
I
0
I
2
3
4
5
n in C , H , ( C H , ) ,
-OH
Figure 7. Strengthening of hydrophobic bonding ability in NaLS vs. the number of methylene groups in the phenol homologue.
concentration. A few lines are not shown in the graphs for clarity. The experimental points for propane-1,3-diol show some scatter. It is clear from these figures that the ability of an amphiphile to decrease the cmc is also reflected in its ability to increase S2,the slope above the cmc. Ethylene glycol, which in this concentration range did not depress the cmc, did not raise S2either. Benzene, cyclohexane, and n-hexane, which decreased the cmc, showed no corresponding increase in S2. This suggests that
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The Journal of Physical Chemlstry, Vol. 87, No. 26, 1983
Abu-Hamdiyyah and El-Danab
TABLE I: Coefficients of the Lines Cmc = a - bC,dd and s, = (I' + b'Cadd Obtained for the Variation of the Cmc of NaLS and of S,, the Slope of the Conductance Line above the Cmc, with Additive Concentration, Respectively, in the Low Concentration Range at 25 "C additive a1103 -b/102 r a'/103 b'/102 r
(1)propane-1,3-diol ( 2 ) bu&e-1,4-diol ( 3 ) hexane-2,5-diol ( 4 ) hexane-1,6-diol ( 5 ) decane-1,lO-diol ( 6 ) ethylene glycol monomethyl ether ( 7 ) propylene oxide (8) propylene carbonate (9) allylthiourea (10) butyramide (11)s -valerolactam (12) n-butylurea (13) caprolactam (14) phenol (15) benzyl alcohol (16) 2-phenylethanol (17) 3-phenylpropanol (18) 4-ethylphenol (19) benzene (20) ethylene glycol (21) cyclohexane (22) n-hexane
8.26 2 8.29 f 8.21 f 8.26 f
0.03 0.02 0.01 0.06
8.26
0.01
f
0.08 f 0.21 1.26 f 2.01 f 86.6 0.18 f
0.03 0.04 0.23 0.24
0.864 0.962 0.939 0.979
23.9 24.2 24.1 24.3
rt
f
0.5 0.01 0.4 0.4
0.04
0.963
23.8
f
0.9
0.999 0.999 0.991 0.97 0.98 0.99 0.99 0.998 0.999 0.996 0.999 0.93 0.92
23.8 f 23.9 f 24.5 f 24.0 f 24.5 f 24.2 f 24.8 f 24.1 f 24.3 f 24.6 f 24.1 f 24.2 f
0.33 f 0.01 0.50 f 0.004 0.96 f 0.06 0.85 f 0.05 2.4 f 0.3 2.8 f 0.2 2.7 f 0.1 4.5 f 0.2 5.4 f 0.2 8.3 f 0.4 17.5 f 0.6 23.2 f 4.6 3.2 f 0.1 0 38.9 f 9.7 300
8.31 f 0.01 8.31 f 0.01 8.26 f 0.03 8.28 f 0.02 8.27 f 0.03 8.2 f 0.1 8.17 f 0.05 8.28 f 0.02 8.25 f 0.03 8.27 f 0.07 8.27 f 0.03 8.2 f 0.2 8.0 f 0.1
8.00 f 0.03
f
f
0.3 0.05 0.2 0.1 0.4 0.7 0.5 0.1 0.3 0.8 0.1 0.1
0.2 f 0.9 1.31 f 0.02 6.46 f 0.86 10.91 f 1.45 24 0 0.8 f 0.1
0.17 0.999 0.966 0.974
1.7 i 0.1 2.91 f 0.03 4.71 f 0.34 4.12 f 0.03 9.2 f 1.8 12.7 f 1.7 12.0 f 3.2 14.6 f 0.9 16.6 f 2.1 21.5 f 4.6 59.9 f 1.6 67.4 f 3.3 0 0
0.993 0.999 0.990 0.999 0.94 0.98 0.91 0.996 0.984 0.94 0.999 0.996
0.98
0 0
0.94
We shall assume that all the amphiphiles fall on the same line which has a slope of unity and any deviation from unity is due to experimental error. Thus, we have for all the additives the empirical relation In (-d(cmc)/dCaddJcadd+ = In (dS2/dCadd)cadd4 - 1.20 f 0.11 (1)
O t
Since the slope above the cmc, Sz, is given bylo S2 = dK/dC = CX(AN~++ FULS-)X
-I
ov
1
2
I
4
n in O H - ( C H z ) ,
I
1
e
6
1
IO
-OH
Flgure 8. Strengthening of hydrophobic bonding ability in NaLS vs. the number of methylene groups in alkanedlol.
benzene, cyclohexane,and n-hexane, which are nonpolar, are accommodated in the micelle on coaggregation such that the surface charge density of the micelle is not significantly affected. Such a site is likely to be in the interior of the micelle. Strengthening of Hydrophobic Bonding and the Increase in Sz. We have plotted the ability of an additive to decrease the cmc against its ability to increase S2 in Figure 6. The figure shows a linear relationship between In (-d(cmc)/dCaddJCa d4 and In (dS,/dC,,Jc,,, with the slope, intercept, and correlation coefficient 1.06 f 0.04, -1.20 f 0.11, and 0.991, respectively. The numbers of Figure 6 correspond to the serial numbers in Table I. Considering each family of the additives alone we obtain for the diols 1.01 f 0.09, -1.37 f 0.34, and 0.988 for the slope, intercept, and correlation coefficient, respectively. The corresponding quantities for phenol, benzyl alcohol, 2-phenylethanol,3-phenylpropanol,and 4-ethylphenol are 0.97 f 0.04, -1.14 f 0.12, and 0.988. For the rest of the additives we obtain 1.05 f 0.04, -1.30 f 0.13, and 0.996, respectively.
(2) where K is the specific conductance, C the concentration of NaLS, a the degree of ionization of the micelle, F the Faraday, ANa+the equivalent conductance of sodium ions, and ULs-the micellar mobility, and since under the conditions we are interested in, i.e., those of infinite dilution of the additive, ANa+and ULs-can be taken as constant at constant temperature and not significantly different from their values in the absence of the additive, we then have Id In Sz/dCaddhadd+ = id
a/dCaddk!,dd+
(3)
with
id
In sddcadd}cadd+ = (1/S20)(dSz/dCadd)c,dd+ (d In
a/dCadd]Cadd+
= (l/cro)(dCX/dcadd)Csdd4
S20 and aoare the slope above the cmc and the degree of ionization of the micelle, respectively, in the absence of the additive. Assuming that1J3the free-additive concentration in the aqueous phase (water) at the cmc is approximately equal to (?add, the total-additive concentration, which is reasonable in view of the fact that the micellar concentration is very small at the cmc, and converting t o molar fraction concentrations using yf = c,dd/55.4 and xp = (cmcIo/55.4 we get
In (dS2/dCadd)cadd+= 1x1 (d In s2/d~fJ,po - 7.742
(4)
= In (-d In xf/dyfIyrcO- 8.808 In (-d(cmc)/dCadd)Cadd+ (5)
which on substitution into eq 1 leads to In (-d In xf/dyfJYrcO = In (d In S2/dyfly+, - 0.13 f 0.13 (6a)
Strengthening of Hydrophobic Bonding
In (-d In xf/dyf}y4 = In (d In a/dyf)y4 - 0.13 f 0.13 (6b) in view of eq 3. We consider the intercept in this particular case to be zero. Thus, when the concentrations are in mole fractions, our results indicate that the initial relative lowering of the cmc with additive concentration is equal to the corresponding relative increase in the degree of ionization of the micelle. Relationship between the Effect of an Amphiphilic Additive on the Cmc and on CY and the Distribution Coefficient, K. Recently2p8J1the empirical linear relationship (eq 7) was found between the distribution coef(7) (-d In xf/dyfJyd = OK ficient of an alkanol and its ability to depress the cmc of NaLS. with 0 being a constant for the homologous alkanols falling between 0.6 and 0.8 and the two variables in eq 7 being independently determined. Since an amphiphilic additive on coaggregation with surfactant ions decreases the cmc and simultaneously increases a , it is not unreasonable to seek a relationship between these two effects and the distribution coefficient of the amphiphile between the aqueous solution (water) and the micelle. This may be obtained by finding the effect of the additive on the electric potential J/ at the surface of the micelle. Putting FJ//RT= \k where F is the Faraday, R the gas constant, and T the temperature and following Manabe et ala1'we have at constant temperature at infinite dilution of the additive \I! = In u2 - In xf + constant (8) with xf being equal to the cmc (no salt added) and u the surface charge density. Differentiating eq 8 with respect to yf and using1' u = (uo/ao)ax,, ax,, K = dy,/dyf, and In (1- y,) = -ym for small y,, we get d\k/dyf = 2(d In a/dyf) - 2K - 2 d In xf/dyf (9) where 0 designates the value in the absence of the additive and x, and y, are the mole fractions of surfactant and additive in the micelle, respectively. As the amphiphile coaggregates with the surfactant ions, the surface charge density of the micelle is reduced; this is accompanied by counterion release from the micellar surface which compensates for the decrease in the surface charge density, thus maintaining the surface electrical potential rather constant.ll Putting d\k/dyf = 0 in eq 9 leads to the general equation (d In xf/dYf)ypo= 2{d In a/dyflyd - 2K (10) which relates the ability of the additive to decrease the cmc and its ability to increase the degree of ionization of the micelle with its distribution coefficient K between water and the micelle. This relation is general and should be applicable to additives that strengthen hydrophobic bonding in ionic surfactant solutions under the specified conditions. Once an empirical relationship is found between the first two terms in eq 10, then K can be determined. For the additives in this study we have the relation 6b, which on substitution into eq 10 leads to (11) (-d In Xf/dYfIyd = %K with 0 = 0.67 which is not much different from that obtained for alkanols in NaLS.ll This provides a new method for the estimation of K and the standard free energy of coaggregation of the amphiphilic additive in aqueous NaLS solutions at 25 "C, -AGOcoag = RT In K. In Table I1 we compare standard free energies of coaggregation of some amphiphiles in NaLS which were determined experimen-
The Journal of Physical Chemistry, Vol. 87,
No. 26, 1983 5447
TABLE 11: Standard Free Energy of Coaggregation of Amphiphiles with NaLS at 25 OC in Aqueous Solutions Calculated According to Eq 11 Compared with the Experimentally Determined Values Taken from the Literature aGocoag/( kcal mol-')
additive 1-butanol
eq 11(cmc data ref)
methylparaben ethylparaben
3.36 3.33 3.24 3.94 3.91 4.53 4.65 5.08 5.19 4.52 5.22
butylparaben
5.16 ( 6 ) 6.37 ( 6 )
1-pentanol 1-hexanol 1-heptanol
exptl (ref)
(2) (3) (7) (3) (7) (3)
3.38 (7) 3.90 (7) 4.57 (,7 ,)
(7j (3) (7)
5.16 ( 7 )
(6)
4.82 (6) 5.39 (6)
(this laboratory)
5.39 ( 6 ) 6.67 ( 6 )
tally and taken from the literature with the calculated values usng eq 11. Depending on the cmc data used the agreement is satisfactory. Equation 10 reduces to {-d In xf/dyf)y4 = 2K when a is not affected by the additive's coaggregation. This is expected to be the case of nonpolar additives which tend to be located in the interior of the micelle. We have measured the effect of benzene, cyclohexane, and n-hexane on the cmc of NaLS and their corresponding effect on Sz. The cmc was depressed in each case but no significant change in Szwas observed. Our results for benzene give, using the above relation, K = 104 f 34 compared with the range 65-85 quoted by Mukerjee and Cardinal.15 This implies that either benzene is coaggregated predominantly in the interior of the micelle which is assumed not to affect a , the degree of ionization, or, if a significant fraction is adsorbed near the micellar surface, then a does not seem to be affected by the adsorption process. The results for cyclohexane and n-hexane give AGOcoag = -4.3 f 0.1 and -5.45 kcal mol-l, respectively. The data obtained by Rehfeld13 by surface tension measurements on the effect of cyclohexane and of n-hexane on the cmc of NaLS yield -4.72 and -5.65 kcal mol-l, respectively, for AGOcoag,using eq 11 with 0 = 2. Standard Free Energy of Coaggreation of Methylene Groups in the Diols and the Phenol Homologues. We have plotted In {-d(cmc)/dCadd)ca,d, against the number of methylene groups in these two series of compounds and a linear relation is obtained in each case. For the phenol homologues we obtain In (-d In xf/dyfJy4 = (0.59 f 0.09)n 5.26 f 0.22 (12) r = 0.987
+
In {-d In xf/dyfJy4 = (1.00 f 0.03)n - 1.29 f 0.22 (13) r = 0.999 for the diols. Assuming the separability of AGOcoagto nAGo(CHz)coag and AG0(remainder),,,,, the slope of eq 12 or 13 is given by
(15) Mukerjee, P.; Cardinal, J.
R.J.Phys. Chem. 1978, 82,
1620.
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The Journal of Physical Chemistty, Vol. 87,
No. 26, 1983
+
the intercept is equal to -AGo(reminder)co,,/RT In 8. The standard free energy of coaggregation per mole of methylene groups in the phenol homologues is -0.35 kcal. In the case of the diols it is -0.59 kcal compared with -0.59 kcal mol-l obtained by Manabe and Koda3for homologous diols, ethers, and alkanols in NaLS systems at 25 "C and -0.60 kcal obtained for alkanols by Hayase and Hayano.' The difference in AGo(CH2)coag values in the diols and phenol homologues, if real, suggests a difference in the environments of the methylene groups in each of these series on coaggregation. This may be related to the tendancy of the benzene ring to be located near the micellar surface as suggested by Mukerjee and Cardinal.15 However, we withhold further discussion of the implications of this awaiting further studies to include other surfactant systems. The intercept for the phenol homologues is 5.26, indicating that the major contribution to AGOcoag is due to the C6H5 OH portion. In the case of the diols the intercept is -1.29, giving a positive free energy change of 0.53 kcal for the OH groups on coaggregation. Physical Meaning of 8. Hayase and Hayanos called -8 the interaction of surfactant and additive coefficient. Manabe et al.ll discussed its significance extensively and concluded that "it is possible that the quantities K and d In xf/dyf or 8 obtained in presence of organic additives give the degree of ionization of "pure" ionic micelles." According to our analysis substituting eq 7 in eq 10 leads to the general equation 8 = 2 - 2(d In a/dym)ym+ (15) when (d In a/dy,)y,+ = 0 , 8 = 2, and 8 = 0 when (d In a/dym)ym-o= 1. The first case is applicable for the case of nonpolar additives which are expected to be located in the interior of the micelle and, in the limit as ym 0, CY would not be significantly affected. In the second case, daldy, = a0meaning the additive has no effect on the cmc, i.e., xf = xP. When daldy, = 4 2 , we get 8 = 1and the initial relative lowering of the cmc with additive concentration is equal to the distribution coefficient K. This is the condition Manabe et a1.l1 likened to Raoalt's law ideality: with 8 > 1 the additive shows negative and with 8 C 1positive deviation from ideality. According to our data, however, we have the empirical relation (-d In xf/ dyf)yd = (d In a/dydyfl from eq 6b, which on equating with OK from eq 7 gives OK = (d In a/dyfJyfl
+
-
and since K = dy,/dyf 8 = (d In ru/dy,)ym+ = 0.67 Thus, according to our data 8 is equal to the initial relative lowering of CY with additive concentration in the micelle. This means that all these amphiphilic additives have approximately the same effect on the micellar degree of ionization (and hance the micellar surface charge density) at the same mole fraction ymof the additive in the micelle
Abu-Hamdlyyah and El-Danab
regardless of the differences in the lengths or shapes of the hydrophobic moieties or the kind of polar group in the amphiphile. This nonspecificity is probably a reflection of the rough and irregular micellar surface.
Summary and Conclusion We have investigated the effect of 19 amphiphilic additives and of benzene, cyclohexane, and n-hexane on the cmc of NaLS and on the slope of the specific conductance-concentration curve above the cmc (which is proportional to the degree of ionization of NaLS micelles) and found that the ability of the amphiphilic additive to strengthen hydrophobic bonding is linearly related to the additive's ability to increase the slope above the cmc (and hence the degree of micelle ionization). When molar fraction concentrations are used, our results produce the following empirical relation: the initial relative lowering of the cmc with additive concentration equals the corresponding initial relative increase in CY (or SJ. The fact that all these amphiphiles fall on the same line although they have aliphatic, aromatic, and cyclic hydrophobic moieties attached to polar heads (aliphatic and aromatic OH, NHCONH2, NHCSNH2, CONH2, CONH, an epoxide, and a carbonato group) under various constraints is indicative of the predominance of the nonspecific nature of the hydrophobic effect as reflected in the ability of the amphiphile to coaggregate with an ionic surfactant and the concomitant diluting of the micellar charge density. We also derived a general equation relating the ability of an additive to depress the cmc of an ionic surfactant and its ability to increase CY with the distribution coefficient of the amphiphilic additive between water (aqueous solution) and the micelle. We then substituted the empirical relation into the general equation and obtained (-d In xf/dyfjyd = OK with 8 = 0.67, an expression which was previously obtained in the literautre for alkanol-NaLS-H20 systems with 8 = 0.69. We thus obtained a simple method for the estimation of the standard free energy of coaggregation of an amphiphilic additive with an ionic surfactant. For nonpolar additives a modified formula is suggested for the calculation of K from cmc data. Finally, a new physical meaning of the constant 8 has been arrived at. Acknowledgment. We thank the Research Council of the University of Kuwait for their support of this work. Registry No. NaLS, 151-21-3; ethylene glycol, 107-21-1; propane-1,3-diol, 504-63-2; butane-1,4-diol, 110-63-4; hexane2,5-diol, 2935-44-6; hexane-1,6-diol, 629-11-8; decane-1,lO-diol, 112-47-0;ethylene glycol monoethyl ether, 109-86-4;allylthiourea, 109-57-9;butyramide, 541-35-5;n-butylurea, 592-31-4; propylene oxide, 75-56-9; propylene carbonate, 108-32-7; 6-valerolactam, 675-20-7;6-caprolactam, 105-60-2;phenol, 108-95-2;benzyl alcohol, 100-51-6; 2-phenylethanol, 60-12-8; 3-phenylpropanol, 122-97-4; 4-ethylphenol, 123-07-9;benzene, 71-43-2; cyclohexane, 110-82-7; n-hexane, 110-54-3.
