Partitioning of amphiphilic additives between the micelles of n

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2518

J . Phys. Chem. 1990,94, 2518-2523

those of S-OH. The transfer characteristics of the up stroke therefore are expected to be somewhat different. The results of the interfacial forces, the transfer properties observed for SA(Cd) monolayers, are shown in Figure 9. The pressure dependencies of the forces during both the up- and down-stroke processes were almost similar to those obtained for S-OH. It was also found that the transfer properties were well elucidated by the dynamic forces. The relationships between the dynamic interfacial forces and the transfer characteristics established in this study were obtained for almost all of the aliphatic molecules that could be transferred uniformly from aqueous subphase onto solid substrates. Therefore it can be concluded that the transfer mechanism of the LB films for both up- and down-stroke processes is rather qualitatively elucidated by the dynamic interfacial force. On the basis of the thermodynamic arguments described in this study, the process having the minimum energy variation prevails against other possible processes. In this study, we have carried out the experiments of the first-layer deposition onto the various hydrophobic substrates. Although the multilayer deposition is done using amphiphilic molecules having various polar and nonpolar groups, the transfer characteristics can be quantitatively analyzed by measuring the dynamic interfacial forces during the processes.

4. Conclusion In this paper, we investigated the mechanism of LB film transfer from the water surface onto the substrate, experimentally. By varying the surface pressure of the monolayer film ( x ) and the hydrophilic/hydrophobic property contact angle (8,) of the substrate, the transfer ratio ( p ) was measured. It was found that transfer ratio ( p ) changes discretely between 0 and 1 at a critical point of x and 8,. To analyze this transition characteristics of film transfer in more detail, the interfacial force Cr, applied to the substrate was observed during the deposition process. It was found that the value off was almost unchanged with varying a for the case where the film was not transferred onto the substrate. On the other hand, for the case where the film was entirely transferred onto the substrate, the value off linearly increases with x for the up-stroke process of hydrophilic substrate and linearly decreases with a for the down-stroke process of the hydrophobic substrate. These results were thermodynamically analyzed by taking into account the energy variation accompanied with a vertical displacement of the substrate. It is confirmed that the characteristics of LB film transfer are consistent with the thermodynamical principle that the process advances toward a direction of smaller energy variation.

Partltloning of Amphiphilic Additives between the Micelles of n-Alkyltrimethylammonium Bromides and the Surrounding Aqueous Solution as a Function of Surfactant Chain Length Mohammed Abu-Hamdiyyah* and Kamlesb Kumari Chemistry Department, University of Kuwait, 13060 Safat, Kuwait (Received: December 13, 1988; In Final Form: August 2, 1989)

The partitioning of 1-propanol, 2-propano1, 1-butanol, 2-butanol,2-methyl-2-propanol, 1-butylurea,tert-butylurea, cyclohexanol, 6-caprolactam, 1-hexanol, 1-octanol,and 1-decanol between the micelles of dodecyl- (C12),tetradecyl- (C14),and hexadecyl(C16)trimethylammonium bromides and the surrounding aqueous phase has been determined at 25 "C. It is found that the ability to depress the critical micelle concentration, the corresponding ability to increase the micellar degree of ionization, and the coaggregation (solubilization) tendency all tend to decrease with increasing surfactant chain length. This is in accord with the results obtained previously for the partitioning of a large number of various amphiphilic additives between the micelles of sodium alkyl sulfates and water. The results are analyzed in terms of the factors contributing to the standard free energy of coaggregation, and the general trend observed is interpreted as due to the tendency of the amphiphilic additive to be coaggregated in the outer rough region of the micelle in contact with water composed of the ionic heads plus portions of the hydrocarbon chains and whose extent decreases with increasing surfactant chain length. Finally, comparative published data on the partitioning of amphiphilic additives in n-alkyltrimethylammoniumbromides have also been discussed.

Introduction

The study of the partitioning of amphiphilic and nonpolar additives in aqueous surfactant solutions as a function of surfactant chain length is of intrinsic interest physiochemically as it throws light on the factors governing the coaggregation (solubilizaton) process. It is also of widespread practical interest, e.g., in tertiary oil recovery, detergency, micellar catalysis, chromatographic separations, and in biomedical fields. This problem was recently treated theoretically.' It was predicted that if different solutes have the same alkane/water partition coefficient, the logarithm of the partition coefficient should depend inversely on the chain length of the surfactant for micelles with radii equal to the length of the surfactant chain. Thus it is also important to have experimental data available for testing theoretical models. Until recently no systematic study of ( 1 ) Marquesee, J. A.; Dill, K. A. J . Chem. Phys. 1986, 85, 434.

0022-3654/90/2094-25 1 S$OZ.SO/O

the partition coefficient of an amphiphilic additive as a function of surfactant chain length was available although many studies on the determination of the partition coefficient have been publ i ~ h e d . * - ~We ~ have developed16 in this laboratory an equation (2) Dougherty, S.; Berg, J. J. Colloid Interface Sci. 1974, 48, 110. (3) Manabe, M.; Shirahama, K.; Koda, M. Bull. Chem. Soc. Jpn. 1976, 49, 2904. (4) Hayase, K.; Hayano, S. Bull. Chem. SOC.Jpn. 1977, 50, 83. (5) Gettins, J.; Hall, D.; Jobling, P. L.; Rassing, J. E.; Wyne-Jones, E. J . Chem. Soc., Faraday Trans. 2 1978, 74, 1957. (6) Mukerjee, P.; Cardinal, J. R. J. Phys. Chem.1978, 82, 1260. (7) Goto, A.; Endo, F. J. Phys. Chem. 1980, 84, 2268. (8) Lissi, E.; Abuin, E. B.; Roche, A. M. J . Phys. Chem. 1980,84, 2406. (9) Hirose, C.; Sepulveda, L. J . Phys. Chem. 1981, 85, 3689. (10) Stilbs, P. J . Colloid Interface Sci. 1982, 87, 385. ( 1 1) Abuin, E. B.; Lissi, E. A. J . Colloid Interface Sci. 1983, 95, 198. (1 2) De Lisi, R.; Genova, C.; Liveri, V. T. J . Colloid Interface Sci. 1983, 95. 428.

0 1990 American Chemical Society

The Journal of Physical Chemistry, Vol. 94, No. 6,1990 2519

Partitioning of Amphiphilic Additives

TABLE I: Initial Slopes of the Lines cmc = B - bCd and S2 = a' + b'CadObtained by the Least-Squares Method for the Variation of the cmc's of the Various Trimethylammonium Bromides Investigated and the Corresponding Slopes of the Conductanceconcentration Lines above the cmc with Additive Concentration in the Low-Concentration Range - at 25 "C c12

no.


1 2 3 4 5 6 7 8 9 IO 11 I2

additive 1-propanol 2-propanol 1-butanol 2-butanol 2-methyl-2-propamol butylurea tert-butylurea hexanol cyclohexanol 6-caprolactam octanol decanol

b 0.005 f 0.00

c16

c14

b'

0.016 f 0.0005 0.004 f 0.00006 0.0115 f 0.0001 0.024 f 0.0002 0.063 f 0.001 0.012 f 0.0005 0.027 f 0.0002 0.0074 f 0.0001 0.022 f 0.0001 0.067 f 0.000 0.125 f 0.009 0.064 f 0.001 0.028 f 0.0004 0.21 1 f 0.0031 0.48 f 0.024 0.068 f 0.0008 0.1314 f 0.0024 0.006 f 0.0001 0.048 f 0.002 0.89 f 0.02 4.235 f 0.089 7.58 f 0.199 37.33 & 1.08

b'

b

0.0012 f 0.00005 0.01 1 f 0.0003 0.0009 f 0.00002 0.008 f 0.0002 0.006 f 0.0002 0.051 f 0.0014 0.003 f 0.0005 0.021 f 0.0004 0.017 f 0.0005 0.002 f 0.0001 0.01 12 f 0.0004 0.082 f 0.004 0.0082 f 0.00009 0.0566 f 0.002 0.059 f 0.002 0.305 f 0.009 0.0162 f 0.0003 0.0976 f 0.002 0.0016 f 0.00015 0.027 f 0.0001 0.290 f 0.004 2.937 f 0.089 2.50 f 0.00 34.93 f 0.791

of state for the coaggregation process (in amphiphilic additiveionic surfactant system) involving the partition coefficient, the depression of the critical micelle concentration (cmc), and the interaction of the additive with the surfactant ions in the micelle as measured by the increase in the effective micellar degree of ionization (CY). This method facilitated obtaining the partition coefficients of amphiphiles as a function of surfactant chain length. Treiner, on the other hand, derived" an equation relating the partition coefficient to the depression of the cmc and a salting-out coefficient, Le., the interaction of the additive with the monomer surfactant ion in the aqueous phase. It was assumed, however, that the additive and the surfactant ion mix ideally in the micelle. Because of the last assumption Treiner's equation proved to be more suitable for nonpolar additives.I6Js We have already reported the behavior of the partition coefficients of amphiphilic'* and of nonpolar additives19as a function of surfactant chain length in the micelles of the anionic surfactants sodium alkyl sulfates. It was found that as the surfactant chain length increases, In K decreases for amphiphilic and increases for nonpolar additives. These results were rationalized in terms of a micelle structure composed roughly of two regions, an outer region containing the ionic heads plus portions of the hydrocarbon chains which are in contact with water and where amphiphilic additives tend to coaggregate and an inner hydrocarbon region not in contact with water where nonpolar additives tend to coaggregate such that the extent of the latter region increases at the expense of the former as the surfactant chain length increases. This trend in the variation of the extent of the hydrocarbon-water contact region with surfactant chain length18 is in accord with recent results obtained by very sophisticated techniques.20,21 Recently, however, the partition coefficient values of 1-pentanol in several n-alkyltrimethylammonium bromides were reported22 showing an increasing solubilization tendency with surfactant chain length. In the present study the solubilization tendency of several amphiphilic additives of various sizes and shapes together with the compensatory effects (the ability to depress the cmc and the corresponding ability to increase the micellar degree of ionization) are reported as a function of surfactant chain length in the micelles of the cationic surfactants of n-alkyltrimethylammonium bromides. It will be shown that the ability to depress the cmc, the ability to increase the micellar degree of ionization, and the solubilization tendency all decrease with increasing surfactant chain length as was found in the anionic surfactants, sodium alkyl sulfates. The (13) De Lisi, R.; Genova, C.; Testa, R.; Liveri, V. T. J . Solution Chem. 1984, 13, 121. (14) Heter, D.; Roux, A. H.; Perron, G.; Desnoyers, J. E. J . Solution Chem. 1987, 16, 529. (15) Armstrong, D. W.; Nome, F. Anal. Chem. 1981, 53, 1662. (16) Abu-Hamdivvah. M.; El-Danab, C. J . Phys. Chem. 1983.87.5443, (17) Treiner, C. j : Colloid Interface Sci. 1982, 90, 444. (18) Abu-Hamdiyyah, M.; Rahman, 1. A. J . Phys. Chem. 1985,89,2377. (19) Abu-Hamdiyyah, M.; Rahman, I. A. J . Phys. Chem. 1987,91, 1530. (20) Ghosh, S.; Petrin, M.; Maki, A. H. J . Phys. Chem. 1986, 90, 5206. (21) Ghosh, S.: Maki, A. H.; Petrin, M. J . Phys. Chem. 1986, 90, 5210.

b b' 0.0003 f 0.000 0.0102 f 0.0004 0.0002 f 0.00001 0.0067 f 0.0005 0.0016 f 0.00003 0.0430 f 0.0039 0.0008 f 0.00007 0.019 f 0.0004 0.016 f 0.0000 0.0005 f 0.00001 0.0025 f 0.00006 0.1029 f 0.0102 0.0018 f 0.0004 0.0430 f 0.0130 0.0143 f 0.00235 0.257 f 0.078 0.0034 f 0.00015 0.1 f 0.00 0.00044 f 0.00001 0.025 i 0.001 2.960 f 0.121 0.0746 f 0.00094 1.065 f 0.018 35.251 f 1.299

results will be analyzed in terms of the effect of increasing the surfactant chain length on the various factors contributing to the standard free energy of solubilization. We will also discuss the method used by De Lisi et for the estimation of the partition coefficient, compare it with that used in this study, and discuss the bearing of this on the reported results.

Experimental Section Chemicals. Tetradecyltrimethylammonium bromide from Fluka was used as received as no minimum in the surface tension-concentration plot was observed. Dodecyltrimethylammonium bromide from Sigma and hexadecyltrimethylammonium bromide from Fluka were recrystallized twice from acetone and dried in vacuo before use. 1-Butanol, 1-hexanol, 1-octanol, and 1-decanol were all 99% pure from Sigma. 2Methyl-2-propano1, proanalysis, from Merck, 6-caprolactam from Fluka, tert-butylurea from Eastman Kodak, and 1-propanol, 2-propano1, and cyclohexanol, laboratory reagents from British Drug Houses, were all used as received. Apparatus and Procedures. All solutions were made up volumetrically. The conductance measurements and the apparatus used have been described previously.16 Results and Discussion The critical micelle concentration values in the absence and in the presence of the additives were determined from the intersections of pairs of straight lines obtained by plotting solution specific conductance against surfactant concentration. The cmc values in the absence of the additives are 15.9, 3.7, and 0.94 mM in dodecyl-, tetradecyl-, and hexadecyltrimethylammonium bromides, respectively. These values are in very good agreement with the values reported in the l i t e r a t ~ r e . ~The ~ - ~slopes ~ of the conductance-concentration lines above (So2)and below (Sol) the cmc for CI2,CI4,and c16, respectively, are (0.0205, 0.0852), (0.0222, 0.0870), and (0.0242, 0.0920) Q-' cm-' L mol-'. The values of the cmc and of S2 as a function of additive concentration in the low concentration range are summarized in Table I in the form of the coefficients of the lines cmc = a - 6Cad and S2 = a ' b'cad. Figure 1 illustrates the trends for the variation of the ability to depress the cmc (In (-(d(cmc)/dCad)c,,+)) and the corresponding ability to increase S2 (In (dS2/dCa,Jc +), respectively, as a function of surfactant chain length for 1-aganols. The rates of change of the ability to depress the cmc with surfactant chain length for propanol, butanol, hexanol, octanol, and decanol are -0.70 (=t0.004), -0.68 (f0.01), -0.67 (*0.02), -0.62 (f0.004),

+

(22) De Lisi, R.; Milito, S.; Triolo, R. J . Solution Chem. 1988, 17, 673. (23) Oakenful, D. J . Colloid Interface Sci. 1982, 88, 562. (24) Zana, R. J . Colloid Interface Sci. 1980, 78, 330. (25) Zana, R.; Yiv, S . ; Strazille, C.; Liano, S. P. J . Colloid Interface Sci. 1981, 80, 208. (26) Mukerjee, P.; Mysels, K. J. M. "Critical Micelle Concentration of Aqueous Surfactant Systems"; US.Department of Commerce, NSRD-NBS 36, 1971.

Abu-Hamdiyyah and Kumari

2520 The Journal of Physical Chemistry, Vol. 94, No. 6, 1990

'1

't'It \\ \ \ I

- 1'' I

1-Decanol 1-Decanol

Q-

7

'(3

Io

'(3

U I

0 -0

U -0

\

U

r

U

-5

-

-10

-

-a I

-

c

C

+I


4 ;

\

-5t

,

12

4\!'l-Butanol

14

16

12

14

-1-2

16

-I a

-5

0

+5

n in C n H 2 " + , N ( C H , ) , B r Figure 1. Ability of 1-alkanolsto depress the cmc and increase S2as a function of surfactant chain length in n-alkyltrimethylammoniumbromides at 25 OC.

Figure 2. Compensatory effects in the coaggregation process in dodecyl-, tetradecyl-, and hexadecyltrimethylammonium bromides. The numbers designate the additives as in Table I.

and -0.49 (f0.035),respectively. The corresponding rates of change of the ability to increase Sz with surfactant chain length are -0.1 1 (f0.04), -0.10 (f0.01), -0.16 (f0.04), -0.09 (f0.05), and -0.02 (fO.O1). The general trend observed of decreasing ability of a given amphiphilic additive at low concentration to depress the cmc and increase S2,the slope of the conductanceconcentration line above the cmc, with increasing surfactant chain length is similar to that found in sodium alkyl sulfate solution.is However, the values of In (dS,/dCad) for decanol in the three surfactant solutions show only a slight decreasing tendency with increasing surfactant chain length. This is probably due to artificially high values of this quantity in and c16. The slope of the S2-Ca, curve for decanol in c16 surfactant was found previously27 to be 27.86 f 0.50 compared to 35.25 f 1.23 in this study. No comparitive data are available for decanol in C i 4 . Similarly the slope of the cmc-C,, curve in Ci6 for decanol appears to be higher than that found previously27(1.065 compared to 0.800). Thus the apparent deviation for decanol in Ci6 from the general trend is most likely due to experimental error. All other compounds investigated follow the trend of decreasing ability to depress the cmc and of increasing S2 with surfactant chain length. It is noteworthy that even the bulky additives such as 2methyl-2-propanol and tert-butylurea depress the cmc of C12,C14, and Cl6 surfactants. It was reported in the literature23 that 2-methyl-2-propanol was able to depress the cmc of decyltrimethylammonium bromide but not that of dodecyl- or hexadecyltrimethylammonium bromides. The latter results were obtained in 0.5 M NaBr and with relatively high alcohol concentration; the lowest concentration used was about 0.5 M. The highest concentration of 2-methyl-2-propanol used in this study is 0.1 M, and the lowest is 0.025 M. The Partition Coefficient and the Compensatory Effects in the Coaggregution Process. Assuming that the monomer-micelle equilibrium is at the cmc by Apom = RT In xf (1)

and that & O m , the difference in the standard chemical potential of the surfactant ion in the micelle and in bulk solution (water), may be split into two components, a hydrophobic and an electrostatic one, a general relation was obtainedz7relating the effect of the amphiphilic additive on the micellar degree of ionization, the corresponding effect on the cmc, and the partition coefficient (eq 2).

(27) Abu-Hamdiyyah, M. J. Phys. Chem. 1986, 90, 1345. (28) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J . Chem. SOC., Faraday Trans. 2 1976, 72, 1525.

xfand yr are the mole fraction of the free monomer surfactant and free additive concentrations, respectively. K is the partition coefficient in mole fraction units b m / y f ) , and ym is the mole fraction of additive in the micelle. In the derivation of eq 2 it was assumed that the solubilization of the amphiphilic additive does not affect the micellar aggregation numberi8 under the conditions of low additive concentration in the micelle. The interaction of the additive and surfactant in the intermicellar solution, Le., the salting-out effect, has also been neglected as it proved to be a relatively small effect compared to K for hydrophobic solutes. To determine K , an empirical relationship must be obtained between the ability to depress the cmc and its corresponding ability to increase the micellar degree of ionization, the first two terms in eq 2, the so-called compensatory effects in the coaggregation process. The above treament stresses two main effects-the interaction of the amphiphilic additive with the surfactant ions in the micelle and the effect of the additive on the main hydrophobic bonding tendency in the bulk solution. As will be shown later, under the conditions of the experiments the mole fraction of the additive in the micelle is quite low (below 0.2 for 1-butanol in C i 2 and as low as 0.004 for decanol in C12). Thus the K values obtained are close to the thermodynamic values which are obtained under conditions of infinite dilution of the additive in the micel1e.l' As the nonionic amphiphile is added to an ionic surfactant solution and both the nonionic amphiphile and the monomeric surfactant ion coaggregate to form mixed micelles resulting in (29) Evans, D. K.; Ninham, B. W. J . Phys. Chem. 1983,87, 5025.

The Journal of Physical Chemistry, Vol. 94, No. 6,1990 2521

Partitioning of Amphiphilic Additives TABLE 11: Distribution Coefficient of Amphiphilic Additives between the Micelles of Dodecyl- (C12),Tetradecyl- (C14),and Hexadecyl(C,& Trimethylammonium Bromides and the Surrounding Aqueous Solutions at 25 OC

14 .

K


additive 1 -propanol 2-propanol

C12

c14

55 39

I-butanol

262

2-butanol 2-methyl-2-propanol butylurea rert-butylurea hexanol cyclohexanol 6-caprolactam octanol decanol

133

30

26 181

21

91 61

81 733 303 2319 743 66 9782

340 249 1792 492 48 8808 75932

83315

C16

37

161 78 53

250

-61

182

1453 344 45 7551 107760

the lowering of the cmc, the micellar surface charge density is reduced with the consequent increase in the micellar degree of ionization. The relationship between the two compensatory effects are depicted in Figure 2. The figure shows that In (-d(cmc)/ dCad)c,d--ois linearly related to In (dS2/dCad),,, in each surfactant solution. The slopes and intercepts of these lines are (0.94 f 0.06, -1.23 f 0.16), (0.97 f 0.04, -2.22 f 0.15), and (1.00 f 0.03, -3.45 f 0.13) in Clz, C14, and cl6, respectively. We shall assume that the value of the slope in each case is equal to unity and any variation from this is due to experimental errors. Using the empirical relations obtained above between the ability to depress the cmc and the corresponding ability to increase S2 and assuming18J9(d In S2/dyf),,+ = (d In cU/dyf)@, eq 2 reduces to the form

[ T]ypO = 0K

(3)

C12

\

5 c

I

1-Butanol

‘1

d In a

0 = 2 - 21 7

1

C16

Figure 3. Logarithm of the partition coefficient as a function of surfactant chain length. The numbers designate the additives as in Table I. 0 , This study; 0, ref 27.

with 0 a constant for a given surfactant independent of the additive as a first approximation and givenI6 by eq 4. c

C1L

n in Alkyl Trimethyl Ammonium Bromides

UYm

JY,*

(4)

The values of 0 obtained for CI2,C14, and c16 are 0.32,0.48, and 0.58, respectively. By use of these 0 values, the partition coefficients of the additives were estimated. These values are given in Table 11. The results show that ( I ) In K increases with increasing alcohol chain length in a given surfactant solution. (2) Increased branching or bulkiness tends to decrease the coaggregation tendency (In K ) (2-methyl2-propanol < 2-butanol < 1-butanol) and cyclohexanol < 1hexanol. Similarly, the coaggregation tendency of tert-butylurea is less than that of 1-butylurea and that of 6-caprolactam is less than that of cyclohexanol. (3) The coaggregation tendency of a urea derivative is greater than that of the corresponding alcohol. This is probably due to a more favorable interaction between -NHCONH2 with the cationic head of the surfactant than that between the -OH and the cationic head. The Coaggregation Tendency as a Function of Surfactant Chain Length. The results show that the logarithm of the partition coefficient In K (-AGoso,ub/R7+)of a given amphiphilic additive tends to decrease with increasing surfactant chain length. This is illustrated in Figure 3. The values for I-decanol in cl6 surfactants appears too high. This is probably due to experimental error as was already pointed out when discussing cmc-c,, and s2-cad initial slopes. If we use the value of 0 in cl6 obtained earlier2’ for paraffinic chain amphiphiles together with the corresponding cmc-Cad slope for decanol, we get a value for In K that makes the coaggregation tendency of decanol fit the general pattern observed as seen in the figure. The slopes of the lines of In K vs surfactant chain length for propanol, butanol, hexanol, octanol,and decanol are -0.1 5 (f0.03), -0.15 (f0.03), -0.12 (f0.01),-0.065 (f0.006), and +0.065

41

3t

-

IO

12

14

16

18

20


Figure 4. Logarithm of the partition coefficient as a function of surfactant chain length. A, Data from ref 25; 0, data from ref 5 ; 0 , data

from ref 22; 0 , using B (see text). (f0.064), respectively. If we consider the new point for I-decanol in C,,, the slope becomes slightly negative (-0.025). If these numbers are taken at face value, there appears to be a change in the direction of In K as a function of surfactant chain length occurring at octanol and which becomes more noticeable at decanol. If this change in direction is confirmed and proves to be true, then it would imply a change in the mechanism of solubilization which is a function of the amphiphilic additive chain length in these surfactant systems. There are no comparative systematic studies published in the literature for the variation of In K of amphiphilic additives of different chain lengths as a function of surfactant chain length to resolve this point. De Lisi et a1.22reported the values of the binding constant Kb (Kb = K/55.5) of 1-pentanol in decyl-, dodecyl-, tetradecyl-, and hexadecyl-trimethylammonium bromides. Their (apparent molar volume) results, which have been converted to mole fraction concentrations, have been plotted in Figure 4. The solubilization tendency is essentially constant in going from Clo to C L 2but increases in going from C I 2to C16. We have also plotted in the same figure two sets of data for the solubilization of 1-butanol, 1-pentanol, and 1-hexanol, one set in CI4and the other set in cl6


2522

The Journal of Physical Chemistry, Vol. 94, No. 6, 1990

surfactant. These two sets of measurements are compatible as both have been obtained by the solubility method.s~2sThe K values obtained by this method tend to be low because the micelles are saturated with the solubilizate.2J1 Taking these two sets together, the results show clearly a decreasing solubilization tendency with increasing surfactant chain length. The opposite trend obtained for 1-pentanol in ref 22 could be due to a number of reasons. For example, in order to get the final equation which is used in the regression analysis (e.g., eq 26 of ref 30), the so-called chemical distribution contribution (cdc) (which is related to -(d(cmc)/dC,d)c-+ in our terminology) was evaluated by a series expansion of In (cmc/cmco), truncating it at the first term. For this approximation to be realistic (cmc)/(cmc") must be much less than 1, which is not the case under the conditions of the experiment. For example,25 (cmc)/(cmc") is 0.78 to 0.05 M 1-pentanol in Cl4 surfactant, which is the concentration used in the experiments. Another approximation involved is essentially the assumption of ideal mixing in the mixed micelle. Although the micellar degree of ionization a in the presence of alcohol was introduced in the treatment, ao,the micellar degree of ionization in the absence of the additive, was substituted for a in the calculations. In order to see how this might affect the final value of K, it is convenient to relate their methods to ours. It was pointed out that30 at the cmc and in the limit of infinite dilution of the alcohol, eq 22 of ref 30 reduces for 1:l ionic surfactants to eq 5 (using our terminology)

In

[z]

= 1[2.3Ks + (1

Abu-Hamdiyyah and Kumari is partly solubilized in the inner H C core, then it is possible for the solubilization to increase with increasing surfactant chain length. This might occur at high 1-pentanol concentration^.^^^^^ Whether it also occurs at lower concentrations for higher alcohols remains to be seen.32,33 Finally, the following numbers give an idea about the mole fraction concentration" in the micelle, y,, under typical conditions of our experiments. For example, for decanol in CI2,C14, and C,, surfactants y , is 0.0036, 0.008, and 0.03 respectively. The corresponding values for I-butanol are 0.18,0.11, and 0.13. This shows we are dealing with concentrations that fall within the dilute range. Factors Affecting the Coaggregation Tendency as a Function of Surfactant Chain Length. The rate of variation of In K with surfactant chain length as represented by n, the number of carbon atoms in the alkyl group in n-alkyltrimethylammonium bromide, is given by eq 7. d- In K dn

The first component, the ability to depress the cmc, depends on the surfactant chain length and on the nature of the additive. It is given by d(cmc) b "n

+

where K , is the salting-out constant and m is the molality, which might be taken as the molarity under these conditions. Equation 5 is Treiner's equation with the correction factor F = 1/(1 a ) . Ignoring K , , which is negligible compared to K for hydrophobic solutes, we have shownls that eq 5 can be put in the differential form given by eq 6.

+

Equation 6 is similar to eq 2 where (1 + a ) / 2 is substituted for 6. Now K values obtained by the two methods may be compared. The values used2*for (1 a ) / 2 expression for 1-pentanol in Clz,CI4,and CI6,respectively, were 0.61,0.595, and 0.58. The corresponding I9 values obtained in this study are 0.32, 0.48, and 0.58. Therefore, if 6 values were used (thus taking into account the effect of the additive on the micellar degree of ionization), the partition coefficients for 1-pentanol would be 999, 888, and 832, respectively, in Clz,C14, and CI6surfactants. These values do not show an increasing coaggregation tendency with increasing surfactant chain length. This is shown by the dotted line in Figure 4. The decreasing coaggregation tendency of amphiphilic additives with increasing surfactant chain length has been rationalized18 in terms of a micellar structure consisting of two regions, an outer region containing the ionic heads plus portions of the hydrocarbon (HC) chains which are in contact with water and an inner region, the HC core, containing the remaining portions of the HC chains. Amphiphilic additives tend to coaggregate in the outer region and nonpolar substances in the inner region. On the basis of several experimental observations it was concludedis*zo~21 that the extent of these regions in both cationic and anionic surfactants depends on the surfactant chain length in such a way that the extent of the H C core increases at the expense of that of the outer region as the surfactant chain length increases. De Lisi et a1.22assumed that 1-pentanol was solubilized in the outer region of the micelle (the palisade layer). If this is so, then according to our model the coaggregation tendency should decrease with increasing surfactant chain length. However, if the alcohol

+

(30) De Lisi, R.; Liveri, V . T.; Castagnolo, M.; Inglese, A . J . Solution Chem. 1986, 15, 23.

(8)

b" is equal to 0.70,0.68,0.67,0.62, and 0.49 for propanol, butanol, hexanol, octanol, and decanol, respectively. The second and third components (xofand 0) are only functions of the surfactant chain length and independent (as a first approximation for 0) of the amphiphilic additive. These two components vary with surfactant chain length according to eqs 9 and 10. In xof = a - bn (9) with a equal to 0.32 and b to 0.71 (compared to b = 0.66 in sodium alkyl sulfates at 44 "C) In 6 = a' b'n (10)

+

with a'equal to -2.89 and b'to 0.15 (compared to b'= 0.14 in sodium alkyl sulfates at 44 "C). According to eq 7 the condition for d In K/dn to be negative is b - b" - d In 6/dn € 0 (11) The value of the left-hand side of relation 11 is equal to -0.14, -0.12, -0.12, -0.06, and +0.07 (-0.025) for propanol, butanol, hexanol, octanol, and decanol, respectively. Putting the conditions in eq 11 in terms of changes in the contributions to the standard free energy of solubilization when the surfactant chain length is increased by one carbon, then relation 11 reads as -AP"SHI - AM'S < AW'mic

(12)

Where Ak" denotes d(AG")/dn and AGO&, AGoSHI,and AGOB denote respectively the standard free energy of micellization in the absence of the additive, the standard free energy term resulting from strengthening of hydrophobic interaction by the amphiphilic additive, and the change in the electrostatic free energy due to solubilization of the amphiphilic additive in the micelle. It is to be noted that according to our treatment the standard free energy of solubilization is given by eq 13 in view of eq 2 AGosolub= -RT In K = AGOSHI+ AGO,,,, + AGO8 (13) where AGOSHI = -RT In (-(d(cmc)/dC,&,+), In xof,and AGO8 = R T In 6. (31) (32) (33) (34)

AGOmic= R T

Lianos, P.; Zana, R. J . Colloid Interface Sci. 1984, 101, 587. Baglioni, P.; Kevan, L. J . Phys. Chem. 1987, 91, 1516. Baglioni, P.; Kevan, L. Prog. Colloid Polym. Sci. 1988, 76, 183. Spink, C. H.; Colgan, S. J . Colloid Interface Sci. 1984, 97, 41.

The Journal of Physical Chemistry, Vol. 94, NO. 6,1990 2523

Partitioning of Amphiphilic Additives

12

14

16

18



Figure 5. Variation of the rate of change of micellar degree of ionization and of the cmc depression with additive concentration in the micelle as a function of surfactant chain length. 0 , ' a by Evans method; 0,( Y O experimentally determined (ref 25).

Thus for the standard free energy of solubilization of a given amphiphilic additive to increase on increasing the surfactant chain length, the contribution of the negative of the standard free energy of micellization term (Le., -Apomic) must be greater than the combined contributions of the compensatory effects (AposHI Apoo) to the standard free energy of s o l ~ b i l i z a t i o n . ~ ~ Thus the diminishing negative slopes of In K vs surfactant chain length observed for the higher alcohols octanol and decanol could be explained by the alcohol of sufficient length penetrating the inner hydrocarbon core of the micelle thus contributing not only to the decrease of the hydrocarbon-water contact region, but also to the hydrocarbon-hydrocarbon interactions in the micellar core. This conclusion is in agreement with that of Baglioni and Kevan32933regarding the location of 2-propanol and 1-octanol, respectively, in sodium dodecyl sulfate micelles. They concluded that 2-propanol is located mainly at the micellar interface while the alkyl chain of I-octanol is located deeper in the micelle. The Standard Free Energy of Solubilization per Mole of Methylene Groups in I-Alkanols. Assuming the additivity of the contributions of the polar and nonpolar parts of the alcohol molecule to the standard free energy of solubilization, the standard free energy of coaggregation per mole of methylene groups has been estimated. These values in CI2,CI4, and C I 6surfactants, respectively, are -1.01 (f0.06), -1.06 (*0.06), and -1.1 1 (f0.06) RT. It shows a slight increase in the coaggregation tendency as the surfactant chain length is increased. However, this increase is at the limit of significance as there is some overlap in these values. These values fall in the range reported in the literature

+

(35) The last sentence before the summary and conclusion in ref 19 should read as follows: "Denoting d(AGoi)/dn by Apoi we then have Aw'sH;,~~ + Apo8 > -Apamic for amphiphilic additives and -Aflomic > A / . L ' S H ~ , ~dor~ responding changes in the signs must be made in the paraphrased conditional sentences in the summary and conclusion of ref 19.

for the transfer of 1 mol of methylene groups (in alkanols or alkanediols) from aqueous solution to ionic 6' and the Ability To Increase the Micellar Degree of Ionization. The micellar degree of ionization in the absence of the additive, a', is constant; thus according to eq 4 6' reflects the ability of an amphiphilic additive to increase the micellar degree of ionization. In order to compare the values of (daldy,), --o in CI2,C,,, and C19surfactants, the values of cyo are needeJ. These have been estimated according to Evans' method.36 Using our conductance data and the aggregation numbers3, 54,72, and 92 for C12,Cl4, and c16, respectively, together with the value of 78.41 R-' cm2 equiv-' for A(Br-), the values of ao obtained are 0.21, 0.20, and 0.19 for CI2,CI4,and c16. The corresponding values for ao in these surfactants determined experimentally by the specific ion electrode method24by Zana are 0.22, 0.19, and 0.16, respectively. By use of these ao values in eq 4, the values of the ability to increase the micellar degree of ionization in the three surfactants were estimated and are shown in Figure 5 . It is clear that as the surfactant chain length increases, (da/ dyJYm4 decreases. This trend for the variation of (dcy/dy,) with surfactant chain length was also obtained in sodium alkyl sulfate micelles.'* This observation together with several other independent observations which are reported in the literature led to the conclusion that the extent of the hydrocarbon-solvent contact region in the micelle decreases with increasing surfactant chain length. Evidence in support of this picture has recently been reported by using more sophisticated experimental techniques.20*21 Figure 5 shows also how the rate of decrease of the cmc with additive concentration in the micelle varies with increasing surfactant chain length. The linear decrease observed with increasing surfactant chain length is expected and is in accord with micellar model and with results previously obtained.I8 It is important to point out that the trends in Figure 5 as well as those of the variations of 6' with surfactant chain length are functions of surfactant chain length only and independent of the individual additives as a first approximation. Summary and Conclusion We have investigated the coaggregation tendency and the strengthening of hydrophobic interaction by amphiphilic additives of various sizes and shapes as a function of the surfactant chain length in n-alkyltrimethylammonium bromide solutions. The results obtained in these cationic surfactant solutions are in accord with those previously obtained in anionic surfactants; namely, the solubilization tendency, the ability to depress the cmc, and the corresponding ability to increase the micellar degree of ionization all tend to decrease with increasing surfactant chain length.

Acknowledgment. This research was supported by the University of Kuwait Grant SC027. Registry No. 1-Propanol, 71-23-8; 2-propanol, 67-63-0; 1-butanol, 71-36-3; 2-butanol,78-92-2; t-butanol, 75-65-0; 1-butylurea, 592-31-4; t-butylurea, 11 18-12-3; cyclohexanol, 108-93-0 6-caprolactam, 105-60-2; 1-hexanol, 11 1-27-3; 1-octanol, 111-87-5; 1-decanol, 112-30-1; C,,N(CH3)3Br,11 19-94-4; C1,N(CH3),Br, 11 19-97-7; C16N(CH3)3Br. 57-09-0. (36) Evans, H.C.J . Chem. SOC.1956,585.

Partitioning of amphiphilic additives between the micelles of n

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