3388
Langmuir 1995,11, 3388-3394
Thermodynamics in Surfactant Solutions: Determination of the Micellization Enthalpy and Entropy of Alcohol/ Surfactant Mixed Micelles. A Comparison of Calorimetric Methods with Temperature Differentiation of the In Xcmc Values Jeffrey C. Burrows, D. Justin Flynn, Susan M. Kutay, Tammy G. Leriche, and D. Gerrard Marangoni* Department of Chemistry, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5 Received September 23, 1994. In Final Form: June 9, 1995@ The variation of the critical micelle concentration(cmc)has been determined for sodium dodecyl sulfate (SDS)in water and in increasing concentrationsof 1-butanol(C40H)at temperatures ranging from 25 to 55 "C. Estimates of the thermodynamic parameters of micellization (AmicGO, A d z , and A,&") are obtained from the variation of the In X,,, with the absolute temperature (method 1). In addition, the enthalpies of micellization have been measured directlyfor the above systems and SDS11-pentanol(C50H) mixed micelles, by use of isoperibol solution calorimetry(method 2) over the same temperature range. The results from both methods, as a function of increasing temperature, indicate a shift in the driving force for the formation of micelles in the direction of decreasing enthalpy, in agreement with the literature. However, as a function of increasing alcohol concentration,the enthalpies from methods 1and 2 are not comparable. Some possible reasons for the discrepancy will be discussed. Finally, we have examined the influence of the cosurfactant (alcohol) chain length on the thermodynamics of mixed micellization.
Introduction
A vast literature has developed on the dependence of the cmc (and, hence, the Gibbs energy of micellization) of ionic and nonionic surfactant systems on the nature and concentration of various additives (e.g., inorganic salts and alc~hols).l-~ However, little work has appeared on the determination of other thermodynamic parameters of micellization (the enthalpy and entropy of micellization) especially in the presence of water-soluble additives like n - a l c ~ h o l s . ~This - ~ situation persists in spite of the fact that a thorough understanding of the phenomenon of micelle formation in binary solvent systems is needed at higher temperatures for a number of important industrial applications. Even at ambient temperature, there is little known about how the enthalpies and entropies of micellization of ionic surfactants change in the presence of increasing amounts of water-soluble additives. Recent work from one of us with ionic surfactant/alcohol mixed micelles has examined the effect of alcohols on the Gibbs energy of mixed micellization and the Gibbs transfer energy of the cosurfactant from the aqueous phase to the mixed micelle interior.*-lo We are interested, therefore, in determining which part of the Gibbs energy (enthalpy or entropy) dominates this decrease of the chemical potential as a function of the alcohol concentration. Also, * Author t o whom correspondence should be addressed. Abstract published inAdvanceACSAbstracts, August 1,1995. ( 1 ) Shinoda, K. J . Phys. Chem. 1964,58, 1136. (2)Singh, H.;Swarup, S. Bull. C h m . SOC.Jpn. 1978, 51, 1534. (3)Abuin, E.;Lissi, E.; Nunez, R.; Olea, A. Langmuir 1989,5, 753. (4)Misra, P. K.; Mishra, B. K.; Behera, G. B. Colloids Surf. 1991,57,
@
1. ( 5 ) Johnson, I.; Olofsson, G.; Landgren, M.; Jonnson, B. J . Chem. Soc., Faraday Trans. 1 1989,85, 4211.
(6)Van Os,N. M.; Daane, G. J.;Handrikkman, G. J.Colloid Interface Sci. 1991, 141, 109. (7)Nishikido, N . ; Moroi, Y.; Uehara, H.; Matuura, R. Bull. Chem. SOC. Jpn. 1974, 47, 2634. (8)Marangoni, D. G.;Kwak, J. C. T. Langmuir 1991, 7 , 2083. (9) Marangoni, D. G.; Rodenhiser, A. P.; Thomas, J.M.; Kwak, J. C. T.Am. Chem. SOC.,Symp. Ser. 1992,45, 194. (10)Marangoni, D. G.;Rodenhiser, A. P.; Thomas, J. M.; Kwak, J. C. T.Langmuir 1993, 9, 438.
in order to predict the variation of the cmc at higher temperatures as a function of the solvent composition, a systematic analysis of the thermodynamics of the alcohol/ surfactant mixed micelles as a function of temperature and solvent composition is needed. Generally, the enthalpy of micellization is obtained usingone oftwo methods: differentiating the mole fraction of surfactant at which micelles form, theX,, values, with respect to temperature according to a mass action or pseudophase micelle model, which we term method 1,or directly via solution calorimetry (method 2). Of the work that exists in the literature in this area, it appears that method 1is often the favored route for obtaining micellization enthalpies,6 in spite of the fact that as early as 1958 White and Benson'l had criticized the use of the temperature derivatives of the In X,, values. Recently, Van Os et al.'j reviewed the methods used to determine A,JP for a number of surfactant systems and concluded that the enthalpy of micellization is best obtained via solution calorimetric techniques.12-14 A number of recent reports in the literature have used method 1to obtain the thermodynamic properties of micelle formation for mixed micellar systems.15J6 In this paper, we report the results of a study of the thermodynamic properties of micelle formation of SDS/1-butanol mixed micelles, a series of mixed micellar systems for which a complete description of the micellar properties (i.e., aggregation numbers of surfactant, N,, and alcohol, Na, cmc's, and apparent counterion dissociation values, a values) exists at low alcohol m o l a l i t i e ~ Method . ~ ~ ~ 1A d J P values are obtained from the measurement of the conductance cmc values as a function of temperature. Isoperibol titration calorimetry, method 2, is used to obtain a rapid, reliable estimate (11)White, P.; Benson, G. C. Trans. Faraday SOC.1959,54, 1025.
(12)Desnoyers, J. E.; De Lisi, R., Perron, G. Pure.Appl. Chem. 1980, 52, 433. (13)De Lisi, R.;Fisicaro, E.; Milioto, R. J . S o h . Chem. 1988, 17,
2015. (14)Woolley, E.M.; Burchfield, T. E. J . Phys. Chem. 1986,89, 714. (15)Onori, G.;Santucci, A. Chem. Phys. Lett. 1992, 189, 598. (16)Callaghan, A.; Doyle, R.; Alexander, E.; Palepu, R. Langmuir 1993, 9, 3422.
0743-746319512411-3388$09.00/00 1995 American Chemical Society
Enthalpies of Alcohol JSurfactant Mixed Micelles of the micellization enthalpy of the surfactant in the mixed solvent systems. The results from both of these methods will be compared as a function of temperature and solvent composition. It will be shown that in some cases, the enthalpies determined via method 1 are very different than those obtained direclty via calorimetry, which suggests that method 1and method 2 do not measure the same quantity. Finally, we will examine briefly the changes in the thermodynamics of mixed micelle formation when the hydrophobicity of the cosurfactant (alcohol) is increased.
Langmuir, Vol. 11, No. 9, 1995 3389 Temp./ "C
Experimental Section Sodium dodecyl sulfate (SDS) was purchased from Fisher Scientific. It was purified by Soxhlet extraction from anesthetic grade diethyl ether and repeated recrystallizations from absolute ethanol. The alcohols, 1-butanol (C40H) and 1-pentanol (CSOH), were high-purity reagents obtained from Aldrich Chemical Co. They were used as received. Conductivity grade water (1.0 x S cm-l) was obtained by passing previously deionized water through a Millipore 4000 S purification system. The alcohol/water solvent mixtures were prepared by mass by mixing the appropriate quantities of alcohol and water. The molalities of the SDS solution are reported as the moles of surfactant per kilogram of mixed solvent. The densities of the titrant solutions were obtained from the literature"J8 or measured directly using an Anton-Parr DMA 45 density meter. Heat capacity data for the titrant solutions were estimated from calibration runs on the titrant solutions (see below). The cmc data and estimates of the apparent counterion dissociation values (avalues) for the SDS/C~EO mixed micelles were from solution conductancemeasurements using aYSI Model 32 conductance bridge, connected to a YSI dip cell (cell constant = 1.0 cm-1). All measurements were done in a custom-designed jacketed vessel, which was maintained at the appropriate temperature (f0.02"C) with a Haake 4000 temperature bath. Calorimetric data were obtained using a Hart 4285 isoperibol solution calorimeter, operating in titration mode, with a 25-mL reaction Dewar. The stability of the precision temperature bath was at least kO.001 "C for all temperatures in the range investigated. Operation of the isoperibol calorimeter is nearly adiabatic, except for the presence of a small heat leak due to the difference between the temperature of the reaction Dewar and the constant temperature of the bath. The continuous injection of the titrant into the reaction Dewar and the collection of the temperature-time data were computer controlled. The buret delivery rate was calibrated by titrating water into an accurately weighed flask. The heat capacity of the reaction Dewar and its contents (the solvent) was obtained from the calibration runs, which consisted of passing a known amount of current through a precision electrical resistor and monitoring the temperature rise in the reactionvessel. Heat capacities ofthe titrant solutions were obtained in a similar fashion. Titration runs were carried out as quickly as possible after the calibration runs were completed. At least three titrations runs were performed for each alcohol/surfactant molality at all temperatures. Attainment of thermal equilibrium inside the reaction Dewar appeared to be instantaneous, as judged by the reproducibility of the titration curves above and below the cmc region (Figure 1).
Theory MicellizationEnthalpiesfrom cmc vs TData. For an alcohoVsurfactant mixed micelle, the AdJF' values refer to the enthalpy change that occurs when n moles of surfactant S (charge a), m moles of counterion C (charge b),and 1 moles of additive A aggregate in aqueous solution to form a mixed micelle, M, of charge b (17) De Lisi, R.;Lizzio, A.;Milioto, S.;Turco Liven, V. J . S o h . Chem.
1986.15.623. (18)Rbux-Desgranges, G.; Roux, A. H.; Viallard, A. J . Chim. Phys.
1986,82,441.
Time / s Figure 1. Plot oftemperature ("C)vs time (s) for three dilutions of 0.200 m SDS into water at 308.15 K.
nSa
+ mC* + ZA
-
[MI&
A,JP
(1)
A number of authors have chosen to obtain the AdJP values by differentiating the Gibbs micellization energy (i.e., In X,, values), obtained from e.g., conductance measurements as a function of temperature, by applying the Gibbs-Helmholtz equation.
Generally, the AdcG0 may be obtained from the simple pseudophase separation model as follows:
AmiCGo= 2RT In Xcm,
(3)
which, when differentiated according to eq 2, yields
(4) Therefore, the enthalpies of micellization may be obtained if the dependence of the cmc on temperature is known. Generally, Xcmcis fitted to a polynomial as a function of temperature6
InX,,
=A
+ BT + C T ~
(5)
so that the micelle formation enthalpy may be found by the application of eq 4 to the fitted function. The above expression for the AdCGo(eq 3) is true only for undissociated micelles (i.e., a = 0). The charged pseudophase separation model and the mass-action model both take the degree of counterion dissociation into account when calculating the AdcGO from the cmc data
AmiCGo= (2 - a)RT In X,,,
(6)
Once the AdcGo and A d J P have been calculated, the A d s o may be found from
Ami$' =
AdJP
- AhcGo T
(7)
Micellization Enthalpies from Calorimetry. It has been stated that the direct measurement of the A d J P by calorimetry is the preferred method of obtaining ther-
3390 Langmuir, Vol. 11, No. 9, 1995 modynamic properties of micelle formation.6 Briefly, A,JP is determined by isoperibol titration calorimetry by measuring the heat changes that occur when small quantities of a concentrated surfactant solution are titrated into a fixed quantity of solvent (either water or a water/nonaqueouscosurfactant mixture)or when a small volume of a concentrated surfactant solution is diluted with the addition of solvent, such that the region of surfactant concentrations investigated includes the cmc. According to Kresheck and Hargraves19 and Beqjamin,2O the temperature vs time data, obtained directly from the isoperibol calorimeter, can be approximated as follows. If n moles ofthe titrant (in this case, surfactant) are titrated in unit time, then the temperature change inside the reaction Dewar per unit time, dO/dt, is represented as
where H*2 andHz(m.dJ are the partial molar enthalpies of the solution in the buret and the Dewar flask at concentration msurft,respectively, and C,,(m,dJ is the heat capacity of the Dewar and its contents at concentration msurf,t. Note that if the heat capacity of the solution changes little during the titration, the heat capacity of the Dewar a t concentration msurf,tmay be replaced, with little error, by the Dewar heat capacity from the calibration runs. Otherwise, the heat capacity of the solution in the buret must be known. If the standard molar enthalpy of micellization is defined as the difference in the partial molar enthalpy of the surfactant at infinite dilution and just above the cmc, then
A,&P = H2(just above cmc) &(infinite dilution) =
Burrows et al. Table 1. Cmc Values and Counterion Dissociation (Apparent a Values) for SDWC4OH Mixed Micelles as a Function of the Alcohol Concentration and Absolute Temperature from Conductance Measurements 298.15 303.2 308.2 313.2 318.2 323.2 328.2 Cddm K K K K K K K Cmc & 0.20 mm 0.000 8.10 8.18 8.29 8.47 8.60 8.93 9.15 0.025 7.56 7.61 7.70 7.90 8.12 8.39 8.65 0.050 6.93 6.95 6.99 7.24 7.60 7.78 8.11 0.075 6.62 6.68 6.77 6.93 7.26 7.45 7.76 0.100 6.23 6.31 6.42 6.53 6.87 7.05 7.36 a Values f 0.04 0 0.41 0.42 0.44 0.44 0.47 0.44 0.47 0.025 0.44 0.45 0.47 0.47 0.49 0.47 0.50 0.05 0.48 0.48 0.50 0.50 0.50 0.50 0.52 0.075 0.50 0.50 0.52 0.52 0.53 0.54 0.54 0.1 0.52 0.53 0.55 0.55 0.55 0.57 0.57
-8.9
1
I
-g-O[ -9.1
where (dO/dt)initidis the observed slope of temperature vs time when the surfactant solution is first diluted into the solvent and (dO/dt), is the observed slope just above the cmc. The cmc may also be determined from the temperature vs time profile, and hence, the Gibbs energy and the entropy of micellization can be obtained directly from the calorimetric experiment via application of eqs 5 and 7, respectively.
Results and Discussion Micelle Formation Enthalpies of SDWC40HMixed Micelles. Critical micelle concentration data and apparent counterion dissociation data for all the SDS/C4Eo systems investigated are given in Table 1. The cmc’s were obtained from the intersection of the linear conductance vs mSDS regions above and below the break region. The counterion dissociation data, the apparent a values, were calculated using the ratio of slopes method (a= Sz/SJ, where Sa and S1 are the slopes of the conductance vs concentration plots above and below the cmc. We note that our values for the cmc’s of SDS in water as a function of temperature are in very good agreement with the results of Goddard and Benson.21 A plot of the InXcmc values vs T for two micellar systems, SDS and SDS/O.100 m C40H mixed micelles, is given in Figure 2. The method 1A,JP values were obtained by application of eq 2 to the fitted
-9.2‘ 293
I
1
303
31 3
323
333
Temp. I K
Figure 2. Plot of In X,, vs temperature (K)for SDS (m) and SDS/O.100 m CdOH (+) mixed micelles. values of In X,,, with temperature. It can be seen from Figure 2 that the variation of In X,,, with T is weak for both systems; however, the slope of the In X,,, curve is more pronounced for the system with added alcohol. It would be expected, therefore, that there is a greater variation of the A,iJP values for the system with added alcohol. This is exactly what we see when we look at the AmiJP values given in Table 1. The method 1 A m i n values are discussed below. The temperature vs time profile for the dilution of a 0.200 m SDS solution into water at 318.15 K is given in Figure 3. We can see from Figure 3 that there are two distinct linear regions in the temperature vs time profile. The initial slope corresponds to the dilution of a very concentrated surfactant solution (%15 x the cmc) into water, resulting in the breakup of the micelles into monomers and interactions between the monomer^.^^,^^ The final slope represents the temperature change for the dilution of the micelle-containing solution to a lower
~~
(19)Kresheck,G.C.;Hargraves,W. A. J . Colloid Interface Sci. 1974, 48,481. (20)Benjamin, L.J. Colloid Interfkce Sci. 1966,22,386. (21)Goddard, E.D.;Benson, G. C. Can. J . Chem. 1967,35,986.
(22)Johnson, I.; Olofsson, G.; J b n s o n , B. J . Chem. SOC.,Faraday Trans. 1 1987,83,3331. (23)Johnson, I.; Olofsson, G. J.Chem. SOC.,Faraday Trans.1 1988, 84,551.
Langmuir, Vol. 11, No. 9, 1995 3391
Enthalpies of Alcohol /Surfactant Mixed Micelles Temp. 1O C 45.020
1
45.015
45.010 -5
45.005 45.000 44.995
-10 44.990 44.985'
350
400
450
500
550 600 time s
650
700
1
750
Figure 3. Plot of temperature ("C)vs time (s) for the dilution of 0.200 m SDS into water at 318.15 K.
-15
I
0
0 0
1
-20 0
O
m
0 0
0.005
0.01
0.02
0.015
m SDS/ (molea/kg)
-4
I
Figure 5. Enthalpic titration curve (A,,& vs msDs) for the dilution of 0.200 m SDS into water at 318.15K.
m
Table 2. Method 1 and Method 2 A d J P Values for (f0.06 kJ/mol) SDWC4OH Mixed Micelles as a Function of the Absolute Temperature and Alcohol Concentration
+
Method 1: Temperature Differentiation of the Conductivity Cmc Values
-a -
C-dm 0.000 0.025 0.050 0.075 0.100
+ -12 -
CdJm
I
- 293
298.15 303.2 308.2 K K K -2.26 -3.66 -5.15 -2.06 -3.80 -5.64 -1.84 -4.10 -6.51 -2.41 -4.44 -6.62 -2.95 -4.91 -7.00
I W
303
31 3
323
333
Tomp. / K
Figure 4. Micellization enthalpies (A,&Y" values) for SDS in water as a h c t i o n of temperature. (1)Present data (+); (2) literature data (W.
micellar concentration, with the monomer concentration remaining essentially ~ o n s t a n t .In~ the ~ ~ cmc ~ ~ region, the temperature changes in the Dewar are due to the dilution of the micelle-containing solution to concentrations near the cmc, resulting in the partial ionization of the micellar solution and a decrease in the inter-micellar interactions. In this cmc region, the transition from monomers to micelles is not sharp, as would be expected if micelle formation was a true phase separation; rather a rapid, but gradual change in the temperature-time profile results. From the slopes of the temperature vs time profiles for the dilution of the concentrated SDS solution into water, we have obtained the micellization enthalpies, A,JP values, of SDS in water at temperatures of 298.15,308.15, 318.15,and 328.15K. These values are plotted in Figure 3,along with the literature values from Olofsson et a1.22 From Figure 3,we observe that there is excellent agree-
0.0000 0.0250 0.0500 0.0750 0.1000
313.2 318.2
K
K
323.2
328.2
K
K
-6.72 -8.40 -10.19 -12.03 -7.58 -9.47 -11.83 -14.18 -9.07 -11.79 -14.66 -17.70 -8.91 -11.26 -13.89 -16.61 -9.22 -11.57 -14.05 -16.67
Method 2: Isoperibol Titration Calorimetry 298.15K 308.15 K 318.15 K 328.15 K -0.22 0.67 1.16 1.35 1.89
-5.08 -4.43 -4.53 -4.78 -4.68
-10.76 -11.21 -11.87 -12.46 -13.19
-13.18 -13.67 -14.28 -14.69 -15.39
ment between our present values and the literature values. A plot of the vs the final SDS molality is given in Figure 5, and this curve should be a reasonable representation of the partial molar enthalpy of dilution of the surfactant solution. This plot yields two essentially linear regions and a middle region of the titration curve where the change in Aob&l with mSDS is rapid; on this curve, the micellization enthalpy is taken as the difference between the linear enthalpy regions.6!22Ifthe formationof micelles was a true phase separation, a discontinuity in this region would be expected, whereas a smooth, but rapid change in is what is found experimentally. These results are in good agreement with the enthalpic titration curves of Olofsson et a1.22and Van Os et a1.6 The results for the A,iJP of SDSIC40H mixed micelles, determined from both method 1 and method 2,are given in Table 2. The method 1 micellization enthalpies have been obtained using the AmicGo values from the simple pseudophase separation model. The Amicevalues for both methods are calculated from the conductance-derived cmc data and are presented in Table 3. The Ami&'" values
Burrows et al.
3392 Langmuir, Vol. 11, No. 9, 1995 Table 3. Method 1and Method 2 Ami# Values (f2J K-' mol-') and AdcGo Values (f0.60 kJ/mol) for SDWCiOH Mixed Micelles as a Function of the Absolute Temperature and Alcohol Concentration Caih
298.15
303.2
308.2
313.2
318.2
323.2
328.2
K
K
K
K
K
K
K
119 116 111 113 113
114 110 102 105 106
108 103 93 97 98
-46.9 -47.3 -47.7 -47.9 -48.2
-47.5 -47.8 -48.2 -48.4 -48.7
0.025 0.050 0.075 0.100
139 141 143 142 141
136 135 136 135 135
Method 1Ami$' 130 124 129 123 128 120 128 121 128 121
0.000 0.025 0.050 0.075 0.100
-43.8 -44.1 -44.7 -44.8 -45.1
-44.4 -44.8 -45.3 -45.5 -45.8
Method 1AmieGo -45.1 -45.8 -45.5 -46.1 -46.0 -46.6 -46.2 -46.8 -46.5 -47.1
-46.4 -46.7 -47.1 -47.3 -47.6
0.000 0.025 0.050 0.075 0.100
146 150 153 155 158
Method 2 Ami$?? 130 133 135 134 136
112 112 111 110 108
105 104 103 103 102
0.000 0.025 0.050 0.075 0.100
-43.8 -44.1 -44.7 -44.8 -45.1
Method 2 Ami@' -45.1 -45.5 -46.0 -46.2 -46.5
-46.4 -46.7 -47.1 -47.3 -47.6
-47.5 -47.8 -48.2 -48.4 -48.7
0.000
,
from both methods are obtained via the experimental enthalpies and Gibbs energy data using eq 7 and presented in Table 3. We discuss the trends in the Gibbs energy and entropy below and concentrate here on the micelle formation enthalpies from both methods. A number of trends are apparent in Table 2. The first of these is that the micellization enthalpies obtained from both method 1 and method 2 decrease as a function of increasing temperature, reflecting a shift in the driving force for mixed micelle formation from an entropycontrolled process at T 5 298.15 K to an enthalpy-driven process at higher temperatures. These trends in the AmiJP values with T are in agreement with the l i t e r a t ~ r e . ~ , ~From , ~ ~ -Table ~ ~ 2, however, we find a discrepancy in the trend of the micellization enthalpies as a function of increasing alcohol concentration, in that the method 1 A m i Z values appear to decrease with increasing alcohol concentration at all temperatures, whereas the AmiJP values determined directly via calorimetry actually increase at 298 K. These results suggest that the micellization enthalpies from method 1are not only different in magnitude but also give the wrong trend in the A , i Z values with increasing cosurfactant concentration. This difference becomes less significant with increasing temperature. However, the results at lower temperatures again suggest that there may be shortcomings in the simple phase separation model, which lead to micellization enthalpies that do not agree with those measured directly with increasing cosurfactant concentration. It has been pointed out by Van Os et al.'jthat this deviation between the measured enthalpy values may be removed, at least in part, if the degree of counterion binding is included in the calculation of the AmicGo(cf. eq 6). In Table 4, we present the method 1values of AmicGo, AmiJP, and AmiSothat are obtained from eq 6, using the conductance-derived apparent a values (Table 1). When we look primarily at the difference in the magnitude between the two sets of enthalpies (the corrected method 1 values and the method 2 values), the discrepancy is indeed removed to some degree, but it is clear that these recalculated method 1 values are still not in agree-
Table 4. Method 1 A d a (fO.60 kJ/mol), A d # (f2J K-l mol-'), and AdcGo Values (f0.60 kJ/mol) for SDW C40H Mixed Micelles as a Function of the Absolute Temperature and Alcohol Concentration, with the Incorporation of the Counterion Dissociation (a Values) from Conductance Measurements Caldm 0.000 0.025 0.050 0.075 0.100
298.15
303.2
308.2
313.2
318.2
323.2
328.2
K
K
K
K
K
K
K
-6.43 -7.30 -8.82 -8.32 -8.37
-7.93 -9.07 -10.97 -10.16 -10.05
-9.21 -10.64 -13.05 -12.08 -11.94
-1.80 -1.60 -1.40 -1.81 -2.18
-2.89 -2.94 -3.12 -3.32 -3.61
AmiJlO -3.98 -5.25 -4.32 -5.81 -4.89 -6.82 -4.90 -6.57 -5.09 -6.69 Ami$'
0.000 0.025 0.050 0.075 0.100
111 110 109 107 104
108 105 104 101 99
102 99 96 95 93
0.000 0.025 0.050 0.075 0.100
-34.9 -34.4 -33.9 -33.6 -33.3
-35.1 -34.8 -34.5 -34.0 -33.6
-35.4 -34.9 -34.6 -34.2 -33.7
97 94 90 89 88
90 88 83 83 82
89 83 76 77 76
83 77 68 71 70
-35.8 -35.3 -35.0 -34.6 -34.2
-35.6 -35.3 -35.2 -34.8 -34.4
-36.8 -36.2 -35.7 -35.0 -34.7
-36.4 -35.9 -35.5 -35.2 -34.9
Ami&'
ment with the mixed micellization enthalpies obtained via solution calorimetry. There are a number of possible reasons for the variance between the two sets of enthalpy data. First, it should be noted that it is more difficult to obtain accurate cmc's in the presence of increasing alcohol molality, since the breaks in the conductance vs plots become less defined at higher alcohol concentrations. We are consistent with the suggestion ofVan Os et al.24in that when we derived the cmc values from the conductance data, at least 10 points were obtained in the linear conductance vs molality regions well away from the cmc region. The cmc data obtained in this manner were quite reproducible. However, given that the deviation between the A m i 8 values at 0.100 m C40H, derived with the two methods, is well outside even the largest estimated error limit, it may be that weaknesses in the simple or charged pseudophase separation model or mass-action model account for the differences in the enthalpies obtained via methods 1and 2. Some of the imperfections in the massaction model have been discussed in detail by A r ~ h e r ~ ~ , ~ ~ and involve the lack of an adequate explanation of how the size of the micelles (or, more accurately, the micelle size and the aggregation number distribution) changes as a function of temperature. It is tempting to extend this explanation to include the case of SDS/C40H mixed micelles. However, the aggregation number distributions of these alcohollsurfactant mixed micelles are unknown as a function of temperature. A detailed description of the micellar aggregation numbers of SDS/CIOH mixed micelles (i.e., the surfactant aggregation number, N,, and the alcohol aggregation number, N,) does exist in the literature as a function of alcoholconcentration at a single temperature. According to Marangoni et al.,839the total aggregation number (i.e., the surfactant the alcohol aggregation numbers) is little changed at 0.100 m C40H (e.g., the N , values are 66 and 55 in water and 0.100 m C40H,respectively, and Nt = N , + Nalcohol increases from
+
(24) Olofsson, G.; Weng, G. Pure Appl. Chem. 1994, 66, 527. (25) Van Os, N. M.; Dame, G.; Boisman, T. A. B. M . J . Colloid Interface Sci. 1987,115, 402. (26) Archer, D. G. J.S o h . Chem. 1987,16, 347. (27) Lam, A. C.; Archer, D. G. J. Chem. Thermodyn. 1988,20,825. (28) Gunnarsson, G.; Jonsson, B.; Wennerstrom, H. J.Phys. Chem. 1980,84,3114.
Enthalpies of Alcohol /Surfactant Mixed Micelles
66 to 71). Since at this particular concentration and temperature there is little change in the size of the micelle, the shifts in the aggregation numbers and aggregation number distributions with temperature should be similar for SDS and SDW0.100 m C40Hmixed micelles. For other micellar systems, the shift in the aggregation number with temperature may make an important contribution to the micelle formation enthalpy obtained via method 1,as was pointed out byArcher.26 In order to assess completely the effect of the change in the aggregation number with temperature on the A , , E values from method 1 for a general surfactant micellar system, we have initiated studies aimed at determining the micellization enthalpies and aggregation numbers for a number of simple surfactant systems and mixed micelles as a function of temperature by time-resolved luminescence probing experiment~.~~-~l A more likely explanation for the differences in the measured micelle enthalpy values is that the two methods actually measure a different quantity. We note that for method 1, the AmieGO values reflect the change in the chemical potential between infinitely dilute surfactant monomers and the surfactant solution at the cmc. At the cmc, there are few micelles, and these micelles are likely to be small with very uncertain aggregation number distributions. Differentiating these chemical potential differences with temperature yields enthalpies of micellization that reflect the shift in the energetics of these small aggregates at the cmc only. It is clear from the enthalpic titration curve in Figure 5 that the calorimetric micellization enthalpies are defined by eq 9, i.e., the difference in the partial molar enthalpies, the H2 values, between the stable micellar solution and the infinitely dilute monomer solution. The final H2 values, i.e., either at the cmc or the stable micelle region, can be very different and, depending on the interactions between the components in solution, may even include different signs. Therefore, it is unlikely that these two estimates of the micelle enthalpy would be in agreement. The micellization enthalpy consists of SDS-SDS interactions, alcohol-SDS interactions, and alcohol-alcohol interactions. These interactions may be broken down into a hydrophobic portion (interactionsbetween the alcoholalcohol, surfactant-surfactant, and alcohol-surfactant alkyl chains) as well as an electrostatic contribution due to the mixing of the surfactant and alcohol groups in the headgroup region of the micelle. There is also a contribution from the interaction of the hydrophobic surfactant and alcohol chains with water, which results in the formation of structured water in the solution. When the surfactant and alcohol coaggregate, interactions between the hydrophobic chains lead to a decrease in the enthalpy of the system, while the release of structured water from around the alkyl chains increases the enthalpy of the system. The relative magnitude of the micellization enthalpy depends on the amount of structured water released on micelle formation vs the electrostatic contributions and hydrophobic interactions. We see from Tables 2 and 3 that the AmcGOvalues from both methods decrease with increasing alcohol concentration at all temperatures studied, indicating that the addition of alcohol promotes micelle formation. This is in excellent agreement with the alcohollsurfactant mixed micelle literature that exists (29)Zana, R.In Surfactant Solutions:New Methods oflnvestigation; Zana, R., Ed.; Surf.Sci. Ser. No. 22;Marcel Dekker: New York, 1987. (30)Malliaris,A.: LeMoigne, - J.: Sturm, J.;Zana, R. J . Phrs. Chem. 1986,89,2709. (31)Cronen, Y.;@lad& E.;Van Der Zegal, M.;Van Der Auwaeraer, M.;Vanderdriessche,H.;De Schreyver,F.;Almgren, M. J . Phys. Chem. 1983,87, 1426.
Langmuir, Vol. 11, No. 9, 1995 3393 Table 5. AJP (*0.50 kJ/mol) for Sodium Dodecyl Sulfate in 1-PentanoyWaterMixtures Determined via Isoperibol Calorimetry Cddm 0.0000 0.0250 0.0500 0.0750 0.1000
,
298.15 K -0.22 0.48 1.66 3.42 5.14
308.15 K -5.09 -4.63 -4.12 -3.82 -3.57
318.15K -10.76 -11.17 -11.59 - 12.09 -12.78
328.15K -13.18 -14.41 -15.93 -17.26 -19.78
at lower temperature^.^,^ As well, the method 1 A d z and Ami&'" values decrease with increasing alcohol concentration and temperature. These trends in the method 1 entropy, enthalpy, and Gibbs energy are consistent with interactions between the surfactant and alcohol alkyl chains, dominating the thermodynamics of mixed micelle formation in the range of alcohol concentrations and temperature investigated. The calorimetrically determined A m i X and A m & 'values are in accord with this explanation only at temperatures I308.15 K. In the lower temperature range, the enthalpy and entropy values increase with increasing alcohol concentration. This suggests that both the alcohol and surfactant are contributing to the hydrophobic effects. Thus, when the mixed micelles are formed in the higher alcohol molality solvents, the A m i E and Ami&" values increase. The hydrophobic effects are diminished at higher temperatures, since a breakdown in the solvent structure occurs. Hence, the driving force for the aggregation of mixed micelles is the decrease in the enthalpy of the system due to the interactions between the alkyl chains. It has been stated by Jonsson and Wennerstrom28that electrical contributions, i.e., packing of the polar headgroups on the micellar surface, may be the controlling factor in the trend of the A m i Evalues. We note that the charged pseudophase and mass-action models both attempt to account for this electrostatic contribution to micelle formation by the incorporation of the a values in the AmicGoequation. Also, it has been shown in the literature8sgthat there is little difference in the a values and the N , values at low alcohol concentrations and that these parameters are a direct measurement of the electrostatic contribution to micelle formation. In this case, the electrostatic contribution to micelle formation, and to the mixed micelle formation enthalpy, is essentially constant over the range of alcohol molalities investigated. It is the increase in the hydrophobic interactions that leads to the increase in the cmc (and the AmicGovalues) when the surfactant and alcohol coaggregate to form the mixed micelle vs the aggregation of the surfactant in the absence of alcohol. As a first step in obtaining the results for the mixed micelles as a function of the alcohol chain length, we have determined the A m i E values for SDSICSOH mixed micelles as a function of the alcohol concentration and temperature (Table 5). It is easy to see from Table 5 that, in agreement with the results for the micellization enthalpy for SDS/C4OH mixed micelles, the A , J P values decrease as a function of temperature at constant alcohol concentration. We find that A,&P changes more rapidly with increasing alcohol concentration then in the case of SDSICIOH mixed micelles at each temperature. Again, this decrease is less pronounced at 308.15 K, and the trend reverses at 318.15K, which indicates a shift in the driving force for micelle formation at higher temperatures. Whether this trend is typical of other surfactantJalcoho1 mixed micelles is being investigated currently.
Conclusions From our analysis of the micellization enthalpies obtained via method 1 and method 2, it is concluded that
3394 Langmuir, Vol. 11, No. 9, 1995 the magnitudes of the A , i T values may be significantly different from the two methods. In addition, the trend in the mixed micellization enthalpy with increasing cosurfactant concentration is not in agreement between both methods. We also note that including the counterion dissociation values from conductance methods in the calculation of the Gibbs micellization energies has little effect in improving the agreement between the A m i T values from the two methods. As well, we consider it unlikely that the neglect of the shift of the surfactant aggregation number with increasing alcohol would affect the mixed micellization enthalpies in any substantive way. It is more likely that the two methods are in poor agreement due to the fact that they measure a different quantity. The method 1micelle enthalpies give information on the change in the energetics of small aggregates with temperature and increasing alcohol concentration at the cmc, whereas the enthalpies from method 2 give a complete description of the change in the partial molar
Burrows et al. enthalpy from the monomeric state to a final concentrated micellar solution and thus include contributions from precmc and larger post-cmc aggregates. Finally, it appears that the release of a larger amount of structured water is responsible for the decreasing Gibbs micellizationenergy (i.e., the A , i T values and the A$,' values increase) when alcohols and surfactants form mixed aggregates at T 5 298 K At higher temperatures, increased interactions between surfactant and alcohol alkyl chains dominate the formation of the mixed micelles.
Acknowledgment. The financial support of NSERC (research grant, D.G.M) and the St. F.X. University Council for Research is greatly appreciated. T.G.L. and D.J.F. acknowledge the grant of NSERC Undergraduate SummerResearchAwards. S.M.K. and J.C.B. aregrateful to St. F.X. University for financial support. LA9407572
