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Thermodynamics of Micellization of Sodium Alkyl Sulfates in Water at High Temperature and Pressure R. De Lisi, S. Milioto,* and N. Muratore Dipartimento di Chimica Fisica, Universita` di Palermo, Viale delle Scienze, Parco D'Orleans II, 90128 Palermo, Italy Received July 25, 2001. In Final Form: September 18, 2001 Apparent molar volumes VΦ,S were determined for sodium octyl, decyl, and dodecyl sulfates in water at 2 and 19 MPa from 25 to 130 °C. The shapes of VΦ,S vs the surfactant concentration curves depend on the surfactant alkyl chain, temperature and pressure. The standard partial molar volumes were calculated from data in the premicellar region whereas the partial molar volumes of the surfactant in the micellar phase were obtained from data in the postmicellar region. The partial molar expansibility and compressibility were evaluated from the dependence of the partial molar volume on temperature and pressure, respectively. Attention was focused to the expansibility and its pressure coefficient since studying the pressure effect on the expansibility is equivalent to studying the temperature effect on the compressibility. The hydrophilic and the hydrophobic (methylene group) contributions to the expansibility were evaluated. The comparison between the present and the alkyltrimethylammonium bromides data evidenced that, contrarily to the expectation, the pressure effect on the expansibility (or temperature effect on compressibility) is the same for the two polar heads in the micelles and independent of the nature solvent (micelles or water) for -SO4Na. The pressure effect on the methylene group expansibility does not depend on the polar head in the micelles whereas it does in water. At a given temperature and pressure, the volume of micellization ∆Vm was calculated by assuming the pseudo-phase transition model. ∆Vm decreases with temperature according to the negative expansibility of micellization. The temperature at which ∆Vm assumes a null value depends on pressure and on the nature of the surfactant. In particular, at a given pressure, the inversion of the ∆Vm sign occurs at lower temperature the longer the alkyl chain is. Moreover, for each surfactant, ∆Vm shows a sign inversion at lower temperature by increasing pressure.
Introduction Micelles are thermodynamically stable aggregates. Their size, shape, charge (for ionic surfactants) may be modulated by other components and/or by varying the surfactant concentration, temperature, pressure, and so on. In the last 20 years, a great deal of physicochemical studies aimed to explore the effect of these variables on the surfactant aggregation process was carried out. The intensive variables are the least studied. Changes of temperature and pressure on the micellization equilibrium may be useful to obtain information at the molecular level. Recently, the structural behavior of tetradecyldimethylaminoxide1,2 and tetradecyltrimethylammonium bromide (TTAB)3 micelles in D2O and of inverse lyotropic mesophases4 upon variations of temperature and/or pressure was studied. Thermodynamic studies, based on direct measurements, generally deal with the enthalpy of dilution, volume, and adiabatic compressibility. Archer5 determined the enthalpy of micellization of TTAB in water at 1.03 MPa in the range 50-175 °C. In addition, activity coefficients, excess apparent molar heat capacity and apparent molar relative enthalpy of decyltrimethylammonium bromide (DeTAB) in water were reported from 50 to 225 °C near the saturation pressure of water.6 Apparent molar volume and adiabatic compressibility of fluorinated and hydrogenated surfactants in water were * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Schwahn, D. Langmuir 1999, 15, 3476. (2) Gorski, N.; Kalus, J.; Schwahn, D. Langmuir 1999, 15, 8080. (3) Gorski, N.; Kalus, J. Langmuir 2001, 17, 4211. (4) Duesing, P. M.; Seddon, J. M.; Templer, R. H.; Mannock, D. A. Langmuir 1997, 13, 2655. (5) Archer, D. G. J. Solution Chem. 1987, 16, 347. (6) Archer, D. G. J. Solution Chem. 1986, 15, 581.
determined in the range of 0.1-80 MPa and 5-35 °C.7,8 Vikingstad et al.9 studied the effect of large change of pressure (1-160 MPa) on the partial molar volume and adiabatic compressibility of sodium decanoate in water. Volumetric studies of DeTAB and dodecyltrimethylammonium bromide in water from 25 to 130 °C and from 0.1 to 19 MPa were carried out.10,11 As a general result, the intensive variables influence the thermodynamic properties of micellization but their role is not straightforward. Large databases of thermodynamic properties of several surfactant systems determined as functions of temperature and pressure provide good tools of theories and models to predict the behavior at high temperature and pressure from data available at ordinary conditions of temperature and pressure. To contribute to this topic, we thought it would be interesting to determine density of water+sodium alkyl sulfate binary systems from 25 to 130 °C at 2 and 19 MPa. The present results compared to those dealing with the alkyltrimethylammonium bromides10,11 may provide information on the effect of the nature of the surfactant polar head on the micellization process at high temperature and pressure. Experimental Section Materials. Sodium octyl sulfate (NaOS, Kodak HPLC grade), sodium decyl sulfate (NaDeS, Kodak HPLC grade), and sodium dodecyl sulfate (NaDS, Sigma 99%) were twice recrystallized (7) Fukada, K.; Oishi, A.; Fujii, M.; Shirakawa, T.; Kato, T.; Seimiya, T. J. Colloid Interface Sci. 1995, 170, 31. (8) Fukada, K.; Kobayashi, Y.; Ota, Y.; Fujii, M.; Kato, T.; Seimiya, T. Thermochim. Acta 2000, 352, 189. (9) Vikingstad, E.; Skauge, A.; Hoiland, H. J. Colloid Interface Sci. 1979, 72, 59. (10) Inglese, A.; De Lisi, R.; Milioto, S.; J. Phys. Chem. 1996, 100, 2260. (11) De Giacomo, A.; D’Angelo, P.; Inglese, A.; Milioto, S.; De Lisi, R. J. Solution Chem. 1999, 28, 1001.
10.1021/la0111607 CCC: $20.00 © 2001 American Chemical Society Published on Web 11/28/2001
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Figure 1. Apparent molar volumes, corrected for the standard partial molar volumes, as functions of concentration for sodium octyl sulfate in water at 2 MPa.
Figure 3. Apparent molar volumes, corrected for the standard partial molar volumes, as functions of concentration for sodium decyl sulfate in water at 2 MPa.
Figure 2. Apparent molar volumes, corrected for the standard partial molar volumes, as functions of concentration for sodium octyl sulfate in water at 19 MPa.
Figure 4. Apparent molar volumes, corrected for the standard partial molar volumes, as functions of concentration for sodium decyl sulfate in water at 19 MPa.
from ethanol (Fluka, puriss 99.8%) and then dried under vacuum at 60 °C for 2 days. Deuterium oxide (99.96 atom % D, Sigma) was used as received. Water was deionized and twice distilled. The concentrated solutions (mS > 0.2 mol kg-1) were prepared by weighing the components to (0.01 mg. The solutions of lower concentrations were obtained from a stock solution (mS ≈ 0.2 mol kg-1) by careful mass dilution. The estimated accuracy of molalities for dilute and concentrated solutions is (0.06% and (0.02%, respectively. A flow vibrating-tube densimeter (Sodev, model 003HP) was used. The equipment permits to measure the period of oscillation of a vibrating tube. A resolution of 100 ns was obtained when the period average meter operated with a time base of 104 cycles (about 25 s). The estimated accuracy on the vibration period was better than 5 × 10-10 s. The period of oscillation of the tube containing the solution τ and water τo is related to the difference ∆d between the density of the solution d and water do as
The measurements were carried out under the following experimental conditions: pressure, 2 and 19 MPa; temperature, 25, 65, 100, and 130 °C; flow rates, 0.008 cm3 s-1 at 25 and 65 °C, 0.0065 cm3 s-1 at 100 °C, and 0.0058 cm3 s-1 at 130 °C. Frequency of the vibrating tube is ca. 450 Hz. The amount of the injected liquid is about 10 cm3. Details on the experimental apparatus were described elsewhere.14 Calculations. The apparent molar volume of the surfactant in water was calculated by means of the following equation
∆d ) d - do ) K(τ2 - τo2)
(1)
where K is the calibration constant of the densimeter. The latter was determined at each temperature and pressure by measuring τ of water and deuterium oxide the densities of which at the experimental conditions were calculated from the equation of state provided by Haar et al.12 and Hill et al.13 The uncertainties in ∆d were estimated to be 0.6 × 10-5 g cm-3 up to 100 °C and (1 × 10-5 g cm-3 at 130 °C. The temperature of the densimeter was controlled with a precise closed-loop programmable circulating thermostat; the fluctuations were within 0.002 °C at 25 and 65 °C and 0.005 °C at 100 and 130 °C. A high-pressure liquid chromatography pump supplied the base flow rate with a stability of (0.02%. (12) Haar, L.; Gallagher, J. S.; Kell, G. S. NBS/NRS Steam Tables; Hemisphere: Washington, DC, 1984. (13) Hill, P. G.; MacMillan, R. D. C.; Lee, V. J. Phys. Chem. Ref. Data 1982, 11, 1.
VΦ,S ) M/d - 103(d - do)/mSddo
(2)
where mS and M represent the surfactant molality and its molecular mass. Critical Micellar Concentration. The critical micellar concentration (cmc) was determined as the intersection point of the VΦ,S vs mS trends in the pre- and postmicellar regions.
Results Sodium Alkyl Sulfates in Water. The apparent molar volumes corrected for VoS, the standard partial molar volume estimated as reported below, of sodium alkyl sulfates as functions of the surfactant concentration (mS) at the working temperatures and pressures are shown in Figures 1-6. The features of some (VΦ,S - VoS) vs mS curves are typical of micellization. Accordingly, the apparent molar volume slightly depends on concentration up to the cmc and monotonically increases tending to a constant value thereafter. Some (VΦ,S - VoS) vs mS curves need a few of considerations. At 19 MPa, by increasing mS, (VΦ,S - VoS) of NaOS sharply increases up to ≈0.2 mol (14) Inglese, A.; Robert, P.; De Lisi, R.; Milioto, S. J. Chem. Thermodyn. 1996, 28, 873.
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Figure 5. Apparent molar volumes, corrected for the standard partial molar volumes, as functions of concentration for sodium dodecyl sulfate in water at 2 MPa.
Figure 6. Apparent molar volumes, corrected for the standard partial molar volumes, as functions of concentration for sodium dodecyl sulfate in water at 19 MPa.
kg-1 beyond which it increases monotonically at 65 and 100 °C, whereas it is nearly constant at 130 °C (Figure 2). The maximum exhibited by the (VΦ,S - VoS) vs mS trend of NaDeS at 130 °C (0.05 and 0.07 mol kg-1 at 2 and 19 MPa, respectively) is an indication of the negative volume of micellization (Figures 3 and 4). The behavior of decyltrimethylammonium bromide (DeTAB)11 is similar in the postmicellar region: VΦ,S monotonically increases with mS at 25 and 60 °C and decreases at 130 °C. As far as NaDS is concerned, at 25 °C and 19 MPa as well as at 65 °C and both pressures, (VΦ,S - VoS) increases monotonically with mS in the whole range of mS studied, and therefore, the cmc is not evident (Figures 5 and 6). NaDS behaves similarly to dodecyltrimethylammonium bromide (DTAB);10 however, for the latter the cmc values were always detected. Standard Partial Molar Volumes as Functions of Temperature and Pressure. The apparent molar volumes in the pre-micellar region were fitted according to
VΦ,S ) VoS + AV(ms)1/2 + BVms
(3)
where VoS, AV, and BV indicate the standard (infinite dilution) partial molar volume, the Debye-Hu¨ckel limiting slope, and the surfactant-surfactant interaction parameter, respectively. The AV values at the experimental conditions were interpolated from Beyer and Staples data.15 They are collected in Table 1 together with VoS and (15) Beyer, R. P.; Staples, B. R. J. Solution Chem. 1986, 15, 749.
Figure 7. Standard partial molar volumes of sodium octyl sulfate (triangles) and sodium decyl sulfate (circles) as functions of temperature at 2 MPa (filled symbols) and 19 MPa (open symbols).
BV values provided by the fitting procedure. Literature VoS data at 0.1 MPa and 25 °C are also reported.16-25 In the case of NaDS, eq 3 was applied to data of the few systems evidencing the premicellar region. Since this region is very narrow, the VoS reliability was checked through the additivity rule by using the NaOS and NaDeS data (Table 1). The experimental and the calculated VoS values fairly agree to each other (Table 1) and, therefore, the additivity rule was used to evaluate VoS of the systems in which the premicellar region is not evident. The standard partial molar expansibility EoS ) (δVoS/δT)P of NaOS and NaDeS was calculated as slope of the VoS vs temperature straight line (Figure 7). Their values are collected in Table 1. EoS of NaDS was not evaluated due to the few VoS experimental values. The standard partial molar isothermal compressibility KoS.T ) -(δVoS/δP)T was calculated as a function of temperature by assuming that KoS.T is independent of pressure. This hypothesis is supported by the literature16-18 data for NaOS, which combined with the present ones, show that at 25 °C the standard partial molar volume is a linear function of pressure in the range 0.1-100 MPa being KoS.T) -0.021 ( 0.001 cm3 mol-1 MPa-1. By using the VoS data at 2 and 19 MPa (Table 1), in the 65 e t e 130 °C range KoS.T (cm3 mol-1 MPa-1) is given by
KoS.T (NaOS) ) [0.06 ( 0.01] + [2.3 ( 0.9] × 10-4t (4) KoS.T (NaDeS) ) [0.11 ( 0.01] + [5 ( 1] × 10-4t (5) where t is the temperature in °C. (16) Musbally, G. M.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1974, 48, 494. (17) Becklund, S.; Hormi, O.; Hoiland, H.; Kvanninen, O.; Sjoblom, J. Finn. Chem. Lett. 1982, 147. (18) Tanaka, M.; Kaneshina, S.; Shin-No, K.; Okajima, T.; Tomida, T. J. Colloid Interface Sci. 1974, 46, 132. (19) Tamaki, K.; Nagai, K.; Ohara, Y. Bull. Chem. Soc. Jpn. 1993, 66, 1292. (20) Corkill, J. M.; Goodman, J. F.; Walker, T. Trans. Faraday Soc. 1967, 63, 768. (21) Shinoda, K.; Soda, T. J. Phys. Chem. 1960, 64, 370. (22) Franks, F.; Quickenden, M. J.; Ravenhill, J. R.; Smith, H. T. J. Phys. Chem. 1968, 72, 2668. (23) Milioto, S.; Crisantino, R.; De Lisi, R.; Inglese, A. J. Solution Chem. 1995, 24, 369. (24) Brun, T. S.; Hoiland, H.; Vikingstad, E. J. Colloid Interface Sci. 1978, 83, 2621. (25) Doughty, D. A. J. Phys. Chem. 1979, 83, 2621.
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Table 1. Standard Partial Molar Properties and Solute-Solute Interaction Parameters of Sodium Alkyl Sulfates in Water at High Temperature and Pressurea t
VoS
P
sodium octyl sulfate 25.00
0.10
64.95 99.96 129.86 25.00 65.00 99.90 129.86 sodium decyl sulfate 25.00
2.00 2.00 2.00 19.24 19.24 19.24 19.17
64.95 99.96 129.87 25.00 65.00 99.90 129.87 sodium dodecyl sulfate 25.00
2.00 2.00 2.00 19.17 19.17 19.17 19.17
64.95 99.96 129.86 25.00 65.10 99.90 129.86
2.00 2.00 2.00 19.17 19.17 19.17 19.17
0.10
0.10
AV
173.3;b 173.1c 172.6;d 174.5e 183.02 ( 0.06 190.81 ( 0.05 196.48 ( 0.06 173.69 ( 0.05 182.06 ( 0.05 189.45 ( 0.04 195.02 ( 0.04
2.836 4.092 5.656 2.011 2.658 3.783 5.163
205.5;c,f 206.0e 204.1g 219.64 ( 0.07 229.56 ( 0.05 237.1 ( 0.1 206.84 ( 0.03 217.53 ( 0.09 227.12 ( 0.01 234.38 ( 0.04
2.836 4.092 5.656 2.012 2.659 3.784 5.164
238.0;c 237.0e 234.4;g 237.7h; 236.8;i 237.2j; 236.9;k 256.3l 268.0 ( 0.1; 268.4l 276.7 ( 0.1; 277.7 240.0l 253.0l 266.1;m 266.5l 274.5 ( 0.03; 273.7l
2.836 4.092 5.656 2.012 2.662 3.784 5.163
EoS
BV
2.4 ( 0.7 -1.6 ( 0.5 -4.9 ( 0.5 3.8 ( 0.6 9.3 ( 0.6 1.5 ( 0.3 0.7 ( 0.4
0.208 ( 0.001 0.2041 ( 0.0006
-5 ( 2
0.274 ( 0.002
5(3 26 ( 1 25 ( 3
0.2647 ( 0.0004
5(1
-14 ( 3 -11 ( 4
Units are °C for t, MPa for P, cm3 mol-1 for VoS, cm3 kg1/2 mol-3/2 for AV, cm3 kg mol-2 for BV, cm3 mol-1 K-1 for EoS. b From ref 17. c From ref 16. d From ref 18. e From ref 19. f From ref 23. g From ref 20. h From ref 22. i From ref 21. j From ref 24. k From ref 25. l Calculated by assuming the additivity rule. m Calculated from two experimental points. a
Equation 4 extrapolates a positive KoS.T value at 25 °C, whereas we reported above that it is negative. On the other hand, Buwalda et al.26 at 25 °C determined negative standard partial molar adiabatic compressibilities KoS.A of sodium alkyl sulfates (from methyl to octyl alkyl chain) and a negative KoS.A value can be also extrapolated for NaDeS. To make appropriate comparisons, KoS.A was converted into KoS.T
KoS.T ) KoS.A +
{
TR2o 2EoS o
σ
R
o
-
}
CpoS o
σ
(6)
where T is the absolute temperature; Ro and σo are the expansibility coefficient and the heat capacity per unit volume of water, respectively, whose values27 are 2.5705 × 10-4 K-1 and 4.1669 J K-1 cm-3, respectively. CpoS and EoS are the standard partial molar heat capacity and expansibility of the surfactant in water, respectively. The CpoS values were taken from the literature,16 whereas EoS values were obtained by extrapolating to 0.1 MPa the data collected in Table 1. The KoS.T values are still negative (-0.0537 and -0.0579 cm3 mol-1 MPa-1 for NaOS and NaDeS, respectively). In conclusion, KoS.T is not a linear function of temperature in the range 25-130 °C. This result is not unusual since several alcohols and ethers in water exhibited the same behavior showing negative KoS.T at low temperatures.28 (26) Buwalda, R.; Engberts, J. B. F. N., Høiland, H.; Blandamer, M. J. J. Phys. Org. Chem. 1998, 11, 59. (27) Mathieson, J. G.; Conway, B. E. J. Solution Chem. 1974, 3, 455. (28) Cabani, S.; Conti, G.; Matteoli, E. J. Solution Chem. 1979, 8, 11.
Partial Molar Volumes of Micellized Surfactant as Functions of Temperature and Pressure. The partial molar volume of the monomeric surfactant in the micellar phase (Vm) was derived by applying the following equation29 to data in the postmicellar region
VΦ,S ) Vm +
FV 1 + EV(mS - cmc)
(7)
Equation 7 was proposed for the additive distribution between the aqueous and the micellar phases30 where Vm represents the partial molar volume of the additive in the micellar phase, FV is the property of transfer of the additive from the aqueous to the micellar phases, and EV is the distribution constant. Since the micellization corresponds to the transfer of the monomeric surfactant from the aqueous to the micellar phases, eq 7 is adequate to evaluate Vm. The fitting parameters (Vm, EV, and FV) values are collected in Table 2. Equation 7 was used to estimate at 25 °C and 0.1 MPa Vm of NaOS and NaDS from literature data16,31 while it was not applied to the following conditions: (i) NaOS-water at 130 °C and 19 MPa since VΦ,S is independent of mS and (ii) NaDS-water at 100 °C and 2 MPa because the very sharp variation of VΦ,S with mS near the cmc region made the minimizing procedure impossible. In these cases, Vm was calculated as averaged values of experimental data. (29) De Lisi, R.; Marongiu, B.; Milioto, S.; Pittau, B.; Porcedda, S. J. Solution Chem. 1997, 26, 319. (30) De Lisi, R.; Turco Liveri, V.; Castagnolo, M.; Inglese, A. J. Solution Chem. 1986, 15, 23. (31) De Lisi, R.; Genova, C.; Testa, R.; Turco Liveri, V. J. Solution Chem. 1984, 13, 121.
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Table 2. Partial Molar Properties of Monomeric and Micellized Surfactants and Properties of Micellization for Sodium Alkyl Sulfates in Water at High Temperature and Pressurea t
P
cmc
Vf
Vm
EV
FV
0.1 2.00
0.15
185.4 ( 0.1
183.7 ( 0.7 190.5 ( 0.3
4.4 ( 0.8
-5.9 ( 0.3
5.1 ( 0.3
99.96 129.86 25.00
2.00 2.00 19.24
0.19 0.19 0.14
192.9 ( 0.1 198.3 ( 0.1 175.9 ( 0.1
196.3 ( 0.6 200.4 ( 0.3 182.7 ( 0.9
2.8 ( 0.9 4.5 ( 1.8 3.0 ( 0.9
-3.8 ( 0.6 -2.2 ( 0.2 -7.2 ( 0.8
3.4 ( 0.6 2.1 ( 0.3 6.8 ( 0.9
65.00 99.90
19.24 19.24
0.18 0.20
188.4 ( 0.1 193.7 ( 0.4
4.6 ( 0.6 3.6 ( 2.2
-3.6 ( 0.1 -1.9 ( 0.4
1.3 ( 0.1 1.1 ( 0.4
129.86
19.17
0.20
187.1 ( 0.1 192.6 ( 0.07 199.1 ( 0.09
sodium decyl sulfate 25.00 64.95
0.1 2.00
0.04
220.1 ( 0.2
99.96
2.00
0.05
129.87
2.00
0.05
230.9 ( 0.05 239.5 ( 0.2
25.00
19.17
0.035
65.00
19.17
0.04
99.90
19.17
0.07
129.87
19.17
0.07
sodium octyl sulfate 25.00 64.95
209.22 ( 0.07 220.3 ( 0.2 228.60 ( 0.01 237.1 ( 0.1
sodium dodecyl sulfate 25.00
0.1
64.95
2.00
