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Vapor Pressures and Osmotic Coefficients of Aqueous Solutions of SDS, C6TAB, and C8TAB at 25 °C Barbara Widera, Roland Neueder, and Werner Kunz* Institut fu¨ r Physikalische und Theoretische Chemie, Universita¨ t Regensburg, D-93040 Regensburg, Germany Received April 28, 2003. In Final Form: June 23, 2003 A comparison is given between the osmotic coefficients inferred from direct vapor pressure lowering and from indirect vapor pressure osmometry, for three aqueous surfactant solutions at 25 °C. The results show that vapor pressure osmometry is a rapid but very reliable technique even at room temperature, in contrast to the indications of the manufacturer. Furthermore, the comparison of both techniques reveals that dissolved gas has no noticeable influence on the osmotic coefficients.
Introduction For the understanding of interactions in liquids, the activity or osmotic coefficients of the different components are of great interest. They are the most relevant thermodynamic reference data, and they are often the starting point of any modeling.1,2 However, in colloidal chemistry, these values seem to be rarely determined experimentally, in contrast to electrolyte solution chemistry or biology. Partly, the apparent lack of precise reference data is due to the difficulty of building up appropriate equipment. Furthermore, as soon as a significant association of the surfactant or polymer molecules occurs, the activity or osmotic coefficients become extremely low and their values only slightly vary. In the case of micellar systems, nearly all standard textbooks of physical chemistry schematically show the variation of the osmotic pressure as a function of surfactant concentration with a characteristic change in the slope of the curve at the critical micelle concentration (cmc). However, such curves are hardly ever measured, mainly because it is nearly impossible to do so for typical surfactants with cmc’s around or lower than 0.01 M. Beyond the cmc, essentially sodium dodecyl sulfate (SDS) was investigated either by direct vapor pressure measurements leading to very bad statistics3 or by membrane osmometers in buffer solutions yielding much more precise results.4,5 Electromotive force (emf) measurements were also used to determine activity coefficients of SDS and some other surfactant solutions.6-8 However, the conversion of emf data to osmotic coefficients is not free from theoretical considerations, because the Debye-Hu¨ckel limit must be assumed at sufficiently dilute solutions. Friberg et al.9 gave an interesting overview about vapor (1) Molero, M.; Andreu, R.; Gonzalez, D.; Calvente, J. J.; Lo´pez-Pe´rez, G. Langmuir 2001, 17, 314. (2) Amos, D. A.; Lynn, S.; Radke, C. J. Langmuir 1998, 14, 2297. (3) Li, P.; Han, B.; Yan, H.; Liu, R. J. Chem. Eng. Data 1996, 41, 285. (4) Amos, D. A.; Markels, J. H.; Lynn, S.; Radke, C. J. J. Phys. Chem. B 1998, 102, 2739. (5) Coll, H. J. Phys. Chem. 1970, 74, 520. (6) Sasaki, T.; Hattori, M.; Sasaki, J.; Nukina, K. Bull. Chem. Soc. Jpn. 1975, 48, 1397. (7) Cutler, S. G.; Meares, P.; Hall, D. G. J. Chem. Soc., Faraday Trans. 1 1978, 74, 1758. (8) Kale, K. M.; Cussler, E. L.; Evans, D. F. J. Phys. Chem. 1980, 84, 593. (9) Friberg, S. E.; Yin, Q.; Aikens, P. A. Colloids Surf., A 1999, 159, 17.
pressure measurements essentially done by headspace chromatography, a technique that can also give osmotic coefficients, but only if the vapor pressure lowering in the solution is high. Otherwise, the error is too important to yield reference data. The simplest technique would be doubtlessly vapor pressure osmometry, but besides the groups of Katime et al.10 and Rajagopalan et al.11 nobody tried to measure at room temperature, because the technique is supposed to yield reliable results only at temperatures higher than 37 °C.12,13 In the present paper, we give highly precise osmotic coefficients of three different aqueous surfactant solutions, containing either SDS or hexyltrimethylammonium bromide (C6TAB) or octyltrimethylammonium bromide (C8TAB), all solutions being measured at 25 °C. SDS is an example of a typical surfactant, C8TAB is a surfactant with a high cmc, and C6TAB is a salt, which does not have a sharp cmc; it is supposed to behave more like a typical organic electrolyte in water. The osmotic coefficients of these two salts complete the corresponding values of nonyltrimethylammonium bromide (C9TAB) and decyltrimethylammonium bromide (C10TAB) as given by Burchfield and Woolley,14 who inferred these data from measurements given by De Lisi et al.15 Two different techniques were used, a direct measurement of the vapor pressure lowering (VPM) of the solutions compared to pure water and an indirect technique, known as vapor pressure osmometry (VPO). In the case of VPM, the solutions are highly degassed, whereas in the case of VPO, the measurements were done at ambient pressure (cf. the Experimental Section). In principle, the dissolved air should not have any noticeable influence on the structuring,16 because of the presence of the hydrophobic tails of the surfactants. However, if the air dissolved in the solutions still had any influence, this influence should lead to differences in the results coming from the two different techniques. If not, the VPO should be a good alternative, because it is much easier and cheaper (10) Katime, I. A.; Allende, J. L. Thermochim. Acta 1984, 74, 215. (11) Rajagopalan, N.; Vadnere, M.; Lindenbaum, S. J. Solution Chem. 1981, 10, 785. (12) Huff, H.; McBain, J. W.; Brady, A. P. J. Phys. Chem. 1951, 55, 311. (13) Crisantino, R.; De Lisi, R.; Milioto, S. J. Solution Chem. 1994, 23, 639. (14) Burchfield, T. E.; Woolley, E. M. J. Phys. Chem. 1984, 88, 2149. (15) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1979, 71, 147. (16) Alfridsson, M.; Ninham, B.; Wall, S. Langmuir 2000, 16, 10087.
10.1021/la034714+ CCC: $25.00 © 2003 American Chemical Society Published on Web 08/19/2003
Osmotic Coefficients of Surfactant Solutions
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Table 1. Parameters of Equation 7a Dj(s) 10-2
j)1 j)2 j)3 j)4 a
1.931487 × 1.082203 × 10-2 -9.568554 × 10-4 3.830374 × 10-5
Dj(0)
Dj(1)
Dj(2)
Dj(3)
-288.0375 74.56777 -8.242194 0.533894
8.999579 -3.315856 0.623503 -0.042681
-0.2525002 0.1584023 -3.569951 × 10-2 2.619678 × 10-3
3.292619 × 10-3 -2.169034 × 10-3 5.003646 × 10-4 -3.729485 × 10-5
Reference 18.
to carry out than VPM and it can be used over wide concentration ranges, provided that the solutions are not too viscous and that there are thermodynamic reference data for solutions in this solvent. Experimental Section Materials. SDS (Merck, LAB) was used as received. C6TAB (Fluka, purum) and C8TAB (Fluka, purum) were dried in a vaccum (p < 0.1 mbar) at a temperature of 40-45 °C. Water from the Millipore purification system with specific conductivity of less than 2 × 10-7 Ω-1 m-1 (25 °C) was used for the preparation of the solutions. Vapor Pressure Measurements. The vapor pressure measurements were performed as differential measurements of the pressure of the solution and that of the pure solvent yielding precise ∆p values. A commercial differential capacitance manometer (Datametrics) with a pressure range of 0-10 Torr (since the reading of the manometer is in Torr, we use this unit for the presentation of the data in this paper; 1 Torr ) 133.32 Pa) is placed in an air thermostat at 40.0 ( 0.1 °C. The samples were held at 25.00 ( 0.01 °C in a high-precision water thermostat, where long time deviations were less than 10-4 °C. The manometer was calibrated with the help of vapor pressures of aqueous solutions of sodium chloride17,18 against pure water. The precision of the calibration is 0.1% for ∆p e 3 Torr, increasing to 0.3% above 3 Torr. The degassing of solutions and pure water, which is essential for precise measurements, was executed by freezing and thawing cycles under a vaccum, yielding totally degassed final products which for different samples show pressure differences of less than 0.001 Torr. This pressure difference may have its origin in small amounts of remaining permanent gas or in temperature fluctuations in the order of 0.0001 °C. For details of the measuring and operating procedures, see ref 19. The activity of the solvent, as, can be calculated from the measured vapor pressure lowering, ∆p, with the help of the relation20
(
ln as ) ln 1 -
(B - Vs*)∆p ∆p p* RT
)
∆p ) p* - p (1)
where m is the molality, p is the vapor pressure of the solution, and p* is that of pure solvent. The nonideality of the solvent vapor is taken into account by the use of the virial equation of state. B is the second virial coefficient, and Vs* is the molar volume of the pure solvent (for water at 25 °C, B ) -1.163 dm3 mol-1 18 and Vs* ) 18.07 × 10-3 dm3 mol-1 21). By definition, the osmotic coefficient Φ is related to the solvent activity as
Φ)-
ln as νmMs
Inc.). With this method, the vapor pressure is measured indirectly by using thermistors to measure voltage changes caused by changes in temperature. The measuring chamber contains a reservoir of solvent and paper wicks to provide a saturated solvent atmosphere. In the beginning, a drop of pure solvent is attached to each thermistor with the help of a syringe, and after 5 min of equilibration the reading is adjusted to zero. Then the pure solvent on one thermistor is replaced by the solution and condensation of solvent from the vapor phase into the solution at the thermistor takes place. Due to the heat of condensation, the thermistor will be warmed and the vapor pressure rises. Condensation continues until the vapor pressure of the solution equals the vapor pressure of the pure solvent. Generally, a time of 4-8 min suffices to reach this steady state. First the instrument was calibrated using aqueous sodium chloride solutions in the concentration range from 0.01 to 1.5 mol/kg, yielding a function which correlates the panel readings to the corresponding concentrations of the sodium chloride solution. Then the measurements for the different surfactant solutions were carried out. Special care was taken to keep the drop size and shape as constant as possible and equal on both thermistors. For each solution, at least five determinations (zero point adjustment and new solution) were performed and the mean value is reported. Generally, the deviations from the mean value were less than 1%. For the surfactant solution with molality m, the osmotic coefficient Φ was obtained according to
Φ)
(17) Gibbard, H. F.; Scatchard, G. J. Chem. Eng. Data 1973, 18, 293. (18) Gibbard, H. F.; Scatchard, G.; Rousseau, R. A.; Creek, J. L. J. Chem. Eng. Data 1974, 19, 281. (19) Barthel, J.; Neueder, R. GIT Fachz. Lab. 1984, 28, 1002. (20) Barthel, J.; Neueder, R.; Lauermann, G. J. Solution Chem. 1985, 14, 621. (21) International Critical Tables; Washburn, E. W., Ed.; McGrawHill: New York, 1928; Vol. III.
(3)
where mNaCl is the molality of a sodium chloride solution showing the same instrument reading as the surfactant solution, which means the vapor pressure (and therefore the solvent activity) is equal in both solutions (cf. the definition of the osmotic coefficient in eq 2). The stoichiometric numbers ν and νNaCl in eq 3 are set equal to 2. ΦNaCl is the respective osmotic coefficient calculated with the help of the following equation set developed by F. Gibbard and G. Scatchard.18
Φ)1-
S ) 1.17284 -
SZ
ω
+
a
∑D m
j
(4)
j
j)1
(
)
τ 6202.357τ + 54.4251 ln 1 + Ts τ 2 Ts 1 + Ts
(
)
0.161993τ + 8.59609 × 10-5(2Tsτ + τ2) (5)
(2)
ν is the stoichiometric number of the solute (here ν ) 2), and Ms is the molecular weight of the solvent (Ms ) 18.015 g mol-1). Vapor Pressure Osmometry. The vapor pressure osmometry was performed with the help of an Osmomat K-7000 (Knauer
νNaClmNaClΦNaCl νm
1+xZ)
1 - 2 ln(1 + x) 1+x 2 x
(6)
with τ ) T - Ts, x ) axm and Ts ) 298.16 K, a ) 1.5. The coefficients Dj of the power series in m of eq 4 are given by ω
Dj ) Dj(s) - 0.2516103
Dj(k)
tk
∑ k! ∫ (t + T ) dt k)0
τ
0
(7)
s
Table 1 shows the parameters up to a value of ω ) 3 necessary for the calculation of osmotic coefficients of aqueous sodium chloride solutions. They are taken from ref 18.
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Widera et al.
Table 2. SDS in Water (Vapor Pressure, 25 °C) m mol/kg
Φ
∆p Torr
m mol/kg
Φ
∆p Torr
m mol/kg
Φ
∆p Torr
0.257 0.273 0.273 0.294 0.297 0.506 0.507 0.513 0.515 0.515 0.540 0.542 0.555 0.557 0.704 0.742
0.120 0.091 0.174 0.130 0.155 0.125 0.099 0.101 0.126 0.146 0.136 0.121 0.120 0.160 0.129 0.131
0.0265 0.0214 0.0406 0.0328 0.0395 0.0543 0.0428 0.0445 0.0554 0.0646 0.0629 0.0562 0.0570 0.0764 0.0778 0.0830
0.752 0.753 0.873 0.875 0.898 0.899 0.978 0.996 0.998 1.043 1.049 1.051 1.064 1.065 1.072 1.224
0.128 0.135 0.124 0.128 0.118 0.120 0.124 0.135 0.126 0.116 0.137 0.115 0.124 0.121 0.119 0.110
0.0822 0.0871 0.0928 0.0961 0.0906 0.0927 0.1040 0.1150 0.1080 0.1033 0.1230 0.1031 0.1130 0.1100 0.1090 0.1150
1.227 1.278 1.282 1.416 1.419 1.448 1.453 1.558 1.602 1.608 1.755 1.759 1.784 1.790
0.132 0.125 0.128 0.113 0.119 0.108 0.125 0.140 0.119 0.122 0.105 0.114 0.116 0.116
0.1380 0.1370 0.1400 0.1370 0.1440 0.1340 0.1550 0.1860 0.1630 0.1680 0.1570 0.1720 0.1770 0.1780
Table 3. SDS in Water (Vapor Pressure Osmometry, 25 °C) mSDS mol/kg
mNaCl mol/kg
0.01 0.02 0.03 0.04 0.05 0.10 0.15 0.20 0.25
0.006 39 0.006 91 0.007 60 0.008 36 0.009 05 0.013 65 0.018 75 0.024 65 0.029 99
Φ
mSDS mol/kg
mNaCl mol/kg
Φ
0.622 0.336 0.246 0.203 0.176 0.132 0.120 0.118 0.114
0.30 0.35 0.40 0.45 0.50 0.75 1.00 1.20 1.40
0.036 70 0.042 19 0.049 06 0.056 89 0.062 81 0.099 10 0.134 32 0.162 47 0.185 47
0.116 0.114 0.116 0.119 0.118 0.123 0.125 0.126 0.123
Table 4. C6TAB in Water (Vapor Pressure Osmometry, 25 °C) mC6TAB mol/kg
mNaCl mol/kg
Φ
0.050 47 0.099 91 0.149 95 0.199 95 0.250 29 0.299 79 0.349 73 0.399 74 0.450 20
0.0514 0.0989 0.1436 0.1872 0.2280 0.2680 0.3060 0.3471 0.3841
0.962 0.925 0.890 0.867 0.842 0.825 0.807 0.800 0.786
mC6TAB mol/kg
mNaCl mol/kg
Φ
0.500 03 0.549 86 0.600 11 0.650 01 0.700 18 0.749 47 0.800 13 1.000 00
0.4203 0.4558 0.4940 0.5281 0.5632 0.5954 0.6266 0.7570
0.775 0.764 0.759 0.750 0.742 0.734 0.724 0.703
Table 5. C8TAB in Water (Vapor Pressure Osmometry, 25 °C) mC8TAB mol/kg
mNaCl mol/kg
Φ
mC8TAB mol/kg
mNaCl mol/kg
Φ
0.0498 0.1000 0.2000 0.2598 0.2799 0.2999
0.0495 0.0956 0.1767 0.2190 0.2325 0.2472
0.939 0.894 0.818 0.779 0.767 0.761
0.3201 0.3401 0.3599 0.3999 0.4502 0.4989
0.2548 0.2629 0.2718 0.2849 0.2950 0.3037
0.735 0.713 0.697 0.657 0.604 0.561
Results Table 2 shows the experimental vapor pressure data of SDS in water at 25 °C (molality m and vapor pressure lowering ∆p, VPM technique). The osmotic coefficients Φ are calculated with the help of eqs 1 and 2. Table 3 gives the data for the same system obtained with the help of the osmometer (VPO technique). The corresponding results for the two cationic surfactant systems are given in Tables 4-6. Discussion The osmotic coefficients from Table 2 and Table 3 are plotted in Figure 1, showing an excellent agreement of the two different experimental methods. This agreement
Figure 1. Osmotic coefficients of SDS in water at 25 °C: 1, osmometry; 2, vapor pressure; 3, data from ref 13. Table 6. C8TAB in Water (Vapor Pressure, 25 °C) m mol/kg 0.395 0.395 0.436
Φ
∆p Torr
0.642 0.2165 0.658 0.2220 0.623 0.2320
m mol/kg 0.492 0.503 0.517
Φ
∆p Torr
0.531 0.2231 0.517 0.2220 0.523 0.2309
m mol/kg 0.577 0.594
Φ
∆p Torr
0.487 0.2397 0.484 0.2453
confirms the good reliability of the vapor pressure osmometry, which is a relative and even a nonequilibrium method. The full circles are literature data (vapor pressure osmometry at 37 °C),13 which were transformed by the authors to 25 °C with the help of enthalpy data and which fit nicely to our experimental data. Furthermore, the results are also in good agreement with the values given by Burchfield and Woolley,14 who reconsidered data measured by Rajagopalan et al.11 The statistics of our VPO measurements seems even better than these data. This result shows that the vapor pressure osmometer yields reliable results even at 25 °C, despite the manufacturer’s lowest recommended temperature of 37 °C (310 K), which we suppose to be somewhat arbitrary. From the measuring principle, this method is not limited to a lowest temperature, but of course the lower the temperature, the lower the solvent vapor pressure and the longer the time needed to obtain a steady state (here up to 8 min), and as a consequence the measuring error increases. Figure 1 shows the well-known pattern of the osmotic coefficient for highly associating electrolytes (cf. osmotic coefficients of electrolytes in nonaqueous solvents22-24). The sharp decrease of the osmotic coefficients is due to the formation of micelles, which takes place at 25 °C at about 0.008 mol/kg.25-28 The concentration range below the cmc is not accessible in this study. Figure 2 shows the osmotic coefficients of C6TAB and C8TAB (from osmometry and vapor pressure measurements) solutions. The values of the C8TAB solutions exhibit a change in slope at about 0.3 mol/kg indicating the (22) Barthel, J.; Neueder, R.; Poepke, H.; Wittmann, H. J. Solution Chem. 1999, 28, 489. (23) Barthel, J.; Neueder, R.; Wittmann, H. J. Solution Chem. 1999, 28, 1263. (24) Barthel, J.; Neueder, R.; Poepke, H.; Wittmann, H. J. Solution Chem. 1999, 28, 1277. (25) Lin, C. E.; Chen, M. J.; Huang, H. C.; Chen, H. W. J. Chromatogr., A 2001, 924, 83. (26) Gadelle, F.; Koras, W. J.; Schechter, R. S. J. Colloid Interface Sci. 1995, 170, 57. (27) Ruiz, C. C. Colloids Surf., A 1999, 147, 349. (28) Benito, I.; Garcia, M. A.; Monge, C.; Saz, J. M.; Marina, M. L. Colloids Surf., A 1997, 125, 221.
Osmotic Coefficients of Surfactant Solutions
Figure 2. Osmotic coefficients of C8TAB (1, osmometry; 2, vapor pressure) and of C6TAB (3, osmometry) in water at 25 °C. For comparison, values given in ref 14 for C9TAB (4) and C10TAB (5) are also included.
formation of micelles at this concentration. In the literature, the cmc of C8TAB at 25 °C is reported as 0.293 mol/ dm3,30 0.3 mol/dm3,31 and 0.225 mol/kg (aggregation number of 17),32 which is very close to our result. For C6TAB, the data points are smoothly curved and there is no sudden change of the slope. In the literature, an aggregation number in the order of 333 is supposed. However, it is more likely that C6TAB does not associate to defined aggregates but that a continuous variation from monomers to oligomers with increasing concentration occurs. This salt is an intermediate between short-chain alkylammonium ions and typical surfactants. Therefore, a modeling of the C6TAB osmotic coefficients is somewhat difficult. On one hand, a simple mass action law14 is certainly not sufficient; on the other hand, a detailed description of the nonideality29 without a firm knowledge of the association equilibria would be arbitrary. Nevertheless, both curves fit nicely into the series of CxTAB solutions, as can be seen from the comparison with the C9TAB and C10TAB solutions, taken from ref 14, so that the conclusions drawn in this paper should also be valid at least for C8TAB. Qualitatively, it can be seen that osmotic coefficients decrease more rapidly with concentration when the alkyl chain is longer. The reason is twofold: (i) the smaller the global number of solute (29) Calmettes, P.; Kunz, W.; Turq, P. Physica B 1992, 180/181, 868. Kunz, W.; Turq, P.; Calmettes, P.; Barthel, J.; Klein, L. J. Phys. Chem. 1992, 96, 2743. (30) Zielinski, R. J. Colloid Interface Sci. 2001, 235, 201. (31) Nishikawa, S.; Huang, H. Bull. Chem. Soc. Jpn. 2002, 75, 1215. (32) D’Errico, G.; Ortona, O.; Padu´ano, L.; Tedeschi, A.; Vitagliano, V. Phys. Chem. Chem. Phys. 2002, 4, 5317.
Langmuir, Vol. 19, No. 20, 2003 8229
Figure 3. Osmotic coefficient of C8TAB (1, osmometry; 2, vapor pressure) in water at 25 °C. The dashed lines indicate an uncertainty of 0.01 Torr in the vapor pressure.
particles (monomers or micelles), the smaller the osmotic coefficient; and (ii) the smaller the particle solvation, the smaller the osmotic coefficient. Finally, in Figure 3 the uncertainty of a typical VPM result is illustrated. Even a precision of 0.01 Torr is not sufficient to yield reliable osmotic coefficients at C8TAB concentrations lower than 0.3 M. The relatively bad statistics can also be seen in Figure 1. Nevertheless, the advantage of VPM is that no reference data are required to calculate the osmotic coefficients, in contrast to VPO, which is more precise but depends on an external standard. As a conclusion, it can be stated that vapor pressure osmometry is a useful and reliable technique to determine osmotic coefficients rapidly. The obtained values for simple surfactant solutions can be used for the modeling of interactions. Obviously, air does not have a noticeable influence on osmotic coefficients. In the future, we plan to study the effect of the change in the counterions on the osmotic coefficients. Such changes can be rapidly detected by VPO and then modeled by statistical mechanics and should yield new insights into phenomena like the Hofmeister series. First studies in this direction are currently under way in our laboratory. Acknowledgment. We thank Drs. M. Dubois and Th. Zemb from the research center in Saclay, France, for helpful discussion on the VPO technique and especially on the Knauer osmometer. LA034714+ (33) Mosquera, V.; del Rio, J. M.; Attwood, D.; Garcia, M.; Jones, M. N.; Prieto, G.; Suarez, M. J.; Sarmiento, F. J. Colloid Interface Sci. 1998, 206, 66.
