Langmuir 1995,11, 1905-1911
1905
Thermodynamic Micellar Properties of n-Octyldimethylamine Oxide Hydrochloride in Water Jacques E. Desnoyers, Gaston Caron,? Sylvie Beaulieu, and G6rald Perron* INRS-finergie & Mathriaux, 1650 monthe Sainte-Julie, Varennes, QC, Canada J3X 1S2 Received October 25, 1994. I n Final Form: February 27, 1995@ The apparent molar volumes and heat capacities of n-octyldimethylamineoxide hydrochloride (OAOHC1) were measured in water as a function of concentration between 2 and 55 "C and the apparent molar relative enthalpies of the same system at 25 "C. The apparent molar expansibilities were calculated from the temperature dependence of the volumes. The volumes and heat capacities were also measured at 25OC for trimethylamine oxide hydrochloride in water in order to check the group additivity. The data for OAOHCl were fitted with a mass-action model (J.Phys. Chem. 1983,87,1397) and compared with those of n-octyldimethylamine oxide (OAO) and n-octylammonium bromide (OABr) in order to investigate the effect of the charge on the thermodynamic micellar properties. A comparison between the properties of OAOHCl and OAl3r shows that OAOHCl behaves as a typical cationic surfactant. The differences in the thermodynamic properties of micellization between OAO and OAOHCl are as expected from a stronger hydration in the premicellar region and counterion binding beyond the critical micellar concentration (cmc) of OAOHCl. The temperature dependence of most micellar properties is comparable for the two surfactants. As it is generally observed with ionic surfactants, the enthalpy of micellization of OAOHCl is endothermic at low temperature and exothermic at high temperature and the cmc goes through a minimum at about 35 "C. However, the cmc ofboth surfactants at 25 "C are of the same magnitude. From the mass-actionmodel, the thermodynamic properties of the surfactant can be predicted at any temperature and concentration in the range measured. 1. Introduction I t is difficult to study the effect of ionization on micellar properties since the Kram temperature of most long-chain amines and carboxylic acids are generally too high for micelle formation. It is also difficult to investigate the effect of charge on micellar properties since ionic and nonionic surfactants usually have vastly different structures. In this respect, alkyldimethylamineoxides are wellcharacterized zwitterionic surfactants which behave a s typical nonionic surfactants at a pH above 7 and as typical ionic surfactants at low pH. These surfactants have been studied extensively with a variety of techniques.l-16 It is generally observed that the micellar size goes through a maximum, especially in the presence of an electrolyte such a s NaC1, when the degree of ionization is about 0.5. It Present address: Tricomatic, 1001 Boul. Industriel, St-Eustache, QC J7R 6C3. * Author to whom correspondence should be sent. Abstract published in Advance ACS Abstracts, June 1, 1995. (1) Benjamin, L. J. Phys. Chem.1964,68, 3575; 1966, 70, 3790. (2) Benjamin, L. J. Colloid Interface Sci. 1988,22, 389. (3) Hermann, K. W. J. Phys. Chem. 1982,66,295;1964,68, 1540. (4) Corkill, J. M.; Hermann, K. W. J. Phys. Chem. 1983, 67, 934. (5) Courchene, W. L. J.Phys. Chem. 1964, 68, 1870. (6) Kolp, D. G.; Laughlin, R. G.; Krause, F. P.; Zimmerer, R. E. J. Phys. Chem. 1983, 67, 51. (7) Ikeda, S.; Tsunoda, M.; Moeda, H. J . ColloidInterface Sci. 1978, 67, 336; 1979, 70, 448. (8) Desnovers. J. E.: Roberts. D.: DeLisi. R.: Perron. G. In Solution Behavior of kuriactants; Mittal, K. L., Fendler, E. J.,' Eds.; Plenum: New York, 1982, p 343. (9) Desnoyers, J. E.; Caron, G.; DeLisi, R.; Roberts, D.; Row, A,; Perron, G. J. Phys. Chem. 1983,87, 1397. (10) Chang, D. L.; Rosano, H. L. In StructurelPerformance Relashionship in Surfactants; Rosen, M. I., Ed.; ACS Symposium Series 253; American Chemical Society: Washington, DC, 1964; p 129. (11) Chang, D. L.; Rosano, H. L.; Woodward, A. E. Langmuir 1985, 1. 669. (12) Hoffmann, H.; Oetter, G.; Schwandler, B. Prog. Colloid Polym. Sci. 1987, 73, 95. (13) Uchiyama,H.; Christian,S. D.;Scamehorn,J. F.;Abe, M.;Ogino, K. Langmuir 1991, 7, 95. (14) Zhang, H.; Dubin, P. L.; Kaplan, J. I. Langmuir 1991,7,2103. (15) Rathman,J. F.; Scheuing, D. R. InFTIR Spectroscopy in Colloid and Interface Science; Gould, R. F., Ed.; ACS Symposium Series 447; American Chemical Society: Washington, DC, 1991; p 123. (16) Brackman, J. C.; Engberts, J. B. F. N. Langmuir 1992,8,424. @
also seems that long-chain amine oxides can undergo a sphere-to-rodtransition in the presence of a n electrolyte.12 The trends with the degree of ionization are less clear in the absence of support electrolytes. Depending on the technique used and on the particular amine oxide, the micelles appear slightly larger or slightly smaller in the ionized form. Thermodynamic functions of micellization, such as critical micellar concentrations (cmc), volumes, and enthalpies of micellization, cannot be measured directly. They must be extracted from the experimental data using a n appropriate model. Usually, some form of pseudophase or mass-action models are used to analyze volumetric or thermochemical data. The mass-action models can also be used in some cases to estimate the aggregation numbers, N. Unfortunately, in view of the assumptions that must be made, the thermodynamic functions of micellization will depend to some extent on the model used and the approximations made. For example, the partial molar enthalpy of a surfactant in the micellar form can be vastly different if the standard or reference state is taken at infinite dilution, a t the cmc or a t infinite concentration. However, despite their limitations, these thermodynamic models and derived micellization functions can in turn be used for the prediction of the pressure and temperature dependences of mi~el1ization.l~They can also be used to study the effect of charge on micellization, provided the same model and approximations are applied to the surfactants in the ionic and nonionic form. The densities, relative heat capacities per unit volume, and enthalpies of dilution of n-octyldimethylamine oxide hydrochloride (OAOHC1) were measured with flow instruments and used to calculate the apparent molar volumes, heat capacities, relative enthalpies, and expansibilities as a function of concentration and temperature. These properties will be compared with those of n(17)Desnoyers, J. E.; Perron, G.; Roux, A. H. In Surfactants Solutions: New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; 1.
0743-746319512411-1905$09.00/0 0 1995 American Chemical Society
Desnoyers et al.
1906 Langmuir, Vol. 11, No. 6, 1995
octyldimethylamine oxide (OAO)9 and of n-octylammonium bromide (OABr).lBThe data at 25 "C were extended above 4 mol kg-l in order to investigate the possibility of a postmicellar transition which is often observed with ionic surfactants. The volumes and heat capacities were also measured at 25 "C for trimethylamine oxide hydrochloride (TMOHC1)in water in order to check the group additivity. In another paperlg we will examine the effect of added NaCl on OAO. 2. Experimental Section OAO was prepared as previously described.8 Essentially, octyldimethylamineis mixed with an equal amount of methanol and a solution of HzOz is added slowly (mole ratio of HzOz to amine is 1.4). The excess oxidizing agent, HzOz was eliminated with MnOz rather than with sodium sulfite. The solution was filtered and the unreacted amine was extracted with petroleum ether. Water was removed by distillation of an azeotrope with 2-propanolleaving a residualsolid, OAO. OAO was recrystallized with dry acetone and dried under vacuum over PzO5. As for many surfactants, it is difficultto exclude water completelyfrom the solid surfactant by recrystalizationand it is equallydifficult to evaluate precisely its residual water content (on the order of 3-5%). As a result, the apparent molar quantities of different batches of surfactant will show small systematicdifferences,but the derived functions of micellization, obtained from the changes in properties, are not much affected. OAOHCl was prepared by dissolving OAO in a mixture of diethylether and absoluteethanol (the alcohol is added dropwise until all the OAO is dissolved). To this solution,anhydrous HC1 gas is added slowly and the salt precipitates. Left overnight,it was filtered,washed with diethylether, and dried under vacuum over PzOb. The concentrationof OAOHCl in water was checked by a conductometric titration with AgNO3 and the purity of differentbatches vaned between 99.4 and 99.8%,indicatingthat the water content in the purified solid is on the order of 0.20.6%. In view of the above comment on the reproducibility of the data from one sample to another,the measurements as afunction of temperature were determinedwith the same batch of OAOHCl solutions. TMOHCl was prepared by titrating purified trimethylamine oxide8 with HC1. The solvent was evaporated, the salt was recrystallized and dried in a vacuum oven at 85 "C. All solutions were prepared with deionized distilled water. The flow techniques that were used to measure the densities, relativeheat capacitiesper unit volume,and enthalpiesof dilution were the same as in the studies of OA0.8,9 3. Results The densities and relative heat capacities per unit volume of OAOHCl were measured between 2 and 55 "C, up to 1.4 mol kg-l, and used to calculate the apparent molar quantities, V Z ,and ~ C P , ~in, ~ the usual way. The data for TMOHCl were obtained at 25 "C only. The original data are available elsewhere (see note on Supplementary Material). The results for OAOHCl are shown in Figures 1and 2. The full lines are from the curve fitting using a mass-action model, as described below. The data at 25 "C were subsequently extended to 4.2 mol kg-l with a freshly prepared sample of OAOHCl. These new results are compared with the first set of data and with the corresponding data for OAO and OABr in Figures 3 and 4. The differences could be due to the uncertainty in the absolute molality, as mentioned in the Experimental Section, or to a small extent of decomposition of the OAOHCl surfactant with time since the first set of data, measured at different temperatures, were not obtained with freshly prepared solutions. The data for OAO were also extended to 4 mol kg-l and some differences were (18)DeLisi, R.; Perron, G.; Desnoyers, J. E. Can.J.Chem. 1980,58, 959. (19)Palepu, R.,; Perron, G.;Desnoyers, J. E. Manuscript in prepara-
tion.
55 45
35 25
15 5
2
1
0.0
1
0.4
1
1
1
0.8
1
I
1.2
I
1.6
mol-kg-I
Figure 1. Apparent molar volumes of OAOHCl at various temperatures; full lines are from the mass-action model.
---
I
2
Figure 2. Apparent molar heat capacities of OAOHCl at varioustemperatures; full lines are from the mass-actionmodel. also observed between the two sets of data as shown for heat capacities in Figure 4. The influence of these uncertainties on the thermodynamic properties of micellization will be discussed later. The apparent molar volumes of TMOHCl were fitted with the relation
v ~- vDHm2112 , ~ = VO, + v22m2 where UDH is the Debye-Huckel limiting slope (see Table l), VO, is the standard partial molar volume, u22 is a n interaction parameter, and m2 is the solute molality. The data for OAOHCl in the premicellar region can be fitted with the same relation. The CH2 contribution, calculated from the difference between the two values of I$ is 15.9 cm3 mol-l, which is in excellent agreement with the accepted value of 16.0 cm3 mol-1.20 The heat capacity (20) Perron, G.; Desnoyers, J. E. Fluid Equil. 1979,2, 239.
Micellar Properties of OAOHCl in Water
Langmuir, Vol.11, No. 6, 1995 1907
Table 1. Least-Squares Parameters for the Thermodynamic Properties of OAOHCl and TMOHCl in Water at Various Temperatures
propertylunits
2 "C
5 "C
15 "C
(201.51) 210.30 (-3.97) (1.479) 16.97 0.258 (658.9) 248.2 -45 (21.42) (16) (0.258) 126.5
(202.36) 210.87 (-3.29) (1.523) 18.56 0.255 (675.9) 263.1 -11.31 (22.52) (16) (0.255) 89.6
(205.00) 212.76 (-3.08) (1.692) 14.83 0.237 (701.9) 308.4 -12.04 (25.84) (16) (0.237) 42.3
25 "C
35 "C
45 "C
55 "C
(207.29) 214.51 (-1.67) (1.867) 16.09 0.231 (720.0) 375.6 -100.00 (28.94) (16) (0.231) 13.9 5287 3910 (1975) -2693 (16) (0.231) 0.221 0.166 0.102 (0.017) (16) (0.231)
(209.45) 216.05 (-0.94) (2.034) 16.36 0.238 (719.6) 385.5 -100.5 (32.13) (16) (0.238) 9.2
(211.65) 217.70 (-0.70) (2.223) 15.67 0.238 (716.5) 418.9 -165.5 (35.76) (16) (0.238) 25.7
(213.65) 219.38 (0) (2.435) 12.21 0.254 (711.3) 450.5 -197.29 (39.67) (16) (0.254) 40.3
OAOHCl V4cm3mol-I e/cm3 mol-' uzdcm3kg mol-z u ~ ~ / kgUz c m mol3l2 ~ N
milmol kg-I Cg,dJK-I mol-l CFdJ K-l mol-l czdJ K-l kg mol-z CDHIJ K-l kgllz mo131z N
milmol kg-I
R E W J K-l mol-' LPlJ mol-l lzdJ kg molP ~ D H J kgUzmoP2
1PdJ kg moP2 N
milmol kg-l E 3 m 3K-l mol-I EP/cm3K-l mol-' ezz/cm3K-l kg mol-z t?DH/Cm3K-' kg" mol3" N
milmol kg-l TMOHCl Vdcm3mol-1 v2dcm3kg molP Cg,dJK-l mol-I
95.87 -0.61 102.6 -19.9
C Z K-l ~ Jkgmol-z
1
1
214 212
800 210
208 182 -I
c
?
! 174
178
:zu 182 0.0
t
I
4
\o
a4Br
186 1
0.0
I
1.o
1
1
1
2.0
1
3.0
1
1
4.0
1
1 5.0
md-kg-1
Figure 4. Apparent molar heat capacities of OAOHCl, OAO, mol-kg"
Figure 3. Apparent molar volumes of OAOHCl, OAO, and OABr at 25 "C; full lines are from the mass-action model and x's are from a second series of measurements.
and OABr at 25 "C; full lines are from the mass-action model and x's and +'s are from a second series of measurements.
Therefore, with OAO and OAOHCl, there is no thermodynamic evidence of a postmicellar transition up to 4 mol kg-', as was observed for dodecyldimethylamine oxide12 and some cationic21p22and anionicz3surfactants.
data can be treated the same way and the CH2 contribution obtained is 88.2 J K-l mol-l, which compares very well with the accepted value of 88.20 This additivity test is a (21) Quirion, F.; Desnoyers, J. E. J. ColloidZnterface Sci., 1986,112, good indication of the accuracy of the data. 565. Inside the experimental uncertainty, no breaks in C P , ~ , ~ (22) DeLisi, R.; Milioto, S.; Triolo, R. J. Solution Chem. 1988,17, can be observed at high concentration ofboth surfactants. 673.
Desnoyers et al.
1908 Langmuir, Vol. 11, No. 6,1995
12m
0.25
7
t
7
0.20
-
OABr
OAOHCl
- - - - Simulation - ._
I
0.0
0.4
0.8
1.2
1.6
0.0
mol-kql
The apparent molar expansibilitiesa t 25 "C, = dVz,J dT, were estimated from the difference in apparent volumes a t 15 and 35 "C and are shown for the two surfactants in Figure 5. Expansibilities a t other temperatures can also be estimated by the same method and the trends with concentration are similar. The original data for the enthalpies of dilution are available in the Supplementary Material. The enthalpies of dilution below the cmc were fitted to a polynomial equation a s previously described.z4
+
+ ... (2)
I,,(mf, - ma) ~,,,{(m%)~ - (m;I2>
The values of the apparent molar relative enthalpies, L2,p.,can then be calculated a t any molality in this concentration range from
+
L , , ~= lDHmiJ2 ~,,m,
+ mi + ...
0.8
I
I
12
I
5
rol-kg"
Figure 5. Apparent molar expansibilitiesof OAOHCl and OAO at 25 "C; full lines are from the mass-action model.
mdil = -a,,, = IDH{(m%)1/2 - (m;)'") +
0.4
(3)
The absolute values of L Z ,in~and above the cmc region are then obtained from AH~diland the values of L z ,at ~ m2 calculated from eq 3. They are shown graphically for OAOHCl, OAO, and OABr in Figure 6. 4. Discussion 4.1 Application of a Mass-ActionModel. Two main mass-action models were proposed for fitting the thermodynamic data of ionic surfactants. The model by R o w et al.9 was developped for nonionic surfactants and extended to ionic ones by the addition of a Debye-Huckel interaction term for the dissociated monomers.z5 The model of Woolley and B ~ r c h f i e l d is ~ ~based , ~ ~ on an extended form of the Pitzer equation for electrolytes modified to take into account micellar association. While there are some advantages to the model of Woolley and Burchfield, as will be discussed below, the model of Roux (23) Row-Desgranges, G; Bordere, S.;Row, A. H. J.Colloid Interface Sci. 1994, 162, 284. (24) Fortier, J. L.; Leduc, P.-A.;Picker, P.;Desnoyers, J. E. J.Solution Chem. 1973, 5, 467. (25) Caron, G.;Perron, G.; Lindheimer, M.; Desnoyers, J. E. J.Colloid Interface Sci. 1985, 106, 324. (26) Burchfield, T.; Woolley, E. J. Phys. Chem. 1984, 88, 2149. (27) Woolley, E.; Burchfield, T. J. Phys. Chem. 1984, 88, 2155.
Figure 6. Apparent molar relative enthalpies of OAOHCl, OAO, and OABr at 25 "C; broken lines are from the massaction model. et al. is more convenient for a study of the effect of charge on micellization since essentially the same model is applied to both the ionic and nonionic surfactants. The details of the Roux model are given e l ~ e w h e r e . ~ J ~ Since the Debye-Hiickel limiting slopes, YDH, are known for all properties in water,25the only adjustable parameters used in the nonlinear least-squares fit of the volumes are VO,, the infinite dilution standard partial molar volume; l$',the partial molar volume of the surfactant in the micellar form; u22, the pair interaction parameter between two monomers in the premicellar region; N , the aggregation number; and mi the molality a t the inflexion point of the dependence of the fraction of monomers on concentration. This latter parameter is equivalent to the cmc. The corresponding terms for enthalpies are LF, 1 2 2 , N, and mi since Li is by definition equal to zero. Contrary to other apparent molar quantities, L z , of ~ ionic surfactants varies significantly in the postmicellar region due to electrostatic interactions. In the model of Woolley and B ~ r c h f i e l d , these ~ ~ , ~ interactions ~ are accounted for by the extended Pitzer equation for electrolytes. With the present model, these interactions can be taken into account to some extent by the addition of an interaction term in the postmicellar region, Zg. For heat capacities, in addition to the terms C,; C;,, c22, N, and mi, a relaxation term is required to take into account the shift in cmc with temperature:
e
where is the enthalpy of micellization. A similar relaxation term, -Al$'IRT, is also required for expansibilities. 4.2 Partial Molar Quantities and Hydrophobic Hydration. Partial molar quantities can be obtained from the mass-action parameters; Y Z values ,~ are generated a t evenly spaced m2 and YZare calculated from a plot of AY2,JAmZ against the mean molality. These quantities are shown for all the measured properties of OAOHC1, as a function ofmolality, a t 25 "C, in Figure 7. All properties change rapidly in the cmc region and these changes are much larger than the corresponding ones accompanying
Micellar Properties of OAOHCl in Water 216
1
Langmuir, Vol. 11, No. 6, 1995 1909 0
Partial Molar Quantities
028
I\,'\, . .
.. .
-66
I
,
,
,
,
_-400
- - - -CR-2 - _ _ _ ,
,
I
,
micellization in nonaqueous solvents. The thermodynamic quantities of solutes in water are interpreted in terms of solute-solvent and solute-solute interactions. While it is now generally a ~ c e p t e d ~ *that - ~ l the main contribution to the attractive force between alkyl chains causing micellar aggregation of surfactants is classical interactions (dispersion forces, etc.), the observed changes in all thermodynamic properties other than free energies are primarily reflecting the partial loss in hydrophobic hydration of the alkyl chain during micellization. There is also a contribution from the changes in hydration of the counterions if the micelles are not fully dissociated. While most properties level off in the postmicellar region, relative enthalpies of ionic surfactants decrease, and as mentioned above, this decrease is primarily due to ionic interactions with the free counter ion^.^^ In view of the strong interactions in the pre- and postmicellar region, it is not easy to extract enthalpies of micellization is of ionic surfactants from enthalpies of dilution. actually fairly small and this is why there is only a small relaxational contribution to the heat capacity, i.e. a small maximum in the cmc region, except at low temperatures. The pronounced maximum in expansibility is due mostly to the relaxational contribution. 4.3 Temperature Dependence of Micellar Properties. The trends in the properties of OAOHCl with molality are similar to those of OABr, as seen from Figures 3-6. Differences between the two systems are primarily due to the nature and size of the ionic head group. Therefore, OAOHCl behaves as a fairly typical ionic surfactant. The volume data can be fitted without futing any of the basic parameters. Inside the experimental uncertainty, the values of obtained from the model are the same as the value from a n extrapolation of the premicellar data to infinite dilution with eq 1. Similarly, the values of obtained using a pseudo-phase model from a plot of
T,
(28)Desnoyers, J. E.; Jolicoeur, C. In Comprehensive Treatise of Electrochemistry; Conway, B. E., Bockris, J. OM., Yeager, E., Ed.; Plenum Press: New York, 1983;p 1. (29)Shinoda, K. J. Phys. Chem. 1977,81,1300. (30)Kronberg, B.;Costas, M.; Silveston, R. Dispers. Sci. TechnoZ. 1994,15, 333. Engberts, J . B. F. N. Angew. Chem. Int. Ed. EngZ. (31)Blokzijl, W.; 1993,32, 1545. (32)DeLisi, R.;Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Znterface Scz. 1979,71, 147.
~~
0
40
20
I
3
TPC
Figure 8. Temperature dependence of volume parameters of OAOHCl and OAO from the mass-action model; +'s are from the second series of measurements. VZ,,against l / m ~give , ~ comparable ~ results, even though
this model yields the volume in the micellar form at infinite concentration. In order to increase the precision of the parameters, the number of adjustable parameters for the least-squares fit was reduced to three by taking E and u22 from the premicellar data using eq 4. The only parameter which changes noticeably was N . The derived parameters are summarized in Table 1. These parameters are shown as a function oftemperature for OAOHCl and OAO in Figures 8 and 9. The trends in and u22 with temperature (Figure 8) are remarkably similar for OAOHCl and OAO. The standard volume and heat capacity changes corresponding to the reaction
E,c,
OAO + HC1- OAOHCl can be calculated from the present data and the values for HC134935 in water at 25 "C: 6.1 cm3mol-l and 35 J K-l mol-'. The same calculation for TMOHC1, using the literature data for trimethyamine oxide: gives 4.6 cm3 mol-l and 46 J K-' mol-'. Assuming the hydration of HC1 and of OAOHCl to be approximately the same, the relatively large values of these changes in volume and heat capacity suggest that OAO is also strongly hydrated. The value of A e , taken as - VO, - u22, is larger for OAOHCl, in agreement with a significant extent of counterion binding (electrostriction contribution decreases more than The values of and obtained
c).
T
(33)Douheret, G.;Viallard, A. J. Chim. Phys.-Chim.Biol. 1981,78, 85. (34)Fortier, J.-L.: Leduc. P.-A.: Desnoyers, J. E. J. Solution Chem. 1974,3,323. (35)Desnoyers, J. E.; Jolicoeur, C. Modern Aspects ofEZectrochemistry, Bockris, J. OM., Conway, B. E., Eds.; 1969;Chapter 1,p 5 .
1910 Langmuir, Vol. 11, No. 6, 1995
Desnoyers et al.
Table 2. Least-Squares Parameters for the Thermodynamic Properties of OAO and OAOHCl in the Temperature Range of 0 to 60°C: Y = A BT + CT2for T in "C
+
propertyhits
A
OAOHCl B
N (from V Z , ~ ) milmol kg-l VOdcm3 mol-' V 3 m 3 mol-' u2z/cm3kg mol+ Cg,dJ K-l mol-' CFdJ K-l mol-' CZJJK-l kg molP
17.7 2.62 x lo-' 201.03 209.96 -4.08 656.2 236.2 -19.3
-7.3 x 10-2 1.94 x 10-3 2.679 x 10-1 1.868 x lo-' 1.024 x lo-' 3.626 5.777 -1.074
OAO
A
C 3.36 -7.088 -3.005 -5.235 -4.878 -3.557 -4.213
L
++
C 2.170 x -1.053 x -7.058 x -1.7117 x -1.018 x lo-' -1.6843 x lo-' -1.172 x
OAOHCI
vo, = A + BT + CP 0.20
-
0.10 I 0
I
I
I
1
40
20
D -1.467 x
cannot be taken as evidence that the charged and uncharged surfactants have the same size. The values of mi, which are equivalent to cmc values, go through a shallow minimum for OAOHCl, while they decrease regularly with OAO, at least up to 55 "C. These are the expected trends for ionic and nonionic surfactants. It is interesting to note however that a t 25 "C both values of mi are approximately equal, in agreement with the observation of Rathman and Scheuing.15 On the other hand, mi is systematically larger than their quoted cmc values since a different definition is used (the present mi is defined as the inflexion point in the variation of the fraction of monomers with mz). Most of these parameters can be expressed as a seconddegree polynomial in T . For example,
+ r
B
-6.7 x lo-' 17.8 10-5 3.89 x 10-1 -1.1 x lo-' x 178.18 1.945 x lo-' x 2.147 x lo-' 183.70 -6.13 x 2.081 x 10-1 779.7 x 1.047 99.0 x 10-2 15.058 9.92 x lo-' x loT2 60.7
I
I 60
T/OC
Figure 9. Temperature dependence of aggregation numbers and cmc values of OAOHCl and OAO from the mass-action model: +'s are from the second series of measurements.
from the second series of data for OAOHCl, which goes up to 4 mol kg-l, are essentially the same. The value of u22 for the second set of data is slightly less negative and this is related to the changes in the values of N , as will be shown below. The values of N (Figure 9) are essentially the same for OAOHCl and OAO and decrease slightly with temperature. This would be in agreement with most of the studies on the effect of ionization on amine oxides in absence of added ~ a l t . ~ JHowever, ~ J ~ the value of N obtained from the second set of data is significantly larger (24 compared to 16). The aggregation number of OABr, which seems quite similar to that of OAOHCl, is even larger (-40). The magnitude of N depends on the number and distribution of data points in the transition zone. The values of N obtained from the data a t different temperatures were all self-consistent since they are essentially based on the same solutions, i.e. on the same number and distribution of data points. This is not so when the two sets a t 25 "C are compared. Large changes in N will be compensated by smaller changes in u22 and mi, but VO, and T are essentially unaffected. The mass-action model is therefore not very reliable to obtain N. The similarity in magnitude of N of OAOHCl and of OAO is largely fortuitous and
(5)
where A is the value of VO, a t 0 "C. These parameters are given in Table 2 and can be used to calculate A T a t any temperature up to 55 "C. The heat capacity data for OAOHCl are more difficult to fit in view of the additional RELAX term. To get proper convergence, it is necessary to fix a t least one parameter. In a first trial, the values of C;,2 and c22 were obtained from a plot of the data in the premicellar region with an equation equivalent to eq 4. The values of N and of mi obtained by least-squares, were then similar to those from volumes, but the scatter as a function of temperature was larger. In order to obtain the maximum precision on Cg2 and on the RELAX term, N was fixed a t 16, independent of temperature. The values of C:,2 were taken from the extrapolation of the data in the premicellar region and those of mi were taken from the volumes. The parameters c22, CE2, and RELAX were then obtained from the mass-action least-squares fit and are given in Table 1. The temperature dependence of C;,?, Cg2, and c22 are shown in Figure 10 and compared m t h the equivalent data for OAO. As in the case of the volumes, the values of CF2derived from the pseudo-phase model are comparable. The temperature dependence of Cgp2and CK?are again quite similar for OAOHCl and OAO. The intrinsic contribution of OAOHCl should increase both C:,2 and Ct2 by 25-50 J K-l mol-lcompared to OAO (two ions). The heat capacity of small ions or ionic groups is particularly sensitive to the structure-breaking effect.2s If there were no counterion binding, this structural contribution to the hydration of the ionic head would cause a comparable decrease in C:,2 and in Cg2. The similarity in the magnitude of the heat capacity data for both OAOHCl and OAO therefore support the volume data in suggesting that the micelles of OAOHCl are only partly dissociated. Despite a n observed difference in heat capacity for the two sets of data in Figure 4, the values
Micellar Properties of OAOHCl in Water
Langmuir, Vol. 11, No. 6, 1995 1911
I\
0
OAO
-
From@
I
I
0-
t ra'A
-10 L 0
h
A
1
I
I
20
40
0
TPC
Figure 11. Temperature dependence of the enthalpies of micellization of OAOHCl and OAO; closed and open circles are
0
20
40
60
TPC Figure 10. Temperature dependence of heat capacity parameters of OAOHCl and OAO from the mass-actionmodel; +'s are from the second series of measurements.
of and CK2 derived from both sets are in excellent agreement. The parameter c 2 2 is positive and relatively constant with temperature in the case of OAO while it is negative and decreases with temperature with OAOHCl. The deviations from the limiting Debye-Huckel theory are large in the case of relative enthalpies of ions. The temperature dependence of these excess enthalpies are therefore not simple and even the sign of c22 is not easy to predict for ionic solutes. The RELAX term, given in Table 1, is related to and the values of can be calculated from eq 3 and also from the mass-action parameters for L Z ,and ~ its temperature, dependence can be calculated from ACK,. If the functions of micellization are defined at the cmc and not at infinite dilution, then
m
m = LF + lgmi - Zz2mi AC;2 = Cz2 - Cg,2- cZ2mi
(7)
and m(T= )-(To)
+ AC;2(T)
(8)
These directly measured w a r e compared with those derived from the RELAX term for OAOHCl and OAO in Figure 11. The agreement between the two sets ofvalues
calculated from the RELAX term while the full line is from the measured enthalpies at 25 "C and the heat capacities of micellization. is good considering the uncertainty on the RELAX terms. If the functions of micellization are defined a t infinite dilution, then the agreement is not satisfactory a t all. This comparison is a severe self-consistency test for the mass-action model and gives faith in the reliability of the values of these micellization functions.
5. Conclusion The usefulness of thermodynamic data of surfactants is in the evaluation of thermodynamic functions of micellization, in the measurement of interactions in the pre- and postmicellar region and in the identification of postmicellar transitions. For long-chain surfactants, a pseudo-phase model is adequate while for short-chain ones a mass-action approach gives more reliable functions of micellization. On the other hand, while in principle aggregation numbers can be obtained from the mass-action model, in practice the values of N obtained are not very reliable. In the present study, OAO was investigated in the ionic and nonionic form. The cmc values are of the same magnitude, but that of OAOHCl goes through a minimum as expected. The differences in thermodynamic properties of micellization can be explained with a stronger hydrophilic hydration of the ionic head compared with the polar nonionic head and with a partial counterion binding of OAOHCl. Acknowledgment. We are grateful to the Natural Sciences and Engineering Council of Canada for financial support. Supplementary Material Available: Original data on densities, heat capacities per unit volume, and enthalpies of dilution (3 pages). Ordering informationis given on any current masthead page.
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