J . Phys. Chem. 1989, 93, 7677-7680 AMP
= A~R-
-
klk:,k3 1 klCe-hr- mklck2c +-('l+kd' k2c - (kl + k3)
[
+
I)
(12)
In order to reduce the number of adjustable parameters, extinction coefficients of product bands that were used for curve fitting were estimated relative to that of the 812-cm-' trans-2butene oxide band. This was done by assuming that the N=O stretching modes of I, and I, have identical extinction coefficients,
7677
and by taking eCBo (997 cm-I) = 0.8tTB0 (812 cm-l) from gasphase spectra of the two molecules.' Then, absorbance changes measured upon photolysis of ICand I,, displayed in Table 111, were combined with relative intensities of product bands given in Tables I and I1 to give ratios t11(921)/&(837)/cTBo(812)/cMP(933)/ tCB0(997cm-I) = 1.0/2.5/1.0/0.7/0.8. Hence along with the six first-order rate constants only the parameter AoR/cR had to be adjusted. Registry No. I,, 121675-47-6; TBO, 21490-63-1; CBO, 1758-33-4; MP, 78-84-2; (z)-H3CCH=CHCH3, 590-18-1; NO2, 10102-44-0; NO, 10102-43-9.
Physicochemical Properties of Decyldlmethylammonlum Propanesulfonate and Its Homologous Compounds in Aqueous Medium Bianca Sesta Dipartimento di Chimica, Universitci di Roma "La Sapienza", Piazzale A. Moro, 5, Roma 00185, Italy (Received: November 14, 1988; In Final Form: May 1 1 , 1989)
The micellar properties of decyldimethylammonium propanesulfonate and its higher homologues, dodecyl and tetradecyl, have been investigated in aqueous solutions by densimetric, cryoscopic, and viscometric methods. The results were analyzed to find the partial molal volume, the osmotic coefficient, and the relative viscosity. The sudden change in these properties allows us to assign the critical micellar concentration, cmc. Data on the solutesolvent interactions and on the aggregation mechanism were drawn from the behavior of solutions. below and above the cmc.
Introduction
The alkylbetaines are well-known zwitterionic surfactants, widely employed for industrial purposes. Thus, scientific interest has been largely focused on the synthesis, on the analytical determination of purity, and on some useful properties, such as their compatibility with ionic and nonionic surfactants and their high solubility in water.'" Some contributionsb1' have been devoted to understand the thermodynamic behavior and the kinetic mechanism of aggregation in water and in organic solvents. The present research, concerning single dispersed and micellar solutions of alkylsulfobetaines, is on these lines. The investigations have been performed on aqueous solutions of decyldimethylammonium propanesulfonate, and its homologues, dodecyl- and tetradecyldimethylammonium propanesulfonates. The dependence of viscosity on surfactant concentration, the changes of the molar volume at the cmc and the deviations of the osmotic coefficients, above the cmc, have been analyzed to obtain information on the shape and the molecular conformation of micelles, the micellization process being interpreted on the basis of the mass-action model. Experimental Section ( A ) Materials. Calbiochem decyl-, dodecyl- and tetradecyl-
dimethylammonium propanesulfonate, hereafter indicated as B10, B 12, and B14, respectively, were purified by crystallization from acetone and dried under vacuum at 70 OC. They have been (1) Ernst, R. US.Patent 3,280,179, 1966. (2) Konig, H. Fresenius' Z.Anal. Chem. 1972, 259, 191. (3) Ernest,R.; Miller, E. J., Jr. In Amphoteric Surfactants; Bluestein, B. R.;Hilton, C. L., Eds.; Dekker: New York, 1982; p 137. (4) Kato, K.; Kondo, H.; Morita, A.; Esumi, E.; Meguro, K. Colloid Polym. Sei. 1906, 264, 737. (5) Essaddam, H.; Pichot, C.; Guyot, A. Makromol. Chem. 1988, 189, 619. ( 6 ) Tori, K.; Nakagawa, T. Kolloid Z.Z . Polym. 1963, 188, 47. (7) Tori, K.; Kuriyama, K.; Nakagawa, T. KolloidZ. Z.Polym. 1964,191, 48. (8) Herrmann, K. W. J. Colloid Interface Sci. 1966, 22, 352. (9) Swarbrick, J.; Daruwala, J. J. Phys. Chem. 1969, 73, 2627. (10) Jansson, M.; hyong, L.; Stilbs, P. J. Phys. Chem. 1987, 91, 5279. (1 1) Marignan, J.; Gauthier-Fourmier, F.; Appel, J.; Koum, A.; Lang, J. J . Phys. Chem. 1988, 92,440.
checked by thermogravimetric methods to determine the water content. Negligible presence of ionic impurity was detected by conductometric analysis. The absence of organic nonionic impurities was ascertained by tensiometric'* and melting point measurements. Water was purified by Millipore columns and degassed under vacuum. Its conductivity was x = lo-' Q-' cm-' , at 25 OC. ( B ) Methods. Solutions were prepared by weighing or by dilution, starting from concentrated stock of solutions. The samples were recovered overnight before being used. Density measurements were carried out at 25 O C on an A. Paar Model 602 apparatus. Frequencies, 1/ T, were converted into density, d, through the equation The constants A and B were determined with water and NaCl solutions as calibrating 1iq~ids.I~ The densimetric cell was connected to a Heto thermostatic bath, assuring a constancy within 0.01 "C. The temperature was tested by a Paar probe just around the samples. The accuracy of density values was 10" g ~ m - ~ . Ubbelhode viscometers, placed into a Haake thermostatic bath, regulated at 25 f 0.02 OC, were used to measure the flow time of the solvent, to, and of the solutions, t. The relative viscosity, qr, was calculated by the equation assuming v0 = 0.8903 cP. d and do are the density of solution and solvent, respectively. The flow time for water was 185 f 0.2 S.
The lowering of the cryogenic temperature was measured on 0.15 cm3 of solutions by a Knauer osmometer, equipped with a digital display and a Leeds and Northrup recorder. The calibration was performed by NaCl aqueous solutions of known molality. Osmotic references have been obtained from Scatchard and (12) Harrold, S. P. J . Phys. Chem. 1959, 63, 317. (1 3) Wagenbreth, H.; Blanke, W. Die Dichte des Wasser im Internationalen Einheitenrystem und in der InternationalenPraktischen Temperatuskaka oon 1968; PTB-Mitteilungen 6/71; Vieweg: Wiesbaden, FRG,1968; p 412.
0022-3654/89/2093-7677$01 .50/0 0 1989 American Chemical Society
Sesta
The Journal of Physical Chemistry, Vol. 93, No. 22, 1989
7678
I:v -.*-
285. p
284-
L 0
5
2832
-0
I>”
Id
282
4
6
8
10
M Figure 3. Osmotic coefficient, CP, for B10 (0),B12 ( O ) , and B14 (A) in aqueous solutions at different molal concentration, M, from freezing 10’
point lowering.
0
4
2
6
8
M (mol.kg”) Figure 1. Apparent molar volume, CP, and the partial molar volume, as a function of decyldimethylammonium propanesulfonatemolal concentration, M,at 25 “C. Change in volume, Av, = 3.6 cm3 mol-’. 10‘
0.4
1
v2,
--
10
,I
I,
#
,
0 0
1
2
3
4
Figure 4. Function 1/C log qr vs log qr for B10 (0) and B12 (0)at 25
10‘ M (mol. kg-’)
P2,as a function of dodecyldimethylammonium propanesulfonate molal
concentration,M , at 25 “C. Points indicated by A refer to the apparent molar volume of tetradecyldimethylammonium propanesulfonate. Prentiss.I4 The accuracy of the results was within 0.002 O C . The osmotic coefficients, 9,have been calculated by the equation
+ 2.1 X 1OdAP)]/m
2 to2 log q ,
Figure 2. Apparent molar volume, CPv ( O ) , and the partial molar volume,
9 = [2.303 X 55.5(0.004207AT
1
(3)
where m is the molality of the solutions.
“C. In the inset, the trend of relative viscosity, T ~ against , the molar concentration of B10 (0)and B12 (0) is shown.
as molecular aggregation processes, Figure 1. An analogous increase may be found, at very low concentration, for B12 and B14 (Figure 2). An inflection point appears at 4.2 X and at about 3 X lo4 in 9,functions, for B10, 3.8 X B12, and B14, respectively. The partial molal volume, V2,has been calculated from a plot of A(9,m) vs the mean molality, Am, according to Vz = 9,+ d(@,m)/dm (5)
where PM (the molecular weight of the betaines) is 307.6, 335.6, and 363.6 for B10, B12, and B14, respectively. As regards B10-water systems, althought the uncertainty on 0,values could reduce data reliability for the less concentrated solutions, a systematic decrease in the trend 9,vs m is evident, up to about 3 X mol/kg. This behavior, typical for solutes with long hydrophobic chains, has been ascribed to second-order hydration effects.16 By extrapolating function 9,to m = 0, the apparent molal volume at infinite dilution, ano= 28 1.9 cm3 mol-’, was obtained. At an intermediate concentration, the apparent molal volume goes through a minimum, thereafter showing a sudden increase. The last feature is reasonably related to competitive phenomena, such
The trend of function V2(m), for B10 and B12, are also shown in Figures 1 and 2. Considering that VZo= 9 , O = 281.9 cm3 mol-’ for B10 and that the molal volume of the -CH2-CH2- group is 32.2 cm3 mol-l,l7 the partial molal volume of B12 and B14 may be estimated to be 314.1 and 346.3 cm3 mol-I, respectively. The osmotic coefficients, @(m)are listed in Table 11. Because of technical limits, they have been determined in the premicellar region of concentrations only for decylsulfobetaine. For very dilute solutions, the osmotic coefficient increases in an unexpected way with increasing B10 concentrations. A similar anomalous feature has been found for some organic solutes such as tetraalkylammonium and alkylsulfonium halides and for several carboxylates, studied by Lindenbaum.I8J9 An evident lowering of 9 values occurs beginning from m = 4.2 X mol kg-’ close to the inflection point of the 9,function for B10, Figure 3. The O(B12) curve, Figure 3, extrapolated up to the B10 mol kg-I. function, crosses it at about 0.4 X
(14)Scatchard, G.;Prentiss, S.S. J. Am. Chem. SOC.1933, 55, 4355. (15)DeLisi, R.;Perron, G.; Paquette, J.; Desnoyers, J. E. Can. J . Chem. 1981, 59, 1865. (16)Laliberte, L. H.;Conway, B. E. J . Phys. Chem. 1970, 74, 4116.
(17)Traube, J. Samml. Chem. u. Chem. Tech. Vortrage 1899, 4, 255. (18) Lindenbaum, S.;Boyd, G. J. Phys. Chem. 1964,68, 911. (19)Lindenbaum, S. J . Phys. Chem. 1968,12,212;J. Phys. Chem. 1971, 75, 3733.
Results
The apparent molal volumes, a,, listed in Table I, have been calculated “via” the equation 9,= [(do- d)lOOO]/(mddO) + P M / d (4)
Physicochemical Properties of Ammonium Propanesulfonate
The Journal of Physical Chemistry, Vol. 93, No. 22, 1989 7679
of B10, B12, TABLE I: Density, d , and Apparent Molar Volume, and B14 Aqueous Solutions at 25 OC m X 102/mol kg-l d / g cm-3 @,,/cm3 mol-I A@../cm3 mol-' B10 0.1 0.9501 0.997324 28 1.6 0.09 1.3284 28 1.4 0.997426 0.08 2.2341 28 1.4 0.997669 0.07 281.3 2.9632 0.997866 0.07 28 1.7 3.8231 0.998078 0.07 28 1.9 3.9260 0.998098 0.06 282.2 4.1810 0.998 177 0.998210 282.6 0.06 4.2823 283.0 0.04 5.1051 0.998347 0.03 7.2415 0.998832 283.5 0.02 9.1263 0.999244 283.9
TABLE III: Molar Concentration, c, and the Logarithm of the Relative Dynamic Viscosity, q, (cP), for Aqueous Solutions of B10 and B12, at 25 OC 1o2c/mol L-I IO2 log n. 1o2c/mol L-1 IO2 Ion n. B10 2.7911 0.5009 5.5148 1.5108 3.5774 0.6851 5.7103 1.6072 0.7577 6.6963 2.0899 3.8353 4.0816 2.2222 0.8898 7.0351 4.2822 1.0597 7.8291 2.7023 4.4346 1.1401 8.1476 2.9343 1.3174 8.4864 3.3906 4.9898
B12 0.2431 0.3153 0.3469 0.3699 0.3727 0.3973 0.4253 0.4597 0.5063 0.5499 0.8616 1.0577 1.6486 2.7192
0.997130 0.997142 0.997 152 0.997155 0.997156 0.997160 0.997165 0.997168 0.997172 0.997176 0.997228 0.997256 0.997364 0.997536
0.07276 0.1901 0.2871 0.3805 0.5471 0.6912 1.1654 2.0334
0.997082 0.997102 0.997109 0.9971 IO 0.997126 0.99715 1 0.997210 0.9973 13
3 12.2 312.9 313.1 313.6 313.7 314.0 314.3 315.3 316.5 3 17.4 318.2 318.5 318.6 3 19.2
0.5 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1
345.3 346.7 350.3 353.6 353.9 352.5 352.3 352.3
2.7
B14 1.o
0.7 0.6 0.5 0.4 0.3 0.3
TABLE II: Osmotic Coefficient, 0, for B10, B12, and B14 Aqueous Solutions, at Concentration m from the Freezing Point Lowering
@I
m/mol kg-l
deg kg mol-l
0.01767 0.01875 0.02086 0.02232 0.02373 0.02500 0.02670 0.02843 0.03202
0.945 f 0.002 0.986 f 0.002 0.993 f 0.002 0.996 f 0.002 1.001 f 0.002 1.040 f 0.002 1.020 f 0.0015 1.014 f 0.0015 1.009f 0.0014
102m/mol kg-l
deg kg mol-'
0.5612 0.7801
0.210 f 0.0025 0.710 f 0.0025
0.5612 0.6967
0.210 f 0.0025 0.181 f 0.0025
m/mol kg-l
deg kg mol-l
0.03425 0.03562 0.037 27 0.03849 0.04395 0.06005 0.07471 0.09627
1.011 f 0.0014 0.985f 0.0014 0.979 f 0.0014 0.983 f 0.0013 0.956 f 0.0013 0.856 f 0.0012 0.769 f 0.0012 0.606 f 0.0012
IO2m/mol kg-'
deg kg mo1-I
1.5097 3.2229
0.371 f 0.0015 0.184 f 0.0015
1.1333 2.1633
0.111 f 0.002 0.064f 0.0015
@/
B10
@I
@I
B12
B14
The logarithms of the relative viscosity, vr, of B10 and B12 aqueous solutions are listed in Table 111. The trends of vr, as a function of the molar concentration, c, are shown in the inset of Figure 4. To draw information on the hydrodynamic volume, V,,of these surfactants, the experimental results have been fitted according to the equation20 log vr = He/(1 - Qc) (6) H and Q are experimental constants, depending on the hydro(20)Fontell, K. Kolloid Z . Z . Polym. 1971,246, 614.
B12 1.9825 2.3856 3.0031 3.2374 3.6019 3.9186 4.0418 4.2257 4.7926
0.5181 0.6594 0.8515 0.9493 1.0724 1.1571 1.2373 1.2922 1.5821
5.2264 5.3234 5.8167 6.2219 6.6713 7.0156 7.8118 7.9708
1.7326 1.7743 1.9988 2.1561 2.5961 3.0600 3.5229 3.9777
dynamic volume, V,,, and on ion-solvent interactions. Parameter H may be obtained from the intercept by plotting log vr/c against log 7, (Figure 4). The experimental points, concerning B 10 solutions, lie on two intersecting straight lines, the junction point occurring at c = 4.35 X mol/L. The steeper segment, a, refers to single dispersed surfactant, while line b refers to the postmicellar region. The intercepts, H(a) = 0.090 (L mol-I) and H(b) = 0.190 (L mol-I), give the hydrodynamic volumes, according to V,, = (2.303H)/a,
(7)
(ai = 2.5 is the Einstein parameter).
By eq 7, V,(a) = 80 cm3 mol-' and V,,(b) = 180 cm3 mol-', for B10 in the monomeric and in the micellar state, respectively, have been obtained. The upper function in Figure 4, concerning B12, ranges in the presumed postmicellar region and its intercept, H = 0.235, gives V, = 216 cm3 mol-'. Taking into account the molecular weight of such compounds, these volumes appear unrealistically low and appear to be in disagreement with density results. Discussion The trends of molar volume, viscosity, and osmotic coefficient allow us to identify with reasonable reliability the critical micellar concentration, cmc, of the studied surfactants. These cmc values (mol kg-I) are evaluated as follows: B10, 4.21 X B12, 3.8 X B14, 3 X they are in approximately logarithmic sequence As and appear in accordance with Hermann's* reports. The cmc for B12 solutions is also in agreement with the data of Faucomprk et ale2*and Malliaris et al.23 These authors, using NMR and fluorescence techniques, have found cmc(B12) = 3.6 X and mol kg-', respectively. 3.4 X The molar changes in volume, AV2, at the cmc, calculated as the difference in V2(cm3 mol-') extrapolated curves at the critical micellar c ~ n c e n t r a t i o n , ~are ~ -as ~ ~follows: B10, 3.6; B12, 8.2; B14, 10 It is generally accepted that the change of molar volume, AV2, during the micellization, is due to a release of water molecules (21) Shinoda. K. Bull. Chem. SOC.Jon. 1953. 26. 101. (22) FaucomprC, B.;Lindman, B. J.'Phys. Chem.' 1987,91,383. (23) Malliaris, A.; Le Moigne, J.; Sturm, J.; Zana, R. J. Phys. Chem.
1985.89.2109. (24)Desnoyers, J. E.;DeLisi, R.; Perron, G. Pure Appl. Chem. 1980,52, 433. (25) Kale, K. M.; Zana, R. J. Colloid Interface Sci. 1977,61, 312. (26)Vikingstad, E.;Skange, A.; Hoiland, H. J. Colloid Interface Sci. 1978,66, 240.
7680 The Journal of Physical Chemistry, Vol. 93, No. 22, 1989
hydrophobically packed around the alkyl chains of the amphiphiles; thus, the core of micelles, could assume the physical properties of a pure liquid hydrocarbon and the restored water molecules the clustering structure of the bulk. However, surfactants with similar hydrocarbon tails exhibit, at the cmc, quite different features; for instance, AV2 is 5.07 cm3 mol-' for decyltrimethylammonium bromide,277.4 cm3 mol-' for decyldimethylamine oxide,28 and 9.0 cm3 mol-' for sodium dec a n ~ a t e ?whereas ~ Ar2= 4.7 cm3 mol-' was found for B10. This means that the alkyl chain length is only one of the phenomenological parameters influencing the physical properties of such compounds. The interaction of a polar group with the surrounding solvent molecules must play an important role. The sulfobetaines molecules bear hydrogen-bonding functional groups. Part of the solvent molecules could persist at the micelle interface, linked to the amino and sulfonate groups. In this case, a strong hydration of head groups of surfactant molecules may be responsible for the moderate Ar2observed. The aqueous solutions of alkylsulfobetaines exhibit high fluidity and low hydrodynamic volume, if compared with other surfactant systems.3b32 This phenomenon could be related with long-range interactions of polar groups with the structured solvent and consequent breaking effects on water clusters. On the other hand, shape factors, namely, symmetrical globular arrangements of micelles* cannot be neglected. Above the cmc, the smooth decrease of the osmotic coefficient with increasing molality of B10 is as expected on the basis of the mass-action mode1.33-34Then, the progress in the micellization depends on the dynamic equilibrium between monomers, B,, and micelles, B,: nB, B,
-
where n is the aggregation number. The equilibrium constant, K,, may be expressed as Ke = [BnI/ [Bml"
(9)
The terms in square bracked are the molar concentrations. (27) DeLisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J . Colloid Interfoce Sci. 1979. 71. 147. (28) Desnoyek, J. E.; Caron, G.; DeLisi, R.; Roberts, D.; Roux, A.; Perron, G . J . Phys. Chem. 1983.87, 1397. (29) DeLisi, R.; Perron, G.;Desnoyers, J. E. Con. J . Chem. 1980,58,959. (30) Ekwall, P.; Eikrem, H.; Mandell, L. Acto Chem. Scond. 1963, 17, -
9
Sesta
On the basis of the above assumptions, in the postmicellar region monomer and micellar species must coexist and both influence the colligative properties of the solutions. If [B,*] represents the molal concentration of free monomers and [B,*] that of micelles, the cryoscopic behavior of micellar solutions is dependent on the cumulative concentration, [B*] = [B,*] + [B,*], obtained from the lowering in freezing point. The stoichiometric concentration (Le., the total number of betaine moles) is [B] = [B,*] n[B,*]. By subtracting [B*] from [B] [B] - [B*] = n[B,*] - [B,*] = (n - l)[B,*] (10)
+
If the surfactant concentrations are maintained within a decade of values, it can be assumed that the activity coefficients, both for monomeric and micellar species, are constant and, for several surfactant concentrations, a single average value n, which gives the same K , values, may be calculated. In this way, n = 14 mol and K , = 1013 have been obtained for B10. Such treatment is a simplified form of calculation elaborated from several authors3s38 in order to obtain the aggregation number from the osmotic coefficients of micellar solutions. It is based on the assumption that the micelles do not change in size, above the cmc, and the solutions are not polydispersed systems. On the other hand, if the osmotic data are analyzed according to the equation27 0 = l / n + ((1 - l/n)cmc)/m (1 1) elaborated on the basis of the pseudophase mode1,25926939.40 an unrealistic value, Le., n = 5, is obtained. To confirm the validity of this method, cryoscopic data for decyltrimethylammonium bromide in water have been analyzed.27 The obtained aggregation number, n = 20, is in good agreement with n = 22, reported from the authors. Unfortunately, because of the uncertainty on Q values of B12 and B14 a t the cmc, the aggregation number cannot be obtained by cryoscopic methods. Other authors, by different methods, have found aggregation numbers averaging between 69 and 7121,22for B12 in aqueous solution, higher than for B10. The increasing number of n values with the increasing of carbon atoms in the alkyl chains is typical for zwitterionic surfactants and has been interpreted in terms of H B L b a l a n ~ e . ~ , ~ Registry No. Decyldimethylammonium propanesulfonate, 1 2229526-5; dodecyldimethylammonium propanesulfonate, 39536-5 1- 1; tetradecyldimethylammonium propanesulfonate, 9 1949- 19-8.
111.
(31) Ekwall, P.; Holmberg, P. Acta Chem. Scand. 1965, 19, 455; Ibid. 1965, 19, 573.
(32) Sesta, B.; La Mesa, C.; Bonincontro,A.; Cametti, C.; Di Biasio, A. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 798. (33) Hall, D. G.; Pethica, B. A. In Nonionic Surfactants; Schick, M. J., Ed.; Dekker: New York, 1967; Chapter 16. (34) Rosenholm, J. B.; Burchfield, T. E.; Hepler, L. G. J . Colloid Interface Sci. 1980, 78, 1981.
(35) Burchfield, T. E.; Woolley, E. A. J . Phys. Chem. 1984,88, 2149. (36) Deanden, L. V.; Wolley, E. M. J . Phys. Chem. 1987, 91, 2404. (37) Benjamin, L. J . Phys. Chem. 1964, 68, 3575. (38) Persson, B. 0.;Drakenberg, T.; Lindman, B. J . Phys. Chem. 1979, 83, 3011. (39) Shincda, K.; Hutchinson, E. J . Phys. Chem. 1962, 66, 577. (40) Rosenholm, J. B. Colloid Polym. Sci. 1981, 259, 1 1 16.
