MEMBRANE OSMOMETRY OF SURFACTANTS
3529
where the Dsa are self-diffusion coefficients and D is assumed to be constant. (For real gas mixtures D may vary by approximately 5% over the whole concentration range; for the liquid systems studied in this work D varies markedly with concentration.) The condition that eq 13 and 25 hold has been given by McCarthy andMasone2as
D2 = DsoDsi
(26)
which they show by example is only true for mixtures of very similar gases (e.g. Hz-Dz), for which systems one would expect A to be very close to zero. For the two systems in Table XIV which show positive excess Gibbs energies, use of the Darken relation,20 equation 11, to predict mutual diffusion coefficients ~ values from corresponding values of D T 2 and D T yields which are much too low. For example, when $0 = $1
= 0.5 the value of D computed for the system benzenecyclohexane is 1.624 X lo9- (25% low) and the value computed for the system benzene-n-heptane is 2.271 X (26% low). These results are presumably due to the fact that eq 12 does not hold for these two systems. Indeed the data in Table XI11 show that the ratio R I O ~ / ( R ~ R isI ~ considerably ) less than unity for systems having positive excess Gibbs energies. One would expect the quantity Rlo2/(RoaRlz)to be greater than unity for systems having negative excess Gibbs energies and hence diffusion coefficients predicted by eq 11 to be too great, although this has yet to be tested. Some of the aqueous systems studied by Mills, Albright, and coworkers fall into this class but, as yet, the tracer diffusion coefficients of water in these systems remain undetermined.
Acknowledgment. It is a pleasure to thank Dr. R. Mills of the National University, Canberra, for helpful discussions concerning counting techniques. This work was supported in part by a grant from the Australian Research Grants Committee. (62) K.P.MoCarthy and E. A. Mason, Phys. Fluids, 3, 908 (1960).
Membrane Osmometry of Aqueous Micellar Solutions of
Pure Nonionic and Ionic Surfactants
by D. Attwood,* P. H. Elworthy, and S. B. Kayne School of Pharmaceutical Sciences, University of Strathclyde, Ghsoow, C . I . , United Kiwdorn
(Received M a y 14, 1970)
Membrane osmometry has been used to determine the number-average micellar molecular weights, M,, of the nonionic surfactants n-dodecyl hexaoxyethylene monoether (Clzne) and n-hexadecyl nonaoxyethylene monoether (C16n9)a t a series of temperatures and of the ionic surfactant N-cetyltrimethylammonium bromide (CTAB). Osmotic pressure measurements on systems permeating the osmometer membrane have been corrected using the partition coefficient of the micelles between the membrane and the solution, as determined from diffusion and dialysis measurements. M , values for Clzna a t all temperatures studied were within the limits of error of the corresponding weight-average values, Mu,determined by light scattering, with a mean M J M , ratio over the temperature range of 1.00 (k0.13). Osmometer measurements on CI6n9indicated a threshold temperature T,similar to that reported from light scattering. At temperatures below T,, the MJM, ratio was 1.10 (&0.14). An M, of 10.5 X IO4was determined for CTAB in 0.025 N KBr a t 30°, which is within the limits of error of the light-scattering value.
Introduction Although several determinations of the numberaverage micellar molecular weight, M,, of aqueous surfactant systems have been reported, these have mainly been restricted to surfactants Of a micellar size (M,< 20,000) to be studied by vapor
pressure osmometry. It is only recently that the technique of ~ ~ m b r a osmometry ne has been applied to a study of micellar systems. In a previous paper' we
* To whom correspondence should be addressed. (1) D. Attwood, P. H. Elworthy, and S. B. Kayne, J. Phavm. Pharmacol., 21, 619 (1969).
The Journal of Physical Chemistry, Vol. 74, No. 19, 1970
3530 reported on the use of this technique in the measurement of M , of the nonionic surfactant Cetomacrogol 1000 in aqueous solution. Comparison with the weightaverage micellar molecular weight, M,, from light-scattering determinations indicated a discrepancy of less than 5% between the two average values, which is well within the limits of error of the light-scattering technique. Membrane osmometry has also been used by Coll in a study of the degree of micellization of an ionic surfactant2 and of several commercial nonionic surf actants. This present investigation reports on the further application of this technique to the study of pure ionic and nonionic surfactants and comments on the polydispersity of micellar size in these systems.
Experimental Section Materials. n-Hexadecyl nonaoxyethylene monoether (CI6n9) was prepared by the Williamson ether ,~ from synthesis as described p r e ~ i o u s l y recrystallized anhydrous ether, and chromatographed on neutral alumina using a 25 :24 : 1 acetone :benzene :methanol solvent system. The sample had an ethylene oxide content, as determined by the method of Siggia, et a1.,6 of 62.07% in agreement with the theoretical value (62.05%) and a melting point of 44’ compared with reported values of 436and 45.7”.7 n-Dodecyl hexaoxyethylene monoether (Clznna) was synthesized and chromatographed in a similar manner to that described above. The sample had an ethylene oxide content of 58,6401,in agreement with the theoretical value (58.650/0). The melting point (24.9’) and refractive index ( n 4 0 ~1.4479) are both in agreement with published values (25.2’ and 1.4483, respectively).8 N-Cetyltrimethylammonium bromide (CTAB) was prepared by reacting equimolar quantities of trimethylamine and cetyl bromide in ethanolic solution for seven days at -3”. Extraction with diethyl ether and recrystallization from absolute ethanol yielded a product with a melting point of 237-239” in agreement with literature values (237-243’) . g A commercial sample (B.D.H.) of polyoxyethylene glycol 6000 (P.E.G. 6000) was ion-exchanged in methanol on a mixed bed resin (“Biodeminrolit”). An ethylene oxide determination indicated 135 ethylene oxide units per molecule. Membrane Osmometry. Measurements were made on a Hewlett-Packard 503 high-speed membrane osmometer with variable temperature control. B.19 cellulose acetate membranes (Schleicher and Schuell) were used which were found to retain the micelles of most of the surfactants studied, but which were freely permeable to monomers. It was therefore necessary to achieve, as far as was possible, an equal concentration of monomers on each side of the osmometer membrane, in order to reduce to a minimum the contributions to the osmotic pressure from the monomeric species. Errors The J O U T d of Physieal Chemistry, Vol. 74,No. 19,1970
D. ATTWOOD,P. H. ELWORTHY, AND S. B. KAYNE arising from possible inequality of monomer concentration in the sample and solvent compartments are not, however, likely to be excessive because of the low critical micelle concentrations (cmc’s) of the surfactants used in this investigation. With the nonionic surfactants, osmotic pressure measurements were made against solutions with a concentration, e’, several times the critical micelle concentration and therefore containing approximately the same concentration of monomers as the test solution. With the ionic surfactant, measurements were made in the presence of 0.025 N KBr and in order to establish conditions of Donnan equilibrium each solution was dialyzed against 0.025 N KBr for 2 days. The dialyses were carried out in specially constructed cells using the osmometer membranes as the dialysis barriers, rather than in the osmometer itself. Osmotic pressure readings on the dialyzed solutions were then taken with the dialysates in the solvent compartment of the osmometer and equilibrium readings were obtained within 10 min for all solutions. I n this way several solutions could be dialyzed simultaneously and also for each concentration sufficient dialyzed solution was available t o enable duplicate measurements to be readily made without the lengthy equilibration periods in the osmometer which would otherwise be required to establish Donnan equilibrium. Any changes in the surfactant concentrations resulting from dialysis will be negligible since the cmc is very low. For all systems studied, graphs of osmotic pressure vs. time were obtained in duplicate for each concentration of surfactant solution. For solutions in which the micellar species were shown to be held by the membrane, equilibrium values of osmotic pressure, reproducible to =kO0.02cm of solvent, were obtained. In cases where membrane permeability to the micelles was demonstrated, an extrapolation procedure was employed (see below) and the reproducibility of the extrapolated osmotic pressure was estimated to be k0.1 cm of solvent. The limits of error of the M , value for nonpermeating micellar systems were estimated as *3%. Measurement of the Membrane Partition Coe&ient. The partition coefficient y of the micelles between the membrane and the solution was determined by a comparison of the diffusion and dialysis coefficients of the (2) H.Coll, J . Phys. Chem., 74, 520 (1970). (3) H.Coll, J . Amer. Oil Chem. Soc., 46, 593 (1969). (4) P.H.Elworthy and C. B. Macfarlane, J . Chem. SOC.,537 (1962). (5) 8.Siggia, A. C. Starke, J. J. Garis, and C . R. Stahl, Anal. Chem., 30, 115 (1958). (6) B. A. Mulley in “Nonionic Surfactants,” M. J. Schick, Ed., Marcel Dekker, New York, N . Y., 1967,p 428. (7) J. E . Carless, R . A. Challis, and B. A. Mulley, J . Colloid Sci., 19, 201 (1964). (8) J. M . Corkill, J. F. Goodman, and R . H. Ottewill, Trans. Faraday SOC.,57, 1627 (1961). (9) R. S. Shelton, M. G . Van Campen, C. H. Tilford, H. C. Lang, L. Nisonger, F. J. Bandelin, and H. L. Rubenkoenig, J . Amer. Chem. SOC., 68, 753 (1946).
MEMBRANE OSMOMETRY OF SURFACTANTS
3531
micel1eslo and was used as a measure of the permeability of the membrane to the micellar species. The diffusion measurements were carried out using the porous plate technique.ll The two halves of the d 8 u sion cell were separated initially by a 16-p Sartorius filter which was completely permeable ( y = 1 ) to the ions of the calibrating solute (potassium chloride) and to the micelles of the surfactant under investigation. Stirring of the cell was effected by its eccentric motion as proposed by Hartley and Runnicles.12 The concentrations of KC1 and of the surfactant in the two cell compartments after diffusion were determined by conductivity and refractive index measurements, respectively, and the rate constants for the diffusion of KCI, ( K p ~ c l ) ,and surfactant, ( K p ) were , calculated from
Kp = (2.303/t) log CO/(CI
- cz)
(1)
where co is the initial concentration of solution, and c1 and cz are the solute concentrations in the sample and solvent compartments, respectively, after diffusion for a time, t. The Sartorius filter was replaced by the osmometer membrane, and dialysis measurements were carried out in a similar manner. The partition coefficient was calculated, assuming the membrane to be completely permeable to KC1, from (KpKCI/Kp)Sartorius
?'(KpKCl/Kp)membrane
(2)
The value of y calculated from eq 2 is a weightaverage rather than a number-average value and this may give rise to error in the M , values determined for the permeating systems, although this error will not be excessive unless there is a significant polydispersity of micellar size. Since it was not practical to use the same membrane in the osmometer as that used in the determination of y, possible variations of permeability throughout a batch of membranes were investigated. Repeated determinations of K , for a solution of given concentration using a series of different membranes yielded a reproducibility to within *2.7% which indicates a reasonable degree of uniformity of the membranes. I n systems where a dependence of y on surfactant concentration was evident, the required values of y were interpolated from graphs of y vs. concentration. Light Xcattering. The construction and calibration of the Iight-scattering apparatus have been described previ~usly.'~Temperature control was to *0.1" and measurements were made at a wavelength of 4358 A. The surfactant solutions were clarified by ultrafiltration through 0.22-p Millipore filters and the concentration of each solutjon after filtration was determined using a Hilger-Rayleigh interference refractometer. Symmetrical scattering envelopes were obtained for all solutions and M , was calculated from the intercept of plots of K(c - cmc)/ARgo against (c - cmc) where c is concentration of surfactant in g/ml, ARgois the scattering a t 90" to the incident beam in excess of that from a
solution at the cmc, and K is the usual optical constant. For systems in which the light-scattering graphs showed a pronounced upward curvature at low concentrations, M , was calculated from the horizontal portion of the graph as suggested previously. l3 Vapor Pressure Osmometry. Measurements were carried out using a Hewlett-Packard 302 vapor pressure osmometer calibrated with aqueous sucrose solutions of known activity. M , was calculated from the intercept of plots of AR/c against c where AR is the measured resistance difference in ohms.
Results and Discussion Treatment of Osmotic Pressure Data. Previous studies on Cetomacrogol 1000 have shown that in cases where the micelles are completely retained by the membrane, Le., where y approaches zero ( y = 0.003 for Cetomacrogol), the osmotic pressure reaches an equilibrium value after about 10 min and remains constant for several hours. The attainment of an osmotic pressure (constant for 1-2 hr) was consequently taken as the criterion for membrane impermeability. For such systems, the measured osmotic pressure, T, between a sample solution of concentration c g/l. and a solvent of concentration c' g/l. is given by2 T
- c')/M, + RBT[(c - c ' ) ~+ 2(c - c')(c'
= RT(c
- cmc)] ( 3 ) where B is the second virial coefficient and RT has the usual meaning. Hence, plots of n / ( c - c') against (c - c') were extrapolated to c = c' and M , was calculated from the intercept which is given by
(TIC - c'),,,~ - R T / M ,
+ 2RTB(c' - cmc)
(4)
Values of 8.7 X mol/l. and 7.2 X mol/l. are quoteds for the cmc's of Clzne at 25 and 35", respectively, values for the intermediate temperatures were obtained by interpolation. Cmc values for Clan9have not been reported for the temperature range involved in this investigation and calculations were carried out using the value of 2.1 x low6mol/l. quoted14 for 25". The cmc of CTAB in 0.025 N KBr at 30" is reported as being too low for accurate determination by light scattering.15 Since in all the systems studied the correction term 2RTB (c' - cmc) had a negligible effect on the value of AI,, accurate values of the cmc's and the second virial coefficients are not essential. (10) J. L.Gardon and S. G. Mason, J. Polym. Sci., 26, 255 (1957)* (11) R. H.Stokes, J . Amer. Chem. SOC.,72, 763 (1950). (12) G.8. Hartley and D. F. Runnicles, Proc. Roy. Soc., Ser. A , 168, 401 (1938). (13) D.Attwood, J. Phys. Chem., 72, 339 (1968). (14) P. H.Elworthy and C. B. Macfarlane, J. Pharm. Pharmacol., 14, l O O T (1962). (15) H. J. L. Trap and J. J. Hermans, Proc. Kon. Ned. Akad. Wetensch., 58B, 97 (1955). The Journal of Physical Chemistry, Vol. 74, No. 19,1970
3532
D. ATTWOOD,P. H. ELWORTHY, AND S. B. KAYNE
0.lb n
Figure 1. Change of osmotic pressure with time for Ciano (concentration = 43.90 g/L) as a function of temperature, showing membrane permeability at 25": A, 25'; B, 27.5'; C, 30'; D, 32.5'; E, 36'.
-
0.05
-
u
*C
-
W
- "
?D
a
n
C-E
U
> K , for all systems investigated here, eq 5 reduces to 7rt
1.4
10
20
30
40 50 Time (mins.)
60
Figure 2 . Decrease of In (osmotic pressure) with time for aqueous C12ns solutions at 25': A, 58.46 g/l.; B, 43.90 g/l.; C, 38.12 g/L; D, 20.72 g/l.
I n systems where osmotic pressure failed t o attain an equilibrium value, the data were plotted as graphs of In T against time and extrapolated to zero time to yield an apparent initial osmotic pressure, A.. The true osmotic pressure, Tt was calculated using an equation derived by Gardon and Mason.1° T t
= n*/[l
+ K,/K.,I
x [1 - Y - (K,kPWK*WI
The Journal of Physical Chemistry, Vol. 74,No. 10, I070
(5)
=
7r./(l
- Y>
(6)
Plots of m / ( c - c') against (c - c') were extrapolated t o c = c' and M , calculated as described above. As a test of the applicability of this treatment of the osmotic pressure data for permeating solutes, the method was applied in the determination of M , of P.E.G. 6000. A mean value of 0.10 was dekermined for y and an M , of 6.91 X 10aobtained, in reasonable agreement with the values obtained by vapor pressure osmometry (6.12 X loa)and by estimation of the ethylene oxide content (5.96 X 10a). n-Dodecyt Hexaoxyethylene Monoether (CI2n6), As seen from Figure 1, a constant osmotic pressure was not attained at 25" suggesting membrane permeation by the micellar species. This was in contrast to the results at higher temperatures where complete impermeability was demonstrated. Similar graphs were obtained for all other concentrations studied. The data at 25" were treated according to the method of Gardon and Mason. Values of r g extrapolated from the linear plots of In A us. time (Figure 2) were corrected using the partition coefficients given in Table I. Values of A were small, indicating only slight permeation of the membrane. The M , values obtained by extrapolation of plots of ./(e - c ' ) us. (c - e') (Figure 3) are given in
3533
MEMBRANE OSMOMETRY OF SURFACTANTS Table I: Osmotic Pressure Data for C1.m in HzO at 25' Conoentration, g/l.
58.46 43.90 38.12 29.72
Apparent osmotio pressure T ~ , am of solvent
Partition ooefficient, 7
10.35 7.47 6.40 4.82
0,022 0.020 0.020 0.016
Corrected osmotio pressure ~ t , om of solvent
10.58 7.62 6.53 4.90
Table I1 : Number-Average Micellar Weights and Second Virial Coefficients for Clme, Glens, and CTAB
Surfactant
Cms
C m
CTAB in 0.025 N KBr
B x 104, ml-mol
Tempperature, OC
M n X 10-6
25 27.5 30 32.5 36 35 45 50 53.5 30
1.69 2.47 3.43 4.89 6.65 1.39 1.61 4.88 7.66 1.05
g
-*
0.22 0.14 0.03 0.03 0.03 1.25 0.95 0.01 0.09 3.35
Table I1 and compared graphically in 'Figure 4 with M , values from light scattering, including literature values. At all temperatures, the osmotic micellar weights fall within the limits of error (i10%)l7 of those I C
6.1
5.z
5.E
5.4
1 10
20(c-c') g/l
30
40
Figure 5. Variation of reduced osmotic pressure with concentration: A, CTAB in 0.025 N KBr at 30'; B, Clenga t 35'; C, 45'; D, 50'; E, 53.5'.
determined by light scattering. The mean M,/M, ratio over the temperature range studied is 1.00 (*0.13), indicating that the micelles are monodisperse or have a very narrow range of sizes. n-Hexadecyl Nonaoxyethylene Monoether ( C m , ) . At all temperatures studied, equilibrium values of osmotic pressure were attained, indicating impermeability of the membrane to the micellar species. M , values calculated from plots of T / ( C - c') vs. (c - c') (Figure 5 ) , are compared with weight-average values determined by light scattering and with literature values of M,,18 in the form of a plot of log M against temperature (Figure 6). The osmotic measurements indicate an abrupt change of slope of the plot in approximately the same temperature region as was reported from the lightscattering study of this compound. Below this threshold temperature, T , the M , values were lower than the corresponding M , values but within the combined limits of error of the two techniques. The mean M,/ M , ratio was 1-10 (i0.14)for this temperature region. The results obtained at temperatures exceeding T h are anomalous, the M , values being 20-3001, higher than the values from light scattering. This is probably attributable to the very pronounced temperature dependence of the micellar weight in this region; a dif-
5.2 3
30
35 Temp
OC
40
Figure 4. Log (micellar weight) against t,emperaturefor Clzns: 0 , M , by osmometry; 0,M , by light scattering; X, M , results of Balmbra, et aZ.,le by light scattering.
(16) R.R.Balmbra, J. S. Clunk, J. M . Corkill, and J. F. Goodman, Trane. Faraday Soc., 58, 1661 (1962). (17) J. N.Phillips and K. J. Mysels, J . Phys. Chem., 59, 325 (1955). (18) P . H.Elworthy and C. McDonald, Kolloid-Z. 2. Polym., 195, 16 (1964). The Journal of Physical Chemistry, Vol. 74, No. 19, 1970
D. ATTWOOD, P. H. ELWORTHY, AND S. B. KAYNE
3534
r
.m
-I
5.8
5.6
5.4
5.2
t
5.0
25
30
35
40
45
50
5 5 TernD'C
Figure 6. Log (micellar weight) against temperature for C I ~ : X, M , by osmometry; 0, M , by light scattering; 0, M , results of Elworthy and McDonald'* by light scattering. Limits of error are uncertain for measurements a t temperatures > 4 5 O .
The Journal of Physical Chemistry, Vol. 74, No. 19, 1970
ference of approximately 1" in the temperatures of measurement of M , and M , would account for the observed discrepancy in these values. Errors in M , may also arise due to nonideality, since solutions of a high concentration were required to produce osmotic pressures of a reasonable magnitude because of the high micellar weights involved at these temperatures. Table I1 indicates a decrease in the values of B with increase of temperature which is particularly pronounced as the threshold temperature is exceeded. This is in agreement with the light-scattering results of Elworthy and McDonald,18 although these workers reported negative values of B above Thwhich were not detected here. N-Cetyltrimethylammonium Bromide (CTAB). Osmotic pressure measurements were made at 30" and for each concentration, equilibrium values were rapidly attained showing that Donnan equilibrium conditions had been established. The reduced osmotic pressure vs. concentration graph (Figure 5 ) extrapolated to an M , value of 10.5 x 104 which is within the limits of error of the quotedlS M , of 9.84 X lo4, both values referring to CTAB in 0.025 N KBr. Hence there is no evidence of any significant polydispersity of micellar sine in this system.
Acknowledgment. The authors wish to thank the Science Research Council for the award of a Research Studentship to S. B. K.
