520
H. COLL
CuSO4 in solutions of NaC103 and Bu4NC103plotted against the molar concentrations of the added salts. I t can be seen that the curves essentially duplicate those of Figure 1. If anything, assuming constant absorptivity coefficients for CuS04 ion pairs, the demixing effect of Bu4NC103 may be greater than that of Bud-
NETS. Spectra were run in 0.02 M CuS04 containing 0.1 M NaBr and 0.1 M Bu&Br. After rough empirical corrections for absorption by the CuBr+ complex, a t 250 mp, the residual absorbance in NaBr was 0.95 arid in Bu4NBr was 1.35. The same demixirig effect is qualitatively evident in this latter system. Up to this point, it has been assumed that the only significant antagonistic interaction is that between the organic cations and the sulfate anions. However, the remaining ions must also play some part, although it is probably less important in the present cases. The anions chlorate and bromide are water structure-breakers,
with negative viscosity-B coefficients.l 2 The ethanesulfonate ion may also be a structure-breaker, or a weak structure-former of the organic type. A structurebreaking anion would exert a cooperative effect in the sense that it can provide loose water molecules to be organized around the quaternary ammoninm ion.2 The small differences between the ethanesulfonate and chlorate solutions may reflect differences in their compatibilities with the quaternary ammonium ion. One consequence of this hypothesis is that the demixirig effect would be very much smaller in solutions of CuSOl and Bu4NF, since both sulfate and fluoride ions are strong water-structure formers of the chargooriented type. Acknowledgment. We thank Professor S. Petrucci of this department for assistance and helpful suggestions. (12) Reference 10,p 241.
Study of Ionic Surfactants by Membrane Osmometry by H. Coll Shell Devehpmenl Company, Emeryville, California $&OS
(Received .May 26, 1969)
The micellar weight of well-purifiedsodium dodecyl sulfate (NttDDS) was determined by means of an automatic osmometer in 0.03,0.1,and 0.342 ?il aqueous sodium chloride solutioii at 36.5’. The respective average numbers of monomer molecules in the micelles, N , were 58.9, 82.9, arid 115; i n 0.03 .M NaCl at 3l0,N = 63.1. The solvent contained a specified amount of NaDDS in order to repress dissociation of the micelles and to minimize the monomer contribution to the osmotic pressure. The dialytic behavior of YaDDS is discussed, and the tnagnitude of the Staverman reflection coefficient is estimated. Saturation of the aqueous solution with benzene was found to increase N .
Introduction Determination of micellar weights of ionic surfactants in aqueous solutions by conventional absolute methods encounters considerable difficulties. Because of the ionic character, one can hardly obtain meaningful micellar weights from measurements of colligative properties such as vapor pressure lowering. Light scattering’s2 has been used extensively for estimating micellar size. The theoretical difficulty lies in accounting for the extent of interaction between the charged micelle and diffusible ions in solution (counterions, added electrolyte). In all cases certain assumptions have to be made with respect to the (negative) adsorption of diffusible ions on the macro-ion. Assumptioiis which use the concept of “effective charge” to account The Journal of Physical Chemistry
for this adsorption have been criticized. H~ismrzn,~ in his studies on sodium alkyl sulfates by light scattering, has overcome this problem by measuring apparent micellar weights in the presence of dissolved sodium fluoride, chloride, bromide, and iodide, respectively, arid extrapolating the result to zero refractive index iricremerit for the added electrolyte which makes the interaction term v a i ~ i s h . ~This approach appears to be loss controversial than earlier ones. It only contains the (1) W.l’riris and J. J. Hcrrnans, Z’TOC. Kon. .Ved. Akad. W’ctensch., B59,298 (1956). (2) K.J. Mysels and L. 1%.Princen, J . Phys. Chem., 63, 1699 (1959). (3) A . Vrij arid J. Th. G . Overbeek, J . Colloid Sci., 17,570 (1962). (4) €1. F. Huisman, Z‘TOC. Kon. .+fed. Akad. Ifetensch., B67, 367 (1964).
STUDY OF IONIC SURFACTANTS BY MEMBRANE OSMOMETRY
52 1
Experimental Section assumption that the nature of the co-ion has no effect on the micelle. The osmometer used was an automatic recording Determinations of micellar weights of ionic detergents instrument of Shell design" manufactured by Halliby osmometry have not come to our attention. We kainen Instrument Company (Richmond, California). hope to show in the following that this method holds One series of osmotic pressure determinations was made considerable promise provided certain precautions are at 21". Because of the positive temperature control of taken. Here the main problem arises from the conthe instrument, an ambient temperature below 16" was dition of nonequilibrium in the osmometer because of required. Most measurements were, therefore, carried the dissociation of micelles into lower association prodout at the more convenient cell temperature of 36.5". ucts and monomer, which are not retained by the The osmometer membranes were supplied by Schleimembrane. cher and Schuell (Keene, N. H.), For some of the Generally, this problem will be most severe with preliminary measurements we used the less retentive rapidly dissociating micelles and whenever the critical membrane B 19, but all further results were obtained micelle concentration (cmc) is high. Osmometric with B 20 which is the most retentive membrane of this determination of micellar weights of nonionic detergents series made of cellulose acetate. This type is recomin benzene have been reported by McBain and Workmended for use with aqueous solutions. The meming6 on aluminum dilaurate and by Singleterry and branes had been stored in 20% ethanol solution. They WeinbergerR on calcium xenylstearate. Singleterry's were thoroughly rinsed with distilled water before being results agreed well with micellar weights determined by installed in the osmometer. other methods. These measurements, however, were Materials. The sodium dodecyl sulfate was of very favored by the great stability of the micelles (very low high purity. Preparation and measurements of cmc cmc).' Similarly, measurements in our laboratory on under various conditions on this particular sample Aerosol OT (Union Carbide) in toluene by means of a of surfactant have been discussed by Rehfeld.12 Sodquick-responding automatic osmometer gave pressures ium chloride and benzene (the latter used as an additive which slowly declined with time. Extrapolation of the in one series of measurements) were of reagent grade. osmotic pressure to zero time resulted in an apparent To avoid the formation of air bubbles in the osmometer micellar weight between 5000 and 6000. This result cell, all solutions were briefly stirred under reduced is in good agreement with the value reported by Corkill, pressure before being introduced in the osmometer. et u Z . , ~ from vapor pressure osmometry, although some Procedure. Because of the more or less extensive doubts about the magnitude of the Staverman effectg!l0 diffusion of surfactant into and across the membrane, and contributions from nonmicellar solution components each determination of osmotic pressure was preceded remain. by rinsing both sides of the membrane (sample as well Yet, the same easy procedure could not be followed as solvent cell of the osmometer) with several portions of in the case of sodium dodecyl sulfate (NaDDS) in solvent, followed by one or more blank runs (solvent on water. First, in order to suppress the very large second both sides of the membrane). Such runs lasted between virial coefficient in pure aqueous solution, electrolyte 1 and 2 hr, until the constancy of pressure had been (sodium chloride) had to be added to the solution. ascertained. About 8-10 ml of sample solution was But, more seriously, the micelles appeared to be too then transferred to the filling funnel, and the sample unstable (cmc too high) for the experimental osmotic valves were opened. This time was taken as t = 0. pressure to be a reliable measure for the micellar weight. The larger first portion of the solution drained through The experimental pressures ( P ) decreased rapidly with the osmometer flushing out the previous contents of the time, and more so at lower concentrations of surfactant. sample cell. Only the last portion (approximately Extrapolation of P to zero time, and subsequent extrap2 ml) was retained in the sample cell by closing of the olation of the reduced osmotic pressures to c + cmc sample inlet valve. Temperature equilibrium was could not be carried out with any confidence. Morereached within 1-2 min after which the sample outlet over, the contribution of monomeric NaDDS to the osmotic pressure was appreciable and could not be accurately assessed. All these complications could be (5) J. W. McBain and E. B. Working, J . Phys. Colloid Chem., 51, 974 (1947). reduced to tolerable proportions by measuring the (6) C. R. Singleterry and L. A. Weinbarger, J. Amer. Chem. Soc., 73, osmotic pressure against a more dilute solution of Na4574 (1951). DDS with a concentration above the cmc rather than (7) C. R. Singleterry, J. Amer. Oil Chem. SOC.,32,446 (1955). measuring against pure solvent (aqueous sodium (8) J. M. Corkill, J. F. Goodman, and T. Walker, Trans. Faraday Soc., 61, 589 (1965). chloride). The resulting micellar weights agreed well Pays-Bas, 70,344 (1951). (9) A. J. Staverman, Rec. Trav. Chi&%. with Huisman's result^.^ (10) A. J. Staverman, D. T. F. Pals, and Ch. A. Kruissink, J . PolyIn addition, experiments such as those to be described mer Sei., 23,57 (1957). below give some information about the dialysis of (11) F. B. Rolfson and H. Coll, Anal. Chem., 36,888 (1964). micellar substances through membranes. (12) S. J. Rehfeld, J . Phys. Chem., 71, 738 (1967); 74, 117 (1970). Volume 74, Number 8 February 6, 1970
522
H. COLL
valve was closed. The contents of the cell a t this point were under a small negative pressure, so that in all cases the pressure balanced by an approach “from below.” This is the procedure which is generally followed with instruments of this kind. But previous cxperiments had indicated that the exchange of liquid in the cell is not complete. Thus, the pressure reading on a polymer solution preceded by a blank was generally lower by about 4% than subsequent repeat measurements on the same so1ution.l’ Since this effect cannot be studied with membrane-permeating solutes such as NaDDS, we made a series of measurements on aqueous solutions of a dextran fraction of sufficiently high molecular weight. Again, a pressure deficiency of about 4% was observed. Hence, all measurements of experimental osmotic pressure in the present work were corrected by adding 4%. The osmotic pressure was recorded over periods of many hours. The logarithms of the pressures were plotted against time and extrapolated to t = 0 by linear least-square fits. The resulting pressures, Po,were then subjected to least-square fits of the form Po = alc a d , c being the concentration in g/l. The micellar weight was calculated from al, the second viral coefficient from az (see below). In one series of measurements, the solutions of NaDDS were saturated with benzene in order to see whether this additive had a measurable effect on the micellar weight. The influence of benzene on the cmc has been demonstrated by Renfeld.l2 For this purpose, sample as well as blanks were gently stirred for several hours at room temperature with a layer of benzene on top. Great care was taken to avoid emulsification. Turbid solutions were discarded. The greater portion of the aqueous phase was subsequently withdrawn by means of a hypodermic syringe and transferred to to osmometer. The ma.jority of the osmotic pressure measurements were carried out with 2 g/l. of NaDDS present in the solvent. We shall refer to this as “background NaDDS.”
+
Results and Discussion Figure 1 compares osmotic pressure-time curves at diff erent concentrations of sodium chloride. The large deviation from ideality in pure water is evident as the extrapolated pressure at t = 0 is about 10 times as high as the corresponding value in 1% sodium chloride solution. The pressure level at 0.1% sodium chloride lies between the two. The nonlinearity of this particular plot is explained by the monomer-micelle equilibrium. This will be discussed in more detail later on. Sodium chloride was added to the solutions in all subsequent measurements. Effects due to an initial difference of chemical potential of sodium chloride between the osmometer cells were not noticeable because of the The Journal of Physical Chemistry
0.1
3 40
20
Time, minutes
Figure 1. Sodium dodecyl sulfate osmotic pressure a t different sodium chloride concentrations.
relatively rapid diffusion of the salt through the membrane. Critical Micelle Concentration (cmc). The crnc depends on the ionic strength, on the level of impurities, and on temperature. The data of FlockhartI3 indicate that raising the temperature from 21 to 36.5” should increase the cmc of NaDDS in water by approximately 3%. Then, with reference to Huisman’s crnc values4 for varying ionic strength (21’) we obtained the crnc shown in column 3 of Table I. Surface tension measurements gave a cmc of 0.96 0.03 g/l. for 0.03 db sodium chloride a t 36.5”. We note that an accurate knowledge of the C M C is in no way necessary for the purpose of determining the micellar weight by the present method. Osmotic Pressure-Time Curves in the Presence of Background NaDDS. The rapid decrease of osmotic pressure with time (cf. Figure 1) is no longer observed if NaDDS, at concentrations above the cmc, is made a component of the solvent, and hence, at all times is present on both sides of the osmometer membrane. We chose a background concentration of 2 g/l. for most measurements. The observed decline of osmotic pressure was found to be exponential within experimental error (see eq 1).
*
(13)
B.D. Flockhart, J . CoZZoid Sci., 16,484 (l961),
523
STUDY OF IONIC SURFACTANTS BY MEMBRANE OSMOMETRY Table I: Association of Sodium Dodecyl Sulfate in Aqueous Sodium Chloride Solutions Salt concn, mol/l.
T,‘C
0.03 0.03 0.10 0.342
21 36.5 36.5 36.5
g/l.
=
Po exp( - at)
63.1 58.9 82.9 115
18,200 17,000 23,900 33,300
0.90 (0.93) (0.43) (0.18)
Based on ref 4; corrected for 36.5” by adding 3% (cf. ref 13). second virial coefficient. 0 Average of two determinations.
P
Nb
Mb
error, % M
1.1 1.5‘ 0.52 0.29
2.7 2.5 2.7 2.0
M , micellar weight; N , number of monomer molecules in micelle; B ,
16
(1)
Figures 2 and 3 show plots of CY (in reciprocal minutes) as a function of excess concentration (c) of NaDDS in the sample cell. The rate constant CY decreases with increasing salt concentration and background concentration. An increase of NaDDS concentration also lowers CY. This ca,n be explained by the fact that beyond the cmc the micellar concentration rises much faster than the monomer concentration; POis primarily determined by the excess concentration of micelles in the sample cell while -dP/dt is governed by the difference of monomer concentration in the two cells. This interpretation, at the same time, suggests that the exponential decline given by eq 1is not strictly correct. Under the assumption of unchanged transport characteristics of the membrane, a comparison of a, at the same Po and background concentration in the solvent cell, may serve as an indicator for the relative
Standard
B X l./g
0
O.IOONiNaCI, 2 g ’ P N a D D S
0 0.343 M NaCI, 5 g/E NaDDS
12
0 0.343M
-.-
NaCI, 2 g / t NaDDS
Temperature:
36.5OC
I
E
v-
8
X U
4
‘0
4
12
8 Excess Concentration, g/Y
Figure 3. Rate constants of pressure decline, NaDDS.
:E; ( 0
294. NaDDS iii Solveni
0 5 g/Q NaDDS 2 g/!
i n Solvent
NaDDS i n Solvert
Saturated w i t h Benzene
0 P
_j.
8-
stability of the micelles. (In this context “stability” is to be understood entirely in terms of a thermodynamic equilibrium constant. It does not refer to dissociation rates of micelles.) This is illustrated by the decrease of a with increasing concentration of sodium chloride (Figures 2 and 3 ) . In the absence of background NaDDS eq 1 does not hold and the plots of log P us. time deviate markedly from straight lines; the rate constants a at the beginning of the run are also considerably larger than those shown in Figures 2 and 3 . Micellar Weight. The experimental osmotic pressure, P, between sample (containing c co g/l. of NaDDS) and solvent (containing co g/l. of NaDDS) can be expressed as
+
+
+
P = SIRT(C1” - Cl’)/Ml sRT[(c co - Cl”) (co - Cl’)]/M s R B T [ ( c co - C1’’)2 -
+
-
0
0
Excerr Concentration, g/Q
12
Figure 2. lZat,e constants of pressure decline, NaDDS, 0.03 M NaCl a t 36.5’.
+
-
(co - c1‘)21 (2) M I is the monomer weight (formula weight = 288.4), M the micellar weight; c is the excess solute added to the sample solution, cO the background concentration of Volume 74s Number 9 February 6 , 1970
524
H.COLL
NaDDS, CI the monomer concentration. The single prime refers to the contents of the solvent cell, the double prime to the contents of the sample cell. The symbols s1 and s designates the effective Staverman coefficient to account for the pressure deficiency as a result of the solute permeation through the membrane. RT has the conventional meaning, B is the second virial coefficient. The first term in eq 2 expresses the contribution to the osmotic pressure from the difference of monomer concentration in the two cells. The difference is small, however (CI" S c1' E cmc). In the present case, SI was estimated as approximately equal to 0.06 (from measurements on WaDDS solutions below the cmc), and the contribution from the first term should not amount to more than 2% of P (strictly speaking, a factor approaching 2 should appear in front of the monomer term to account for ionic dissociation; then s1 N 0.03). The difference between cl" and c1' is even less significant in the further terms of eq 2. We can therefore write
P
=
sRTc/M
+ s R T B [ c 2+ 24c0 - cmc)]
(3)
Kext, we assume that for the present case s = 1. This will be justified later on. Then, in a conventional plot of reduced osmotic pressure, P/c, os. c we obtain as intercept at c = 0
(P/c),,o
=
RT/M
+ 2RTB(co - cmc)
I 0 Backgrovnd NaDDS = 2 g / a 0 Background NaDDS = 5 g/t (Adjuited to 2 g / t )
0 Saturated with C,H,
2.0
t
.
/I*
Benzene Added (0.03 M NaCI, 36.5'C)
0,L' M = 23,900 N = 83 ( 0 , l M NaCI, 36.5'C)
i.0
0.8
F
N = 115 (0.342M NaCI, 36.5OC)
M 5: 33,300
-
0 I1
2
4
6
8
IO
2
c, 9 P
Figure 4. Sodium dodecyl sulfate (NaDDS) reduced osmotic: pressure us. concentration.
(4)
Since B is obtained from the slope of the plot of reduced osmotic pressure, and the crnc is assumed as approximately known, M can be calculated. Figure 4 shows plots of reduced osmotic pressure obtained under different experimental conditions. The results are summarized in Table I. The constant RT was calculated for the appropriate cell temperature and solvent density, the osmotic pressures being expressed as cm of solvent head. At this point, we shall review the approximations and corrections made in the calculation of the micellar weights. (1)The use of concentrations expressed as g/l. instead of molalities introduces a small error ( 0.96, and the resulting error should be less than 4% ( M too high). The errors from ( 2 ) and (3) will at least partially cancel. (4) A correction of +4% was applied to all pressure readings. This has been discussed in the Experimental Section. ( 5 ) Finally, as discussed, the term 2RTB (CO - cmc) has to be subtracted from ( P / C ) ~ =toO allow calculation of M . This correction term is small, so that an accurate knowledge of B and the crnc is not important. The Journal of Physical Chemistry
2'4
Figure 5 compares the present results with those of Huisman obtained by light ~ c a t t e r i n g . ~The two sets differ by 10 to 20%, the difference being larger at low salt concentrations. From our value for 0.03 M sodium chloride solution at 21" and 36.5" it appears that the temperature effect on M is small, although the low value for B (cf. Figure 6 ) suggests that the result for 21" may be somewhat low. The closeness of weight-average and number-average micellar weights indicates that in the present case polydispersity of the micelles is not very pronounced, if it exists a t all. Measurements with 6 g / l . N a D D S as Background. At two instances 5 instead of 2 g/l. of NaDDS was added to the solvent. The resulting osmotic pressures were corrected for the now larger contributions from the term containing the second virial coefficient to allow a comparison with the data for 2 g/l. background. In the case of 0.342 M sodium chloride the agreement is excellent, while at 0.03 M sodium chloride, on the average, the pressures are higher by approximately 1.7% (the scatter of the points, however, is such that least-square extrapolation yields the same intercept as for 2 g/l. background). As already mentioned, the rate constants, a, were lowered by an increase of background NaDDS. Second Virial Coejicients. Figure 6 shows a comparison of second virial coefficients with the results of H u i ~ m a n . ~Because of the limited number of experi-
STUDYOF IONIC SURFACTANTS BY MEMBRANE OSMOMETRY
0
3.5
Huirmarr’i Rerultr ( Z I T )
36’50c }This Work
A zi0c
3.c
b x
2.9
I
2.(
I
1.:
!
I
I
I l ! I I
I
! I l l l
I
I
0. I Totel Counterion Concentration, mole/!.
Figure 5. Comparison with Huisman’s light-scattering results.
0.11 0.01
I
I
I
I
I I I I I
I
I
I
I I l I l
0. I Concentration NaCI, rnoler/Q
I
Figure 6. Sodium dodecyl sulfate; second virial coefficients.
mental points, an appreciable error in our results is quite possible. A significant effect due to the temperature difference of 15.5” is not likely, and the solid line in Figure 6, equal to B = 8.3 X 10-sm-0.84 (I./g), where m is the molar concentration of sodium chloride,
525
may be taken as a representation of the combined results. Eject of Benzene. Additives and impurities in surfactants often have a pronounced effect on the cmc and on micellar size. The effect of benzene on the cmc of sodium dodecyl sulfate has been reported by Rehfeld.12 We were interested to find out whether osmometry would reveal a corresponding effect on the number of monomer molecules associated in the micelle. For this purpose all solutions (blanks included) were saturated with benzene (see Experimental Section). As shown in Figure 4, appreciably lower osmotic pressures were observed from which can be concluded that the average number of monomers in the micelle increased by roughly 2 5 3 0 % (0.03 M sodium chloride, 36.5”). The results are somewhat erratic, however; they would, in our opinion, be improved by saturating the surfactant solutions with benzene under better controlled conditions (thermostating, saturation via the vapor phase). It is interesting that the rate constants, a, are also appreciably lowcred by the presence of benzene (Figure a), which can again be interpreted in terms of enhanced micellar stability, as this is also indicated by lowering of the in cmc the presence of benzene.12 Staverman Coejicient. S t a ~ e r m a nhas ~ ~shown ~ ~ by arguments of irreversible thermodynamics that a deficiency of osmotic pressure has to be expected whenever the membrane is permeable to the solute. It may be assumed that in the present case the intact micelles are too large for passing through the membrane. Yet, the micelles are in equilibrium with monomer which is capable of diffusing through the membrane. Monomer which has diffused out of the sample cell is replenished by dissociation of micelles, while association to form micelles occurs in the solvent cell once the total concentration there is equal to or higher than the cmc. Thus, from a phenomenological standpoint, a transport of micelles across the membrane takes place. The condition of thermodynamic equilibrium no longer prevails, and we may, therefore, expect the experimental osmotic pressure, P , to be lower than the theoretical equilibrium pressure, II, Le., s = P/II < 1. It may appear desirable to use a very retentive membrane which also holds back the monomer while allowing comparatively easy passage for water and supporting electrolyte. In the first place, such a membrane is not likely to exist. Secondly, a great disadvantage would be the very extensive contribution of monomer to the total osmotic pressure, which may be many times larger than the contribution from the micelles. In order to calculate the micellar weight, a very accurate knowledge of monomer concentration would be required. It would be inadequate to assume the latter to be equal to the cmc. The “leakiness” of the membrane with respect to monomer should therefore rather be Volume 74, Number S PebruarQ 6,1970
526
H. COLL
considered an advantage, although it makes the addition of background surfactant to the solvent necessary. Several attempts have been made to predict theoretically the magnitude of the Staverman coefficient. An example is the equation derived by Vink14
taken as typical for t,he ratio of rate constants, a/a* (Figure 2). Then, from eq 8, s = 0.965. Applying the same argument to the results obtained for 0.342 M sodium chloride solutions where the experimental pressures appeared to be identical, we conclude that s* = s = 1. It should be noted that eq 7 describes P = [I - (0 V Z / V I ) ~ b p~(Z - /at) L~ -I an exponential decline of P. This, in a strict sense, exp(-ad)]RTc/M(l - a/al) ( 5 ) cannot be the correct function for the present situation where nonpermeating micelles are in equilibrium with CY = A ’ L ~ ~ V ~ R T / M (6) permeating monomer. Here, then, may be a further where L11 is the permeation constant of solvent, LZ2 objection against the use of eq 7. Deviations from an exponential decline were not evident within experiis the permeation constant of solute, p is the “drag” mental error, however, whenever the solvent contained (co-transport) coefficient to account for the number of background NaDDS. solvent molecules carried along by the permeating It should be borne in mind that the present applicasolute, v1 and u2 are (partial) specific volumes of solvent tion of Vink’s equation only concerns a limiting case; and solute, respectively, a1and a are rate constants for the purpose is to demonstrate that the Staverman solvent and solute flow, respectively, c is concentration, coefficient, under the present experimental conditions, M , is the molecular weight of the solute, and A’ is an is close to unity. In this special case, we believe the apparatus constant. foregoing approach to be fully justified. If a
