1388
Communications to the Editor
present membranes will store approximately 30 C/g a t room temperature. T h e charged membranes (ca. 0.005 cm thick) retain a potential of about 2.5 V. For purposes of comparison, a commercial mercury battery, rated a t 1.35 V, stores approximately 270 C/g. Taken in this light, the present results appear very promising. O=Linder et al (66°C) O=This work (65.5'C)
Acknowledgment. We hereby acknowledge t h e generous support of t h e National Science Foundation under terms of grant GK 43294.
References and Notes (1) C. Linder and I. F. Miller, J. Phys. Chem.. 76, 3434 (1972)
(2)C.Linder and I. F. Miller, J. Nectrochem. SOC..120, 498 (1973). (3) S.Bini and R. Capelletti in "Electrets", M. M. Perlman. Ed.. Electrochemical Society, N.J., 1973, p 66. (4) E. B. Podgorsak, G. E. Fuller, and P. R. Moran, ref 3, p 172.
College of Engineering University of lllinois at Chicago Circle Chicago, lllinois 60680
19'
'o-*v
10-q
0
Irving F. Miller' Joaquin Mayoral
Received October 28. 7975
I
I
I
I
,
0.2
0.4
0.6
0.8
1.0
MOLE FRACTION PSSNa in P V A Figure 2. Membrane polarization in PVA.
as a function of mole fraction PSSNa
SlOC). Figures 1 and 2 represent the results obtained. Each point reported is an average of a minimum of four experiments involving a t least two separate membranes. T h e average standard deviation was 20.1% while the maximum standard deviation found was 36.4%. Figure 1 is a comparision of the membrane conductance obtained in this work with t h e work of Linder e t al. It should be noted that although the curves have essentially the same shape, the present curve is displaced upward by more than 2 orders of magnitude. This displacement is almost certainly a result of the reduced contact resistance between t h e electrodes and the membranes brought about by t h e presence of colloidal graphite. Figure 2 shows the membrane polarization obtained by integrating the measured current vs. time curves as compared with those of Linder e t al. Again, it should be pointed out t h a t although the curves have roughly t h e same shape, t h e present curve is displaced upward by more than 2 orders of magnitude. T h e fact that the polarization curves now obtained have essentially the same shape as those reported by Linder e t al. indicates that the model formulated to explain those results is still valid. T h e model (involving an electret formation and stabilization mechanism in which an ion became displaced in t h e direction of t h e applied field via a positive feedback between a local field and its reactive field components and the stabilization of these displacements by hydrogen bonding) was dependent on the shape of a polarization curve but not on the absolute values obtained. T h e significance of the values now obtained lies in the very real possibility that membrane electrets of this type might prove to be practical sources of electrical power. On a weight basis the 0.6 mole fraction membrane stores approximately I C/g. Linder found that raising the polarization temperature from 66 to 93 OC increased the polarization of the membranes by about 1.5 orders of magnitude. I t is reasonable to expect, therefore, that if the polarization temperature is 90 "C, t h e The Journal of Physical Chemistry, Vol. 80, No. 72, 7976
Nonideality of Mixing of Micelles of Fluorocarbon and Hydrocarbon Surfactants and Evidence of Partial Miscibility from Differential Conductance Data Publication costs assisted by the Petroleum Research Fund
Sir: Although fluorocarbons and hydrocarbons are individually typical nonpolar substances, they exhibit considerable so much so t h a t departure from ideality in their heptane and perfluoroheptane, for example, are only partially miscible a t room temperature.' We wish to report some critical micellization concentrations (cmc) and differential conductance data on mixtures of sodium perfluorooctanoate (SPFO) with some hydrocarbon chain surfactants in aqueous solution which point out how intense this nonideality effect is in small systems such as micelles. These observations, along with some others recently made regarding the anomalous behavior of partially fluorinated surfactants,* suggest t h a t such nonideality effects may be widespread and may significantly affect the properties of (a) carbon-fluorine compounds in biological systems,3 (b) fluorine-labeled molecules for probing or studying hydrophobic environments of proteins, of enzymes, or of lipid membra ne^,^-^ and, (c) surfactants a t interfaces where fluorocarbon-hydrocarbon interactions are involved. Figure 1 shows the cmc values of mixtures of S P F O with sodium laurate (SL) and sodium decyl sulfate (SDeS), in presence of 0.001 N NaOH added to suppress any hydrolysis. T h e data were obtained from plots of equivalent conductance against t h e square root of the concentration, C, in equivalentsfliter, a procedure particularly useful for mixtures of ionic surfactants.l0 T h e conductance was corrected for the contribution of the NaOH." Its effect on the high cmc values of Figure 1 through the common-ion effect13 may be considered negligible for comparative purposes. Previous studies have shown that the cmc's of binary mixtures of ionic hydrocarbon chain surfactants fall within the range of the values of the individual pure ~ o r n p o n e n t s , ' ~ J ~ - ' ~ and that the mixing of the chain moieties is nearly idea1,l4J5J8
1389
Communicationsto the Editor
1
50F
01
02
03
04
05
06
07
08
09
I IO
Mole Fraction of Hydrocarbon Surfactonf
Figure I.Critical micellization concentrations of mixtures of SPFO with SDeS (A)and SL (0)at 25 'C. Dashed lines show expected values on ideal mixing of the micelles,'* assuming 8(eq 2) = 0.645 for all three components. Curves 1,2,3,and 4 shows expected values for complete demixing of micelles (eq 3).Cwves 2,3, and 4 calculated for 8 = 0.645. Curve 1 calculated for 8 = 0.53.
presumably because their cohesive energy densities are cornparable.' In our work, SL and SDeS were chosen to match t h e cmc of S P F O closely so t h a t the pure surfactants are of comparable hydrophobic character. T h a t the mixing of the carboxyl and sulfate head groups is of relatively little consequence by itself is shown by the cmc of a n equimolar mixture of SL and SDeS, 0.0294 M as compared to 0.0256 M for SL and 0.0315 M for SDeS (all measurements in 0 . 0 1 N NaOH). T h e cmc values expected from ideal mixing of S P F O with SL and SDeS are shown by the dashed line in Figure 1.T h e experimental values, in contrast, are considerably higher, particularly in the middle of the mixing range. T h e higher cmc values are consistent with the positive deviations from Raoult's law t h a t mixtures of fluorocarbons and hydrocarbons exhibit.' Such nonidealities lead to higher activity coefficients of the individual chains in the mixed micelles, resulting in lower stability of t h e mixed micelles as compared to homogeneous micelles. T o examine the magnitude of the nonideality of mixing, the cmc values of the mixed systems were calculated assuming the extreme case of complete demixing of micelles (Figure 1).In such a case, on increasing t h e overall concentration C of a binary mixture of components 1 and 2, micelle formation begins when the concentration of either 1or 2 attains its cmc. If the surfactants are nonionic, the cmc-mole fraction diagram is composed simply of two curved lines for the two components given by t h e equation cmc = cmc,-,/X
(1)
where cmw is the value for a pure surfactant, and X is its mole fraction. For ionic surfactants, however, the counterion of one component affects the cmc of t h e other through the common-ion effect.13 On using t h e well-known relation between t h e cmc and t h e concentration of counterions (Na+) log cmc = A
- R log [Na+]
(2)
where A and B are c ~ n s t a n t s , ' ~t hJ e~cmc of a mixed system is given by cmc = cmco antilog
eg:3 ___
(3)
Equation 3 must be applied to each component separately. A reliable experimental value of 0.645 for A has been obtained for SDeS.l9 We have used this representative ~ a l u e ' ~forJ all ~
i:
103 (molen1
-
Figure 2. Differential conductance. 1 0 3 ( ~ 2 K,)/(CP- CI), plotted against mean concentration C = (C, C1)/2: curve 1, SDS; curve 2, SDS 4- SPFO (SDS mol fraction 0.5); curve 3, SDS 4-SDeS (SDS mole fraction 0.29, data from ref 10); curve 4, SDS -I-SPFO (SDS mole fraction 0.2); curve 5,SPFO; curve 6, SDeS.
+
three surfactants. For SPFO, a lower estimate of 0.53 from limited d a t a for the potassium salt20 is also used to indicate a measure of t h e uncertainty of this calculation (Figure 1 ) . Figure 1 shows t h a t the experimental cmc data are not too far from the calculated case of no mixing of micelles, indicating t h a t the nonideality of mixing is indeed severe. Partially Miscible Micelles and "Phase Separation" i n Small Systems. T h e intensity of the nonideality of mixing indicated by t h e cmc data of Figure 1suggests the interesting possibility of the coexistence of two kinds of micelles, one rich and t h e other poor in t h e fluorocarbon component, under suitable conditions.2 This phenomenon of a "phase separation" in small systems is likely to be of interest for lipid membranes. T h e cmc data by themselves do not provide conclusive evidence on this point. T o investigate this possibility we have studied the conductance of mixtures of sodium dodecyl sulfate (SDS) and SPFO. T h e data are exhibited in Figure 2 as differential conductance, 1o"AK/Ac = 10"(~2K1)/C2 - c1)where Kp and ~1 are the specific conductance a t two adjacent concentrations C2 and C1, plotted against the mean concentration c = (C2 Cl)/2. A K I A C is thus an average value of dK/dC over t h e concentration range C2-Cl. Its importance lies in its ability to indicate clearly the relatively abrupt change in solution composition a t the cmc.10*21 Curves 1 , 5 , and 6 of Figure 2 show data for the three single surfactants, SDS, SDeS, and SPFO, the latter two having similar cmc values. T h e AK/AC typically shows an abrupt drop in the region of the cmc and then attains a nearly constant value: each curve shows one inflection point. Mixtures of the two homologous surfactants, S D S and SDeS, have been studied by Mysels and Otter.'O A representative example (curve 3, Figure 2) shows t h a t here the initial sudden drop a t the cmc is followed by a further gradual decrease over a wide concentration range, corresponding to a slow change in the composition of the mixed micelles and the monomers, before the final leveling off. When SDeS is replaced by SPFO, however (curves 2 and 4, Figure 2), the AKIAC curve changes its character and becomes biphasic: it shows two inflection points before leveling off a t high concentrations. T h e first drop corresponds t o t h e onset of micelle formation, Le., t h e cmc. T h e high value of AK/ACat concentrations following this first transition and t h e presence of a second transition resembling the first one are consistent with the following initially
+
The Journal of Physical Chemistry, Vol. 80,No. 11,1976
1390
Communications to the Editor
suggested for explaining some complex surface tension data.2 T h e micelles t h a t form first are composed primarily of the more hydrophobic SDS component. As the total concentration increases, the concentration as also the fraction of monomeric SPFO increases. At about the second inflection point, the activity of S P F O becomes high enough to form micelles which are composed primarily of the SPFO component. At the highest concentrations, the two kinds of micelles exist together. T h e present work demonstrates that the severe nonidealities of interactions t h a t fluorocarbons and hydrocarbons exhibit are present in small systems such as the micellar systems and that the surfactants show mutual phobia in addition to their well-known hydrophobiciy.* Achnowledgrnent. Acknowledgment is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. We are grateful to Karol *J. Mysels for many helpful discussions.
References and Notes (1)J. H. Hildebrand, J. M. Prausnitz, and R. L. Scott, "Regular and Related Solutions", Van Nostrand-Reinhold, New York, N.Y., 1970. (2)P. Mukerjee and K. J. Mysels. ACS Symp. Ser., No. 9,239 (1975). (3)"Carbon-Fluorine Compounds, Chemistry, Biochemistry and Biological Activities", Ciba Foundation Symposium, Elsevier, New York, N.Y.. 1972. (4)N. J. M. Birdsall, A. G. Lee, Y. K. Levine, and J. C. Metcalfe. Biochim. Biophys. Acta, 241, 693 (1971). (5) (a) N. Muller and R. H.Birkhahn, J. Phys. Chem., 71,957 (1967); (b) N. Muller and R. J. Mead, Jr.. Biochemistry, 12,3831 (1973). (6)E. Zeffren, Arch. Biochem. Biophys.. 137. 291 (1970). (7)K. L. Gammon, S.H. Smallcombe:and J. H. Richards, J. Am. Chem. Soc., 94. 4573 11972). (8) J. T. &rig and k. A. Rimerman, J. Am. Chem. SOC.,94,7558 (1972). (9)6 . D. Sykes, J. Am. Chem. SOC.,91,949 (1969). (10)K. J. Mysels and R. J. Otter, J. ColloidSci., 16,462 (1961). (11) Conductance measurements were carried out in a doughnut type dilution cell, equipped with a magnetic stirrer,'* placed in an oil bath at 25 O C (controlled within f0.015 OC). A Beckman Model RC-18A conductivity bridge, capable of capacitance balancing, was used for resistance measurements. The average precision of the measurements was about 0.03%. (12) K. J. Mysels, J. Phys. Chem.. 65, 1081 (1961). (13)P. Mukerjee, K. J. Mysels, and P. Kapauan. J. Phys. Chem., 71,4166(1967). (14)K. Shinoda, T. Nakagawa. B. Tamamushi. and T. Isemura, "Colloidal Surfactants", Academic Press, New York, N.Y.. 1963. (15)H.Lange, KolloidZ.. 131,96 (1953). (16)F. Tokiwa, K. Ohki, and I. Kokubo, Bull. Chem. Soc. Jpn., 41,2845 (1968). (17)Y. Moroi, K. Motomura. and R. Matuura, J. Colloid Interface Sci., 47,1 1 1
(1974). (18)K. J. Mysels and R. J. Otter, J. ColloidSci., 16,474 (1961). (19)K. J. Mysels and P. Kapauan. J. Colloid Sci., 481 (1961). (20)K. Shinoda and K.Katsura, J. Pbys. Chem., 68, 1568 (1964). (21)G.S. Hartley, ''Aqueous Solutions of ParaffikChain Salts", Hermann. Paris, France, 1936. (22)K. J. Mysels and P. Mukerjee,paper presentedat the 169th National Meeting of the American Chemical Society, Philadelphia, Pa.. 1975.
School of Pharmacy University of Wisconsin Madison, Wisconsin 53706
Pasupati Mukerjee' Alex Y . S. Yang
Received December 8, 1975
The Low Apparent Permittivity of Adsorbed Water in Synthetic Zeolites
tivity of hydrated zeolites NaX and NaY over the frequency range 1-150 MHz; this range is too low at room temperature t o include the dispersion region predicted for the included water from the N M R interpretation yet high enough so t h a t the dispersion frequencies from MaxwellWagner4 and ionic effects4 are exceeded. We thus are able t o estimate the upper limit to the magnitude of the zero frequency dielectric constant for the included water to be 14 for NaX and 21 for N a y . This apparently is a n extreme example of the well-known ability of ions to depress the dielectric constant of water.jP6 In effect, we have extended previous studies on the dielectric permittivity of concentrated electrolyte solutions to the very high concentrations (ca. 18 M) of mobile Na+ ions present in the hydrated crystals. T h e composition of zeolites N a X and NaY are described by the formula^:^ Naa6[(A10*)~6(Si02)106]264H20 (NaX) and Naj6[(A102)js(Si02)1~6] 264H20 ( N a y ) . Their crystal structure consists of an open framework of aluminate and silicate tetrahedra enclosing interstitial voids of approximately 13 8, diameter. Negative charges in the lattice resulting from the substitution of Si4+by A13+ reside on lattice oxygen atoms, and are neutralized by Na+ counterions which, in the fully hydrated crystal, float about in the interstitial voids. A previous N M R study of H20 and D203 adsorbed in N a X has shown that ( I ) the rotational and translational correlation times of the interstitial water molecules are equal and are about twenty times longer than those of bulk water molecules; and (2) the observed proton and deuteron relaxation times can be fit t o theoretical expressions by assuming a relatively narrow distribution of correlation times ( 7 ) of the form:
-
P ( T )d r = (Bfi)exp(-B2z2) dz z = In T*
=
TO
(T/T*)
exp(A/(T - T o ) )
B = a ( T - To) where, for zeolite NaX, over the temperature range 250450 K TO
= 1.86 f 0.6 X
s
a = 4.4 =k 0.1 X lo-" K-'
To = 173 f 3 K A = 650 f 47 K
(The quoted uncertainties are the standard errors in a least-square fit of the N M R data to theoretical expressions.) Observation (1) rules out the possibility of longlived attachments ("binding") between the water and the lattice; (2) can be used to predict the water dipolar dielectric dispersion by integrating the Debye equations over this distribution (Figure la).8 We assume the Debye correlation time ( T D ) to be given by the formula: TD
= 3T*
Publication costs assisted by the Naval Research Laboratory
Sir: Recent nuclear magnetic resonance studies have shown t h a t the included water in synthetic zeolites is in many respects similar to the normal fluid, b u t with a viscosity 20fold higher than that of the "bulk" variety.'-3 In this study we report measurements of the relative dielectric permitThe Journal of Physical Chemistry. Vol. 80,No. 12, 1976
T h e rotational correlation time (and thus, the center frequency of the dielectric dispersion) of the interstitial water molecules is thus closely determined from the NMR data. Note that a t room temperature the frequency range of this study does not include the dispersion region predicted by NMR; all data reported here a t 100-150 MHz thus reflect
