3824
NOTES log cmc
=
AG/2.303RT
+ aDC,/n
(11)
eq 3 gives eq 11, which has the correct form but predicts increase in cmc with increasing C, contrary to experience, since D is positive for the salts in question. Let us next apply eq 7-10 to the conventional pseudophase model, for which eq 12 a p p l i e ~ . ~The resulting expression is eq 13. The sign of the coefficient of C, log cmc = AG/2.303RT
- log fmonoRX
(12)
is now correct, and its magnitude can be compared with log cmc = AG/2.303RT
- (k,RX)monoCs
(13)
estimates of kERXfor the same systems used by Mukerjee to test eq 6. These estimates depend upon the additivity of group contributions to k,.7 The first system is octyl glucoside, for which Mukerjee showed (ksx)mono to be near zero. Thus (ksRX)mono= (ksR)mono in this case, and Mukerjee's estimate of the log cmc us. C, slope via eq 6 applies also to the present model. This was made2 by extrapolating Morrison and Billett's8 IC, values for the lower alkanes in sodium chloride solutions (interpolated to 25") to give k,C8H18 = (ksR)mono = 0.36, vs. 0.35 observed. The second system was octylbetaine (observed slope = 0.13). With ksC8H18 = 0.36, eq 6 requires (k,x)mono - (kax)mio to be -0.23 (X = -CH(N+Me3)COO-). Mukerjee considered this reasonable in view of the k, values for glycine = -0.28 in dilute solution and -0.02 at 2 M glycine (approximately the concentration in the micelle surface). Equation 13 requires (kax)mono = -0.23, equally reasonable in relation to the glycine value. Finally, both equations predict the same average increment per CH2 group in the log cmc us. C, slopes for homologous amphiphiles. This was estimated2 from ref 8 as 0.032 us. a mean observed value of 0.040. All of these estimates, however, should be viewed with caution since the values of (ksR)monoestimated would be more than twice as large if the k, values of Schrier and Schrierl for CH2 and CHI were used. A stringent test must await further experience with k , additivity or direct measurement of (ksRX)mono by distribution experiments. I n summary, the pseudophase model of micelle formation, although serious objections to it have been p r e ~ e n t e d ,accounts ~ reasonably well (in conjunction with the McDevit-Long theory) for the effects of salt on the crnc of nonionic amphiphiles while the mass-law model does not.
(7) E.E.Schrier and E. B. Schrier, J . Phys. Chem., 71, 1851 (1967). (8) T.J. Morrison and F. Billett, J . Chem. SOC.,3819 (1952). The Journal of Physical Chemistry, Vola74?N o . 81, 1970
Salt Effects on the Critical Micelle Concentrations of Nonionic Surfactants
by Pasupati Mukerjee School of Pharmacy, University of Wisconsin, Madison, Wisconsin 63706 (Received June Q, 2970)
Gordon' has criticized the use of the mass-action model of micelle formation in the previous analysis2 of the effect of inorganic salts on the critical micelle concentrations (cmc) of nonionic surfactants and has suggested that the two-phase modela of micelle formation accounts reasonably well for the salt effects. The discussion below is concerned with the nature of the assumptions involved in the application of the massaction model and the limitations of the two-phase model in describing the salt effects. Gordon's criticism of the mass-action model is based on a too literal application of the RiIcDevit-Long equaIf the activity coefficient, f,of tion for the salt e f f e ~ t . ~ a nonelectrolyte solute in a salt solution of molar concentration C, is represented by the equation log f = k,C,, where k, is the salt effect constant, the McDevitLong equation states that k, is proportional to ?$, the partial molal volume of the nonelectrolyte. The RiIcDevit-Long equation provides a better explanation of the salt order than the older electrostatic t h e o r i e ~ . ~ The equation, however, applies only to nonpolar solutes and even for such solutes it predicts k, values which are much larger than experimental values. Subsequent research on salt effects has continued to emphasize their complexity.s I n our previous work,2 although the McDevit-Long equation was cited to provide the rationale for the assumed additivity of the salting-out coefficients of the hydrocarbon chains of the surfactant monomers, the additivity relation actually used was derived as an empirical relation based on the experimental data of Morrison and Billete6 This empirical relation is in no way dependent on the McDevit-Long equation. The important assumption in the previous work that Gordon focuses attention on is that the salt effect on the micelle is mainly due to the effect on the hydrophilic head groups which are exposed to water; i.e., the effect on the hydrocarbon portion of the micelle is small when compared with the combined effect on the hydrocarbon moiety of the constituent monomers. If the McDevit(1) J. E.Gordon, J . Phys. Chem., 74, 3823 (1970). (2) P. Mukerjee, {bid., 69, 4038 (1965). (3) P. Mukerjee, Advan. Colloid Interface Sci., 1, 241 (1967). (4) W.F. McDevit and F. A . Long, J . Amer. Chem. Soc., 74, 1773 (1952);F.A. Long and W. F. McDevit, Chem. Rev., 51, 119 (1952). (5) B. E. Conway, J. E. Desnoyers, and A. C. Smith, Phil. Trans. Roy. Soc. London, 256, 389 (1964); W. L. Masterton and T. P Lee, J. Phys. Chem., 74, 1776 (1970). (6) T.J. Morrison and F. Billet, J . Chem. SOC.,3819 (1952).
NOTES
3825
Long equation is applied without modification, the salting-out of the micellar hydrocarbon core may actually overcompensate for the salting-out of the hydrocarbon portion of the free monomers.’ The assumption above thus seems to be incompatible with the McDevitLong theory. I n defense of the above assumption, as also the AIcDevit-Long theory, it must be emphasized that the surface of the micelle is essentially hydrophilic or polar’ and, therefore, the McDevit-Long equation cannot be applied without modification. Thus, the fact that the polar mannitol, in spite of having a hydrocarbon framework, is actually salted-in very slightly8 by sodium chloride cannot be held against the McDevit-Long theory. Theories of salt effects on polar molecules are unsatisfactory. For the micelles, comparisons with proteins should be relevant. The k, values for prot e i n ~are ~ usually higher than those for small nonpolar solutes such as benzene, but they are very much less than what would be expected from volume ratios by using the XcDevit-Long equation. Fibrinogen, for example, with a molecular weight of 330,000,10has a k, value in NaCl solution of 1.079compared to the value of 0.195 for b e n ~ e n e . ~The k , value of fibrinogen calculated from that of benzene using the volume ratio is about 500. Thus, empirically, to the extent the micellar core with its immediately adjacent protective polar groups can be compared with a compact protein molecule, both containing a distribution of polar and nonpolar groups at the surface, the salt effect on the hydrocarbon part of the micelle with its polar sheath is expected to be small when compared to the combined effecton the hydrocarbon part of the monomers. This, of course, means that the separate accounting of the k, values for the polar and nonpolar parts of micellized monomers, as also for free monomers, on the basis of an additivity relationship,, can only be approximate. Even if the McDevit-Long theory is literally applied, assuming that in its interaction with salt solutions the micellar hydrocarbon behaves like the hydrocarbon chains of the monomers, the above assumption still appears to be reasonably justified. McDevit and Long4 stated quite clearly that their limiting equation is expected to apply only to very small nonpolar solutes and they ascribed the difference between the high k , values predicted for benzene and low values observed to the finite size of benzene. For spherical solutes, they suggested that the theoretical k , value should be reduced b ) when a is an ionic by roughly the factor of a / ( a radius and b the radius of the nonpolar solute. As the micelle radius is much larger than the thickness of the monomeric hydrocarbon chains, this factor alone would reduce the k , value of the micelle very considerably. The a / ( a b) correction factor, or similar factors applicable to nonspherical solutes, suggest that k , may not be proportional to Vi for large solutes. The rough proportionality that is observed experimentally for ordi-
+
+
nary nonpolar solutes such as aliphatic and aromatic hydrocarbons2v1’may be due in part to the fact that these hydrocarbons have similar thicknesses and, therefore, similar distances of closest approach for ions, and similar values of the effective correction factors. It is thus felt that the assumption of a low IC, value for the hydrocarbon part of the micelle, when compared to the combined k, values for the constituent monomers in their unmicellized form, is both theoretically and empirically justified. As regards the two-phase model favored by Gordon,’ it is certainly curious that the model leads to similar predictions for octyl glucoside and alkyl betaines when compared to the mass-action model. This agreement appears to be fortuitous, however. The two models give very different results for alkyl polyoxyethylene type surfactants. Polyoxyethylenes (polyethylene glycols) are known to exhibit strong salt effects.12 The difference between the two models can be shown by numerical calculations for a typical system, a branched nonylbenzene where EO stands for an oxyethylene group. For this surfactant, the salt effect constant, k,, in the equation log cmc = constant - k,Cs,2 has been estimated to be 0.342 from the variation of the cmc in NaCl solution^.'^ The k, value for nonyl benzene itself, estimated from the value of 0.195 for benzene4 and 0.032 for each CH, group,2 is 0.45. For the oxyethylene groups, the k, value must include the values for the CH, groups as also the ether oxygens. The k , value estimated from the solubilities of diethyl ether in NaCl solutions14 is 0.31 a t 25”. When compared to the value of 0.22 for butane,6it is clear that the ether oxygen is salted-out with a k, coefficient of about 0.09, if an additivity relation is employed. For (EO)5o, the calculated k, for the 100 CH, groups alone is 3.2, even if the salting-out of the ether oxygen is ignored. The combined k , value for the monomer should thus exceed 4. The two-phase model thus predicts a k,value of more than 4 as compared to the experimental value of 0.34. The mass-action approach, on the other hand, allows for the cancellation of the salting-out of the oxyethylene groups of the monomers and the micelle.* If the cancellation is exact, the predicted k,n value (0.34) should be the same as the k, value for the nonyl-phenyl (7) A micelle may be appropriately described as “an oil drop with a oolar coat.” a descriotion used for comaact orotein molecules bv Eric Rideal and Irving Langmuir, according to D. A. Phillips, Sci. Amer., 215, 78 (1966). (8) E. J. Kelly, R. A . Robinson, and R. H. Stokes, J. Phys. Chem., 65, 1958 (1961). (9) J. T. Edsall and J. Wyman, “Biophysical Chemistry,” Academic Press, New York, N.Y., 1958, Vol. 1, p 274. (10) C. Tanford, “Physical Chemistry of Macromolecules,” Wiley, New York, N.Y., 1961, p 381. (11) N. C. Den0 and C. H. Spink, J . Phys. Chem., 67, 1347 (1963). (12) F. E. Bailey, Jr., and R . W. Callard, J . A p p L Polvm. Sci., 1, 56 (1959). (13) M. J. Schick, J. CoZloid Sci.,17, 801 (1962). (14) P. C. L. Thorne, J. Chem. Soc., 119, 262 (1921).
The Journal of Physical Chemistry, Val. 7 4 , N o . 21, 1970
NOTES
3826 group, the estimated k, for nonyl benzene being 0.45. Because of the approximate nature of the additivity relationships employed, and the lack of information on how complete the cancellation of the salt effects on the oxyethylene groups are, exact agreements are not to be expected. The mass-action model, however, is clearly superior to the two-phase model. The experimental fact that k, values for the polyoxyethylene type surfactants tend to be independent of the EO chain length1a~'6 also argues against the two-phase model and suggests that the cancellation of the EO chain effects in the salt effects on the cmc is a good approximation in the massaction model. To summarize, although the two-phase and the massaction models give similar results for the salt effects on the cmc's of octyl glucoside and alkyl betaines,' the salt effects on polyoxyethylene type nonionic surfactants are in poor accord with the two-phase model of micelle formation, various arguments against which have been summarized el~ewhere.~The mass-action model, as used earlierj2appears to be better. (15) F. Becher, J. Colloid Sci., 17, 325 (1962).
Evaluation of the Basicity of Methyl Substituted Nitroguanidines by Ultraviolet and Nuclear Magnetic Resonance Spectroscopy
by E. Price, L. S. Person, Y. D. Teklu, Department of Chemistry, Howard University, Washington, D. C. 20001
and A. S. Tompa Applied Science Department, U.S. Naval Ordnance Station, Indian Head, Maryland 20640 (Received M a y 6,1970)
The position of protonation of 1,1,3,3-tetramethyl2-nitroguanidine (TMNG) in strong acid has been shown to occur primarily at the dimethylamino site, b. Lockhart, however, has presented evidence that proto-
b
H&-
II
II
NNC' I N-CH3\ CH3 CH3 TMNG
H--Y/C>-CH, H CHB DMNG
I
H-N
/c\
N-CH3 I A H MNG
Tiie Journal of Physical Chemistry, Vol. 74,No.21,1970
nation occurs primarily a t the nitrimino site, a, in other methyl nitroguanidines such as 1-methyl-2-nitroguanidine (MNG) and l,l-dimethyl-2-nitroguanidine(DMNG). The evidence presented to support protonation at the amino site for TMNG and a t the nitrimino site for MNG and DIVING was based on the proton magnetic resonance spectra of these compounds in concentrated nitric, sulfuric, and hydrochloric acids. In very concentrated acid media, it has also been assumed that these compounds are likely to be diprotonated and that denitration occurs under these conditions. A mechanism for denitration has been suggested. a , 4 H+
fast
H+ fast
A
slow
+
P PH+ PH2++ GH+ N02+ (G guanidine, P nitr~guanidine).~However, the question as to where the first proton adds to the nitroguanidine seems to depend on the type of nitroguanidine and the number of different basic sites in the molecule. For nitroguanidine and symmetrically substituted nitroguanidines, we are limited to only two basic sites excluding the nitro group whereas in unsymmetrically substituted nitroguanidines there are three basic sites. How these basic sites are influenced by methyl substitution and their contributions to the pK, of RtNG and DNING have been discussed by Bonner and LockharL6 However, the pK, and the effect of methyl substitution were not reported for TMNG and 1,3-dimethylnitroguanidine. Now we wish to report the pK, value of TMNG and to further discuss the effect of methyl substitution on the basicity of nitroguanidines. The pK, value of TMNG was determined in concentrated sulfuric acid solutions from ultraviolet absorption data. Tl\ING in water absorbed at 265 mp and followed Beer's law. Upon the addition of TMNG of a definite concentration to sulfuric acid solutions of concentrations ranging from 1 to 29%, the absorption band at 265 mp decreased to a minimum value and remained constant upon increasing the sulfuric acid concentration from 30 to 69%. For sulfuric acid concentrations above 69y0, the absorption band decreased rapidly.6 The absorbance values at 265 mp for solutions of TIMNG in 15 to 61% sulfuric acid were unchanged after three weeks,* and the wavelength was free of medium effectsin the pK, region. We also wish to point out that (1) E. Price, R. D. Barefoot, A. S. Tompa, and J. U. Lowe, Jr., J . Phys. Chem., 71,1608 (1967). (2) J . C. Lockhart, J . Chem. SOC.B , 1174 (1966). 70 (1957). (3) M. L. Hardy-Klein, J . Chem. SOC., (4) R . J. Simkins and G. Williams, ibid., 3086 (1952) ; 1386 (1953). (5) T. G. Bonner and J. C. Lockhart, ibid., 3858 (1958).
(6) All spectral measurements were carried out very rapidly on freshly prepared solutions (10-5 M ) . These solutions were prepared by mixing a suitable quantity of T M N G in water with 10 to 90% sulfuric acid solutions. The procedures were similar to those described by Arnett and Wu.7 (7) E. M. Arnett and C. Y . Wu, J . Amer. Chem. SOC.,82, 5660 (1960). (8) It has been reported that nitroguanidines do not begin to appreciably denitrate until the acid concentration is above 7 0 % ~ ~ ~
