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study with theoretical treatments based on infinite adsorbing planar surfaces and static systems.23 Acknowledgment. The author gratefully acknowl-
edges Mr. J. A. Herbig's encouragement of this work as well as many stimulating discussions with Dr. Hans F. Huber.
Partial Molal Volume Changes during Micellization and Solution of Nonionic Surfactants and Perfluorocarboxylates Using a Magnetic Density Balance
by L. Benjamin Miami Valley Labm-atm-ks, the Procter & Gamble Co., Cincinnati, Ohw
(Received March 24, 1966)
A simple magnetic density balance is described for obtaining partial molal volume data at The data show that the standard volume change of micellization per mole, AVO,, is always positive and becomes increasingly so the longer the alkyl chain length of the dimethylalkylamine oxides (DC,AO). For these compounds AVO, approaches zero at -Ca chain length below which micelles do not form. It is inferred that a part of the alkyl chain near the head group retains its hydration in the micellar state. Solution of the fluorinated molecules studied is attended by more contraction than with their hydrogen counterparts and this leads to larger positive AVO, values.
25" for various nonionic surfactants and perfhorocarboxylates.
Aqueous solutions of compounds partially or totally hydrophobic in character often exhibit unusual thermodynamic properties associated with ordering of water molecules around the solute. Thus the unfavorable positive free energy of solution of, for example, hydrocarbons has favorable enthalpy contributions (hydrogen bond formation) but overriding negative entropy contributions from the resulting water structure. Although such unusual properties had been recognized for some time previously,' the classification of various solutes as structure makers and structure breakers in aqueous solution was first generalized by Frank and Evans. More recently, considerable interest has developed in entropic contributions arising from the breakdown of such water structure during hydrophobic bonding-the nonspecific interaction accompanying the transfer of hydrophobic groups from an Volume aqueous to a less aqueous en~ironment.~-'~ The Journal of Physical Chemistry
changes associated with this process, all positive in nature, have been discussed. 3*18-18 (1) J. A. V. Butler, Trans. Faraday sot., 33, 229 (1937) (2) H. 9. Frank and M. W. Evans, J . Clam. Phys., 13, 507 (1945). (3) W. Kaurmann, Advan. Protein Chem., 14, 1 (1959). (4) I. M. Klotr and S. W. Luborsky, J . Am. C h a . soc., 81, 5119 (1959). (5) H. A. Scheraga, G. Nbmethy, and I. Z. Steinberg, J . Biol. Chem., 237,2506 (1962). (6) G. NQmethy and H . A. Scheraga, J . Phys. Chem., 66, 1773 (1962). (7) E. D. Goddard, C. A. J. Hoeve, and G. C. Benson, ibid., 61, 593 (1957). (8) H. Schneider, G. C. Kresheck, and H. A. Scheraga, {bid., 69, 1310 (1965). (9) W. P. Jencks, Federation Proc., 24, Suppl. 15, S-50 (1965). (IO) C. Tanford, J . Am. Chem. soc., 84, 4240 (1962). (11) L. Benjamin, J. Phys. Chem., 68, 3575 (1964). (12) G. C. Kresheck and L. Benjamin, ibid., 68, 2476 (1964).
PARTIAL MOLALVOLUME CHANGES DURING MICELLIZATION
The present study is of the partial molal volumes of surfactants and other compounds in aqueous solution and how these values change during micellization where hydrophobic bonding is involved, l1 particularly as a function of surfactant alkyl chain length. Data were obtained with a simple magnetic density balance.
\
\
\ I I I I I
I
Experimental Procedure Magnetic Density Balance. Volume changes occurring on micellization are small and require the detection of density changes of the order of 1 in lo6. This was achieved using the apparatus shown in Figure 1 drawn roughly to scale. As in other magnetic density balance^,'^-^^ :t glass float (volume -6 ml) containing a soft iron core is just buoyant in the solution studied at the given temperature and floats against a stop. Thus the float is immersed at all times, eliminating effects due to the air-solution interface. In the conventional procedure the float is attracted by the field of a small solenoid, SI, and the current, io, which just fails to cause the float to move away from the stop, is determined by extrapolation of the measured float velocity as a function of current i. It can then be shown that io2 a pZ3 where p is the solution density. In the present instrument another solenoid has been added, S2, in which a constant current (io = 0.1 amp) is passed in the reverse direction to the current i flowing in &. This has the effect of producing a stationary position of the float at a distance xo above SI. Mechanical movement of the float allows it to oscillate about xo, but at a sufficient height xe above SI the float escapes from the magnetic field. Thus at xo and xe for a given solution of density p and a fixed value of i, the force ( F ) on the float is zero. The magnetic field H, at a point distant z along the axis of a “point” solenoid, or single wire carrying current i, is (2mPi)/[(x2 d2)’”], where d is the solenoid In the present apparatus if I is the separation of SI and SZ, F = koH,(dH,/dx) k z p , or
+
+
that is
In general for a given z value there are thus two i values at which F is zero, corresponding to either the float equilibrium or escape. At a particular i value
3791
I
SMALL MANUAL STIRRING ROD
I
U Figure 1. Magnetic density balance.
(io), however, the quadratic equations, eq 1 and 2, have a singular solution for F = 0, and the positions of equilibrium and escape are coincidental at xoe. In this case i o = -icf2(xoe)/2fi(~oe)
(3)
and
Thus p is seen to be proportional to io when the float is at position x~e. It is worth pointing out that the dimensions and construction of the balance are not critical. A number of balances have been made in which the float size, number of turns in the coils SI and S2, etc., have been varied, giving different sensitivity, range of density, and ease of operation. For a sensitivity of about 1 part in lo6 required in these studies, the coils contain (13) G. NQmethy and H. A. Scheraga, J . Chem Phys., 36, 3401 (1962). (14) K. Shinoda and T. Soda, J . Phys. Chem., 67, 2072 (1963). (15) W. L. Masterton, J . Chem. Phys., 2 2 , 1830 (1954). (16) F. Franks and H. T. Smith, J . Phys. Chem., 68, 3581 (1964). (17) H. Lal, J . Colloid Sci., 8,414 (1953). (18) D . N . Glew, J . Phys. Chem., 66, 605 (1962). (19) A. B. Lamb and R. E. Lee, J . A m . Chem. SOC.,35, 1666 (1913). (20) D. A. MacInnes, M. 0. Dayhoff, and B. R. Ray, Rev. Sci. Instr., 22, 642 (1951). (21) W. Geffcken, C. Beckmann, and A. Kruis, Z . Physik. Chem., BZO, 398 (1933). (22) J. W. Beams and A. M. Clarke, Rev. Sci. Instr., 33, 750 (1962). (23) A. R. Richards, Ind. Eng. Chem., Anal. Ed., 14, 595 (1942). (24) S. G. Starling, “Electricity and Magnetism,” 7th ed, Longmans Publishing Co., 1941, p 228.
Volume 70,Number 1% December 1966
L. BENJAMIN
3792
1
P
0.08-
0.06-
6 i2 (amps2
0.04 -
O t 005
/---"*"*
0.I
015
0.2
0.25
0.02-
i (amps)
Figure 2. Float position us. current for NaCl solutions of concentrations (% w/w) shown. 0
approximately 30 turns wound on a 1-cm diameter. The float can contain a little mercury to aid in correcting for buoyancy while the final adjustment is conveniently made by grinding away some of the glass stem. A cathetometer measures the float position to within 0.05 mm and a potentiometer is used to determine i. Either a constant current device or a reliable storage battery can be used to maintain i,. Experimental Method. The use of eq 4 is illustrated by the curves shown in Figure 2 where xo vs. i curves for various solutions are almost parallel, especially at high xo values where xoe is approached. Because of the steepness of the curves in this region, values of i corresponding to xo values somewhat lower than xOe still satisfy eq 4 and show p to be proportional to i2 as in other magnetic density balances. Examples of this are shown in Figure 3 for NaCl solutions using three x positions for estimating i values (an arbitrary zero for the x scale has been chosen). The balance sensitivity is seen to vary slightly with the x value chosen and the latter should be as close to xoeas possible for eq 4 to be most applicable. The applicability of eq 4 in this way is also seen in Figure 4, where the buoyancy of the float in water is varied by adding platinum wire to the float. Calibration of the float at a given temperature is achieved by measuring the slope in Figure 4. This calibration gives density variations for NaCl solutions in agreement with literature values. The addition of platinum also adjusts the buoyancy of the float for using it in the required density range. The reproducible departure from linearity of the curve in Figure 4 indicates that i values less than 50-60 ma should not be used. Data for protein solutions obtained with a similar balance agree well with those determined pycnometrically.25 The Journal of Physical Chemistry
0:2
0.6
0:4.
6.8
% NaCl (w/w)
Figure 3. Changes in (current)z vs. NaCl concentration for various float positions as shown.
AP = 0.0861A i
0.10-
gm. Pt
0.09-
Figure 4. Float calibration showing change in (current)2 us. weight Pt added to float for a fixed xo position.
A typical run involves measuring a series of curves as in Figure 2 for water and solutions prepared in the cell by adding a strong solution from a buret and manually stirring (Figure 1). Because of the parallel nature of the curves only three or four points about the chosen xo need be obtained and the method is thus rapid. The cell is thennostated at 30.00 f 0.02'. Results typical of surfactant solutions are shown in Figure 5. The partial molal volume, Vz, is derived from such data using eq 5. (25) W.
L. Gagen, Biochemistry, 5 , 2553
(1966).
PARTIAL MOLALVOLUME CHANGES DURING MICELLIZATION
3793
6
where c is the weight per cent concentration and M z the solute molecular weight. An abrupt change in V2 occurs on micellization as can be seen from the change in slope for dimethyldecylamine oxide (DCloAO) at the critical micelle concentration (cmc). The cmc for dimethylhexaclecylammoniopropane sulfonate (DClGAPS) is too low to be discernible by such measurements. An abrupt, small, apparent density change is often measured at extremely low concentrations, as in Figure 5 , and then p changes smoothly at a normal rate. This is probably due to adsorption of the surfactant on the glass float requiring a modification of Archimedes' principle, Le., the displacing body is now the float plus that amount of the adsorbed layer unable to exert buoyancy due to kinetic motion. Crystal Densities. Certain of the dry solutes were powdered in an agate ball mill (in a drybox in the case of the amine oxides) and pressed at 2000 psi into 1.3-cm diameter disks approximately 1 mm thick. This was achieved using a process in which the powder is subjected to a vacuum as normally employed for preparing KBs powder disks for infrared spectroscopy. Disks were then weighed and measured to obtain densities of the solid solute. Values obtained in this way may be a little lower than the true densities because of remaining voids in the pellets. For instance, a value was obtained of 2.663 g/ml for KBr compared to the reported value of 2.75.26 Molal volumes in the crystalline state, I'M, are readily derived from such data. Materials. Deionized water was used and the amine oxides (DC,AO) were prepared in the manner previously de~cribed.~' The preparation of the dimethylalkylphosphine oxides (DC,PO) has also been described28and their purity was assessed as >99% using gas chromatography techniques. Various preparations of dirnethylalkylammoniopropane sulfonates (DC,APS) were used as indicated elsewhere and purities of the samples were estimated as being 99% or better.29 The perfluorocarboxylates were prepared by neutralizing the acids (perfluorobutyric and perfluorocaproic from the Minnesota Mining and Manufacturing Co., and trifluoroacetic and perfluorooctanoic acid from Matheson Coleman and Bell) with sodium or potassium hydroxide. The perfluorooctanoic acid was recrystallized from benzene and the trifluoroacetic acid was distilled prior to neutralization. The sodium perfluorobutyrate was recrystallized from dioxane solution and gently heated to remove the solvent, although nmr spectral data indicated that about 0.2%
0013-
% (w/w) SURFACTANT
Figure 5. Density (proportional to i2) changes of solutions as a function of concentration: 0 , dimethyldecylamine oxide; 0, dimethylhexadecylammoniopropane sulfonate.
(w/w) dioxane remained in the sample. Fluorine magnetic resonance spectra showed that the trifluoroacetate and n-perfluorobutyrate contained no detectable amount of fluorine-containing unidentified impurity, while -5% of a fluorinated impurity (probably branched chain) was present in the n-perfluorocaproate and somewhat greater than 10% of such impurity was present in the n-perfluorooctanoate. The sample of sodium n-butyrate used was obtained from best grade Matheson Coleman and Bell reagent which was recryst,allized from slightly aqueous ethanol. No hydrogen-containing impurities were detectable from the proton nmr spectrum. All samples were vacuum dried over Pz05 prior to use.
Results and Discussion Data of the type shown in Figure 5 give the partial molal volumes shown in Table I for monomer (at infinite dilution) and micellar species (just above the cmc). Also included are the molal volumes, VM, and cmc values as determined where possible from density-concentration plots similar to those in Figure 5 . These cmc values are in agreement with data obtained by other methods (light ~ c a t t e r i n g ,~~a~l ,o~r~i m e t r y , ~ ~ + ~ ~ vapor pressure lowering, and surface tension) for these surfactants. I n some cases monomer or micelle data (26) "Handbook of Chemistry and Physics," 43rd ed, Chemical Rubber Publishing Co., Cleveland, Ohio, 1961. (27) K. W. Herrmann, J . Phys. Chem., 6 6 , 295 (1962). (28) R. G . Laughlin, J . Org. Chem., 30, 1322 (1965). (29) K. W. Herrmann, J . Colloid Sci., in press. (30) L. Benjamin, unpublished data.
Volume 70, Number 12 December 1966
3794
L. BENJAMIN
Table I: Partial Molal Volumes of Crystal, Monomer, and Micelle Species of Surfactants ( d / m o l e ) Surfactant
DC,AO,
n
=
1
7 8 9 10 11 12 DC,PO, n = 8 10 12 DC,APS, n = 8 10 12 16 CF3COONa C3F7COONa
CsFiiCOOK C,Fi&OOK C3H7COONa
68.3 170.5 181.4
7 2 . 2 f0 . 5 171.2 f 1 183.9 f 1 2 0 4 . 0 =t1 216.5 f 1 231.7 f 2 242 f 5 202.7 f 0 . 5 238.1 f 1
205.9 222.4 233.2 194.7 224.6 253.1 243.5 273.3 305.9 371.3
... 246.0 f1 279.0 f1 316.3 f 1
=
... ... 1 7 9 . 4 f3 205.2 f 2 222.8 f 1 241.1 f 1 255.0 f1 207.1 =t2 240.9 f 0 . 5 2 7 3 . 0 f2
2.4 1.1 0.33 0.13 0.045 0.8 0.07
282.9 f 1 321.0 & 1 386.0 f 0 . 5
1.1 0.12
+
82.3
pz (just above cmc) - 8 0 2 (at infinite dilution)
(6)
and the data in Table I show that this is always positive. Furthermore, all literature data for surfactant solutions support this conclusion as can be seen from Table 11. These values are either as reported or have been calculated from published data where indicated. It has been shown for sodium dodecyl sulfate that the positive A V O , value agrees with that calculated from the increase in cmc with increasing pre~sure.~' A thermodynamic process analogous to micellization is the reverse of solution of a liquid phase," Le., where aggregation numbers approach infinity. Thus VW (liq) - Poz values (standard molal volume change of solution, A V O S ) for alcohols, ethylene glycol, and glycerol are also positive when HzO is the solvent.32 These A V O S values increase with the degree of branching as can be seen from Table 111. The data show that branching of the chain increases VM values and also increases 8 0 2 in the case of propanol. Lowering of P2values results from branching with butanol. The agreement between the two sets of data for 1-butanol The Journal of Phglshl Chemistry
Cmc,
% w/w
32.5 f2 7 2 . 2 =IC5 126.3 + 8 1 4 0 . 0 10 5 9 . 9 f4
115.5 171.7
were not obtained because the cmc values were too low or too high, respectively. The estimated errors in v O 2 are largely dependent on the particular range of monomer concentration, i.e., the cmc value. Using conventional standard states for the micellization process,ll the standard molal volume change of micellization, A V O , , is given by A V O ,
f* micelle (30")
is excellent and indicates that A V O S does not vary from 20 to 30". It may also be noted from Table I11 that, whereas A V O S increases by 1.4 ml/mole from methanol to ethanol and from ethanol to 1-propanol, no further increase is observed from 1-propanol to 1-butanol. It has previously been shown" that the standard entropy and enthalpy of solution also tend to show leveling off tendencies with increasing chain length near 1-butanol and such an effect has been held to be consistent with curling of hydrocarbon chains in solution for chain lengths greater than C4-G. Returning to the data in Table I, the A V O , values for the amine oxides are found to increase for longer chain lengths and approach a zero value near the C S - G members. This is evident from Figure 6, where VM data are also seen to approach Poz values near these chain lengths. Transfer of nonpolar molecules such as hydrocarbons from aqueous to nonaqueous environments has been known to occur with an increase in volume due, presumably, to the contraction associated with the water structure surrounding the nonpolar group, the so-called "iceberg" region.2 Such volume increases associated with hydrophobic bonding are consistent with the data in Figure 6 since A V O , is zero at just the chain length below which micelles do not form, even though some trimers, tetramers, etc., may be present a t shorter chain lengths. (31) E. Hutchinson, V. E. Sheaffer, and F. Tokiwa, J. Phys. Chem., 6 8 , 2818 (1964).
(32) E.Nakanishi, Bull. Chem. SOC.Japan, 33, 793 (1960).
PARTIAL MOLALVOLUMECHANGES DURING MICELLIZATION
3795
~ _ _ _ _ ~
~~~
Table 11: Partial Molal Volumes of Monomeric and Micellar Surfactant Species a t 25' Except Where Specified in Superscripts monomer, ml/mole
micelle, ml/mole
Fox
Surfactant
?z
213d 198d 226d 240. 5d 236.
Glucosyltoluene Glucosylethylbenzene Glucosylpropylbenzene Glu cosy1butylbenzene Sodium dodecyl sulfate Sodium decyl sulfate Sodium tetradecyl sulfate Dodecylammonium chloride Dodecyltrimethylammonium chloride Tetradeoyltrimethylammonium chloride Dodecyl sulfonic acid Sodium dodecyl sulfonate Sodium tetradecyl sulfonate Potassium laurate
228 228.781.6 265 . 202.4 192. go*' 81. lo 85. 636
Igepal CO-710" Surfonic ~ - 9 5 ~ Triton X-100' Sodium hutylbenzene sulfonate Sodium octylbenzene sulfonate
31
232d 249. 5d 248. 728 219.5 281. 6 g 6 241ao 29323 32023 239 238. 731.6 277.339.' 217.7 211.20.2 -87.00 -90.4.36 621.5 582.4 581.7
265.726
Butyric acid
Ref
f
e
14
f
f f 14 14 14 17 17 Estd from
1
168 223
9
11
239 179
i 14, h
" Polyoxyethylated nonylphenol, av no. of EO groups = 10.3. Polyoxyethylated nonylphenol, av no. of EO groups = 9.5. Polyoxyethylated octylphenol, av no. of EO groups = 9.7. v 2 values are concentration dependent. Also the 9 " ~ values for glucosyltoluene and glucosylethylbenzene may have been switched in the source publication. E. Hutchinson and C. S. Mosher, J . Colloid Sci., 11,352 (1956). P. Mukerjee, J. Phys. Chem., 66, 1733 (1962). ' J. Grindley and C. R. Bury, J. Chem. Soc., 679 (1929). R. G. Paquette, E. C. Lingafelter, and H. V. Tartar, J . Am. Chem. Soc., 65, 686 (1943). ' C. W. Dwiggins, Jr., R. J. Bolen, and H. N. Dunning, J. Phys. Chem., 64,1175 (1960).
'
Table I11 : Partial Molal Volumes of Alcohols (ml/mole)
Alcohol
Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol 2-Methyl-2propanol Ethylene glycol Glycerol
VY
to*
AVO8
T, OC
40.25d 58.05d 74.37d 76.14d 91.53d 92.35d 91.738 93.98'
37.75 54.15 69.07 70.04 86.2b 87.02" 84.93 85.98
2.5" 3.9" 5.3" 6.1" 5.33 5.33 6.8" 8.0"
15 15 15 15 20 30 20 20
55.64* 73.09"
54.44 70.29
1.20 2.8"
20 20
200-
v,
81
9
ml /mole
/
100;
t
" Ref
32. Estimated from data in ref 32. W. H. Pasfield, J. Phys. Chem., 69,2406 (1965). From data in "International Critical Tables," McGraw-Hill Book Co., New York, N. Y., 1928. e From data in ref 26.
The data in Table IV illustrate the disappearance of micelles at short chain lengths. That AVO, is zero near Cc chain length and increases for longer chains
I
~
2
,
3
.
4
,
5
,
6
,
7
,
8
,
9
,
1011
,
,
12
C otoms
Figure 6. A, crystal molar volumes (25') and partial molal volumes of . , micelle and 0 , monomer species (30') of dimethylalkylamine oxides as a function of alkyl chain length.
suggests that some portion, approximately four to six carbon atoms in length, of the chain next to the head group remains almost unchanged in the micellization Volume 70, Number 1.2 December 1966
L. BENJAMIN
3796
process and contributes little to the volume change associated with the release of "iceberg" water. Nmr data for sodium alkylsulfate solutions support this c o n c l ~ s i o n . ~Such ~ a process is not unreasonable for strongly polar surfactants such as the amine oxides (dipole moment -4.8 D.) which would tend to resist packing and retain maximum hydration. Heat capacity data also support this conclusion.'O For a given chain length above CIOthe cmc of a surfactant is generally higher the more polar the head group (cj., e.g., Table I for Clo species) and the chain length below which micelles do not form decreases the less polar the head group becomes. Thus ionic, zwitterionic, and very polar nonionic surfactants require long chain lengths (C8-C,) for micelle formation, while weakly polar nonionic surfactants (e.g., the phosphine oxides), carboxylic acids, amines, alcohols, etc., form micelles or separate as liquid phases even with short chain length species (>C,). Aggregation numbers of five to ten would seem to be a reasonable requisite for micellization in such a discussion since the cooperative, and therefore critical, nature of the aggregation process decreases markedly in this region." An increase in AVO, with chain length is also observed (see Table 11) for the glucosylalkylbenzenes, the sodium alkylsulfates, and the sodium alkylbenzene sulfonates.
Table IV : Critical Micelle Concentrations and Aggregation Numbers for Amine Oxides Near 25' Chain length
7% W/W
CS
estd -30
CI CS C9
ClO CLI
C*Z
Cmc,
-10 2.4 1.1 0.33 0.13 0.045
15 32
76
Interpretations of AVO, data as outlined above, only in terms of the positive volume change associated with hydrophobic bonding, may be oversimplified for a number of reasons. First, one must consider volume changes which might occur due to decreased hydration of the head group and possible electrostriction effects. If the above interpretation is correct and the head group and adjacent alkyl chain remain essentially unchanged during micellization, such hydration changes should not be an important factor. Secondly, the interior of micelles is under pressure due to the electrostatic forces at the surface.34 Although The Journal of Physical Chemistry
this excess pressure is difficult to estimate in absolute terms for the amine oxides (treating the dipole as two separated charges), calculations based on estimated micelle diameters and aggregation numbers (n) show that this pressure is approximately the same for the Cs and Clz species. Thus volume changes due to compression should be roughly equivalent and not affect differences in AVO, with chain length. Thirdly, the question arises of how efficiently molecules constrained to a spherical micelle configuration can pack together. The increment in V2 per CH2 group in the micellar state is 16-17 ml/mole (cf. Table I), which is in agreement with values for liquid hydrocarbons.26*35*36 A liquidlike hydrocarbon interior for the micelles is therefore strongly indicated. This is supported by heat capacity measurement~~~ and by the observations that V2 values for molecules solubilized in micelles are close to their liquid VM values.37 Thus any inefficient packing leading to voids, say, between head groups, even if it exists, does not appear to change as chain length and micelle size increase. Figure 7 shows a similar increment in Vt per CH2 group for the carboxylates, differences between the sodium and potassium salts being equal to the predicted values at infinite dilution, namely 10.2m l / m ~ l e . ~ ~ The increase in V2 for the micellized carboxylates between 20 and 90" can be seen from the data in Figure 7 to be -5%, which compares with similar increases in micellar V2 values of 3% for sodium dodecyl sulfonate between 40 and 70" (see footnote f of Table II), 4% for butyric acid between 0 and 35" (Table II), 3% for sodium tetradecyl sulfate between 25 and 45",14 and 3% for potassium laurate between 0 and 25" (Table 11). These increases in molar volume are similar to those of comparable liquid h y d r o c a r b o n ~ and ~ ~ , again ~ ~ support the idea of a liquid hydrocarbon interior for the micelle. It is also worth noting, from the data in Table 11, that an ethylene oxide group in the micellar surface has a partial molal volume of 48.9 niI/mole-a reasonable value, close to that of three CH2 groups. It is difficult to interpret differences in V2 (solution) and the crystal V Mvalues because the latter depend on the lattice structure and can show alternation with chain length, some of which is even carried over into (33) J. Clifford, Trans. Faraday Soc., 61, 1276 (1965). (34) A. E. Alexander and P. Johnson, "Colloid Science," Vol. I, Clarendon Press, Oxford, 1949, p 87. (35) F. Krafft, Ber., 15, 1687 (1882). (36) A, K. Doolittle, J. Chem. Em. Data, 9, 275 (1964). (37) W. D. Harkins, R. W. Mattoon, and M. L. Corrin, J. CoEioid Sci., 1 , 105 (1946). (38) H. S.Harned and B. B. Owen, "Physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958, p 361.
PARTIAL MOLAL VOLUMECHANGES DURING MICELLIZATION
0
5
IO
15
C
20
25
atoms
Figure 7. Micellar partial molal volumes of n-alkanoates. A, sodium salts at 20°, estimated from data in K. Hess, W. Philippoff, and H. Kiessig, KoZEoid-Z., 88, 40 (1939); 0 , sodium salts a t go", estimated from data in "International Critical Tables," hIcGraw-Hill Book Co., New York, N. Y., 1928; 0 , potassium salts at go", estimated from data in above ref; 0, potassium laurate at 25';" A, potassium octanoate at 25", D. G. Davies and C. R. Bury, J . Chem. SOC.,2263 (1930); W, sodium octanoate at 18' (using data in footnote d of Table 111). The low temperature data have been displaced downward bj7 50 ml/mole.
the liquid state Vhf values at the melting point.39 I n the present study, VMcrystal values vary approximately linearly with chain length when this is greater than C7. Such linear variation does not extrapolate for DC,AO data to the value for trimethylamine oxide (CI), however (cf. Figure 6), and this may be due to changes in crystal structure between C1 and C, members. Likewise, P:!values do not increase with chain length as rapidly at, longer (>G) chain lengths as in the shorter (Cl--C:7) chain length region and this may result from curling of the longer hydrocarbon chains, as
3797
deduced previously from entropy data. l 1 The higher values of P", and V2 (micelle) compared to VM (crystal) are consistent with a partial melting process since the increase in volume for homologous series of paraffins, alcohols, and carboxylic acids during fusion is of the order of 10-20%.39 Fluorinated Molecules. Thermodynamic data for fluorocarbon surfactants are scarce. Values of V, for monomer and micellar pefiuorooctanoic acid were found by Shinoda and Soda to be 206 and 227.5 ml/ mole at 30°, re~pective1y.l~The value of 8'2 in Table I for the potassium salt of this acid is much lower than expected from the above value and from extrapolation of the data for shorter chain lengths (Table I). This may result from the presence of branched-chain isomers in the sample used, as inferred from the nmr spectrum (see earlier). A larger decrease in volume is associated with the solution of fluorinated molecules than with their hydrogen counterparts as can be seen from the butyrate data (Table I). This in turn is reflected in higher AVO, values for fluorocarbon surfactants. l4 Higher compressibilities of fluorinated chains may explain these effects since heat capacity studies30 do not show fluorinated molecules to order more water in the "iceberg" sense than their hydrogen analogs. The increment in P2(monomer) is approximately 21 ml/ mole of CF2 from C1 to Cg (allowing for V'z(K+ Na+) = 10.2 m l / m ~ l e ~ ~ ) .
Acknowledgments. The author wishes to thank i l k . Ruth Callahan for synthesizing many of the surfactants used and Illr. ?T. E. Gilman for his invaluable experimental assistance. (39) H. Sackmann and F. Sauerwald, 2. Physik. Chem. (Leipzig), 195, 295 (1950).
Volume 70, Number 12 December 1966
