130
H. B. KLEVESS
REFEREXCES ( 1 ) BERNAL, J. D . , A N I J I.'AXKC'CFfKh', E'.: .J. Gen. Physiol. 25, 111 (1941). (2) ROEDEKER,K . : Kolloid-%. 94, 161 (1041). (3) HARKINS, W . D.. hI.%woox-.R. W . q A N I ) CORRIS,31. I,,: J. Xrn. Chem. Soc. 68, 220 (1946). (4) HARKIKS, W .D . , MATTOOX, R. IT., C ~ H R IXI. X ,I,.: J. (:olloid Sci. 1 , 105 (1946). (5) HESS,K . : Fette u. Seifen 49, 81 ( 1 (6) HESS,K . , A N D G ~ - X D E R X ~JX. :S Rer. , 70B,llioo (193i). I O , H . , A N D PHILIPPOF'F, W . : Saturwissenschafteii 26, 184 (1938). ( 6 ) HESS,K., KIESSIG,H . , ANI) I'HILIPPOFF, W.:Kolloid-%.88, 40 (1939). (9) HESS,IC.,KIESSIG,H . , A N D PHILII'POFF, W . : Fette u. Seifen 48, 377 (1941). (10) HUGHES, E . W . , SAWYER, R. AI,, A N I ) \~rzioc;aai),J . I-.:J . Clieni. Phys. 13, 131 (1945). (11) KIESSIG,H.: Iiolloid-Z. 96, 252 (1941). (12) KIESSIG,H . : Kolloid-%. 98, 213 (1942). (13) KIESSIG,H . , A N I ) PHII.IPPOFF, W.: Saturwissenschaften 27, 593 (1939). (14) LONSDALE, K . , A N D SMITH, H . : ,J. Sci. Instrunientsl8, 133 (1941). (15) MALKIN, T., ASD EL SHURBAGY, ?VI. R . : ,J. Chem. Soc. 1936, 1628. (16) XARSDEN,S.S.: Rev. Sri. Instruments 16, 192 (1945). (17) MATTOON, R . W . , STEARNS: R. S.,.IND HARKINS, W.D . : .J. C'hem. Phys. 16, 209 (1947). (18) PALMER, K. J., A N D SCHMITT, F.0.: J. Cellular Comp. Physiol. 1'7, 385 (1941). (19) PHILIPPOFF, W . : Kolloid-%. 96, 255 (1941). (20) Ross, S., .%xnMCHAIN,J. W . : J . Am. Chem. Soc. 68, 296 (1946). (21) STAUFF,J . : Kolloid-%. 89, 224 (1939). (22) STAUFF, J.: Kolloid-%.96, 244 (1841) (abstractrtlj.
13. H I\I,EYESP Geoi qe Htrbert .Jones C'hrvi ical Laborato7 11, 1 *ri 1 t e m i t i l o j ('ti rrago, C'hic uycr , II(i rioL8
Received Airq~tst25, 1947
There are a numl-jer of methods which have been applied to the determination of the critical micelle concentration (('.JI.C'.) of soaps and detergents, hut most of them h a w involved some eytraneous influence. For example, conductivity and transport-number determinations require the application of external electric forces (24,30); the spectral dye method requires the use of dyes (3,13) ; sohihilization studies require the use of dyes or hydrocarbons (10,19, 21); and viscosity involve\ the application of a shearing force (28). S o evidence has been advanced to shov that the application of electric force> as in conductivity measurements hwi any effect on the C.M.C. value, but this possibility muqt not b e precluded. 1
1"Ic~rntcda t the Twenty-hrst Sational ('olloid Symposiun1,
hich was hcltl undrr t h r
aiispiws of the Division of Colloid C'hrniistij of the .Imciican Chrmical Sorirty at Palo
Alto, California, June 18-20, 1947 * Prcsrnt address: Chemical 8r 1'11) ,iral Reseaic 11 Iaboratoriw Fireatonr Tirr 8r n u b b r r C'ompanx I k r o n , Ohio
CRITICAL MICELLE C O S C E S T I L ~ T I O S S
131
It has been shonn (16) that the C.M.C. values determined by ube of the spectral dye method were a t all times smaller than thobe determined by conductivity and by solubility-temperature measurements. In addition, those C'.M.C'. values which were determined by solubilization were also lower than thoqe obtained from other measurements. This is in agreement nith the reported louering of C.1I.C. which occurs upon the addition of a hydrocarbon t o a soap solution (17). The use of refraction to show changes in aggregation has been applied to many colloid systems, and its direct application to the determination of C.1I.C. in the case of sodium lauryl sulfate has been demonstrated by Hess, Philippoff, and Kiessig (11). Further preliminary studies on various fatty acid soaps and on a series of sodium alkyl sulfonates have substantiated the validity of this method (12, 15). S o changes can occur in the equilibrium composition of soap solutions during measurement of refraction, for this method does not involve the addition of an extraneous substance or the application of some external field of force. The instrument used for these measurements was a Rayleigh-Haber-Lowe type of interferometer. The portable model used contains a mirror system which allows the light beam to pass twice through the sample. Thus the effective length of the cell is doubled, increasing the range and accuracy considerably. The effective layer thickness used for most measurements, especially those of dilute solutions, was lG0.290 mm. The entire instrument, except for the operating and recording portion, \vas placed in a thermostat and the temperature was controlled by water circulation. Temperatures did not vary by more than f0.003"C. For a large number of organic compounds the refractive index changes by 1-2 in the fourth place upon a change in temperature of l°C. However, extreme care did not have to be taken as to temperature control in these measurements, for the interferometer is a differential-type instrument, i.e., the optics permit the determination of the difference in refractive indices of solvent and solution simultaneously. Although the temperature a t which the measurements were made did not have to be carefully controlled, it it-as necessary t o determine accurately the temperature of solvent and solution a t the time the readings were made. To insure equilibrium between solvent and solution and the small separate water bath in which the interferometer cell was suspended, dial readings were made a t intervals of 5 min. until constant values irere obtained. The water bath was stirred to hasten this equilibrium. Temperature readings were made with a calibrated Beckmann thermometer. At higher temperatures, use of the standard cover slips supplied n i t h the interferometer cells was not sufficient to prevent evaporation, as was seen by the schlieren effect of the interference bands which are used to measure A n , the difference in refractive index between solution and solvent. A set of cell covers which could be sealed to the glass and metal portion of the interferometer cell by x i x e r which were not solubilized by soap solutions n-as used at higher temperatures. Wax seals were made semipermanent, and the cells were filled through a hole in the cover slip to which a tube with a standard taper at its end n-as attached. By means of this assembly, An values could be determined a t temperature\ as high as io"('. n-ithout any error due to the instability of the inter-
ference bands. h similar assembly proved very satisfactory in previous work with volatile solvents. .Ill dial readings were made in triplicate and the average value used for the determination of An. The instrument was calibrated by the use of standard sodiuin chloride solutions. The usual accuracy in An in these measurements was 2 x 10-7. Kruis and Geffcken ( 5 ) have described prebut cautions and refinements which would allow an accuracy in An of 1 X this degree of accuracy was not necessary in these determinations. The fatty acid soaps were prepared by multiple fractionation of the corresponding esters, followed by saponification and repeated recrystallizations first
Normality (N), FIG.1. Variation i n refractivc indices of sodiunl alkyl sulfonates with concentration. .Irrow denotes break in curve which is thc critical micelle concentration.
from ethanol and finally from acetone. The ;-odium alkyl sulfonates, kindly supplied by Professor H. T. Tartar, are samples similar t o those used by him and his coworkers as reported in their publications (28, 29, 30). The amine hydrochlorides, supplied by the Research Laboratories of Armour and Company, were subsequently recrystallized five times. Tarious properties of these cationic detergents have been described by Ralaton, Hoerr, and others in various papers (24) * The change in degree of aggregation of soap molecules as the C.iL1.C. is passed is shown by a change in slope of two lines which represent the measured refractive-index difference between that of the total system and that of water
133
CRITICAL MICELLE COI;C~STH.'LTIOI;S
( A n ) as 3 function of concentration. The curves in figure 1 show the changes in refractive index with concentration for the sodium alkyl sulfonate series. Thc value of the slope, A(An>/'Ac, where A(h) is the difference in refractive-index increments of two solutions whose concentration difference is Ac, for these detergents as well as those obtained for the fatty acid soaps and the cationic amine hydrochlorides are collected in table 1. The tlificrence in the slopes in TAI31,F: 1 Values o j alope, A ( A n ) , A c , fo, curious s o a p s
-~
I
SOAP
_-
___
____
SLOPE
CHABGE Ih' SLOPE BETWEEN &T:GRROPIXG MEMBERS I N I R E SER:ES ( X 104)
(x 104)
Helow
_____
c.sf.c. j
,
1 '
.4bove C.M.C.
1
:36
'
~
PER CENT IXCREASE IR SLOPE
___
l'otassiiiin f a t t y acid soaps
cio.. .
. . . . . . . . .
.~
312
1
202
~
.iT (.$22..
. . . . . . . . . . . . . .
c14..
. . . . . . . . . . '
~
3G9
?J 4 5
403
?AI
I
34
I
C'l4..
. . . . . . . ..
13
13.5
30
15.0
30
10.0
41
8.5
32
7.5
30
6.5
.....
c,s... . . . . . . . .. . . . . . . ___
9.5
_Alkylainine hydrochlorides
a homologous series seemb, n-ithin experimental error, to be fairly uniform and is probably a function of additivity due to the stepwise increase in chain length. These increments are included in table 1 and, although their numerical increase is not uniform per unit increase in chain length, the percentage rise in slope values is numerically similar to the corresponding changes in C'.M.C. These data are shown in table 2. The regularity of the per cent decrease in the fatty acid soaps and in the alkyl sulfonates n-as indicative of a relationship which has been developed below. Measurements at different temperatures as seen in the results in table 2 probably account for some of the irregularity noted.
13-1
H. B. I i L E V E S S
The data for typical qystems, n-here the changes in refractive index a t 25°C. of potassium laurate and sodii-lm dodecyl sulfonate a t 3 5 T . n-ith concentration are shown, are collected in tables 3 and 4. The reliability of the data is illustrated in figure 2. where chord plots of the valuei: in table 3 are dran-n. These plots are TXBLE 2 C i. i't i' c a l ?nicel/t? concentrations a s d e t e r m i n e d b!j r e f r a c t i o n I
,I
SOAP
TEYPERATURE
i
c.nI.c.
1
~
DECREASE I N
c,>I,c,
F a t t y acid soaps g e r cent
moles per /iter
75
BCK . . . . . . . . . KClJ..
25
0.098
. . . 11
2.5
0.0259
'
I
25
0.0066
I
. . . . . . . . . . . . . . . .
74 74
I
I
~
35
0.0018
73
~
~
~~~~
Sodium alkyl sulfonates
cs.
...................
Cia.. . . . . . . . . . . . . . . . . . . I
25
. . . . . . . . . . . . . . . . . . . . .
35
(:I?.
C14.. .
. . . . . . . . . . . . . . . .
45
52
.......................
C'lO..
1
25
0.155 74
0.041
I
76
I
0.010
:
71 0,0029
69 0.0009
Alkylamine hydrochlorides
Clo.. . . . . . . . . . . . . . . . . . . . . . . . . .
25
el?... . . . . . . . . . . . . . . . . . . . . . . .
30
1 ~
0.01 0.013
I
CL, . . . . . . . . . . . . . . . . . . . . . . . CIS
.......................
C18..
. . . . . . . . . . . . . . . . .
40
50 60
0.0031 ~
I
I
1
76
i
69
74
0.00s 0.00025
I
measure- of the change in A n with concentration, i.e., l ( A n ) 'IC, as functions of concentration. This manner of plotting theye data shows more strikingly the break in An n i t h concentration a t the C.IL1.C'. The averages of the chord plot values are those 'I\ hich n ould correspond to the vahiei; of the ..lopes of the lines in the plot; of I n ns a function of concentration.
135
CRITICAL MICELLE COSCcSTR.LTIOSS TEJIPER.iTTRE
EFFECTS
T'ai ious results ha1-e been reported regarding the effect of temperature on the C.3I.C'. From conductivity measurements of sodium alkyl sulfonate solutions by TT'right, ,Ibhott, Sirertz, and Tartar (30), of alkylamine hydrochlorides hy
TABLE 3 R e j t a c f i i e i n d i c e s o j potassium l a u i a t e 1?5"C'.\
0.432
0.1633
I ,083 0.274 1. 789
3.78
1.027
3.76
1.120
3.73
0.979
3.77
0 496
3.11
0.247
3.75
0.202
3.54
0 191
3.60
0.502
3.39
0 . 401
3.45
1.140
3.51
1.522
3.19
5.219
3.50
3,793
3.48
2.381
3.46
3,755
3.45
0,6760
0.300 2 . os9
0.7880 0.259
2.348
0,8859 0.132
2.480
0.9357 0.066
2.546
0.9604
0.057 2.603
0 . 9S06
0.052
2.655
0.999; 0.14s
2.803
1.0491) 0.116
2.919
1.0900 0.110
3.321)
1.2340 0.436
3.765
1 .3S62 1.490
5.255
1.go81
1.089 6.344
2,2874
0.973 7.317
2.6265
1.083 8 ,400
4,100
0.5733
1.515
3.0020
Ralston and Hoerr (24), and of other soap qolutions by various n-orkers it has been shoit-n that the C.3l.C'. increa+es 11ith increasing temperature. Bury and Parry, from density measurements of potassium laurate solutions, hare shon 11 that the C.3I.C. decreases with increabing temperature (1). Ekwall has stated that the C.3I.C. iq temperature independent, on the ha+ of conductivity measurements on sodium fatty acid soap solutions (4). The application of the spectral dye method to temperature effects indicated that the C.1I.C'. decreased
1.36
H. B. KLEVESS
with increasing temperature, but these results were shov n t o be a property of this particular method (1G). These observations are due to changes in the spectra of the dyes which shift xrith changes in temperature. The decreases noted are caused by changes in the aggregation of the dye, and it is this factor rather than the formation of micelle* n-hich brings aborit this reported decrease in C.31.C.
~0.662
0 . TZ6 0 . b83
0 . 906
0,935 0.063 0.090
7 .04b 1.116
1.20s 1.349 1.528 1.7.54 1.044 2.160
2.320
The data in table 5 indicate that the C'A1.C'. of various soaps and detergents increases with increase in temperature as determined by refraction. This is true not only of anionic but also of cationic detergents. A plot of a portion of these data as seen in figure 3 indicates that the C.?rf.C'. does not change much in the region between 20-40°C. but that the increase is much larger above 40°C'. This suggests that this temperature dependence of micelle formation might yield some information as t o forces of attraction hetween molecules in a micelle.
13i
CI1ITIC.IL MICELLE C O S C E S T I { . ~ ' l T O ~ S
i i
i - --
I
I
-I
3.2 -
1.6
-
I
4.8
6.4
J
1
I
N,x IO2 FIG,. 2 . ('hord area plot of cahange i n refractive-index increnient u ith potassium laurate conrent rat ion (25'C.), shon ing hreak a t critical n i i c ~ l l cc~onc-eiit rat i o r i .
TARLE 5 Change in critirnl micelle concentrations with t e m p e r a t u r e
_____
~
TLMl'ER.4TU.E
__
I
c.k!.c.
Sotiium decyl sulfonate
2.j
moles per lifer
c
I
C.M.C.
Potassiuril laurate
".
25 30 35 45
I
____
. .
TEMPEPATCRE
___ - _ _ _ _ _ ~
..
"C .
I/
55 65
.___
I
moles per litrr
0 I0255 0 ,02611 0.0270 C ,0305 0.0350 0.012r1
The r e d t s in table 5 indicate that the C.3I.C. as measured by refraction increases with increasing temperature, iq symbatic with corresponding changes ohserr-ed from conductivity and density measurements (24, 29, 30), and is anti-
138
H. B. KLEVENS
batic ivith the C.111.C values as determined by the spectral dye method. These refraction data seem to agree with the conception that most colloidal aggregations are temperature dependent and that they will have less tendency to aggregate a t elevated temperatures, owing to increased thermal agitation of the coalescing units . =i presentation of the data shon-ing the change in V.11.C. Jvith increase in chain length a t a definite temperature as seen in table G indicates that there is a definite correlation betn-een C.11I.C. and chain length. The data are batisfied approximately by the following equation: b-c
V.11.C.
I
35
I
=
a(2n)"
45
I
55
FIG.3. Effect of temperature upon critical micelle concentration of (.I)socliuni decy1 sulfonate and (B) potassium laurate.
in which b = f(a, 5"). In the above a = a constant characteristic of the most insoluble member of the particular homologous series a t the temperature at which the measurements are made; b = a constant equal to the maximum number of carbon atoms in the least soluble member of the particular homologous series a t a definite temperature ( b thus is dependent on a and the temperature, 5") ; c = the number of carbon atoms in the hydrocarbon chain; and n = 2 for an even number of carbon atoms and 1 for an odd number of carbon atoms. The values of the constant, a , a t various temperatures are presented in table '7. These data are used to calculate the C.1I.C. of various qoaps at definite temperatures. h comparison of the experimental with the calculated \-dues, as 11-ell as predicted values for the various soaps containing odd numbers of carbon atoms, is included in table 6. There are at the present time no data ztvailahl~
139
CRITIC.IL MICELLE COSCESTR.4TIOSS
on these soaps with an odd number of carbon atoms except those of Hess, Philippoff, and Kiessig (11). Since their data do not agree ivith the present results nor Tvith those of Ekn-all (4) or Stauff (27) in the case of the soaps with TABLE 6 Effect
c$ c h u n g e i i i chairr l e n g t h oi?
the c t i t i c a l micelle coucerilration T = 25T.
XUMBEB OF C A R B O S A T O M S IS CE.4IS
I
Observed
CIS., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
......................
1
ci,.. .
0.0066
1
I
Calculated
0.0066
T = 45'C. Observed
,
0.0074
1
Calculated
0.0038 0.0076
PI6
C1,
(0 004)
0 004
T-cilues oJ
T.\13Id1: 7 constant a a t z ' a r i o m t e m p e r a t u r e s
__
SOAP SEPITS
-
1 ..,I
~, - -- TEBLPEEATUBE
Potassium f a t t y acid.. . , . . . . . , . . ,
,
b
-,
"C .
I
25
I
45
I
.
.
. . ,
33
1
!
40
!
I
+
0.3
I
I
I
16
1
i
0.0066
0.010
o.oo25 0.0007
I
I
02 03
- 0.5 -
2J 1.3
I
t:
I
50
'
o.ooio 0.001!1
i
1
i
I
~
Sodium alkyl sulfonates
a
i4 14
Xi
I
lI- -
\\
e 4,5
\
2
W
2 2.1 0' U
m
0 -I ,
- 2.9
- 3.7
I
I
I
I
I
6 IO 14 18 Number Carbon Atoms in Chain
F I ~4.. Change in critical micelle concentration with increase in vhain length as determined by various methods. Curve 1, potassium f a t t y acid soaps (G'C., refraction) ; clear circles are d a t a on sodium f a t l y arid soaps (li-SO'C., conductivity (4)); curve 2 , potassium f a t t y acid soaps (2joc.,refraction) ; curve 3, alliyltrimetliylanimonium bromides (25"C., conductivity ( 2 5 ) ); rurve 4, sodium alkyl sulfonates (55"C., refraction) ; curve 5, sodium alkyl sulfonates (60°C.. conductivity (3)). 140
salts of various fatty acids, although quite different as to solubility, h a w identical values of C.M.C. The values obtained by these two authors scatter somev hat from the data obtained in the present measurements. Ekn-all's measurements were made a t various temperatures between 17" and 80"C'., and he reported no change in C.1l.C'. with temperature which does not agree with other results. The effect of temperature on the C.Tt1.C'. can he noted by a comparison of curves 1 and 2 in figure 4. Curve 1 incliides the data of the fatty acid soaps a t 25°C.; curve 2 those a t 43°C. The values of C.M .C. a t 60°C. for the sodium alkyl wlfonates (30) a s determined by conductivity are compared T\-ith values as determined by refraction a t 50°C'. in curves 4 and 3 . The refraction data are obtained from interpolation of the curves of C.3I.C. cs. temperature. I t can be seen that there is again good agreement between these two methods of C'.M.('. determinoa t'loll. One important series of cationic detergent., the alkylamine hydrochloride-, was found not to fit this general relationship. These values 11 ere taken from the conductivity data of Halston and Hoerr (2-4). I t n-as thought that perhaps only the anionic soaps follox-ed the proposed equation, but the data on the alkyltrimetliylammonium bromides (26) (curve 3, figure 4) indicate that the cationics also can be cquated similarly. The data in ciiiyes 1-5 are for boaps which were prepared from highly purified alcohols and esters previoui to snponification. The amine hydrochlorides may contain a small amount of the nest higher homolog and the system would act like a soap mixture having a lower C'.JI.C'. than the piire soap (13). The addition of a small amount of an impurity,-another soap, an electrolyte, a hydrocarbon or oil, or the fatty acid of the soap,-v ill cause a decrease in the C.M.C. of the piire soap. EFFECT O F .\DDED ELECTHOLYTI2h
d s has been stated above, the addition of an electrolyte will a t all times cause some decrease in the C.1l.C'. of a soap. JIuriay (22) indicated that the Kraflt, point (temperature above TI hich a substance is exceedingly soluble) of potassium cetyl sulfonate is raised by the addition of potassium chloride. Hartlcy ant1 Runnicles (9) noted that in rodium chloride solutions there 11 as a decrease in the amount of paraffin-chain salts necessary to obtain the same diflusion coefficient obtained with R salt-free system. Hartley (6, 8) reported a decrease in the C.1I.C. of cetylpyridinium chloride from 0.0009 -Yto less than 0.0001 3-in the preqence of 0.032 S sodium chloride. Tartar and Cadle (28) have -hovn that the breaks in the solubility curves of sodium alkyl sulfonates shift ton-ard higher temperatures and lower concentrations as the concentration of sodium chloride increases. On the basis of the above results, it was stated that the solubility of the detergents, a t temperatiires which are belon- those required for micelle forniation, can be described by an activity product relationship. Using the DebyeHuckel theory for the activity coefficient of an electrolyte in solutions of different ionic strengths, they show that the mass action law is valid in the case of the transition from ionic to micellar soap as well as in the transition from ionic to crystalline solid soap. Wright and Tartar (29) stated that a decreaw in the
142
€1.
n.
KLEVESS
degree of ionization r~ouldincrease the stability oi the micelle. on ing to a lon-ering of the electrical charge. Since thii n o d d be affected by cation concentration in the case of anionic soaps, a decrease in C.1I.C'. i\ould be expected in the caSe of the addition of sodium chloride. Wright, Xbbott, divertz, and Tartar (30) have shov n that in solutiom n hich 11 ere equimolal 11ith respect t o sodium chloride and to sodium laurj 1 sulfonate the ('.lI.C. decreased by 26 per cent. If an addition of a number of positive ions is made t o a solution of an anionic soap, the concentration of gegenions in the vicinity of the soap molecules will increase considerably. This TI o d d bring about a decrease in the degree of ionization and should enhance the stability of the micelle. I t would follon then that this addition of an electrolyte would be coupled TI ith a loner value of the C.M.C. Tartar and his conorkers (28, 30) had previously stated that, on the basis of their preliminary conductivity and solubility studies, the addition of electrolytes indicates that the behayior of micellization in soap solutions follon-s the principle of ionic strength or the Debye-Huckel relationships. Corrin and Harkins ( 2 ) , in their more extensive n ork in n-hich they used various dyes to follon- micelle formation, state that these relationships do not explain the behavior of micelle formation. The use of the dye technique (3), baqed on the earlier reported work of Hartley ( i )and Sheppard and Geddes (2G), has been shonn to yield values which 11 ere a t all times smaller than thoie determined by conductivity, by solubility, or by refraction (13, 10). This may be due to one of a number of factors: ( 1 ) the dye could act a5 a salt and, as has been shonn by reference t o previous work, nould cause a decrease in the C.L\I.C'.;( 2 ) the dye could act like a hydrocarbon and in this n a y uould al-o cause a decrease in the C.1I.C'. (17, 20, 23); and ( 3 ) from previous reported data on the increase in fluorescence of dye- at the C.1I.C'. (14, l i ) due to ad-orption and orientation of the dye in or on the micelle, it can be deduced that the dye forms a complel or a mixed micelle n ith the soap. It has been shon n recently that the (?.SI.(' of a soap is decreased by the addition of another soap nith a loner C.1I.C. (13'1 A\l-o, some unreported uork of the author indicates that the addition of long-chain alcohols and fatty acids to soaps depresses the C'.lI.('., and theie is some suggestion that as in the case of the dye-boap and the soap-soap mixtures, a mixed micelle is formed. of interest to determine 11hether the results reported as to the nonapplicability of the maw action laiv could be obtained by refraction studies. Since it had been shon n that hydrolysis played no part in these results, for similar results had been found in the case of alkyl -ulfonates, alkyl sulfates, and fatty acid soaps (2, 30), the follon ing study \\as made with potassium laurate. The procedure used involved the addition of potassium laurate to salt solutions, folloned by the determination of the refractive indices of these solutions. For each series, tn o straight lines weie obtained 11liich TT ere -1rnilar to those shon n in figure 1 . The inteisection of each pair oi lines i h the C'.lL.C'., and the value3 obtained tor theye are collected in table 8. It can be qeen from these data that the C.1I.C'. is reduced to a fairly constant value, u-hich i t not affected by further increase in wlt concentration. This would indicate a high degree of saturation of gegenions vhicli form an ionic cloud in the region of the micelles. Further in-
113
CRITIC.\L MICELLE C O S C E S T R l T I O S S
crease in salt concentration to about 0.5 S TI-ouldthen have little effect on the degree of ionization, for the added ionq would not on the average approach the micelle through the ionic cloud of the gegenions. ;It higher salt concentrations TABLE 8 Eflect of added electrol?ytes u p o n critical micelle concentration of potassium laztrate c.!fI.c. f P L R E C.M.C. (IVITA
SOAP)
SALT’
1
ACTIVITY PRODUCT
(x 103)
Potassium chloride I
0 ~
0.0252
0.06TO
1
0.10045 0.2124 0.3825 0.5014
I
I I
I
moles p e r liter
2.55 1.59 1.19 1.02 0.71 0.46 0.41
I
5.32 6.22
0.40 0.79 1.02 1.51 1.83 2.02
1. e 4 4.04
0.2-5 1.37
1. A 1 -1.04
0.m 2 . !51
I
i I
2.50
Potassium bromide 0 0265 0 1735
i
1.55 0.79
I
P o t assiurri iodide
0,0166 0.2615
I
I
1.s1 0.63
I
Pot assiuni nit rat e 1.54 0.8% 0.53
0,0306 0.1380 0.3331
1.65 2.90 4.81
0.47 1.21 1.70
Potassium sulfate 0,0188 0.0525 0 . 137.5
I I ~
1.41 1.03 0.59
i i
1.s1 2.47 4.33
I
0.53 1.13 1 .e2
~
Potassium pyrophosphate 0.0167 0.0507 0,0742
0.8s 0.69 0.53
I I
2.38 3.70 4.80
I
0.66 1.30 1.66
the typical halting-out effect ould occur, with crystallization of the soap taking place. This would probably involve a fairly definite and somewhat orderly aggregation of micelles. When the above data are plotted as in figure 5 , it can be seen that the decrease in C.1f.C. of potassium laurate, an anionic soap, is affected only by the equivalent
144
H. B. HLEVEKS
concentration of the added electrolyte. The use of Rr-, I-, or SOd- in place of C'1- has little or no measurable effect on the change in C'J1.C. 'Thcsce results, although the actual Yalues are different from those determined by dye titration, are in agreement with previous findings (2). 'rhe data showing the effect of the addition of potassium sulfate and potassium pyrophosphate aic incliiiietl in table 8 and these (".M.C. x-aluw are shown to fall on the curve in figii'e 5 . I I
I
I
I
E
l
12.7 I
r
u
-1
t-3
I1
I
0.1
, I
03
I
0.5
1
EQUIV, ADDED ELECTROLYTES
It is evident from the above that the wti\-ity producat concept c a a u . ) ~fit the data, and that the clonccpt adyanccd by Corrin and Harkins is prol~ablycorrect. Data in table 8 intlicatc that the actix-ity prot1iic.t increases with increasing equivalent concentration of aclditix-e. S O h P MIXTURES
liecently a preliminary report has shown the change in C'.M.C. in thc. case of soap mixtures, as determined by spectral changes in (lye solutions (1.7 I . These preliminaiy results indicated that over a certain mole fraction rang? the soap with the higher C.M.C. acted like a salt, depressing the C.1l.C. of the other soap.
Corresponding changes in refraction could be used to determine additional properties of these mixed micelles. It TWS necessary, in order to obtain C.3I.C. from the intersection of t n o lines of refractive index 1's. concentration, t o ha\-e a constant mole ratio (moles of one soap/'total moles of soap in mixture) for each series. Dilutions Jjere made then, by weight, from stock solutions having definite mole ratios. The data in table 9 and figure G are the C.M.C. values obtained by the above method for various soap mixtures. The curves obtained are similar t o those obtained by the spectral dye method, except for a vertical displacement of the TABLE 9 ('ritirul riincelle concentrations of soup mzrfiires YULE PR.4CIION
c.?rf.c.OF YlXTlTPE
KCid
Potsssiurii myristate
I
1)
-
0 132 11 301 9 452 0 645 1 0
I
-- -
0.0255 0 014 0 011 0 010 0 0078 0 0066
I _ _ _ _ I _
Potassium iriyristate f)
0.110 0.305
I I
'I 450 1. 0 -- -
. --
I
i o -
--____
I I
3.86 2 12 1 67 1 52 1.18 1.0
I I
I
I
+ potassium caprate
0.099 0.052 0.015 0,012 0 0066
Potassiuiii 1113ristate
'1 0.380 0 645
+ potassium lauratt,
15.63 7.88 2.27 1 82
I
1 .o
,
+ sodium lauryl sulfatc
-__-_I__
I
I
0.0058 0 0061 0.0062 0.0066 I _
__
-_
.______
0.88 0.97 0.94 1.0 I _ _
curves, irllic.11 can be explained by the difierences found in the C.M.C. of the pure sonps due to the method used. The spectral dye values \\-ere found in all cases to he 3maller than those determined by refraction or 1)y conductivity as has been bhonn previously (16). The data in figure G indicate that the largest change in C.3I.C. occurs when there is the largest difference in the C.M.C. of the pure soaps. -it all times the ('.JI.c'. of the mixture lies betneen those of the pure soaps. This is further exemplificd in the case of mistures of potassium myristate and sodium dodecyl sulfate, which have about the same initial C.M.C. There is, as can he seen in figure 6, practically no change in C.3t.C'. upon the mixing of these t n o soap$.
146
H. B. KLEVEXS
The dift'erence in the tendency of pure ioaps to iorm micelles will control the micelle formation of their mixtures. The rate of decrease in C.1I.C. of the mixture lyill be largest a t lov- mole fractions of the hoap u i t h the lower C'.M.C.; the greater the difference in the C'.11.('. of the pure soaps, the greater TI ill be the effect on the more soluble (higher. C.11.C.) soap. The C.M.C. of these mixtures u-ould correspond to the C.1I.C. of the mixture of sodium dodecyl sulfonate and calcium dodecyl sulfonate. The latter C.1I.C.
, i
b
b
02
I.
Mole Fraction KC,, FIG.6 . Critical micelle concentrations of mixtures of potassium myristate and other soaps (25°C.).
value could be obtained, as has been shoivn in the case of soap-hydrocarbon mixtures (lo), from the minimum of thc solubility curve of the calcium soap in sodium dodecyl sulfonate. This latter effect has been shown t o he one of a number of solubilization types in which solubilization in\-okes t,he formation of mixed aggregates (18). From this point of vie\\, it is obvious that a t concentrations above the C. X.C. soluhilization is occurring in ~r-hichthe less soluble soap is being soluhilizetl by the more soluble one. SU~lMhIlT
1. Refractive indices of dilute soap solutions are characterized 12s tiyo straight lines which intemect at the critical micelle concentration ( C " . C ' . ) .
2. The critical micelle concentration of soap solution5 is seen to increase with temperature. There \ \ a i little incrtaqe ol-er the range 20-40°C., but a marked inrrense occurred above 40°C. 3 . .Irelationship iq pre4ented I\ hich shou s that the critical micelle concentration of a member of a seriei (ann be determined it the values of other members of the qnme series are known. The critical micelle concentration is a logarithmic fiinction of the num1,er of carlion atom- in the hydrocarbon chain. 1.The addition of electrolyteb to soap solutions decreases the critical micelle concentration but this decrea>e does not follow the mass action law. The addition of potassium chloride to potassium laurate decreases the critical micelle concentration t o less than 15 per cent of the original value. 5 . Soap mixtures have critical micelle concentration values which are intermediate hetTveen the original values. Small mole ratio. of the less soluble soap will show the largest changes in critical micelle concentration of the mixtures. In considering soap mixtures, the difference in the tendency of different soaps to form micelle. controls the micelle formation of their mixtures.
148
R.
D. TOLD .4XD If. J. RELDhZ1-h;
(26) SHEPPARD, Y. E., , ~ X DGEDDES,A. L.: J. Chem. Phys. 13,63 (1918). (27) STAUFF,J . : 2. physik. Chem. A183, 55 (1938). (28) TARTAR, H. V., A N D CADLE,R. D.: J. Phys. Chem. 43, 1173 (1939). (29) WRIGHT,K. A., AND TART.4R, H. v.: J. -4m. Chem. sot. 61,544 (1939). K. 9., ABBOTT, A. D., SIVERTZ, V., AKD TARTAR, H. V.: J. Am. Chcm. SOC. (30) WRIGHT, 61, 549 (1939).
ELECTRICAL CONDUCTIVITY O F CRYSTALLINE AND LIQUID-CRYSTALLIKE SOAP-WATER SYSTEMS' R. D. VOLD AND M. J. HELDMrlW Department of Chemistry, University of Southern California, Los dngeles 7, Caltfornia Receaved August 26, 1947
The present study was undertaken with a twofold objective: first, to detesmine phase boundaries in soap systems in regions of composition and temperature where other methods have failed, and second, LO learn more about the nature of the various phases and the changes occurring a t the observed transitions. Phase changes can be deduced from changes in slope of the resistancetemperature curves, while the absolute values of the conductance, both A.C. and D.c., and their dependence on temperature and frequency help t o distinguish between dipole oscillation, surface conductivity, and ionic or micellar migration as the mechanism of the process. In some instances these data can also be used to deduce possible internal structures of the different phases. Preliminary experiments were carried out with anhydrous sodium palmitate. Systems of anhydrous and hydrous sodium stearate up to 12.8 weight per cent water were then investigated lvith varying thermal and pressure treatment before and during measurement. Specific conductances of two of the liquid-crystalline phases-soapboiler's neat and middle soap-\\-ere also determined. Previous attempts t o study the electrical properties of solid and semisolid soap systems haye been few and relatirely unsuccessful. Fischer and Hooker (9) determined the change in conductivity rcsulting from \\-hat we now ~ O T toV be the separation of solid soap from solution, although they believed that it was due t o inversion of an eniulsion or solution. Bhatnagar and Prasad ( 2 ) s t u d i d the conductivity of "molten" alkali metal soaps at 182-20i"C., but did not estahlish sufficiently the purity a i d moisture content or' their qamples, nor nerc the questions of adequate clectrodc contact and possible chemical decomposition carefully considered. In the present investigation great pains were takcn t o 1 Presented a t tlic T n e n t ) -hi>t S a t i o n a l Colloid Symposium, mhich was l i ~ ~ !w ~ !t l e r t h e auspices of thc Divisiriii of Co!loicl Cliernistrv of t h c .lmeric i n Chemical S o r i c ~ y.it Pa!o Alto, California, June 18-20,1947. 2 Present address. Depai tiiient of Chemistiy, East 1 x 1 l!~gtbl ~ Junior C olicgt,, Los .ingeles, California.
