31. J. SCHICK
1796
Vol. 67
EFFECT OF TEMPERATURE ON THE CRITICAL MICELLE CONCENTRATION OF NONIONIC DETERGENTS. THERMODYNAMICS OF MICELLE FORMATION' BY M. J. SCHICK Lever Brothers Company, Research Center, Edgewater, New Jerseil Received February 1.9, 1963 The c.m.c.'s of nonionic detergents, viz., ethylene oxide condensates of n-dodecanol and n-hexadecanol, in aqueous and aqueous electrolyte solutions have been determined from the concentration dependence of surface tension a t temperatures from 1.0 to 55.0". For comparison, related determinations on sodium n-dodecyl ether alcohol sulfates, sodium n-dodecyl alcohol sulfate, and ndodecyl trimethylammonium bromide have been included in this study. Values of the change in heat content, ATrn, aasociated with micelle formation have been estimated from the teEpcrature variation of the c.m.c. using an equation of the Clausius-Clapeyron type. The significance of these - AHmvalues and their relation to the theory of micelle formation is considered. For nonionic detergentsthe AH,, values and the corresponding 23, values under these equilibrium conditions are positive; e.g., the AH,,, values of aqueous solutions of n-dodecanol 30 EO, n-dodecanol f 7 EO, and n-hexadecanol 30 EO are 3.7, 5.0, and 6.6 kcal./mole in this temperature range. It is concludcd that the entropy loss caused by aggregation of nonionic detergents must be offset by desolvation.
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Introduction Relatively few papers on the thermodynaniics of micelle formation of nonionic detergents have appeared so far in the literature,2-6 in contrast to the numcrous papers published on the therniodynamics of micelle formation of ionic detergents.'j The object of this investigation was an experimental study to provide data which are pertinent for the calculation of enthalpy and entropy of micellization in aqueous solutions of nonionic detergents such as the temperature dependence of the critical micelle concentration (c.ni.c.). A few preliminary results have been reported previously.' Some related data on ionic detergents have been included in this study. The significance of the enthaIpy and entropy of micellization of nonionic detergents and their relation to the theory of micelle formation is considered. Experimental Molecularly distilled ethylene oxide (EO) condensates of ndodecanol and n-hexadecanol have been obtained from General Aniline and Film Corporation. The average chain length of the ethylene oxide adducts has been determined from their hydroxyl values. The homogeneity of the nonionic detergenta has been assessed from the observed sharp breaks in the surface tension us. logarithm of concentration plots; only samples exhibiting sharp breaks have been used. Corkill, et nl., have found that nonionic detergents prepared by the Williamson synthesis are prone to oxidation.' I n contrast, none of the ethylene oxide condensates of aliphatic alcohols used in this investigation exhibited carbonyl peaks in their infrared spectra a t 5.8 p . Sodium ndodecyl ether alcohol sulfates, sodium ndodecyl alcohol sulfate (SDS), and ndodecyl trimethylammonium bromide (DT-IBr) have been prepared in this Laboratory. The purity of these materials wm readily checked from the shape of the surface tension us. logarithm of concentration plots near the c.m.c. The water was redistilled from alkaline permanganate and the electrolytes were of C.P. grade. The surface tensions were determined by means of a Wilhelmy balance with a sand-blasted platinum plate a t temperatures from 1.0 3= 0.1" to 55.0 f 0.1' on 50-ml. solutions in 100-ml. crystallizing dishes. Equilibrium measurements were taken 1 hr. after cleaning the solution surface by suction with a fine glass capil( 1 ) Paper presented a t the 143rd National Meeting of the American Chemical Society, Lo8 Angoles, Calif.. M a r r h 31-April 5, 1963. (2) I. Itcich. J . P h y s . Chsm., 60, 257 (1956). (3) C. A. J. Hoeve anti G. C. Henson, z h d . , 61, 1149 (1957). (4) J. BI. Corkill, J. F Qoodmun and lt. I1 Otteaill, T r a m . Faraday Soc., 87, 1027 (1961). (5) K. W. IIerrmnnn, J . Phus. Chem., 66, 205 (1962). (6) 13. A. Potliica. Proc. 3rd Intern. Congr. Surface Activity, Cologne, 1960, Section A, No. 30, p. 212. (7) M. J. Srhick, J . C o l l a d Sci.. 17, 801 (1962).
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lary; this time interval was sufficient to allow reaching equilibrium even with solutions of the lowest detergent concentration.7 Establishment of equilibrium surface tension was checked by repeat measurements after a 5min. interval beyond the 1-hr. period. In order to eliminate evaporation losses and contamination from thc atmosphere, the crystallizing dishes were covcrcd with aluminum foil immediately after cleaning the solution surface and for the measurements a t temperatures above 25.0' inserted 30 min. before the surface tension measurements into the thermostated bath; equilibrium was reached more rapidly a t these elevated temperatures. Establishment of the desired bulk temperature in the detergent solutions was rechecked on duplicate solutions. The accuracy of the measurements was within rt0.l dyne/cm.
Results The concentration dependence of the surface tension 30 EO, nof aqueous solutions of n-dodecanol 7 EO, and n-hexadecanol 30 E O has dodecanol been determined as a function of temperature over the range of 1.0to 55.0'. I n addition, measurements covering the same temperature range of n-dodecanol 30 EO in 0.43 ill Il'aC1, 0.86 AI KaC1, 0.86 A I SaCKS, and 0.86 M i/2SazS04solutions have been carried out. For each system the temperature variation produced a family of curves similar to those shown in Fig. 1 of ref. 7 and 8. The c.m.c. values, taken from the sharp breaks in the surface tension us. logarithm of concentration plots, are given in Fig. 1 and 2. The plots of log c.ni.c. us. 1/T arc linear as shown in these figures. With no exception, the c.m.c. values increase on lowering the temperature, which is in line with the inverse tempcrature solubility relation of nonionic detergents. It is evident from the results of Fig. 1 for aqucous solutions of ndodecanol 30 EO, n-dodecanol 7 EO, and nhexadecanol 30 EO that a t a specific temperature the c.m.c. is a function of the length of both the hydrophobic and hydrophilic groups; increased hydration of the hydrophilic group resists aggregation, whereas increased hydrocarbon-chain attraction enhances aggregation. It follows from the results of Fig. 2 that a t a specific temperature the lowering of the c.ni.c. on electrolyte addition is proportional to the electrolyte concentration, but inversely proportional to the lyotropic nuniber of the anions. These effects of electrolyte concentration and of lyotropic number of the 'Lcounteranioii" follow a 8 salting out mechanism as postulated Thc effect of KaC1 concentration on the c.m.c. of n-
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(8) M. J. Schick, S. hi. Atlas. and (1962).
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F. R. Finch J .
Phiis. Chrm
66, 132G
EFFECT OF TEMPERATURE ON C.M.C.OF NOMONIC DETERGENTS
Sept., 1963 150
I
2oo 150
1'797
c
:1:
80
lo
i 0
0.2 0.4 0.6 0.8 Concentration of NaC1, M.
1.0
Fig. 3.-Effect of NaCl concentration on log c.m.c. of n-dodecanol 30 EO aolutions w a function of temperature.
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I
I
I
3.0
1/T
1
100
-
DO 80 70 00 50 40
3.6
105
OK-'.
1
-
-
30-
;?
20
-
l
;
2
x
I
I
I
3.4
of log c.m.c. us. 1/T of nonionic detergents in a,queous solutions.
Pig. 1.-Plot 150
I
3.2
u: f
y
8
6
,
k
+
;
,
~
5 4
3
3.0
Fig. 2.-Plot
3.2
of log
3.4
1/T x 102, OK.-'. c.m.c. us. 1/T of n-dodecmol
electrolyte solutions.
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3.6
+ 30 EO in
dodecanol 30 EO solutions as a function of temperature is shown in Fig. 3. The semilogarithmic plots are linear a t temperatures from 1.0 to 10.Oo, which correspond to the region of appreciable hydration of the nonionic detergents. In contrast the negative slopes decrease with increasing NaCl concentration a t temperatures exceeding 10.Oo, ie., in the region of diminished hydration. For comparison with these data on nonionic detergents, the concentration dependence of the surface tension of aqueous solutions of n-ClzH26-(EO)3-S04Na, n-ClzHz6-(EO)17.6S04r\;SL1 and SDS has been determilled as a function of tenlperatureOver the range of 1.0 to 55.0". I n addition, measurements of SDS in
0.2 BII NaCl solutions have been carried out over the 10.0 to 55.0" temperature range. The c.m.c. values taken from the sharp breaks in the surface tension vs. logarithm of concentration plots are given as a function of temperature in Fig. 4 and 5. It is worth noting that the c.m.c. values of SDS determined by the surface tension method are somewhat lower compared to those of the conductivity method, but the shapes of the c.m.c. us. temperature curves are ~ i m i l a r . ~ I n aqueous solutions the c.m.c. values of polyoxyethylene ndodecanols increase on lowering the temperature, whereas those of SDS pass through a minimum a t 25.0" as shown in Fig. 1,4, and 5. It is evident from the plots of Fig. 5 that this behavior is reflected in the c.m.c. values of aqueous solutions of sodium ndodecyl ether alcohol sulfates. For the homolog nC12H~-(E0)3S04Ka with the short polyether groups the results follow the pattern of SDS, whereas for the 6 S 0 4 K awith the long polyhomolog n-C12Hzr(Il:O)17 ether group that of a polyoxyethylene n-dodecanol. In the latter case the c.m.c. values decrease with increasing temperature; in other words the well known dehydration phenomena of nonionic detergents with increasing temperature predominate. The effects of the chain length of the hydrophobic and hydrophilic groups on the c.m.c. of sodium n-alkyl ether alcohol sulfates a t 25.0" may be deduced from the results shown in Fig. 5 and those given by Weil, Uistline, and Stirton.1O In line with results reported on ionic and nonionic detergents, the c.m.c. values decrease with increasing length of the hydrophobic group for sodium n-alkyl ether alcohol sulfates with comparable hydrophilic groups. The hydrocarbon-chain attraction rises a t constant hydration and electrostatic repulsion in the hydrophilic group and enhances aggregation.8 For a specific hydrophobic group, such as n-C12H26,. n-C16H33, or n-C18H3,,the c.m.c. values decrease with increasing length of the polyether groups. Thus, for each increnierit of one ethylene oxide unit the transition from the high c.m.c. value of an ionic to the low c.m.c. value of a nonionic detergent becomes more apparent. Finally, the temperature dependence of the c.m,c. of DTABr in aqueous and 0.2 M KaBr solutions is shown in Fig. 4 over the 10.0 to 55.0" temperaturc (9) E. D. Goddnrd and G.C. Bcnson, Can. J . Chem., 36,086 (1957). (10) J. K . Weil. R. G. Ilistline, and A. J. Stirton, J . P h p Chem.. 63. 1083 (1958).
1798
M. J, SCHICK
assumptions which must be made in order to reconcile the two approaches in any thermodynamic calculations of heat and entropy of micellization based on the c.m.c., ie., the maximum concentration of molecular dispersion. l 2 The heat of micellization in aqueous solutions of various ionic detergents has been measured by direct calorimetric determinations of the heat of dilution.14-16 So far no corresponding investigation of nonionic detergents has been reported. Alternatively the heat of micellization has been determined from the temperature dependence of the c.m.c. by means of an equation of the Clausius-Clapeyron type426 9, 17-20
180 160
140
2 s
_.
120 100
-
E;
x
8o
SDS in HO , n
Y
E 60
" I.
40
Vol. 67
DTA Br in 0.2 M NoBr
-
e-9L-Q
@---
20
B
m
=
. - , e I
0
10
,
1
20 30 Temp., OC.
(1)
P
S D S in 0.2 M NoCl
0
)
8 In c.111.c. 6T
-RX~(
I
40
50
60
Fig. 4.-C.m.c. of sodium n-dodecyl alcohol sulfate and ndodecyl trimethylanimonium bromide solutions a8 a function of temperature. I4O
This method has also been applied in this investigation. I n the derivation of eq. 1 the phase separation treatment has been used, which is readily applicable to solutions of nonionic detergents and to solutioiis of ionic detergents iii the presence of swamping electrolyte. 12.17.21 Under these equilibrium conditions, a F m = 0, the entropy of micellization may be readily obtained4J from
The a H m values obtained for nonionic detergents by eq. 1 are of higher accuracy compared to those of ionic detergents, because of the almost linear nature of the In c.m.c. us. 1/T plot for nonionic detergents.4s6-12
2o O
t 0
Fig. 5.--C.m.c.
"=* L
10
20 30 Temp., " C .
I
L
40
50
60
of n-dodecyl ether alcohol sulfates as a function of temperature.
PARTIAL
TABLE I MOLALHEATSAND ENTROPIES O F MICELLE FORMATION OF SONIONIC DETERQESTS~ AHm,
Hydrophobic group
n-EO
Solvent
n-Dodecanol 30 HzO 7 HzO n-Dodecanol HzO n-Hexadecanol 30 n-Dodecanol 30 0 43 M Sac1 n-Dodecanol 30 0.86 M NaCl 30 0.86 144 NaCNS n-Dodecanol n-Dodecanol 30 0.86 1%' l/zPl'a&Oa a Mean value for temperature region of 1.0 to I
range.l' In analogy with the data of SDS a minimum was observed in both curves at 25.0". As anticipated the c.m.c. values for the 0.2 144 NaBr solutions mere much lower a t comparable detergent concentration than those for the aqueous solutions; a similar behavior was shown for SDS in aqueous and 0.2 M NaCl solution in Fig. 4. The ionic repulsion of the long chain ammonium or sulfate ions is diminished by shielding of electrostatic charges with free bromide or sodium ions with consequent lowering of the c.Iy1.c. Discussion A number of suggestions have been made in the literature for methods of estimating the heat and entropy of micellization, but there is still some confusion about the thermodynamic basis for such estimates. This subject has recently been discussed by Pethica,6 Shinoda and Hutchinson,12 and hlukerjee.I% Two approaches have been advanced, (a) the phase separation treatment and (b) the mass action treatment. Shinoda and Hutchinson point out some of the implicit (11) H. J. L. Trap and J. J. Hermans, Proc. Konmkl. N e d . Akad. Wetenshap, B68, 97 (1955). (12) K. Shinoda and E. Hutchinson, J . Phys. Chem., 66,577 (1962). (13) P. Mukerjee, d i d . , 66, 1375 (1962).
as,,
kcal./ mole
cal./ mole deg.
3.7 5.0 6.6 6.0 6.5 4.1 9.1 55.0'.
12.3 16.6 21.9 19.9 21.6 13.6 30.2
The partial molal heats and entropies of micelle formation, a H m and a m , of ethylene oxide condensa,tes of n-dodecanol and n-hexadecanol in aqueous and in aqueous electrolyte solutions have been estimated by means of eq. 1and 2 from the slopes of Fig. 1and 2 for the temperature range of 1.0 to 55.0' and the results are given in Table I. With no exception the A N m values are positive over this temperature range and, hence, under these equilibrium conditions the
am
(14) P. White and G. C. Benson, J . Colloid S e i . , 18, 584 (1958); Trans. Faiaday Soc., 56, 1025 (1959); J . P h y s . Chem., 64, 599 (1960). (15) E. D. Goddard, C . A. J. Hoeve, and G. C. Benson, ihid., 61, 593 (1957). (16) E. Hutchinson, K. E. Manchester, and L. Winslow, ibid., 58, 1124 (1954). (17) E. Matijevih and B. A. Pethics, Trans. FaTaday SOC.,64, 587 (1958). (18) G. Stsinsby and A. E. Alexander, ihid., 46, 587 (1950). (19) E. Hutchinson, A. Inaba, and L. G . Bailey, Z. physik. Chem. (Frankfurt), 5, 344 (1955). (20) B. D. Flockhart, J . Colloid Sci., 16,484 (196% (21) According t o Pethica.8 the main objection to A H m from eq. 1 is that i t implies as a standard state the micelle a t equilibrium near the c.m.c.
I’ARTlAL
Detergent
Solvent
SDS o2 PDS 0.2 DTABr 0 . 2 DTABr 0 . 2
SDS SDS SDS
1i99
EFFECTOF TEMPERATURE ON C.M.C.OF SOWOSIC DETERGENTS
Sept., 1963
MxaC1 iM NaCl M NaBr M NaBr
0.01kf S a C l 0.I KaCl 0.2 1 M NaCl L~
----___
ama a m b
Bm“
smb ama AH,“ a m “
loo
SDS HzO a Kcal./mole.
TABLE I1 HEATB AND ENTROPIES O F MICELLE FORMATION O F I O N I C DETERGENTS
MOLAL
a,“ 1.0
25’
26-55’
Method
0.4
0 0 0 0
-2.6
S.T. S.T.
20-40°
20-800
40-80°
-0 4 -0.5 -1.3
-0.9 -1.5 -3.1
-1.5 -2.3 -5.2
1.4 0.9 3.1
20°
25O
30°
0 . 4 0.0
-0.5
15O
0.7
-8.3 -1.7 -5.4
Ref.
Data of Fig. Data of Fig. Data of Fig. Data of Fig.
S.T. S.T.
35’
40°
45‘
50’
55’
-1.0
-1.1
-1.4
-1.7
-1.8
S.T. S.T. S.T.
17
Conductivity
9
4 4 4 4
17 17
Cal./mole deg.
values are also positive. It is worth noting that the values is inversely proporincrease of the mean tional to the c.m.c.’s a t the mean temperature. A positive entropy change indicates increased randomness. Since it does not appear likely that increased disorder of the totall system would result from the aggregation of detergent monomers into micelles, the necessity arises to look for other causes to explain these positive entropy changes. For example, a positive entropy change taking place in micelle formation o l a nonionic detergent may be attributed either to desolvation or to increases in the configurational entropy of the detergent monomers. Since it is a well known fact that the solubility of nonionic detergents is affected by the hydration of the ethylene oxide chains through hydrogen bonding between the water molecules and the ether oxygens of the ethylene oxide chains, desolvation is a more likely candidate to explain the positive entropy changes than increases in the configurational entropy of the detergent monomer.’** This follows from the increase in ZS, values, viz., results of n30 EO, n-dodecanol 7 EO, and ndodecanol 30 EO, with decreasing resistance to hexadecanol aggregation from lhydration of the ethylene oxide chains, which opposes the hydrocarbon chain attraction, and the concomitant increased desolvation on aggregation. ?v’Ioreover, the increase of the a m values with increasing electrolyte concentration and with decreasing lyotropic number of the “counteranion” (as well as solvent depolymerization in the presence of electrolyte) suggests also desolvation of the ethylene oxide chains as a major contributing factor to the positive entropy changes.’
