2627
THERMODYNAMICS OF MICELLIZATION OF ZWITTERIONICN-ALKYLBETAINEB
Thermodynamics of Micellization of Some Zwitterionic N-Alkyl Betaines by J. Swarbrick and J. Daruwala' Division of Pharmaceutics, Pharmacy Research Institute, The University of Connecticut, Stows, Connecticut 06868 (Received December 6,1088)
The variation of cmc with temperature of the decyl ( G o ) and undecyl (GI) N-alkyl betaines (N-alkyl-N,Ndimethylglycines) has been studied by light scattering. The standard free energies of micellisation, AGm", have been calculated at various temperatures using both the phase separation and mass-action models; good agreement between the two approaches is found. The phase separation model was used to compute the standard enthalpy, AH,', and standard entropy, Urno,of micellization. With increasing temperature, AH," for both the Clo and C11 homologs changes from positive to negative. A similar change in the sign of AH,' is observed with increasing chain length at 25'. While the entropy of micellisation, AS,', is positive over the temperature range studied, it becomes less so at higher temperatures. Estimates of the enthalpy and entropy contributions attributable to the head group and alkyl chain have been made. The enthalpy change of the head group, AHrn(W-),is positive and intermediate between values derived for nonionic and ionic surfactants of equivalent chain length. The entropy contribution of the head group, ASrn(W-), to the total entropy change is negative, indicating restriction of the head groups at the micelle surface. The enthalpy and entropy changes per methylene group increase and decrease, respectively, with increasing chain length. The results are discussed in terms of current theories of micellization.
Introduction A survey of the literature reveals that, compared to ionic2-6 and nonionic7-12 surface-active agents, few workers have reported on the thermodynamics of micellization of zwitterionic compounds. A previous study" reported the standard free energy changes of micelliaation, AGm", for five homologous, zwitterionic N-alkyl betaines. From these data, AGmo was resolved into the separate contributions from the hydrophilic head group, AGm(W-), and the lipophilic methylene groups in the alkyl chain, AGm(-CH2-). When compared with results derived from other studies on ionic, nonionic, and zwitterionic surfactants, AGm (-CH2-) was found to be negative and independent of the type of surfactant. On the other hand, AGm(W-) varied with the head group, although it was positive in the ten cases examined. By following the variation in the critical micelle concentration (cmc) with temperature for the dodecyl N-alkyl betaine, the free-energy change for this homolog was separated into the enthalpy change, AH,", and Since only one homolog was entropy change, Ah','. studied, it was not possible to resolve AH," and AS," into the separate contributions from the head group and the alkyl chain. Tori and Nakagawals have also derived AH," for C-alkyl betaines from studies on the temperature dependence of cmc. Although the phaseseparation model was used in both these studies, the effect of temperature on micellar molecular weights (mmw), which can affect the validity of the model, was not determined. I n the present work, we have studied the influence of temperature an the cmc's of the decyl and undecyl homologs. These data have been converted to stan-
dard free energies using both the phase-separation and mass-action models of micellization and the values were compared. The free-energy changes have been split into the separate enthalpy and entropy contributions. These data, in conjunction with those for the CIS homolog,l4 have allowed the enthalpy and entropy changes per methylene group to be resolved. The energetics attributable to the head group on micellization have also been estimated. The results are discussed in terms of existing theories on the energetics of micellization and compared to those 'reported for ionic and nonionic surfactants.
Experimental Section Materials. The N-alkyl-N,N-dimethylglycines,C,(I) Ciba Pharmaceutical Company, Summit, N. J. (2) E.D. Goddard and G. C. Benson, Can. J. Chem., 35, 986 (1957). (3) E.D. Goddard, C. A. Hoeve, and G. C. Benson, J. Phys. Chem., 61, 593 (1957). (4) B. D. Flockhart, J. Colloid Sei., 16, 484 (1961). (5) H. F. Huisknan, Koninkl. Ned. Akad. Wetenschap., Proc., B67
(4), 367 (1964). (6) M.F.Emerson and A. Holtzer, J. Phys. Chem., 71, 3320 (1967). (7) M, J. Schick, ibid., 67, 1796 (1963). (8) E.H. Crook, G. F. Trebbi, and D. B. Fordyce, ibid., 68, 3592 (1964). (9) J. M.Corkill, J. F. Goodman, and 5. P. Harrold, Trans. Faraday Soc., 60, 202 (1964). (10) P. H. Elworthy and C. McDonald, Kolloid-2. 2. Polym., 195 (l),16 (1964). (11) J. M.Corkill, J. F. Goodman, and J. R. Tate, Trans. Faraday Soc., 60, 996 (1964). (12) L. Benjamin, J. Phys. Chem., 68, 3575 (1964). (13) K. Tori and T. Nakagawa, KolloicGZ. Z . Polym., 189 (l), 50 (1963). (14) P. Molyneux, C.T. Rhodes, and J. Swarbrick, Trans. Faraday Soc., 61, 1043 (1965). Volume 73,Number 8 August 1069
2628
J. SWARBRICK AND J. DARUWALA homolog is plotted against total concentration in Figure 1. The straight lines were drawn using least-squares analysis and the crnc a t each temperature was taken as the intercept. This was calculated from the formula cmc = (YZ
- YI + mlxl - mzx~)/(ml- m)
(1)
where (zlyl) and (xzyz) are the coordinates for any point on the least-squares line and ml and m2are the statistical slopes below and above the cmc, respectively. A similar plot was obtained for the C11 homolog and the same procedure was used to calculate the cmc's. The data for the Cloand C1lhomolog are presented in Table I and the plots of the logarithm of cmc us. ?'(OK)-' are shown in Figure 2. Data obtained previously for the C12 homologi4are also included in Figure 2.
Table I: Temperature Variation of Cmc and Standard Free Energies of Micellization of Cto and CII N-Alkyl Betaines Temp,
0.4
1.2 Concentration,
0.8
1.6
2.0
2.4
w/v.
Surfactant
2.383 2.327 2.269 2.183 2.186 2.206 2.244 2.336
-4.07 -4.18 -4.30 -4.41 -4.49 -4.58 -4.65 -4.71
-4.51 -4.60 -4.71 -4.83 -4.92 -5.03 -5.14 -5.22
c 1 1
25 35 45 55 65
0.723 0.682 0.715 0,736 0.763
-5.05 -5.29 -5.44 -5.59 -5.71
-5.30 -5.52 -,5.70 -5.83 -5.98
H2,+1N+(CH3)JJH&OO- (N-alkyl betaines), in which
Discussion Two models are commonly applied to the phenomenon of micellization. The phase-separation model regards micelles as a separate phase and assumes that the monomer activity remains constant above the cmc. Using this model, Molyneux, et aZ.,14 have shown that for a zwitterionic or nonionic surfactant AG,"
=
RT In Xf
(2)
where AG," is the standard free energy change (kcal mol-') of micellization for the transfer of a mole of free monomer to the micellar form and Xf is the mole fraction of monomer at the cmc. The mass action model regards micelle formation as an equilibrium condition in which the monomer activity continues .to increase, although a t a much reduced rate, above the cmc. According to Corkill, et aL9
Results
The Journal of Physical Chemistry
102
20 25 31 37 43 50 58 65
n = 10 and 11, have been described elsewhere.'*
The ratio of the intensity of scattered light a t 90" to , the CIO the intensity of the incident light, i ~ ~ / l ofor
x
koa1 mol-I-Phase separation
Cro
Figure 1. Scattering ratio, iso/lo, as a function of concentration of the CtoN-alkyl betaine. (Note: the y axis is displaced 10 units for each temperature below 65".)
Method. The change in cmc with temperature was studied using a Brice-Phoenix light-scattering photometer with narrow slits and a cylindrical cell (catalog No. C-101) painted black. At the wavelength employed (4.358 @, no absorbance or fluorescence was detected with the N-alkyl betaine solutions. All solutions were prepared in double-distilled water and were clarified by repeated filtration through a 100 mp on 10 mp Millipore filter disk combination a t a pressure sufficient to give a flow rate of 1 ml/min. The solutions were assumed to be free of extraneous matter when the dissymmetry, x451135, was 1.04 or less. Temperature control of the sample, to j=O.l", was achieved by means of a cell jacket.'5 The temperature of the sample was read by means of a thermometer inserted through holes drilled in the photometer lid and the jacket and cell covers. Sufficient sample was placed in the cell so that the bulb of the thermometer, while completely immersed, was 5-6 cm above the light path. The bulb was rinsed with filtered sample prior to insertion. Readings with and without the thermometer in place showed it to have no effect on the scattering ratio.
"C
-----AG,", Mass action
cmc (molar)
AGm" = R T [ ( l - l / A w ) 1nXf (15)
+ f(A,)]
Q. A. Trementozai, J . Polymer Sci., 23, 887 (1857).
(3)
2629
THERMODYNAMICS OF MICELLIZATION OF ZWITTERIONICN-ALKYLBETAINES
related to the magnitude and sign of the enthalpy and entropy changes on micellization, as will be discussed in subsequent sections. The agreement between the two models is good, especially with the Cll N-alkyl betaine. Thus, for the Clo homolog, the free energies based on the mass action model are within 9-10% of the values derived from the phase-separation model. With the Cll betaine, the values agree to within 4-574. These data support the earlier statement that the higher the aggregation number, the better the agreement between the two models. For zwitterionic and nonionic surfactants, AG," can be resolved into the standard enthalpy change, AH,", and entropy change, AS,", of micellization as follow^'^
1.3k
1
1.o
I
log CY
AH," eRT
= -
AS,"
- __ eR
+ 1% w
(5)
When log cy is plotted against 1/2' (Figure 2), the slope is equal to AH,"/eR while the intercept equals log w AS,"/eR. The values of AH,,," and AS," obtained in this manner are shown in Table 11. 2.9
3.0
32
3.1
3.3
3.4
3.5
8
T,"K-' X IO?
Figure 2. Variation of the logarithm of cmc with T ("K)-1 for the CIO, (211, and CISN-alkyl betaines.
where A, is the weight-average aggregation number and f(A,) is a function of the aggregation number. As a homologous series is ascended, A, increases while f(A,) decreases rapidly. Thus, as the alkyl chain length is increased eq 3 reduces to eq 2 and the models approach one another. Assuming AG," to result from the additive contributions of the free energy changes associated with the polar head group and the nonpolar alkyl chain, it has been shown14 for zwitterionic or nonionic surfactants that log
Cf
=
[AGm(IViT-
-1
1.33 +
where cy is the cmc (molar), e = In 10, AG,(W-) and AGm(-CH2-) are the free energy contributions from the head group and each methylene group in the alkyl chain, respectively, and w is the molar concentration of water (55.4 M). Table I shows the effect of temperature and the model used on the free energy of micellization of the Clo and Cl1 N-alkyl betaines. The functions f(A,) were calculated according to Corkill, et using values of A , reported elsewhere.l6 At equivalent temperatures, the Clo homolog loses less free energy than the Cll compound. With both homologs, the free-energy loss increases with temperature. These two effects are
Table 11: Standard Enthalpies and Entropies of Micellization of the N-Alkyl Betaines N-Alkyl betaine
G O c 1 1
a
Temp range,
Train,
AHm', koa1
cal mol-'
OC
OC
mol-'
dsg -1
20-37 43-65 25-35 35-65 10-57
41
Reference 14.
35 6
0.92 -0.61 0.95 -0.78 -1.40
ASmO
18.5 13.7 21 .o 15.4 15.5
' Absent in temperature range studied.
Enthalpy of Micellization. I n contrast to the behavior observed with the C, homolog,14 the cmc's of both the Clo and C11 N-alkyl betaines show a minimum at a particular temperature, Tmin. I n accordance with eq 5 , this results in positive values of AH," at the lower temperatures and negative values above Tmin(Table 11). This behavior may be rationalized in the following manner, Goddard, et al., have proposed that, at low teniperatures and below the cmc, water forms an iceberg structure around the alkyl chain of the free monomer. This leads to a considerable loss in the entropy of the sysSince this restricts free rotation about the C-C bond, the configurational entropy of the chain is also reduced although this is not likely to be a large effect. The heat content of the system is reduced and the partial molal heat capacity of the monomer species is increased. Upon micellization, the iceberg structure is disrupted and the flexibility of the alkyl chain is in(16) J. Daruwala, Ph.D. Thesis, University of Connecticut, 1968.
Volume 73, Number 8 August 1969
2630
J. SWARBRICK AND J. DARWWALA
Table 111: Effect of Temperature and Alkyl and Polyoxyethylene Chain Lengths on AH,' Temp range, "C
Surfactant
Tmin, ~------AHme, O C
25'
for Various Surfactants
kea1 mol-L-40'
---.
50'
60'
65'
-0.6
-0.6
-0.6
-0.6
-0.8
-0.8
-0.8
-0.8
-0.8
-1.4
-1.4
This Paper This Paper
-1.4
-1.4
-1.4
14
450
Ref
N-Alkyl betaine
ClO
20-65
41
0.9
Cll
25-65
35
0.9
CIZ
10-58
a
6-60 10-60 10-60
a a
Sodium alkyl sulfate CS ClO ClZ ClC
10-70 10-70 10-70 10-70
29 29 26 21
%-Alkyl hexaoxyethylene glycol monoether CS ClO CI 2
15-45 15-45 15-.35
a
15-85 15-85 15-85 15-85 15-85 15-85 15-85 15-85 15-85 15-85
50 49 51 51 47 39 25
-1.4
C-Alkyl betaine
CS ClO ClZ
p-t-Octylphenoxyethoxyethanol Eio
Eo E8
E7 E8
E; E4
E8 Ez El a
a
a a
a a a
0.67 0.57 0.55
0.67 0.57 0.55 -0.7 -0.6 -1.1 -1.5
0.3b
4.3 4.2 3.9
1.5 1.4 1.3 1.2 1.0 0.5
0.3 0.3 0.3 0.2 0.2 -0.1 -0.7 -1.3 -2.2 -3.2
0.1
-0.4 -1.0 -1.6
-
1
heat content of a mole of surfactant in the free state at infinite dilution
[
(6)
then at low temperatures AH," will be positive since the first term in eq 6 will exceed the second. As the temperature is raised, the entropy loss of the free monomer below the cmc is reduced because of the decrease in the structure of water. Any rotational restrictions of the alkyl chain would also be less severe. The nionomer in the free state below the cmc is already, therefore, a higher energy system than the same concentration of €ree monomer a t the lower temperatures. The Journal of Physical Chemistry
0.67 0.57 0.55
0.67 0.57 0.55
13 13 13 4
-1.8 -2.6 -3.1
4 4 4
9 9 9
-1
.o
-1.1 -1.2 -1.3 -1.6 -1.9
-2.4 -3.1 -4.1 -5.7
8 8 8 8 8 8 8 8 8 8
' Extrapolated from values a t 20 and 30".
creased. The resultant gain in entropy produces a higher heat content and the partial molal heat capacity of the monomer in the micelle decreases to approximately one-third of that in the free states3 Since
1
0.67 0.57 0.55 -1.2 -1.2 -1.8 -2.3
4.3 4.2 3.9
Tn,innot observed within temperature range studied.
heat content of a mole of surfactant in the micellar state just above the crnc
0.67 0.57 0.55
Consequently, upon raising the temperature, the second term in eq 6 increases. When the two terms are equal, AH," = 0 and the temperature is Tmin. When the temperature exceeds Tmin,AH,' becomes negative. According to other workers,"s18 micellization is mainly an interfacial effect. Due to the exposure of alkyl chains to water below the cmc, there certainly exists a large hydrocarbon-water interface and this could represent a high energy state with a large heat content. However, if micelliaation was predominantly an interfacial effect, the incorporation of monomers into a micelle would always be an exothermic process, regardless of temperature. Although a negative AH," has been observed over the temperature range 10-57" for the CIS N-alkyl betaine14 and 15-85" for certain homologs of p-t-octylphenoxyethoxyethanolI8 this is not always the case as shown by the present study and (17) Y . Ooshika, J. Colloid Sei., 9 , 254 (1954). (18) I. Reich, J . Phys. Chem., 60, 257 (1956).
263 1
THERMODYNAMICS OF ~IICELLIZATION OF ZWITTERIONIC N-ALKYLBETAINES other r e p o r t ~ ~where * ~ r ~AH," changes from positive to negative. The C-alkyl betaines have been shown to have a positive AH," over the range 10-60°.'3 Consequently, while interfacial effects can be expected to exist over the entire temperature range and be exothermic, the sign of AH," depends on whether the structural effector the interfacial effect predominantes. Thus, we can write
AN,"
=
1
AH," contribution due to structural (entropy) effects
[
-
]
AH," contribution due to interfacial energy effects
[
(7)
The observation that AX," is higher a t the lower temperatures (Table 11) supports the theory that the entropy effects are greater a t low temperatures. While eq 7 rationalizes the observed changes in AH," with temperature, it does not predict Tmin. I n those cases where no Tminis observed (Table III), it may well be that the values lie outside the temperature range studied. According to Goddard, et aL18the AH," contribution due to interfacial energy effects is -13 kcal mol-' for sodium decyl sulfate a t 25'. The influence of the head group was neglected since the effective charge on the micelle was considered to be small. Applying this value to the Clo N-alkyl betaine at 25", then the value of AH," due to structural effects is approximately 14 kcal mol-'; L e . , the structural effects predominate over the interfacial effects at this temperature and give rise to a net positive enthalpy. As the alkyl chain length is increased, the interfacial energy effects can also be expected to increase. Therefore, as any one homologous series is ascended a t a constant temperature, AH," should become less positive or more negative. Such a trend is apparent with the data in Table 111. Decreasing the number of polyoxyethylene groups in a surfactant, which makes the molecule more lipophilic, has the same effect. As will be seen later, the rate a t which the structural effects increase does in fact decrease with chain length; the net result is the eventual predominance of the interfacial effects. It is apparent from Table I11 that the temperature a t which AH," = 0 (Tmin) decreases with increasing alkyl chain or decreasing polyoxyethylene chain. One can therefore reasonably assume that the more lipophilic a surfactant, the wider the temperature range over which micellization is an exothermic process. As the surfactant becomes more hydrophilic, micelliaation will be endothermic over a widening temperature range. Just how far this can be extrapolated is uncertain. Presumably, T m i n for the CSN-alkyl betaine will be higher than that for the Clo homolog. However, the freezing
point will limit extrapolation in many cases as the alkyl chain length is increased. Further, it may be less than coincidence that all reported values of Tmin in Table I11 lie within the range 25-50". I n this regard, it is perhaps significant that the heat capacity of water increases either side of a minimum value at 35". Unfortunately, there are insufficient data available to make any unequivocal statement regarding AH, (-CH2-). The relevant data in Table I11 suggest that AH,(-CH2-) for the Clo-C1l homologs in any one series are 2-3 times the values for those homologs with less than 10 carbon atoms. While this is speculative, it is in line, however, with the proposal that as the chain length is increased, the interfacial effects become more pronounced and micellization becomes more exothermic. Some idea of the effect of the head group on the enthalpy of micellixation can be deduced from the data in Table 111. To do this it is necessary to choose a reference alkyl chain and assume that
AH,"
=
AHn,(W-)
+ AHm(-R)
(8)
where AH,(W-) and AH,(-R) are the enthalpy contributions of the head group and alkyl chain, respectively. Taking a Clo alkyl chain as a reference, the enthalpy change for the process n-decane in water -t n-decane liquid a t 25" has been estimated to be -1.4 kcal This figure may be verified by reference to the work of Benjamin12 which shows that AH" for the removal of n-decanol from an aqueous solution to pure liquid decanol is - 1.1 kcal mol-'. Assuming that the contribution of the -OH group is positive and small, the value of -1.4 kcal mol-' for a Clo alkyl chain is a reasonable estimate. Substitution of the AH," values at 25" from Tawe I11 into eq 8 results in the data presented in Table IV, from which it is evident that incorporation of the head group into a micelle is an endothermic process. This may be due to desolvation, since heat is evolved in solvation. While too much weight should not be attached to the actual values shown in Table IV, the rank order can be regarded as significant. Thus, understandably, more heat is required to desolvate the hexaoxyethylene group than the sulfate group, which is probably riot completely desolvated due to the presence of gegenions. The betaine head groups are intermediate between the nonionic and ionic surfactants. It seems possible with the zwitterions that, in addition to the endot,hermic desolvation effect, there is an exothermic effect due to mutual charge desaturation brought about by the head groups adopting a "checkerboard" pattern. 14,19 However, the overall process is endothermic, suggesting that desolvation outweighs any charge saturation effect. Entropy of Micellization. As recorded in Table 11, AS," for the CIO and Cll homologs decreases with (19) A. H. Beckett and R. J. Woodward, J . Pharm. Pharmacol., IS, 422 (1963).
Volume 73, Number 8 August 1969
2632
J. SWARBRICK AND J. DARUWALA
Table IV: Heat of Micellization of Various Head Groups a t 25'
Surfactant
n-Alkyl hexaoxyethylene glycol monoethers N-Alkyl betaines C-Alkyl betaines
-(OCH2CH&OH
5.6
-Nf(CHa)2CH2COO(CH8)aN +CIICOO-
2.3 2.0
Sodium alkyl sulfates
-SOd-Na+
1.7
I
increasing temperature. Such behavior has been noted with nonionic" and cationid surfactants. The Clz homolog does not exhibit this trend, there being no minimum in the plot shown in Figure 2. Even though micelles represent an ordered arrangement of monomers, the data in Table I1 indicate a net gain in entropy on micellization. As discussed earlier, this is due to the breakdown of the iceberg structure of water around the monomer when it enters the mi~ e l l e .This, ~ ~ ~plus ~ the gain in configurational entropy of the monomers, leads to a net entropy increase. As the temperature is increased, the structuring effect is decreased and the net gain in entropy is progressively reduced. Nevertheless, it would appear that some structuring around the monomers is still present a t the higher temperatures since AS," is positive over the entire range studied. Some worker^^,^ have computed values for AS," that changed from positive to negative as the temperature was raised. However, the entropy change was calculated on the unlikely assumption that AG," was zero and therefore AS," could be regarded as equal to AH,,,",fT. Under these conditions, AS," necessarily had the same sign and changed in the same manner as AH,". This point has been discussed in detail elsewhere.l4 The effect of chain length on AS," can be surmised from Table 11. At temperatures in excess of Tmin, AS," increases with chain length of the N-alkyl betaines. A similar trend apparently exists a t temperatures below Tminalthough no data are available for the Clz homolog. A similar increase in the entropy change
The Journal of Physical Chemistry
with chain length has been reported for the n-alkyl hexaoxyethylene glycol monoethers. l 1 While both of these data indicate that the structuring of water around the alkyl chain of the monomer increases with chain length, the entropy change per methylene group, ASm(-CHZ-), decreases with increasing chain length, and will presumably approach zero. This implies a decrease in the surface-to-volume ratio, brought about by the longer alkyl chains tending to curl up, so as to minimize their contact with water. The reduction in ASm(-CHz-) with chain length, together with the previously observed increase in - AHm(-CHz-), supports the proposal of Corkill, et al.," and Benjamin12 that at shorter chain lengths entropy is the main driving force for micellization. However, as the chain length increases, the enthalpy contribution to the whole process becomes increasingly significant. Assuming,AS," to be comprised of the separate contributions of the polar head, ASm(W-), and the alkyl chain, ASm(-R), then
AS,"
= AS,(W-)
+ ASn,(-R)
(9) The entropy change for the transfer of n-decane in water to n-decane liquid a t 25" has been estimated as 29 cal mol-' deg-la3 Substitution of this value into eq 9 gives AS,(W-) for the Clo N-alkyl betaine as -10 cal mol-' deg-l. This loss in entropy upon micellization indicates that the head groups are more restricted in the micelle than when present as free monomers. With nonionic, polyoxyethylene heads, ASm(W-) is not always negative. Thus, Corkill, et U Z . , ~ used eq 3 to obtain a value of 35.9 cal mol-' deg-' for the n-decyl hexaoxyethylene glycol monoether at 25". Substitution into eq 9 yields a value for AS,(W-) of 7 cal mol-' deg-l. A positive entropy is not unexpected, since water must be presumed to form an iceberg structure around the polyoxyethylcne chain in the head group of nonionic monomers, This is disarranged on micellization and contributes to the observed gain in entropy. Acknowledgments. The authors wish to thank the University of Connecticut Research Foundation for support under grant NO. 1002-35-068. (20) P. Mukerjee, Advan. Colloid Interface Sci., 1, 241 (1967).
