J. Phys. Chem. 1985, 89, 1473-1477 apparent. Self-diffusion constants calculated from the slopes of the liquid-state curves are also listed in Table 11. It is interesting to note that the contribution to D due to the long-time tail which is not given by the model Gaussian memory function is quite significant, often amounting to more than 30% of the total.
Conclusions Both molecular translational and rotational motions are highly hindered in the fluids simulated in this study-translations, because of the relatively high density, and rotations, because of the high density and the nonspherical potentials chosen. Upon melting, the nature of the motions changes from what appears to be coupled oscillations to what is basically diffusive. However, translations and rotations in the liquids are far from simple random walk. In particular, it is necessary to take umemoryninto account and, in addition, to deal with “cage effects” which produce damped oscillatory features in the velocity correlation functions. The rotational librations are reproduced reasonably well by a model embodying these ideas. In the translational case, the memory function used does not explicitly include a description of the translational cage effect, not is it capable of reproducing the long-time tails observed in the Cu(t).Nevertheless, the transla-
1473
tional Gaussian memory function seems to give correlation functions significantly closer to the simulations than does the exponential form suggested earlier. (Additional comparisons of simulation results and the C,(t) obtained from the memory functions are under way.) As is often the case the reasons for the success (or lack of it) for this simple memory function are not clear. We note that Lucas and co-workers10have obtained reasonable agreement between theory and experimental or simulated viscosities and self-diffusion constants for liquid argon by using Gaussian memory functions with parameters numerically evaluated from expressions relating them to equilibrium averages of functions of the interatomic potential. The work reported here is similar in spirit but indicates that much of their observed differences between experiment and theory may be due to difficulties in handling the long-time tails expected in the relevant time-correlation functions for these systems.
Acknowledgment. Support from the N.S.F. for this work via grant CHE-8305735 is gratefully acknowledged. (10) K. Lucas and B. Moser, Mol. Phys., 37, 1849 (1979); 38, 1855 (1979); M. Luckas and K. Lucas, Mol. Phys., 48,989 (1983).
Microtitration Calorimetric Study of the Micelllzatlon of Three Poly(oxyethylene) Glycol Dodecyl Ethers Gerd Olofsson Division of Thermochemistry, Chemical Center, University of Lund, S - 221 00 Lund, Sweden (Received: October 5, 1984)
A new microtitration calorimetric technique has been utilized to determine the enthalpy of micelle formation AH(mic) and cmc for three poly(oxyethy1ene) glycol dodecyl ethers, C12H25(OC2H4),0H(x = 5,6, and 8), in water. Measurements were made at 10 and 25 “C and for C&8 also at 40 “C. The values of cmc determined in the present study are considered to be at least as accurate as previously reported values. Titration calorimetry offers a useful method for the determination of cmc, particularly for nonionic surfactants with low cmc’s. Measurements were also made of enthalpies of solution of pure liquid C12E, in aqueous solution. Comparison between the micellization enthalpies and solution enthalpies makes it possible to see how changes in head-group size and temperature influence the amphiphiles in the monomer and micellar states separately. The enthalpies of micelle formation are endothermic and vary only little with the size of polar group, the values (in kJ mol-’) being at 25 “C 13.5 0.3 for C12E5, 14.8 0.4 for C&6, and 16.3 0.4 for C1&. The enthalpies of solution to give aqueous monomers are strongly exothermic and vary considerably with head-group size, the exothermic contribution being 7 kJ mol-’ per (-OCZH4-) group. The contribution to the solution enthalpy from the C12alkyl chain is close to zero at 25 OC. The.observed AH(mic) therefore corresponds to the enthalpy of dehydration of 2-2.5 ethylene oxide groups. The values for the entropy of micelle formation are large and positive while the heat capacity changes are large and negative. The values for both properties are nearly the same for the three C12E, studied. Contributions from the dehydration of the alkyl chain dominate M(mic) and ACJmic). The temperatures for the minima in the cmc do not correlate with the cloud-point temperatures.
*
*
Introduction Nonionic surfactants have critical micelle concentrations (cmc’s) in water that are substantially lower than ionic surfactants having the same size of nonpolar group. For instance, poly(oxyethy1ene) glycol dodecyl ethers have cmc’s of the order 5 X 10-5-104 mol kg-’ at room temperature while the cmc of sodium dodceyl sulfate is 8 X mol kg-’. Calorimetric measurements are needed to give reliable information about enthalpy, entropy, and heat capacity changes for micelle formation,’ but only few studies have been made on nonionic surfactants?+ The scarcity of calorimetric (1) D. G. Hall and B. A. Pethica in “Nonionic Surfactants”, Vol. 1, M. J. Schick, Ed., Marcel Dekker, New York, 1966,p 549. (2) L. Benjamin, J . Phys. Chem., 68, 3575 (1964). (3) J. M. Corkill, J. F. Goodman, and J. R. Tate, Trans. Faraday SOC., 60, 996 (1964). (4) J. L. Woodhead, J. A. Lewis,G. N . Malcolm, and I. D. Watson, J. Colloid Interface Sci., 79, 454 (1981).
0022-3654/85/2089-1473$01.50/0
*
data is due at least in part to their low cmc’s. A new microtitration calorimetric method has been developed that allows the direct determination of both the enthalpy of micelle formation PJl(mic) and the cmc. Results of measurements on the pentakis-, hexakis-, and octakis(oxyethy1ene) glycol dodecyl ethers (C12E5, C1&, and C12E8)at various temperatures are reported in the present paper. The study was made to see how changes in size of the polar group affect the micellization. In a previous paper calorimetric measurements on C12E5 were reported and the thermodynamics of micellization of C12E5in water were discussed? The present study gave more precise results for AH(mic), and in addition values of cmc have been determined. Measurements have also been made on the dissolution of pure liquid C12E,in aqueous solution. These results make it possible (5) J. E. Desnoyers, G. Caron, R.DeLisi, D. Roberts, A. Roux, and G. Perron, J . Phys. Chem., 87, 1397 (1983). (6) G. Olofsson, J . Phys. Chem., 87, 4000 (1983).
0 1985 American Chemical Society
Olofsson
1474 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985
to discuss the influence of variation in the head-group size and temperature on the monomer-micelle equilibrium in terms of the separate contributions from the monomer and micellar states.
Experimental Section Materials. High-purity pentakis-, hexakis-, and octakis(oxyethylene) glycol dodecyl ethers, Ci2E5, C12E6,and C I Z E ~were , obtained from Nikko Chemicals Co., Ltd., Tokyo, Japan, and used without further treatment. Judging from gas chromatograms provided by the manufacturer, the punty of the samples was better than 99%. The molar masses and melting points of the fompounds are the following: CI2E5,406.61 g mol-' and 22.8 OC; & el,, 450.66 g mol-' and 24.8 OC; Cl2E8,538.77 g mol-' and 31.4 OC. Densities for the liquid amphiphiles and 20 wt % solutions in water were determined at 25.0 OC from pycnometric measurements. It was found to be 0.956 g cm-3 for pure Ci2E5 and 0.971 g cm-) for C&. The density was 0.995 g cm-3 for the Ci2E5 solution, 0.994 g cm-3 for the CI2E6solution, and 1.002 g cm-3 for the C12& solution. The uncertainty is estimated to be less than 0.001 g ~ m - ~ . Reagent-grade water produced by a Milli-Q filtration system (Millipore AB, Goteborg, Sweden) was used. Calorimetry. The calorimetric measurements were made by using an LKB reaction-solution calorimeter with a 100-cm3 glass reaction vessel.' Two different types of measurements were made, namely batch and titration measurements. In the first type of operation the samples to be dissolved or diluted were placed in cylindrical glass ampules of 1-cm3volume. The ampules had thin end walls and narrow necks which were sealed under low flame and detached. In the experiments the ampules were lowered over a glass pin with a sapphire tip which penetrated the end walls. This breaking of the ampules can give rise to disturbing heats of friction, and the end walls need to be very thin for experiments with small temperature changes. The ampules then become difficult to handle. To overcome this problem, the calorimeter was modified to operate as a titration calorimeter. The samples were introduced into the calorimeter vessel by means of a thin steel tube (length 1 m, i.d. 0.15 mm) fastened by epoxy to a Hamilton 100-mm3 gas-tight syringe (1710 LT). The capillary tube passes through a tube (i.d. 1 mm) in a slit at the inside of the stirrer holder and ends about 30 mm below the surface of the calorimeter liquid. The syringe is motor driven, and the samples were injected at a rate of 0.14 mm3 s-l. The sample sizes varied between 5 and 25 mm3, and dilution ratios of up to 1/20000 were achieved. Due to the small sample sizes, the temperature changes in these experiments were small, between IO4 and K. The resulting resistance changes of the thermistor used as temperature sensor are too small to be measured accurately by manually balancing the dc Wheatstone bridge of the LKB system. Instead, the off-balance of the Wheatstone bridge caused by the temperature change during the experiment was amplified and the resulting voltage read by a digital voltmeter once a second. The signal was averaged over 1-min periods to reduce the noise. The amplification was such that a temperature change of 0.001 K corresponded to an output signal of 0.5-1 V depending on the thermistor used. In this way enthalpy changes as small as 0.01 J could be determined to better than 20%. A HP 3455 A Digital voltmeter and a HP desk-top computer were used. Results
Enthalpy of Micelle Formation and Cmc. The enthalpy of micelle formation, AH(mic), and critical micelle concentration, cmc, have been determined from dilution experiments at two different temperatures for CI2E5and CI2E6and at three temperatures for C&,. In the experiments 5-10-mm3 portions of 20 wt % (0.5-0.6 mol kg-I) amphiphile solutions were added consecutively to the calorimeter containing at the beginning 100 cm3of pure water. Results of seven series of experiments for Cl,E, at 25 O C are summarized in Figure 1 where the observed molar enthalpy changes are plotted against amphiphile concentration. The results of the individual experiments are represented by (7) S. Sunner and I. Wadd, Sci. Tools, 13, 1 (1966).
Figure 1. Differential enthalpies of dilution of 20 wt % CIZE6as function of CI2E6concentration at 25 OC. The results of the individual experiments are represented by horizontal lines whose end points indicate the CI2E6concentration before and after each addition. Below the cmc, AHow is the enthalpy change for dilution and complete demicellization
of the concentrated micellar solution, while for experiments crossing the cmc only partial demicellization takes place. horizontal lines. Plots of the results for the other systems show the same general features. There is a very rapid increase in the observed enthalpy change AHobsd with concentration in the beginning, but after four to five injections AHoMbecomes fairly constant. These titration curves can be described in the following way. All CI2E, added in the first injection will demicellize and give aqueous monomers, the final molality lying below the cmc: CI2Ex(mic,20 wt %)
+ aq
-
ClZE,(mon, aq)
AHl
(1)
The measured enthalpy change AH1is the sum of the enthalpy changes for dilution and demicellization. After the second injection the final molality lies above the cmc, and for this step only partial demicellization will take place: ClzEx(mic, 20 wt %) + aq aCI2Ex(mon,aq) + (1 - a)ClzEx(mic,aq) AH, ( 2 )
-
The degree of dimicellization is denoted a. The observed enthalpy change AH,consists of the enthalpy of dilution and the fraction a of the demicellization enthalpy. For the fourth or fifth and later injections no demicellization takes place and the measured enthalpy change AH3 is the differential enthalpy of dilution of the concentrated micellar solution to the final molality mc ClzE,(mic, 20 wt %) + aq -.+ CI2E,(mic, mr) (3) AH3 From such titration curves both the enthalpy of micelle formation iw(mic) and the cmc can be derived. As can be Seen from Figure 1, there is a tailing in the titration curve indicating that micellization extends over a concentration range. It is possible that in some cases there is a continuing growth of micelles. This could lead to a significant variation of the dilution enthalpy with concentration which will make the determination of AH(mic) somewhat arbitrary. Therefore, measurements were made of enthalpies of dilution to final concentrations well above the cmc. In the ampule calorimetric measurements 0.7-0.8 g of concentrated CL2Exsolution was diluted in 100 g of 0.001 mol kg-' CI2E, solution to give final molalities of on the average 0.004 mol kg-I. The dilution enthalpy of the C,,E8 solution at 10 and 40 O C was determined from titration experiments in which about 30 mm3 of concentrated solution was diluted into 100 g of CIzE8solution containing respectively 0.004 and 0.0025 mol kg-l of C&& Results of the titration and ampule dilution measurements are summarized in Table I. The second column gives the temperature for the measurements, the third column the molality of the concentrated C,,E, solution, and the fourth column the change in
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1415
Micellization of ClZEx TABLE I: Enthalpies of Dilution, AH(diI), of 20 wt % C12E, Solutiom Close to the Cmc and at Higher Molalities m(sample), m,(cal) mf, M(dil), s," kJ C12Ex t , OC mol kg-' mol kg-' kJ mol-' mo1-I CI2E5 11.75 0.61 (18 to 35) X -2.07* 0.20 -0.47' 0.04 10.20 0.55 (1.0 to 4.1) X lo-' -0.46b 0.05 24.96 0.61 (7 to 30) X -0.23c 0.02 24.96 0.55 (1.0 to 4.1) X
-
n 6 3 6 3
CI2E6 10.02 10.02 25.0 24.80
0.55 0.55 0.55 0.54
(20 to 50) X (1 to 5) x 10-3 (13 to 30) X (1 to 5) X
-1.2Sb -0.99' -2.08b -1.42'
0.11 0.08 0.13 0.08
6 4 8 6
CI2E8 10.02 10.02 25.0 25.0 40.16 40.16
0.51 0.51 0.46 0.46 0.48 0.48
(29 to 60) X 4 x 10-3 (13 to 25) X lom5 (1 to 3.5) X lo-' (20 to 55) X 2.5 X
-0.90* -0.64d -0.90* -0.49' -1.72b -1.22d
0.20 0.14 0.08 0.02 0.09 0.16
6 7 5 4 5 4
a Error limits are expressed as standard deviations of the means estimated from n experiments. From titration measurements close to the crnc. From ampule experiments. dTitration calorimetric experimol ments in which the final concentration was changed 0.1 X kg-I in each step.
TABLE II: Enthalpy of Micelle Formation, AH(mic), and Critical Micelle Concentration, Cmc, for C12E5,C12Ee and C12& Determined from Calorimetric Titration Exwriments M(mic), s, kJ 1O5cmc, 1oss, t , OC kJ mol-l mol-' n mol kg-' mol kg-' C12E5 11.75 21.47 0.26 4 7.86 0.08 25.00 13.46 0.16 14 5.78 0.08 C12E6
10.05 25.05
24.30 14.79
0.26 0.19
4 7
10.16 6.45
0.09 0.10
CI2ES
10.02 24.88 40.16
27.33 16.34 7.90
0.34 0.18 0.25
6 5 4
14.36 9.04 7.30
0.08 0.04 0.20
molality of the calorimeter solution in the experiment. The enthalpy of dilution calculated per mole of amphiphile is shown in column six and its estimated standard deviation in column seven, with n the number of experiments being given in the last column. There is a significant difference between AH(di1) at the two molalities for Cl2E5at 11.75 OC and possibly for C1& at 25 OC while for the other series the agreement is reasonable considering the uncertainty in particularly the titration experiments. As AH(di1) referring to mf = 0.004 mol kg-' shows the smallest variation with temperatures and has been measured with better precision, it will be used to calculate AH(mic). Thus, AH(mic) is defined in the present study as the difference between the partial molar enthalpy content of the amphiphile in the micellar state at molality 0.004 mol kg-' and that of the aqueous monomer. The cmc is so low for these amphiphiles that is is not possible to study concentration effects on the enthalpy content in the premicellar region. The micellization enthalpies were calculated from the observed enthalpy changes according to AH(mic) = -AHl + AH(di1, 0.004 m) The results are summarized in Table I1 where column two shows the temperature of the measurements, column three shows the values of AH(mic), and column four gives their calculated standard deviation based on the number of experiments n shown in column five. The observed enthalpy changes in the second titration steps AHz can then be expressed as AH2 = -aAH(mic) + AH(di1) = aAHl + (1 - a)AH(dil, 0.004 m) Values of cmc were calculated from the relation cmc = (nl + a n z ) / V where nl and nz denote the number of moles of amphiphile in the first and second injections, respectively, and Vdenotes the mass of water in the calorimeter vessel. The resulting cmc's are given
in column six of Table 11with their estimated standard deviation in column seven. The number of series of measurements n was the same as for AH(mic). The observed curvature of the titration curves indicating that micelle formation extends over a concentration range up to about 2 times the cmc is fully consistent with the variation of degree of association with concentration calculated for the formation of micelles having aggregation number of 50 or 100 by using the mass action law model (see Figure 7.1 in ref 8 and Figure 3.1 in ref 9). The C12Exstudied give micelles that are of this size close to the crnc.lo," Dissolution of Liquid Cl2EX.Enthalpies of solution of liquid C12Exto give micelles in aqueous solution have been measured, CI2Ex(l) aq = l/n(C12Ex),,(mic). The observed enthalpy changes are denoted R(rnic) - H(1). C1ZE5. A series of 12 injections of 5.04 mm3 of C12E5(corresponding to l.185X mol) was made in 100 g of water to which varying amounts of C12E5 were added so that the molality and 9.5 X varied between 0.2 X mol kg-I. It gave R(mic) - H(1) = -23.78 kJ mol-'. The reproducibility expressed as the estimated standard deviation of the single experiment was 0.34 kJ mol-'. The measurements were made at 25.05 OC, and no significant variation of the solution enthalpy with molality was observed. The present value is in satisfactory agreement with the value of -24.08 f 0.06 kJ mol-' previously determined from ampule calorimetric measurements.6 C12& Two series of measurements were made of dissolving small amounts of liquid Cl& in aqueous solution containing between 0.11 X and 8.8 X mol kg-' of CI2E6. In the experiments 5.04 mm3 of liquid sample was injected into 101.5 g of water to which varying amounts of ClzE6were added. The experiments were made a t 25.05 OC. The 18 experiments gave R(mic) - H(1) = -30.4 kJ mol-'. The estimated standard deviation of the single experiment was 0.46 kJ mol-'. There was no obvious trend in the values with concentration. C12E8.The enthalpy of solution of liquid C12E8 was determined from ampule calorimetric measurements in which about 3 X lo4 mol of C12E8was dissolved in 100 g of water containing 2 X lo4 mol kg-' of C&,. Measurements at 32.32 O C gave R(mic) H(1) = -40.98 f 0.03 kJ mol-' and at 40.07 OC R(mic) - H(1) = -38.64 f 0.17 kJ mol-'. The error limits are expressed as standard deviations of the means calculated from the results of four and five experiments, respectively. The results give the value 302 f 22 J K-' mol-' for the heat capacity of solution CJmic) - CJl). Extrapolation to 25 OC (where C&8 is solid) gives R(mic) - H(1) = -43.2 f 0.3 kJ mol-'. Thermodynamics of Micelle Formation. Values of cmc, AG(mic), AH(mic), AS(mic), and ACJmic) at 25.0 OC for the three amphiphiles in the present study are given in Table 111. The heat capacity change for micelle formation ACJmic) = C,,(mic) CJmon) was calculated from measured AH(mic) (see Table 11). The values of ACJmic) given in Table I11 therefore refer to the mean temperature of the experiments. However, the temperature dependence of ACJmic) is probably small, and the error introduced when they are ascribed to 25 OC is small in comparison with other uncertainties in the values. The following relations were derived to express the temperature variation of cmc by using the values of cmc, AH(mic), and ACJmic) shown in Table 111. C12E5: In cmc = 23314.1/T + 72.7662 In T - 502.547 Cl2E,j: In cmc = 24514.0/T + 76.2542 In T - 526.335 C1& In cmc = 25163.5/T 77.4570 In T - 535.028 The heat capacity changes are negative which means that AH(mic) will decrease with increasing temperature. At the temperature
+
+
(8) C. Tanford, "The Hydrophobic Effect", 2nd ed., Wiley-Interscience, New York, 1980. (9) B. Lindman and H. Wennerstrom in "Topics in Current Chemistry", Vol. 87, F. L. Boschke, Ed., Springer-Verlag, West Berlin, 1980. Nilsson, H. Wennerstrom, and B. Lindmu., J. Phys. Chem., (10) P.-G. 87,'1377 (1983). (11) W. Brown, R. Johnsen, P. Stilbs, and B. Lindman, J. Phys. Chem., 87,'4548 (1983).
1476 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985
01ofsson
TABLE IIk Thennodynamic Properties for Micelle Formation of CI2ELC12Estand CI2& in Aqueous Solution at 25.0 O C '
ACJmic), ClZEJ C12E6
ClZE8
cmc, mol kg-l
AG(mic),b kJ mol-'
AH(mic), kJ mo1-l
M(mic), J K-' mo1-I
J K-I mol-l
(5.78 0.16) X 10" (6.45 0.20) x 10-5 (9.04 f 0.08) X
-24.19 f 0.06 -23.92 f 0.10 -23.08 f 0.04
13.5 f 0.3 14.8 f 0.4 16.3 f 0.4
126 f 2 130 2 132 f 2
-605 f 50' -634 f 40d -6'M) f 75'
*
"The error limits are expressed as twice the overall standard deviation of the means. bAG(mic) = RT In cmc. eRefers to 17.5 "C. dRefers to 18.3 "C. CRefersto 25.0 "C. A
TABLE I V Minimum Values of the Critical Micelle Concentration, Cmc& for CI2Exin Water and the Temperatures t h at Which They Occur
mon-mic
cmcmin,mol kg-I zminr "C
4.77 X 47.2
5.17 X 48.3
6.74 X 51.7
where AH(mic) = 0, the cmc will show a minimum. The minimum values of cmc and the temperatures a t which they occur are given in Table IV. Comparison with Previous Results. Critical micelle concentrations determined from surface tension measurements at 10.25, and 40 O C have recently been reported for C12ES,CI2E8,and four other C12E, compounds.12 The samples of the amphiphiles were purchased from Nikko Chemicals Co., Tokyo, Japan. They were further purified by repeated passage of aqueous solutions through columns of octadecylsilamized silica gel. The observed values for and 6.4 X mol dm-3 at the cmc were for ClzES9.0 X 10 and 25 OC, respectively, and for C12E8 15.6 X and 10.9 X mol dm-3 a t the same two temperatures. These values are higher than the values determined in the present study (see Table 11). Values of AH(mic) were derived from the variation of cmc with temperature and found to be 9.9 and 13.2 kJ mol-' at 25 OC for CI2E5and C12E8,respectively.12 These values are about 3 kJ mol-' lower than the present values. For C12E5,the value 5.6 X mol dm-3 has been reported previously for cmc at 25 OC,I3 which is in good agreement with our value. It was determined from surface tension measurements using a sample from Nikko Chemicals Co. A slightly lower value, (5.5 f 0.2) X mol dm-3 at 22.0 OC, has been found from fluorescence quenching mea~urements.'~This latter determination of the cmc was made on one of the lots of C12E5used in the present study. In a study of C,Es with n = 10-15, the cmc's were determined from surface tension measurements at five different temperatures between 15 mol For C12E8the cmc was found to be 7.1 X and 40 dm-3 at 25.0 OC and the value derived for AH(mic) was 15.3 kJ m01-l.I~ The samples were from Nikko Chemicals Co. and were further purified by repeated passage through a gel permeation chromatographic column. A value of 8.0 X mol dm-3 at 25.0 OC for the cmc of CI2E8 has been derived from results of 7,7,8,8-tetracyanoquincdimethanesolubilization measurements. l6 These cmc values are significantly lower than the value found by us and by Rosen et a1.I2 while the value of AH(mic) agrees satisfactorily with the present result. There appears to be only one previously reported value for the cmc of CI2E6which has been determined on a well-characterized sample. From surface tension measurements at 25.0 O C the value 8.7 X mol cm-3 was found,I7 which is somewhat higher than our value. Thus, there is a significant scatter among the reported cmc values probably reflecting the varying influence of impurities on the different methods. The present calorimetric method is not sensitive to small amounts of impurities, and it can therefore be considered more (12) M. J. Rosen, A. W. Cohen, M. Dahanayake, and X.-Y. Hua, J. Phys. Chem., 86, 541 (1982). (13) H. Akasu, M. Ueno, and K. Meguro, J. Am. Oil Chem. Soc., 51, 519 (19741. (14) S. Swarup, private communication. (15) K. Meguro, Y.Takasawa, N. Kawahashi, Y. Tabata, and M. Ueno, J. Colloid Interface Sci., 83, 50 (1981). (16) Y. Takasawa, M. Ueno, T. Sawamura, and K. Meguro, J . Colloid Interface Sci., 84, 196 (1981). (17) R. R. Balmbra, J. S. Clunie, J. M. Corkill, and J. F. Goodman, Trans. Faraday SOC.,58, 1661 (1972).
-
a
-201
1
1
1
6
7
8
X
-40
I
\
Figure 2. Enthalpies of micelle formation AH(mic) and enthalpies of solution of liquid CI2Exto give micelles and aqueous monomers, respectively, at 25 "C.
robust than the more sensitive surface tension methods. It can be noticed that fairly long equilibration times are needed in the surface tension measurements, 0.5 hI2 to 2 h.I4 In the calorimetric measurements, equilibrium is reached within 2 min after the sample has been added, which is within the normal equilibration time of the calorimeter. We consider the cmc values determined in the present study to be at least as accurate as the previously reported values and regard titration calorimetry as a useful method for the determination of cmc. It will be particularly useful for nonionic surfactants with low cmc for which only a limited number of methods are available. In the previous study of C12E5values of AH(mic) equal to 25.7 f 3.6 kJ mol-' at 10 OC and 14.0 f 1.6 kJ mol-I at 25 OC were reported for CI2E5. They agree within the uncertainty limits with the more precise values found in the present study.
Discussion The formation of micelles of C12Ex in aqueous solution, C12E,(aq) l/n(C12E,),(aq), is fairly endothermic at room temperature, being 14-16 kJ mol-' for the amphiphiles in the present study. Both M ( m i c ) and cmc vary only slightly with the length of the polar group. Contrary to this, the formation of aqueous micelles from liquid amphiphiles, C12Ex(l) l/n(C12E,),(aq), is strongly exothermic and the enthalpy change H(mic) - H(1) shows a pronounced decrease with increasing size of the polar group. This means that the dissolution of liquid amphiphiles to give aqueous monomers, C12Ex(l) C12E,(aq), is an even more exothermic process.I8 The enthalpy changes for the three processes are plotted in Figure 2 against x , the number of ethylene oxide groups. It shows that the enthalpy changes vary linearly with x , the slope being close to -7 kJ mol-l for the two
-
-
-
(18) The enthalpy change for this process, H(aq) - H(I), was calculated from the measured enthalpy changes of the two previous processes: H(aq) - H(1) = [H(mic) - H(1)] - Aff(mic).
Micellization of C12Ex lines representing the dissolution enthalpies while the slope of the line representing M ( m i c ) is much smaller, about 1 kJ mol-'. Micelle formation can be seen as the formation of spherical aggregates in which the hydrocarbon chains in the interior are completely dehydrated and in a state that in many respects resembles that of a hydrocarbon 1 i q ~ i d . l ~In the previous paper discussing C12E56we suggested that the contribution of the ethylene oxide groups dominates the dissolution enthalpy [H(aq) - H(1)] a t room temperature. The E5 group was estimated to contribute -35 kJ mol-' to the solution enthalpy of C12E5, the measured value being -37.7 kJ mol-'> The estimate was based on values of enthalpies of solution in water of triethylene glyco120 and of poly(ethy1ene oxide)m together with values for the enthalpy of melting and C, of solid and liquid poly(ethy1ene oxide).21 This estimate indicates that the contribution of the alkyl chain to the hydration enthalpy is very small, --3 kJ mol-' which in fact is consistent with the observation that the enthalpy of dissolution of alkanes in water is close to zero at 25 0C.22 Further, the estimated group contribution of (-OC2H4-) to the solution enthalpy of -6.7 kJ mol-' is close to the observed value of -7 kJ mol-' which is the slope of the dissolution curves in Figure 2. When the micelles are formed, the hydration of the ethylene oxide groups closest to the micellar surface is probably altered while the outer parts of the polar group remain in full contact with water. The endothermic enthalpy changes for micelle formation then correspond to the dehydration of between 2 and 2.5 ethylene oxide groups. The change in hydration of the amphiphiles upon micellization is reflected in the large negative values of AC,(mic). The amphiphiles in the present study give values of on the average -625 J K-' mol-'. The heat capacity change for transfer of a C12alkyl chain from water to liquid alkane is estimated to be -770 J K-' mol-' 23 so it is likely that the dominant contribution to AC,(mic) stems from the dehydration of the alkyl chain. The contribution from changes in hydration of the ethylene oxide groups closest to the micellar surface would be much smaller as the heat capacity change for transfer from water to liquid poly(ethy1ene oxide) is only about 30 J K-' per (-OCzH4-) group at 25 OC. The values of AC,(mic) have been derived from AH(mic) measured at two or three temperatures. While CI2&forms spherical micelles whose size varies only little with concentration and temperature, substantial growth of micelles in both the CI2E5and CI2E6systems has been inferred from results of various types of measurements (see ref 10 and 11 and references therein). Results from dynamic and intensity light scattering, spin-echo N M R self-diffusion, and sedimentation measurements in the recent study of the CI2E6 system showed the micelles to have constant size and probably a spherical shape up to 20 OC; between 20 and 35 OC a marked increase in size was indicated, and then a more gradual increase in size up to the cloud point at about 50 OC." Thus, while AH(mic) at 10 OC probably refers to the formation of small spherical micelles, the value determined at 25 OC may refer to the formation of larger micelles. Likewise, the AH(mic) values ~~
(19) G. S. Hartley, J . Chem. SOC.,1968 (1938). (20) K. Bystrbm and G. Olofsson, unpublished results. (21) U. Gaur and B. Wunderlich, J. Phys. Chem. Ref. Data, 10, 1001 (1 98 1). (22) S. J. Gill, N . F. Nichols, and I. Wadso, J. Chem. Thermodyn., 8,445 (1976). (23) The value is calculated as the difference between q,2, estimated by using values for CHI and CH2group contributions (N. Nichols, R. Skbld, C. Spink, J. Suurkuusk, and I. Wadsb, J . Chem. Thermodyn., 8, 1081 (1976), and C, for liquid dodecane.
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1477 determined for C12E5may refer to different micellar size. However, in this system micellar growth would take place at the lower but not at the higher ternperature.'O Accordingly, if Nil(mic) varies with micellar size, which seems plausible, the calculated values of AC,(mic) for CI2E5and CI2E6may contain in addition to the "true" AC,(mic) refemng to the same micelle size at the two temperatures a contribution stemming from a difference in enthalpy content of the amphiphile in micelles of two different (average) sizes. This contribution may be small and is not seen in the present results. In any case it can be concluded that the change in size of the polar group does not significantly affect AC,(mic). The large negative values of AC,(mic) mean that AH(mic) will decrease rapidly and become zero and then negative above room tempature. This gives minima in the cmc at temperatures which are very closely the same, between 47 and 52 OC, for the three CI2Exin the present study (see Table IV). These minima are not correlated with the cloud points, that is the critical points for the separation of the isotropic micellar solution into two liquid solutions which occur at about 30,50, and 75 OC for x equal to 5, 6 , and 8, respectively. The entropy changes for micelle formation W m i c ) are closely the same for the C12E, studied (see Table 111) and thus not noticeably affected by the lengthening of the polar group. From the equation of state for the hydrophobic effect devised by Gill and Wadsb, the entropy of transfer of a C12alkyl chain from water to a hydrocarbon environment at 25 OC was estimated to be 132 J mol-' K-'.24 This figure is surprisingly close to the values of U ( m i c ) found in the present study and indicates that the dominant contribution to AS(mic) stems from the transfer of the alkyl chain from the aqueous environment to the hydrocarbon-like interior of the micelles.
Conclusions From enthalpies of micelle formation and enthalpies of solution of Cl2EXin the present study ( x = 5, 6 , and 8), the following observations can be made: The enthalpies of solution to give aqueous monomers are strongly exothermic and decrease about 7 kJ mol-' per OCzH4 group as the chain length increases. The contribution to the solution enthalpy from the alkyl chain is close to zero at room temperature. The micellization enthalpies AH(mic) are endothermic and correspond at 25 OC to the dehydration of 2-2.5 ethylene oxide groups. The micellization process is characterized by positive entropy changes and large negative heat capacity changes. The values for the hS(mic) and for AC,(mic) are nearly the same for the three CI2Exstudied. The dominating contribution to both properties stems from the dehydration of the alkyl chain. AH(mic) becomes zero, and accordingly the cmc will have minima a t nearly the same temperatures for the three C12E, studied. Thus, the temperatures for the minima in the cmc do not correlate with the cloud-point temperatures. Acknowledgment. I am grateful to Mrs. Stina Bergstrbm and Mrs. Inger Johnson for their assistance in performing the measurements. The work was supported by grants from the Swedish Natural Science Research Council. Registry NO. CIZES, 3055-95-6; C12E.5, 3055-96-7; C12E8, 3055-98-9. (24) S. J. Gill and I. Wadsb, Proc. Natl. Acad. Sci. W.S.A., 73, 2955 ( 1976).
