The enthalpy of micellization of potassium decanoate in solutions of H2O and D2O determined with microcalorimetry

The Enthalpy of Micellization of Potassium Decanoate in Solutions of H20 and D20 Determined with Microcalorimetry Y. F. MAA AND S. H. CHEN 1 Department of Chemical Engineering, University of Rochester, Rochester, New York 14627 Received January 23, 1986; accepted April 4, 1986 The microcalorimetrically determined heat of dilution data are used to evaluate the enthalpy of micellization at the C M C ( A H ~ ) for potassium deeanoate in H 2 0 and D20. The values for AHM based on a mass-action model are in good agreement with those determined graphically. That AHM in D20 is higher by 30% than in H 2 0 at 298.4°K and that diminution in AHM at 307.9°K is observed in H 2 0 are both consistent with the hydrogen bonding treatment of hydrophobic association. © 1987 Academic Press,Inc. I. I N T R O D U C T I O N

Understanding the thermodynamic behavior of surfactants in aqueous solutions is important from both fundamental and practical standpoints. Above a critical concentration, surfactant molecules aggregate to form micelles, which have been found to be useful in a number of applications, including tertiary oil recovery (1) and micellar catalysis (2). Obviously, thermodynamic parameters governing micelle formation are the key to effective physical or chemical processing. Furthermore, from an understanding of micellar aggregation one can possibly gain better insights into the more intricate behavior of biopolymers in solution. Historically, the enthalpy and entropy of micellization were obtained from the temperature dependence of the critical micelle concentration (CMC) on the basis of pseudophase separation (3) or mass-action (4) models. The accuracy of the resultant enthalpy and entropy of miceUization have been questioned (5-8). As a result, direct measurement of the thermodynamic quantities using the microcalorimetry technique has been actively pursued in recent years to reexamine the thermodynamics of micellization (9-12). l Author to w h o m correspondence should be addressed.

In the present study a batchwise microcalorimeter with high sensitivity (tO 80 #J) was employed to measure the heat of dilution of potassium decanoate as a function of concentration in solutions of both natural and heavy water. Potassium decanoate was selected because of the combination of its critical micelle concentration and micellar aggregation number (around 0.1 m and 39, respectively) that facilitates the extraction of the enthalpy ofmicellization from the heat of dilution data. Because of its adverse effects on the viability and growth of living organisms and its toxicity to higher animals (13), heavy water was included in the present investigation in the hope of providing a better understanding of the "hydrophobic" effect via studies on micellar aggregation and ultimately of its biological implications. II. E X P E R I M E N T A L SECTION

Microcalorimeter The microcalorimeter employed here is similar in design to the one reported by Lovrien et al. (14). It is a twin batch mixing instrument housed in a thermostatted enclosure. The temperature of the enclosure is controlled by four Peltier pumps to within +__0.1K. Two mixing vessels, sample and reference, are made

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Journalof ColloidandInterfaceScience,Vol. 115,No. 2, February 1987

0021-9797/87 $3.00 Copyright© 1987by AcademicPress,Inc. All rightsof reproductionin any formreserved.

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MAAAND

of 18K gold and designed to mix up to 1.0 ml with up to 0.5 ml of solutions. Each vessel interfaces with two Seebeck thermopiles which monitor heat fluxes between the vessels and the aluminum heat sinks encasing the thermopiles. Both sets of thermopiles are so connected that the heat from the reference vessel is substracted from that of the sample vessel by means of electrical substraction of the thermoelectric signals. Because of the very low resistance of the thermopiles, the microcalorimeter has a figure of merit of 6.8 ___0.2/zW/gV output. Thus, the instrument is a highly sensitive differential calorimeter (to 80 #J), and heat in the 0.01-1.17 joule range can be measured with a precision better than + 1%. The mixing drum is held in position by a yoke which can be rotated to mix the contents of the mixing vessels. Having been charged with solutions at different concentrations (solution diluted with solvent in our experiments), the microcalorimeter is left to reach internal thermal equilibrium for about an hour for the thermal shock of solution loading to vanish. At that point the reading of the voltameter should be essentially zero. The drum is then rotated to initiate mixing. The net signal is fed to two amplifiers in series and from there to a chart recorder and an analog/digital converter which is connected to a microcomputer. A microcomputer is used to perform the data acquisition and peak area integration. The area under the heat flux tracing integrated with respect to the baseline should be directly proportional to the heat. Chemical calibrations using Tris-amine buffer reacting with HC1 [-47.31 KJ/mole (H ÷) at 298.2°K] were carried out to obtain the linear correlation between area and heat. The performance of the instrument was further checked by measuring the heat of dilution of sodium chloride solutions and comparing it to the literature value (15). Both accuracy and precision were found to be better than + 1%. Materials

Potassium decanoate was prepared by neutralizing a slight excess of decanoic Journal of Colloid and Interface Science, Vol. 115,No. 2, February 1987

CHEN

acid (99%, Sigma) with potassium hydroxide ("Baker Analyzed" reagent) following Herzfeld's method (16). The unreacted decanoic acid was extracted three times from solution with anhydrous diethyl ether (Mallinckrodt). The precipitated potassium decanoate was purified by recrystallizing first from 95% ethanol and then twice from absolute ethanol (both solvents procured from the Medical Center of the University of Rochester). The pulverized product was dried under vacuum at 323°K for 48 h. The absence of cloudiness in aqueous solutions around and below the critical micelle concentration was taken as an indication that the potassium salt is free from contamination with free acid or higher alcohols (10). Reagent grade hydrochloric acid (Mallinckrodt) was standardized with anhydrous sodium carbonate (J. T. Baker) prior to its reaction with tris(hydroxylmethyl)aminomethane (99.9+%, Aldrich Chemical Co., and recrystallized from ethanol) for area-heat calibration. Sodium chloride (Analar, J. T. Baker) was dried under vacuum at 323°K for over 48 h before use. Deionized water distilled from potassium hydroxide/potassium permanganate solution was used in all solution preparations. Deuterium oxide (100.0 at.%) was used as received from the Aldrich Chemical Company. III. R E S U L T S A N D D I S C U S S I O N

The enthalpy of dilution was determined by mixing a given amount of potassium decanoate solution with a measured quantity of H20 or D20. Over the concentration range from 0.01 to about 0.8 m, the uncertainties of the measured values of the enthalpy of dilution were consistently within __+1% of the mean of three to five measurements. The apparent relative molal enthalpy, eL, was then obtained by taking infinite dilution as the standard state. The partial molal enthalpy of the solute,/~2, was calculated using the following expression (17): m O(~L

,

439

ENTHALPY OF MICELLIZATION

where m is the solute concentration in mole/ kg. Note that in the computation of/72(m) from 4~z(m) using Eq. [1], the experimental data were fitted to a linear relationship for m below the break point in qSLVS m. For m above the break point, the experimental data were found to be represented by the following function: q~L(m ) = dpL( OO) -- fl e x p ( - 3 , m )

[2]

to within _+1%. Equation [2] was established by the Gauss-Newton nonlinear least-squares method, with predetermined ~bL(~), and the fitted values for/3 and 3' are listed in Table I. In the neighborhood of the break point in ~bL vs m, a cubic spline method with continuous first and second derivatives was followed to establish the transition region for physical interpretation of micellization. As an example, both q~Land/$2 are plotted in Fig. 1 for potassium decanoate in D20 at 298.4°K with the experimentally determined values for q~L designated as triangles. The graphical method proposed by Desnoyers and his co-workers (10) was then applied to the/72 vs m curves, with the first inflection point in/$2 vs m identified as the critical micelle concentration (CMC) to determine the enthalpy of micellization at the CMC (AHM). The results for both CMC and AHM are reported in Table II. Note that the uncertainties on AH M associated with experimental errors for all data points were estimated at +6% of the reported values. An alternative approach to the determination o f A H M is t o fit the experimentally observed ~bLvs m relationship to physical models of micellization, but the result becomes model dependent. Thus, the adoption of a particular

"8°°t 18600 t

..............L2

144001 13200~

12ooo~

/. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10800 t 9600~ 8400 t

;ZI 4800~ 3600~

f

2400 t 120;t ,z~K

0.0

0.2

FIG. 1. eL and/52 vs m for potassium decanoate in D20 at 298.4K.

micellization model for such a purpose deserves justification. Although it has been claimed that the mass-action model is better suited for a relatively short-chain surfactant (18), the objection being that the aggregation number is too small for phase separation model to apply, Rusanov's view (19) on micelle formation as phase transition involving small systems with curved surface seems to have reconciled the two fundamentally different approaches. The extension of both pieces of work (18, 19) for nonionic surfactants to ionic counterparts apparently introduces

TABLE II The Values of CMC and AHM Determined Graphically or Based on a Mass-Action Model for Potassium Decanoate Micelles in D20 and H20 Solvent

Temperature (°K)

D20

298.4

G M

0.093 0.101

H20

298.4

G M

0.107 b 0.112 b

9.11 9.72

H20

307.9

G M

0.092 0.106

5.70 6.04

TABLE I The Values of/3, % and q~L(OO)and in Eq. [2] for Potassium Decanoate in DzO and H20 Solvent

Temperature (°K)

/3 (kJ/mole)

3"(kg/mole)

~L(~) (kJ/mole)

D20 H20 H:O

298.4 298.4 307.9

24.62 19.43 15.34

10.49 8.814 11.69

11.69 10.33 7.05

m (mole/k 9 ) ......... i ...... 0.4 0,6

Method"

CMC (m)

AHu (kJ/mole)

11.64 11.42

G, graphical method; M, mass-action model. b Compared to 0.108 mole/kg at 298.2 K reported by K. M. Kale and R. Zana ( I Colloid Interface Sci. 61, 312 (1977)). a

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440

MAA AND CHEN

complications arising from counterion binding. However, two recent studies (20, 21) have concluded that ion-binding effects are of secondary importance as far as the energetics of a micellar solution is concerned. This is in fact the idea behind some existing models (22-24) that presume that micelles are completely dissociated. The consequence of this observation is that both the graphical method based on the phase-separation model (10) and the mass-action model, as recently applied to nonionic surfactants (18), appear to be applicable to potassium decanoate, of interest here. It seems reasonable to accept the graphical method and then test the applicability of the mass-action model (18) since the former is not only physically based but also verified by Burchfield and Woolley (25), for ionic surfactants using a more elaborate mass-action model in which both counterion binding and solution nonideality are considered. Thus, one of the objectives of the present work is to verify whether or not the more primitive version of massaction representation (18), which involves a smaller number of system parameters, is adequate for predicting the enthalpy of micellization. To calculate the values of A H ~ for potassium decanoate in solutions of H 2 0 and DaO based on Desnoyers and his co-workers' (18) mass-action model the following procedures were formulated: (1) The aggregation number n from an independent source was used to calculate ax from al =

"[

l

n-1

J

,

[3]

1 -a

1 -

-

-

O/I

aInmin-1

(aL =AL(a2m) +LM(1 -- a)

[4]

which originates from the single "chemical" equilibrium constant being applicable over the entire range of m. Journal of Colloid and InteoCaceScience, Vol. 115, No. 2, February 1987

[5]

to permit parameters AL, LM, and mi to be estimated using Marquardt's nonlinear leastsquares algorithm (26). (4) Finally, AHM was calculated using A HM = LM-- almIAL.

[6]

The solid curve plotted in Fig. 2 represents the ~bLvs m relationship for potassium decanoate in D20 at 298.4°K described by the model using the optimal set of parameter values given in Table III. The values of AHM resulting from the model are given in Table II for comparison to those evaluated with graphical method. Within experimental uncertainties the two sets of values for 2xH~ are in good agreement with each other. Note that in the above treatment of experimental data we employed a constant value 39 (see Ref. (27)) for aggregation number n in both H20 and D20 in view of a recent study by Chang and Kaler (28), in which they demonstrated that in the absence of added salts, sodium dodecyl sulfate (SDS) micelles in both solvents are comparable in size and that across the limited temperature range (298 to 313°K) the aggregation number stays constant. It was also found that over the range of

18800156001440013200 :

-6 E

\

12OOO ~

where a~ represents the fraction of singly dispersed surfactants at the CMC. (2) At total surfactant concentrations other than the CMC, the fraction of free surfactant a as a function of m is related to a~ and mi (i.e., CMC) by anmn-1

(3) The experimentally determined ~bL vs m along with a(m) evaluated from Eq. [4] was then fitted to the model equation, namely,

108009600$400 ~ 72006000-

~

J

~

0

~

A

~

4800 ~

3600 ~ 240012oo: / 0- . . . . . . . . 0.0

m ( m o l e / k 91 q......... , ......... O~ 0.4

, ...... 0.6

FIG.2. ~L vs m for potassium decanoatein D20 at 298.4 K; the solidcurverepresentsdata correlationwiththe massaction model.

ENTHALPY OF MICELLIZATION TABLE III The Values of AL, and LMin Eq. (5) for Potassium Decanoate in D20 and H20 Solvent

Temperature (°K)

AL (kg. kJ/mole2)

LM (kJ/mole)

mt (m)

D20 HzO H20

298.4 298,4 307.9

26.20 23.43 23.88

13.82 12.11 8.30

0.101 0.112 0.106

aggregation number n = 39 _+ 10 the variations in the values of CMC and AHM extracted from the heat of dilution data are both within + 1% of those for n = 39, based on the mass-action model as applied here. The other point made by Chang and Kaler (28) is that the head group repulsions between surfactant molecules and intermicellar interaction for SDS micelles are virtually the same in H 2 0 and D20. It seems logical to apply this observation to potassium decanoate micelles in both solvents. Hence, the fact that the value of AHM in D 2 0 is about 30% higher than that in H 2 0 (11.6 vs 9.11 kJ/mole) at 298.4°K can be attributed to the more pronounced "hydrophobic" effect (28, 29) promoted by the stronger hydrogen bonding (30) in D20. The interpretation of hydrophobic association of surfactant molecules in terms of hydrogen bonding (3 l) is further supported by the measured value of A H ~ in H 2 0 at 307.9 °K, where presumably the local ordering surrounding the hydrocarbon moiety is expected to be diminished by thermal agitation compared to 298.4°K. IV. CONCLUSIONS The enthalpy of micellization at the critical micelle concentration AH~t extracted from the heat of dilution data determined with microcalorimetry for potassium decanoate micelles in both H 2 0 and 1)20 has led to the following observations: (1) The values of AHM based on a massaction model agree with those determined with the graphical method to within ___6%, suggesting that counterion binding is of secondary

441

importance as far as energetics of micellar aggregation is concerned. (2) The fact that the value of ~ H M in D 2 0 is higher than that in H 2 0 at 298.4°K by about 30% is consistent with the interpretation of the "hydrophobic" effect in terms of hydrogen bonding. (3) As temperature is raised from 298.4 to 307.9°K, a decrease in the value of ~ H M is observed for potassium decanoate micelles in H20, which is in further support of the Hbonding treatment of hydrophobic association. ACKNOWLEDGMENT The authors are grateful to Standard Oil Company (Ohio) for providingthe equipment funds for the present research. REFERENCES 1. Shah, D. O., and Schechter, R. S., "Improved Oil Recoveryby Surfactant and Polymer Flooding," Academic Press, New York, 1977. 2. Fender, J. H., and Fender, E. J., "Catalysisin Micellar and Macromolecular Systems," Academic Press, New York, 1975. 3. Shinoda, K., and Hutchinson, E., J. Phys. Chem. 66, 577 (1962). 4. Phillips, J. N., Trans. Faraday Soc. 51, 561 (1955). 5. Holtzer, A., and Holtzer, M. F., J. Phys. Chem. 78, 1442 (1974). 6. Birdi, K. S., in "Colloidal Dispersions and Micellar Behavior" (K. L. Mittal, Ed.), ACS Symposium Ser. No. 9, Arner. Chem. Soc., Washington, D.C., 1975. 7. Muller, N., in "Micellization, Solubilization and Microemulsions" (K. L. Mittal, Ed.), Vol. 1, p. 229, Plenum, New York, 1977. 8. Hamann, S. D.,Aust. J. Chem. 31, 919 (1978). 9. (a) Goddard, E. D., Hoeve, C. A. J., and Benson, G. C., aT.Phys. Chem. 61, 593 (1957); (b) Corkill, J. M., Goodman, J. F., and Tate, J. R., Trans. Faraday Soc. 60, 996 (1964). 10. (a) Desnoyers,J. E., De Lisi, R., Ostiguy, C., and Perron, G., in "Solution Chemistry of Surfactants" (K. L. Mittal, Ed.), Vol. 1, p. 221, Plenum, New York, 1979; (b) De Lisi, R., Perron, G., and Desnoyers, J. E., Canad. Z Chem. 58, 959 (1980). 11. Olofsson,G., J. Phys. Chem. 87, 4000 (1983). 12. Archer,D. G., Albert, H. J., White, D. E., and Wood, R. H., J. Colloid Interface Sci. 100, 68 (1984). 13. Emerson, M. F., and Holtzer, A., J. Phys. Chem. 71, 3320 (1967). Journal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

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14. Lovrien, R., Jorgenson, G., Ma, M. K., and Sund, W. E., Biotechnol. Bioeng. 22, 1249 (1980). 15. Rossini, F. D., Wagman, D. D,, Evans, W. H., Levine, S., and Jaffe, I., "Selective Values of Chemical Thermodynamic Properties," National Bureau of Standards, Washington, D.C., 1952. 16. Herzfeld, S. H., J. Phys. Chem. 56, 953 (1952). 17. Harned, H. S., and Owen, B. B., "The Physical Chemistry of Electrolytic Solutions," Reinhold, New York, 1958. 18. Desnoyers, J. E., Caron, G., De Lift, R., Roberts, D., and Perron, G., J. Phys. Chem. 87, 1397 (1983). 19. Rusanov, A. I., J. Colloid Interface Sci. 85, 157 (1982). 20. Gunnarsson, G., Jonsson, B., and Wennerstr6m, H., J. Phys. Chem. 84, 3114 (1980). 21. Evans, D. F., and Ninham, B. W., J. Phys. Chem. 87, 5025 (1983). 22. Tanford, C., "The Hydrophobic Effect," Wiley, New York, 1973.

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23. Mitchell, D. J., and Ninham, B. W., J. Chem. Soc., Faraday Trans. 2 77, 601 (1981). 24. Wennerstr6m, H., and Lindman, B., Phys. Rep. 52, 1 (1979). 25. Burchfield, T. E., and Woolley, M., Fluid Phase Equilib. 20, 207 (1985). 26, Marguardt, D. W., J. Soc. Indus. AppL Math. 11,431 (1963). 27. Woolley, E. M., and Burchfield, T. E., aT.Phys. Chem. 89, 714 (1985). 28, Chang, N. J., and Kaler, E. W., J. Phys. Chem. 89, 2996 (1985). 29. Oakenfull, D., and Fenwick, D. E., Aust. J. Chem. 28, 215 (1975). 30. Nemethy, G., and Scheraga, H. A., J. Chem. Phys. 41, 680 (1964). 31. Conway, B. E., "Ionic Hydration in Chemistry and Biophysics," p. 518, Elsevier, Amsterdam, 1981.