Enthalpy of Micelle Formation of Mixed Sodium Dodecyl Sulfate and

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Enthalpy of Micelle Formation of Mixed Sodium Dodecyl Sulfate and Sodium Deoxycholate Systems in Aqueous Media K. S. BIRDI Fysisk-Kemisk Institut, The Technical University of Denmark, Building 206, DK-2800 Lyngby, Denmark

The enthalpy of micelle formation of various mixed sodium dodecylsulfate (NaDDS) and sodium deoxycholate (NaDOC) systems was measured by calorimeter in aqueous systems. The heat of micelle formation,ΔΗΘm,showed a maximum around NaDDS:NaDOC molar ratio 1. These data are analyzed in comparison to the aggregation number of mixed micelles and the second virial coefficient, Β . 2

The thermodynamic understanding of the aggregation phenomena of surfactant molecules i n aqueous media have been investigated by using a wide variety of physico-chemical methods. In recent years, due to the advent of sensitive calorimeters, some enthalpy data on micelle formation have been reported i n the l i t e r a t u r e (1-11). This study i s a continuation of our previous investigations, i n which the aggregation phenomena of surfactant molecules (amphiphiles) i n aqueous media to form micelles above the c r i t i c a l micelle concentration (c.m.c.) has been described based on d i f ferent physical methods (11-15). In the current l i t e r a t u r e , the number of studies where mixed micelles have been investigated i s scarcer than f o r pure micelles ( i .e., mono-component). Further, i n t h i s study we report various themodynamic data on the mixed micelle system, e.g., C^pI^SO^Na (NaDDS) and sodium deoxycholate (NaDOC), enthalpy of micelle formation (by calorimetry), and aggregation number and second v i r i a l c o e f f i c i e n t (by membrane ο smometry ) ( 1_6 ). Materials and Methods The microcalorimeter used (LKB, Sweden, bartch 2107) was described i n d e t a i l i n Ref. 11. The mixing procedure was the same as that described i n Ref. 11, i . e . , the heat of d i l u t i o n of a surfactant solution (2 mL) was measured on mixing with 2 mL of solvent. In the reference c e l l the heat of mixing of 2 mL solvent with the 0097-6156/85/0272-0067$06.00/0 © 1985 American Chemical Society

Shah; Macro- and Microemulsions ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

MACRO- AND MICROEMULSIONS

68

same volume of solvent was used, in order to correct f o r any heat of wetting, e t c . , inside the c e l l s . The calorimeter was main tained at a constant temperature, 2 5 ± O . 0 1 °C. A l l chemicals used were of a n a l y t i c a l purity grade. NaDDS was used as purchased from B.D.H., U. K. (purity about 99% (17)). NaDOC was used as supplied by Sigma. Theoretical Analysis. In these d i l u t i o n experimentsinthe calorimeter, the t o t a l heat of d i l u t i o n , q , c f a surfactant solution w i l l be related to the t o t a l concentration and c.m.c. (1-8,11): t

q = q; t

=

< c.m.c

i r

in

+

q

+

dii

[1]

c

W

m

c

[

> - - -

2

]

where q^Q and q^Q denote heats of d i l u t i o n of monomer and mi c e l l a r species, respectively; and qd is the heat of demicellization. Because the magnitude of monomeric species, dil ' (1-1D 9 t h i s quantity can be neglectedinthe following analyses (8,11). Therefore, i f we d i l u t e a solution of concentration twice c.m.c. by a factor of two, then we can write (il): em

q

is

v

e

r

y

s m a 1 1

.

ro q

t,2

q

r

+ q

o

[ 3 ]

c.m.c. = d i l dem

The heat of demicellization,ΔH , can be written (8,11): dem

AH

1η

t 4 ]

dem = «t,2 c.m.c. Μ

q

1n

[

= dem M

where T J is the concentration of micelles and Δ Η ^ =-AH (heat of micelle formation). Further, because the experiments are carried out near the c.m.c, it has been argued that the enthalpy measured, Δ Η , can be assumed equal to the standard mi c e l l a r enthalpy change, Δ Η ^ (1-8,11). A l l the data measured so f a r in our laboratory c l e a r l y indicate that the heats of d i l u t i o n show a d i s t i n c t break, which indicates the difference between the terms q and q ^ , as expected from the preceding discussion, ail cii-im

Θ Π Ι

mic

ι η 1 ο

0

m

j n

The p a r t i a l molar enthalpy can be estimated from the slopes of (q /Am) (10). This analysis w i l l be reported when more data become a v a i l a b l e . At t h i s stage it is evident that A H and AHmic are constant below and above c.m.c, respectively. t

m


i

5. BIRDI

Enthalpy of Micelle Formation

69

Results A t y p i c a l plot of t o t a l heat d i l u t i o n , qt, measured as a function of concentration (after d i l u t i o n by as factor of two) of NaDOC:NaDDS (1:1 molar r a t i o ) is given in Figure 1. The heat of d i l u t i o n is endothermic, which means that the heat of micelle formation, when the concentration is above c.m.c, would be exothermic. These data also show a break around a region which corresponds to the c.m.c. as determined by other methods. This observation was reported from other surfactant systems, e.g., NaDDS and NdeS (sodium decyl sulfate) (VI). Further, it is important that the micellar e q u i l i b r i a region, i . e . , the c.m.c. region, is d i s t i n c t l y observed in a l l the systems, regardless of the sizes of micelles (as discussed l a t e r in t h i s chapter). In other words, in the non-ideal region near c.m.c, the formation of pre-c.m.c. aggregates ( i . e . , dimers, trimers, . . . η-mers) is e a s i l y observed from such measurements in a l l systems with varying aggregation numbers.

Discussion In a l l the measurements carried out in t h i s study, f o r different r a t i o s of NaDDS:NaDOC, the d i l u t i o n curves (Figure 1) of surfac tant solution exhibited a clear break that corresponded with the c.m.c. as determined by other methods. This observation agrees with l i t e r a t u r e reports (1-11,18). The present data, however, show f o r the f i r s t time that mixed micelle systems also behave the same way as pure micellar systems, as measured by calorimetry. Further, because the aggregation number, N, of NaDDS is much larger than that of NaDOC (16), Table I, the variation of enthalpy around the c.m.c. region is not related to the size of micelles. At t h i s stage, t h i s analysis cannot be carried out quantitatively. However, as more data become available such analysis w i l l be reported. The purpose of t h i s study was to analyze the enthalpy data with the help of data from membrane osmometry on the NaDDS-NaDOC system (16). This analysis was considered to be necessary, based on the fact that a l l current micellar t h e o r e t i c a l treatments, which are based s o l e l y on free energy c a l c u l a t i o n s , are empirical; these theories break down completely f o r systems at a temperature different from the one the theory was made to f i t (K. S. B i r d i , unpublished). For example, the following relationship between c.m.c and the aggregation number, N, was given (19):

ln(c.m.c) = (2ya + g - g')kT o

2

= ((36nv /N)

2γ + g - g')/kT

V3


[6]

70

M A C R O - A N D MICROEMULSIONS

3

9

/lfefter)

F i g u r e 1. A p l o t o f t o t a l heat o f d i l u t i o n (q^) v e r s u s concen t r a t i o n o f NaDDS-NaDOC (1:1 molar r a t i o ) ( g / L ) a f t e r d i l u t i o n by a f a c t o r two ( a t 25 C , I o n i c s t r e n g t h = O.033, pH = 7.4). U

Table I. Μ , Ν , Β η η

and

ΔΗ

Θ

. mic

Data f o r Mixed NaDDS -NaDOC M i c e l l e s

NaDOC:NaDDS 5

(xlO ) ,m mol kg > 3

N

1

(J/mol)

1:0

7354

18

3.0

-920

1:1

13400

38

2.5

-5360

1:2

17730

54

1.9

-4190

0:1

22000

76

O.8

-1590

Data from Réf. 16 Note: C o n d i t i o n s , 25 °c,i o n i c 3

s t r e n g t h = O.033, pH = 7.4


5. BIRDI


71

where the standard free energy of each monomer in a m i c e l l e of aggregation number Ν is = 2 i a + g; Ν = 4π(3v) /a^; a is the optimal surface area per amphiphile at the micelle-water interface; the quantity (g - g) is the hydrophobic energy required to transfer a methylene group (ca. 825 cal/mol or 345 J/mol) from aqueous to micellar phase; ν is the volume per monomer; and k«j and k2 are constants. 2

Q

Q

1

The much-studied NaDDS system was used as a unique example by these investigators to determine the v a l i d i t y of Equation 6. From plots of In (c.m.c.) versus N~3 f o r NaDDS data in aqueous solu tions with varying NaCl solutions (at 21 ° C ) , it was reported that k,j = 44 and k = 20. From these values, the magnitudes of α = 37 erg dyne/cm (mN/m) and ( g - g) = k2 kT = 20 kT = 12 kcal/mol (or 49 kJ/mol) were determined. These values were acceptable and of correct magnitudes. We therefore applied the r e l a t i o n s h i p in Equation 6 to another system, DTAB (dodecyltrimethyl ammonium bromide in aqueous solutions with varying concentration of added KBr) at 40 °C. The In (c.m.c.) versus N 3 plot was v e r t i c a l because Ν remains unaffected by the addition of e l e c t r o l y t e ; t h i s result was also reported f o r NaDDS systems at high temperatures, i . e . , ca. 50-60 °C (20, K. S. B i r d i , unpublished). We thus f i n d convincing evidence that the exhaustive theories delineated (19,21) are not v a l i d under these circumstances. 2

1

- 1 /

Therefore, the present approach was i n i t i a t e d , together with the second v i r i a l c o e f f i c i e n t , B , analyses. I t was also shown f o r the f i r s t time (Iji) that in the case of i o n i c micelles, the Donnan term of B is proportional to the added s a l t concentration, ΠΙ5, as expected from theory. This r e l a t i o n s h i p was v a l i d only in those systems where the aggregation number, N, d i d not change appreciably with increased 1115. I t is thus obvious that i o n i c micelles must be treated as macro-ions (macromolecules). In the same context, we showed that B goes to zero as the temperature of non-ionic micellar solutions approaches t h i s cloudpoint ("poor solvent") (15). 2

2

1

2

The mixed NaDDS-NaDOC systems gave the enthalpy of micelle formation,ΔΗ^ , which varies with composition as shown in Figure 2. 0

Q As the amount NaDOC is increased, the magnitude o f tt ± decreases, but after a minimum (around 1:1 molar r a t i o ) the value increases. In other words, the micellar systems of pure NaDDS and NaDOC exhibit properties that are d i f f e r e n t with regard to the enthalpic interactions. The value o f B i varies very l i t t l e when NaDDS:NaDOC increases from 1:1. These data are in agreement with the H ^ i , where the NaDDS micelles, as formed by the l i n e a r a l k y l chain, exhibit d i f f e r e n t energetics than the non-linear a l k y l chains o f NaDOC. This observation was expected. m

Q[

2

c

Conclusions The present study reports the v a r i a t i o n of enthalpy of micelle formation of mixed NaDDS-NaDOC systems. Our current enthalpy


MACRO- AND MICROEMULSIONS

72

F i g u r e 2. V a r i a t i o n of heat o f m i c e l l i z a t i o n , Δ Η . (atc.m.c) w i t h the molar r a t i o NaDDS:NaDOC ( a t 25 °C, I o n i c S t r e n g t h = Q.033, pH = 7 . 4 ) . V a r i a t i o n of second v i r i a l c o e f f i c i e n t , (xlO m mol k g " ) , w i t h molar r a t i o o f NaDDS:NaDOC. 3


5. BIRDI

73


studies of micellar systems have shown the following (K. S. B i r d i , unpublished) :

Increase in Alkyl chain

Anionic micelles

Δ .mi more c exothermic

Cationic micelles

AH

more

m,-^ mi c

exothermic

Addition of counter-ions

Anionic micelles

Cationic micelles

η ΔΗ. more mic exothermic

mic endothermic

The enthalpy of a monomer to a micelle of aggregation number, N, can be written as ( 1 1 ) :

AriJ. mic = ΔΗ* pho + ΔΗ* el + ΔΗ£ hyd.

[71

where enthalpies a r i s i n g from different forces are given: Δ Η ρ ^ is the hydrophobic e f f e c t ; Δ Η ^ arises from the e l e c t r o s t a t i c interactions; and A H ^ arises from the hydration of the polar groups. This procedure is analogous to the description used f o r the free energy of micelle formation, Δ ΰ ^ ( 1 3 ) . 0

yd

0

If we compare these ΔΗπίο value variations with the enthalpy of s o l u b i l i t y of alkanes in water ( 2 1 ) , we f i n d that the l a t t e r enthalpy becomes more endothermic with increase in a l k y l chain length. The same is v a l i d in the case of η-alcohols s o l u b i l i t y data in water (21^, K. S. B i r d i , unpublished). Hence, i f we argue that the a l k y l group of NaDDS is more hydrophobic than NaDOC, then we should have expected endothermic increase with addition of NaDOC. However, from Figure 2 we f i n d the reverse. Thus we conclude that, due to the s t e r i c hindrance in the packing of NaDDS and NaDOC a l k y l parts, the enthalpy of mixed micelles behaves non-ideally. These conclusions are in agreement with the data of second v i r i a l c o e f f i c i e n t , B,2 (Figure 2).

At t h i s stage, it is not possible to give a quantitative analysis of these enthalpy data (for each term in the equation). However, work is in progress which is designed to provide the necessary data which would enable us to achieve the former goal.


74

MACRO- AND

MICROEMULSIONS

I t is also clear that studies based on c.m.c. and aggregation number data are empirical and cannot provide any quantitative analyses without the enthalpy (and B ) data. 2

Acknowledgments It is a pleasure to thank the Danish Natural Science Research Council f o r research support of t h i s project. The excellent technical help of J . Klausen is acknowledged. Literature Cited

1. Pilcher, G.; Jones, M. N.; Espada, L.; Skinner, H. A. J. Chem. Therm. 1969, 1, 381. 2. Goddard, E. D.; Benson, G. C. Trans. Faraday Soc. 1956, 52, 409. 3. Kreschek, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. 4. Espada, L.; Jones, M. N.; Pilcher, G. J. Chem. Therm. 1970, 2, 1. 5. Jones, M. N.; Pilcher, G.; Espada, L. J. Chem. Therm. 1970, 2, 233. 6. Jones, M. N.; Piercy, J. Colloid Polym. Sci 1973, 251, 343. 7. Kishimoto, H.; Sumida, K. Chem. Pharm. Bull. Japan 1974, 22(5), 1108.

8. Pavedes, S.; Tribout, M.; Ferriera, J.; Leonis, J. Colloid Polym. Sci. 1976, 254, 637. 9. De L i s i s i , R.; Ostiguy, C.; Perron, G.; Desnoyers, J. Ε. J. Colloid Interface Sci. 1979,71,147. 10. Desnoyers, J. Ε.; Roberts, D; De L i s i s i , R.; Perron, G. in "Solution Behaviour of Surfactants"; Mittal, K. L.; Fendler, J. E., Eds.; Plenum: New York; Vol. 1, 1982, p. 343. 11. Birdi, K. S. Colloid Polym. Sci. 1983, 261, 45. 12. Birdi, K. S. in "Colloidal Dispersion and Micellar Behavior"; Mittal, K. L., Ed.; ACS SYMPOSIUM SERIES 9, American Chemical Society: Washington, D.C.; 1975. 13. Birdi, K. S. in "Micellization, Solubilization and Microemulsions"; Mittal, K. L., Ed.; Plenum: New York; 1977. 14. Chattoraj, D. K.; Birdi, K. S. in "Solution Behavior of Surfactants"; Mittal, K. L.; Fendler, J. Ε., Ed.; Plenum: New York; 1982. 15. Birdi, K. S.; Stenby, E.; Chattoraj, D. K. in "Surfactants in Solution"; Mittal, K. L., Ed.; Plenum: New York; 1983. Proc. Intl. Symp., Lund, Sweden, 1982. 16. Birdi, K. S. Finnish Chem. Lett. 1982, 73(6-8). 17. Birdi, K. S. Anal. Biochem. 1976, 74, 620. 18. Birdi, K. S.; Dalsager, S.; Backlund, S. J. Chem. Soc. Faraday I 1980, 76, 2035. 19. Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. Faraday Trans. II 1976, 72, 1525. 20. Mazer, N.; Benedek, G.; Carey, M. C. J. Phys. Chem. 1976, 80, 1075. 21. Tanford, C. "The Hydrophobic Effect"; Wiley: New York; 1973. R E C E I V E D January 8, 1985


Enthalpy of Micelle Formation of Mixed Sodium Dodecyl Sulfate and

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