Thermodynamics of Micelle Formation

16 Thermodynamics of Micelle Formation K. S. BIRDI

Downloaded by OHIO STATE UNIV LIBRARIES on October 14, 2014 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/bk-1975-0009.ch016

Fysisk-Kemisk Institut, Technical University of Denmark, Lyngby, Denmark 2800

Introduction The understanding of the thermodynamics of micelle form ation i s of much theoretical and p r a c t i c a l importance.Even though a great many studies on the thermodynamics of micelle formation have been reported i n the l i t e r a t u r e (1-14), the data available are not completely consistent. The purpose of this study i s to report on the current theories and to comment on the data reported i n the l i t e r a t u r e on the thermodynamics of micelle formation. The variation of c r i t i c a l micelle con centration (CMC) and the aggregation number (N) of a nonionic surfactant (Triton-X-100) with temperature were measured,since these data are essential i n order to discuss the current theories reported on the micelle formation i n the l i t e r a t u r e . Experimental Triton X-100 (OPE1o) was used as supplied by Rohm and Haas Co. The sample i s reported to be polydisperse with respect to the ethyleneoxide adducts. C r i t i c a l micelle concentration (CMC) of OPE1 o i n water and 0.025 M-KBr was determined at three different temperatures,viz.,25,35 and 45°C by the U.V. difference spectrophotometric method,as reported i n litera ture (10). The values of CMC i n water and i n 0.025 M-KBr were i d e n t i c a l , i . e . within the experimental accuracy. Furthermore, these results agreed with the data reported by other investig ators i n water at these temperatures (1 θ ) . The micellar molecular weights (number average,M ) of OPE^ were determined i n 0.025 M-KBr aqueous solutions by using membrane osmometry, as reported by us elsewhere i n d e t a i l ( 1 5 . 1 6 ) . The micelle molecule weights,and subsequently the aggregation numbers,N,were determined at various temperatures r

Ψ

e.g.,5,10,15,25,30,35*40

a

n

d

e

*5 C

233

In Colloidal Dispersions and Micellar Behavior; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

234

C O L L O I D A L DISPERSIONS A N D M I C E L L A R

BEHAVIOR

Results and Discussion It i s of interest to describe the micellar system of a nonionic surfactant, before discussing the data on the var i a t i o n of aggregation number of micelles,N, and the CMC with temperature. The process of micellization involves the rever s i b l e aggregation of Ν molecules of the amphiphile to form a micelle ( 2 » 1 7 . 1 6 , 1 9 ) as given below: Downloaded by OHIO STATE UNIV LIBRARIES on October 14, 2014 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/bk-1975-0009.ch016

N-m

f

- M

(1)

The equilibrium constant of this reaction i s given by:

where A and A^ are the a c t i v i t i e s of monomer and micelles respectively. At low surfactant c o n c e n t r â t i o n , h o w e v e r , i t i s reasonable to replace the a c t i v i t i e s of monomer and micelles by t h e i r respective concentrations (12.) :

where C and C., are the concentrations of monomer and micelle ,m M respectively. Assuming i d e a l i t y , the chemical potential of micelles is given by: μ

- μ°

Μ

+

RT In C

(4)

M

and for monomer: = μ° m m

U

+ RT In C m

(5)

At equilibrium we have : N

\

- M,,

From these relations the standard free energy of m i c e l l i z a t i o n , AG°,per monomer is found to be given by (19)s 0

AG » RT In C - RT / Ν In C RT In Cm + RT / Ν In Ν - RT / Ν In CM M

M

(7) (θ)

where Ο. = Ν. Ο. . It i s generally assumed that i f Ν i s large, then at CMC , tKe Equation (8) reduces to (2,19)? 0

AG %zRT In C « RT In CMC


(9)

16.

BIRDI

235

Micelle Formation

Many investigators have further assumed that i f the variation of Ν with temperature is negligible 0 . 2 6 - 1 0 , 1 £ ) , t h e enthalpy of micelle formation,AH°,can be obtained by using a Clausius-Clapeyron type of relationship: t

0

ΔΗ

= - T

2

(dâa°/T

/&T)

(10)

2

= - RT ('d In CMC / d T)

(.11)


0

A great number of investigations on the determination of ΔΗ by applying Equation ( 1 1 ) have been reported i n the l i t e r a t u r e for both the ionic and nonionic micellar systems ( 1 , 2 » 6 - 1 0 ) . These ΔΗ® values reported,however,do not a l l give a s t r i c t l y consistent description of the micellar formation. For instance, the heat of m i c e l l i z a t i o n of N-dimethyldodeeylamine oxide as determined from Equation ( 1 1 ) i s reported to be 1 9 0 0 cal/mole (I) f while the calorimetric value is reported to be 2 6 0 0 cal/mole ( j j . Another t y p i c a l example i s that of the n-dodecylpyridinium bromide i n 2Μ urea solutions f the ΔΗ values by Equation ( 1 1 ) and by calorimetric method are reported to be - 7 9 8 cal/mole and - 3 4 9 6 cal/mole,respectively (lj.)» This indicates that the method of using the r e l a t i o n i n Equation (II) to obtain ΔΗ· i s imprecise,probably due to certain ass umptions used i n the derivation of this relation,as discussed further below. Further,in many investigations reported on the determination of ΔΗ by using Equation ( l l ) , t h e data obtained does not give a s t r i c t l y consistent description of the micelle formation ( 7 , 8 , 1 0 - 1 3 ) . T h i s analysis therefore c l e a r l y indicates that the usage of the relationship given i n Equation ( l l ) , i s not s t r i c t l y v a l i d for obtaining the heat of m i c e l l i z a t i o n , as also pointed out by other investigators (19)* It was therefore considered of interest to reconsider the assumptions made i n the derivations of Equations (9) and ( 1 1 ) . Since μ° is a function of T,p and Ν (12.), the v a r i a tion of CMC and Ν with temperature of a nonionic surfactant, OPE^ ,was determined. The values of CMC were found to agree with the values reported by other investigators ( 1 0 ) . The aggregation number,N,was determined by using membrane osmomet ry as described under experimental section. The relationship i n Equation ( β ) at the CMC,can then be r e written as Î 0

0

0

àG° = RT In CMC + RT / Ν In Ν

(12)

It i s thus seen that the r e l a t i o n given i n the above Equation ( 1 2 ) d i f f e r s from that given i n Equation ( 9 ) » i n that while former i s a function of both CMC and N, l a t t e r i s only a function of CMC. The results of CMC and Ν versus temperature of 0 ? are given i n Figure 1 . It is seen that the CMC decreases with E

1 O



C O L L O I D A L DISPERSIONS A N D M I C E L L A R

BEHAVIOR

Temperature (°C) Figure 1.

Aggregation number (N) and CMC vs. temperature of OPE in 0.025M KBr 10



16.

BiRDi

237

Micelle Formation

temperature, and f i n a l l y around 40-45°C no change i n CMC with temperature i s observed,as also reported by other investigators ( 10 ).The aggregation number,N, on the other hand increases with temperature from 5 - 45°C. This i s t y p i c a l f o r the non ionic micelles,as reported i n l i t e r a t u r e , and discussed else where (jhSj.The results i n Figure 1 thus c l e a r l y show that the heat of micellization i s not zero around 40 - 45°^* as has been reported i n l i t e r a t u r e (lO)by using the Equation (11).The second term i n the Equation (12) relates to the transfer of material to and from already exsisting micelles. Since the Equations (12) and (9) d i f f e r by the term: HT / Ν In Ν

(13) 0

we find that the difference i n ΔΗ determined after making this correction f o r A G , i s 130-170 cal/mole,in the range of 5-45 C (from the data given i n Figure 1). The aggregation 0

c

E

number , N , of C. Eg, i 2 6

, C

E

14 6

3 1 1 ( 1C

E

16 6

h

a

v

e

b

e

e

n

(5.)to change wixR temperature^" as expressed below:

r

e

P

Coin N/dT) » 0.109

o

r

t

e

d

(14)

p

This shows that the Ν increases with increasing temperature, and that the alkyl chain has no effect on this change. It i s also reported that the rate of change of Ν with temperature decreases as the number of ethyleneoxide adducts increases ( i f u ^ h u s i n Figure 1, the change of Ν f o r 0PE i s about four times lesser than that reported f o r the a l k y l chain with s i x ethyleneoxide adducts,as mentioned above (^).In other words,the AH values w i l l d i f f e r by about 600 cal/mole due to the term i n Equation (13) i n the case of these surfactants with s i x ethyleneoxide adducts. To summarize,we have shown that the aggregation number ,N,of nonionic micelles changes appreciably with temperature.Prelim inary results of another nonionic surfactant,nonylphenol with 10 ethyleneoxide units,also indicates that Ν changes with temperature quite appreciably,as determined by membrane osmometry. Since the r e l a t i o n given i n Equation (9) f o r AG does not seem to give consitent results f o r the heat of m i c e l l i z a t i o n , i t i s clear that at this stage the thermodynamics of micelle formation i s f a r from well understood. In the case of nonionic micelles,the determination of Ν as a function of temperature gives a more consistent description. It shows that this process has positive enthalpy over a large temperatu re range (from 5 - 45°C , f o r both OPE^ and nonylphenol with 10 ethyleneoxide adducts). 1

0


COLLOIDAL DISPERSIONS AND MICELLAR BEHAVIOR

238 Acknowledgements

It is a pleasure to thank Prof. J^rgen Koefoed for many helpful suggestions. The excellent technical assistance of Mrs. H. Birch is acknowledged.


Literature

Cited

1. Herman,K.W.,J.Phys. Chem.(1962)66, 295 2. Schinoda,K. and Hutchinson,E.,J.Phys.Chem.(1962)66 , 5 7 7 3. B a l a m b r a , R . R . , C l u n i e , J . S . , C o r k i l l , J . M . and Goodman,J.F., Trans. Faraday Soc. ( 1 9 6 2 ) 58, 1661 4. Benjamin,L.,J.Phys.Chem. ( 1 9 6 4 ) 6 8 , 3575 5. B a l a m b r a , R . R . , C l u n i e , J . S . , C o r k i l l , J . M . and Goodman,J.F., Trans. Faraday Soc. ( 1 9 6 4 ) 6 0 ,979 6. Adderson,J.E. and T a y l o r , H . , J . C o l l o i d S c i . ( 1 9 6 4 ) 1 9 , 4 9 5 7. Corkill,J.M.,Goodman,J.F. and Harrold,S.P.,Trans. Faraday Soc.(1964)60 ,202 8. Corkill,J.M.,Goodman,J.F.,Robson,P. and T a t e , J . R . , T r a n s . Faraday S o c . ( 1 9 6 6 ) 6 2 , 987 9. Corkill,J.M.,Goodman,J.F.,Harrold,S.P. and T a t e , J . R . , Trans. Faraday Soc. ( 1 9 6 7 ) 6 3 , 2 4 0 10.Ray,A. and Nemethy,G.,J.Phys. Chem.(1971)75, 809 1 1 .Elias,Hans-Georg,J.Macromol.Sci.(1973)A-7,(3)601 12.Piercy,J.,Jones,N.M. and Ibbotson,G.,J.Colloid Interface S c i . ( 1 9 7 1 ) 3 7 , 165 13.Jones,M.N.,Agg,G. and Pilcher,G.,J.Chem. Thermodynamics, ( 1 9 7 1 ) 3 , 801 14.Poland,D.C. and Scheraga,H.A.,J.Phys.Chem.(1965)69,2431 and 4 4 2 5 . 15.B i r d i , K . S . and Kyllingsbæk,H.,J.Pharm. Pharmacol.(1971) 23, 900 16.B i r d i , K . S . , K o l l o i d - Z . Z. Polym. (1972) 250, 731 17.Murray,R.C. and Hartley,G.S.,Trans.Faraday S o c . ( 1 9 3 5 ) 3 1 , 183 18.V o l d , M . J . , J . C o l l o i d S c i . ( 1 9 5 5 ) 5 1 , 561 1 9 .H a l l , D . G . and P e t h i c a , B . A . , i n "Nonionic Surfactants", M . J . S c h i c k , E d . , p p . 5 1 6 - 5 5 7 , M a r c e l Dekker,Inc.,New York, 1967.


Thermodynamics of Micelle Formation

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