Nonideal Mixed Micelles - ACS Symposium Series (ACS Publications)

2 Nonideal Mixed Micelles Thermodynamic Models and Experimental Comparisons 1

Irvin W. Osborne-Lee and Robert S. Schechter Department of Chemical Engineering, The University of Texas at Austin, Austin,TX78712

Downloaded by HARVARD UNIV on June 17, 2014 | http://pubs.acs.org Publication Date: June 5, 1986 | doi: 10.1021/bk-1986-0311.ch002

The variation of the mixture critical micelle concentration (CMC ) with temperature and with overall surfactant composition has been studied using ultrafiltration for two binary mixed nonionic/anionic systems. The data are then compared to predictions based on a new model which includes an excess enthalpy of mixing and two contributions to the excess entropy of mixing. One of the contributions to the excess entropy of mixing is related to the order-disorder problem associated with strong interactions and the second is associated with the greater freedom accorded the ethylene oxide chain because of the greater area per chain in a mixed micelle as compared to the pure nonionic micelle. The latter contribution, which represents a configurational one, tends to increase the entropy whereas the former tends to decrease it. The new model predicts monomer and micellar compositions as a function of temperature when the ethylene oxide chain is relatively short (~ 10 units) but requires some modification of the parameters to predict the behavior of mixed micelles with nonionic components of relatively long chain length (~50 units). A method of extracting the enthalpy of mixing from knowledge of the variation of mixture CMC with temperature is developed. It is shown that the micellar composition must be known to calculate the enthalpic changes. The procedure is described. The comparison between calculated and predicted enthalpies of mixing is not satisfactory. M

In most applications surfactant mixtures rather than pure species are used. These mixtures are usually composed of homologous surfactants, but in some cases mixtures of different surfactant types have Current address: Oak Ridge National Laboratory, Building 4500N, MS-228, P.O. Box X, Oak Ridge, TN 37831.

1

0097-6156/ 86/ 0311 -0030$06.00/ 0 © 1986 American Chemical Society

In Phenomena in Mixed Surfactant Systems; Scamehorn, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1986.


2.

Nonideal Mixed Micelles

OSBORNE-LEE A N D SCHECHTER

31

a l s o proved advantageous. K u r z e n d o r f e r e t a l . (_1) have n o t e d t h a t m i x t u r e s o f a l k y l s u l f a t e s and o c t y l p h e n o l e t h o x y l a t e s e x h i b i t ex c e l l e n t powers o f d e t e r g e n c y . Other a p p l i c a t i o n s o f n o n i o n i c - a n i o n i c m i x t u r e s have been r e p o r t e d ( 2 , 3 ) . I n a d d i t i o n t o b e i n g o f con siderable practical i n t e r e s t , mixed m i c e l l e s composed o f both n o n i o n i c and a n i o n i c s u r f a c t a n t m i x t u r e s a r e s c i e n t i f i c a l l y i n t e r e s t i n g because o f the s t r o n g i n t e r a c t i o n which a t t e n d s t h e i r forma tion. The e x i s t e n c e o f t h i s i n t e r a c t i o n i s e v i d e n t when t h e m i x t u r e critical micelle concentration i s compared w i t h t h a t predicted assuming the mixed m i c e l l a r pseudophase t o be an i d e a l m i x t u r e (4,5). The d e v i a t i o n s from i d e a l i t y a r e l a r g e and i n any thermody namic treatment f o r c e s the i n t r o d u c t i o n o f a c t i v i t y c o e f f i c i e n t s t o c o r r e l a t e the d a t a ( 6 - 9 ) . R e c e n t l y , Rubingh (_7) and Scamehorn e t a l . (9^) have shown t h a t the a c t i v i t y c o e f f i c i e n t s o b t a i n e d by f i t t i n g the m i x t u r e CMC d a t a can be c o r r e l a t e d by assuming the mixed m i c e l l e t o be a r e g u l a r so lution. T h i s model proposed by Rubingh f o r b i n a r y m i x t u r e s has been extended t o i n c l u d e multicomponent s u r f a c t a n t m i x t u r e s by H o l l a n d and Rubingh ( 1 0 ) . Based on t h i s concept Kamrath and F r a n c e s (11) have made e x t e n s i v e c a l c u l a t i o n s f o r mixed m i c e l l e systems. While a c t i v i t y c o e f f i c i e n t s based on the r e g u l a r s o l u t i o n theo r y model a r e adequate f o r r e p r e s e n t i n g t h e m i x t u r e CMC, i t has been shown t h a t the monomer c o m p o s i t i o n i s n o t w e l l p r e d i c t e d by such a model (12) and t h a t the heat o f m i x i n g o f sodium d o d e c y l s u l f a t e w i t h e t h y l e n e g l y c o l monodecylether does n o t compare f a v o r a b l y w i t h the v a l u e p r e d i c t e d by the r e g u l a r s o l u t i o n model ( 1 3 ) . These d i s c r e p a n c i e s make c l e a r the i n a d e q u a c i e s i n c o n s i d e r i n g the m i c e l l a r pseudophase t o c o n s i s t o f a r e g u l a r s o l u t i o n o f n o n i o n i c - a n i o n i c surfactants. Osborne-Lee e t a l . (12) have proposed t h a t t h e s e d i f f i c u l t i e s a r i s e p r i m a r i l y because the excess e n t r o p y o f m i x i n g does not v a n i s h as i s assumed by the r e g u l a r s o l u t i o n model. There a r e two c o n t r i b u t i o n s t o the e x c e s s e n t r o p y ; namely, t h e nonrandom a r rangement o f n o n i o n i c and a n i o n i c s u r f a c t a n t s i n t h e mixed m i c e l l e and the c o n f o r m a t i o n a l e n t r o p y changes o f the l o n g - c h a i n h y d r o p h i l i c group f o r the p o l y e t h y l e n e o x i d e s u r f a c t a n t s . This l a t t e r contribu t i o n w i l l be s i g n i f i c a n t f o r l o n g e r e t h y l e n e o x i d e c h a i n s . The f o r mer c o n t r i b u t i o n s must always be s i g n i f i c a n t s i n c e r e d u c t i o n o f charge d e n s i t y by a r r a n g i n g a n i o n i c s u r f a c t a n t s i n t e r s p e r s e d among n o n i o n i c s i s thought t o be the p r i m a r y mechanism r e s p o n s i b l e f o r the s t r o n g i n t e r a c t i o n (14-15). Because t h e arrangements i n c r e a s i n g the number o f c o n t a c t s are only a f r a c t i o n o f the t o t a l possible arrangements, t h e e n t r o p y i n such mixed m i c e l l e s i s , then, l e s s than t h a t f o r m i c e l l e s which r e s u l t from random m i x i n g . Osborne-Lee e t a l . (12) have a c c o u n t e d f o r the a d d i t i o n a l con t r i b u t i o n t o the excess e n t r o p y o f m i x i n g and found the f o l l o w i n g excess f r e e energy o f m i x i n g p e r a m p h i p h i l e

F

E

=

Φ

1 2

*Ηη(γ

Φ

1 2

Ηη(γ

2

2

- φ - φ

1 2

1 2

*) - (y

- Hn(

x

12

)} - kTny ( 2

X f

-

X q

yi

- φ

1 2

>

)


(1)

32

P H E N O M E N A IN M I X E D S U R F A C T A N T S Y S T E M S

where ζ i s t h e average c o o r d i n a t i o n number between s u r f a c t a n t mole c u l e s i n a m i c e l l e , w i s t h e i n t e r a c t i o n energy parameter, y \ and y 2 a r e t h e n o n i o n i c and a n i o n i c m i c e l l a r mole f r a c t i o n s , r e s p e c t i v e l y , and η i s the number o f r e p e a t i n g u n i t s i n the head group c h a i n (3 times t h e number o f e t h y l e n e o x i d e u n i t s ) . The s u b s c r i p t f de n o t e s the mixed m i c e l l e and the s u b s c r i p t ο denotes t h e pure n o n i o n ic micelle. φ^2 r e p r e s e n t s t h e f r a c t i o n o f the t o t a l number o f ζ c o n t a c t s which a r e between n o n i o n i c and a n i o n i c s u r f a c t a n t s . The Φ ΐ 2 * i s f r a c t i o n o f such c o n t a c t s i n a random d i s t r i b u t i o n ; where as Ψ12 i s a f r a c t i o n o f c o n t a c t s d e t e r m i n e d by the q u a s i c h e m i c a l a p p r o x i m a t i o n (16) a

1 "Λ


φ

1 2

+ 4

= 2[1

The

quantity

y [exp(- ^ ) - 1] ^ - exp( )] y i

2

(2)

χ i s g i v e n by X

=

- 2 £n(l - f )

(3)

where f r e p r e s e n t s the f r a c t i o n o f t h e a v a i l a b l e space o c c u p i e d by an e t h y l e n e o x i d e u n i t composing a p o r t i o n o f t h e s u r f a c t a n t h y d r o phile. U s i n g a s e l f c o n s i s t e n t a p p r o x i m a t i o n ( 1 7 ) , f c a n be d e t e r mined as f o l l o w s : f/-

2

y A £n(l

- f)

=

νζ

(4)

2

where ζ 2 i s the c h a i n d e n s i t y g i v e n by y 2 / ( y i l + Y 2 2 ^ » l e n g t h o f each s t e p taken i n t h e p o s i t i o n i n g o f t h e c h a i n , t h e ex c l u d e d volume p e r r e p e a t i n g u n i t , v, i s e q u a l t o t h e volume o f a sphere w i t h r a d i u s A/2 and and A 2 a r e , r e s p e c t i v e l y , t h e a r e a p e r a m p h i p h i l e o f n o n i o n i c and a n i o n i c components. The development o f t h e s e e q u a t i o n s has been r e p o r t e d e l s e w h e r e ( 1 2 ) , and i t has a l s o been shown u s i n g u l t r a f i l t r a t i o n t e c h n i q u e s t h a t t h e c o m p o s i t i o n o f t h e monomer i s w e l l p r e d i c t e d by t h e equa t i o n (12) A

yiYiCMCi

= XjCMC

M I X

,

A

i-1,2

which have been d e v e l o p e d based on t h e phase s e p a r a t i o n y I a r e o b t a i n e d from the e x c e s s f r e e energy e x p r e s s i o n , and the c l a s s i c a l e q u a t i o n

γ.

1

=

f

E

λ

i

s

t

n

e

(5) model. The E q u a t i o n 1,

+ (1 - y.) Ί dy.

(6)

E q u a t i o n 1 has proved t o be a b e t t e r p r e d i c t o r o f t h e e q u i l i brium which e x i s t s between monomer and m i c e l l e s f o r mixed s u r f a c t a n t systems than i s the r e g u l a r s o l u t i o n t h e o r y model. I t also predicts w e l l t h e m i x t u r e CMC and shows t h e heat o f m i x i n g t o be s m a l l e r than t h a t p r e d i c t e d by t h e r e g u l a r s o l u t i o n t h e o r y i n agreement w i t h t h e experiment ( 1 3 ) . The purpose o f t h i s paper i s t o f u r t h e r explore



2.



33

the v a l i d i t y o f the thermodynamic model f o r mixed m i c e l l e s as expressed by E q u a t i o n 1. Using u l t r a f i l t r a t i o n t e c h n i q u e s , the e q u i l i b r i u m between monomer and m i c e l l e s has been measured f o r mix t u r e s o f an a l k y l b e n z e n e s u l f o n a t e and two e t h o x y l a t e d n o n y l phenols as a f u n c t i o n o f temperature. I t w i l l be seen t h a t when t h e average number o f e t h y l e n e oxide units i s modest 1 0 ) , the t h e o r y a c c u r a t e l y p r e d i c t s the changing monomer c o m p o s i t i o n w i t h o u t chang i n g any o f the p h y s i c a l parameters. However, f o r l o n g e t h y l e n e o x i d e c h a i n s (~ 50), the p r e d i c t i o n d e v i a t e s from the measured v a l ues i n d i c a t i n g a d d i t i o n a l f a c t o r s and must be i n c o r p o r a t e d i n t o the f r e e energy e x p r e s s i o n . These a d d i t i o n a l terms a r e b e l i e v e d t o be r e l a t e d t o the changing h y d r a t i o n o f the e t h y l e n e o x i d e c h a i n s w i t h changing temperature. There have been few r e p o r t s on the e f f e c t o f temperature on the CMC o f s u r f a c t a n t m i x t u r e s , and t o the a u t h o r s ' knowledge none have r e p o r t e d the monomer c o m p o s i t i o n s i n e q u i l i b r i u m with m i c e l l e s . Thermodynamics o f Mixed M i c e l l e

Formation

A b r i e f a c c o u n t i n g o f the thermodynamics o f mixed m i c e l l e f o r m a t i o n i s g i v e n here p r i m a r i l y t o c l a r i f y c e r t a i n i m p o r t a n t i s s u e s which appear t o have been p r e v i o u s l y o v e r l o o k e d . The n e c e s s i t y f o r mea s u r i n g the monomer and m i c e l l a r c o m p o s i t i o n w i l l be demonstrated. C o n s i d e r t h e f o r m a t i o n o f a mixed m i c e l l e i n aqueous s o l u t i o n from a b i n a r y s u r f a c t a n t s o l u t i o n c o n s i s t i n g o f a n o n i o n i c and an a n i o n i c s u r f a c t a n t . The p r o c e s s i s d e p i c t e d as the a g g r e g a t i o n o f ng m o l e c u l e s o f n o n i o n i c s u r f a c t a n t B, o f molecules of a n i o n i c s u r f a c t a n t A", and i n a d d i t i o n t h e r e w i l l be c o u n t e r i o n s , C , o f the a n i o n i c s u r f a c t a n t i n the amount o f a n ^ where a i s the f r a c t i o n o f the c o u n t e r i o n s a s s o c i a t e d o r bound w i t h the s u r f a c t a n t a n i o n s i n the m i c e l l e . The p r o c e s s as d e p i c t e d i s +

n A~ + η Β + a n C A Β A A

For t h i s r e v e r s i b l e

μ

Μΐο

+

Φ A Β C„ n n„ n . A Β A

A

(7)

a

A

process

=

VA

+

a

V c

+

VB

(

8

)

Assuming t h a t the CMC i s s m a l l , so t h a t the a c t i v i t y c o e f f i c i e n t s may be n e g l e c t e d , the monomer phase c h e m i c a l p o t e n t i a l s a r e g i v e n by E q u a t i o n s 9-11.

=

ο μ . + kT i n

Ά

A

w

Ο =

μ D

ο =

μ L

+ kT i n c " w C _Ç + kT An c w


34


where C i s the molar c o n c e n t r a t i o n o f water and y i s an a c t i v i t y coefficient. Based on the phase s e p a r a t i o n model, the m i c e l l a r phase a c t i v i t y c o e f f i c i e n t i s the c h e m i c a l p o t e n t i a l o f the m i c e l l a r standard s t a t e , or w

c

In the presence o f added e l e c t r o l y t e Cq = Cs + CMC. F o r C$ >> CMC, C i s v e r y c l o s e l y g i v e n by CsN o t i n g t h a t yx = n ^ / ( n ^ + ng) and Y2 ~ B / ( A β)> that C^ = x\CKC^ and Cg = χ ΰ Μ % , E q u a t i o n 8 becomes, a f t e r rearrangement C

n

n

+

η

a

n

d

2


A G

°MIC,M

=

( U

°MIC

CMC

W

y

y

m

t J

" l °A " V %

W

CMC

x

m

"

y

2

^„c

" V V 0

«yi

,

x

W

where the b r a c k e t e d term on the l e f t s i d e o f the e q u a t i o n may be de f i n e d as the s t a n d a r d f r e e energy f o r the f o r m a t i o n o f the m i c e l l e (per s u r f a c t a n t c h a i n i n the m i c e l l e ) . An e q u i l i b r i u m c o n s t a n t Κ can be d e f i n e d as C M C

Κ(Τ,α, ) Υ ι

=

M [ — ϋ

y

][χ

l 1 [xJ l

y

2 2

Ύ C [ -5-5.

ay, ]

1

(14)

The s t a n d a r d f r e e energy i s t h e r e f o r e determined by measurement o f the m i x t u r e CMC h o l d i n g the m i c e l l a r c o m p o s i t i o n f i x e d . This a n a l y s i s assumes t h a t α i s known as a f u n c t i o n o f temperature and m i c e l l a r c o m p o s i t i o n and i s independent o f the e l e c t r o l y t e composi tion. The heat o f m i c e l l i z a t i o n cannot be determined from measure ment o f the temperature dependence o f CMC^ w i t h o u t knowledge o f the m i c e l l a r c o m p o s i t i o n and o f a. I n t e r p r e t a t i o n of c a l o r i m e t r i c data i s not p o s s i b l e w i t h o u t i n f o r m a t i o n r e g a r d i n g m i c e l l a r c o m p o s i t i o n . U l t r a f i l t r a t i o n t e c h n i q u e s d e s i g n e d to measure m i c e l l a r compositions, take an added importance when c o n s i d e r i n g h e a t s o f m i c e l l i z a t i o n . Experimental The experimental methods have been described in previous publications (12,18). The d e c y l benzene s u l f o n a t e used i n t h i s study i s i s o m e r i c a l l y pure w i t h the benzene r i n g a t t a c h e d t o the t h i r d carbon o f the a l k y l c h a i n . T h i s s u r f a c t a n t i s d e s i g n a t e d as 3Ci0* The n o n y l phenol e t h o x y l a t e s were o f the I g e p a l CO s e r i e s , donated by GAF C o r p o r a t i o n . The p a r t i c u l a r s p e c i e s used were the C0660 and the CO970 s u r f a c t a n t s . These commercial s u r f a c t a n t s a r e each a p o l y d i s p e r s m i x t u r e , the average number o f e t h y l e n e o x i d e u n i t s b e i n g 10 and 50, r e s p e c t i v e l y . These s u r f a c t a n t s are abbre v i a t e d as ΝΡΕχο and N P E 5 0 . Sodium c h l o r i d e , 0.17 M, was s t u d i e d to p r e v e n t e l e c t r o s t a t i c

added t o a l l s u r f a c t a n t s o l u t i o n s f o r c e s from becoming s i g n i f i c a n t


2.

OSBORNE-LEE AND SCHECHTER


35

a c r o s s the membrane. This also i s a s u f f i c i e n t e l e c t r o l y t e t r a t i o n so t h a t the a p p r o x i m a t i o n >> C M C ^ i s s a t i s f i e d .

concen-

The c o n c e n t r a t i o n and c o m p o s i t i o n o f the f i l t r a n d and f i l t r a t e were d e t e r m i n e d by r e v e r s e - p h a s e l i q u i d chromatography w i t h an e s t i mated e r r o r o f l e s s than 5%.


R e s u l t s and D i s c u s s i o n The CMC can be d e t e r m i n e d using u l t r a f i l t r a t i o n (18). Figure 1 shows the CMC o f N P E ^ Q as a f u n c t i o n o f temperature and the thermodynamic p r o p e r t i e s d e t e r m i n e d u s i n g t h e s e d a t a a r e g i v e n i n T a b l e I t o g e t h e r w i t h those o f the o t h e r s u r f a c t a n t s s t u d i e d . The v a l u e s a r e s u b j e c t t o some u n c e r t a i n t y because the complex CMC/temperature b e h a v i o r r e n d e r s d i f f e r e n t i a t i o n o f the d a t a i n a c c u r a t e . The v a l u e s a r e , however, comparable t o those f o r s i m i l a r s u r f a c t a n t s r e p o r t e d by o t h e r s . Table I .

Thermodynamic P r o p e r t i e s o f S u r f a c t a n t M i c e l l i z a t i o n i n Aqueous S o l u t i o n s a t 300°K AG°MIC (kcal/mol)

Surfactant NPE NPE 34C

-8.15 -7.23 -8.13

1 0

5 0

1 0

(kcal/mol)

TAS° (kcal/mol)

3.0 5.0 -7.5

11.10 12.00 + 1.38

AH°MIC

M I C

F i g u r e 2 compares the m i x t u r e CMC t o the v a l u e s c a l c u l a t e d u s i n g b o t h E q u a t i o n 1 and the r e g u l a r s o l u t i o n model. T h i s comparison i s s i m i l a r t o those f o r o t h e r systems which we have s t u d i e d and r e p o r t e d elsewhere ( 1 2 ) . The p a r a m e t r i c v a l u e s used i n c a l c u l a t i n g the m i x t u r e CMC, as w e l l as the m i c e l l a r c o m p o s i t i o n p r e s e n t e d i n F i g u r e 3 are l i s t e d i n T a b l e I I . T h e i r s i g n i f i c a n c e has been d i s c u s s e d e l s e w h e r e ; however, i t i s r e l e v a n t t o n o t e t h a t w, the i n t e r a c t i o n parameter, i s r e l a t e d t o the h e a t o f m i x i n g m i c e l l e s which w i l l be i n v e s t i g a t e d h e r e . Experiments conducted on a l a r g e number o f m i x t u r e s a l l at 27°C have suggested w t o be independent o f EON. The m i c e l l a r c o m p o s i t i o n shown i n F i g u r e 3 a g r e e s w e l l w i t h p r e d i c t i o n s based on E q u a t i o n 1 and r e a s o n a b l y w e l l w i t h the r e g u l a r s o l u t i o n model. S i m i l a r agreement has been found a t 37 and 50°C f o r the 3Cio/ 10 system w i t h o u t any m o d i f i c a t i o n o f the p a r a m e t e r s . This is reflected by the values shown i n Table I I for the 3 4 > C i o / 1 0 system which a p p l y over the temperature range between 27 and 50°C. Both the m i x t u r e CMC and the m i c e l l a r c o m p o s i t i o n a r e w e l l f i t u s i n g these parameters. NPE

NPE

npe

The 3CIQ/ 50 system d i d not y i e l d a similar agreement. Shown by F i g u r e s 4 and 5 a r e the CMCj^ and m i c e l l a r c o m p o s i t i o n s a t 50°C. To f o r c e E q u a t i o n 1 t o f i t t h e s e r e s u l t s , i t was n e c e s s a r y t o m o d i f y the parameters. These changes a r e r e f l e c t e d by the temp e r a t u r e dependence shown i n T a b l e I I f o r the system 3CIQ/ ]? 50· Note t h a t b o t h the i n t e r a c t i o n parameter, w, and the m o l e c u l a r a r e a r a t i o , R, change as the temperature i s changed. No d e f i n i t e t r e n d is indicated. The v a l u e o f w f i r s t i n c r e a s e s and then d e c r e a s e s and R i s somewhat i n c r e a s e d . The i n c r e a s e i n temperature i s known to i n f l u e n c e the hydrogen b o n d i n g between water and the p o l y e t h y l e n e n


e


ΝΡΕκ) i Ultrafiltration Data 0.171 M NACL 80.00

70.00 =1 60.00 UL

ϋ


50.00

40.00 20.00 1

Figure

1.

1

1

30.00

1

1

•

40.00 50.00 60.00 Temperature (Celsius)

CMC v e r s u s temperature f o r ΝΡΕχο e f f e c t o f temperature on t h e CMC f o r NPE i n 0.171 M NaC£. Σ

1 0

0.00 0.00 1

F i g u r e 2.

1

1

1

1

0.20 0.40 0.60 0.80 Monomer Mole Fraction 3ΦΟιο

1

1.00

CMC's f o r 3 φ ΰ χ ο / 5 0 m i x t u r e s : vari a t i o n o f the m i x t u r e c r i t i c a l m i c e l l e c o n c e n t r a t i o n w i t h monomer phase compo s i t i o n f o r m i x t u r e s o f d e c y l benzene s u l f o n a t e w i t h a n o n y l phenol ethyoxyl a t e h a v i n g an e t h y l e n e o x i d e chain l e n g t h o f 50, a t 27 °C. Ν Ρ Ε




0.00

0.20


0.40

0.60

0.80

1.00

Monomer Mole Fraction 3Cio F i g u r e 3.

Phase c o m p o s i t i o n s f o r 3

Nonideal Mixed Micelles - ACS Symposium Series (ACS Publications)

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