Effects of Surfactant Structure on the Thermodynamics of Mixed

10 Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 30, 2016 | http://pubs.acs.org Publication Date: May 21, 1984 | doi: 10.1021/bk-1984-0253.ch010

Effects of Surfactant Structure on the Thermodynamics of Mixed Micellization PAUL M. H O L L A N D Miami Valley Laboratories, The Procter & Gamble Company, Cincinnati, OH 45247

Calorimetric measurements are used to examine interactions between different surfactant components in nonideal mixed micelles and assess the effects of surfactant structure on the thermodynamics of mixed micellization. Results for some anionic/nonionic surfactant mixtures show that variations in surfactant structure can have important effects on heats of mixing in the micelles and significantly influence the critical micelle concentration (cmc) of the mixed surfactant systems. Here, both the heats of mixing and deviations of the cmc from ideality are smaller for alkyl ethoxylate sulfates than alkyl sulfates when mixed with alkyl ethoxylate nonionics. The calorimetric results for these systems are also used to examine the appropriateness of the regular solution approximation used in pseudo-phase separation models for treating mixed micellization. The failure of the regular solution approximation to account for the observed heats of mixing in these systems suggests that the net interaction parameter of the nonideal mixed micelle models be interpreted as an excess free energy parameter in such cases. The formation of mixed micelles in surfactant solutions which contain two or more surfactant components can be significantly affected by the structures of the surfactants involved. The observed critical micelle concentration (cmc) is often significantly lower than would be expected based on the cmc s of the pure surfactants. This clearly demonstrates that interactions between different surfactant components in the mixed micelles are taking place. 1

0097-6156/ 84/ 0253-0141 $06.00/0 © 1984 American Chemical Society

In Structure/Performance Relationships in Surfactants; Rosen, Milton J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 30, 2016 | http://pubs.acs.org Publication Date: May 21, 1984 | doi: 10.1021/bk-1984-0253.ch010

142

S T R U C T U R E / P E R F O R M A N C E R E L A T I O N S H I P S IN S U R F A C T A N T S

N o n i d e a l m i x e d m i c e l l e m o d e l s b a s e d on t h e pseudo-phase s e p a r a t i o n a p p r o a c h and a r e g u l a r s o l u t i o n a p p r o x i m a t i o n have been d e v e l o p e d (1-4) t o d e s c r i b e t h i s b e h a v i o r . H e r e , the d e t a i l s o f m i c e l l a r s t r u c t u r e a r e i g n o r e d and t h e i n t e r a c t i o n s b e t w e e n two d i f f e r e n t s u r f a c t a n t components a r e a c c o u n t e d f o r by a s i n g l e g e n e r a l i z e d p a r a m e t e r w h i c h r e p r e s e n t s an e x c e s s heat of m i x i n g . T h i s a p p r o a c h has b e e n s u c c e s s f u l l y a p p l i e d (2,3,5) to a c o n s i d e r a b l e v a r i e t y of b i n a r y n o n i d e a l s u r f a c t a n t m i x t u r e s i n c l u d i n g m i x e d n o n i o n i c and i o n i c s u r f a c t a n t s even t h o u g h t h e m o d e l n e g l e c t s e f f e c t s due t o t h e b o n d i n g o f c o u n t e r ions. In the d e s c r i p t i o n of n o n i d e a l mixed t e r n a r y s u r f a c t a n t s y s t e m s (_3) no a d j u s t a b l e p a r a m e t e r s beyond t h o s e f o r the b i n a r y m i x t u r e s a r e r e q u i r e d t o o b t a i n good r e s u l t s . Together these r e s u l t s show t h a t t h e n e t i n t e r a c t i o n p a r a m e t e r s (β) o b t a i n e d f o r b i n a r y s u r f a c t a n t m i x t u r e s can p r o v i d e a u s e f u l measure o f n o n i d e a l m i x i n g i n m i c e l l e s . However, i t i s n o t as c l e a r how w e l l t h i s a p p r o a c h ( u s i n g the r e g u l a r s o l u t i o n a p p r o x i m a t i o n ) a c t u a l l y r e f l e c t s the thermodynamics of mixed m i c e l l i z a t i o n . C a l o r i m e t r i c measurements r e p r e s e n t a p r o m i s i n g way o f g a i n i n g thermodynamic i n f o r m a t i o n about mixed m i c e l l i z a t i o n . Of t h e p o s s i b l e t y p e s o f m e a s u r e m e n t s , h e a t s o f m i c e l l a r m i x i n g o b t a i n e d from the m i x i n g of pure s u r f a c t a n t s o l u t i o n s are p e r haps o f t h e g r e a t e s t i n t e r e s t . A l s o o f i n t e r e s t i s the t i t r a t i o n ( d i l u t i o n ) of mixed m i c e l l a r s o l u t i o n s to o b t a i n mixed cmc s. W h i l e c a l o r i m e t r i c measurements have b e e n a p p l i e d i n s t u d i e s o f p u r e s u r f a c t a n t s (6,7) and t h e i r i n t e r a c t i o n w i t h p o l y m e r s (8^), t o o u r k n o w l e d g e , a p p l i c a t i o n s o f c a l o r i m e t r y t o p r o b l e m s o f n o n i d e a l m i x e d m i c e l l i z a t i o n have n o t been p r e v i o u s l y r e p o r t e d i n the l i t e r a t u r e . Among t h e p u r p o s e s o f t h i s p a p e r i s t o r e p o r t the r e s u l t s o f c a l o r i m e t r i c measurements o f t h e h e a t s o f m i c e l l a r m i x i n g i n some n o n i d e a l s u r f a c t a n t s y s t e m s . H e r e , a t t e n t i o n i s f o c u s e d on i n t e r a c t i o n s o f a l k y l e t h o x y l a t e n o n i o n i c s w i t h a l k y l s u l f a t e and a l k y l e t h o x y l a t e s u l f a t e s u r f a c t a n t s . The use o f c a l o r i m e t r y as an a l t e r n a t i v e t e c h n i q u e f o r the d e t e r m i n a t i o n o f t h e cmc s o f m i x e d s u r f a c t a n t s y s t e m s i s a l s o d e m o n s t r a t e d . Besides p r o v i d i n g a d i r e c t measurement o f the e f f e c t o f t h e s u r f a c t a n t s t r u c t u r e on t h e h e a t s o f m i c e l l a r m i x i n g , c a l o r i m e t r i c r e s u l t s can a l s o be compared w i t h n o n i d e a l m i x i n g t h e o r y . This allows the a p p r o p r i a t e n e s s of the r e g u l a r s o l u t i o n a p p r o x i m a t i o n used i n m o d e l s o f m i x e d m i c e l l i z a t i o n t o be a s s e s s e d . 1

1

Theory The d e r i v a t i o n o f a p s e u d o - p h a s e s e p a r a t i o n model f o r t r e a t i n g n o n i d e a l m i x e d m i c e l l i z a t i o n i s g i v e n i n d e t a i l i n r e f e r e n c e _3. T h i s leads t o the g e n e r a l i z e d r e s u l t


10.

HOLLAND

143

Thermodynamics of Mixed Micellization

^LfiCi

c*

1

i=i

(1)

1

w h i c h c a n be u s e d t o r e l a t e t h e m i x e d cmc ( C * ) o f a n o n i d e a l s u r f a c t a n t system t o the a c t i v i t y c o e f f i c i e n t s ( f ^ ) o f the s u r f a c t a n t components i n t h e m i x e d m i c e l l e s , t h e i r m o l e f r a c t i o n s (a^) and p u r e cmc s ( C ^ ) . I n t h e c a s e where t h e a c t i v i t y c o e f f i c i e n t s equal u n i t y t h i s e x p r e s s i o n reduces i n form t o t h a t p r e v i o u s d e r i v e d f o r i d e a l mixed m i c e l l e s ( 1 , 9 ) . C o n s i d e r a t i o n o f the thermodynamics o f n o n i d e a l m i x i n g p r o v i d e s a way t o d e t e r m i n e t h e a p p r o p r i a t e f o r m f o r t h e a c t i v i t y c o e f f i c i e n t s and e s t a b l i s h a r e l a t i o n s h i p b e t w e e n t h e measured e n t h a l p i e s o f m i x i n g and t h e r e g u l a r s o l u t i o n a p p r o x i mation. F o r example, the excess f r e e energy o f m i x i n g f o r a b i n a r y m i x t u r e c a n be w r i t t e n as


1

G

E

= RT(

X 1

ln f

x

+ (1 - χ ) I n f ) χ

2

(2)

T a k i n g t h e p a r t i a l d e r i v a t i v e w i t h r e s p e c t t o t h e mole f r a c t i o n s i n t h e m i c e l l e ( x ^ ) and u s i n g t h e Gibbs-Duhem r e l a t i o n t o e l i m i n a t e some o f t h e r e s u l t i n g terms g i v e s

/Μ\

= RT ( I n f i - I n f ) 2

(3)

3X

V I/T,P Combining these r e l a t i o n s h i p s then c i e n t s t o be e x p r e s s e d i n terms o f mixing / I n f , = L _ (G E + ( 1 - X I ) RT \

allows the a c t i v i t y c o e f f i the excess f r e e energy o f ν

3GM

( 4 )

3x]_ /

e

W G - X! (5) RT \ 9x! ) The r e g u l a r s o l u t i o n a p p r o x i m a t i o n i s i n t r o d u c e d by a s s u m i n g ( b y d e f i n i t i o n ) that the excess entropy o f mixing i s zero. This r e q u i r e s t h a t t h e excess f r e e energy e q u a l the excess e n t h a l p y of m i x i n g . For b i n a r y mixtures the excess enthalpy of m i x i n g i s o r d i n a r i l y r e p r e s e n t e d by a f u n c t i o n o f t h e f o r m In f

H

E

2

=

= βχχ(1 - x ) R T x

(6)

where β t i m e s RT r e p r e s e n t s a d i f f e r e n c e i n i n t e r a c t i o n e n e r g y between t h e m i x e d and unmixed s y s t e m s . This corresponds to t h e l e a d i n g t e r m i n t h e l a t t i c e model d e s c r i p t i o n o f l i q u i d m i x t u r e s (10). When t h i s e x p r e s s i o n i s s u b s t i t u t e d f o r G i n e q u a t i o n s 4 and 5 t h e r e s u l t i n g b i n a r y a c t i v i t y c o e f f i c i e n t s ( i n the r e g u l a r s o l u t i o n a p p r o x i m a t i o n ) take the form E



144

exp β ( 1 - χ χ )

(7)

2

(8)

fo = exp

w i t h β p r o v i d i n g a measure o f t h e n o n i d e a l i t y o f m i x i n g i n t h e system. The β p a r a m e t e r s i n t h e above e x p r e s s i o n s a r e d e t e r m i n e d f r o m t h e e x p e r i m e n t a l m i x e d cmc s o f b i n a r y s y s t e m s . This r e q u i r e s s o l v i n g i t e r a t i v e l y f o r x ^ ( a t t h e cmc) u s i n g a r e l a t i o n s h i p such as Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 30, 2016 | http://pubs.acs.org Publication Date: May 21, 1984 | doi: 10.1021/bk-1984-0253.ch010

1

aiC* 1

In 1

Γ

0

a 2 C

(11 - X = ( x i] .. ))' I n 2

—

(9)

-

f o l l o w e d by s u b s t i x tuC t i Jo n i n t o t h e e x p r e[s(s1i-oxni ) 1

1

Γ^Ί

in D

LXTCT

=

(1 -

X

)

l

J

(10)

2

While t h i s treatment i s s t r i c t l y developed f o r n o n i o n i c s u r f a c t a n t m i x t u r e s i t c a n o f t e n be a p p l i e d e m p i r i c a l l y t o mixtures containing ionic surfactants with success. Some e x a m p l e s o f t h e t y p e s o f s u r f a c t a n t m i x t u r e s t o w h i c h t h i s model h a s been s u c c e s s f u l l y a p p l i e d and t h e c o r r e s p o n d i n g β p a r a m e t e r s a r e g i v e n i n Table I . I t i s r e a d i l y seen t h a t n e g a t i v e v a l u e s a r e t y p i c a l l y seen f o r d e v i a t i o n from i d e a l b e h a v i o r . These w o u l d c o r r e s p o n d to exothermic heats o f m i x i n g i n the m i c e l l e s . Assuming t h e v a l i d i t y o f t h e r e g u l a r s o l u t i o n a p p r o x i m a t i o n , i t s h o u l d t h e n be p o s s i b l e to d i r e c t l y r e l a t e heats o f mixing i n the m i c e l l e s (as a f u n c t i o n o f mole f r a c t i o n ) t o t h e v a l u e o f t h e β p a r a m e t e r v i a e q u a t i o n 6. Table

I . V a l u e s o f t h e N e t I n t e r a c t i o n P a r a m e t e r β f o r Some B i n a r y S u r f a c t a n t M i x t u r e s ( f r o m R e f . _3) Conditions

Binary Mixture

3 -3 7

C

-2 4

C (CH )SO/C OSO3" · N a

0

( C H

1 0

)

3 2

P O / C

3

12

O S 0

3

*

N

a

2

+

+

3

-3 6 -0 8 2

2

Π

II

II

It

II

II

1 0

C (CH ) NO/C OS0 1 2

C

1 0

3

(

O C H

2

2

1 2

C H

)

2 4

O H

·Na

3

C

/ 12

O S 0

3~

0.5mM N a C 0 ( 2 3 ° C )

+

2

'

N

a

+

Οχ2(CH ) NO/C (OCH CH ) 0H 3

C

2

1 0

+

1 Q

N (CH ) 3

2

2

· Br"/C OS0 " ·Na

3

1 0

-1 8

C

2

4

+

1 0

N (CH ) 3

3

1 0

II

II

It

II

π

.05M

+

3

C (OCH CH ) OH/C OSO " · N a 2

3

II

4

-4 1

8

3

1 2

Cio(CH ) PO/C (CH3)SO

-4 4

-13

10

ImM N a C 0 ( 2 4 ° C )

+

NaBr (23°C)

II

II

II

II

II

II

3

· Br~/C (OCH CH ) OH 8

2

2

4


10.

HOLLAND


Experimental

145

Thermodynamics of Mixed Micellization Section

I s o p e r i b o l c a l o r i m e t r i c measurements were c a r r i e d o u t u s i n g a T r o n a c , I n c . M o d e l 550 C a l o r i m e t e r i n t e r f a c e d w i t h a d i g i t a l v o l t m e t e r and m i c r o - c o m p u t e r f o r d a t a a q u i s i t i o n . In these e x p e r i m e n t s a Dewar f l a s k r e a c t i o n v e s s e l was s t i r r e d a t a c o n s t a n t r a t e w h i l e immersed i n a c o n s t a n t t e m p e r a t u r e b a t h ( a t 25°C) w i t h m i x i n g i n i t i a t e d by e i t h e r i n j e c t i o n o r t i t r a t i o n o f another s o l u t i o n h e l d at b a t h temperature i n t o the v e s s e l . The e x p e r i m e n t s were i n i t i a t e d when t h e b a t h and r e a c t i o n v e s s e l t e m p e r a t u r e s were e q u a l and t h e changes i n t e m p e r a t u r e were m o n i t o r e d by a t h e r m i s t o r r e f e r e n c e d t o t h e b a t h . A s l i g h t l y m o d i f i e d v e r s i o n o f a s o f t w a r e p a c k a g e d e v e l o p e d by Grime e t . a l . ( 1 1 ) was u s e d f o r d a t a a c q u i s i t i o n and r e d u c t i o n ( i . e . , c o r r e c t i o n f o r s t i r r i n g heat, e t c . ) . The compounds u s e d i n t h i s s t u d y were p u r e s i n g l e s p e c i e s u r f a c t a n t s d e t e r m i n e d t o be g r e a t e r t h a n 98% p u r i t y by t h i n - l a y e r o r gas chromatography. H e a t s o f m i x i n g f o r m i c e l l a r s o l u t i o n s were d e t e r m i n e d by m i x i n g v a r i o u s r a t i o s o f p u r e e q u i m o l a r s u r f a c t a n t s o l u t i o n s by injection. These measurements were c a r r i e d o u t f o r p e n t a o x y e t h y l e n e g l y c o l monodecyl e t h e r ( C 1 0 E 5 ) w i t h sodium d o d e c y l s u l f a t e ( S D S ) , s o d i u m d o d e c y l d i o x y e t h y l e n e s u l f a t e ( C j ^ E ^ i O and sodium d e c y l p e n t a o x y e t h y l e n e s u l f a t e ( C 1 0 E 5 S ) , r e s p e c t i v e l y a t 25°C. I n o r d e r t o s u b t r a c t o u t e f f e c t s due t o a d d i t i o n a l m i c e l l i z a t i o n o f p u r e s u r f a c t a n t monomers on m i x i n g , t h e e x p e r i m e n t s were c a r r i e d o u t a t two c o n c e n t r a t i o n s above t h e cmc (.02M and .08M) and t h e d i f f e r e n c e i n t h e r e s u l t s t a k e n . Under t h e s e c o n d i t i o n s t h e c o m p o s i t i o n o f t h e m i x e d m i c e l l e s and s o l u t i o n s h o u l d be a p p r o x i m a t e l y e q u a l s i n c e t h e c o n c e n t r a t i o n s a r e on t h e o r d e r o f 20 t o 100 t i m e s t h e m i x e d cmc i n e a c h c a s e . The f i n a l d i f f e r e n c e d r e s u l t s s h o u l d then c o r r e s p o n d to the m i x i n g o f pure m i c e l l e s t o f o r m m i x e d m i c e l l e s , and t h e r e f o r e t o good a p p r o x i m a t i o n , t o t h e e x c e s s h e a t s o f m i c e l l a r m i x i n g as a f u n c t i o n o f mole f r a c t i o n . 1

The m i x e d cmc s o f m i c e l l a r s o l u t i o n s o f t e t r a o x y e t h y l e n e g l y c o l m o n o o c t y l e t h e r ( C 3 E 4 ) w i t h SDS and C ^ 2 2 > r e s p e c t i v e l y were a l s o d e t e r m i n e d by c a l o r i m e t r y . M i x t u r e s w i t h C 3 E 4 were c h o s e n due t o t h e h i g h e r cmc and c o n s e q u e n t l a r g e r and more a d e q u a t e t o t a l e n t h a l p i e s o f d e m i c e l l i z a t i o n compared t o m i x t u r e s w i t h C10E5. The measurements were c a r r i e d o u t by t h e t i t r a t i o n ( d i l u t i o n ) of mixed s u r f a c t a n t s o l u t i o n s w i t h v a r y i n g r a t i o s of components and .12M t o t a l c o n c e n t r a t i o n i n t o d i s t i l l e d w a t e r . Under t h e s e c o n d i t i o n s t h e h e a t o f d e m i c e l l i z a t i o n i s o b s e r v e d as a f u n c t i o n o f t i t r a n t added, w i t h a s h a r p b r e a k o c c u r r i n g once t h e cmc i s r e a c h e d i n t h e r e a c t i o n v e s s e l . V a l u e s f o r t h e cmc e n d p o i n t were t a k e n f r o m t h e i n t e r s e c t i o n o f l e a s t s q u a r e s f i t s o f l i n e segments i m m e d i a t e l y b e f o r e and a f t e r t h e b r e a k i n t h e t i t r a t i o n r e s u l t s ( c o r r e c t e d f o r s t i r r i n g h e a t and volume changes). Cmc s were d e t e r m i n e d f o r t h e p u r e s u r f a c t a n t s i n a s i m i l a r manner e x c e p t f o r t h a t o f SDS. Here, the heat o f E

S

1


146

STRUCTURE/PERFORMANCE RELATIONSHIPS IN SURFACTANTS

m i c e l l i z a t i o n i s q u i t e s m a l l and d i l u t i o n e f f e c t s a r e s i g n i f i c a n t m a k i n g an a c c u r a t e d e t e r m i n a t i o n o f t h e cmc by c a l o r i m e t r y d i f f i cult. T h e r e f o r e t h e cmc o f SDS i n d i s t i l l e d w a t e r was d e t e r m i n e d by s u r f a c e t e n s i o n measurements u s i n g a t e n s i o m e t e r w i t h du Nouy r i n g , as i n p r e v i o u s work (_3) .


R e s u l t s and

Discussion

R e s u l t s from the h e a t s of m i c e l l a r m i x i n g experiments are shown i n F i g u r e 1. H e r e , t h e h e a t o f m i x i n g p e r mole ( a f t e r d i f f e r e n c i n g t o c o r r e c t f o r monomer c o n t r i b u t i o n s ) i s p l o t t e d v e r s u s t h e mole f r a c t i o n o f C ^ Q 5 ^ t h e m i x e d m i c e l l a r s y s t e m . I t i s c l e a r l y s e e n t h a t t h e i n t e r a c t i o n o f SDS w i t h C^o 5 ^ s i g n i f i c a n t l y s t r o n g e r than t h a t o f the a l k y l e t h o x y l a t e sulfate surfactants with C^Q 5 ^ a d d i t i o n , t h e symmetry i n the heat of m i x i n g curves i s s t r i k i n g l y d i f f e r e n t w i t h those for C^2 2^ * ^ 1 0 5 ^ s h o w i n g an a s y m m e t r i c maximum a t a b o u t a w n 1 : 2 mole r a t i o w i t h C^o 5 -> u e t h e SDS r e s u l t s a r e s y m m e t r i c a b o u t a 1:1 r a t i o . These o b s e r v a t i o n s c l e a r l y d e m o n s t r a t e t h a t the presence of e t h o x y l a t i o n i n the s t r u c t u r e of the s u l f a t e s u r f a c t a n t s has a p r o n o u n c e d e f f e c t on t h e i r h e a t s o f mixing. T i t r a t i o n r e s u l t s f o r t h e m i x e d cmc s o f t h e S D S / C 3 E 4 and ^ 1 2 2 ^ / ^ 8 4 s y s t e m s as a f u n c t i o n o f t h e i r r e l a t i v e mole f r a c t i o n i n s o l u t i o n a r e shown i n F i g u r e s 2 and 3 , r e s p e c t i v e l y . H e r e , t h e e x p e r i m e n t a l l y d e t e r m i n e d p o i n t s a r e compared w i t h c a l c u l a t e d r e s u l t s from the n o n i d e a l mixed m i c e l l e model ( s o l i d l i n e ) and t h e i d e a l m i x e d m i c e l l e model ( d a s h e d l i n e ) . Good agreement w i t h t h e n o n i d e a l model i s s e e n i n e a c h c a s e . F i g u r e 2 shows t h a t t h e b i n a r y S D S / C 3 E 4 s y s t e m d e v i a t e s s i g n i f i c a n t l y from i d e a l i t y w i t h a β v a l u e of - 3 . 3 . This r e s u l t i s comparable to the parameters found f o r o t h e r a l k y l s u l f a t e / a l k y l e t h o x y l a t e n o n i o n i c systems (see T a b l e I ) . In the case o f t h e C i 2 2 / 8 4 s y s t e m ( s e e F i g u r e 3) a s i g n i f i c a n t l y s m a l l e r d e v i a t i o n from i d e a l i t y i s observed, g i v i n g a v a l u e of -1.6 f o r β. T h i s seems t o be c o n s i s t e n t w i t h t h e s m a l l e r h e a t s o f m i x i n g o b s e r v e d f o r C ^ 2 2 ^ compared t o SDS i n F i g u r e 1. n

e

E

e

E

a n c

s

n

E

E

1

Ε

Ε

E

s

c

E

E

T o g e t h e r t h e s e r e s u l t s show t h a t t h e n o n i d e a l b e h a v i o r o f s u l f a t e s u r f a c t a n t s can be s i g n i f i c a n t l y a f f e c t e d by t h e presence or absence of e t h o x y l a t i o n i n t h e i r s t r u c t u r e s . Here, b o t h t h e h e a t s o f m i x i n g and d e v i a t i o n s o f t h e cmc f r o m i d e a l i t y are s m a l l e r f o r a l k y l e t h o x y l a t e s u l f a t e s than a l k y l s u l f a t e s when m i x e d w i t h a l k y l e t h o x y l a t e n o n i o n i c s . This i s presumably due t o i m p r o v e d s c r e e n i n g o r s e p a r a t i o n o f c h a r g e i n p u r e a l k y l e t h o x y l a t e s u l f a t e m i c e l l e s compared t o a l k y l s u l f a t e micelles. T h i s i n t e r p r e t a t i o n w o u l d be c o m p a t i b l e w i t h t h e "charge s e p a r a t i o n " e f f e c t p r e v i o u s l y used i n e x p l a i n i n g the m i x e d cmc d a t a o f u n e t h o x y l a t e d s u l f a t e / a l k y l e t h o x y l a t e n o n i o n i c surfactant mixtures ( 5 , 1 2 ) . The s u r p r i s i n g d i f f e r e n c e s


10.

HOLLAND


147


1.4 r

0

.2

.4 .6 .8 Mole Fraction C E 10

Figure

1.

1.0

5

H e a t s o f m i c e l l a r m i x i n g a f t e r c o r r e c t i o n f o r monomer

contributions

( s e e t e x t ) as a f u n c t i o n o f c o m p o s i t i o n f o r SDS,

C 1 2 E 2 S and C 1 0 E 5 S w i t h

C

1 0

E

5

^

a t

2

5°C).

American Chemfcal Society Library 1155 IBîh St. N. W. In Structure/Performance Relationships in Surfactants; Rosen, Milton J.; Washington, D. Chemical C. 20038 ACS Symposium Series; American Society: Washington, DC, 1984.

STRUCTURE/PERFORMANCE RELATIONSHIPS IN SURFACTANTS

148

10

r

^5 6


o 4 ϋ

0


F i g u r e 2. ( a t 25°C).

1

Cmc s o f m i x t u r e s The p l o t t e d

l i n e i stheresult

.8

1.0

4

o f SDS and C g E

4

f o r t h e n o n i d e a l mixed m i c e l l e

0

.2

1

Cmc s o f m i x t u r e s

d i s t i l l e d w a t e r ( a t 25°C).

The p l o t t e d

data, the s o l i d l i n e i s the r e s u l t

with

mixing.

1.0

4

C x 2 2 ^ ^ 3 ~ · E

model

for ideal


micelle

water

points areexperimental data, the s o l i d

β = - 3 . 3 , and t h e dashed l i n e i s t h e r e s u l t

Figure 3.

i ndistilled

a

n

(

*

CgE

4

^

n

points are experimental

f o r t h e n o n i d e a l mixed

model w i t h β = - 1 . 6 , and t h e d a s h e d l i n e i s t h e r e s u l t

for ideal

mixing.



10.

HOLLAND


149

o b s e r v e d i n t h e symmetry o f t h e m i c e l l a r m i x i n g h e a t s w i t h c o m p o s i t i o n ( F i g u r e 1) a r e more d i f f i c u l t t o u n d e r s t a n d . Here, i t may be p o s s i b l e t h a t d i f f e r e n c e s i n t h e r a t i o where t h e maximum i n t h e h e a t o f m i x i n g o c c u r s a r i s e f r o m d i f f e r e n c e s b e t w e e n t h e p r e f e r r e d minimum e n e r g y p a c k i n g g e o m e t r y o f t h e a l k y l e t h o x y l a t e s u l f a t e and a l k y l s u l f a t e s u r f a c t a n t s w i t h a l k y l e t h o x y l a t e s i n the m i c e l l e . The i n f o r m a t i o n o b t a i n e d a b o u t t h e h e a t s o f m i x i n g i n n o n i d e a l m i x e d m i c e l l e s c a n a l s o be u s e d t o examine t h e a p p r o p r i a t e n e s s of the r e g u l a r s o l u t i o n a p p r o x i m a t i o n used i n n o n i d e a l mixed m i c e l l e models. Here, e q u a t i o n 6 a l l o w s a c o m p a r i s o n b e t w e e n t h e o b s e r v e d c a l o r i m e t r i c r e s u l t s and b o t h t h e symmetry and m a g n i t u d e o f t h e e x c e s s h e a t s o f m i x i n g t h a t w o u l d be 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 a p p r o x i m a t i o n used i n the models. R e f e r r i n g t o F i g u r e 1, t h e S D S / C 1 0 E 5 r e s u l t s show a good f i t t o t h e f o r m o f t h e r e g u l a r s o l u t i o n a p p r o x i m a t i o n ( s o l i d l i n e ) c a l c u l a t e d from e q u a t i o n 6 w i t h β=-8.4. W h i l e i t i s s e e n t h a t t h e p r e d i c t e d symmetry o f t h e r e g u l a r s o l u t i o n a p p r o x i m a t i o n i s reproduced q u i t e w e l l , the magnitude of the β parameter n e c e s s a r y to o b t a i n the f i t i s s i g n i f i c a n t l y o u t s i d e the range of β v a l u e s n o r m a l l y found when a p p l y i n g t h e n o n i d e a l m i c e l l e model t o m i x t u r e s o f a l k y l s u l f a t e s and a l k y l e t h o x y l a t e n o n i o n i c s ( s e e F i g u r e 2 and Table 1 ) . T h i s i n d i c a t e s t h a t the r e g u l a r s o l u t i o n approxima t i o n does n o t a d e q u a t e l y d e s c r i b e m i x i n g i n t h i s s y s t e m . An e x a m i n a t i o n of the heats of m i x i n g f o r 0^2 2^ * ^10 5^ w i t h C i o 5 c l e a r l y shows t h a t t h e p r e d i c t e d symmetry o f t h e r e g u l a r s o l u t i o n a p p r o x i m a t i o n used i n the mixed m i c e l l e models i s not observed. Together these r e s u l t s c l e a r l y demonstrate t h a t i n s p i t e of the success o f the n o n i d e a l mixed m i c e l l e models i n d e s c r i b i n g n o n i d e a l b e h a v i o r , the r e g u l a r s o l u t i o n a p p r o x i m a t i o n does n o t p r o p e r l y a c c o u n t f o r the heats of m i x i n g i n these systems. Ε

a n c

E

E

T h i s c o n c l u s i o n i m p l i e s t h a t the excess entropy of m i x i n g i s n o n - z e r o and t h a t t h e m i x e d m i c e l l e s p r e s u m a b l y a c q u i r e more i n t e r n a l o r d e r t h a n t h e y w o u l d by random m i x i n g . An e x a m i n a t i o n o f t h e m a g n i t u d e o f t h e d e v i a t i o n s f r o m t h e r e g u l a r s o l u t i o n a p p r o x i m a t i o n shows t h a t t h e r e must be a large TS c o n t r i b u t i o n to the excess f r e e energy of m i x i n g . A s i m i l a r s i t u a t i o n i s commonly o b s e r v e d i n m i x t u r e s o f l i q u i d s , where t h e r e g u l a r s o l u t i o n a p p r o a c h o f t e n g i v e s good r e s u l t s f o r t h e e x c e s s f r e e e n e r g i e s , b u t p o o r r e s u l t s f o r t h e h e a t s o f m i x i n g (L3). U n f o r t u n a t e l y , the excess e n t r o p i e s c a n n o t be e a s i l y e x t r a c t e d f r o m c a l o r i m e t r i c mea s u r e m e n t s o f m i c e l l a r m i x i n g h e a t s s u c h as t h o s e i n F i g u r e 1 and measurements o f t h e m i x e d cmcs t o o b t a i n G . This i s b e c a u s e t h e c o m p o s i t i o n o f t h e m i c e l l e s a t t h e cmc a r e n o t known and may v a r y s i g n i f i c a n t l y f r o m t h e c o m p o s i t i o n o f t h e overall surfactant mixture. E

E


150


The f i n d i n g t h a t t h e a s s u m p t i o n s o f the r e g u l a r s o l u t i o n a p p r o x i m a t i o n do n o t h o l d f o r the m i x e d m i c e l l a r s y s t e m s i n v e s t i g a t e d h e r e s u g g e s t s a r e - e x a m i n a t i o n o f how the t h e r m o dynamics of m i x i n g e n t e r the n o n i d e a l mixed m i c e l l e model. F o r e x a m p l e , i t i s r e a d i l y s e e n ( e q u a t i o n s 4 and 5) t h a t when t h e f u n c t i o n a l f o r m o f e q u a t i o n 6 i s s u b s t i t u t e d f o r G , t h e f o r m o f t h e a c t i v i t y c o e f f i c i e n t s i n e q u a t i o n s 7 and 8 r e s u l t s . I t i s c l e a r t h e n t h a t f o r c a s e s where t h e e x c e s s e n t r o p y i s not z e r o , e m p i r i c a l l y assuming the form Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 30, 2016 | http://pubs.acs.org Publication Date: May 21, 1984 | doi: 10.1021/bk-1984-0253.ch010

E

G

E

= 3χχ(1

- xi)RT

(ID

f o r the e x c e s s f r e e e n e r g y o f m i x i n g (as i n r e f e r e n c e 4 ) , w i l l g i v e t h e same f o r m f o r t h e a c t i v i t y c o e f f i c i e n t s . Under these circumstances, t h e β v a l u e f r o m the n o n i d e a l m i x e d m i c e l l e model s h o u l d be i n t e r p r e t e d as a d i m e n s i o n l e s s excess f r e e e n e r g y p a r a m e t e r , r a t h e r t h a n an e x c e s s h e a t o f m i x i n g parameter. Conclusions C a l o r i m e t r i c measurements can be u s e d t o o b t a i n h e a t s o f m i x i n g b e t w e e n d i f f e r e n t s u r f a c t a n t components i n n o n i d e a l m i x e d m i c e l l e s and a s s e s s the e f f e c t s o f s u r f a c t a n t s t r u c t u r e on t h e thermodynamics of mixed m i c e l l i z a t i o n . C a l o r i m e t r y can a l s o be s u c c e s s f u l l y a p p l i e d i n m e a s u r i n g t h e cmc s o f n o n i d e a l m i x e d s u r f a c t a n t s y s t e m s . The r e s u l t s o f s u c h measurements show t h a t a l k y l ethoxylate sulfate surfactants exhibit smaller deviations f r o m i d e a l i t y and i n t e r a c t s i g n i f i c a n t l y l e s s s t r o n g l y w i t h a l k y l ethoxylate nonionics than a l k y l s u l f a t e s . The m i x e d cmc b e h a v i o r o f t h e s e (and many o t h e r ) m i x e d s u r f a c t a n t s y s t e m s can be a d e q u a t e l y d e s c r i b e d by a n o n i d e a l m i x e d m i c e l l e model b a s e d on the p s u e d o - p h a s e s e p a r a t i o n a p p r o a c h and a r e g u l a r s o l u t i o n a p p r o x i m a t i o n w i t h a s i n g l e n e t i n t e r a c t i o n p a r a m e t e r 3. However, t h e h e a t s o f m i c e l l a r m i x i n g m e a s u r e d by c a l o r i m e t r y show t h a t t h e a s s u m p t i o n s o f t h e r e g u l a r s o l u t i o n a p p r o x i m a t i o n do n o t h o l d f o r t h e s y s t e m s i n v e s t i g a t e d i n t h i s paper. This suggests that i n these cases the net i n t e r a c t i o n parameter i n the n o n i d e a l mixed m i c e l l e model s h o u l d be i n t e r p r e t e d as an e x c e s s f r e e e n e r g y p a r a m e t e r . 1

Acknowledgments The a u t h o r w i s h e s t o t h a n k Mr. R. P. B u r w i n k e l and Mr. D. F. E t s o n f o r e x p e r i m e n t a l work i n the a u t h o r ' s l a b o r a t o r y , Dr. J . B. K a s t i n g f o r a l l o w i n g h i s C a l v e t i s o t h e r m a l c a l o r i m e t e r t o be u s e d f o r some p r e l i m i n a r y measurements and Dr. D. N. R u b i n g h f o r helpful discussions.


10.

HOLLAND


151

Legend o f Symbols f-[

a c t i v i t y coefficient of surfactant i i n mixed m i c e l l e s

xi

mole f r a c t i o n o f s u r f a c t a n t i i n m i x e d m i c e l l e s


cmc

o f pure s u r f a c t a n t i

Ctj_

mole f r a c t i o n o f s u r f a c t a n t solute

C*

cmc o f m i x e d

β

dimensionless net i n t e r a c t i o n

system

G

E

excess

H

E

excess enthalpy o f mixing

S

E

excess entropy o f m i x i n g

f r e e energy

R

gas c o n s t a n t

Τ

absolute

i i n t o t a l mixed

parameter

of mixing

temperature

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Lange, H.; Beck, K. H. Kolloid Ζ.Z. Polym. 1973, 251, 424. Rubingh, D. Ν., in "Solution Chemistry of Surfactants"; Vol. 1, Mittal, L., Ed.; Plenum Press: New York, 1979; p. 337. Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983, 87, 1984. Kamrath, R. F.; Franses, Ε. I. Ind. Eng. Chem. Fundam. 1983, 22, 230. Scamehorn, J. F.; Schechter, R. S.; Wade, W. H. J. Disp. Sci. Tech. 1982, 3, 261. Benjamin, L. J. Phys. Chem. 1964, 68, 3575. Mazer, N.A.; Olofsson, G. J. Phys. Chem. 1982, 86, 4584. Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1981, 83, 1. Clint, J. J. Chem. Soc. 1975, 71, 1327. Munster, A. "Statistical Thermodynamics"; Springer -Verlag: Berlin-Heidelberg-New York, 1974, Vol. 2, p. 650. Grime, J. K.; Staab, R. Α.; Wernery, J. D., SAC '83 International Triennial Conference and Exhibition on Analytical Chemistry, Univ. of Edinburg July 1983. Schick, M. J.; Manning, D. J. J. Amer. Oil Chem. 1966, 43, 133. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. "Regular and Related Solutions"; Van Nostrand: New York, 1970; Chap. 7.

RECEIVED January 10, 1984


Effects of Surfactant Structure on the Thermodynamics of Mixed

Recommend Documents