Phenomena in Mixed Surfactant Systems - American Chemical Society

11 Molecular Interaction and Synergism in Binary Mixtures of Surfactants

Downloaded by STANFORD UNIV GREEN LIBR on February 15, 2013 | http://pubs.acs.org Publication Date: June 5, 1986 | doi: 10.1021/bk-1986-0311.ch011

Milton J. Rosen Department of Chemistry, Brooklyn College, The City University of New York, Brooklyn, NY 11210

Non-ideal solution theory is used to calculate the value of a parameter, β, that measures the inter action between two surfactants in mixed monolayer or mixed micelle formation. The value of this parameter, together with the values of relevant properties of the individual, pure surfactants, determines whether synergism will exist in a mixture of two surfactants in aqueous solution. The conditions for synergism in surface tension reduction efficiency, mixed micelle formation, and surface tension reduction effectiveness in aqueous solution have been derived mathematically together with the properties of the surfactant mixture at the point of maximum synergism. This treatment has been extended to liquid-liquid (aqueous solution/hydrocarbon) systems at low surfactant concentrations.) The effect of chemical structure and molecular environment on the value of β is demonstrated and discussed. During the past few years, the determination of the interfacial properties of binary mixtures of surfactants has been an area in which there has been considerable activity on the part of a number of investigators, both in industry and in academia. The interest in this area stems from the fact that mixtures of two different types of surfactants often have interfacial properties that are better than those of the individual surfactants by themselves. For example, mixtures of two different surface-active components sometimes reduce the interfacial tension at the hydrocarbon/water interface to values far lower than that obtained with the individual surfactants, and certain mixtures of surfactants are better foaming agents than the individual components. For the purpose of this discussion we define synergism as existing in a system when a given property of the mixture can reach a more desirable value than that attainable by either surface-active component of the mixture by itself. 0097-6156/ 86/ 0311 -0144$06.00/ 0 © 1986 American Chemical Society In Phenomena in Mixed Surfactant Systems; Scamehorn, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1986.


11.

145

Synergism in Binary Mixtures of Surfactants

ROSEN

In my l a b o r a t o r y a t B r o o k l y n C o l l e g e , we have been i n v e s t i g a t i n g m o l e c u l a r i n t e r a c t i o n s and s y n e r g i s m i n b i n a r y m i x t u r e s of s u r f a c t a n t s f o r the p a s t f i v e y e a r s ( 1 - 6 ) . The key t o both i n v e s t i g a t i o n s i s the d e t e r m i n a t i o n o f the v a l u e o f a parameter, 3, t h a t measures the n a t u r e and the e x t e n t o f the i n t e r a c t i o n between the two surfactants. I f the i n t e r a c t i o n between the two s u r f a c t a n t s i s a t t r a c t i v e , 3 i s n e g a t i v e ; i f the i n t e r a c t i o n i s r e p u l s i v e , then 3 is positive. The l a r g e r the v a l u e o f 3, the s t r o n g e r the i n t e r a c t i o n , e i t h e r a t t r a c t i v e o r r e p u l s i v e , between t h e two s u r f a c t a n t s . To d a t e , 3 v a l u e s , d e t e r m i n e d e i t h e r i n our l a b o r a t o r y or i n the l a b o r a t o r y o r i n the l a b o r a t o r i e s o f o t h e r i n v e s t i g a t o r s , have ranged from 0 t o -30; 0 i n d i c a t i n g no i n t e r a c t i o n and -30 an e x t r e m e l y strong i n t e r a c t i o n . The 3 v a l u e s f o r m i x t u r e s o f two g i v e n s u r f a c t a n t s a t a s p e c i f i e d t e m p e r a t u r e v a r i e s , depending upon the p a r t i c u l a r i n t e r f a c i a l phenomenon b e i n g i n v e s t i g a t e d . For example, f o r mix t u r e s o f sodium n - o c t y l s u l f a t e and n - o c t y l trimethylammonium bromide, the 3 v a l u e f o r mixed monolayer f o r m a t i o n o f 25°C at the aqueous s o l u t i o n / a i r i n t e r f a c e i s -14.2, w h i l e t h a t f o r mixed m i c e l l e f o r m a t i o n a t 25°C i n water i s -10.2 (6). The e v a l u a t i o n o f the i n t e r a c t i o n parameters i s based upon e q u a t i o n s (1 and 2 ) , d e r i v e d by Rubingh (7) f o r mixed m i c e l l e f o r m a t i o n from the thermodynamics o f the system:

Μ

= χ \ \ (1-cO

=

(1)

(l-x") f

M 2

α = mole f r a c t i o n o f s u r f a c t a n t s o l u t i o n phase; M M M C^jC^

=

, C^

c r i t i c a l micelle

surfactants

1 and

v a l u e o f α;

M

X

2 and

C

M

(2)

2

1 i n the

t o t a l surfactant

c o n c e n t r a t i o n s of

in

the

individual

t h e i r mixture, r e s p e c t i v e l y ,

at a

given

« mole f r a c t i o n o f s u r f a c t a n t 1 i n the t o t a l s u r f a c t M M ant i n the mixed m i c e l l e ; f ^ , f ^ = a c t i v i t y c o e f f i c i e n t s o f i n d i v i d u a l s u r f a c t a n t s 1 and 2, r e s p e c t i v e l y , i n the mixed m i c e l l e ; M M and e q u a t i o n s (3 and 4) f o r the a c t i v i t y c o e f f i c i e n t s , and *

i*

f

= exp M

= exp 0

2

using regular

M

solution

From e q u a t i o n s

(X*)

f5

2

M

(1-xV

(3)

(XV

(4)

theory.

( 1 - 4 ) , we

in

obtain

(aC^/xV) = 1

(1-xV

in [ ( l - a ) ^ /

(l-xV/

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

(5)

146

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

M

and

=

R

/Χ^Λ

i n (aC* -

β

X

X

—

(6)

U-xV M


Equation

(5) i s s o l v e d n u m e r i c a l l y f o r X ,

and s u b s t i t u t i o n o f

i n e q u a t i o n (6) y i e l d s the v a l u e o f 3 (the molecular i n t e r a c t i o n parameter f o r mixed m i c e l l e f o r m a t i o n i n aqueous s o l u t i o n ) . We have e x t e n d e d t h i s treatment ( e q u a t i o n s 7 and 8) t o mixed monolayer f o r m a t i o n ( 1 ) ,

ac~

= X f ^

2

(l-a)C

(7)

0

= (1-X) f C °

1 2

2

(8)

2

X = mole f r a c t i o n o f s u r f a c t a n t 1 i n the t o t a l s u r f a c t a n t i n the mixed monolayer; 0 ^ ° , C ° , C 2

1 2

= s o l u t i o n phase m o l a r c o n c e n t r a t i o n s

of s u r f a c t a n t s 1, 2, and t h e i r m i x t u r e , produce a g i v e n s u r f a c e t e n s i o n v a l u e ; f

1^2

=

act

v

t

^ ^- y

respectively, required to

c o e f f i c i e n t s o f i n d i v i d u a l s u r f a c t a n t s 1 and 2,

respectively,

i n t h e mixed monolayer;

u s i n g the n o n - i d e a l s o l u t i o n a p p r o x i m a t i o n s coefficients, = exp 3

f

±

f

= exp

2

σ

3

(1-X)

σ

X

(8) f o r t h e a c t i v i t y

2

(9)

2

(10)

where $ ° i s t h e m o l e c u l a r i n t e r a c t i o n parameter f o r mixed monolayer f o r m a t i o n s a t the aqueous s o l u t i o n / a i r i n t e r f a c e . E q u a t i o n (7-10) yield

2

x m (ac^/xc^) (1-X)

β

Μ

2

1 =

I n [(1-a)

Π

( a C

12

/ X C

( n )

C /(1-X)C °] 1 2

2

i°>

2

(12)

analogous t o equations

(5) and ( 6 ) , from w h i c h (3° c a n be e v a l u a t e d .

(1-X)

We have shown ( 1 ) , n o t o n l y t h a t t h e s i n g l e p a r a m e t e r , (3°, can be used t o p r e d i c t

surface tension values

f o r any

v a l u e o f a,


11.


ROSEN

147

as Rubingh d i d f o r 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 s u s i n g 3 , b u t t h a t the v a l u e s o f X, o b t a i n e d by u s e o f the e q u a t i o n f o r mixed monolayer f o r m a t i o n , agree w e l l w i t h those c a l c u l a t e d by an i n d e p e n dent method from s u r f a c e e x c e s s c o n c e n t r a t i o n s by u s e o f the Gibbs adsorption equation. σ M The e x p e r i m e n t a l d e t e r m i n a t i o n o f 3 and 3 i s shown i n F i g u r e 1. I t i n v o l v e s d e t e r m i n i n g the s u r f a c e t e n s i o n - l o g concen t r a t i o n c u r v e s f o r each o f the pure components and f o r a t l e a s t one m i x t u r e o f them a t a s p e c i f i c v a l u e o f a . For c a l c u l a t i n g 3 ( t h e M

σ


i n t e r a c t i o n parameter f o r mixed monolayer f o r m a t i o n ) , C*12

2

3^ ( t h e i n t e r a c t i o n parameter f o r

a r e needed; f o r de t e r m i n g

mixed m i c e l l e f o r m a t i o n M M concentrations, C ,

C ° , C , and

i n aqueous s o l u t i o n ) , the c r i t i c a l M , and > required. a

r

micelle

e

Synergism i n s u r f a c e t e n s i o n r e d u c t i o n e f f i c i e n c y . The e f f i c i e n c y o f s u r f a c e t e n s i o n r e d u c t i o n by a s u r f a c t a n t i s d e f i n e d (9) as the s o l u t i o n phase c o n c e n t r a t i o n r e q u i r e d t o produce a g i v e n s u r f a c e t e n s i o n ( r e d u c t i o n ) . Synergism i n t h i s r e s p e c t i s p r e s e n t i n a b i n a r y m i x t u r e o f s u r f a c t a n t s when a g i v e n s u r f a c e t e n s i o n ( r e d u c t i o n ) c a n be a t t a i n e d a t a t o t a l mixed s u r f a c t a n t c o n c e n t r a t i o n lower than t h a t r e q u i r e d o f e i t h e r s u r f a c t a n t by i t s e l f . This i s i l l u s t r a t e d i n F i g u r e 2. From e q u a t i o n s (7) and ( 9 ) , we o b t a i n in C The

1 2

- in C° = in a+f

(1-X)

c o n d i t i o n f o r synergism i s : C^

Thus in X - in a + 3° ( 1 - X )

2

2

2

< C°> C

2

< 0

When s y n e r g i s m e x i s t s , a minimum w i l l vs. α curve,

(13)

(14) exist

i n the C ^

2

i.e., dC /da = 0 1 2

From the p r e c e d i n g ,

i t can be shown (1) t h a t when d C / d a = 0, 1 2

then X = α , i . e . , the mole f r a c t i o n o f each s u r f a c t a n t i n the t o t a l s u r f a c t a n t i n the t o t a l s u r f a c t a n t i n the mixed monolayer e q u a l s i t s mole f r a c t i o n i n the s o l u t i o n phase a t the p o i n t o f maximum synergism. S u b s t i t u t i n g t h i s i n t o e q u a t i o n s ( 7 ) , ( 8 ) , and ( 1 4 ) , we o b t a i n the c o n d i t i o n s f o r s y n e r g i s m i n t h i s r e s p e c t : Λ

o

n

1.

ρ

must be n e g a t i v e .

2.

Itoc°/c° j < I β

σ

I

where C ° and C ° a r e the s o l u t i o n phase m o l a r c o n c e n t r a t i o n o f p u r e , i n d i v i d u a l s u r f a c t a n t s 1 and 2, r e s p e c t i v e l y , r e q u i r e d t o a t t a i n a given surface tension (reduction). At the p o i n t o f maximum s y n e r g i s m , the mole f r a c t i o n a , o f A

s u r f a c t a n t 1 i n the s o l u t i o n phase e q u a l s i t s mole f r a c t i o n i n t h e mixed monolayer a t the aqueous s o l u t i o n / a i r i n t e r f a c e , and i s g i v e n

American Chemical Society Library 1155 16th St., N.W. In PhenomenaWashington, in Mixed Surfactant Scamehorn, J.; D.C.Systems; 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1986.


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

\

φ

\

c

V

î

> log

4

C

F i g u r e 1. Experimental evaluation of 3 or 3 . (Ï) Pure s u r f a c t a n t 1; (2) Pure s u r f a c t a n t 2; @ Mixture of s u r f a c t a n t s 1 and 2 a t a g i v e n mole f r a c t i o n , a, i n s o l u t i o n .



11.


ROSEN

©

Ο

149

Θ

log C

2.

Figure (C^2 (C

o r ^ 2 ° ) o r i n mixed m i c e l l e

< M

1 2

Synergism i n s u r f a c e t e n s i o n r e d u c t i o n

g no s y n e r g i s m ; d a t a from Ingram, Β. T. and A.H.W. L u c k h u r s t , i n " S u r f a c e A c t i v e A g e n t s " Soc. Chem. Ind., London, 1979, p.89. Adapted w i t h p e r m i s s i o n from Ref. 3. C o p y r i g h t 1982, American O i l Chemists Society . 1




ROSEN

Ο

Θ

Θ

log C

Figure

5.

(Ycmc^ @

l

M

*

l


where γ

,' γ „ a r e t h e s u r f a c e t e n s i o n s o f pure s u r f a c t a n t s cmcl cmc2 1 and 2 by themselves i n aqueous s o l u t i o n and Κ i s t h e s l o p e o f t h e s u r f a c e t e n s i o n - n a t u r a l l o g c o n c e n t r a t i o n curve of that s u r f a c t a n t h a v i n g t h e l a r g e r s u r f a c e t e n s i o n v a l u e a t i t s cmc. Data on systems showing s y n e r g i s m i n t h i s r e s p e c t i n d i c a t e t h a t f o r s u r f a c t a n t s c o n t a i n i n g a s i n g l e h y d r o p h i l i c and a s i n g l e h y d r o p h i c group, t h e p o i n t o f maximum s y n e r g i s m i s r e a c h e d when X

= 0.5

t h a t i s , when t h e r e a r e a p p r o x i m a t e l y e q u a l numbers o f t h e two d i f f e r e n t s u r f a c t a n t s a t the i n t e r f a c e . With t h i s assumption, a t t h e p o i n t o f maximum s y n e r g i s m in t h i s respect,

(2D

a* -

Phenomena in Mixed Surfactant Systems - American Chemical Society

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