Thermodynamic Study of the Surface Adsorption and Micelle

12 Thermodynamic Study of the Surface Adsorption and Micelle Formation of Mixed Surfactants

Downloaded by PENNSYLVANIA STATE UNIV on February 16, 2013 | http://pubs.acs.org Publication Date: June 5, 1986 | doi: 10.1021/bk-1986-0311.ch012

Kinsi Motomura, Hidetsugu Matsukiyo, and Makoto Aratono Department of Chemistry, Faculty of Science, Kyushu University 33, Fukuoka 812, Japan

The surface tension of the aqueous solution of dodecylammonium chloride (DAC)—decylammonium chloride (DeAC) mixture was measured as a function of the total molality m of surfactants and the mole fraction X of DeAC in the total surfactant in the neighborhood of the critical micelle concentration (CMC). By use of the thermodynamic equations derived previously, the mole fraction X in the mixed adsorbed film was evalu ated from the γ vs. X and m vs. X curves. Further, the mole fraction X in the mixed micelle was evalu ated from the CMC vs. X curve. By comparing these values at the CMC, it was concluded that the behavior of DAC and DeAC molecules in the mixed micelle is fairly similar to that in the mixed adsorbed film. H

M

It was recently ascertained that the behavior of the adsorbed film of two surfactants in equilibrium with their micelle can be ex plained by assuming both the surface region and the micelle particle to be mixtures of the surfactants (1-6). Further, the application of the regular solution theory to the mixtures was shown to be use ful to describe the nonideal behavior of ionic surfactants (_4-j6). However, the above treatments are incomplete from the thermodynamic viewpoint, because they do not consider the dissociation of surfac tants and ignore the presence of solvent (_7). In addition, it is impossible to suppose that the regular solution theory is applicable to both the adsorbed film and the micelle of ionic surfactants accompanied by the electrical double layer (8). On the other hand, we showed that the composition of surfactant in a mixed adsorbed film can be estimated thermodynamically from experimental results without introducing such a supposition (9-11). Further, the composition of a mixed micelle was calculated assuming that the micelle behaves thermodynamically like a macroscopic bulk phase whose thermodynamic quantities are given by the excess thermo dynamic quantities similar to those used for the adsorbed film (8). Therefore, we can now compare the composition of surfactant in the mixed adsorbed film with that in the mixed micelle at the critical micelle concentration (CMC). 0097-6156/ 86/ 0311 -0163$06.00/ 0 © 1986 American Chemical Society

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

164

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

In t h i s p a p e r , dodecylammonium c h l o r i d e (DAC) and decylammonium c h l o r i d e (DeAC) a r e chosen t o r e v e a l t h e fundamental b e h a v i o r o f s u r f a c t a n t s i n the mixed a d s o r b e d f i l m and m i c e l l e . The s u r f a c e t e n s i o n o f t h e i r aqueous s o l u t i o n i s measured as a f u n c t i o n o f t h e i r c o n c e n t r a t i o n s i n the n e i g h b o r h o o d o f t h e CMC and the comparison between the mixed a d s o r b e d f i l m and t h e mixed m i c e l l e i s made i n terms o f t h e c o m p o s i t i o n evaluated.


Experimental Dodecylammonium c h l o r i d e and decylammonium c h l o r i d e were s y n t h e s i z e d and p u r i f i e d by the method d e s c r i b e d p r e v i o u s l y (9^,12) . Water was d i s t i l l e d t r i p l y from a l k a l i n e permanganate. S u r f a c e t e n s i o n was measured by means o f t h e d r o p volume t e c h n i q u e , o f which t h e de t a i l e d p r o c e d u r e was d e s c r i b e d i n t h e p r e v i o u s p a p e r (13). The measurements were c a r r i e d o u t a t 298.15 Κ under a t m o s p h e r i c p r e s s u r e ; the s u r f a c e t e n s i o n v a l u e s were r e p r o d u c i b l e t o ± 0.05 mN m"^-. R e s u l t s and

Discussion

U s e f u l i n f o r m a t i o n r e g a r d i n g the a d s o r b e d f i l m and m i c e l l e i n e q u i l i b r i u m w i t h t h e aqueous s o l u t i o n o f s u r f a c t a n t m i x t u r e a t c o n s t a n t t e m p e r a t u r e and p r e s s u r e i s p r o v i d e d by a d o p t i n g as the e x p e r i m e n t a l v a r i a b l e s the t o t a l m o l a l i t y m o f s u r f a c t a n t s and t h e mole f r a c t i o n X o f s u r f a c t a n t 2 i n t h e t o t a l s u r f a c t a n t d e f i n e d by m = mi

+

m

2

and X = m /m

(2)

2

r e s p e c t i v e l y (8-11). Here i s the m o l a l i t y of s u r f a c t a n t i . The s u r f a c e t e n s i o n γ o f t h e aqueous s o l u t i o n o f dodecylammo nium c h l o r i d e — decylammonium c h l o r i d e m i x t u r e was measured as a f u n c t i o n o f m a t a g i v e n v a l u e o f t h e mole f r a c t i o n X o f DeAC a t 298.15 Κ under a t m o s p h e r i c p r e s s u r e . The r e s u l t s a r e shown i n F i g u r e 1. I t i s seen t h a t t h e γ v s . JH c u r v e s a r e s i m i l a r i n appear ance. T h i s b e h a v i o r i s i n harmony w i t h t h a t o b s e r v e d p r e v i o u s l y i n a low c o n c e n t r a t i o n range (j)) . Moreover, t h e f o r m a t i o n o f m i c e l l e i s found t o cause the c u r v e s t o b r e a k s h a r p l y a t the CMC which i n c r e a s e s w i t h X. I t s h o u l d be n o t e d , however, t h a t t h e γ v s . m c u r v e o f a m i x t u r e has a v e r y s h a l l o w minimum i n t h e immediate v i c i n i t y o f the CMC. The v a r i a t i o n o f γ w i t h X can be examined by c o n s u l t i n g F i g u r e 1. In F i g u r e 2, t h e γ v s . X c u r v e s a t c o n s t a n t m a r e drawn f o r t h e s o l u t i o n s which c o n t a i n o n l y t h e monomers o f s u r f a c t a n t s . F o r com p a r i s o n , the s u r f a c e t e n s i o n y a t t h e CMC a r e p l o t t e d a g a i n s t X i n the f i g u r e . I t i s seen t h a t the c u r v e d e v i a t e s downward from the s t r a i g h t l i n e j o i n i n g t h e γ v a l u e s o f p u r e DAC and DeAC. Further, we a r e i n t e r e s t e d i n examining how t h e t o t a l m o l a l i t y y i e l d i n g 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 v a r i e s w i t h the c o m p o s i t i o n . Figure 3 shows t h e m v s . X c u r v e a t c o n s t a n t γ o b t a i n e d from F i g u r e 1; i n c l u d e d i n t h i s f i g u r e f o r comparison i s t h e CMC v s . X c u r v e . Again C M C



12.

M O T O M U R A ET A L .

0

Surface Adsorption and Micelle

10

20

30 AO m / mmol kg

50

Formation

60

165

70

-1

F i g u r e 1. S u r f a c e t e n s i o n v s . t o t a l m o l a l i t y c u r v e s a t c o n s t a n t composition: 1, X = 0; 2, 0.500; 3, 0.700; 4, 0.833; 5, 0.915; 6, 0.965; 7, 1.

F i g u r e 2. S u r f a c e t e n s i o n v s . c o m p o s i t i o n c u r v e s a t c o n s t a n t t o tal molality: 1, m = 6 mmol kg"" ; 2, 8 mmol k g " ; 3, 10 mmol k g " ; 4, 12 mmol k g " ; 5, 14 mmol k g " ; 6, 20 mmol k g " ; 7, 30 mmol k g ; 8, y v s . X. 1

1

1

- 1

1

1

1

C M C


166


the c u r v e i s o b s e r v e d t o d e v i a t e from t h e s t r a i g h t l i n e . Comparing F i g u r e 3 w i t h F i g u r e 2, we n o t i c e t h a t t h e CMC v s . X c u r v e i s s i m i l a r i n shape t o t h e m v s . X c u r v e w h i l e t h e y vs. X curve i s d i f f e r e n t from t h e γ v s . X c u r v e . Taking i n t o account t h a t both the /π v s . X and γ v s . X c u r v e s a r e l i k e w i s e r e l a t e d t o t h e c o m p o s i t i o n o f s u r f a c t a n t i n t h e adsorbed f i l m (9-11), t h i s f a c t may suggest t h a t the y v s . X and CMC v s . X c u r v e s a f f o r d d i f f e r e n t i n f o r m a t i o n w i t h regard t o the m i c e l l e . F i r s t , l e t us c o n s i d e r t h e s u r f a c e d e n s i t y o f s u r f a c t a n t . The t o t a l s u r f a c e e x c e s s number o f moles p e r u n i t a r e a Γ o f s u r f a c t a n t s i s e v a l u a t e d by u s i n g t h e r e l a t i o n C


C

Γ

Η

= -

M

M

C

C

(m/2RT) Ογ/3ιη)_ ^ Τ,ρ,Χ

(3)

where Τ i s temperature, ρ p r e s s u r e , and R t h e gas c o n s t a n t (9). Here t h e s o l u t i o n i s assumed t o be i d e a l . By a p p l y i n g E q u a t i o n 3 t o the γ v s . τη c u r v e s g i v e n i n F i g u r e 1, t h e v a l u e s o f Γ were c a l c u l a t e d ; t h e y a r e p l o t t e d a g a i n s t 277 i n F i g u r e 4. I t i s seen t h a t t h e v a l u e i n c r e a s e s s t e e p l y w i t h i n c r e a s i n g 277 and a p p r o a c h e s t h e s a t u r a t i o n v a l u e i n t h e v i c i n i t y o f t h e CMC. Furthermore, t h e ΓΗ v s . 277 c u r v e changes i t s shape r e g u l a r l y . T h e r e f o r e , i t may be s a i d t h a t t h e DAC and DeAC m o l e c u l e s a r e m i s c i b l e w i t h each o t h e r a t t h e s u r f a c e and form a homogeneous adsorbed f i l m . The c o m p o s i t i o n o f s u r f a c t a n t i n t h e mixed adsorbed f i l m i s e s t i m a t e d by v i r t u e o f t h e r e l a t i o n Η

H

X

= X -

U

[(1 - X)X/RTT ]

(dy/dx)

(4) T,p,277

H

where X i s t h e mole f r a c t i o n o f DeAC i n t h e adsorbed f i l m d e f i n e d by t h e a n a l o g o f E q u a t i o n 2 (9^, 10) . By a p p l y i n g t h i s e q u a t i o n t o t h e γ v s . X c u r v e s g i v e n i n F i g u r e 2, t h e v a l u e s o f X were e s t i mated n u m e r i c a l l y . The v a l u e s a t m = 6, 10, and 14 mmol k g " are i l l u s t r a t e d i n t h e form o f t h e γ v s . X curve together w i t h the c o r r e s p o n d i n g γ v s . X c u r v e i n F i g u r e 5. I t i s i m p o r t a n t t o note t h a t t h e c o m p o s i t i o n i n t h e a d s o r b e d f i l m i s remarkably d i f f e r e n t from t h a t i n t h e s o l u t i o n and e n r i c h e d i n t h e more s u r f a c e - a c t i v e DAC though t h e DAC and DeAC m o l e c u l e s d i f f e r i n t h e number o f c a r b o n atoms o n l y by two. S i m i l a r l y , the r e l a t i o n o f X t o X can be c o n s i d e r e d under t h e condition that γ i s constant. By use o f t h e e q u a t i o n H

1

H

H

K

X

= X -

[2(1 - X)X/m](dm/dX)

(5) Γ,ρ,γ

d e r i v e d p r e v i o u s l y (10) , t h e 277 v s . X c u r v e was o b t a i n e d from t h e 227 vs. X curve. In F i g u r e 6, t h e y a r e drawn a t γ = 60, 50, and 40 mN m . I t i s observed again t h a t the X value i s s i g n i f i c a n t l y s m a l l e r t h a n t h e X v a l u e . T h e r e f o r e , we may say t h a t a s l i g h t d i f f e r e n c e i n t h e s u r f a c e a c t i v i t y o f s u r f a c t a n t e x e r t s a remarkable e f f e c t on i t s a d s o r p t i o n b e h a v i o r a t c o n c e n t r a t i o n s n e a r t h e CMC. Moreover, such a diagram i s found t o be u s e f u l i n s t u d y i n g t h e m i s c i b i l i t y of s u r f a c t a n t s i n the f i l m s t a t e . On t h e o t h e r hand, t h e mole f r a c t i o n X o f DeAC i n t h e mixed m i c e l l e , which i s d e f i n e d by t h e e q u a t i o n analogous t o E q u a t i o n 2, can be e s t i m a t e d a t t h e CMC by making use o f t h e r e l a t i o n H

-1

H

M



MOTOMURA ETAL.

Surface Adsorption and Micelle

Formation

F i g u r e 3. T o t a l m o l a l i t y v s . c o m p o s i t i o n c u r v e s a t c o n s t a n t face tension: 1, γ = 60 mN m" ; 2, 50 mN m" ; 3, 45 mN m" ; 40 mN m" ; 5, 35 mN m ; 6, CMC v s . X. 1

1

1

1

sur 4,

-1

m/mmol kg F i g u r e 4. T o t a l s u r f a c e d e n s i t y v s . t o t a l m o l a l i t y c u r v e s a t constant composition: 1, X = 0; 2, 0.500; 3, 0.700; 4, 0.833; 5, 0.965; 6, 1.


168



70 h

I

ι

ι

ι

1

1

0

0.2

OA

0.6

0.8

1

X

F i g u r e 5. S u r f a c e t e n s i o n v s . c o m p o s i t i o n c u r v e s a t c o n s t a n t t o tal molality: X ( ), X ( ) : 1, m = 6 mmol k g " ; 2, 10 mmol k g ; 3, 14 mmol k g . H

- 1

1

- 1

50k

I 0

ι 0.2

ι 0.4

ι 0.6

ι 0.8

I

1

X

F i g u r e 6. T o t a l m o l a l i t y v s . c o m p o s i t i o n c u r v e s a t c o n s t a n t s u r face tension: X ( ), X ( ) : 1, γ = 60 mN m" ; 2, 50 mN m" ; 3, 40 mN m" . e

1

1

1


12.

X

Surface Adsorption and Micelle Formation

M O T O M U R A ET AL.

K

169

X - [2(1 - X)X/CMC](3CMC/9X) T,p

(6)

m

t h e s o l u t i o n b e i n g assumed t o be i d e a l ( 8 ) . Thus we c a n o b t a i n t h e CMC v s . X c u r v e from t h e CMC v s . X c u r v e g i v e n i n F i g u r e 3. Both the c u r v e s a r e d e p i c t e d i n F i g u r e 7. I t s h o u l d be n o t e d t h a t t h i s f i g u r e i s q u i t e s i m i l a r t o t h a t o f t h e sodium t e t r a d e c y l s u l f a t e — sodium d o d e c y l s u l f a t e system (8^ 14). Comparing F i g u r e 7 w i t h F i g ure 6, we n o t i c e t h a t t h e r e i s a s t r i k i n g resemblance o f shape b e tween them. T h i s f a c t s u g g e s t s t h a t t h e mixed m i c e l l e b e a r s a s i m i l a r i t y i n t h e m i s c i b i l i t y o f s u r f a c t a n t s t o t h e mixed a d s o r b e d f i l m . Now t h e r e l a t i o n s h i p between X and X needs t o be examined a t the CMC. The mole f r a c t i o n x ' o f DeAC i n t h e a d s o r b e d f i l m a t t h e CMC c a n be e s t i m a t e d by e x t r a p o l a t i o n o f t h e X v s . m p l o t t a k e n from F i g u r e 6 t o t h e CMC. However, i t i s i n s t r u c t i v e t o d e r i v e t h e thermodynamic e q u a t i o n r e l a t i n g x ' t o X . As c a n be seen from E q u a t i o n s 3 and 4, t h e t o t a l d i f f e r e n t i a l o f γ i s e x p r e s s e d a t con s t a n t Τ and ρ as M

H


H

M

C M C

H

H

H

dy

E

= - (2RTY /m)6m

H

- [RTT (X

C M C

M

- X)/(1 - X)X]dX

(7)

T a k i n g i n t o a c c o u n t t h a t m i s assumed t o be e q u a l t o CMC a t t h e CMC and t h a t E q u a t i o n 6 y i e l d s dCMC = - [CMC(X

M

- X ) / 2 ( l - X)X]âX

(8)

E q u a t i o n 7 i s r e w r i t t e n a t t h e CMC as dy

H

CMC

=

[ i ? r r

'

C M C

(X

M

_ χ

H

- X 'CMC

) / ( 1

) Χ ] ά

χ

(9)

H CMC where Γ ' i s t h e t o t a l s u r f a c e d e n s i t y o f s u r f a c t a n t s a t t h e CMC. A c c o r d i n g l y , we c a n d e r i v e t h e r e l a t i o n H,CMC Μ _ _ H,CMC CMC τ ,p

X

=

χ

[

(

1

x ) x / j R T r

] ( 3 y

/ 9 x )

(

H

C M C

1

0

)

1

E q u a t i o n 10 s t a t e s t h a t t h e d i f f e r e n c e between x ' and X ^ a r e c o r r e l a t e d t o the slope o f the y v s . X curve. Inspecting Figure 8 where t h e y v s . X c u r v e t a k e n from F i g u r e 2 a r e i l l u s t r a t e d together with the y v s . X curve, therefore, x * may be sup p o s e d t o have a v a l u e f a i r l y c l o s e t o X . Evaluating the derivative of y w i t h r e s p e c t t o X and r ' by e x t r a p o l a t i o n o f t h e c u r v e i n F i g u r e 4 t o t h e CMC and t h e n sub s t i t u t i n g them i n t o E q u a t i o n 10, t h e x ' v a l u e was c a l c u l a t e d as a f u n c t i o n o f X. F o r t h e p u r p o s e o f comparison, t h e r e s u l t i s drawn i n t h e form o f t h e CMC v s . x 'CMC i i F i g u r e 7. The CMC v s . X and CMC v s . X c u r v e s seem n o t t o d i f f e r t o o g r e a t l y from each o t h e r when compared t o t h e CMC v s . X c u r v e . T h e r e f o r e , we may c o n c l u d e t h a t t h e b e h a v i o r o f DAC and DeAC m o l e c u l e s i n t h e mixed m i c e l l e i s f a i r l y s i m i l a r t o t h a t i n t h e mixed a d s o r b e d f i l m . This c o n c l u s i o n i s c o n s i s t e n t w i t h t h e view, o b t a i n e d i n t h e p r e v i o u s p a p e r s (15,16), t h a t t h e m i c e l l e r e s e m b l e s t h e a d s o r b e d f i l m c l o s e l y i n t h e thermodynamic b e h a v i o r . C

C

M

M

C

C

C

M

C

M

H

C M C

M

C

M

C

H

H

C

M

C

C M C

H

p

H

/

C

M

C

o

t

n

M

F i n a l l y , i t i s h e l p f u l i n u n d e r s t a n d i n g t h e dependence o f γ on m i n t h e c o n c e n t r a t i o n range above t h e CMC t o examine t h e d i f f e r e n c e between t h e y v s . X and y v s . X curves. From F i g u r e 8, we can e x p e c t t h a t t h e s u r f a c e t e n s i o n o f t h e m i c e l l a r s o l u t i o n o f a C

M

C

M

C

M

C


170



Figure Y

c

S

c

Surface

8.

vs.

X,

2,

C Y

M

tension C

vs.

X

M

at

the

CMC

vs.

composition

curves:

.


1,


12.

MOTOMURA ET AL.

Surface Adsorption and Micelle Formation

171

mixture increases s l i g h t l y with i n c r e a s i n g m i f those o f pure sur f a c t a n t s remain c o n s t a n t . Taking account o f the f a c t t h a t the γ v s . m c u r v e s o f p u r e DAC and DeAC shown i n F i g u r e 1 have s m a l l n e g a t i v e s l o p e s , t h e o b s e r v a t i o n t h a t t h e c o r r e s p o n d i n g c u r v e o f t h e i r mix t u r e has a v e r y s h a l l o w minimum f o l l o w e d by a i n d i s t i n c t maximum i s i n accord with our expectation. The above c o n s i d e r a t i o n has p r o v e d t h a t s u r f a c e t e n s i o n mea surements a r e u s e f u l i n e l u c i d a t i n g t h e b e h a v i o r o f s u r f a c t a n t s i n t h e mixed a d s o r b e d f i l m and m i c e l l e . The c o n c l u s i o n r e a c h e d h e r e w i l l be c o n f i r m e d by measuring t h e v a r i a t i o n o f t h e s u r f a c e t e n s i o n w i t h t e m p e r a t u r e and t h e n e v a l u a t i n g thermodynamic q u a n t i t i e s . Fur t h e r i n f o r m a t i o n w i l l be o b t a i n e d from s i m i l a r i n v e s t i g a t i o n s made f o r combinations o f d i f f e r e n t types o f s u r f a c t a n t s . Acknowledgments T h i s work was s u p p o r t e d i n p a r t by a G r a n t - i n - A i d f o r S c i e n t i f i c R e s e a r c h No. 59470005 from t h e M i n i s t r y o f E d u c a t i o n , S c i e n c e and Culture.

Literature Cited 1. Lange, H.; Beck, Κ. H. Kolloid Ζ. u. Ζ. Polymere 1973, 251, 424. 2. Clint, J. H. J. C. S. Faraday I 1975, 71, 1327. 3. Rubingh, D. N. In "Solution Chemistry of Surfactants"; Mitall, K. L., Ed.; Plenum: New York, 1979; Vol. I, p. 337. 4. Ingram, B. T.; Luckhurst, A. H. W. In "Surface Active Agents"; SCI Symposium Proceeding, SCI: London, 1979, p. 89. 5. Hua, Χ. Y.; Rosen, M. J. J. Colloid Interface Sci. 1982, 90, 212. 6. Zhu, Β. Y.; Rosen, M. J. J. Colloid Interface Sci. 1984, 99, 435. 7. Lucassen-Reynders, E. H. J. Colloid Interface Sci. 1982, 85, 178. 8. Motomura, K.; Yamanaka, M.; Aratono, M. Colloid & Polymer Sci. 1984, 262, 948. 9. Aratono, M.; Uryu, S.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1983, 93, 164. 10. Uryu, S.; Aratono, M.; Yamanaka, M.; Motomura, K.; Matuura, R. Bull. Chem. Soc. Jpn. 1983, 56, 3219. 11. Uryu, S.; Aratono, M.; Yamanaka, M.; Motomura, K.; Matuura, R. Bull. Chem. Soc. Jpn. 1984, 57, 967. 12. Aratono, M.; Yamanaka, M.; Matubayasi, N.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1980, 74, 489. 13. Motomura, K.; Iwanaga, S.; Hayami, Y.; Uryu, S.; Matuura, R. J. Colloid Interface Sci. 1981, 80, 32. 14. Moroi, Y.; Nishikido, N.; Matuura, R. J. Colloid Interface Sci. 1975, 50, 344. 15. Motomura, K.; Iwanaga, S.; Yamanaka, M.; Aratono, M.; Matuura, R. J. Colloid Interface Sci. 1982, 86, 151. 16. Motomura, K. J. Colloid Interface Sci. 1984, 102, 303. RECEIVED

February 3, 1986


Thermodynamic Study of the Surface Adsorption and Micelle

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