Computer Applications in Applied Polymer Science - American

25 Mathematical Treatment of the Emulsification of Benzene and Styrene in Aqueous Hexadecyltrimethylammonium Bromide—Cetyl Alcohol Mixtures Downloaded by NATL UNIV OF SINGAPORE on May 6, 2018 | https://pubs.acs.org Publication Date: September 24, 1982 | doi: 10.1021/bk-1982-0197.ch025

1

Y. J. CHOU , M. S. EL-AASSER, and J. W. VANDERHOFF Lehigh University, Emulsion Polymers Institute and Departments of Chemistry and Chemical Engineering, Bethlehem, PA 18015 Styrene or benzene "mini-emulsions" of 0.1-0.3μm diameter were prepared at 63° using aqueous hexadecyltrimethylammonium bromide-cetyl alcohol mixtures; the most stable emulsions, formed at 1:3-1:1 molar ratios, contained crystalline, rodlike particles of hexadecyltrimethylammonium bromide and cetyl alcohol, 1-2μm in length and 0.1-0.2μm in diameter. Conductometric titration of these optimum systems with styrene or benzene gave a near-linear leg descending to an in flection point followed by another near-linear leg ascending to a second inflection point and a near -constant or slowly-decreasing leg thereafter. The descending leg was interpreted as solubilization of the o i l in micelles or crystalline complex, the as cending leg as emulsification to form tiny droplets which grew by coalescence and diffusion, and the near-constant or slowly decreasing leg to droplet growth by diffusion. The conductometric titration curves were expressed by an exponential step function in terms of the initial conductance, the conductances at both inflection points, a solubilization constant, an emulsification constant, and a droplet growth con stant. Iterative computer solution of this mathema tical model gave a reasonable fit of the different experimental titration curves, and the calculated parameters were correlated with the hexadecyltrimethylammonium bromide and cetyl alcohol concentra tions, to give the distributions of the emulsifier as solute emulsifier, micellar emulsifier, and emul sifier in the crystalline complex. The correlation of emulsion stability with the presence of the cry stalline, rodlike particles allowed a prediction of emulsion stability. Finally, a three-dimensional 1

Current address: Avery International, 325 N. Altadena Drive, Pasadena, C A 91107.

0097-6156/82/0197-0399$06.00/0 © 1982 American Chemical Society Provder; Computer Applications in Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

400

COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE

Downloaded by NATL UNIV OF SINGAPORE on May 6, 2018 | https://pubs.acs.org Publication Date: September 24, 1982 | doi: 10.1021/bk-1982-0197.ch025

plot of conductance as a function of added benzene and cetyl alcohol concentration at a given hexade cyltrimethylammonium bromide concentration was cal culated by computer curve-fitting and used to vis ualize the conductance surface at any desired angle.

The e m u l s i f i c a t i o n o f o i l i n w a t e r u s i n g i o n i c o i l - i n - w a t e r e m u l s i f i e r s i n c o n c e n t r a t i o n s o f 0.5-5.0% b a s e d on d i s p e r s e d p h a s e w i t h c o n v e n t i o n a l a g i t a t i o n g i v e s f l u i d , opaque "macroemuls i o n s " , i . e . , emulsions w i t h average d r o p l e t s i z e s o f c a . lym o r greater. S i m i l a r l y , the e m u l s i f i c a t i o n of o i l i n water u s i n g mix tures of i o n i c o i l - i n - w a t e r e m u l s i f i e r s w i t h f a t t y a l c o h o l s i n c e r t a i n m o l a r r a t i o s and i n c o n c e n t r a t i o n s o f 1 0 - 5 0 % b a s e d on d i s persed phase g i v e s t r a n s p a r e n t o r t r a n s l u c e n t v i s c o u s "microemuls i o n s " , i . e . , e m u l s i o n s w i t h a v e r a g e d r o p l e t s i z e s o f O.lum o r smaller. The use o f s i m i l a r i o n i c e m u l s i f i e r - f a t t y a l c o h o l m i x t u r e s i n c o n c e n t r a t i o n s o f 0.5-5.0% b a s e d on d i s p e r s e d p h a s e g i v e s f l u i d , opaque " m i n i - e m u l s i o n s " , i . e . , e m u l s i o n s w i t h a v e r a g e d r o p l e t s i z e s o f 0.1-0.3um. Thus t h e e m u l s i f i c a t i o n o f s t y r e n e i n water u s i n g sodium l a u r y l s u l f a t e a l o n e g i v e s average d r o p l e t s i z e s o f l y m o r g r e a t e r w h i l e t h e e m u l s i f i c a t i o n i n aqueous s o d i u m l a u r y l s u l f a t e - c e t y l a l c o h o l mixtures with simple s t i r r i n g gives a v e r a g e d r o p l e t s i z e s o f c a . 0.2ym ( 1 ) . S i m i l a r r e s u l t s w e r e ob tained w i t h the corresponding hexadecyltrimethylammonium bromidec e t y l a l c o h o l m i x t u r e s (2_) . The a p p l i c a t i o n o f t h i s e m u l s i f i c a t i o n technique to polymer s o l u t i o n s u s i n g i o n i c e m u l s i f i e r - f a t t y alcohol or i o n i c emulsifier-n-alkane mixtures gives latexes with a v e r a g e p a r t i c l e d i a m e t e r s i n t h e r a n g e 0.1-0.2ym ( 3 - 7 ) . The mechanism o f t h i s m i n i - e m u l s i o n e m u l s i f i c a t i o n p r o c e s s was i n v e s t i g a t e d by t h e c o n d u c t o m e t r i c t i t r a t i o n o f aqueous h e x a decyltrimethylammonium b r o m i d e - c e t y l a l c o h o l m i x t u r e s w i t h benzene o r s t y r e n e combined w i t h t r a n s m i s s i o n e l e c t r o n m i c r o s c o p i c e x a m i n a t i o n o f t h e m o r p h o l o g y o f t h e m i x e d e m u l s i f i e r s and t h e s t y r e n e d r o p l e t s f o r m e d (2,8) . F i g u r e 1 shows t h a t t h e t i t r a t i o n c u r v e s w i t h and w i t h o u t c e t y l a l c o h o l a r e q u i t e d i f f e r e n t : that for hexadecyltrimethylammonium bromide alone comprises a n e a r - l i n e a r d e c r e a s e t o an i n f l e c t i o n p o i n t VQ f o l l o w e d by a s e c o n d n e a r l i n e a r d e c r e a s e o f much s m a l l e r s l o p e ; t h a t f o r t h e h e x a d e c y l t r i methylammonium b r o m i d e - c e t y l a l c o h o l m i x t u r e o f 1:1 m o l a r r a t i o c o m p r i s e d a l o w e r i n i t i a l c o n d u c t a n c e and a s h o r t n e a r - l i n e a r de c r e a s e t o an i n f l e c t i o n p o i n t V-i , an i n c r e a s e t o a s e c o n d i n f l e c t i o n p o i n t V^i and a v e r y s l o w d e c r e a s e o r c o n s t a n t r e g i o n . The f o r m o f t h e t i t r a t i o n c u r v e w i t h c e t y l a l c o h o l v a r i e d a c c o r d i n g to the hexadecyltrimethylammonium b r o m i d e - c e t y l a l c o h o l molar ratio. F i g u r e 2 shows t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e s f o r h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e - c e t y l a l c o h o l r a t i o s o f 1:0.33 t o 1:6. T h e s e c u r v e s show t h a t , w i t h i n c r e a s i n g p r o p o r t i o n o f

Provder; Computer Applications in Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1982.


CHOU ET AL.

Emulsification

2

of Benzene

4

and

Styrene

401

6

V O L U M E OF BENZENE (cc) Figure 1. Conductometric titration at 63° C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and 0.10 g cetyl alcohol (1:1 molar ratio) with benzene at a constant rate of 1 cc/min. Key: I, no cetyl alcohol; II, 0.10 g cetyl alcohol. (Reproduced, with permission, from Ref. 2. Copyright 1980, Plenum Press.)



402


VOLUME OF BENZENE

(cc)

Figure 2. Conductometric titration at 63 °C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and varying quantities of cetyl alcohol with benzene at a constant rate of 1 cc/min. Hexadecyltrimethylammonium bromide-cetyl alcohol molar ratios: I, 1:6; II, 1:3; 111, 1:1; IV, 1:0.5; and V, 1:0.33. (Reproduced, with permission, from Ref. 2. Copyright 1980, Plenum Press.)



25.

CHOU ET AL.

Emulsification

of Benzene

and Styrene

403

c e t y l a l c o h o l , t h e i n i t i a l conductance decreased, t h e s l o p e o f the d e s c e n d i n g l e g i n c r e a s e d , a n d t h e i n f l e c t i o n p o i n t occured a t a s m a l l e r v o l u m e o f b e n z e n e t i t r a n t ; f o r t h e 1:6 m o l a r r a t i o , the d e s c e n d i n g l e g was n o t o b s e r v e d a t a l l . The s l o p e s o f t h e a s c e n d i n g l e g s b e t w e e n i n f l e c t i o n p o i n t s V.. a n d V~ w e r e a b o u t t h e same, a s w e r e t h e s l o p e s b e y o n d t h e i n f l e c t i o n p o i n t The e l e c t r o n m i c r o s c o p i c i n v e s t i g a t i o n showed t h a t r o d l i k e p a r t i c l e s l-2um i n l e n g t h a n d 0.1-0.2um i n d i a m e t e r w e r e f o r m e d a t h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e - c e t y l a l c o h o l r a t i o s o f 1:3 to 1:1 ( F i g u r e 3 ) . T h e s e r o d l i k e p a r t i c l e s showed a n e l e c t r o n d i f f r a c t i o n p a t t e r n ( F i g u r e 4 ) t h a t was n o t shown b y e i t h e r h e x a decyltrimethylammonium bromide o r c e t y l a l c o h o l a l o n e . Moreover, heating these p a r t i c l e s i n the transmission e l e c t r o n microscope showed t r a n s i t i o n s n e a r t h e m e l t i n g p o i n t s o f b o t h c e t y l a l c o h o l and h e x a d e c y l t r i m e t h y l a m m o n i u m bromide. M e a s u r e m e n t o f t h e s t y r e n e d r o p l e t s i z e s showed t h a t t h e i n i t i a l d r o p l e t s i z e s w e r e r e l a t i v e l y l a r g e ( c a . 0.5um) b u t d e c r e a s e d g r e a t l y t o c a . O.lum a s t h e c o n d u c t a n c e d e c r e a s e d t o t h e i n f l e c t i o n p o i n t V,, t h e n i n c r e a s e d b y c o a l e s c e n c e t o t h e i n f l e c t i o n p o i n t V and i n c r e a s e d s l o w l y t h e r e a f t e r , p r i n c i p a l l y by growth. The r o d l i k e p a r t i c l e s , w h i c h w e r e o b s e r v e d b e f o r e t h e t i t r a t i o n , began t o d i s a p p e a r d u r i n g t h e d e c r e a s e i n conductance to t h e i n f l e c t i o n p o i n t and d i s a p p e a r e d c o m p l e t e l y b e f o r e t h e i n f l e c t i o n p o i n t V~ was r e a c h e d . The p u r p o s e o f t h i s p a p e r i s t o p r o p o s e a n i n t e r p r e t a t i o n o f the f o r e g o i n g r e s u l t s , t o d e v e l o p a m a t h e m a t i c a l m o d e l w h i c h u s e s the c a p a b i l i t y o f t h e c o m p u t e r t o e s t a b l i s h t h e p a r a m e t e r s t h a t are i m p o r t a n t i n t h e e m u l s i f i c a t i o n p r o c e s s , t o p r e d i c t t h e shape of t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e s , a n d , f i n a l l y , t o v i s u a l ize the conductometric t i t r a t i o n curves as three-dimensional con ductance-oil volume-cetyl alcohol concentration plots. 2

I n t e r p r e t a t i o n o f t h e Conductometric T i t r a t i o n

Curves

I n t h e aqueous m i x e d e m u l s i f i e r s y s t e m , t h e h e x a d e c y l t r i methylammonium b r o m i d e e x i s t s i n o n e o f t h r e e f o r m s : ( i ) solute m o l e c u l e s i n t h e aqueous p h a s e ; ( i i ) m i c e l l e s o f a g g r e g a t e d m o l e c u l e s ; ( i i i ) c r y s t a l l i n e complex w i t h c e t y l a l c o h o l . The c o n d u c t a n c e o f t h e s e t h r e e forms s h o u l d d e c r e a s e i n t h e o r d e r : solute m o l e c u l e s > m i c e l l a r m o l e c u l e s >> c r y s t a l l i n e c o m p l e x . The c e t y l a l c o h o l does n o t c o n t r i b u t e t o t h e c o n d u c t a n c e . The c h a r a c t e r i s t i c c o n d u c t o m e t r i c t i t r a t i o n c u r v e c a n b e d i v ided i n t o three stages: ( i ) an i n i t i a l n e a r - l i n e a r descending l e g d e c r e a s i n g t o t h e i n f l e c t i o n p o i n t V^; ( i i ) a n e a r - l i n e a r l e g a s c e n d i n g t o t h e i n f l e c t i o n p o i n t V2; ( i i i ) a s l o w l y d e c r e a s i n g or c o n s t a n t n e a r - l i n e a r l e g . The i n i t i a l d e s c e n d i n g l e g i s i n t e r p r e t e d a s t h e s o l u b i l i z a t i o n p r o c e s s . I f m i c e l l e s a r e p r e s e n t , t h e added o i l w i l l b e s o l ubilized. A l s o , t h e added o i l may b e s o l u b i l i z e d i n t h e h e x a d e cyltrimethylammonium b r o m i d e - c e t y l a l c o h o l complex. That t h e s o l -



404


Figure 3. Transmission electron micrograph of diluted hexadecyltrimethylammonium bromide-cetyl alcohol (1:1 molar ratio) mixed emulsifier system showing rodlike particles. (Reproduced, with permission, from Ref. 2. Copyright 1980, Plenum Press.)

Figure 4. Selected-area transmission electron microscope diffraction pattern of the rodlike particles of hexadecyltrimethylammonium bromide-cetyl alcohol (1:3 molar ratio) produced by 100 KV electron beam. (Reproduced, with permission, from Ref. 2. Copyright 1980, Plenum Press.)



25.

CHOU ET AL.

Emulsification

of Benzene

405

and Styrene

u b i l i z a t i o n i s n o t i n s t a n t a n e o u s i s shown b y t h e p r e s e n c e o f b o t h r e l a t i v e l y l a r g e s t y r e n e d r o p l e t s and t h e c r y s t a l l i n e r o d l i k e par ticles. This stage terminates a t the i n f l e c t i o n point where t h e v o l u m e o f o i l added i s j u s t e q u a l t o t h e amount t h a t c a n b e s o l u b i l i z e d i n the m i c e l l e s o r complex. The f o l l o w i n g a s c e n d i n g l e g i s i n t e r p r e t e d a s t h e e m u l s i f i c a t i o n process. The volume o f o i l added i s g r e a t e r t h a n c a n b e s o l u b i l i z e d i n t h e m i c e l l e s o r c o m p l e x and t h e r e f o r e i s e m u l s i f i e d , f i r s t a s v e r y f i n e d r o p l e t s t h a t grow i n s i z e b y c o a l e s c e n c e a n d p r o b a b l y a l s o b y s w e l l i n g b y added o i l . A t t h e same t i m e , t h e c r y s t a l l i n e r o d l i k e p a r t i c l e s d i s a p p e a r , e i t h e r by d i s r u p t i o n from i n t e r n a l s w e l l i n g o r d i s i n t e g r a t i o n and r e f o r m a t i o n o f t h e complex on t h e s u r f a c e o f t h e s t y r e n e d r o p l e t s . T h i s p a r t i c l e g r o w t h b y c o a l e s c e n c e a n d s w e l l i n g c o n t i n u e s up t o t h e s e c o n d i n f l e c t i o n point V . The s e c o n d s l o w l y d e c r e a s i n g l e g i s i n t e r p r e t e d a s t h e p a r t i c l e g r o w t h p r o c e s s i n w h i c h t h e number o f s t y r e n e d r o p l e t s i s a p p r o x i m a t e l y c o n s t a n t and t h e added s t y r e n e d i f f u s e s t h r o u g h t h e aqueous phase a n d s w e l l s t h e s e d r o p l e t s f u r t h e r . 2

Mathematical

Model o f t h e Conductometric

Titration

Curves

The t h r e e s t a g e s o f t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e w e r e expressed as an e x p o n e n t i a l s t e p f u n c t i o n w i t h t h e r e q u i s i t e para meters . F = PdJe^^^IUCVj-UCV-Vp] + P(3)e +

p

(

5

)

e

P(6)(V-V ) 2

[

u

(

v

_

V

P ( 4 ) ( V

V

)

" l [U(V-V )-U(V-V )] 1

]

2

(

1

+

)

where F i s t h e c o n d u c t a n c e , P ( l ) t h e i n i t i a l c o n d u c t a n c e , P ( 2 ) t h e s o l u b i l i z a t i o n c o n s t a n t , P ( 3 ) t h e c o n d u c t a n c e a t t h e end o f t h e s o l u b i l i z a t i o n s t a g e , P(4) t h e e m u l s i f i c a t i o n c o n s t a n t , P(5) t h e c o n d u c t a n c e a t t h e end o f t h e e m u l s i f i c a t i o n s t a g e , P ( 6 ) t h e p a r t i c l e growth c o n s t a n t , V the volume a t a g i v e n time t , U(V)-U(VV i ) t h e s t e p f u n c t i o n when V i s l e s s t h a n V^, U ( V - V i ) - U ( V - V ) t h e s t e p f u n c t i o n when V i s b e t w e e n V*i a n d V , U ( V - V ) t h e s t e p f u n c t i o n when V i s g r e a t e r t h a n V , and V^ a n d V t h e v o l u m e s a t t h e inflection points. T h i s e q u a t i o n was s o l v e d b y i t e r a t i v e c o m p u t e r r e g r e s s i o n a n a l y s i s (9) u s i n g t h e d a t a o f t h e c o n d u c t o m e t r i c t i t r a t i o n o f 0,6% aqueous h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e s o l u t i o n s w i t h t h e d i f f e r e n t hexadecyltrimethylammonium bromide-cetyl a l c o h o l molar r a t i o s shown i n F i g u r e 2. T a b l e I g i v e s t h e r e s u l t s o f t h i s analysis. 2

2

2

2

2


406


Table I Regression A n a l y s i s o f Conductometric T i t r a t i o n Data u s i n g Equation 1


Molar Ratio HTAB:CA*

P(D

P(2)

1: 6.00

P(3)

P(4)

P(6)

P(5)

3.98x10

-1 •3 2.11x10" 7.42x10 -9.07x10"

1: 3.00

5.39x10

-1 3.85x10"

4.99x10

•3 -1 1.61x10" 8.03x10 -7.24x10"

1: 1.00

8.67x10

-1 3.44x10"

6.06x10

-2 •3 7.52x10 -3.98x10" 9.42x10"

1: 0.50

1.08xl0

2

-1 1.61x10"

7.33x10

-2 7.99x10 2.48x10"

-3 1.11x10'

1: 0.33

1.14xl0

2

-2 7.29x10"

7.68x10

-3 7.87x10 6.37x10'

•3 1.73x10"

^hexadecyltrimethylammonium bromide-cetyl a l c o h o l

F i g u r e s 5-9 compare t h e c a l c u l a t e d c u r v e s w i t h t h e e x p e r i m e n t a l curves f o r hexadecyltrimethylammonium bromide-cetyl a l c o h o l r a t i o s o f 1:0.33, 1:0.5, 1:1, 1:3, a n d 1:6, r e s p e c t i v e l y . The f i t between t h e c a l c u l a t e d and e x p e r i m e n t a l curves i s r e a s o n a b l y good, and t h e c h a r a c t e r i s t i c p a r a m e t e r s o f e a c h c u r v e a r e d e f i n e d .

Discussion The p a r a m e t e r s P ( l ) a n d P ( 2 ) d e f i n e t h e s o l u b i l i z a t i o n s t a g e . I n t h e a b s e n c e o f m i c e l l e s , t h e r e i s no s o l u b i l i z a t i o n o f t h e o i l p h a s e . T h e r e f o r e , i n t h i s c a s e , t h e r e a r e no v a l u e s o f P ( l ) a n d P ( 2 ) , e . g . , a s f o r t h e 1:6 h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e c e t y l a l c o h o l molar r a t i o . The p a r a m e t e r P ( l ) r e p r e s e n t s t h e i n i t i a l c o n d u c t a n c e . Table I I compares t h e e x p e r i m e n t a l a n d c a l c u l a t e d v a l u e s o f t h i s p a r a meter.



CHOU ET AL.

Emulsification

of Benzene

4

2 VOLUME

and Styrene

407

6

OF BENZENE (cc)

Figure 5. Conductometric titration at 63 °C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and 0.033 g cetyl alcohol (1:0.33 molar ratio) with benzene at a constant rate of 1 cc/min. Key: , conductometric titration curve; and , calculated using Equation 1.



408


2

4 VOLUME

6

OF BENZENE (cc)

Figure 6. Conductometric titration at 63°C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and 0.050 g cetyl alcohol (1:0.5 molar ratio) with benzene at a constant rate of 1 cc/min. Key: , conductometric titration curve; , calculated using Equation 1.



25.

Emulsification

CHOU ET AL.

100

of Benzene

and Styrene

-

< o o o

0

2 VOLUME

4 OF

BENZENE (cc)

Figure 7. Conductometric titration at 63 °C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and 0.10 g cetyl alcohol (1:1 molar ratio) with benzene at a constant rate of 1 cc/min. Key: , conductometric titration; , calculated using Equation 1.


409


410


S

20

h

4

2 VOLUME

OF

6

8

BENZENE (cc)

Figure 8. Conductometric titration at 63° C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and 0.30 g cetyl alcohol (molar ratio 1:3) with benzene at a constant rate of 1 cc/min. Key: , conductometric titration; , calculated using Equation 1.



CHOU ET AL.

r t

Emulsification of Benzene and Styrene

41

so 60 -

O

2

4 6 8 VOLUME OF BENZENE (cc)

Figure 9. Conductometric titration at 63 °C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and 0.60 g cetyl alcohol (1:6 molar ratio) with benzene at a constant rate of 1 cc/min. Key: , conductometric titration; , calculated using Equation 1.


412


TABLE I I C o m p a r i s o n o f E x p e r i m e n t a l and C a l c u l a t e d V a l u e s o f P ( l )


Molar Ratio HTAB:CA

I n i t i a l Conductance Regression Analysis Experimental

1:0.33

110.5

114.4

1:0.50

103.1

107.9

1:1.00

83.0

86.7

1:3.00

53.1

53.9

1:6.00

41.0

The agreement b e t w e e n t h e c a l c u l a t e d and t h e e x p e r i m e n t a l v a l u e s i s good. A c c o r d i n g t o the proposed model, the descending l e g o f the conductometric t i t r a t i o n curve represents the s o l u b i l i z a t i o n pro cess. With decreasing hexadecyltrimethylammonium b r o m i d e - c e t y l a l c o h o l m o l a r r a t i o , t h e i n i t i a l c o n d u c t a n c e d e c r e a s e s and t h e d e s c e n d i n g l e g becomes s h o r t e r and d i s a p p e a r s a t t h e 1:6 r a t i o . Assuming t h a t t h e c r y s t a l l i n e r o d l i k e p a r t i c l e s a r e non-conducting, the conductance i s a t t r i b u t e d p r i n c i p a l l y t o t h e s o l u t e h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e m o l e c u l e s . The d e s c e n d i n g l e g i s a t t r i buted t o the s o l u b i l i z a t i o n of the o i l i n the m i c e l l e s . Since the t o t a l amount o f h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e i n t h e m i x e d e m u l s i f i e r s y s t e m i s known, i t s c o n c e n t r a t i o n i n t h e c r y s t a l l i n e r o d l i k e p a r t i c l e s c a n be o b t a i n e d by s u b t r a c t i n g t h e c o n c e n t r a t i o n o f s o l u t e and m i c e l l e m o l e c u l e s f r o m t h e t o t a l e m u l s i f i e r c o n c e n tration. The c o n d u c t a n c e o f t h e b r o m i d e c o u n t e r i o n a s s o c i a t e d w i t h t h e e m u l s i f i e r m i c e l l e s i s 4 . 2 1 2 x 1 0 % d i v i d e d by t h e conductance r e a d out ( 8 ) . The c o n c e n t r a t i o n o f h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e i n t h e m i c e l l e s a t a 1:3 m o l a r r a t i o i s ( 5 3 . 1 - 4 1 . 0 ) / 4 . 2 1 2 x l 0 o r 2 . 8 7 x 1 0 " % . The t o t a l c o n c e n t r a t i o n o f h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e i n t h e s y s t e m i s ( 0 . 1 5 / 3 6 4 . 6 ) ( 1 0 0 0 / 2 5 ) o r 1 . 6 5 x l O ~ M . The s o l u t e and m i c e l l a r h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e c o n c e n t r a t i o n s a r e s u b t r a c t e d from t h e t o t a l c o n c e n t r a t i o n t o g i v e t h e con centration i n the c r y s t a l l i n e rodlike p a r t i c l e s . Table I I I gives these c o n c e n t r a t i o n s f o r the hexadecyltrimethylammonium bromidec e t y l a l c o h o l r a t i o s o f 1:6 t o 1:0.33. 3

2


25.

CHOU ET AL.

Emulsification

413

of Benzene and Styrene

TABLE I I I D i s t r i b u t i o n o f Hexadecyltrimethylammonium Bromide i n the M i x e d E m u l s i f i e r System


Molar Ratio HTAB:CA

Concentration, M Solute Micelles

1:6.00

8.28xl0"~

4

1:3.00

8.28xl0"

4

2.87xl0"

1:1.00

8.28xl0"

4

1:0.50

8.28xl0"

1:0.33

8.28xl0"

Rodlike

Particles

1.56xl0"

2

3

1.28xl0"

2

9.97xl0"

3

5.66xl0"

3

4

1.47xl0"

2

9.35xl0"

4

4

1.65xl0"~

2

0

-8.65xl0"

4

The a c t u a l s o l u t e a n d m i c e l l a r c o n c e n t r a t i o n s o f h e x a d e c y l t r i methylammonium b r o m i d e s h o u l d b e l o w e r t h a n t h e c a l c u l a t e d v a l u e s b e c a u s e t h e r o d l i k e p a r t i c l e s a n d m i c e l l a r a g g r e g a t e s a r e assumed t o b e n o n - c o n d u c t i n g . The n e g a t i v e v a l u e c a l c u l a t e d f o r t h e c o n c e n t r a t i o n i n r o d l i k e p a r t i c l e s f o r t h e 1:0.33 h e x a d e c y l t r i m e t h y l ammonium b r o m i d e - c e t y l a l c o h o l m o l a r r a t i o i s e s s e n t i a l l y z e r o . F i g u r e 2 shows t h a t t h e b e n z e n e c o n d u c t o m e t r i c t i t r a t i o n c u r v e f o r t h e 1:0.33 h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e - c e t y l a l c o h o l r a t i o i s v e r y c l o s e t o t h a t f o r t h e same c o n c e n t r a t i o n o f h e x a decyltrimethylammonium bromide without c e t y l a l c o h o l ( F i g u r e 1 ) . The p a r a m e t e r P ( 2 ) , t h e s o l u b i l i z a t i o n c o n s t a n t , h a s a f i n i t e v a l u e when m i c e l l e s a r e p r e s e n t i n t h e m i x e d e m u l s i f i e r s y s t e m . The s m a l l e r t h e v a l u e o f P ( 2 ) , t h e s m a l l e r t h e c o n c e n t r a t i o n o f m i c e l l a r hexadecyltrimethylammonium bromide and t h e b e t t e r t h e b a l a n c e between t h e hexadecyltrimethylammonium bromide and c e t y l alcohol i nthecrystalline rodlike particles. I t i s assumed t h a t t h e optimum h e x a d e c y l t r i m e t h y l a m m o n i u m bromide-cetyl alcohol r a t i o for the formation o f perfect c r y s t a l s a l s o corresponds t o t h e f o r m a t i o n o f t h e h i g h e s t - s t a b i l i t y emul sions. The measurement o f e m u l s i o n s t a b i l i t y b y u l t r a c e n t r i f u g a t i o n ( 8 ) showed t h a t e m u l s i o n s p r e p a r e d w i t h a 1:3 h e x a d e c y l t r i methylammonium b r o m i d e - c e t y l a l c o h o l m o l a r r a t i o showed t h e b e s t stability. T h e r e f o r e , t h e r o d l i k e p a r t i c l e s formed i n t h i s s y s tem s h o u l d h a v e t h e h i g h e s t c r y s t a l l i n i t y , w h i c h was c o n f i r m e d b y e l e c t r o n d i f f r a c t i o n measurements i n t h e t r a n s m i s s i o n e l e c t r o n m i c r o s c o p e ( 2 ) . The r a t i o P ( 2 ) / P ( 2 ) ^ , w h e r e t h e s u b s c r i p t b d e n o t e s t h e s y s t e m o f h i g h e s t c r y s t a l l i n i t y , h a s v a l u e s o f 0.894, 0.419, a n d 0.189 f o r h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e - c e t y l a l c o h o l m o l a r r a t i o s o f 1:1, 1:0.50, a n d 1:0.33, r e s p e c t i v e l y , r e l a t i v e t o a v a l u e o f 1.000 f o r t h e 1:3 r a t i o . The s l o p e o f t h e d e s c e n d i n g l e g o f t h e t i t r a t i o n d e c r e a s e s and t h e v a l u e o f increases with increasing hexadecyltrimethyl-



414


ammonium b r o m i d e - c e t y l a l c o h o l r a t i o . The p a r a m e t e r i s re l a t e d t o t h e time p e r i o d d u r i n g w h i c h s o l u b i l i z a t i o n o c c u r s and t h e r e f o r e i n c r e a s e s when more m i c e l l e s a r e p r e s e n t . The d e c r e a s e i n the slope o f the descending l e g i sa t t r i b u t e d t o the poorer c r y s t a l l i n i t y o f t h e r o d l i k e p a r t i c l e s formed w i t h e x c e s s hexade c y l t r i m e t h y l a m m o n i u m b r o m i d e . A s t h e o i l i s added t o t h e s y s t e m , t h e r o d l i k e p a r t i c l e s d i s i n t e g r a t e more r e a d i l y , r e l e a s i n g s m a l l c o n c e n t r a t i o n s o f h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e t o t h e aqueous phase c o n t i n u o u s l y . The p a r a m e t e r P ( 3 ) r e p r e s e n t s t h e c o n d u c t a n c e a t t h e e n d o f t h e s o l u b i l i z a t i o n s t a g e . T a b l e I I I shows t h a t t h e c o n c e n t r a t i o n of hexadecyltrimethylammonium bromide i n t h e c r y s t a l l i n e r o d l i k e p a r t i c l e s increases with increasing c e t y l alcohol concentration. T h e r e f o r e , t h i s p a r a m e t e r r e p r e s e n t s t h e number o f c r y s t a l l i n e r o d l i k e p a r t i c l e s i n t h e system p r i o r t o e m u l s i f i c a t i o n . The p a r a m e t e r P ( 4 ) , t h e e m u l s i f i c a t i o n c o n s t a n t , i s r e l a t e d t o t h e number o f c r y s t a l l i n e r o d l i k e p a r t i c l e s a v a i l a b l e t o s t a b i l i z e t h e v e r y s m a l l e m u l s i o n d r o p l e t s formed d u r i n g t h e e m u l s i f i c a t i o n p r o c e s s . The h i g h e r t h e c e t y l a l c o h o l c o n c e n t r a t i o n a t a g i v e n hexadecyltrimethylammonium bromide c o n c e n t r a t i o n , t h e more c r y s t a l l i n e r o d l i k e p a r t i c l e s a r e g e n e r a t e d , b u t t h e d e g r e e of c r y s t a l l i n i t y i s b e t t e r r e l a t e d t o t h e parameter P(2) than t o P(4). The p a r a m e t e r P ( 5 ) r e p r e s e n t s t h e c o n d u c t a n c e a t t h e e n d o f the e m u l s i f i c a t i o n p r o c e s s and t h e b e g i n n i n g o f t h e p a r t i c l e growth p r o c e s s ; i t s v a l u e s a r e n e a r l y constant. The p a r a m e t e r P ( 6 ) , t h e p a r t i c l e g r o w t h c o n s t a n t , i s r e l a t e d t o t h e number o f c r y s t a l l i n e r o d l i k e p a r t i c l e s . The l a r g e r t h e number o f t h e s e r o d l i k e p a r t i c l e s , t h e s m a l l e r t h e v a l u e o f P ( 6 ) . T h i s parameter i s a l s o r e l a t e d t o t h e r e t a r d a t i o n e f f e c t on t h e conductance. E x t e n s i o n and V e r i f i c a t i o n o f t h e M a t h e m a t i c a l M o d e l To c o n f i r m t h e v a l i d i t y o f t h e m a t h e m a t i c a l m o d e l , two s e r i e s of c o n d u c t o m e t r i c t i t r a t i o n s were c a r r i e d o u t : ( i ) t h e hexadecyl t r i m e t h y l a m m o n i u m b r o m i d e c o n c e n t r a t i o n was d e c r e a s e d t o 0.4% a t 1:1 a n d 1:3 h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e - c e t y l a l c o h o l r a t i o s a n d i n c r e a s e d t o 0.8% a t t h e 1:3 m o l a r r a t i o ( F i g u r e 1 0 ) ; ( i i ) t h e hexadecyltrimethylammonium b r o m i d e - c e t y l a l c o h o l molar r a t i o was i n c r e a s e d t o 1:7 a t 0.6% h e x a d e c y l t r i m e t h y l a m m o n i u m bromide ( F i g u r e 1 1 ) . F i g u r e 10 shows t h a t v a r y i n g t h e h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e c o n c e n t r a t i o n a t t h e same h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e - c e t y l a l c o h o l r a t i o changed t h e c o n d u c t o m e t r i c t i t r a t i o n curve. F o r 0.4% h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e a t t h e 1:3 m o l a r r a t i o , t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e showed no i n i t i a l d e s c e n d i n g l e g , s u g g e s t i n g t h a t t h i s s y s t e m c o n t a i n e d no e m u l s i fier micelles. I n comparison, the conductometric t i t r a t i o n curve f o r 0.6% h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e - c e t y l a l c o h o l a t t h e


25.

CHOU ET AL.

Emulsification

415



same 1:3 m o l a r r a t i o ( F i g u r e 2) showed a s m a l l i n i t i a l d e s c e n d i n g l e g , s u g g e s t i n g t h a t t h i s s y s t e m c o n t a i n e d a s m a l l number o f m i celles. F o r 0.8% h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e a t t h e 1:3 m o l a r r a t i o , t h e l e n g t h o f t h e i n i t i a l d e s c e n d i n g l e g was e v e n greater. T a b l e I V compares t h e d i s t r i b u t i o n s o f h e x a d e c y l t r i methylammonium b r o m i d e b e t w e e n m i c e l l e s , s o l u t e m o l e c u l e s , a n d r o d l i k e p a r t i c l e s f o r these systems. TABLE I V D i s t r i b u t i o n o f Hexadecyltrimethylammonium i n t h e Mixed E m u l s i f i e r System

% HTAB

Molar Ratio HTAB :CA

Concentration, M Micelles Solute

0.4

1 :3

8.28xl0"

4

0.6

1 :3

8.28xl0"

4

2.87xl0"

0.8

1 :3

8.28xl0"

4

0.4

1 :1

8.28xl0~

0.6

1 :1

8.28xl0"

Bromide

Rodlike

Particles

1.06xl0"

2

3

1.28xl0"

2

7.60xl0""

3

1.35xl0"

2

4

4.34xl0"

3

5.72xl0""

3

4

9.97xl0"

3

5.66xl0"

3

0

T h e s e r e s u l t s show t h a t , a t a g i v e n hexadecyltrimethylammonium b r o m i d e - c e t y l a l c o h o l molar r a t i o , t h e c o n c e n t r a t i o n o f hexade cyltrimethylammonium bromide i n t h e m i c e l l e s i n c r e a s e s w i t h i n creasing e m u l s i f i e r concentration while that i n the r o d l i k e par t i c l e s i s a b o u t t h e same o r i n c r e a s e s o n l y s l i g h t l y . F o r 0.4% h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e a t t h e 1:3 m o l a r r a t i o , t h e r e a r e no m i c e l l e s , w h i c h e x p l a i n s t h e a b s e n c e o f a d e s c e n d i n g l e g i n the t i t r a t i o n curve; moreover, t h e c o n c e n t r a t i o n o f e m u l s i f i e r i n t h e r o d l i k e p a r t i c l e s i s s l i g h t l y l e s s t h a n a t 0.6% a n d 0.8% e m u l s i f i e r a t t h e same m o l a r r a t i o . I n these l a t t e r cases, t h e concentration i nmicelles increases with increasing emulsifier c o n c e n t r a t i o n , w h i l e t h a t i n t h e r o d l i k e p a r t i c l e s i s about t h e same o r i n c r e a s e s o n l y s l i g h t l y . F o r 0.4% h e x a d e c y l t r i m e t h y l ammonium b r o m i d e a t t h e 1:1 m o l a r r a t i o , m i c e l l e s a r e o b s e r v e d and t h e c o n c e n t r a t i o n i n t h a t f o r m i n c r e a s e s w i t h i n c r e a s i n g e m u l s i f i e r c o n c e n t r a t i o n ; however, t h e c o n c e n t r a t i o n i n r o d l i k e p a r t i c l e s i s a b o u t t h e same f o r b o t h 0.4% and 0.6% h e x a d e c y l t r i methylammonium b r o m i d e . Furthermore, t h e c o n c e n t r a t i o n o f emul s i f i e r i n r o d l i k e p a r t i c l e s i s c o n s i s t e n t l y s m a l l e r f o r t h e 1:1 m o l a r r a t i o t h a n f o r t h e 1:3 m o l a r r a t i o ; a p p a r e n t l y , t h e g r e a t e r p r o p o r t i o n o f c e t y l a l c o h o l r e s u l t s i n t h e i n c o r p o r a t i o n o f more emulsifier i ntherodlike particles. The f o r e g o i n g e x p e r i m e n t a l r e s u l t s w e r e a l s o a n a l y z e d the r e g r e s s i o n Equation 1 described e a r l i e r .


using

416


Regression


Molar Ratio % HTAB: HTAB CA

P(D

TABLE V A n a l y s i s o f Conductometric Data using Equation 1

P(2)

P(3)

1: 3

0.6

1: 3

5.39x10 3.85x10"

0.8

1: 3

7.30x10 5.99x10"

0.4

1: 1

5.97x10 3.98x10"

0.6

1: 1

8.67x10 3.44x10"

1 1 1 1

4.99x10 1.61x10" 3.22x10 1.63x10" 3.73x10 9.10x10"

P(6)

P(5)

P(4)

3.26x10 1.03x10"

0.4

Titration

1

6.24x10

•2 2.87x10"

1

•3 8.03x10 - 7 . 2 4 x 1 0 "

1

•2 8.20x10 -2.42x10"

2

7.20x10

•2 1.57x10"

•2 •3 6.06x10 9.42x10" 7.52x10 -3.98x10"

The r e s u l t s o f T a b l e V a r e c o n s i s t e n t w i t h t h o s e o f T a b l e I V . T h e v a l u e s o f P ( l ) were i n r e a s o n a b l e agreement w i t h the i n i t i a l con d u c t a n c e s o f the t i t r a t i o n c u r v e s , and the v a l u e s o f P(2) i n c r e a s e d w i t h i n c r e a s i n g e m u l s i f i e r c o n c e n t r a t i o n a t t h e 1:3 m o l a r r a t i o , a n d d e c r e a s e d s l i g h t l y a t t h e l e s s e f f i c i e n t 1:1 r a t i o ( t h e r e a r e no v a l u e s o f P ( l ) a n d P ( 2 ) f o r 0.4% e m u l s i f i e r a t t h e 1:3 m o l a r r a t i o b e c a u s e o f t h e a b s e n c e o f a d e s c e n d i n g l e g ) . A t b o t h t h e 1:3 a n d 1:1 m o l a r r a t i o s , t h e v a l u e s o f P ( 2 ) w e r e s m a l l e r f o r t h e 0.6% e m u l s i f i e r t h a n f o r t h e 0.8% a n d 0.4% e m u l s i f i e r , r e s p e c t i v e l y , w h i c h suggests a b e t t e r b a l a n c e between the hexa d e c y l t r i m e t h y l a m m o n i u m bromide and c e t y l a l c o h o l i n t h e r o d l i k e p a r t i c l e s , d e s p i t e the i n c r e a s e i n m i c e l l a r e m u l s i f i e r w i t h i n creasing emulsifier concentration. The v a l u e s o f P ( 3 ) w e r e i n r e a s o n a b l e a g r e e m e n t w i t h t h e c o n d u c t a n c e s a t t h e i n f l e c t i o n p o i n t V-j f o r t h e s a m p l e s c o n t a i n i n g 0.6% e m u l s i f i e r , b u t s i g n i f i c a n t l y l o w e r t h a n t h e e x p e r i m e n t a l c o n d u c t a n c e s f o r t h e s a m p l e s c o n t a i n i n g 0.4% a n d 0.8% e m u l s i f i e r ( t h a t f o r t h e 0.4% e m u l s i f i e r a t t h e 1:3 m o l a r r a t i o , w h i c h c o n t a i n e d no m i c e l l e s was i n good agreement w i t h t h e i n i t i a l c o n d u c t a n c e ) , p e r h a p s b e c a u s e t h e t i t r a t i o n c u r v e s o f F i g u r e 10 a r e more r o u n d e d a t t h i s i n f l e c t i o n p o i n t t h a n t h o s e o f F i g u r e 2; e x t r a p o l a t i o n o f these curves t o a sharp endpoint would g i v e lower exper imental values. The v a l u e s o f P ( 4 ) i n c r e a s e d s l o w l y w i t h i n c r e a s i n g e m u l s i f i e r c o n c e n t r a t i o n a t a g i v e n m o l a r r a t i o i n much smaller p r o p o r t i o n than the i n c r e a s e i n e m u l s i f i e r c o n c e n t r a t i o n . These v a l u e s s u g g e s t t h a t t h e number o f c r y s t a l l i n e r o d l i k e p a r t i c l e s a v a i l a b l e t o s t a b i l i z e t h e v e r y s m a l l e m u l s i o n d r o p l e t s i s more dependent on the hexadecyltrimethylammonium b r o m i d e - c e t y l a l c o h o l molar r a t i o than on the e m u l s i f i e r c o n c e n t r a t i o n , b e i n g s i g n i f i c a n t l y s m a l l e r f o r t h e 1:1 r a t i o t h a n f o r t h e 1:3 r a t i o .



CHOU ET AL.

0

Emulsification

2


4

All

6

VOLUME OF BENZENE (cc) Figure 10. Conductometric titration at 63°C of 25 cc water containing 0.20 or 0.10 g hexadecyltrimethylammonium bromide and varying amounts of cetyl alcohol with benzene at a constant rate of 1 cc/min. Key: 1, 0.20 g hexadecyltrimethylammonium bromide and 0.40 g cetyl alcohol (1:3 molar ratio); II', 0.10 g hexadecyltrimethylammonium bromide and 0.067 g cetyl alcohol (1:1 molar ratio); and III, 0.10 g hexadecyltrimethylammonium bromide and 0.20 g cetyl alcohol (1:3 molar ratio).


418


The v a l u e s o f P ( 5 ) w e r e i n r e a s o n a b l e a g r e e m e n t w i t h t h e conductances at the i n f l e c t i o n p o i n t s V b e i n g a b o u t t h e same o r s l i g h t l y s m a l l e r . The v a l u e s o f P ( 6 ) w e r e p o s i t i v e o n l y f o r t h e 0.4% e m u l s i f i e r a t t h e 1:3 and 1:1 m o l a r r a t i o s . The n e g a t i v e v a l u e s f o r t h e 0.6% e m u l s i f i e r a t 1:3 and 1:1 m o l a r r a t i o s and 0.8% e m u l s i f i e r a t 1:3 m o l a r r a t i o a r e e q u a l t o z e r o w i t h i n e x perimental error. T h e s e v a l u e s s u g g e s t t h a t t h e number o f c r y s t a l l i n e r o d l i k e p a r t i c l e s i s g r e a t e r f o r t h e 0.6% and 0.8% e m u l s i f i e r t h a n f o r t h e 0.4% e m u l s i f i e r . F i g u r e 11 shows t h a t the conductometric t i t r a t i o n c u r v e s f o r 0.6% h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e w e r e e s s e n t i a l l y t h e same f o r m o l a r r a t i o s o f 1:6 and 1:7. I n b o t h c a s e s , the absence o f a de s c e n d i n g l e g s u g g e s t s t h a t no m i c e l l e s w e r e p r e s e n t . Therefore, a f u r t h e r i n c r e a s e i n t h e c e t y l a l c o h o l c o n c e n t r a t i o n r e s u l t e d i n an i n c r e a s e of that i n c o r p o r a t e d i n t o the r o d l i k e p a r t i c l e s , which d i m i n i s h e s t h e c r y s t a l l i n i t y b u t g i v e s no s i g n i f i c a n t change i n the conductometric t i t r a t i o n curve. Thus b o t h o f t h e s e e x t e n s i o n s o f t h e c h a n g e s i n t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e s r e s u l t i n g f r o m a change i n e m u l s i f i e r and c e t y l a l c o h o l c o n c e n t r a t i o n s were c o n s i s t e n t w i t h the proposed mathematical model.


2 >

Three-Dimensional

Conductance-Oil

Volume-Cetyl

Alcohol Plots

The c o m p l e x v a r i a t i o n o f t h e c o n d u c t a n c e w i t h added o i l v o l ume a t a g i v e n h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e c o n c e n t r a t i o n was shown by a t h r e e - d i m e n s i o n a l c o n d u c t a n c e - o i l v o l u m e - c e t y l alcohol concentration plot. The c o n d u c t o m e t r i c t i t r a t i o n c u r v e s of F i g u r e 2 were f i t t e d u s i n g v a r i o u s e q u a t i o n s . The b e s t f i t was obtained w i t h the f o l l o w i n g e x p r e s s i o n . F = AQ +

jj { A X L

+ B /X 1

+ A X 2

2

+ B /X 2

2

+

AgX

6

6

+ B /X } 6

(2)

n=l w h e r e X i s t h e v o l u m e o f added b e n z e n e , and Ao, A^...A^, and B ^ . . . B^ are c o e f f i c i e n t s . The f i r s t p a r t o f E q u a t i o n 1 e x p r e s s e s t h e o s c i l l a t i n g p a r t o f t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e and t h e s e c o n d p a r t , t h e d e c a y i n g p a r t . F i g u r e 12 compares t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e f o r 0.6% h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e a t 1:3 h e x a d e c y l t r i m e t h y l - a m m o n i u m b r o m i d e - c e t y l a l c o h o l m o l a r r a t i o ( F i g u r e 2) w i t h t h e f i t t e d c u r v e . The a g r e e m e n t b e t w e e n e x p e r i m e n t a l and c a l c u l a t e d c u r v e s i s e x c e l l e n t ; t h e t h r e e p a r t s o f t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e a r e f i t t e d by E q u a t i o n 2 u s i n g thirteen coefficients. Table VI g i v e s the v a l u e s of these t h i r t e e n c o e f f i c i e n t s f o r t h e c o n d u c t o m e t r i c t i t r a t i o n c u r v e s o f F i g u r e 2 and 0.6% h e x a d e c y l t r i m e t h y l a m m o n i u m b r o m i d e a t m o l a r r a t i o s o f 1:0.33, 1:0.50, 1:1, 1:3, and 1:6.



25.

CHOU ET AL.

Emulsification


100 -

-

60

o z < o o o

4

6

VOLUME OF BENZENE (cc) Figure 11. Conductometric titration at 63 °C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and 0.60 or 0.70 g cetyl alcohol with benzene at a constant rate of 1 cc/min. Key: , 0.60 g cetyl alcohol (molar ratio 1:6) and , 0.70 g cetyl alcohol (molar ratio 1:7).


419


420


VOLUME OF BENZENE (cc) Figure 12. Conductometric titration at 63°C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and 0.30 g cetyl alcohol (molar ratio 1:3) with benzene at a constant rate of 1 cc/min. Key: |, experimental curve and , calculated using Equation 2.


25.

CHOU ET AL.

Emulsification

421


TABLE V I C o e f f i c i e n t s o f Equation 2 f o r Conductometric T i t r a t i o n Curves o f F i g u r e 2 Co effi cient

1:6

M o l a r R a t i o HTAB:CA 1:1 1:3


-1288.8 727.69 -219.6 38.297 -3.7978 0.19637 -0.0040359

1:0.50

1:0.33

250.49

-2924.4

3097 .8

-6.3251

-218.39

1788.1

-1903 .4

36.704

126.88 -37.271 5.8106 -0.46015 -0.014581

-627.84

708 .03

-3.9731

131.93

156 .44

-2.1492

-16.279 1.0857 -0.030164

20 .138

0.67757

-1 .392

-0.071166

0 .039874

0.0026112

1408.0

-65.353

2887.3

2837 .1

160.41

-870.49

-23.786

-1630.5

1624 .1

-113.21

313.83

24.789

543.70

-554 .99

-63.701

-7.4121

103.52

108 .5

6.5860 -0.2612

0.9416 -0.042428

10.187 -0.39016

44.035 -9.3678

-10 .929 0 .42607

0.99793 0.040321

The t h r e e - d i m e n s i o n a l p l o t s w e r e c o n s t r u c t e d i n a r e c t a n g u l a r box w i t h t h e volume o f added benzene f o r m i n g t h e X - a x i s , t h e c e t y l a l c o h o l c o n c e n t r a t i o n o f t h e Y - a x i s , a n d t h e c o n d u c t a n c e t h e Zaxis. The c o e f f i c i e n t s g i v e n i n T a b l e V I w e r e u s e d t o c a l c u l a t e the conductance a t a g i v e n c e t y l a l c o h o l c o n c e n t r a t i o n f o r each 0.4 c c added b e n z e n e f r o m 0 t o 8.0 c c , t o g i v e t w e n t y v a l u e s o f t h e c o n d u c t a n c e . T h i s c a l c u l a t i o n was r e p e a t e d f o r t w e n t y - t h r e e c e t y l a l c o h o l c o n c e n t r a t i o n s r a n g i n g f r o m 1:0.25 t o 1:6 m o l a r r a t i o s , i . e . , o v e r t h e r a n g e shown i n F i g u r e 2. E q u a t i o n 2 was t h e n used t o f i t t h e v a r i a t i o n o f conductance w i t h t h e f i v e d i f f e r e n t c e t y l a l c o h o l c o n c e n t r a t i o n s o f F i g u r e 2 a t each o f t h e twenty b e n z e n e c o n c e n t r a t i o n s o v e r t h e r a n g e 0.0-8.0 c c . T h e c o e f f i c i e n t s o b t a i n e d , analogous t o those o f T a b l e V I , were used t o c a l c u l a t e the conductance a t each o f t h e twenty benzene c o n c e n t r a t i o n s f o r each o f twenty-three increments o f c e t y l a l c o h o l c o n c e n t r a t i o n r e -



422


p r e s e n t e d by v a r i a t i o n o f t h e m o l a r r a t i o o v e r t h e r a n g e 1:0.251:6.00 t a k e n e v e r y 0.25 u n i t o f c e t y l a l c o h o l r a t i o . These results gave 460 c o n d u c t a n c e v a l u e s a s a f u n c t i o n o f v o l u m e o f added b e n z e n e and c e t y l a l c o h o l c o n c e n t r a t i o n . T h e s e 460 p o i n t s w e r e a r r a n g e d i n a t h r e e - d i m e n s i o n a l p l o t i n t h e r e c t a n g u l a r b o x , and the p o i n t s were connected t o form the t h r e e - d i m e n s i o n a l s t r u c t u r e . T h i s b o x w i t h t h e t h r e e - d i m e n s i o n a l p l o t was t h e n r o t a t e d h o r i z o n t a l l y and t i l t e d v e r t i c a l l y t o o b t a i n t h e b e s t v i e w o f t h e s t r u c ture. F i g u r e 13 shows t h e t h r e e - d i m e n s i o n a l p l o t v i e w e d f r o m a h o r i z o n t a l a n g l e o f 250° and a v e r t i c a l a n g l e o f 65°. T h i s v i e w shows that the descending l e g of the conductometric t i t r a t i o n curve d i minished w i t h increasing c e t y l alcohol concentration u n t i l i t d i s appeared. Beyond t h e d i s a p p e a r a n c e o f t h e d e s c e n d i n g l e g , t h e t i t r a t i o n c u r v e changed o n l y s l i g h t l y upon f u r t h e r a d d i t i o n o f cetyl alcohol. F i g u r e 14 shows t h e t h r e e - d i m e n s i o n a l p l o t v i e w e d f r o m a h o r i z o n t a l a n g l e o f 30° and a v e r t i c a l a n g l e o f 5°. T h i s v i e w shows t h e deep v a l l e y f o r m e d by t h e i n f l e c t i o n p o i n t and i t s d i s a p pearance w i t h i n c r e a s i n g c e t y l a l c o h o l content. Moreover, the r e g i o n beyond the i n f l e c t i o n p o i n t V i s shown a s a b r o a d , r e l a t i v e l y f l a t p l a t e a u . Thus t h e t h r e e - d i m e n s i o n a l p l o t on t h e r e c t a n g u l a r box c a n be t i l t e d a t any a n g l e d e s i r e d t o show t h e s p e c i f i c f e a t u r e s of i n t e r e s t . Furthermore, the l i n e s c o n n e c t i n g the conductance curves a t e a c h b e n z e n e c o n c e n t r a t i o n c a n be o m i t t e d t o g i v e t h e f a m i l y o f conductometric t i t r a t i o n curves c o r r e s p o n d i n g t o each c e t y l a l c o h o l c o n c e n t r a t i o n . F i g u r e 15 shows t h e s e c o n d u c t o m e t r i c t i t r a t i o n c u r v e v i e w e d f r o m a h o r i z o n t a l a n g l e o f 275° and a v e r t i c a l a n g l e o f 50°; t h e r a n g e i n w h i c h t h e d e s c e n d i n g l e g d i s a p p e a r s c a n be seen c l e a r l y . 2

Summary The c o n d u c t o m e t r i c t i t r a t i o n o f a q u e o u s h e x a d e c y l t r i m e t h y l ammonium b r o m i d e - c e t y l a l c o h o l m i x t u r e s w i t h b e n z e n e a l l o w s d e t e r m i n a t i o n o f t h e mechanism o f e m u l s i f i c a t i o n . However, t h e s h a p e s of the c o n d u c t o m e t r i c t i t r a t i o n c u r v e s a r e complex: the most s t a b l e s y s t e m s show a n e a r - l i n e a r d e s c e n d i n g l e g f o l l o w e d by a n e a r l i n e a r a s c e n d i n g l e g f o l l o w e d by a n e a r - l i n e a r n e a r - c o n s t a n t r e g i o n ; the l e s s s t a b l e systems, a n e a r - l i n e a r ascending l e g f o l l o w ed b y a n e a r - l i n e a r n e a r - c o n s t a n t r e g i o n . T h e s e c o n d u c t o m e t r i c t i t r a t i o n c u r v e s h a v e b e e n f i t t e d b y a m a t h e m a t i c a l m o d e l u s i n g an i t e r a t i v e computer t e c h n i q u e . T h i s mathematical model g i v e s the d i s t r i b u t i o n of the hexadecyltrimethylammonium b r o m i d e as s o l u t e e m u l s i f i e r , m i c e l l a r e m u l s i f i e r , and c o m b i n e d i n c r y s t a l l i n e r o d l i k e p a r t i c l e s w i t h t h e c e t y l a l c o h o l , as w e l l as t h e r e l a t i v e number and c r y s t a l l i n i t y o f t h e r o d l i k e p a r t i c l e s . The e m u l s i f i c a t i o n t o f o r m 0.1-0.3um e m u l s i o n d r o p l e t s i s a t t r i b u t e d t o t h e s e r o d l i k e p a r t i c l e s so t h a t the d e t e r m i n a t i o n o f t h e i r e m u l s i f i e r



CHOU ET AL.

Emulsification


423

Figure 13. Three-dimensional conductance-benzene volume-cetyl alcohol concentration plot calculated using Equation 2 for conductometric titration at 63 °C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and varying concentrations of cetyl alcohol with benzene at a constant rate of 1 cc/min viewed at a horizontal angle of 250° and a vertical angle of 65°.

Figure 14. Three-dimensional conductance-benzene volume-cetyl alcohol concentration plot calculated using Equation 2 for conductometric titration at 63 °C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and varying concentrations of cetyl alcohol with benzene at a constant rate of 1 cc/min viewed at a horizontal angle of 30° and a vertical angle of 5°.



424


VOLUME OF BENZENE Figure 15. Three-dimensional plot of family of conductometric titration curves calculated using Equation 2 for titration at 63 °C of 25 cc water containing 0.15 g hexadecyltrimethylammonium bromide and varying concentrations of cetyl alcohol with benzene at a constant rate of 1 cc/min viewed at a horizontal angle of 275° and a vertical angle of 50°.


25.

CHOU ET AL.

Emulsification


425


content allows p r e d i c t i o n o f r e l a t i v e emulsion s t a b i l i t y . Fur thermore, a three-dimensional p l o t o f conductance as a f u n c t i o n o f added v o l u m e o f b e n z e n e and c e t y l a l c o h o l c o n c e n t r a t i o n a t con s t a n t hexadecyltrimethylammonium bromide c o n c e n t r a t i o n a l l o w s v i s u a l i z a t i o n o f t h e conductance s u r f a c e a t any d e s i r e d a n g l e .

Literature Cited 1. Ugelstad, J., El-Aasser, M. S., Vanderhoff, J. W. J. Polymer Sci., Polymer Letters Ed. 1973, 11, 503-13. 2. Chou, Y. J., El-Aasser, M. S., Vanderhoff, J. W. J. Dispersion Sci. Tech. 1980, 1, 129-50; ibid, in "Polymer Colloids II", R. M. Fitch, ed., Plenum Press, New York, 1980, p. 599-618. 3. Vanderhoff, J. W., El-Aasser, M. S., Hoffman, J. D., U.S. 4,070,323 (to Lehigh University), Jan. 24, 1978. 4. Vanderhoff, J. W., El-Aasser, M. S., Ugelstad, J . , U.S. 4,177,177 (to Lehigh University), Dec. 4, 1979. 5. El-Aasser, M. S., Misra, S. C., Vanderhoff, J. W., Manson, J. A. J. Coatings Tech. 1977, 49(635), 71-8. 6. El-Aasser, M. S., Vanderhoff, J. W., Poehlein, G. W. Preprints Organic Coatings Plastics Chem. 1977, 37(2), 92-7. 7. El-Aasser, M. S., Hoffman, J. D., Manson, J. A., Vanderhoff, J. W. Preprints Organic Coatings Plastics Chem. 1980, 43, 136-41. 8. Chou, Y. J. Ph.D. Dissertation, Lehigh University, 1978, p. 156-186. 9. Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431-41. RECEIVED May 4, 1982.


Computer Applications in Applied Polymer Science - American

Recommend Documents