Application of the Gibs Absorption Theory to Films Absorbed at Oil-Water Interfaces

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FORDHAM UNIVERSITY G r a d u a t e S c h o o l o f A r t s a n d S cie n c e s

_________February 1,

19

..50

This dissertation prepared under my direction by

Duncan Randall entitled

A pplication of th e Gibbs Absorp tio n Theory to Films

Absorbed a t Oil-W ater In te rfa c e s ,

has been accepted in partial fulfilment o f the requirements for the

Degree o f

................................................................ .

JSric Hutchinson ( Faculty A dviser )

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APPLICATION CP THE GIBBS ADSORPTION THEORY TO FILMS ADSORBED AT OIL-WATER INTERFACES

BY DUNCAN RANDALL, A .B ., A.M.

DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE DEPARTMENT OF CHEMISTRY AT FORDHAM UNIVERSITY

NEW YORK

1949

J

ProQuest Number: 10992994

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is d e p e n d e n t upon the quality of the copy subm itted. In the unlikely e v e n t that the a u thor did not send a c o m p le te m anuscript and there are missing pages, these will be noted. Also, if m aterial had to be rem oved, a n o te will ind ica te the deletion.

uest ProQuest 10992994 Published by ProQuest LLC(2018). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346

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TABLE CF CONTENTS

Page ACKNOWLEDGEMENT................................................................................................. I. II. III.

THEORY...........................................................................................................

iv 1

METHODS.................................

50

EXPERIMENTALDATA...............................

59

Observed d a t a t a b u l a t e d and graphed I ? . CALCULATED RESULTS

/

94

Derived t h e o r e t i c a l d a t a t a b u l a t e d and graphed V. VI.

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INTERPRETATION.......................................................

122

SUMMARY......... ..................................................

150

BIBLIOGRAPHY .....................................................................................................

154

APPENDIX..............................................................................................................

158

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AOKNOWLEDCJEMENT

The a u th o r w ish es to acknowledge h i s in d e b te d n e s s to Dr. E ric H utchinson, whose guidance and i n s p i r a t i o n made p o s s i b l e t h i s study.

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APPLICATION OF THE GTBBS ADSORPTION THEORY TO FILMS ADSORBED AT OIL-WATER INTERFACES

1

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“i I . THEORY

Between any two a d jo in in g d i s t i n c t , m e c h a n ic a lly s e p a ra b le p h a s e s , t h e r e e x i s t s a r e g io n o f d i s c o n t i n u i t y whose p r o p e r t i e s a r e n o t th o s e o f e i t h e r o f th e two b u lk p h a se s. This t r a n s i t i o n re g io n i s n o t o f i n f i n i t e t h i n n e s s i n ■;th e sense o f a m ath em atical p la n e or bounding s u r f a c e in g e n e r a l , nor y e t i s i t a t r u e phase i n th e above s e n s e , even one in which i t i s c o n sid e re d t h a t p ro p­ e r t i e s c h a r a c t e r i s t i c o f one a d j a c e n t b u lk phase

-

th e s u rfa c e c o n ta i n s r e l a t i v e l y few m o lecu les o f (2) th e v a rio u s

P \ w ill

be p r a c t i c a l l y

p r o p o r t i o n a l to Ns , i . e .

-- p j h'1 - p j y) = kMo.

=.

In th e same l i q u i d d i l u t e w ith r e s p e c t to N2 i t can be shown t h a t

. r (Nt *

and we see t h a t whereas

_

^

Mi.

r,w . - 1

k

p,(’V

- P .^ , and -P ,^ te n d to zero a s Ns approaches

z e r o , - P ^ a p p r o a c h e s a c o n s ta n t v alu e K. The e q u a tio n s developed so f a r a r e p u re ly thermodynamic (e x c e p t /

j _ t h a t i n - a sense any c o n ven tion used i s extra-therm odynam ic in t h a t i t

20 r i s n o t d e riv e d from thermodynamic c o n s i d e r a t i o n s ) , t h a t i s , no hypo­ t h e s i s a s to th e m o le c u lar s t r u c t u r e o f e i t h e r volume o r s u rfa c e phases e n te r e d in to c o n s i d e r a t i o n . This tr e a tm e n t o f m a tte r in b u lk , which does n o t in v o lv e t h e o r i e s o r a ssum ptio n s as to d e t a i l e d s t r u c t u r e , i s a t once th e g r e a t s t r e n g t h and t h e g r e a t weakness o f th e s t r i c t l y thermodynamic method. The s t r e n g t h l i e s in th e f a c t t h a t w hatever c o n c lu s io n s a re reached a s to th e b e h av io r o f a system o f m a tte r en masse w i l l b e , and rem ain, v a lid r e g a r d l e s s o f whatever t h e o r i e s a r i s e (p e rh a p s to be d is c a rd e d a t some l a t e r d a te ) as to th e minute p h y s ic a l s t r u c t u r e o f th e m a t e r i a l . The weakness stems from th e same r o o t ; t h a t i s , pure thermodynamics, simply because i t does n o t concern i t s e l f w ith such q u e s ti o n s , i s , o f and by i t s e l f , pow erless t o f u r n i s h t h e s l i g h t ­ e s t in fo rm a tio n a s t o th e a c t u a l u n d e rly in g p h y s ic a l s t r u c t u r e and mechanisms. Some s o r t o f extra-therm odynam ic assum ptions or h y p o th e se s must be added. While i t i s t r u e t h a t in so d o in g , one lo s e s th e r i g o r and g e n e r a l i t y of c l a s s i c a l thermodynamics, and t h e r e s u l t s so o b ta in e d a r e s u b j e c t to r e v i s i o n , improvement, and perh aps r e j e c t i o n , y e t t h i s proced ure a t l e a s t a llo w s th e p o s s i b i l i t y o f a t t a i n i n g knowledge f a r w ider in scope and deeper in i n s i g h t th a n could i n i p r i n c i p l e ev er be a t t a i n e d by p u re ly thermodynamic means. This does n o t , o f c o u rs e , imply a r e j e c t i o n o f th e thermodynamic method, b u t r a t h e r a su p p lem en ta tio n o f i t byy methods t h a t add th e le a v e n o f im a g in a tio n to th e r i g o r o f th e rmodynami c s . Guggenheim and Adam, h y p o th e s iz in g a s to a p o s s i b l e s t r u c t u r e f o r th e s u rfa c e o f w a te r - e th a n o l s o l u t i o n s , f e l t t h a t th e s im p le s t s o r t o f s t r u c t u r e would be t h a t in which th e non-homogeneous l a y e r were one m o lecule t h i c k (w ith o u t, i t should be n o te d , r e fe re n c e t o any p a r t ­ i c u l a r s p e c i e ) . T& i n v e s t i g a t e t h i s p o s s i b i l i t y th e y adopted a con­ v e n tio n design ed t o p la c e th e Gibbs s u rfa c e a d is ta n c e o f one mole­ c u l a r t h i c k n e s s below th e p h y s ic a l boundary l a y e r . T his convention th e y termed th e P ^ c o n v e n tio n . I f th e s u rfa c e f ilm i s indeed a mono­ l a y e r , th e n

L

(77)

J

where Ai i s th e a re a /m o le occupied by component ( l ) , and As i s the:, a re a /m o le occupied by component ( 2 ) , in th e s u r f a c e . P h y s ic a l ly t h i s i s p a t e n t l y re a s o n a b le . From e q u a tio n s (7 6 ) and (77) i s o b ta in e d r v(“t

A .r J t N,

N, A, -+

N,A,-e NvAx

(78) I t w i l l be observed t h a t th e fundam ental d i f f e r e n c e between th e s e r 's and th o s e p r e v io u s ly d is c u s s e d l i e s in, th e f a c t t h a t non-therm o­ dynamic d a ta a re n e c e s s a r y f o r t h e i r c a l c u l a t i o n , v i z . th e v a lu es o f Ai and A2 . Such d a ta may be d e riv e d from, f o r example, f il m p r e s s u r e measurements on i n s o l u b l e f i l m s , or from x -r a y d a t a . In th e l a s t r e ­ s o r t th e j u s t i f i c a t i o n : f o r such a p rocedure i s pra g m a tic - a re th e r e ­ s u l t s re a s o n a b le i n 1th e l i g h t o f o th e r knowledge, in which case th e th e o ry s t i l l sta n d s ? o r a r e th e r e s u l t s nonsense? in^;which case th e p a r t i c u l a r h y p o th e s is must be r e j e c t e d . The d a ta c i t e d by Guggenheim and Adam b e a r o u t th e e s s e n t i a l re a s o n a b le n e s s o f t h i s h y p o th e s is . B efore p ro c e ed in g f u r t h e r , i t i s o f i n t e r e s t t o show t h a t th e convention o f Guggenheim and Adam r e a l l y does p la c e th e d iv id in g s u r f a c e one m o le c u lar t h ic k n e s s below th e p h y s ic a l boundary l a y e r . We have, a s b e f o r e , r\- ^ But

= 0 , a s from th e very manner th e Gibbs s u rfa c e i s l o c a t e d ,

no c o n t r i b u t i o n from phase

ot i s p e r m itte d ; hen ce,

nf -

p -

_TL_

Since B i s a d i l u t e v ap o r, 1 0 ^ Tj =

•f

, so t h a t

= th e a c t u a l number o f moles o f i / u n i t a r e a

22

r

1

of su rface. In c o n tin u in g th e work o f H utchinson 47»4,6 th e p r e s e n t i n v e s t i g a ­ t i o n makes use o f s t i l l a f u r t h e r h y p o th e s is a s to th e s t r u c t u r e o f th e s u rfa c e l a y e r . I n t e r f a c i a l t e n s i o n s between w ater and benzene s o l u t i o n s o f lo n g -c h a in a l i p h a t i c a c i d s and a l c o h o l s , a s w ell as e s t e r s , have been d e term in e d . In t h i s case th e aqueous phase may be re g a r d e d , as f a r a s th e s o l u t e i s concerned, as a d i l u t e vapor, owing t o th e extreme i n s o l u b i l i t y o f such s o l u t e s in w a te r; hence th e methods o f Guggenheim and Adam may be employed. But i f one wished to c a l c u l a t e a P ^ , because o f th e a p p r e c ia b le d i s p a r i t y in l e n g th between a m olecule o f benzene and a m olecule o f , say , m y r i s ty l a l c o h o l , one i s c o n fro n te d w ith th e dilemma o f j u s t where to p la c e th e d iv id in g s u r f a c e in o rd e r to s e p a r a te th e assumed monolayer from th e b u lk phase ol (th e benzene s o l u t i o n ) . For i f th e s o l u t e m olecule i s a p p ro x im a te ly v e r t i c a l l y o r i e n t e d in ^ th e f i l m ,

a P ^ w o u ld r e s u l t a p p r e c ia b ly d i f f e r e n t ( e . g . 5-10 $) from th e Plu^ c a l ­ c u la te d i f i t were assumed t h a t th e a l i p h a t i c m olecule i s o r i e n t e d s la n t w i s e or perhaps l i e s f l a t in th e s u r f a c e . Hence from th e v a lu e s o f r M i t should be p o s s i b l e to g a in some id ea a s to w hether o r n o t a p p ro x im a te ly v e r t i c a l o r h o r i z o n t a l o r i e n t a t i o n in such f i l m s i s th e c a s e . To d e r iv e th e a p p r o p r i a t e convention, (which we shal'l now c a l l L.PM to d i s t i n g u i s h i t from th e

o f Guggenheim^ and Adam a s g iv e n hy

-J

e q u a tio n s ( j 8 ) } n o t on ly w i l l d a ta a s to th e c r o s s - s e c t i o n a l a r e a o f th e m o le c u lar s p e c ie s p r e s e n t be need ed , b u t a l s o an e s ti m a te o f th e r e s p e c t i v e le n g th s l± and l g of. th e m o lecules w i l l be r e q u i r e d . This in fo rm a tio n i s a v a i l a b l e and d e t a i l e d c a l c u l a t i o n s w i l l be made l a t e r . The l e n g th l g i s c o n sid e re d t o be th e l e n g th of th e hydrocarbon­ l i k e p a r t o f th e a lc o h o l o r a c i d , th e hydrosqyl or carboxyl group p r e ­ sumed immersed in th e aqueous l a y e r |i . The o b j e c t i o n may be r a is e d t h a t on t h i s m ic ro sco p ic s c a le of o b s e r v a tio n th e p h y s ic a l boundary l a y e r i s indeed i l l - d e f i n e d , and t h a t we a r e n o t j u s t i f i e d in making any such assum p tio n. To t h i s , a n s w e r,may be made t h a t a s t a t i s t i c a l , tim e -a v e ra g e i n t e r p r e t a t i o n o f th e p h y s ic a l boundary l a y e r and th e f r a c t i o n o f a g iv e n m olecule immersed in one phase a s opposed to t h a t in th e o t h e r , i s p rob ab ly n o t u n re a so n a b le . We can say t h a t on th e a v e r a g e , l g of th e s o l u t e m olecule w i l l be e s s e n t i a l l y in th e aqueous l a y e r , o r we can say t h a t th e p r o b a b i l i t y o f f in d i n g a le n g th l g in th e aqueous l a y e r and l g in th e benzene l a y e r i s a maximum. S im ila r ly we can say t h a t w hile th e p h y s ic a l boundary l a y e r i s o f course in p o i n t - t o - p o i n t s p a t i a l f l u c t u a t i o n due to random therm al a g i t a t i o n , y e t th e p r o b a b i l i t y o f i t s e x is t e n c e in some giien p la n e i s c l e a r l y a maximum, and t h a t p la n e we s h a l l term th e p h y s ic a l boundary l a y e r itse lf. I To o b ta in ' th e co n v en tio n ("V* we proceed a f t e r th e f a s h io n o f Guggenheim and Adam. Inasmuch a s i f th e Sibbs s u rfa c e i s p laced a t th e bottom o f th e s o l u t e m olecule (so t h a t t h e l a y e r i s monomolecular w ith r e s p e c t to th e s o l u t e ) t h e r e w i l l be an in c re a s e d number o f m o le c u les o f benzene in th e l a y e r over and above what ivould be p r e s e n t had th e Gibbs s u rfa c e been p la ce d a t th e bottom of th e benzene mole­ c u le . T h e re fo re the a r e a per mole w i l l be e f f e c t i v e l y d e crea se d by th e f a c t o r l ^ / l g ; now i f Ai be th e a r e a o f a benzene m olecule i n . t h t t s u rfa c e and As be t h e a r e a o f a s o lu te m o le c u le, we may th e n w rite

24

r

"i Then by e q u a tio n ( 7 6 ) ,

- r• I^ - r . X-^ we have ,

r n ,t v

p11vx _- N PV vU>)- r vi N^

n

t o

U\

n lO

- h 1.17

1 where

p1' l x ^=p I'U V » 1

(80)

Combining w ith e q u a tio n (79) we r e a d i l y o b ta in . .

p(uV _

>fti k n '.1

(8 l )

f o r th e s u rfa c e c o n c e n tr a tio n o f th e s o l u t e m o lecules on th e assum ption t h a t th e s o lu te m olecule i s v e r t i c a l l y o r i e n t e d w ith th e p o la r group in th e aqueous ph ase. Now th e re a s o n a b le n e s s o f th e r e s u l t s may be su b je c te d to t e s t in th e fo llo w in g manner. We have se e n , e q u a tio n ( 2 6 ) , t h a t

i r \ r r - - p- r

s cc*jx

so t h a t r > ;', P; + c ? h

(82) And we have seen t h a t th e co n vention V p la c e s th e d iv id in g s u rfa c e very n e a r l y a t th e p h y s ic a l boundary l a y e r ; hence we may w r i t e i f '-

c \S

c

(85)

and by i n s e r t i n g a p p r o p r i a t e v a lu e s f o r dx we can see d i r e c t l y w hether or n o t a s h i f t o f th e Gibbs s u rfa c e from th e p h y s ic a l boundary l a y e r a d is ta n c e o f dx c e n ti m e te r s i n t o phase oC c o rre sp o n d in g to a ri (v)' v alu e of th e o rd e r o f magnitude o f 13 w ill r e s u l t in v a lu e s o f P*, in agreem ent w ith v a lu e s o f

c a l c u l a t e d upon th e assum ptions i m p l i c i t

in e q u a tio n (81) a s to th e p h y s ic a l s t r u c t u r e o f th e s u r f a c e l a y e r . In o th e r words, e q u a tio n (81 ) c o n ta i n s extra-thsrm odynam ic assum ptions which may be t e s t e d by com parisonrw ith th e r e s u l t s o f th e p u re ly thermodynamic e q u a t i o n - (85)• I f s u b s t a n t i a l agreement between th e L_

—’

25 F

,

v a lu e s

of

~1

and P ^ i s o b ta in e d , t h i s may be reg ard ed a s confirm ing /

th e model p o s t u l a t e d ; i f v a lu e s o f of

uy PvM,

s u b s t a n t i a l l y exceed th e v a lu e s

i t might be re g a rd ed a s an i n d i c a t i o n o f d i s t i n c t l y t i l t e d or

a c t u a l l y h o r i z o n t a l o r i e n t a t i o n o f th e s o lu te m olecule i n th e s u rfa c e la y e r. The c a l c u l a t i o n s o f Ht', Pl ^ fo llo w th e method o f H utchinson. At c o n s ta n t te m p e ra tu re th e Gibbs a d s o r p tio n e q u a tio n may be w r i t t e n as

-c)< r-

(84) L

Although t h e r e a r e th r e e components in th e p re s e n t system , namely, w a te r , benzene, and s o l u t e , i t can re a so n a b ly be assumed t h a t th e chemical p o t e n t i a l o f w a ter in th e benzene phase i s c o n s t a n t , in which case e q u a tio n (84) re d u c es to

r, dp,

(85)

where t h e s u b s c r i p t ( 2 ) a s alw ays r e f e r s t o th e s o lu te and th e su b s c i r p t ( l ) t o th e s o l v e n t , benzene. Now u s in g th e Gibbs convention r ^ = O, we have

~

(86 )

Once P ^ has been e v a lu a te d , by t h e use o f e q u a tio n (75) P t^ a n d P ^ a r e c a l c u l a t e d ; and by th e use o f e q u a tio n s ( 8 1 ) and ( 8 5 ) >P i^ and P ^ a r e o b ta in e d . S o lu tio n s o f th e c o n c e n t r a t i o n s used cannot be c o n sid e re d a s i d e a l , a s indeed f r e e z i n g p o in t d e p re s s io n measurements in d ic a te , th e y a r e n o t , so t h a t f o r th e s o lv e n t we may w r ite

where g i s th e osm otic c o e f f i c i e n t o f th e s o lv e n t and L

(87) i s th e mole -J

26

r

1

f r a c t i o n o f th e s o lv e n t. From th e Gribbs-Duhem e q u a tio n f o r a b in a ry so lu tio n ,

( 88 ) we o b ta in (89) But f o r th e f r e e z i n g p o in t d e p r e s s io n o f a n o n - id e a l s o l u t i o n we know t h a t

- s where

=

(90)

© = f r e e z i n g p o in t d e p r e s s io n of th e s o lu tio n L = molar h e a t of f u s io n o f benzene a t T0 = 2^5^ c a l./ra o le T0= f r e e z i n g p o i n t o f pure benzene = 5 .4 2 ° 0 89 = 28^.58° K.

The only assumptions made in c o n n ec tio n w ith t h e use o f e q u a tio n (90) a r e ( a ) th e constancy o f L over th e small te m p e ra tu re range

$

(b ) th e v alu e o f g a t th e f r e e z i n g p o in t o f a g iv e n s o l u t i o n rem ain­ in g th e same a t 25° C. Whence H g .L tO = -

(91)

t\ 10

which to g e t h e r w ith e q u a tio n s ( 8 6 ) and ( 8 9 ) y i e l d s

x

" T C LT

^

1

;

Since th e i n t e r f a c i a l t e n s i o n 0" i s determ ined a t s e v e ra l c o n c e n tra ­ t i o n s , and th e f r e e z i n g p o in t d e p re s s io n s o f such s o lu tio n s a r e measured d i r e c t l y o r c a l c u l a t e d by an a n a l y t i c a l e x t r a p o l a t i o n , a l l n e c e s s a r y in fo rm a tio n i s a t hand to c a l c u l a t e

and hence th e o th e r

v a r io u s l \ * s . B e t a i l s o f th e a n a l y t i c a l p ro c e d u res follow ed to e v a lu a te th e d i f f e r e n t i a l c o e f f i c i e n t "Wbfe , a s w ell a s th e method L

o f e s t i m a t i n g Ax , As , I * , and 1 2 w i l l be found in the fo llo w in g

J

27

r

~] c h a p te r on methods. The d e r i v a t i o n and e x te n s io n o f th e Gibbs a d s o r p tio n theoryp re s e n te d up to t h i s p o in t h as been c a r r i e d o u t f o r th e case o f two volume phases b u t o nly a d e ­

fo rm a tio n o f th e s u rfa c e so t h a t i t i s no lo n g e r plane n e c e s s i t a t e s th e a d d i t i o n o f c o r r e c t i v e te rm s . Gibbs shows t h a t ”I t i s always p o s s i b l e t o give such a p o s i t i o n to th e s u rfa c e so t h a t Gi -f Gs s h a l l v a n i s h . ” , and f u r t h e r t h a t t h i s p o s i t i o n ” . . . w i l l in g e n e ra l be s e n s ib ly c o in c id e n t w ith th e p h y s ic a l s u rfa c e o f d i s c o n t i n u i t y . ” He c o n tin u e s , ”Now on a c c o u n t o f th e th i n n e s s o f th e non-homogeneous f i l m , we may always re g a rd i t as composed o f p a r t s which a re approx­ im a te ly p la n e . T h e re fo re , w ith o u t danger o f s e n s ib le e r r o r , we may a ls o cancel t h e term l / 2 (C-L - Cs ) £ (c^ - Qg)” , which re d u c es e q u a tio n (95) ^0 e q u a tio n (57)* In th e case o f th e p la n e s u r f a c e , however, i t i s n o t n e c e s s a r y t o p la c e th e d iv id in g s u rfa c e in any p a r t i c u l a r p o s i t i o n 30 t o e f f e c t th e s i m p l i f i c a t i o n o f e q u a tio n (9 5 )> as th o s e c o r r e c t i o n term s a r e i d e n t i c a l l y z e ro ; th e only r e s t r i c t i o n i s t h a t th e d i v i d i n g s u rfa c e be p a r a l l e l to th e s u rfa c e o f d i s c o n t i n u i t y . In t h a t c a s e , ”We a r e t h e r e f o r e a t l i b e r t y to choose such a

,28 “! p o s i t i o n f o r th e d iv id in g s u rfa c e a s may f o r any purpose be c o n v e n ie n t." I t may be noted in p a s s in g t h a t th e d e f i n i t i o n o f Lewis and R andall 60 f o r s u rfa c e t e n s i o n , -

(T d - il

*

i s n o t s u f f i c i e n t l y g e n e ra l in t h a t they speak o f Cl as a f u n c t i o n of te m p e r a tu r e , n^ . . . n ^ , JX , and P, where F i s th e p r e s s u r e in th e system . This i s n o t i n c o r r e c t f o r a pla n e s u r f a c e , b u t f o r a curved i n t e r f a c e th e p re s s u r e on th e concave sid e i s g r e a t e r th a n th e p r e s s u r e on th e convex sid e 1 , a s indeed was shown e x p l i c i t l y by Gibte' e q u a tio n 5CC: crlc » + O

- Y*- y

(>>5 )

which i f Ci = cs re d u c es to th e f a m i l i a r K elvin e q u a tio n H _ r p 01- p(*

0 f course f o r a plane s u rfa c e

(96) p* = p(* = ,F.

R.G. tolman 97, t r e a t i n g th e case o f a s p h e r ic a l s u rfa c e (where ci = cs , Ox - Gg = C and hence v a n is h e s ) h as worked o u t in d e t a i l th e e q u a tio n ( h i s e q u a tio n 12 . 7 ) f i x i n g th e p o s i t i o n o f th e d iv id in g s u rfa c e such t h a t th e term l / 2 (C^. 4 Cs ) ^ ( c 1

4

c2 ) becomes z e ro . His

e q u a tio n 1 2 .6 g iv e s th e v alu e f o r (T in t h a t s u rfa c e o f t e n s i o n . Both e q u a tio n s a re somewhat complex. The main p o in t i s a g a in th emphasize t h a t i f th e d i s c u s s i o n be n o t con fin ed to a plane s u r f a c e , t h e r e i s no lo n g e r th e p o s s i b i l i t y o f a r b i t r a r i l y s e l e c t i n g some p a rtic u la fc p o s i t i o n f o r th e Gibbs s u rfa c e to s u i t whatever purpose may be in mind. 'The q u e s tio n o f dependence d f i n t e r f a c i a l t e n s i o n on c u rv a tu re i s th o ro u g h ly examined by Guggenheim 36 in h i s t r e a t m e n t o f th e i i n t e r f a c i a l l a y e r a s a volume phase o f t h i c k n e s s T . By i n t e g r a t i n g

LJ

- 29

r

~! d(T-=

from P a t a p la n e s u rfa c e t o P on e i t h e r sid e of a curved

s u r f a c e , he shows t h a t d(T i s n e g l i g i b l e and t h a t 11. . . f c o r r e c t i v e f a c t o r s f o r th e simple equation/X 833 33 , th e fo llo w in g a p p a r a tu s was used (se e f i g u r e ( 8 ) . ) s a r e c t a n g u l a r o p t i c a l c e l l w ith fused Fyrex w a lls ;was

4-5 r

”1 Cr

—-----

i

'th erm o s'tjt Wafter

Hi_o

f i g . (8 ) sup p o rted i n a t h e r m o s ta t a t such a l e v e l t h a t th e th e r m o s ta t w ater d id n o t re a c h th e to p o f th e c e l l , which remained open e x c e p t f o r a l o o s e l y - f i t t i n g cardb oard cover d esig n e d to p ro v id e a t l e a s t p a r t i a l p r o t e c t i o n from a tm o sp h eric d u s t . F^rex tu b e s o f v a r io u s dim ensions ( i n n e r d ia m e ter a b o u t 2 cm. f o r most o f th e work) were sup po rted w ith t h e ground end d ip p in g below th e s u r f a c e o f th e c o n d u c ti v ity w ater c o n ta in e d in th e o p t i c a l c e l l . The tu b e was c lo se d a t th e to p w ith a l o o d e l y - f i t t i n g g l a s s cap t o ex clu d e d u s t and minimize e v a p o r a tio n o f th e s o lv e n t benzene d u rin g a ru n . V e r tic a l o r i e n t a t i o n o f th e tube was checked by means o f a plumb l i n e , ^he benzene s o l u t i o n o f th e p a r t i c u l a r s o lu te ( a c i d , a l c o h o l , o r e s t e r ) a t th e s p e c i f i e d mole f r a c t i o n was p i p e t t e d slow ly down t h e i n s i d e o f th e tube u n t i l a bubble o f t h e s o l u t i o n . e x h i b i t i n g a d e f i n i t e maximum d ia m e te r was o b ta in e d . P ro v id in g such a maximum dia m e ter e x i s t s , t h e t o t a l bubble s i z e i t s e l f does n o t in f l u e n c e th e c a l c u l a t e d v a lu e s o f t h e i n t e r ­ fere i a l t e n s i o n , n e i t h e r does t h e d ia m e ter o f t h e tu b e employed. The dim ensions h and r o f th e bubble were measured w ith a t r a v e l l i n g m icroscope re a d in g d i r e c t l y t o C.0C1 cm. and p e r m itti n g ready e s t i ­ m ation t o 0.0001 cm. I t should be noted in t h i s c o n n ec tio n t h a t r need n o t be measured a s p r e c i s e l y a s h (a lth o u g h t h i s was done) a s i t e n t e r s in to t h e c a l c u l a t i o n s o n ly a s a c o r r e c t i o n term . The ^ f i n a l v a lu e s o f b o th h and r r e s p e c t i v e l y f o r a g iv e n bubble were

46 "1 ta k e n a s th e average o f a t l e a s t f o u r in depen dent r e a d in g s o f each , u s u a l l y some t e n to f i f t e e n m in utes 10 a f t e r fo rm a tio n o f th e bubble. The th e r m o s ta t window between th e bubble and th e m icroscope c o n s is te d o f an o p t i c a l f l a t , th u s a v o id in g d i s t o r t i o n o f th e image. The e n t i r e a p p a r a tu s was su p po rted on a fir m sto n e bench. A slow r a t e o f a g i t a ­ t i o n was provided in th e t h e r m o s ta t by an independently-m ounted m o to rs t i r r e r . With th e s e p r e c a u t i o n s , v i b t r a t i o n s as a source o f e r r o r were a p p a r e n tly e l i m i n a t e d ; o b s e r v a tio n o f th e drop th ro u g h th e microscope d id n o t r e v e a l any d i s tu r b a n c e o f th e s u r f a c e . The te m p e ra tu re was m a in ta in ed a t 2 5 .CO ± 0 .0 1 ° 0. f o r most o f th e work, b u t f o r a few c a s e s i t was h e ld a t 4 0 .0 0 ± 0 ,0 5 ° C. To measure r (o r r a t h e r th e diameter 2 r ) th e microscope was mounted in a p o s i t i o n f o r h o r i z o n t a l t r a v e l , th e bubble illu m in a te d from th e r e a r by d i f f u s e d l i g h t p a s s in g th ro u g h th e o r d in a r y therm o­ s t a t window, and i n n t h i s manner t h e bubble was s h a rp ly s i l h o u e t t e d , p e r m i t t i n g ready d e te r m in a tio n o f th e maximum d ia m e te r. I m t h e measurement o f h , somewhat more d i f f i c u l t y i s e n c o u n te re d . With th e m icroscope mounted in i a p o s i t i o n f o r v e r t i c a l t r a v e l (checked by a small s p i r i t l e v e l ) , re a d in g s must be ta k e n on th e apex o f th e bubble and a l s o upon t h e e q u a to r l i n e o f th e bubble a s re v e a le d by th e sharp a s t i g m a t i c image o f a sm all ( l x 0 .5 cm.) l i g h t source about t h r e e f e e t behind th e m icroscope b u t on th e same l e v e l a s th e bubble 8 3 . I t i s o bvious from f i g . (9 ) t h a t th e p o s i t i o n o f th e maximum d ia m e ter ( i . e . t h e e q u a to r ) B and th e apex A a r e n o t in th e same f o c a l plane

w ith r e s p e c t to th e m icroscop e. R efocu ssing i s o u t o f th e q u e s ti o n , a s th e l a t e r a l p la y in th e f o c u s s in g a d ju stm e n t i f th e r e t a i n i n g c o l l a r were loosened would be o f r e l a t i v e l y l a r g e magnitude and th e extreme acc u ra cy n e c e s s a ry f o r th e measurement o f h would be u t t e r l y l o s t . The d i f f i c u l t y was overcome by cementing a g l a s s p l a t e f l a t upon th e s u r f a c e o f t h e bench in f o r n t o f th e t h e r m o s t a t ’s o p t i c a l g l a s s window, and h a v in g l i g h t l y l u b r i c a t e d th e s u rfa c e o f th e g l a s s p l a t e , s l i d i n g th e m icroscope b o d ily to and f r o th e n e c e s s a ry c e n tim e te r o r so t o allow sharp fo c u s s in g uponr.A and B, w ith o u t d i s t u r b i n g th e f o c u s s in g a d j u s t ­ ment o f th e m icroscope i t s e l f S3. Upon s e v e ra l o c c a s io n s a bubble was viewed from d i f f e r e n t p o s i t i o n s o f th e m icroscope onnthe g l a s s p l a t e and i n v a r i a b l y i d e n t i c a l v a lu e s o f h were o b serv ed ; hence i t would a p p ea r t h a t no s e n s i b l e e r r o r was in tro d u c e d by t h i s d e v ic e . Before each d e te r m in a tio n t h e o p t i c a l c e l l and tu b e were cleaned w ith a c e to n e , r i n s e d , f i l l e d w ith c o n c e n tra te d n i t r i c a c id and allowed t o s ta n d a t l e a s t h a l f an h o u r, th e n th o ro u g h ly r in s e d w ith d i s t i l l e d and f i n a l l y c o n d u c ti v ity w a te r . Gaddum’s m o d if ic a tio n 88 o f t h e drop-volume a p p a r a tu s was em­ ployed t o d eterm in e th e i n t e r f a c i a l t e n s i o n by t h i s method. A two ml. s y rin g e was f i r m l y mounted t o a micrometer i n 1such a manner t h a t th e p lu n g e r o f th e m icrom eter o p e ra te d upon th e p i s t o n o f th e s y rin g e .

48 r The m icrom eter could be re a d d i r e c t l y t o 0.001" and 0.0001" could e a s i l y be e s ti m a te d , so t h a t th e volume o f l i q u i d e x p e lle d from th e s y rin g e t i p could be e s tim a te d t o ± 0.0001 cc. The g l a s s t i p o f th e s y rin g e i t s e l f was used a s th e d ro p -form ing t i p , b ein g i n s e r t e d , when th e a p p a r a tu s was assem b led, j u s t below t h e l e v e l o f th e benzene s o lu ­ t i o n c o n tain ed i m a n a t t a c h e d v e s s e l . The whole p e rm itte d ready therraos t a t i n g . The volurrje d e liv e r e d by th e a p p a r a tu s p e r inch o r f r a c t i o n t h e r e o f on t h e m icrom eter was determ ined by w eighing the) amount o f a i r - f r e e (by b o i l i n g ) d i s t i l l e d w ater e x p e lle d a t 25° C (o r 40° C .) . Since th e t i p o f th e s y rin g e i s n o t ground p e r p e n d i c u l a r l y , b u t h as a s l i g h t b e v e l, th e v a lu e o f r could n o t be measured d i r e c t l y w ith s u f f i c i e n t a c c u ra c y . I t was t h e r e f o r e found n e c e s s a ry t o c a l c u l a t e a v a lu e o f r in th e fo llo w in g manners th e i n t e r f a c i a l t e n s i o n

between

c o n d u c ti v ity w ater and C.P. d i s t i l l e d benzene was determ ined by th e s e s s i l e bubble method and fou$d t o be 54*68 dynes/cm. a t 25° (a s compared to 54.71 dynes/cm. a t 25° from I.G .T . d a t a ) ; e q u a tio n (129) was r e - a r r a n g e d t o y i e l d

Ethyl Caprylate

12 = 10.06 & cXT c>©

N8

C

F

0.01007 e

0.11125

0 .8 0

0 .7 6 9

-0 .9498

0.02517s

0.27284

1 .5 9

1.805

0.0 5 0 ^8 !

0.52995

2.77

0 .075153

0.76855

0 .1 0 0 6 !

V!

v8

-0.00266

89.47

200.56

-0 .7 5 4 4

-0.00261

89.47

200.51

5 .6 0 0

-0 .4 8 5 8

-0.00254

8 9 .4 9

200.26

5 .7 4

5 .585

-0 .5 7 5 5

-0.00247

8 9 .4 9

0,99977

4 .2 0

7 .2 2 9

- 0 .5188

-0.00241

8 9 .5 0

200.19 200.14

0 .1 2 4 7 5

1.20757

4*67

9.115

-0 .2928

-O.CO255

89.51

200.10

0 .1 5 1 0 e

1.59905

5 .5 2

10.957

-0 .2 8 1 0

- c . 00229

8 9 .5 2

200.04

0.1755*

1.61169

5.7 8

12.755

-0 .2 7 5 5

- 0.00225

8 9.55

199.99

0 .1 9 9 9 i

1.79121

6 .5 0

14.551

-0.2728

-0.00218

89 .5 5

199.95

0 .2 5 0 2 9

2.15651

7.5 1

18.296

-0 .2 7 0 9

-0.00208

8 9 .5 5

199.87

0* P018 9

2.45770

7 .8 5

2 2 .1 8 0

-0 .2 7 0 5

-0 .0 0 1 9 9

89 .5 6

199.79

r f

a

r (gV

1%

r* 0'

. \t>A r (gVc

n(uV

1X

r* *

A

0.2 5 6

0.255

0 .2 5 0

0.506

O . 56I

0.417 ’ 0 .5 6 9

0.554

4 6 9 .0

0.501

0.488

0.475

0.609

0 .7 4 6

0 .8 8 2

0.771

0.756

225.6

0.678

0.644

0.606

0.871

1.156

1.401

1.199

1.154

146.4

0 .8 0 2

0.7 4 2

0.679

1.447

1.464

115.4

0.848

0.754

1.754

1.851 2.254

1.556

0 .9 4 5

1.065 1.254

1.918

1.804

92 .0 5

1.105

0.965

0.856

1 .4 4 0

2.0 4 4

2.647

2.267

2.156

7 7 .7 5

1.522

1.122

0.946

1.646

2.545

5.045

2.666

2.520

65.89

1 .5 5 0

1.278

1.0 5 0

1,856

2.6 6 2

p .468

5.057

2.881

5 7 .6 5

1.8 0 2

1,442

1.157

2.948

5.844

5.405

5.245

5 1 .2 0

2 .5 9 0

1.792

1.5 7 0

2.055. 2.458

5.506

4.5 7 4

4.147

4.001

4 1 .5 0

5 .0 9 2

2.159

1.574

2.805

4 .0 5 2

5.261

4 .8 7 9

4.727

5 5 .1 5

L

J

0 .0 0

_

3

c l g

_

_________________________________ :—

y

. o

a

a i9

o

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o

120

r A s s o c ia tio n Data from F re e z in g P o in t D ep ressio n M easurem ents: ( l ) L au ry l a lc o h o l:

x2

0

Ms

Ms/Mo

K

0.C0818

0.556

0.00816

185.19

0 .9 9 4

0.01599

0.889

0.01552

220.96

1 .1 8 6

15.74

0.02576

1.199

0.01820

265.72

1.426

25.41

0.C60C5

2.018

C .05054

577.85

2.028

55.66

0.08055

2.467

0.05728

4 2 1 .4 2

2.262

55.84

0.10105

2.898

0.04570

4 5 8 .5 6

■ 2 .4 6 0

55*41

0.12059

5.529

0.05012

485-55

2.594

5 1 .8 0

0.257

(2 ) Q a p ry lic a c i d :

Xs

0

Ns

0.00252

0.095

0.00145

0.00505

0.199

0.00504

0.01005

0.558

0.02011

Mg

Mg/Mo

K

250.62

1.758

508.8

1.664

218.4

0.00546

259.97 266.76

1 .8 5 0

155.6

0.754

0.01118

261.75

1.815

7 2 .8 9

2154

0.05001

1 .0 8 0

0.01642

267.29

1.855

51.98

2424

0.05045

1 .8 0 0

0.02728

275.18

1.894

52.78

0.08054

2.952

0.04452

270.59

1.875

1 9 .6 5

0.10004

5.7 1 0

0.05576

275 .5 0

1.895

15.82

0.11958

4 .5 0 0

0.06744

270.84

1.878

15.02

0.14027

5.524

0.07950

272.45

1.889

11.18

0.16111

6 .2 5 2

0.09500

270 .1 0

1.875

9 .5 9

L

K_

1926

-8 0 .1 2

1258 857 -51

-2 .0 7

J

121 1

*RaVvo o f ^ p p a r e n t t b

theoretical mbleu-lar uieigM; \*\

Wv\xe,*\c Solution'. O caprvjUc Bci34>54 ,57.,64,67,78

in c o rp o ra tin g v a rio u s

m o d if ic a tio n s b u t e s s e n t i a l l y o p e ra tin g upon t h i s p r in c ip le have been d e sig n e d . With t h i s a p p a ra tu s b o th th e s u rfa c e p re s s u re and th e a re a per m olecule a re d i r e c t l y m easured. I t i s o b v io u s, how ever, t h a t such a method can n o t be used to o b ta in F and A f o r film s formed by a d s o r p tio n from s o lu tio n . P o ck els 8 1 , in h e r im p o rta n t p io n e e r work upon in s o lu b le f i l m s , m easured th e d im in u tio n o f th e s u rfa c e te n s io n o f w ater a t v a rio u s film a r e a s determ ined by th e p o s it io n o f moving b a r r i e r s . Here a g a in A i s d i r e c t l y o b s e rv a b le , b u t n o t F; f o r th e l a t t e r i t i s a p p a re n t t h a t F = (T 0 - CT , where b u t a c tu a lly /d e c r e a s e s s u rfa c e a c t i v i t y by sm all b u t d e f i n i t e am ounts. For exam ple, from th e smoothed 4 >13 Cne may ta k e th e a s s o c ia ti o n f a c t o r a t a k in k to be e i t h e r th e concen­ t r a t i o n r a t i o c x /cg o r th e d e n s ity r a t i o pjp/j^y * Both liq u id - v a p o r and l i q u i d - 1 iq u id system s e x h ib i t s im ila r phenomena: b o th have a c r i t i c a l p o in t, b o th show o p a le sc e n c e and have a f l a t m eniscus in th e c r i t i c a l r e g io n , bo th u s u a lly fo llo w th e r e c t i l i n e a r d ia m e te r law o f C a i l l e t e t t-

J

165 rand M athias (which may be a z ig -z a g' l i n e due to k in k s in .,th e p a ra b o la ,- n r a t h e r th a n a s t r a i g h t l i n e 4 ). The problem a ss ig n e d to th e w r i te r was tw o -fo ld i f i r s t , to confirm th e ap p earan ce o f f l u c t u a t i o n s a s p r e d ic te d by, Bridgman, and second, to e s t a b l i s h th e p re sen c e and p o s itio n o f d i s c o n t i n u i t i e s in some p r o p e r tie s o f c e r t a i n l i q u i d - l i q u i d system s. The system f i r s t in v e s t ig a te d was t h a t o f iso-am yl a lc o h o l and w a te r. Over a p e rio d o f s e v e ra l m onths, d a ily d e te rm in a tio n s o f th e d e n s i t i e s and s u rfa c e te n s io n s o f each o f th e two l a y e r s , and th e i n t e r ­ f a c i a l te n s io n .b e tw e e n th e p h a se s , were made. One such system was ex­ posed to th e d i r e c t r a d i a t i o n from 5^0 mg. o f radium , a n o th e r such system was k e p t a t a d is ta n c e o f ab o u t s ix f e e t and s h ie ld e d by over two cm. o f le a d . A fte r a b o u t fo u r m onths, th e radium was e n t i r e l y r e ­ moved fro m 'th e la b o r a to r y and o b s e r v a tio n s on b o th system s c o n tin u ed f o r an o th e two m onths. D e n s i ti e s , c o rre c te d f o r a i r buoyancy, were d eterm in ed by th e use o f c a l i b r a t e d 25 m l. pycnom eters. S u rface and i n t e r f a c i a l te n s io n s were d eterm in ed by th e c a p i l l a r y r i s e method (c o r r e c te d f o r c u rv a tu re o f th e m en iscu s, assum ing a s p h e r ic a l sh a p e ), th e r a d iu s o f th e c a p i l l a r y h av in g been c a lc u la te d from th e w eight o f m ercury d e liv e re d p e r u n i t le n g th . O.P. iso-am yl a lc o h o l and d i s t i l l e d w ater were used a s such w ith o u t f u r t h e r p u r i f i c a t i o n . Both system s were in d iv id u a lly th e rm o s ta te d a t 5 ^ .0 0 ± 0 .0 1 ° 0. S u rface and i n t e r f a c i a l te n s io n s were c a lc u la te d from

13 w herein th e c r i t i c a l d a ta was re p o rte d to be 6 8 .5 ° a t

p h e n o l, can no lo n g e r be re g a rd ed as

a c c u r a te .

L

J

167

r

In t h i s c a s e , d e n s i t i e s and s u rfa c e te n s io n s were a ls o o b ta in e d

a t th e r e s p e c tiv e s o lu tio n te m p e ra tu re s on th e , o r ig i n a l sam ples o f s o lu tio n . Here a g a in a p l o t o f d e n s ity v s. s o lu tio n te m p e ra tu re r e ­ s u lte d in a smooth p a ra b o la so t h a t a R e c tilin e a r d ia m e ter p lo t o f J5! + ^ 2/2 v s. te m p e ra tu re i s very n e a r ly l i n e a r The d a ta a re ta b u la te d a t th e end o f th e c h a p te r. In c o n c lu sio n i t may be s a id t h a t th e ev id en ce c o lle c te d in t h i s stu d y do n o t te n d to su p p o rt A n to n o fffs th e o r i e s in a c o n c lu s iv e m anner, e i t h e r w ith re g a rd to f l u c t u a t i o n s in p r o p e r t i e s , o r d i s c o n t i n u i t i e s in p r o p e r tie s o f liq M d sy stem s. That i s to sa y , any anomalous b e h a v io r observed by th e w r ite r i s f e l t to be n o t s u f f i c i e n t l y g r e a te r th a n a re a so n a b le e s tim a te o f e x p e rim e n ta l e r r o r to allo w one to a s s e r t w ith c o n fid e n ce t h a t such e f f e c t s a re indeed r e a l . P erhaps more re f in e d te c h n iq u e s m ight d is c lo s e th e p re se n c e o f such f l u c t u a t i o n s o r d i s ­ c o n t i n u i t i e s - a lth o u g h th e u n lim ite d e x te n s io n o f t h i s l i n e o f re a s o n ­ in g could e v e n tu a lly le a d to a

r e d u c tio ad absurdum inasmuch a s th e

very concept o f d e n s ity o r s u rfa c e te n s io n o f a li q u i d can have o n ly s t a t i s t i c a l m eaning. The p o in t i s t h a t , a t l e a s t down to th e l i m i t s in d ic a te d in n t h i s c h a p te r ,

th e d a ta do n o t , in th e o p in io n o f th e

w r i t e r , p r e s e n t unambiguous s u b s t a n t ia t io n o f th e views espoused by A n to n o ff.

L

J

168 System a n i l i n e + p -iso am y len e N - mole f r a c t i o n a n i l i n e , T = s o lu tio n te m p e ra tu re , °G. N 0.1291

T c a . —2.70

N

T

0 .5970

1 4 .7 0

0.1624

4 .0 1

0.4091

1 4.96

0.1 7 8 0

5 .1 0

0.4228

1 4 .9 0

0.18^6

6.01

0.4294

1 4.92

0.2056

7.8 7

0.4511

1 4 .8 2

0.2521

9.91

0.4517

1 4.89

0.2454

1 0 .8 0

0.4526

0.2520

11.09

0.4420

14.75 1 4 .9 0

0.2765

12.05

0.4517

14.98

0.2768

1 2 .2 0

0.4521

1 4 .9 0

0.2785

12.69

0.4554

1 4.89

0 .2 7 9 0

12.59

0 .4 6 4 0

14.95

0.2858

15.05

0.4848

1 5 .0 0

0.2898

12.70

0.4886

15.05

0.2908

12.71

0.4905

1 5 .1 0

0.2947

12.91

0.4957

14.99

0.5021

15.10

0.4998

15.15

0.5045

15.00

0.5220

1 5 .1 0

0.5061

1 5.55

0 .5 5 4 0

14.98

0 .5 1 5 0

15.55

0 .5 5 6 0

14.86

0.5261

15.87

0.5672

1 4 .7 2

0.5562

14 .2 0

0.5804

14.28

0.5500

l4.G 2

0.6102

15.74

C.5529

0.6248

15.12

0.5556

14.09 14.24

0.6447

12.51

0.5564

14.15

0.6595

11.64

0.5698

1 4 .4 2

0.6665

11.19

0 .5 7 4 0

14.51

0.6685

11.09

0.5 7 5 0

14.46

0.7152

7 .5 8

C.5788

.14.59

0.7557

5 .5 0

0.5828

14.49

0 .7492

5.68

0.5856

1 4 .5 0

0.7847

-1 .8 6

169 % stem

a n i l i n e + |i-iaoam ylene

N =: inole f r a c t i o n r i a n i l i n e , % - w eight p er c e n t, a n i l i n e , T = e stim a te d s o lu tio n te m p e r a tu r e ,° C ., J3 = d e n s ity a t l6 ° 0 , d e n s ity a t T°C .,