Critique of Diffuse Double Layer Models

8/3/2019 Critique of Diffuse Double Layer Models

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Vol. 45, No. 4, 1997 Critique of double layer models 599

are commo nly described in terms of the predictions ofDLVO theory. In most cases, long-r ange forces do notneed to be invoked to satisfactorily explain adsorptionprocesses, but it will be shown that for processeswhere long-range forces are involved, such as colloid-al dispersion, electrostatic attraction provides the mostacceptable explanation, in contradiction to the DLVOmodel. Adsorption behavior of mineral surfaces canusually be understood in terms of simple mass actionprinciples and coordination chemistry without invok-ing diffuse double layer models.

A BRIEF HISTORY OF DLVO ANDALTERNATIVE (ELECTROSTATIC

ATTRACTION) THEORIESThe DLVO version of the diffuse double layer the-

ory, in which the electrical force in clay dispersions isassumed to be repulsive at all interparticle separationsbeyon d the primary energy min imum, yet aggregationis consider ed the thermodyn amical ly favored state, ispresently accepted by most colloid scientists. Thismodel was championed by Verwey and Overbeek(1946), although it is clear from the paper and thepublished general discussion following the paper thatOverbeek considered the actual origin of the repulsionto be at least partly osmotic (generated by entropy as-sociated with the counterions). In direct opposition,Langmuir and several others argued that the attractiveforce was of electrostatic origin (Langmuir 1938; Lev-ine 1946; MacEwan 1948; Norrish 1954) and that theoverall force could change from attractive to repulsivedue to osmotic forces once the clay plates separatedby more than some distance (suggested by MacEwanand Norrish, based upon their clay studies, to be onthe order of 10-30 ,~). Neither Langmuir nor Mac-Ewan believed that the attractive van der Waals forcewas important in clay-water systems, arguing that itcould not operate in water over the distances necessaryto explain particle-particle attraction. Levine (1946)main tai ned that the Verwey--Overbeek model had notconsidered the rearrangement of counterions thatwould automatically result from double-layer overlap,and that the chemica l potential, Ixi, of the counterio nswould depend on R, the particle separation distance.In effect, a merging of double layers upon particleapproach would cause redistribution of counterionsinto a single layer, and an attractive electrostatic forcewould result (Langmuir 1938; MacEwan 1948), withthe repulsiv e force ori ginating in the osmotic force ofthe counterions. The DLVO theory is unable to con-sider the counterions as mobile species that can adjusttheir positions to minimize free energy as interparticledistance is altered. Therefore, only at large particleseparations, where diffuse double-layer overlap issmall, could this model be expected to produce a goodapproximation of the potential energy. Modem simu-lation studies utilizing the Monte Carlo technique ap-

pear to support Langmuir's belief, predicting that theswelling pressure of clays always has an a t t r a c t i v eelectrostatic compone nt (Guldbra nd et al. 1984; Kjel-lander et al. 1988). Nevertheless, for clays with smalllayer charge and mo nova lent counterio ns, this attrac-tion is overcome by the osmotic (entropic) contribu-tion. In any event, the co ntribu tion of van der Waalsdispersion forces to attraction between particles canonly be estimated, and a recent study in dicates that theaccuracy with which the Hamaker con stant for silicate-water systems is known may be quite low (Ackler etal. 1996).

Langmuir (1938) considered the electrostatic con-tribution to the force betwee n particles as separatefrom the osmotic contribution, as do modern physical-chemical treatments of the system. He used the De-bye-Huckel electrolyte theory to argue that cationswould be free to distribute around the macro-anions(particles), and the electrostatic force would be attrac-tive at all particle-particle distances. Verwey and Ov-erbeek (1946) stated that this result was in error as aresult of his "use of the linear Debye -Huck el approx-imation". (Note that the Debye-Huckel theory is de-rived assuming that the ionic interaction energies areweaker than the thermal energy, kT, and therefore canonly be applied to quite dilute ionic solutions, equiv-alent to large average particle-particle separations).The Verwe y-Overbe ek model, on the other hand, cal-culated the force between the plates due to the elec-trical interaction of static double layers. It predicted arepulsive potential at intermediate separations, with adeep primary minimum of potential energy at closeparticle approach, and a shallow min im um at large dis-tances which was a consequence of assuming the ex-istence of a long-range van der Waals force. This po-tential energy function was used to explain the kineticstability of colloidal dispersions, predictin g a large po-tential barrier to coagulation in dilute electrolytes.

The Langmuir concept of long-range electrostaticattraction has been revitalized by the electrostatic in-teraction theory of Sogami (Sogami 1983; Sogami andIse 1984; Smalley 1990). The attractive electrostaticmodel of dispersions is supported by observations thatparticles in stable dispersions do not necessarily oc-cupy all of the volume of the solution as would beexpected from the long-range repulsive force of theDLVO model, but rather tend to cluster at separationsthat are not space-filling (Ito et al. 1994; Dosho et al.1993).

The concept of an attractive interaction can be il-lustrated in a simple way by comparing the electro-static interac tion betwe en 2 clay plates for differentsimplified geometric arrangements of counterions. Ifthe counterions are grouped along the midplane be-tween plates (Figure la), an attractive interactionclearly results (van Olphen 1977), somewhat analo-gous to the net attraction resulting from the arrange-


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600 McBr ide C l a y s a n d C l a y M i n e r a l s+

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F i g u r e 1 .b dD i a g r a m s o f a l t e r n a t i v e s i m p l i f i e d v i e w s o f c o u n t e r i o n d i s t r i b u t i o n s b e t w e e n l i k e - c h a r g e d p l a t e s .


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Figure 2. Electrostatic attraction (Sogami) model of electri-cal potential as a function of distance, x, between 2 clayplates.

ment of Na and C1- ions in a cubic array to fo rmNaC1 crystals. The lattice energy calculated from theBorn -Lan de equation is negative, indicating a net at-tractive electrostatic energy despite the greater ionicrepulsion in the crystal. In other words, the electro-static energy t erm favors the crysta llizatio n of NaC1from ions separated by large distances in solution.Similarly, the arrang ement depicted in Figure la low-ers its electrostatic energy as the 2 plates are broughtcloser together. Total collapse is prevented i n real claysystems by hydration and osmotic forces.

If, in contrast, the counterions are depicted as as-sociated with their respective layers (Figure lb), theelectrostatic energy of the system could be evaluatedin terms of the intera ction betwee n 2 dipoles andwould be repulsive (van Olphen 1977). However, thisarrangement is not reasonable once diffuse double lay-ers beg in to interact, since indi vidua l cations are freeto change to positions that lower the free energy ofthe system. Thus, the less-ordere d counter ion arrange-ment in Figure lc may be more realistic. Calculatingthe electrostatic energy for the arrangement depictedin Figure lc is more involved, but statistical mechan-ical calculations by Sogarni and others show that theelectrostatic component of the overall free energy isoften attractive (Guldb rand et al. 1984; Engstr6m etal. 1985; Ise 1986; Sogami et al. 1992). Because forcesare balanced across the midplane, some have arguedthat "on the average, the electr ical field generated byone half of the lamellar systems is zero at the positionof the other hal f" (Guldb rand et al. 1984), and noelectrostatic attraction between the plates can exist onaverage. Thus, attraction could only result from dy-namic processes in which the counterio ns influe nce thepositions of one another. In this way, Kje lland er et al.(1988) have explained the restricted swelling ofCa(II)-smectites by a fluctuating electrostatic forcewhose time-averaged value is attractive. Although thisforce could be important, the lack of a net electrostaticinteract ion across the midp lane is not evidence that theplates are not attracted or repelled. Thus, in Figure la,

brin ging the plates closer together lowers the electro-static energy of the system because the cation-plateattractive energy term increases to a greater extentthan the c ation- cation repulsive energy term.

The traditional approach in DLVO is to considereach charged plate with its counterions as a single en-tity, which then possesses a negative electrical poten-tial that decays with distance from the plate surface.Thus, if 2 plates approach (see Figure ld), the poten-tials at the midp lane are assumed to be additive as longas the interaction is weak, and the repulsive pressureis given by (van Olphen 1977):

p = 2nkT(cosh %if m - - 1) (1)where ~m is the mid-plane potential, and n is the

ion concentration in the external solution (assuming a1:1 electrolyte). This equation originates from the De-bye-Hiickel theory of osmotic pressures (Langmuir1938), so that the swellin g pressure in the DLVO the-ory is clearly a consequence of the osmotic force ofinterlayer cations. In this regard, there is no subs tan-tive disagreement between the electrostatic attractiontheory of Sogami and the DLVO theory regarding thenature of the repulsive force. However, the Sogamitheory differs from DLVO in that the situation de-picted in Figure ld would result in an electrostaticattraction (at least for highly charged particles), as thecounterions are restricted to a reduced volume due totheir interaction with the particles (Ise 1986). Themodel predicts that the electrical potential betweenclay plates is lower than that external to the plates, asshown diagrammatically in Figure 2, causing an elec-trical interparticle attraction.

SWELL/NG AND SHORT-RANGEFORCES IN COLLOIDS

The DLVO theory fails to account, even qualita-tively, for the short-range interactive behavior of hy-drated clay particles. Smalley (1990) has argued thispoint persuasively, noting that DLVO theory, becauseit assumes the interparticle attractive force to be theshort-range van der Waals force, predicts a primaryenergy mini mum that is lower than the secondary min-imum. If this were true, clays already in the aggregatedstate (such as dry clay powders) could not spontane-ously disperse in water. The fact that many clays dospontaneously disperse in water is probably the con-sequence of the strong short-range hydration forcesthat are clearly non-DLVO in character (Christenson1988). These forces extend beyond 10 A at mica sur-faces (Pashley 1981; Israelachvili 1985). In addition,osmotic forces contr ibute to swelling well beyond the10-A range.

Empirical evidence that the short-range interactionin layer silicate clays has an attractive electrostaticcontribu tion is convinc ing. The fact that, when thenegative layer charge of smectites is increased upon


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602 McBr ide Clays and Clay Minerals

c h e m i c a l r e d u c t i o n o f s t r u c t u r a l F e ( I I I ), th e r e i s a d e -c r e a s e d t e n d e n c y o f t h e c l a y to s w e l l i n w a t e r ( L e a ra n d S t u c k i 1 9 8 9 ), i m p l i e s t h at t h e o v e r a l l s h o r t -r a n g ee l e c t r o s t a ti c f o r c e o f t h e c l a y p a r t i c l e - c o u n t e r i o n s y s -t e m i s a t t r a c t i v e . I t i s w e l l k n o w n t h a t N a + - s m e c t i t e sw i t h r e l a t i v e l y l o w l a y e r c h a r g e t e n d t o e x p a n d m o r ef r e e l y i n w a t e r o r e l e c t r o l y t e s o lu t i o n s t h a n t h o s e w i t hh i g h e r l a y e r c h a r g e, a l t h o u g h l o c a t i o n a s w e l l a s m a g -n i t u d e o f s t r u c t u r a l c h a r g e i s i m p o r t a n t ( S l a d e e t a l .1 9 9 1 ) . A g a i n , i t is d i f f i c u l t t o r a t i o n a l i z e t h e s e o b s e r -v a t i o n s u n l e s s t h e e l e c t r o s t a ti c f o rc e b e t w e e n c l a yp l a t e s i n a q u e o u s s o l u t i o n s i s a t t r a c t i v e , a t l e a s t a t r e l -a t i v e l y s m a l l s e p a r a t i o n d i s t a n c e s . A t s p a c i n g s m u c hb e l o w 5 0 / ~ , a r e p u ls i v e f o r c e b e t w e e n h y d r a t e d m i c ap l a t e s h a s b e e n m e a s u r e d , a n d a t t r i b u te d t o s h o r t - ra n g eh y d r a t i o n e f f e c t s ( P a s h l e y 1 9 8 1 ; I s r a e l a c h v i l i 1 9 8 5 ;C h r i s t e n s o n 1 9 8 8 ) . T h i s f o r c e i n c r e a s e s w i t h i n c r e a s -i n g e l e c t r o l y t e c o n c e n t r a t i o n , a f a c t i n c o n s i s t e n t w i t hD L V O . A l t h o u g h t h e s e s h o r t - ra n g e i n t e r a c ti o n f o r c e sa r e c l e a r l y n o n - D L V O i n o r i g in , t h e y a r e n o t d e fi n i t iv ei n t e s t i n g c o n t i n u u m t h e o r i e s s u c h a s D L V O a n d S o -g a m i b e c a u s e t h e a s s u m p t i o n s i n h e r e n t i n t h e s e t h e o -r i e s b r e a k d o w n a t s h o r t s p a c i n g .

E x p e r i m e n t a l ly , i t m a y b e p o s s i b l e t o p r o v i d e s o m ef u r t h e r i n s i g h t i n t o th e n a t u r e o f th e f o r c e s c a u s i n g a n dr e s t r i c ti n g c l a y s w e l l i n g b y o b s e r v i n g e f f e c t s o f e n v i -r o n m e n t a l f a c t o r s s u c h a s t e m p e r a t u r e a n d p r e s s u r e .W i t h i n th e r a n g e o f " c r y s t a l l i n e " c l a y e x p a n s i o n , t h a ti s , d ( 0 0 1 ) s p a c i n g < - 2 0 /~ , it h a s g e n e r a l l y b e e n a c -c e p t e d t h a t t h e o p p o s i n g f o r c e s a r e h y d r a t i o n o f i n t e r-l a y e r c a t i o n s a n d s u r f a c e s ( r e p u l s i v e ) a n d e l e c t r o s t a ti ca t t r a c t i o n a c r o s s c h a r g e d p l a t e s ( K i t t r i c k 1 9 6 6 ) . B o t ha r e s t r o n g f o r c e s , a n d n e i t h e r i s e x p e c t e d t o b e i n f l u -e n c e d b y r e l a t i v e l y s m a l l te m p e r a t u r e o r p r e s s u r ec h a n g e s . T h u s , t h e o b s e r v a t i o n t h a t c h a n g i n g t h e t e m -p e r a t u r e f r o m 1 0 t o 7 0 ~ h a d n o i n f l u en c e o n t h ed ( 0 0 1 ) s p a c i n g o f e i t h e r C a ( I I ) - m o n t m o r i l l o n i t e ( 1 9 .5/ k ) i n w a t e r o r N a + - m o n t m o r i l l o n i t e i n 0 .3 M N a C I( 2 0 . 4 / ~ ) ( u n p u b l i s h e d d a t a ) w a s e x p e c t e d . S i m i l a r l y ,Z h a n g e t a l . ( 1 9 9 3 ) f o u n d n o e v i d e n c e t h a t t e m p e r a -t u r e c h a n g e s a l t e r e d th e s t a b l e i n t e r l a y e r s p a c in g o fN a + - m o n t m o r i l l o n i t e , e v e n a t s p a c i n g i n e x c e s s o f 6 0/ ~. I n m a r k e d c o n t r a st , a r e v e r s i b l e c o l l a p s e o f m a c -r o s c o p i c a l l y s w o l l e n n - b u t y l - a m m o n i u m v e r m i c u li t ei n w a t e r i s i n d u c e d b y s l i g h t h e a t in g ( B r a g a n z a e t a l .1 9 9 0 ) , s u g g e s t i n g t h a t h i g h e r t e m p e r a t u r e s e i t h e rw e a k e n t h e r e p u l s i v e f o r c e o r s t re n g t h e n t h e a t t r a ct i v ef o r c e r e l a t i v e to i t s o p p o s i n g f o r c e i n t h e h i g h l y e x -p a n d e d p h a s e . I f a n a t t e m p t w e r e m a d e t o e x p l a i n t h ist r a n s i t io n b y D L V O t h e o r y , i t w o u l d r e q u i r e t h a t t h er e p u l s i v e e l e c t r o s t a t i c f o r c e d i m i n i s h , o r t h a t t h e v a nd e r W a a l s f o r c e i n c r e a s e , a t h i g h e r t e m p e r a t u r e . N e i -t h e r o f t h e s e r e q u i r e m e n t s i s p h y s i c a l l y re a s o n a b l e . O nt h e o t h e r h a n d , t h e S o g a m i m o d e l b a s e d o n a n e l e c -t r o s t a ti c a t t r a c ti v e f o r c e a n d a n o s m o t i c r e p u l s i v e f o r c e( S o g a m i a n d I s e 1 9 8 4 ) m a y a c c o u n t m o r e e a s i l y f o rt h e t e m p e r a t u r e - d e p e n d e n c e o f p h a s e t r a n s i t io n b e -

t w e e n t h e h i g h l y - e x p a n d e d ( g e l ) st a te a n d t h e m o r ec o l l a p s e d ( c r y s t a l l i n e ) s t at e . S i n c e h i g h e r t e m p e r a t u r ew o u l d i n c r e a s e o s m o t i c p r e s s u r e w i t h i n b o t h t h e c l a ya n d t h e e x t e r n a l s o l u t i o n , t h e r e m a y b e l i t t l e o v e r a l li n f l u e n c e o f o s m o t i c f o r c e o n t h e t e m p e r a t u r e - d e p e n -d e n c e o f t h e p h a s e t r a n s it i on . H o w e v e r , h i g h e r t e m -p e r a t u r e d e c r e a s e s t h e d i e l e c t ri c c o n s t a n t o f w a t e r( f r o m 8 0 .1 at 2 0 ~ t o 6 9 . 9 a t 5 0 ~ w h i c h c o u l ds u b s t a n t i a l l y i n c r e a s e t h e a t t r a c t i v e f o r c e a c r o s s p l a t e s ,i n d u c i n g c o l l a p s e t o t h e c r y s t a l l i n e s t a t e . T h e m e a -s u r e d t h e r m a l c o m p r e s s i o n o f c h a r g e d l a t e x p a r t i c l es u s p e n s i o n s h a s s i m i l a r l y b e e n i n t e r p r e t e d a s a c o n t r a -d i c t i o n o f D L V O t h e o r y , a n d e v i d e n c e i n f a v o r o fe l e c t r o s t a t i c i n t e r p a r t i c l e a t t r a c t i o n ( I s e a n d S m a l l e y1 9 9 4 ) .

L O N G - R A N G E F O R C E S I N C O L L O I D ST h e p r e d i c t i v e a b i l i ty o f t h e D L V O m o d e l i n c l a y

s t u d i e s h a s b e e n t e s t e d l a r g e l y b y t h e e f f e c t o f s a l tc o n c e n t r a t i o n o n i n t e r l a y e r e x p a n s i o n o f s w e l l i n gc l a y s , a n d h a s b e e n m o d e r a t e l y s u c c e s s f u l i n t h i s r e -g a r d , a t l e a s t f o r N a + - s a t u r a t e d s m e c t i t e s . H o w e v e r , t h em o d e l h a s g e n e r a l l y n o t b e e n c o m p a r e d w i t h o t h e rm o d e l s h a v i n g d i f f e r e n t a s s u m p t i o n s a b o u t t h e n a t u r eo f t h e f u n d a m e n t a l a t t ra c t i v e an d r e p u l s i v e f o r ce s .

R e c e n t d e v e l o p m e n t s , b o t h t h e o r e t i c a l a n d e x p e r i -m e n t a l, h a v e u n d e r m i n e d a s s u m p t io n s o f t h e D L V Ot h e o r y . T h e l o n g - h e l d a s s u m p t i o n t h a t t h e e l e c t r o st a t ic( a s o p p o s e d t o o s m o t i c ) i n t e r a c t i o n b e t w e e n l i k e -c h a r g e d c l a y p l a t e l e t s i s r e p u l s i v e a t a l l b u t c l o s e s e p -a r a t io n h a s b e e n c h a l l e n g e d o n a t h e o r e t i c a l b a s i s b ys t a ti s ti c a l m e c h a n i c a l m o d e l s ( G u l d b r a n d e t a l. 1 9 84 ;E n g s t r t i m e t a l . 1 9 8 5 ; K j e l l a n d e r e t a l . 1 9 8 8 ) a n d m e a nf i e l d t h e o r y ( S o g a m i e t a l . 1 9 92 ) . F u r t h e r m o r e , e x p e r -i m e n t a l o b s e r v a t i o n s , s u c h a s t h e a p p e a r a n c e o f v o i d si n c o l l o i d a l d i s p e r s i o n s o f u n i f o r m l i k e - c h a r g e d l a t e xp a r t i c l e s , a t t e s t t o t h e e x i s t e n c e o f a l o n g - r a n g e a t t r a c -t i v e f o r c e ( D o s h o e t a l . 1 9 9 3 ; I t o e t a l . 1 9 9 4 ) w h i c hp r e v e n t s p a r t i c le s f r o m a s s u m i n g a n e v e n d i s t r ib u t i o nd u e t o r a n d o m ( B r o w n i a n ) m o t i o n .

T h e r e i s l i m i t e d e x p e r i m e n t a l e v i d e n c e t o r e s o l v et h e n a t u r e o f th e e l e c t r o s t a t i c f o r c e a t l a r g e r i n t e r p a r -t i c l e d i s t a n c e s i n l a y e r s i l i c a t e c l a y s , b u t s i n c e e l e c t r o -s t a ti c f o r c e s a r e r e l a t i v e l y l o n g - r a n g e c o m p a r e d t o v a nd e r W a a l s a n d h y d r a t i o n f o r c e s , i t i s n o t u n r e a s o n a b l et o e x p e c t t h a t t h e e l e c t r o s t a ti c a t t ra c t i o n w o u l d r e m a i ns i g n i f i c a n t a t i n t e r p a r t i c l e s e p a r a t i o n s o f 1 0 0 _& o rh i g h er . F o r s e p a r a t i o n s o f 30 t o m o r e t h a n 1 0 0 / ~ , t h ec - a x i s s p a c i n g i n m o n t m o r i l l o n i t e , d , v a r i e s i n v e r s e l yw i t h t h e s q u a r e r o o t o f e l e c t r o l y t e c o n c e n tr a t i o n , c ,a c c o r d i n g t o t h e e q u a t i o n :

11 . 4d = 21 + ~ [2 ]a n d t h i s b e h a v i o r l e d t o a n o n - D L V O m o d e l i n w h i c ha n o s m o t i c r e p u l s i v e f o r c e b a l a n c e s a n a t t ra c t i v e e l e c -t r o s t a t i c f o r c e ( N o r r i s h 1 9 5 4 ). T h e o r i g i n o f t h e r e-


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Vol . 45 , No . 4 , 1997 Cr i t ique o f doub le l aye r mod e l s 603

1 4 0 I I I I I I I

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Figure 3 . Com par i s on o f Norr i s h and Sogam i re la tions h iPso f d -s pac ing to NaC1 concen t ra t ion wi th in the concen t ra tionrange o f the Norr i s h expe r imen t s , ba s ed on E qua t ions [3 ] and[4].

p u l s i v e f o r c e i s t h e t h e r m a l m o t i o n ( e n t r o p y o f m i x -i n g ) o f t h e c o u n t e r io n s w h e n d i f f u s e d o u b l e l a y e r so v e r l a p ( E n g s t r r m e t a l. 1 9 8 5 ), n o t e l e c t r o s t a t i c r e -p u l s i o n b e t w e e n o v e r l a p p i n g d o u b l e l a y e r s a s c o m -m o n l y i m p l i e d i n r e f e r e n c e s t o D L V O . I t i s in t e r e s ti n gt h a t N o r r i s h d e r i v e d a s i m p l e e q u a t i o n f r o m t h i s m o d e lo f c l a y s w e l l i n g t h a t e s t a b l i s h e s a c o n s t a n c y f o r t h ep r o d u c t o f t h e in v e r s e D e b y e s c r e e n i n g le n g t h , K( u n it s o f / ~ - 1 ) , a n d t h e d - s p a c i n g , w h i c h a t l a r g e s p a c -i n g i s :

K . d - ~ 3 . 8 [3 ]M o r e r e c e n t l y , th e C o u l o m b i c a t t r a c ti o n t h e o r y o f S o -g a m i h a s b e e n s h o w n t o p r e d i c t :

K . d = 4 . 0 [ 4 ]( W i l l i a m s e t a l. 1 9 9 4 ), i n r e m a r k a b l y c l o s e a g r e e m e n tw i t h N o r r i s h ' s d a t a , a s F i g u r e 3 i l l u s t r a t e s c l e a r l y . T h ep r e d i c t e d S o g a m i s p a c i n g s a r e c a l c u l a t e d f r o m t h e r e -l a t i o n s h i p o f K t o m o l a r c o n c e n t r a t i o n o f e l e c tr o l y t e ,c ( S m a l l e y 1 9 9 4 ) , K 2 = 0 . 1 0 7 c . N o t e t h a t t h e p r e d i c t e di n t e r p a r t i c le s p a c i n g f r o m t h e S o g a m i t h e o r y h a s b e e na d j u s t e d f o r t h e t h i c k n e s s o f t h e s i l i c a t e p l a t e s ( 1 0 , ~ )i n o r d e r t o c o m p a r e w i t h N o r r i s h ' s m e a s u r e d d - s p a c -i n g s .

P H A S E T R A N S I T I O N S I N C O L L O I D SA s p o i n t e d o u t b y S m a l l e y ( 1 99 0 ) , a n d m u c h e a r l i e r

b y L a n g m u i r ( 1 9 3 8 ) , th e o b s e r v e d c o e x i s t e n c e o f s e p -a r a t e p h a s e s ( c o n c e n t r a t e d a n d d i l u t e ) a t r e v e r s i b l ee q u i l i b r i u m i n c o l l o i d a l d i s p e r s i o n s i s , in i t se l f , e v i-d e n c e t h a t p a r t i c l e - p a r t i c l e i n t e r ac t i o n i s n o t r e p u l s i v ea t a l l s e p a r a t i o n s , a s r e q u i r e d b y D L V O . I n o t h e rw o r d s , t h e d i s p e r s e d s t a t e m u s t b e t h e r m o d y n a m i c a l l y

s t a b le i f i t c a n b e r e v e r s i b l y c o n v e r t e d t o t h e c o n c e n -t r a t e d s t a t e . T h e s e 2 p h a s e s h a v e b e e n o b s e r v e d i ns u s p e n s i o n s o f v a r i o u s a n i s o d i m e n s i o n a l p a r t i c le s( s u c h a s s m e c t i t e s , i r o n h y d r o x i d e s , v a n a d i u m p e n t -o x i d e a n d t u n g s t en t r i o x i d e ) a s w e l l a s in s u s p e n s i o n so f m o n o d i s p e r s e l a t e x p a r t i c le s ( C o p e r a n d F r e u n d l i c h1 9 3 7 ; O v e r b e e k 1 9 5 2 ; D o s h o e t al . 1 99 3 ) . T h e c o n -c e n t r a t e d p h a s e h a s a h i g h d e g r e e o f o r d e r, o f te n l e a d -i n g t o v a r i o u s o p t i c a l e f f e c t s s u c h a s b i r e f r i n g e n c e a n di n t e r f e r e n c e c o l o r s . T h e d i l u t e p h a s e c o n s i s t s o f f r ee ,r a n d o m l y o r i en t e d p a rt i c le s u n d e r g o in g B r o w n i a n m o -t i o n .

F r e e e n e r g y m i n i m a e v i d e n t l y e x i s t i n N a -t e s a t s i l i c a t e l a y e r s e p a r a t i o n s l e s s t h a n 1 0 0 , ~, e v i -d e n c e d b y t h e c o e x i s t e n c e o f p h a se s w i t h c - a x i s s p a c -i n g o f 2 0 / ~ a n d 4 0 ] k ( N o r r i s h 1 9 5 4 ; V i a n i e t a l .1 9 8 5 ) . P h a s e t r a n s i t i o n s a r e a l s o s e e n i n n - b u t y l - a m -m o n i u m v e r m i c u l i t e , w h i c h s w e l l s m a c r o s c o p i c a l l y i nw a t e r ( B r a g a n z a e t a l . 1 9 9 0 ) , a n d l i k e t h e s m e c t i t e ,s h o w s n o c o h e r e n t c - a x i s s p a c i n g i n t h e t r a n s i t i o nf r o m t h e c r y s t a l l i n e to o s m o t i c s w e l l i n g s t at e . T h e f a c tt h a t t h e s e a r e r e v e r s i b l e t r a n s i t i o n s i n d i c a t e s t h a t t h ec o e x i s t i n g g e l a n d c r y s t a l l i n e p h a se s r e p r e s e n t e q u i l i b -r i u m s t at e s, w h i c h a r e n o t p o s s i b l e w i t h i n t h e f r a m e -w o r k o f t h e D L V O t h e o r y ( S m a l l e y 1 9 9 0) .

T h e c o e x i s t e n c e o f S c h i l l e r l a y e r s o r t a c to i d s ( p l a t e-l e ts o r r o d - s h a p e d p a r t i c l es a l i g n e d i n t o o r d e r e d s t a t es )w i t h a n i s o t r o p i c p h a s e i n v a r i o u s c o l l o i d a l d i s p e r s i o n si n d i c a t e s t h a t a b a l a n c e o f f o r c e s i s a l s o p o s s i b l e a tl a r g e p a r t i c l e s e p a r a t io n s ( > 1 0 0 0 / ~ ) i n c la y - s i z e m a -t e r i a l s . T h i s b a l a n c e o f f o r c e s h a s u s u a l l y b e e n a s -s u m e d t o b e t h e r e p u l s i v e e l e c t r o s ta t i c f o r c e o f D L V Ot h e o r y w i t h g r a v i t y , s i n c e S c h i l l e r l a y e r s a n d t a c t o i d so f t e n f o r m a f t e r a p e r i o d o f s e tt l in g , a n d a r e d e s t r o y e dr e v e r s i b l y b y a g i t a ti o n . H o w e v e r , O n s a g e r ( 1 9 4 9) h a sp o i n t e d o u t t h a t e n t r o p y - d r i v e n p h a s e t r a n s i t i o n s a r ep o s s i b l e i n s u s p e n s i o n s o f a n i s o t r o p i c p a r ti c l e s a s ac o n s e q u e n c e o f B r o w n i a n m o t i o n , w h i c h p r o d u c e s an" o s m o t i c " r e p u l s i o n t h a t s t ab i l i z e s c o l l o i d a l d i s p e r-s i on s . T h i s p h e n o m e n o n i s s e p a r a te f r o m ( o r i n a d d i -t i o n t o ) t h e o s m o t i c p r e s s u r e o r i g i n a t i n g f r o m t h ec o u n t e r i o n s , i n d i c a t i n g t h a t s t a b l e d i s p e r s i o n s a n dp h a s e t r a n s i t i o n s c a n , i n p r i n c i p l e , o c c u r i n u n c h a r g e dc o l l o i d a l p a r t i c l e s . I n f a c t , i t i s i n t e r e s t i n g t h a t t h e r e -m a r k a b l e 3 - d i m e n s i o n a l o r d e r i n g o f l a t e x p a r t ic l e s i ns u s p e n s i o n a t s e p a r a t i o n d i s t a n c e s o f - ~ 1 0 0 0 , ~ i s e v -i d e n t o n l y a t v e r y l o w i o n i c s t r e n g t h ( I s e 1 9 8 6 ) , a c o n -d i t i o n t h a t c a u s e s t h e s e c h a r g e d p o l y m e r s t o u n f o l da n d o c c u p y a l a r g e r v o l u m e . T h u s , t h e r e p u l s i v e f o r c et h a t m a i n t a i n s t h e l a r g e s e p a r a t i o n m a y b e d u e t oB r o w n i a n m o t i o n . W h e n g r a v i t y i s e l i m i n a t e d a s af o r c e b y m a t c h i n g t h e d e n s i t y o f th e p a r t i c l e s a n d s o l -v e n t , l o n g - r a n g e 3 - d i m e n s i o n a l o r d e r ( -- ~1 00 0 .~ ) o ft h e s e c h a r g e d l a t e x p a r t i c l e s s t i ll o c c u r s , s u g g e s t i n gt h a t a n a t t r a c t i v e l o n g - r a n g e f o r c e i s p r e s e n t ( D o s h oe t a l . 1 9 9 3 ) .


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Figure 4 . Sch i l l e r l aye r d -s pac ing fo r tungs ten ox ide p la te -le ts measured a s a funct ion of NaC1 concentra tion. The br o-ken l ine deno te s the p red ic ted d -s pac ing o f the Sogam i theoryf rom E qua t ion [4 ].

T h e d e p e n d e n c e o f c - a x i s s p a c i n g i n S c h i l l er l a y e r so n e l e c t r o l y t e c o n c e n t r a t i o n i s q u a l i t a t iv e l y d e s c r i b e db y D L V O t h e o r y , b u t t h e t h e o r y o f t e n f a il s q u a n t i ta -t i v e ly . F o r e x a m p l e , i t d o e s n o t e x p l a i n t h e r e s is t a n c eo f l a t h - s h a p e d t u n g s t e n o x i d e p a r t i c l e s t o a p p r o a c hc l o s e r t h a n a b o u t 2 0 0 0 A , a t i n c r e a s i n g i o n i c s t r e n g t h( B e r g m a n n e t a l . 1 9 3 8 ). I n c o n t r a s t , a s s h o w n i n F i g -u r e 4 , t h e s p a c i n g s a r e f a i r l y c o n s i s t e n t w i t h t h e 1/X//cr u l e o f s w e l l i n g t h a t f o l l o w s f r o m t h e S o g a m i t h e o r y .A l t h o u g h t h e a c t u a l d - s p a c i n g s o f t h e t u n g s te n o x i d ep l a t e s a r e h i g h e r t h a n t h e p r e d i c t e d s p a c i n g s f r o m S o -g a r n i t h e o r y , c o r r e c t i o n f o r t h e p l a t e - t h i c k n e s s w o u l db r i n g t h e p r e d i c t e d a n d m e a s u r e d s p a c i n g s i n t o c l o s e ra g r e e m e n t .

I n s u m m a r y , t h e r e a r e a s u b s ta n t i a l n u m b e r o f e x -p e r i m e n t a l o b s e r v a t i o n s o n c l a y s a n d o t h e r c o l l o i d a ls y s t e m s t o s u p p o r t t h e h y p o t h e s i s o f a t t r a c ti v e e l e c t r o -s t a ti c f o r c e s b e t w e e n l i k e - c h a r g e d p a r t i c l e s , n e c e s s i -t a t in g a r e a s s e s s m e n t o f t h e b a s i c a s s u m p t i o n s o f t h eD L V O t h eo r y.

C H A R G E A N D A D S O R P T I O N O NV A R I A B L E - C H A R G E S U R F A C E S

T h e D L V O t h e o r y a p p e a r s t o h a v e b e e n p a r t i c u l a r l ym i s a p p l i e d t o a d s o r p t io n p h e n o m e n a a t o x id e a n d o t h e rv a r i a b l e - c h a r g e s u r f a c e s , b e c a u s e m o s t r e s e a r c h o nt h e s e s y s t e m s h a s s h o w n a d s o r b e d i o n s t o b e i n n o n -d i f f u se b o n d i n g a s s o c i at i o n s w i th t h e s u r f a ce ( M c B r i d e1 9 8 9 b ) . N e v e r t h e l e s s , t h e o f t e n - p r e s e n t e d d e s c r i p t i o n o fs u r f a c e c h a r g e o n v a r i a b l e - c h a r g e m i n e r a l s s u c h as o x -i d e s e m p l o y s t h e N e r n s t e q u a t i o n t o c a l c u l a t e a s u r f a c ep o t e n t i a l , w h i c h i s t h e n u s e d i n t h e d i f f u s e d o u b l e l a y e rm o d e l t o c a l c u l a t e s u r f a c e c h a r g e ( G a s t 1 9 7 7 ) . T h e r e -

s u i t i n g p r e d i c t e d s u r f a c e - c h a r g e d e p e n d e n c e o n p H i s af u n c t i o n o f i o n i c s t r e n g t h , w i t h c h a r g e c u r v e s a t a ll io n -i c s t r en g t h s c r o s s i n g o v e r a t th e p o i n t o f z e r o c h a r g e( P Z C ) . T h e s e p r e d i c t e d s u r f a c e c h a r g e c u r v e s a r e q u a l -i t a t i v e l y c o n s i s t e n t w i t h m e a s u r e d s u r f a c e c h a r g e o fp u r e o x i d e s , d e s p i t e a r g u m e n t s t h a t t h e N e r n s t e q u a t i o ni s n o t a p p r o p r i a t e f o r o x i d e m i n e r a l s ( M c B r i d e 1 9 8 9 a ).T h e y a r e , h o w e v e r , a l s o c o n s i s t e n t w i t h a s i m p l e r L a n g -m u i r - b a s e d a d s o rp t i o n t h e o r y o f H + a n d O H - o n v a r i-a b l e - c h a r g e d s u r f a c e s ( M c B r i d e 1 9 9 4 ). F u r t h e r m o r e ,t h e l a t t e r m o d e l , u n l i k e t h e N e r n s t d o u b l e l a y e r m o d e l ,p r e d i c t s a l i m i t o n s u r f a c e c h a r g e a s p H i s a d j u s t e da w a y f r o m t h e P Z C v a l u e . E x p e r i m e n t a l e v i d e n ce ,w h e n c o r r e c t e d f o r m i n e r a l d i s s o l u t io n , is c o n s i s t e n tw i t h a s u r fa c e c h a r g e m a x i m u m ( S c h u lt h e ss a n d S p a r k s1 9 86 ; M a r c a n o - M a r t i n e z a n d M c B r i d e 1 9 89 ) . T h eL a n g m u i r - b a s e d a p p r o a c h t o o x i d e s u r f a c e c h e m i s t r y ,r e l y i n g o n l y o n t h e s i m p l e r e q u i r e m e n t s o f c h a r g e b a l -a n c e , m a s s a c t i o n a n d c o o r d i n a t i o n c h e m i s t r y , a d e -q u a t e ly e x p l a i n s p H - d e p e n d e n t c h a r g e a n d a d s o r p t i o nb e h a v i o r o n o x i d e s . S p o s i t o ( 1 9 9 5 ) h a s d e t a i l e d t h e s u c -c e s s e s o f th i s a p p r o a c h t o o x i d e s , m u c h o f i t a t t r i b u t a b l et o W . S t u m m a n d c o w o r k e r s .

A n i o n s a n d c a t i o n s a d s o r b o n v a r i a b l e - c h a r g e m i n -e r a l s u r f a c e s b y b o t h i n n e r - s p h e r e c o m p l e x a t i o n ( l i -g a n d e x c h a n g e ) a n d o u t e r - s p h e r e ( e l e c tr o s t a ti c ) a s s o -c i a t io n ( M c B r i d e 1 9 8 9 b; B r o w n e t al . 1 98 9 ), b e h a v i o rt h a t is p r o b l e m a t i c f o r t h e a p p l i c a t i o n o f d i f f u s e d o u -b l e l a y e r m o d e l s t o s u c h s u r f a c e r e a c t i o n s . In n e r -s p h e r e a n d o u t e r - s p h e r e m e c h a n i s m s a r e d is t i n g u i s h a -b l e i n d i r e c t l y b y t h e e f f e c t o f i o n i c s t r e n g t h ( t h a t i s ,t h e p r e s e n c e o f a n i n d i f fe r e n t e l e c tr o l y t e ) o n d e g r e e o fa d s o r p t i o n ( H a y e s e t a l . 1 9 8 8 ) . A n i o n s t h a t a d s o r b b yo u t e r - s p h e r e a s s o c i a t i o n ( f o r e x a m p l e , s e l e n a t e ) a r es t r o n g l y s e n s i t i v e t o i o n i c s t r e n g t h ; t h a t i s , a d s o r p t i o no f t h e s e a n i o n s i s s u p p r e s s e d b y c o m p e t i t i o n w i t hw e a k l y a d s o r b i n g a n i o n s su c h a s C I - o r N O ~ . C o n -v e r s e l y , a n i o n s t h a t a d s o r b b y l i g a n d e x c h a n g e e i t h e rs h o w l i t t le s e n s i t i v i t y t o i o n i c s t r e n g t h ( f o r e x a m p l e ,s e l e n i t e ) o r r e s p o n d t o h i g h e r i o n i c s t r e n g t h w i t hg r e a t e r a d s o r p t i o n ( f o r e x a m p l e , b o r a t e) . A l a c k o fr e s p o n s e t o i o n i c s t r e n g th i s r e a d i l y u n d e r s t o o d f o rs u c h a n i o n s , s i n c e t h e b o n d t h a t t h e y f o r m w i t h t h es u r f a c e i s s t r o n g . C o n s e q u e n t l y , a n i o n s t h a t a r e w e a kL e w i s b a s e s ( s u c h a s N O ~ a n d C 1 0 ~ ) a r e u n a b l e t oc o m p e t e f o r c o o r d i n a t i o n s i t e s a t s u r f a c e s ( M c B r i d e1 9 9 4 ) .

I n c o n t r a s t , t h e i n c r e a s e i n a d s o r p t i o n i n r e s p o n s et o h i g h e r i o n i c s t r e n g th , s h o w n i n F i g u r e s 5 a n d 6 f o rb o r a t e a n d p h o s p h a t e ( B a r r o w e t a l . 1 9 8 0 ; G o l d b e r ge t a l . 1 9 93 ; K e r e n a n d S p a r k s 1 9 9 4 ) , d o e s n o t h a v e s os t r a i g h t f o r w a r d a n e x p l a n a t io n . O b v i o u s l y , t h e t r e n d i so p p o s i t e t o t h a t p r e d i c t e d b y e x p l a n a t i o n s b a s e d o na n i o n - a n i o n c o m p e t i t i o n f o r s i t e s . W h e n i t i s o b -s e r v e d , t h e e x p l a n a t i o n u s u a l l y o f f e r e d i s t h e e f f e c t o fi o n i c s t r e n g th o n t h e d i f f u s e d o u b l e l a y e r t h i c k n e s s;t h a t i s , a s i o n i c s t r e n g t h i s i n c r e a s e d , t h e d o u b l e l a y e r


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