Polymer Adsorption and Dispersion Stability - American Chemical

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25 Rheological Studies of Aqueous Concentrated Polystyrene Latex Dispersions with Adsorbed Poly(vinyl alcohol) Layers

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TH. F. TADROS I.C.I. Plant Protection Division, Jealott's Hill Research Station, Bracknell, Berkshire RG12 6EY, England The viscoelastic behavior of concentrated (20% w/w)aqueous polystryene latex dispersions (particle radius 92nm), in the presence of physically adsorbed poly(vinyl alcohol), has been investigated as a function of surface coverage by the polymer using creep measurements. From the creep curves both the instantaneous shear modulus, G , and residual viscosity, η , were calculated. The yield value, τ , was also measured as a function of surface coverage. A l l the rheological parameters decreased with increasing surface coverage. This was related to the reduction in particle interaction with increase of polymer adsorption. At full coverage the residual G , η and τ values were attributed to the combined action of long-range electrostatic repulsion and steric interaction due to the presence of long, dangling tails. Rheological measurements were also carried out on flocculating, concentrated (25% w/w) aqueous polystyrene latex dispersions (particle radius 115nm). The flocculation was produced either by addition of Na SO or raising the temperature of the dispersion at constant Na SO concentration. Both the yield value and shear modulus were mea­ sured and the results obtained analyzed using two models, namely the floc rupture and elastic floc models proposed by Hunter and coworkers. Good agreement between the experimental yield values and those calculated using the elastic floc model was obtained, thus confirming its applicability to the case of flocculating, sterically-stabilized dispersions. o

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0097-6156/ 84/ 0240-0411 $06.00/ 0 © 1984 American Chemical Society Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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P O L Y M E R A D S O R P T I O N A N D DISPERSION STABILITY

I n v e s t i g a t i o n s of the r h e o l o g i c a l p r o p e r t i e s of disperse systems are very important both from the fundamental and a p p l i e d points of view (1-5). For example, the non-Newtonian and v i s c o e l a s t i c behaviour of concentrated d i s p e r s i o n s may be r e l a t e d t o the i n t e r a c t i o n forces between the dispersed p a r t i c l e s (6-9). On the other hand, such studies are of v i t a l p r a c t i c a l importance, as, f o r example, i n the assessment and p r e d i c t i o n of the longterm p h y s i c a l s t a b i l i t y of suspensions ( 5 ) . Any fundamental study of the rheology of concentrated suspensions n e c e s s i t a t e s the use of simple systems of w e l l defined geometry and where the surface c h a r a c t e r i s t i c s of the p a r t i c l e s are w e l l e s t a b l i s h e d . F o r that purpose w e l l c h a r a c t e r i z e d polymer p a r t i c l e s of narrow s i z e d i s t r i b u t i o n are used i n aqueous or non-aqueous systems. For i n t e r p r e t a t i o n of the r h e o l o g i c a l r e s u l t s , the i n t e r - p a r t i c l e p a i r - p o t e n t i a l must be w e l l - d e f i n e d and theories must be a v a i l a b l e f o r i t s c a l c u l a t i o n . The simplest system to consider i s that where the p a i r p o t e n t i a l may be represented by a hard sphere model. T h i s , f o r example, i s the case f o r polystyrene l a t e x d i s p e r s i o n s i n organic solvents such as benzyl a l c o h o l or c r e s o l , whereby e l e c t r o s t a t i c i n t e r a c t i o n s are w e l l screened (1). Concentrated d i s p e r s i o n s i n non-polar media i n which the p a r t i c l e s are s t a b i l i z e d by a " b u i l t - i n " s t a b i l i z e r l a y e r , may a l s o be used, since the p a i r - p o t e n t i a l can be represented by a hard-sphere i n t e r a c t i o n , where the hard sphere radius i s given by the p a r t i c l e s radius plus the adsorbed l a y e r thickness. Systems of t h i s type have been r e c e n t l y studied by Croucher and coworkers. (10,11) and S t r i v e n s (12). F a i r l y r e c e n t l y the v i s c o e l a s t i c p r o p e r t i e s of aqueous, e l e c t r o s t a t i c a l l y s t a b i l i z e d polystyrene l a t e x d i s p e r s i o n s have been i n v e s t i g a t e d by Russel and Benzig (6^, 7_) and by B u s c a l l et_ a l . (8,9). These perhaps c o n s t i t u t e one of the f i r s t studies whereby an attempt has been made to r e l a t e r h e o l o g i c a l parameters to the i n t e r a c t i o n f o r c e s between the p a r t i c l e s . Although such studies are of fundamental importance, t h e i r a p p l i c a t i o n to p r a c t i c a l disperse systems of the aqueous type i s not s t r a i g h t forward s i n c e , i n most p r a c t i c a l cases, adsorbed polymer l a y e r s are used f o r s t a b i l i z a t i o n of such suspensions. Only a few i n v e s t i g a t i o n s have been reported on the rheology of these r e l a t i v e l y more complex systems. For example, Hunter et a l (13,14) have i n v e s t i g a t e d the flow behaviour of aqueous poly (methyl methacrylate) (PMMA) l a t i c e s s t a b i l i z e d by a b l o c k copolymer of poly(ethylene oxide-b-methylacrylate) which was adsorbed onto the surface of the PMMA spheres by the smaller PMMA anchor groups of the copolymer. The authors used a s i m p l i f i e d r h e o l o g i c a l approach, whereby the energy d i s s i p a t i o n i n a f l o c c u l a t i n g system was assumed to a r i s e mainly from the rupture between doublets i n a shearing f i e l d . Using t h i s approach the authors were able t o i n v e s t i g a t e the i n t e r a c t i o n

Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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p r o p e r t i e s of the f l o c c u l a t i n g d i s p e r s i o n s . I n t e r a c t i o n energies of the order of 5 kT (where k i s the Boltzmann constant and Τ the absolute t e m p e r a t u r e ) were obtained f o r the PMMA system s t a b i l i z e d by adsorbed p o l y ( e t h y l e n e o x i d e ) . In t h i s paper we r e p o r t some r h e o l o g i c a l s t u d i e s of aqueous concentrated p o l y s t y r e n e l a t e x d i s p e r s i o n s , i n the presence of p h y s i c a l l y adsorbed p o l y ( v i n y l a l c o h o l ) . T h i s system has been chosen i n view of i t s r e l e v a n c e to many p r a c t i c a l systems and s i n c e many of the parameters needed f o r i n t e r p r e t a t i o n of the r h e o l o g i c a l r e s u l t s are a v a i l a b l e (15-18). The v i s c o e l a s t i c p r o p e r t i e s of a 20% w/w l a t e x d i s p e r s i o n were i n v e s t i g a t e d as a f u n c t i o n of polymer coverage, using creep measurements. Moreover, r h e o l o g i c a l s t u d i e s were c a r r i e d out on a d i s p e r s i o n (25% w/w) which was f l o c c u l a t e d e i t h e r by a d d i t i o n of s u f f i c i e n t e l e c t r o l y t e (Na S04) or by r a i s i n g the temperature a t a constant e l e c t r o l y t e c o n c e n t r a t i o n . 2

Experimental M a t e r i a l s Water was d o u b l y - d i s t i l l e d from a l l g l a s s apparatus. A l l other m a t e r i a l s were a n a l y t i c a l grade and used as r e c e i v e d . P o l y ( v i n y l a l c o h o l ) (Alcotex 88/10, s u p p l i e d by Revertex L t d . , London) was the same sample used p r e v i o u s l y i n t h i s l a b o r a t o r y (15-18); i t has a weight average molecular weight M^, of 45,000 and 12% acetate groups. Two 50 1 batches of p o l y s t y r e n e l a t e x were prepared using the method d e s c r i b e d by Goodwin et a l (19); these w i l l be r e f e r r e d to as l a t e x A and B, r e s p e c t i v e l y . Both l a t i c e s were d i a l y z e d against d i s t i l l e d water u n t i l there was no f u r t h e r change i n the c o n d u c t i v i t y of the d i a l y z a t e . Two procedures were used to concentrate the l a t i c e s . Latex A (which was 3.32% w/w) was concentrated i n two stages. In the f i r s t stage, the l a t e x was placed i n V i s k i n g tubing and suspended i n a r e f r i g e r a ­ t o r f o r one week at 5°C to evaporate as much water as p o s s i b l e . The l a t e x was then t r a n s f e r r e d to 28 mm diameter V i s k i n g tubing and a weight of approximately 4kg was placed on the top of the tubing which was immersed i n d i s t i l l e d water. A f t e r four weeks the volume of the l a t e x was reduced reaching a c o n c e n t r a t i o n of 46% w/w. Latex Β (which was 4% w/w) was concentrated by r o t a r y evaporation to 28.3% w.w. The p a r t i c l e s i z e of the two l a t i c e s was determined u s i n g e l e c t r o n microscopy and a "Quantimet image a n a l y z e r . Latex A had an average r a d i u s of 92+3nm and l a t e x Β 115+2nm. 11

Adsorption Isotherm The d e t a i l s o f the technique used have been d e s c r i b e d b e f o r e (15). B a s i c a l l y , 0 . 5 g of the d i l u t e l a t e x was added to p o l y ( v i n y l a l c o h o l ) (PVA) s o l u t i o n s covering the range 50-1000 ppm. These were then r o t a t e d end-over-end f o r 24 hours a t room temperature (22+2°C) f o r e q u i l i b r a t i o n .

Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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The p a r t i c l e s were then separated by c e n t r i f u g a t i o n and the supernatant was analyzed f o r PVA using the c o l o r i m e t r i c t e c h ­ nique d e s c r i b e d p r e v i o u s l y (15).

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C r i t i c a l F l o c c u l a t i o n E l e c t r o l y t e Concentration The c r i t i c a l f l o c c u l a t i o n e l e c t r o l y t e ( N a 2 S 0 # ) c o n c e n t r a t i o n was determined by f o l l o w i n g the average p a r t i c l e s i z e of the d i l u t e d i s p e r s i o n (where the p a r t i c l e s were coated with PVA corresponding to the p l a t e a u adsorption) as a f u n c t i o n of N a 2 S 0 ^ c o n c e n t r a t i o n , using a C o u l t e r s Nanosizer (Coulters E l e c t r o n i c s Ltd) as d e s c r i b e d before ( 2 0 ) . R h e o l o g i c a l Measurements Three types of r h e o l o g i c a l measure­ ments have been c a r r i e d out. In the f i r s t type, t r a n s i e n t (creep) measurements were performed on a 2 0 % w/w d i s p e r s i o n of l a t e x A, as a f u n c t i o n of coverage by PVA. These experiments were c a r r i e d out using a "Deer" rheometer (PDR 81, Integrated P e t r o n i c Systems, London) f i t t e d with a s t a i n l e s s s t e e l con­ c e n t r i c c y l i n d e r . The procedures used have been d e s c r i b e d i n d e t a i l before ( 2 1 , 2 2 ) . Secondly, steady s t a t e measurements were c a r r i e d out to obtain shear s t r e s s - s h e a r r a t e curves and the Bingham y i e l d v a l u e . Two methods were used. In the f i r s t method the v i s ­ c o s i t y was measured as a f u n c t i o n of shear r a t e (using the Deer rheometer) by a p p l y i n g a s e r i e s of t o r s i o n a l f o r c e s and r e c o r d i n g each time the angular v e l o c i t y . These experiments were performed on a 2 0 % l a t e x A, as a f u n c t i o n of PVA coverage. The Deer rheometer was a l s o used to determine the y i e l d value f o r these l a t e x d i s p e r s i o n s , by applying a s e r i e s of s t r e s s values of equal increments and r e c o r d i n g the response u n t i l flow occurred. In the second method, shear s t r e s s - s h e a r r a t e curves were obtained using a Haake "Rotovisko" (model RV100 f i t t e d with an M 150 measuring head) as d e s c r i b e d before ( 2 1 , 2 2 ) . From the shear s t r e s s - s h e a r r a t e curves, the p l a s t i c v i s c o s i t y , ηρτ_, was c a l c u l a t e d from the slope of the l i n e a r p o r t i o n of the curve. The Bingham y i e l d v a l u e , x , was obtained by e x t r a p o l a t i n g the l i n e a r p o r t i o n of the curve to zero shear r a t e . In these experiments, a 25% w/w l a t e x Β was used, where the p a r t i c l e s were f u l l y coated w i t h PVA, and r e s u l t s were obtained as a f u n c t i o n of N a 2 S 0 4 c o n c e n t r a t i o n at constant temperature (20+l°C) or as a f u n c t i o n of temperature at a constant N a 2 S 0 ^ ( 0 . 2 or 0.25 mol dm ) concentration. F i n a l l y , the shear modulus, G , was measured using a pulse shearometer (Rank Bros, Bottisham, Cambridge) as d e s c r i b e d before ( 2 1 , 2 2 ) . G was measured as a f u n c t i o n of Na SO^ con­ c e n t r a t i o n f o r 25? w/w l a t e x Β with the p a r t i c l e s f o l l y coated w i t h PVA. 5

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Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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Results Adsorption Isotherm The adsorption isotherm of PVA on polystyrene l a t e x was of the high a f f i n i t y type, as p r e v i o u s l y found (15). The s a t u r a t i o n a d s o r p t i o n (plateau) was found to be 4.26 mg m~^, which i s i n close agreement with the value obtained before (18) for the same PVA sample on a s i m i l a r l a t e x . Influence of surface coverage of PVA on r h e o l o g i c a l parameters F i g u r e 1 shows creep curves f o r 20% w/w l a t e x A at three d i f f e r e n t concentrations of PVA f o r 20% w/w l a t e x A(0.05, 0.15 and 0.30g PVA per 20g d i s p e r s i o n ) corresponding to adsorption amounts of 0.87, 2.56 and 4.76 mg m~ , i . e . roughly at the point where the isotherm leaves the y - a x i s , h a l f coverage and f u l l coverage, r e s p e c t i v e l y . A l l the creep curves show the behaviour to be expected with a v i s c o e l a s t i c system. They c o n s i s t of three regions: (a) d i r e c t l y a f t e r the a p p l i c a t i o n of the s t r e s s a r a p i d e l a s t i c deformation occurs, r e s u l t i n g i n an instantaneous compliance J (instantaneous shear modulus G^V γ = 1 / J , where τ i s the a p p l i e d s t r e s s ) ; (b) a slow e l a s t i c deformation, i . e . mixed v i s c o e l a s t i c r e g i o n . In t h i s region bonds are broken and reformed at v a r i o u s r a t e s r e s u l t i n g i n a spectrum of i retarded e l a s t i c compliances; (c) a r e g i o n of v i s ­ cous deformation, whereby the s t r a i n v a r i e s l i n e a r l y with time. In t h i s r e g i o n i n d i v i d u a l u n i t s flow past each other, s i n c e the time r e q u i r e d to r e s t o r e bonds i s l a r g e r than the t e s t p e r i o d . Since the s t r e s s a p p l i e d was f a i r l y small(0.015 NnT ) i t i s h i g h l y l i k e l y that the measurements f a l l w i t h i n the l i n e a r region. Moreover, since t h i s was the smallest s t r e s s that could be a p p l i e d whereby a response was obtained, the v i s c o s i t y c a l ­ culated from the l i n e a r p o r t i o n of the curve i s very c l o s e to the l i m i t i n g ( r e s i d u a l ) v i s c o s i t y η . The l a t t e r i s more ac­ c u r a t e l y obtained by applying a s e r i e s of reducing s t r e s s e s , e s t a b l i s h i n g the creep curve i n each case and p l o t t i n g η at each s t r e s s τ versus τ. U s u a l l y η increases with decreasing τ, but reaches a l i m i t i n g (Newtonian) value over a range of s u f f i c i e n t l y small s t r e s s e s . T h i s l i m i t i n g value i s u s u a l l y r e f e r r e d to as the r e s i d u a l v i s c o s i t y η . However, s i n c e creep measurements are time consuming, the creep curves were only obtained at one shear s t r e s s . The l a t t e r was the s m a l l e s t value that could be a p p l i e d to produce a measurable creep curve. Thus, s t r i c t l y speaking, the v i s c o s i t y c a l c u l a t e d from these creep curves may not be i d e n t i c a l to the r e s i d u a l v i s c o s i t y , but i t does correspond to the v i s c o s i t y at some very low shear r a t e . However, f o r the sake of comparison, we s h a l l s t i l l r e f e r to t h i s v i s c o s i t y as η . Both G and r\ have been c a l c u l a t e d from the creep curves shown i n f i g u r e 1 and p l o t t e d versus surface coverage, as shown i n f i g u r e 2. The y i e l d v a l u e , τ^,obtained using the procedure of applying a s e r i e s of successive t o r ­ s i o n a l s t r e s s e s , i s a l s o shown as a f u n c t i o n of surface

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Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

P O L Y M E R A D S O R P T I O N A N D DISPERSION STABILITY

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Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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coverage i n the same f i g u r e . A l l the r h e o l o g i c a l parameters show the same trend, namely a continuous decrease with i n c r e a s e of s u r f a c e coverage by the polymer. F i g u r e 3 shows p l o t s of η versus shear r a t e at three d i f ­ f e r e n t temperatures f o r the same l a t e x (20% w/w l a t e x A) at f u l l coverage with PVA. These curves are t y p i c a l of a pseudop l a s t i c system showing a r e d u c t i o n of η with i n c r e a s i n g shear r a t e , γ ; η reaches a l i m i t i n g value at If 50 s ~ l . It i s also c l e a r from f i g . 3 that at Ύ 10 s~^, n increases r a p i d l y with r e d u c t i o n i n Ύ . Comparison with n values obtained from the creep curves would i n d i c a t e the η should i n c r e a s e very s t e e p l y with r e d u c t i o n of Ύ, i n the low shear r a t e region (η i s the l i m i t of η as 0) . ° >


0.2 mol dm"^, the flow curves were t y p i c a l of a t h i x o t r o p i c system, showing a y i e l d value and a h y s t e r e s i s loop which increased i n magnitude with i n c r e a s e of C. Figure 4 shows the v a r i a t i o n of the e x t r a p o l a t e d y i e l d v a l u e , To (obtained from e x t r a p o l a t i o n of the ascending p a r t of the flow curve) as a f u n c t i o n of C. The shear modulus, G , measured using the pulse shearometer, i s a l s o shown as a f u n c t i o n of C i n the same f i g u r e . A measurable and G i s obtained above a c r i t i c a l value of C, which i n both cases i s -0.22 mol dm~3. As we w i l l see l a t e r , t h i s e l e c t r o l y t e concentration should be taken as the c r i t i c a l f l o c c u l a t i o n concentration (CFC) f o r the concentrated d i s p e r s i o n . Above the CFC, τ^ i n c r e a s e s r a p i d l y with i n c r e a s i n g C whereas G i n i t i a l l y i n c r e a s e s g r a d u a l l y with i n c r e a s i n g C u n t i l C = 0.3 mol dm~"3, above which there i s a more r a p i d increase of G . The CFC obtained with the d i l u t e d i s p e r s i o n ( ~10~ %) using the Nanosizer was -0.28 mol dnT^, i . e . s i g n i f i c a n t l y l a r g e r than that f o r the concentrated d i s p e r s i o n . F i g u r e 5 shows the v a r i a t i o n of with temperature at two C values (0.20 and 0.25 mol dm~^). In both cases is e s s e n t i a l l y zero u n t i l a c r i t i c a l termperature i s reached, above which τ^ i n c r e a s e s r a p i d l y with i n c r e a s i n g temperature reach­ ing a maximum above which there i s a tendency f o r x ^ to f a l l again with f u r t h e r increase i n temperature. The c r i t i c a l temperature corresponding to the abrupt i n c r e a s e i n 3 i s 20 and 25°C f o r C equal to 0.25 and 0.20 mol dm , r e s p e c t i v e l y This temperature may be i d e n t i f i e d with the c r i t i c a l f l o c ­ c u l a t i o n temperature (CFT) of the concentrated d i s p e r s i o n . Q

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Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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V a r i a t i o n of G , by PVA Q

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Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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TADROS

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C

Figure 4

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V a r i a t i o n of extrapolated y i e l d with Na S04 concentration 2

30k

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Figure 5

V a r i a t i o n of concentrations

with temperature a t two Na^SO^

Goddard and Vincent; Polymer Adsorption and Dispersion Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

P O L Y M E R A D S O R P T I O N A N D DISPERSION STABILITY

420 Discussion

V i s c o e l a s t i c P r o p e r t i e s The v i s c o e l a s t i c behaviour of the p o l y ­ styrene l a t e x d i s p e r s i o n s , i n which the p a r t i c l e s carry p h y s i c a l ­ l y adsorbed p o l y ( v i n y l a l c o h o l ) l a y e r s , i s the r e s u l t of i n t e r ­ a c t i o n of the polymer chains, which are close to each other i n concentrated d i s p e r s i o n s . For PVA w i t h an average molecular weight of 45,000, the adsorbed l a y e r thickness at f u l l cover­ age i s of the order of 47 nm (17). Such t h i c k adsorbed l a y e r s are due to the presence of long dangling t a i l s (23-25). For a l a t e x d i s p e r s i o n w i t h a p a r t i c l e volume f r a c t i o n , Φ , o f 0.2 and an average r a d i u s of 92 nm, the e f f e c t i v e volume f r a c t i o n of the p a r t i c l e s plus adsorbed l a y e r , 4> f i s ~0.69 (Φ f ^ ^ l+(6/a) ] (10,11). At such a high volume t r a c t i o n (which i s close to the packing f r a c t i o n f o r hexagonal c l o s e packing) i n t e r a c t i o n between the polymer t a i l s i s strong. Such i n t e r a c t i o n accounts, at l e a s t i n p a r t , f o r the v i s c o e l a s t i c behaviour observed at f u l l coverage. In the present system, when no e l e c t r o l y t e was added, there must be a c o n t r i b u t i o n from the i n t e r a c t i o n of the double l a y e r s . The presence of extended double l a y e r s leads to v i s c o e l a s t i c behaviour i n concentrated d i s p e r s i o n s (7-10). Evidence f o r the e l e c t r o s t a t i c c o n t r i b u t i o n w i t h s t e r i c a l l y s t a b i l i z e d d i s p e r s i o n s has been r e c e n t l y obtained (21) from a study of the e f f e c t of the a d d i t i o n of NaCl to a l a t e x d i s p e r ­ s i o n c o n t a i n i n g adsorbed PVA l a y e r s . The r e s u l t s showed a p r o g r e s s i v e r e d u c t i o n i n r e s i d u a l v i s c o s i t y , shear modulus and Bingham y i e l d v a l u e with 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 . The f a c t that there was a measurable and G at a NaCl c o n c e n t r a t i o n of 1 0 m o l dm~ (where double l a y e r e f f e c t s are n e g l i g i b l e ) a l s o i n d i c a t e s a c o n t r i b u t i o n from s t e r i c interactions. With d i s p e r s i o n s where the i n t e r a c t i o n i s p u r e l y e l e c t r o s t a t i c , such as those i n v e s t i g a t e d by R u s s e l l and Benzig (7,8) and B u s c a l l et a l . (9,10), G tends to zero at high e l e c t r o l y t e (>10~2mol dm~3) c o n c e n t r a t i o n s . Thus, the r e s i d u a l modulus, y i e l d v a l u e and η values obtained at f u l l coverage i n the present system with adsorbed PVA are due to the combined a c t i o n of long-range e l e c t r o s t a t i c r e p u l s i o n and s t e r i c i n t e r a c t i o n r e s u l t i n g from the presence of long dangling t a i l s . I t should be mentioned, however, that the e l e c t r o s t a t i c r e p u l s i o n i s s i g n i f i c a n t l y modified due to the e f f e c t of the adsorbed polymer l a y e r on the d i s t r i b u t i o n of ions i n the e l e c t r i c a l double l a y e r . The increase i n the r h e o l o g i c a l parameters, η , G and το, w i t h r e d u c t i o n i n surface coverage p o i n t s towards an i n ­ crease i n p a r t i c l e i n t e r a c t i o n . T h i s could be the r e s u l t of e i t h e r f l o c c u l a t i o n by polymer " b r i d g i n g " (which i s favourable at coverages