Cationic starches on cellulose surfaces : a study of polyelectrolyte adsorption

a study of polyelectrolyte adsorption

"The first man I saw was of a meagre aspect, with sooty hands and face, his hair and beard long, ragged and singed in several places. His clothes, shirt, and skin were all of the same colour. He had been eight years upon a project for extracting sunbeams out of cucumbers, which were to be put into vials

hermetically sealed, and let out to warm the air in raw inclement summers. He told me, he did not doubt in eight years more, that he should be able to supply the Governor's gardens with sunshine at a reasonable rate; but he complained that his stock was low, and entreated me to give him something as an encouragement to ingenuity, especially since this had been a very dear season for cucumbers. I made him a small present, for my Lord had furnished me with money on purpose, because he knew their practise of begging from all who go to see them."

Jonathan Swift: Gulliver's Travels, Part 3, A Voyage to Laputa (1726)

: LANDBOUWCATALOGUS

Hoogleraar in de fysische en kolloïdchemie

Co-promotor: Dr. A. de Keizer

Universitair docent bij de vakgroep Fysische en Kolloïdchemie

H.G.M. van de Steeg

Cationic starches on cellulose

surfaces

a study of polyelectrolyte adsorption

Proefschrift

ter verkrijging van de graad van doctor in de landbouw- en milieuwetenschappen op gezag van de rector magnificus,

dr. H.C. van der Plas,

in het openbaar te verdedigen op dinsdag 14 april 1992

des namiddags te vier uur in de Aula

van de Landbouwuniversiteit te Wageningen.

1 INTRODUCTION

1.1 S t a r c h and p a p e r m a k i n g 1 1.2 A colloid-chemical a p p r o a c h 4

1.3 Outline of this thesis 5

1.4 References 5 2 POLYELECTROLYTE ADSORPTION: A SUBTLE BALANCE OF FORCES

2.1 Introduction 7 2.2 Results a n d discussion 9

2.2.1 Parameters used in the calculations 9

2.2.2 Pure electrosorption 11 2.2.3 Effect of specific adsorption of s e g m e n t s 18

2.2.4 The b o u n d a r i e s of the regimes 2 1 2.2.5 Specific adsorption of counterions 2 2

2.3 Conclusions 2 4 2.4 References 2 5 3 MATERIALS AND METHODS

3.1 Cellulose 2 9 3.1.1 Properties of cellulose 2 9

3.1.2 Materials 3 0 3.1.3 The a p p e a r a c e of cellulose: electron m i c r o g r a p h s 3 0

3.1.4 X-ray diffraction 3 3 3.1.5 Hemicelluloses 3 4

3.1.5.1 Hemicelluloses in microcrystalline cellulose 3 4

3.1.5.2 Cleaning procedure 3 6 3.1.6 Potentiometrie titrations 3 7 3.1.7 Specific surface area of microcrystalline cellulose 3 9

3.2 Cationic s t a r c h 4 1 3.2.1 Properties of native s t a r c h 4 1 3.2.2 S t a r c h derivatives 4 3 3.2.3 Materials 4 4 3.2.4 P h o s p h o r u s content 4 5 3.2.5 Preparation of s t a r c h solutions 4 6 3.2.6 Sedimentation coefficients 4 7 3.2.7 Changes of molecular volume with salt concentration

m e a s u r e d by viscosity a n d dynamic light scattering 4 9

3.2.8 Density of s t a r c h solutions 5 0 3.2.9 Fractionation of cationic potato s t a r c h by

ultra-centrifugation 5 1 3.3 Determination of s t a r c h concentrations 5 1

3.3.1 Carbohydrate determination according to Dubois et al. 5 1

3.3.2 S t a r c h determination with iodine 5 2

3.4 Adsorption m e a s u r e m e n t s 5 7 3.4.1 Adsorption isotherms 5 7 3.4.2 Measurement of adsorption plateau values 5 8

3.4.3 Calculation of the adsorption isotherks of amylose a n d

amylopectin 5 9 3.5 Acknowledgements 6 0 3.6 References 6 0 BIBLIOTHEEK!

r\NDBOuwi3NiyEasrjEH

WAGENINGEN

STELLINGEN I

D a a r vrijwel alle belangrijke t r e n d s in polyelectrolytadsorptie r e e d s in 1977 door Hesselink zijn beschreven, is de o n d e r s c h a t t i n g v a n zijn werk door latere onderzoekers op dit terrein volstrekt onterecht.

F.Th. Hesselink: "On the theory of polyelectrolyte adsorption. The effect on adsorption behavior of the electrostatic contribution to the adsorption free energy". Journal of

Colloid and Interface Science, 60: 448 (1977).

Dit proefschrift, hoofdstuk 2.

II

In v e r b a n d m e t de invloed v a n d e z o u t c o n c e n t r a t i e k u n n e n i n polyelectrolytadsorptie twee r e g i m e s o n d e r s c h e i d e n w o r d e n , namelijk h e t "screening r e d u c e d adsorption" regime en h e t "screening e n h a n c e d adsorption" regime. Als de z o u t c o n c e n t r a t i e groter wordt, n e e m t in h e t eerste regime de adsorptie af, terwijl in h e t tweede de adsorptie d a n j u i s t stijgt.

Dit proefschrift, hoofdstuk 2.

III

Specifieke a d s o r p t i e van s e g m e n t e n k a n niet altijd desorptie v a n e e n polyelectrolyt door zout verhinderen.

Dit proefschrift, hoofdstukken 2 en 4.

IV

Het zou voor p a p i e r m a k e r s geen v e r r a s s i n g m o e t e n zijn d a t "anionic trash" uit Ca2 +-ionen k a n bestaan.

Dit proefschrift, hoofdstuk 5.

V

Voor h e t s l a g e n v a n I n n o v a t i e v e O n d e r z o e k s p r o g r a m m a ' s is h e t noodzakelijk d a t de b e l a n g h e b b e n d e bedrijven actief m e e d e n k e n m e t de o n d e r z o e k ( s t ) e r s .

VI

Door preoccupatie m e t h u n eigen werk lopen experimentalisten die zelf een theorie ontwikkelen h e t risico d a t zij belangrijke implicaties hiervan over h e t hoofd zien.

VII

Het grensvlak t u s s e n kolloid chemie en NMR is nog vrijwel onverkend.

Het milieubeleid van de Europese Gemeenschap is vaak weinig vooruitstrevend. Dit heeft onder meer te maken met de ongrijpbaarheid van de baten van milieumaatregelen. Deze leidt er namelijk toe dat concessies a a n dwarsliggende lidstaten doorgaans b e s t a a n uit vermindering van kosten.

F.W. Scharpf: "Die Politikverflechtungs-Falle: Europäische Integration und deutscher Föderalismus im Vergleich", Polüische Vterteljahresschrift 26(4):323-356 (1985).

J.D. Liefferink: "Probleme der Gestaltung einer gemeinschaftlichen Umweltpolitik - Der Fall der Luftverschmutzung durch Grossfeuerungsanlagen", te verschijnen in 1992.

IX

In het promotiereglement van de Landbouwuniversiteit worden vrouwen alleen expliciet genoemd in de opmerking "voor dames: de meisjesnaam", terwijl de promovendus uitsluitend wordt aangeduid met "hij". Dit valt moeilijk te rijmen met het streven van dezelfde instelling naar een groter aantal vrouwelijke promovendi.

X

Het is opmerkelijk dat in het Christendom de maagdelijkheid van Maria heeft geleid tot prediking van een ascetische levenshouding en onderdrukking van vrouwen, terwijl maagdelijkheid in de Griekse en Romeinse cultuur j u i s t op vrijheid en onafhankelijkheid van de betreffende vrouw duidde.

Marina Warner: "Alone of all her sex. The myth and the cult of the virgin Mary", Picador, Londen (1976).

XI

Hoewel natuurwetenschappers denken dat zij op de hoogte moeten zijn van de relativiteitstheorie, is kennis van de geschiedenis der natuurwetenschappen veel nuttiger om hun activiteiten te relativeren.

XII

De originaliteit van een proefschrift zou beter uitkomen als voor het omslag een één-(of meer-)procentsregeling voor de k u n s t e n werd toegepast.

H.G.M, van de Steeg

Cationic starches on cellulose surfaces, a study of polyelectrolyte adsorption

CRYSTALLINE CELLULOSE

4.1 Introduction 6 5 4.2 Experimental 6 7 4.3 Results a n d discussion 6 7

4.3.1 Adsorption i s o t h e r m s 6 7 4.3.2 Effect of simple electrolyte on the p l a t e a u value 6 7

4.3.3 Effect of type of electrolyte 6 9 4.3.4 Effect of pH a n d electrolyte concentration on the p l a t e a u

value 7 0 4.3.5 Comparison with model calculations 7 2

4.4 Conclusions 7 7 4.5 References 7 8 5 ADSORPTION OF CATIONIC POTATO STARCH ON

MICRO-CRYSTALLINE CELLULOSE

5.1 Introduction 8 3 5.2 Experimental 8 5 5.3 Results a n d discussion 8 6

5.3.1 Starch: a mixture of amylose and amylopectin 8 6

5.3.2 Influence of cellulose concentration 9 2 5.3.3 Influence of simple electrolyte concentration 9 3

5.4.4 Influence of type of electrolyte 9 5 5.4.4.1 Monovalent cations 9 5 5.4.4.2 Divalent cations 9 6 5.3.5 Influence of pH 9 7 5.3.6 Influence of degree of s u b s t i t u t i o n 9 9 5.4 Conclusions 101 5.5 References 102 6 CONCLUSIONS

6.1 Use of theory a n d model systems 1 0 7 6.1.1 General considerations 1 0 7 6.1.2 Relevance for p a p e r m a k i n g 1 0 8 6.2 Cationic s t a r c h a s a polyelectrolyte 1 0 9 6.3 Comparison of the adsorption behaviour of cationic waxy maize

and cationic potato starch 1 12 6.4 Some r e s u l t s with direct relevance for p a p e r m a k i n g 114

6.4.1 Retention 1 1 4 6.4.2 Retention of cationic s t a r c h v e r s u s cationic s t a r c h a s a

retention aid 1 1 5 6.4.3 Cationic s t a r c h a s a dry strength agent 1 1 6

6.5 References 116 APPENDIX 1 Adsorption of cationic waxy maize 1 1 9

APPENDIX 2 Adsorption of cationic potato s t a r c h 121

SUMMARY 129 SAMENVATTING 1 3 3 CURRICULUM VITAE 1 4 0

NAWOORD 141 COLOFON 1 4 3

a study of polyelectrolyte adsorption") was supported by the Dutch Program for Innovation Oriented Carbohydrate Research (IOP-k), with financial aid from the ministry of economic affairs and the ministry of agriculture, nature management and fisheries.

1.1 Starch and papermaking

Plant fibers are the basic material of which paper is made. These cellulosic fibers are the main constituents of plant cell walls and, for papermaking, they are mainly obtained from wood in a chemical (pulping) process.

A scheme of the papermaking process is given in figure 1. The first step is to disperse the fibers in water, usually a few grams per liter, after which they are beaten in the refiner to roughen the surface of the fibers, so that they will better stick together and therefore increase the dry strength of the paper. From the headbox the cellulose dispersion flows out on a moving, endless, fine mesh screen called the wire. Part of the water seeps through the holes in the screen and the fiber mat, which still contains about 80% of water, is formed. This part of the paper machine is often referred to as the wet-end. After formation, the fiber mat is pressed

cellulose refiner

I

Œ

D O

headbox moving wire press drying section section

and dried, so that finally paper is obtained with a water content of 5-8%. Apart from fibers, many other components are usually present in paper, namely the fillers (inorganic particles such as titaniumdioxide, clay or Calciumcarbonate) and several chemicals of which starch is an important one. Starch constitutes the major food reserve of all the higher plants and is laid down in seeds, roots and tubers in the form of particles which are insoluble in cold water, the so-called starch granules. This means that starch must be cooked in order to be used in papermaking.

Starch is applied to improve the dry strength of paper and 0.5-2% on fiber dry weight is added somewhere between the refiner and the headbox (wet-end). If native starches are used for this purpose, the amount held in the sheet is rather low and papermakers say that the retention of starch is poor. According to Cushing and Schuman [1] the retention of native starches is about 60%, so that the rest is lost in process water (so-called white water). In the 1950's, researchers in applied starch chemistry tried to overcome this problem by synthesizing new starch derivatives. Cationic starch proved to be very effective, since at the generally encountered level of addition in paper industry, virtually 100% can be retained by fibers [2]. The first patent for a cationic starch for commercial use was issued in 1957 to Caldwell and Wurzburg [3].

Cationic starch improves dry strength by making the interfiber bonding stronger [4]. Beating requires energy and to save a portion of this expense, starch should be added to obtain a similar increase in strength. Addition of cationic starch is most effective if the starch paste is thoroughly cooked, so that most granules will be broken and thus the starch well dispersed [5]. Roberts et al [6] concluded that native starch and cationic starch equally improved paper strength if the retention was the same, and this is the reason that in most cases cationic starch is more effective.

In filled papers, for instance printing papers, the addition of cationic starch is of special importance. Fillers are highly desirable in printing papers, since they increase opacity and improve printing properties. Higher filler loads tend to improve the optical and printing properties, whereas economic considerations also seem to favour an increased use of fillers. However, the strength properties are severely impaired. Fortunately this loss in strength can be overcome by the addition of cationic starch [7, 8, 9]. Lindström and Floren [7] found that adding cationic starch in combination with an anionic Polyacrylamide (a-PAM), is a very effective way of obtaining a sufficiently large amount of starch in their papers. They suggested that the cationic starch which was not

a d s o r b e d o n t o t h e fibers a n d fillers, w a s p r e c i p i t a t e d o n t o t h e s e c o m p o n e n t s in the form of a polyelectrolyte complex with a-PAM.

Cationic s t a r c h not only affects the dry strength, b u t also t h e retention of fines, small fiber p a r t s , a n d fillers. Fines a n d fillers are m u c h smaller t h a n fibers a n d t h i s m e a n s t h a t it is difficult keeping t h e m in t h e p a p e r s h e e t (or in p a p e r m a k i n g t e r m s , to retain them) simply b y t h e sieve w o r k i n g of t h e fiber web. Moreover, fibers, fines a n d fillers are all negatively c h a r g e d a n d therefore repel e a c h o t h e r . Large c a t i o n i c p o l y m e r s , like c a t i o n i c s t a r c h , a d s o r b on t h e s e negatively c h a r g e d surfaces a n d are able to flocculate fillers a n d fines with fibers by t h e formation of bridges. A good retention of fines a n d fillers also improves drainage of the wet web. It a p p e a r s t h a t the optimal a m o u n t of cationic s t a r c h a s a retention aid, is m u c h lower t h a n the a m o u n t needed to obtain optimal dry s t r e n g t h [10]. So it is often considered more effective to u s e cationic s t a r c h a s a dry s t r e n g t h a g e n t in c o m b i n a t i o n w i t h a n o t h e r retention aid [11]. However, Alince et al. [9] have shown t h a t in clay filled p a p e r s , added cationic s t a r c h both improves filler retention a n d increases strength, which m a k e s the u s e of cationic s t a r c h superior to t h e u s e of only a synthetic retention aid (polyethylenimine).

The beneficial effects of cationic s t a r c h on p a p e r m a k i n g and final p a p e r quality, combined with its low price a s c o m p a r e d to t h a t of s y n t h e t i c p o l y m e r s , m a k e s s t a r c h a n i m p o r t a n t a n d p o p u l a r w e t - e n d additive, especially for fine p a p e r s . Apart from addition a t t h e wet-end to improve the s t r e n g t h of paper, s t a r c h c a n also be added a t the size press, located behind the drying section (figure 1). S t a r c h solutions with c o n c e n t r a t i o n s between 5 a n d 15% are pressed into the r a t h e r dry p a p e r sheet, so t h a t it is absorbed quickly, a n d t h e n the paper is dried again after t h e size p r e s s . Large volumes of s t a r c h are u s e d at the size p r e s s , for i n s t a n c e in t h e p r o d u c t i o n of b o a r d . T h e c o m b i n a t i o n of w e t - e n d a n d size p r e s s applications m a k e s the p a p e r i n d u s t r y t h e worlds largest p u r c h a s e r of s t a r c h . Basic s t a r c h e s , u s e d for cationics, are mostly from corn or potato. World wide corn s t a r c h r e m a i n s dominant, while potato s t a r c h is a close second [12]. Although p a p e r m a k e r s agree on t h e superiority of potato s t a r c h for wet-end applications [13], they b u y more corn s t a r c h b e c a u s e it is cheaper. The lower price of corn s t a r c h also m a k e s it the m o s t popular s t a r c h for size p r e s s applications.

A good retention of cationic s t a r c h a t the wet-end is very i m p o r t a n t . Loss of cationic s t a r c h not only m e a n s loss of dry strength, b u t also loss of fillers a n d fines a n d on top of t h a t the process water and, eventually, the waste water, is polluted. Due to environmental legislation concerning the discharge of w a s t e water, p a p e r mills w a n t their w a s t e w a t e r to be a s

clean as possible. Nowadays most paper mills operate with closed water circuits in order to use this water more effectively, so that polluted process water is a problem first inside and finally also outside the mill. Closure of the water circuits leads to higher concentrations of all kinds of substances in the process water [14, 15] and also the retention of cationic starch can become very poor. It is shown that substances such as aluminium sulphate (so-called papermaker's alum), which is often used, and anionic polymers dissolving from wood [16], reduce the retention of cationic starch.

1.2 A colloid-chemical approach

Although cationic starch is used to such a large extent, neither the mechanism by which it is retained by cellulose fibers, nor the way in which the retention is disturbed, are well understood. Only a small amount of the research efforts in the field of papermaking is devoted to starch. The reason for this could be twofold. Firstly, starch is such a common chemical that it is not considered worthy of research. This was once expressed to the author in the following way: "Starch? You just dig it out of the ground!" Secondly, for those interested in the retention mechanism, the combination of starch and cellulose fibers is far too complex, since neither the characteristics of starch nor those of cellulose fibers are thoroughly known. As stated by Wàgberg and Ödberg [17]: "The porous nature of the fibers obviously makes it important to use well characterized polymers for adsorption studies".

In line with the last anotation, this study was undertaken as a first step to gain more fundamental knowledge about the retention, or in colloid-chemical terms, the adsorption of cationic starch on cellulose and how it can be disturbed. Our approach is a colloid-chemical one, which means that our experimental system was kept as simple as possible in order to facilitate physical interpretation and was therefore far from the reality of papermaking. This has been done very seldom, especially in research related to starch. We studied the adsorption of two different kinds of cationic starch on microcrystalline cellulose as a model for cellulose fibers, in the presence of simple electrolytes and at different pH values. Moreover, we studied an equilibrium situation (or one close to it) in contrast to the very dynamic papermaking process. We also tried to generalize the specific problem of the adsorption of cationic starch on cellulose to polyelectrolyte adsorption, a step which has hardly ever been done in paper research.

1.3 Outline of this thesis

In chapter 2 we investigate the adsorption of polyelectrolytes on oppositely charged surfaces with calculations based on a recent polyelectrolyte adsorption theory [18]. It turns out that polyelectrolyte adsorption is a subtle balance of electrostatic and short-range nonelectrostatic interactions. For a given combination of surface charge density, segment charge and nonelectrostatic interactions, this balance can be affected by changing the concentration of simple electrolytes. In an experimental system the effect of salt concentration on polyelectrolyteadsorption can be accurately determined. Hence, from a comparison between model calculations and experimental data, we can gain insight in the balance between electrostatic interactions, which are usually known best and the, mostly unknown, nonelectrostatic interactions. The characterization of our experimental system, microcrystalline cellulose and cationic starches, as well as the methods we used are described in chapter 3. Chapter 4 deals with the adsorption of cationic amylopectin from waxy maize, the branched starch molecule, on microcrystalline cellulose, and how it is affected by changes in electrolyte concentration, changes in type of electrolyte and changes in pH. The trends in the results can be well described with our theoretical model, which of course helps in understanding the adsorption mechanism. The experimental system in chapter 5 is more complicated since it contains cationic potato starch and thus both the linear and the branched starch components, amylose and amylopectin. Again the effects of electrolyte concentration, type of electrolyte and pH are studied, as well as the charge of the polyelectrolyte (degree of substitution) and the competition between amylose and amylopectin. In this case, we can also understand the trends in the adsorption with help of our theoretical model. Finally, in chapter 6, we compare the adsorption behaviour of cationic amylopectin from waxy maize with that of cationic potato starch and we evaluate the use of our experimental and theoretical model systems for the papermaking process.

1.4 References

1. Cushing, M. L. and K. R. Schuman: Fiber attraction and interfiber bonding-the

role of polysaccharide additives. Tappi Journal 42(12): 1006-1016 (1959).

2. Moeller, H. W.: Cationic starch as a wet-end strength additive. Tappi Journal

49(5): 211-214(1966).

4. Howard, R. C. and C. J. Jowsey: The effect of catlonlc starch on the tensile strength of paper. Journal of Pulp and Paper Science 15(6): J225-J229 (1989). 5. McKenzie, A. W.: The structure and properties of paper. XVII. The mode of action

of carbohydrate beater additives. Appita 19(1): 79-85 (1965).

6. Roberts, J. C , C. O. Au and G. A. Clay: The effect of 14C-labelled cationic and native starches on dry strength and formation. Tappi Journal 69(10): 88-93 (1986). 7. Lindström, T. and T. Floren: The effects of cationic starch wet end additon on

the properties of clay filled papers. Svensk Papperstidning 87(12): R99-R104 (1984). 8. Lindström, T., P. Kolseth and P. Näslund: The dry strengthening effect of

cationic starch wet-end addition on filled papers, in: Papermaking raw materials. Transactions of the 8th Fundamental Research Symposium held at Oxford., V. Punton ed., Mechanical Engineering Publications Ltd., London (1985), pp. 589-611. 9. Alince, B., R. Lebreton and S. St.-Amour: Using cationic starch in filled papers.

Tappi Journal 73(3): 191-193(1990).

10. Stoutjesdijk, P. G. and G. Smit: Einsatz von kationischer Stärke bei der Papierherstellung. Wochenblatt für Papierfabrikation 103(23/24): 897-901 (1975). 11. Harvey, R. D.: Retention of cationic starches. Tappi Journal 68(3): 76-80 (1985). 12. Kirby, K. W.: Specialty starches. Use in the paper industry, in: Agricultural and

synthetic polymers: biodegradability and utilization. ACS Symposium Series 433, J. Edward, J.E. Glass and G. Swift ed., (1990), pp. 274-287.

13. Hofreiter, B. T.: Natural products for wet-end addition, in: Pulp and paper chemistry and chemical technology. Vol. III. 2nd edition., J.P. Casey ed., Wiley -Interscience, Toronto (1981), pp. 1475-1514.

14. Auhorn, W. and J. Melzer: Untersuchung von Störsubstanzen in geschlossenen Kreislaufsystemen. Wochenblatt für die Papierfabrikation 107(13): 493-502 (1979). 15. Auhorn, W.: Das Störstoff-Problem bei Verringerung der spezifischen

Abwassermenge. Wochenblatt für Papierfabrikation 112(2): 3-14 (1984).

16. Halabisky, D. D.: Wet-end control for the effective use of cationic starch. Tappi Journal 60(12): 125-127(1977).

17. Wàgberg, L. and L. Ödberg: Polymer adsorption on cellulosic fibers. Nordic Pulp and Paper Research Journal 4(2): 135-140 (1989).

18. Böhmer, M. R., O. A. Evers and J. M. H. M. Scheutjens: Weak polyelectrolytes between two surfaces: adsorption and stabilization. Macromolecules 23(8): 2288-2301 (1990).

FORCES

2.1 Introduction

When a polyelectrolyte adsorbs on an oppositely charged surface, it is often found t h a t the adsorbed amount compensates, or slightly overcompensates, the surface charge and that the adsorption increases with increasing salt concentration [1, 2, 3]. At low electrolyte concentration the adsorbed layers are thin and the adsorbed amount hardly depends on molecular weight. This indicates a flat conformation of the polyelectrolyte and these trends refer to highly charged polyelectrolytes. Recent theories on polyelectrolyte adsorption [4, 5, 6] are in agreement with these experimental findings. The somewhat older treatment of Hesselink [7] predicts very thick adsorbed layers, but finds the same effect of increasing salt concentration. The usual argument is that for highly charged polyelectrolytes the repulsion between the segments dominates the adsorption behaviour. At high salt concentration the repulsion is screened, hence the polyelectrolytes behave more like uncharged polymers. They can adopt conformations with loops and tails and the adsorbed amount increases. Naturally, a fully screened polyelectrolyte can only adsorb if there is an attractive interaction between segments and surface which is not electrostatic in nature.

However, sometimes the adsorption of polyelectrolytes is found to decrease with increasing salt concentration [8-14], or is not affected at all [8]. In most of these cases the polyelectrolytes have a low charge [8, 9,

12, 13], but highly charged polyelectrolytes can also show this behaviour [10, 11, 14]. Theoretically, decreasing adsorption, or even complete desorption, with increasing salt concentration is considered by Hesselink, Wiegel and Muthukumar [7, 15, 16]. This effect is expected if the attraction between polyelectrolyte and surface is mainly electrostatic in nature, since salt not only screens the segment-segment repulsion, but also the segment-surface attraction. Thus, in polyelectrolyte adsorption, added salt has two antagonistic effects and it depends on the balance between electrostatic and nonelectrostatic attraction whether or not increasing the salt concentration leads to an increase or a decrease in adsorption. If this force balance is changed, for instance by increasing the segment charge, the influence of the salt concentration can be reversed. Durand et al. [8] found such a reversal for cationic Polyacrylamides (copolymers of acrylamide and an acrylate with a quaternary ammonium group) adsorbing on montmorillonite. With a cationic monomer content (T) of 1% the adsorbed amount decreased with increasing salt

c o n c e n t r a t i o n , for x=5% t h e r e w a s no salt effect, w h e r e a s for cationic Polyacrylamides with x=13% a n d x=30% the adsorbed a m o u n t increased with increasing salt concentration.

Having m a d e these observations, we propose to distinguish two regimes in polyelectrolyte a d s o r p t i o n . We will call t h e m t h e screening-reduced

adsorption regime a n d the screening-enhanced adsorption regime. In order

to m a k e t h i s d i s t i n c t i o n o p e r a t i o n a l , we will c o m p a r e t h e a d s o r b e d a m o u n t in t h e limit of negligible s c r e e n i n g , r0, i.e. a t very low s a l t

c o n c e n t r a t i o n w h e r e t h e a d s o r b e d a m o u n t of p o l y e l e c t r o l y t e c o m p e n s a t e s , or slightly o v e r c o m p e n s a t e s , the surface charge, with r „ the adsorbed a m o u n t at very high salt concentration, where electrostatic interactions are virtually eliminated and the polymer c a n be considered a s uncharged. So we have:

1. r"o>roo, screening-reduced adsorption. Electrostatic a t t r a c t i o n between s e g m e n t a n d surface d o m i n a t e s : the a d s o r b e d a m o u n t r d e c r e a s e s with i n c r e a s i n g ionic s t r e n g t h . Salt c a n s c r e e n t h i s a t t r a c t i o n a n d r e d u c e adsorption.

2 . ro<r\*,, screening-enhanced adsorption. N o n e l e c t r o s t a t i c a t t r a c t i o n between segment a n d surface dominates: r i n c r e a s e s with increasing ionic s t r e n g t h . Salt c a n s c r e e n t h e r e p u l s i o n b e t w e e n t h e c h a r g e d s e g m e n t s a n d e n h a n c e the adsorption.

In t h e i n t e r m e d i a t e c a s e , w h e n b o t h forces are of r o u g h l y e q u a l importance, changing the salt concentration will hardly affect r .

In t h i s p a p e r we explore these regimes by numerical calculations b a s e d on a recent theory for polyelectrolyte adsorption [6] which is a n extension of the Self Consistent Field theory for polymer adsorption by Scheutjens a n d Fleer [17, 18]. Here, we will only expound the m a i n features of this t h e o r y (for t e c h n i c a l d e t a i l s t h e r e a d e r is referred to t h e p a p e r by B ö h m e r et al. [6]). The polymers are considered to be flexible linear c h a i n s in a solution, which is modelled a s a lattice. E a c h lattice site is either occupied by a cluster of solvent molecules, or by a hydrated ion or a polymer s e g m e n t . T h e n o n e l e c t r o s t a t i c energy for i n t e r a c t i o n b e t w e e n p a i r s of c o m p o n e n t s is expressed t h r o u g h Flory-Huggins % p a r a m e t e r s . The nonelectrostatic interaction of a c o m p o n e n t i with t h e surface (S) is described formally by a similar Xis parameter. In the m e a n field a p p r o a c h c h a r g e s on the surface a n d on the polymer are s m e a r e d o u t in layers parallel to the surface. The charges are located in a plane in the center of e a c h layer a n d t h e s p a c e b e t w e e n t h e s e p l a n e s is free of electrical c h a r g e s . The electrical potential in every p l a n e is obtained by solving a d i s c r e t e v e r s i o n of t h e P o i s s o n - B o l t z m a n n e q u a t i o n . T h e p o t e n t i a l difference between the equidistant planes t h e n d e p e n d s on the charge on

each plane, on the separation distance (d) between the p l a n e s and on the dielectric c o n s t a n t . However, for a surface p o t e n t i a l of 100 mV, t h e p o t e n t i a l d e c a y for v a r i o u s v a l u e s of d c a l c u l a t e d w i t h t h i s m o d e l , completely coincides with t h a t calculated from t h e G o u y - C h a p m a n theory [31. Only if volume exclusion effects play a role, n a m e l y for very high surface p o t e n t i a l s a n d at high salt c o n c e n t r a t i o n s , does t h e value of d affect t h e potential decay [61. The dielectric c o n s t a n t in a lattice layer c h a n g e s according to the composition of t h i s layer a n d is t a k e n to be a linear combination (volume fraction weighted) of the dielectric c o n s t a n t s of t h e polyelectrolyte, salt a n d water.

The configuration of a polyelectrolyte molecule c a n be modelled a s a step-weighted walk in t h e lattice. The weighting factors for each s t e p c o n t a i n t h e n e a r e s t - n e i g h b o u r c o n t a c t e n e r g y (Flory-Huggins), t h e electrical potential a n d the mixing entropy. The mixing entropy a c c o u n t s for t h e fact t h a t t h e probability of a s t e p t o w a r d s a given lattice layer, d e c r e a s e s a s t h e s e g m e n t c o n c e n t r a t i o n in t h i s layer b e c o m e s higher. F r o m all t h e s e weighted w a l k s t h e v o l u m e fraction profile a n d t h e adsorbed a m o u n t are calculated.

One might argue t h a t the m e a n field approximation is a d r a w b a c k of t h i s model. Especially for polymers with a low charge density t h e local electrical p o t e n t i a l m a y differ significantly from t h e a v e r a g e v a l u e . However, the model r e p r o d u c e s m a n y experimental features quite well, so we believe the m e a n field a s s u m p t i o n to be acceptable.

In t h i s p a p e r we restrict ourselves to the adsorption of polyelectrolytes on oppositely c h a r g e d s u r f a c e s a n d we investigate t h e effects of salt c o n c e n t r a t i o n , s e g m e n t c h a r g e , s u r f a c e c h a r g e d e n s i t y a n d n o n 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 on t h e a d s o r p t i o n . First we c o n s i d e r t h e effects of salt concentration, segment charge and surface charge density for c a s e s with electrostatic interactions only (pure electrosorption). Then we t r e a t c a s e s where t h e s e g m e n t s a d s o r b specifically a n d we investigate how the force b a l a n c e is affected by changing the salt concentration, the s t r e n g t h of the nonelectrostatic attraction, the s e g m e n t charge a n d the s u r f a c e c h a r g e d e n s i t y . Finally, we e x a m i n e t h e effect of specific a d s o r p t i o n of c o u n t e r i o n s . We c o m p a r e o u r t h e o r e t i c a l r e s u l t s with reported experimental results, where possible.

2 . 2 R e s u l t s and d i s c u s s i o n

2.2.1 Parameters used in the calculations

C a l c u l a t i o n s were performed u s i n g a h e x a g o n a l lattice with a layer spacing d of 0.6 nm, which is a b o u t the diameter of a hydrated ion. In the

model calculations all c o n c e n t r a t i o n s are expressed in volume fractions. In experimental s y s t e m s , c o n c e n t r a t i o n s of t h e small ions a r e u s u a l l y given a s molarities a n d h e r e we will do t h e s a m e . For conversion of volume fractions to concentrations, the lattice cell volume, determined by the value of d, is n e c e s s a r y [61. Since we allow only one ion p e r lattice site, t h e value of d should not be too high in order to avoid ions filling the complete lattice a t high salt concentration. The multiplication factor to convert volume fractions to concentrations is 4.85 for d=0.6 n m [6].

The surface charge w a s always negative a n d it w a s k e p t c o n s t a n t . In this p a p e r t h e surface charge density is u s u a l l y given in C / m2, b u t it c a n

b e converted to u n i t charges per lattice site multiplying with 2 . 2 5 . The calculations p r e s e n t e d here were all performed for polyelectrolytes with

100 s e g m e n t s , b u t t h e t r e n d s were t h e s a m e for longer c h a i n s . The model polyelectrolytes are polyions with a fixed n u m b e r of u n i t c h a r g e s p e r s e g m e n t x a n d a relative dielectric c o n s t a n t of 2 0 . T h e relative dielectric c o n s t a n t s of all o t h e r c o m p o n e n t s were t a k e n a s 8 0 . The r e s u l t s of t h e c a l c u l a t i o n s are n o t sensitive to t h e exact v a l u e of t h e dielectric c o n s t a n t s , since the b u l k volume fraction of the polyelectrolyte, w h i c h w a s k e p t c o n s t a n t a t 1 0 0 0 p p m , is low. T h e Flory-Huggins % p a r a m e t e r s for t h e interaction between ions a n d solvent molecules were t a k e n to b e zero. The interacting molecules b e h a v e like h a r d s p h e r e s if X=0. They do n o t have s h o r t - r a n g e i n t e r a c t i o n s , only excluded volume effects play a role; by definition %=0 for molecules of t h e s a m e kind a n d Xij=5Cji [191- T n e X v a l u e s for t h e i n t e r a c t i o n b e t w e e n polyelectrolyte

s e g m e n t s a n d solvent or salt ions, were t a k e n a t 0 . 5 . For u n c h a r g e d polymers x=0-5 indicates a 0-solvent.

For t h e n o n e l e c t r o s t a t i c i n t e r a c t i o n of a polymer s e g m e n t P a n d a solvent molecule O with the surface S, similar Flory-Huggins p a r a m e t e r s c a n b e defined. T h r o u g h o u t t h i s p a p e r , however, we will u s e t h e adsorption energy p a r a m e t e r Xs. defined by Silberberg [20] a s -(UA-UOI/JCT, where UA is the adsorption energy of a polymer segment or a salt ion a n d u o t h a t of a solvent molecule, k is Boltzmann's c o n s t a n t and T t h e absolute t e m p e r a t u r e . T h u s , Xs is positive if A a d s o r b s preferentially from t h e solvent. The relation between the Flory-Huggins p a r a m e t e r s XAS a n d Xos. a n d Xs is XS=_Ä.I(XAS-XOS). since only a fraction %i (0.25 in a hexagonal lattice) of a n adsorbed segment is in a c t u a l contact with the surface, so UA/W=^I3CAS arid uo/kT=X\Xos- In our calculations Xs for the solvent a n d

for t h e salt ions w a s zero. In t h e last section, where we will investigate t h e effect of specific adsorption of c o u n t e r i o n s , t h e Xs of the salt cation w a s larger t h a n zero. To d i s t i n g u i s h b e t w e e n t h e a d s o r p t i o n e n e r g y

parameter of counterions C+ and that of polymer segments, we use Xsc and

Xs» respectively.

2.2.2 Pure electrosorption

In order to obtain a good insight in the effect of the electrostatic interaction, both the attraction between polyelectrolyte and surface and the repulsion between the segments, we first examine the adsorption r (expressed in equivalent monolayers) of a polyelectrolyte which has only electrostatic interactions with the surface (Xs=0). The effects of the salt concentration and the segment charge x are shown in figure la. The adsorbed amount at very low salt concentration, r0, is always higher than

the adsorbed amount at high salt concentration, T„, which even drops down to zero. At high salt concentration the range of the electrostatic interaction becomes smaller, i.e. the attraction between polyelectrolyte and surface is screened. Since the salt ions have a finite volume, the cations also compete with the polyelectrolyte for adsorption sites on the surface. The polyelectrolyte desorbs if the salt cations are more effective in compensating the surface charge. Therefore, we are clearly dealing with the screening-reduced adsorption regime. This behaviour was experimentally found for cationic Polyacrylamide adsorbing on silica [10], for cationic Polyacrylamide adsorbing on montmorillonite [8] and also in some other systems [11, 12, 13, 14].

Although the uncharged (x=0) polymer does not adsorb, since it has no adsorption energy to overcome the loss in conformation entropy, a small charge per segment (x=0.005) suffices to make the polymer adsorb, at least at low salt concentration. The adsorbed amount decreases very quickly with increasing salt concentration. A polyelectrolyte with x=0.015 has a much higher adsorbed amount at low salt concentration, but the adsorption also decreases with increasing ionic strength. Polyelectrolytes with higher charges per segment adsorb less at low salt concentration, but stay attached to the surface up to higher salt concentration. It is clear that changing x can have a dramatic effect on the adsorbed amount. Some experimental evidence for this large effect of x on the adsorption behaviour of a strong polyelectrolyte is available [8, 9, 10]. It also emerged from a recent study about the pH effect on the adsorption of a weak polyelectrolyte [21].

The increase in adsorbed amount when going from x=0 to t = 0 . 0 1 5 , followed by a decrease in adsorbed amount with further increasing x, is more clearly depicted in figureslb and lc, where the adsorbed amount is plotted as a function of x, for different salt concentrations. The sharpest peak occurs at very low salt concentration. At the right side of the peak

t h e adsorbed a m o u n t decreases with increasing s e g m e n t charge, d u e to c h a r g e c o m p e n s a t i o n . This h a s b e e n called "1:1 c h a r g e stoichiometry" between charges on the adsorbed polyelectrolyte a n d the total a m o u n t of charged g r o u p s on t h e surface (Wâgberg et al. [22, 2 3 , 24]). If x is high less polyelectrolyte is needed to c o m p e n s a t e t h e surface charge density. No m o r e polyelectrolyte t h a n n e c e s s a r y for c h a r g e c o m p e n s a t i o n is adsorbed, d u e to repulsion between the s e g m e n t s . Hence, r is given by r-x= I Go I (öo in u n i t charges/lattice site), so a hyperbolic curve is obtained with T °CT- 1 if Go is c o n s t a n t . The dotted lines in figures l b a n d l c

r e p r e s e n t t h i s relation. For very low x, the surface charge is only partly c o m p e n s a t e d , since t h e affinity of t h e polyelectrolyte for t h e surface d e c r e a s e s w i t h d e c r e a s i n g x a n d d i s a p p e a r s if T = 0 . In t h i s c a s e t h e a d s o r p t i o n affinity of t h e m a c r o - i o n is so low t h a t it c a n n o longer c o m p e t e w i t h t h e s m a l l c o u n t e r i o n s . T h e m a x i m u m , a t low s a l t c o n c e n t r a t i o n , s e e m s to occur w h e n t h e total c h a r g e on t h e c h a i n becomes of order unity, i.e. x ^ r- 1, where r is the c h a i n length, since t h e n

t h e affinity of the macro-ion is comparable to t h a t of t h e small ions. We also notice t h a t the position of the m a x i m u m moves towards higher x with increasing salt concentration. The polyelectrolyte n e e d s more affinity for the surface, t h u s a higher charge, to enable compensation of the surface charge a n d to compete effectively with the c o u n t e r i o n s . Hesselink also predicted [7] a m a x i m u m in the adsorbed a m o u n t , which he expected to occur for x=0.1 at a salt concentration of 0.01 M, i.e. a b o u t t h e s a m e a s we found (figure lc).

A m a x i m u m in t h e a d s o r b e d a m o u n t a s a function of t h e s e g m e n t charge w a s experimentally found by Wang a n d Audebert [10] a n d D u r a n d et al. [8, 9] for the adsorption of cationic Polyacrylamide on, respectively, silica a n d montmorillonite, a n d also by T a n a k a et al. [25] a n d McKenzie [26] for t h e a d s o r p t i o n of, respectively, several polyelectrolytes a n d cationic s t a r c h on cellulose. In the above mentioned d a t a of Wang a n d Audebert [10] a n d T a n a k a et al. [25], the m a x i m u m occurred at x=0.01 for

a very low electrolyte concentration (no a d d e d electrolyte). Blaakmeer et al. [21] found a m a x i m u m in t h e a d s o r b e d a m o u n t of polyacrylic acid adsorbing on a positively charged latex a s a function of pH. Again the m a x i m u m o c c u r r e d w h e n t h e degree of dissociation of t h e PAA w a s approximately 0 . 0 1 . The effect of the salt c o n c e n t r a t i o n w a s studied by D u r a n d et al. [8] for only five v a l u e s of x. The a d s o r b e d a m o u n t w a s maximal if x w a s 0 . 0 1 , for all salt concentrations, which differs from our model calculations in figures l b a n d l c . However, t h i s contradiction is caused by the fact t h a t in their system %s w a s larger t h a n zero. Our model

logcs

Figure l a . Effect of segment charge T

on the adsorption of a fully dissociated polyelectrolyte of 100 segments on an oppositely charged surface (-0.01 C/m2) a s a function of the 1:1 electrolyte concentration cs (M). The adsorbed a m o u n t r is given in equivalent monolayers. 0.5 r-r 0.25 -2 r 1.5 0.5 0.4 0.6 t

Figure l c . Essentially the same graph

a s figure l b , with different scales for both axes. The adsorbed amount r as a function of the segment charge x at two different salt concentrations.

1 \ charge compensation r

In. s-

J

/

°

II JNC

°'

function of the segment charge t at four different salt concentrations. The dotted line represents the adsorbed a m o u n t n e c e s s a r y for c h a r g e compensation. 0.12 0.08 0.04 / _\

1

s

// V

-

Figure Id. The volume fraction profile

for various segment charges, cs= 1 0- 5 M. Other parameters as in figure la.

20

calculations for polyelectrolytes with Xs>0. in figure 4a, agree very well with the results of Durand et al., as will be discussed in section 2.2.3.

The change in conformation of the adsorbed polyelectrolyte with increasing t, at low salt concentration, is displayed in figure Id. At very low values of x, the polyelectrolyte is hardly attached to the surface, long loops and tails dangle in the proximity of the oppositely charged surface. The layer with the highest volume fraction of polyelectrolyte segments

lies far from t h e surface. I n c r e a s i n g t h e s e g m e n t c h a r g e l e a d s to a s h a r p e r p e a k in the volume fraction profile, w h i c h lies closer to t h e surface. If x=l, t h e volume fraction of polyelectrolyte is h i g h e s t in the first layer, so the conformation becomes r a t h e r flat. It is obvious t h a t at low salt c o n c e n t r a t i o n polyelectrolytes do n o t always a d s o r b in a flat conformation. They c a n even be depleted from the first layer(s), which is d u e to t h e long r a n g e of electrostatic i n t e r a c t i o n s . The polyelectrolyte does not have to a d s o r b in the first layer to gain adsorption energy, since adsorption in layers further away from the surface is also energetically favourable. With m a n y s e g m e n t s in t h e first layer, the polyelectrolyte would loose too m u c h conformation entropy. From a n entropie point of view a conformation with long loops and tails is the m o s t favourable. At higher salt c o n c e n t r a t i o n s the conformation of polyelectrolytes b e c o m e s more extended, irrespective of x (not shown), since a n increasing a m o u n t of s e g m e n t s is displaced from the surface by salt cations. Eventually the last s e g m e n t is detached a n d the polyelectrolyte d e s o r b s . We will come back to t h i s desorption later.

The next variable we will consider is the surface charge density. As in the case of the s e g m e n t charge, for all surface c h a r g e s t h e a d s o r p t i o n d e c r e a s e s with increasing salt c o n c e n t r a t i o n (figure 2a). r0 h a s a finite

value w h e r e a s r«,=0, so we are still in the screening-reduced adsorption regime. Increasing the surface charge density leads to a n increase in the adsorbed a m o u n t b e c a u s e polyelectrolytes a d s o r b until they c o m p e n s a t e t h e surface charge, so r = o o / x , a s d i s c u s s e d earlier. C o n s e q u e n t l y , t h e adsorbed a m o u n t varies linearly with the surface charge a t different salt concentrations, provided it is not so high t h a t the polyelectrolyte c a n not a d s o r b a n y m o r e . In figure 2 b we show how r varies with t h e relative segment charge at different surface charges. As in figure l e , a m a x i m u m o c c u r s which moves t o w a r d s h i g h e r x if the surface charge d e n s i t y is increased, m e a n i n g t h a t the polyelectrolyte needs higher affinity, h e n c e a higher x, in order to be able to c o m p e n s a t e the surface charge. On the r i g h t h a n d side of t h e m a x i m u m , t h e polyelectrolyte is a b l e to c o m p e n s a t e the surface charge, w h e r e a s on the left h a n d side the affinity for the surface decreases to zero for the u n c h a r g e d polymer.

From t h e s e g m e n t density profile in figure 2c we c a n see t h a t a t the lowest surface charge densities the volume fraction of t h e polyelectrolyte in the first layer is lower t h a n in the second layer, indicating a fairly e x t e n d e d conformation. At higher surface c h a r g e density, t h e volume fraction in t h e first layer is t h e h i g h e s t , so t h e larger e l e c t r o s t a t i c attraction forces the polyelectrolyte into a flatter conformation, or, to p u t

1 d. r 0.8 0.4 -0.001 C/m2 \ 2 ^0.1 C/m \ \ \ \ -0.01 C/m2 \ - 3 - 2 1 loge

Figure 2a. The effect of surface charge

d e n s i t y on t h e a d s o r p t i o n of a polyelectrolyte of 100 segments with x=0.2 and Xs=0. on an oppositely charged surface as a function of the salt concentration cs (M). 0.6 0.4 0.2 \ \ - 0 1 C/m2 \ \ -0.05 C/m' " ~ V . \ -0.03 C / m2\ \ -0.01 C/m2 ï £ ^ \ \ -0.1 C/m' _\ ,» -0.01 C/m

•'V

function of the segment charge x for three different surface charge densities at cs= 1 0 "5 M. For x>0.2 the adsorbed amount equals the amount required for charge compensation at all three surface charges (not shown). Other parameters as in figure 2a.

0 2 4 6 8 10

layer

Figure 2c. Volume fraction profile for different surface charge densities, cs= 1 0- 3 M. Other parameters as in figure 2a.

it a n o t h e r way, at high potentials the energy gain of adsorption in the first layer is enough to compensate the loss in conformational entropy.

As we have seen in figures l a and 2a, a polyelectrolyte can be displaced from the surface by salt ions. The salt concentration where the adsorption v a n i s h e s , w h i c h we call the critical s a l t c o n c e n t r a t i o n cs c, s e e m s to

depend on t h e segment charge x and the surface charge density oo, since cs c is larger if x or o0 are larger. A polymer (either charged or uncharged)

is desorbed if the adsorption energy no longer c o m p e n s a t e s the loss in conformational entropy. This m e a n s t h a t the net adsorption energy h a s to

be larger t h a n a critical value, Xsc- From t h e definition of Xs (see 2.2.1) for a n u n c h a r g e d polymer it is clear t h a t we a r e dealing with a n exchange energy. A t t a c h m e n t of a polymer segment to t h e surface is accompanied by displacement of solvent molecules, or of other molecules s u c h a s salt i o n s , from t h e a d s o r p t i o n sites. Desorption o c c u r s if t h e a d s o r p t i o n energy of molecules other t h a n those from t h e solvent, displacers, is large enough to decrease the adsorption energy of a polymer segment below %sc

[27, 28]. In polyelectrolyte adsorption we also have to t a k e into a c c o u n t the electrostatic i n t e r a c t i o n s . Salt ions c a n , therefore, a c t a s displacers for a polyelectrolyte even if their "chemical" interaction with t h e surface is negligible.

An analysis of t h e criteria for electrosorption (%s=0) of a polyelectrolyte

c h a i n in a s a l t s o l u t i o n w a s m a d e by Wiegel [15] a n d e x t e n d e d b y M u t h u k u m a r [16] u s i n g m e a n field a r g u m e n t s . For a G a u s s i a n poly-electrolyte w i t h o u t i n t e r n a l r e p u l s i o n , Wiegel o b t a i n e d t h e following relation between the surface charge density Go a n d t h e segment charge z on the one h a n d a n d the Debije screening length K- 1 on t h e other h a n d :

IT-CO I •* K3 (1)

Wiegel's t h e o r y w a s e x t e n d e d by M u t h u k u m a r [16] for flexible poly-electrolytes. D u e to i n t e r n a l repulsion, polyelectrolytes a r e swollen a n d s h r i n k w h e n t h e s e g m e n t - s e g m e n t repulsion is screened. Therefore, t h e effect of t h e salt c o n c e n t r a t i o n on t h e a d s o r b e d a m o u n t is s m a l l e r . M u t h u k u m a r showed t h a t Wiegel's K3 h a s to be multiplied by a factor of

K4/5, SO

It-Go I « K U / 5 or cs c- (t-Go)10/11 (2)

With our model we calculated at which salt concentration the adsorbed amount of a polyelectrolyte is zero. We determined the critical salt concentration for polyelectrolytes with various segment charges adsorbing on a surface with a charge density of -0.01 C / m2, and for a

polyelectrolyte with x=0.2 adsorbing on a surface with various charge densities. The relations between cs c and i, and between cs c and Go were

both power laws, with exponents of 0.88 (correlation coefficients.9995) and 0.85 (correlation coefficients.9999) respectively. Hence, the exponents obtained with the Böhmer model agree very well with

10/11=0.91 of equation (2). This agreement between Muthukumar's analytical theory and the numerical calculations based on the Böhmer theory is to be expected, since both theories use a mean field approach and flexible chains.

We noticed that for absolute surface charge densities larger than 0.02 C/m2 the double logarithmic plot of csc as function of OQ is not linear

anymore. This non-linearity is caused by high potentials, for which the Debije-Hückel approximation can not be used. Muthukumar derived equation (2) using this approximation, whereas in the Böhmer model the exact solution of the Poisson-Boltzmann equation is used. The DH-approximation holds reasonably well for potentials smaller than 50 mV. For the salt concentrations that we are dealing with, the surface potential is about 50 mV at c0=0.02 C/m2.

We should note here, that a different relation between cs c and the

product of x and Oo, was obtained by Evers et al. [29], who used an earlier version of the Böhmer model. Evers et al. studied the adsorption of polyelectrolytes with xs>0, and derived a simple expression for the

critical surface charge density CTOC, by only considering the electrostatic

interactions in the first layer (i.e. within a distance d from the surface). His result was:

KEçEg (Xs+XlX-Xsc) (3)

xe

where eo is the permittivity of vacuum, es the relative dielectric constant

of the solvent and e. the elementary charge. If one varies ionic strength rather than surface charge density, expression (3) reads:

cs c = (T-ÖO)2 (3a)

Now the exponent is 2 instead of 10/11. Hence, equation (3) does not correctly describe the displacement by salt studied here. The assumption t h a t only electrostatic interactions in the first layer need to be considered, is probably not justified. Yet, Evers found a fairly good agreement between equation (3) and his numerical calculations. The reason for this is that he used highly charged (T=1) polyelectrolytes and Xs=l- From figures Id, 2c and 3b it can be seen that a high segment charge, high surface charge density and a not too small nonelectrostatic affinity for the surface (xs>0), promote a flat conformation of the adsorbed polyelectrolyte. So, in Evers' calculations, all the segment-surface interactions are indeed short range. The difference of a factor K2 between

Evers' and Wiegel's analysis, or, equivalently the factor K9/1 1 between the

analyses of Evers and Muthukumar, is due to the neglect of adsorbed polyelectrolyte segments that interact with, but do not touch the surface.

2.2.3 Effect of specific adsorption of segments 0.24 r 0.18 0.12 0.06 0.00 -/ / y X =0.35 / s ' X = 0 . 2 9 \ n \ 0.08 0.06 0.04 0.02 \ Xs= 0 3 5

/ V

Figure 3a. The adsorbed amount, r as a

function of the salt concentration cs (M) for different v a l u e s of X s . t h e nonelectrostatlc Interaction with the surface; t=0.2, o-o=-0.01 C/m2.

0

0 2 4 6 8 10 layer

Figure 3b. Volume fraction profile for

different values of Xs: cs= 1 0- 3 M. Other parameters as in figure 3a.

In the previous section we have seen that only the screening-reduced adsorption regime is found if the interaction between polyelectrolyte and surface is merely electrostatic. The screening-enhanced adsorption regime emerges when a non-electrostatic interaction [%s) is introduced, as is

shown in figure 3a. It is more difficult to desorb the polyelectrolyte with salt if 5Cs>0> even for very small Xs- since a nonelectrostatlc attraction is added to the electric attraction. The effect of added salt is already nearly eliminated for the curve in the middle (xs=0.29): at first the adsorption

increases a little with increasing salt concentration, after which it finally decreases slightly. A modest further increase in %s, modifies the

behaviour entirely: now the adsorption clearly increases with increasing salt concentration. This is the onset of the screening-enhanced adsorption regime. Repulsion between the segments suppresses the adsorption at low salt concentration but screening of this repulsion at high salt concentration leads to development of loops and tails and, therefore, to an increase in the adsorbed amount. From the volume fraction profile (figure 3b) we can see that for Xs>0, much more polyelectrolyte is present in the first layer, because the polyelectrolyte only gains the nonelectrostatic adsorption energy when adsorbing in the first layer. For the conformation of a polyelectrolyte at the surface, therefore, it is quite important whether or not a nonelectrostatic attraction between polyelectrolyte and surface exists.

2.0 r 1.5 -1.0 0.5 0.0 \ ^ • T = 0 . 0 1 5 0.005 s . T«0 ^""* 7^Ö"03 T-0.05 T = 0 . 2 5 . -^ ~^~-_ - - ' " ' . -y 1 „.charge compensation screening reduced for x =0.6 1.25 - 5 - 4 - 3 - 2 - 1 0 logcs

Figure 4a. The adsorbed amount r as

function of the salt concentration cs (M) for different values of the segment charge x. Xs=0.6 and ao=-0.01 C/m2.

0.2

Figure 4b. The adsorbed amount r as a

function of segment charge T for Xs=0 and Xs=0.6 at cs=10"5 M; o"o=-001 C/m2 in both cases. The horizontal line in the graph is drawn at the level of the adsorbed amount for an uncharged polymer with

Xs=0-6-The balance between nonelectrostatic and electrostatic attraction can be varied by changing %s, which however, is not easily accomplished in an

experiment. Usually it is easier to change the segment charge or the surface charge density, and this may serve the same purpose. In figure 4a it can be seen how varying x affects the influence of the salt concentration. First of all, the uncharged polymer is also adsorbed; its adsorbed amount is hardly affected by the salt concentration. Then, a

1.2

r 0.8

-0.1 C/m * - » . _ uncharged polymer, uncharged surface ' \

-0.05 C/m2

logo.

Figure 5. The adsorbed amount r as a function of the salt concentration cs (M) for different values of the surface charge density. Xs=0.6; T=0.2.

g r a d u a l increase in a s e g m e n t charge x t a k e s u s t h r o u g h the

screening-reduced adsorption a n d into the screening-enhanced adsorption regime.

Notice t h a t t h e a d s o r b e d a m o u n t of t h e polyelectrolytes a t h i g h s a l t c o n c e n t r a t i o n d o e s n o t always completely r e a c h t h a t of t h e u n c h a r g e d polymer, a l t h o u g h %s is the s a m e for all values of x (r(x=0)=r\J.

In figure 4 b we c a n see how c h a n g i n g x affects V for %s=0 (see also

figure lc) a n d xs= 0 . 6 respectively. Both curves show a m a x i m u m in the

adsorbed a m o u n t , which for %s=0 occurs at x=0.015, w h e r e a s it is slightly

shifted to x=0.01 for Xs=0.6. The larger adsorbed a m o u n t s for Xs=0.6 t h a n for Xs=0 in t h e range 0<x<0.01, are a n o t h e r difference between t h e two c u r v e s . For t h e s e s m a l l v a l u e s of x, t h e a d s o r b e d a m o u n t for a polyelectrolyte is larger t h a n for a n u n c h a r g e d polymer with t h e s a m e Xs. since a polyelectrolyte also gains adsorption energy for s e g m e n t s in layers further from the surface (figures Id, 2c a n d 3b). With figure 4 b we c a n determine where the transition from t h e screening-reduced adsorption to t h e enhanced adsorption regime t a k e s place. The

screening-reduced adsorption regime occurs if r0>ro t J. If we draw a horizontal line at

the level of r « , the adsorbed a m o u n t of the u n c h a r g e d polymer a t xs= 0 . 6 ,

we are dealing with the screening-reduced adsorption regime for all values of x smaller t h a n t h a t a t the intersection point of t h e curve a n d t h e line: x=0.03. The salt concentration will hardly affect the adsorbed a m o u n t for x=0.03 b e c a u s e To^r^. It should be noted t h a t if xs>0, charge reversal can

t a k e place. This is not yet t h e case in figure 4b, since for Xs=0.6 t h e a d s o r b e d a m o u n t s a r e e q u a l to t h o s e n e c e s s a r y for s u r f a c e c h a r g e c o m p e n s a t i o n . This transition of the screening-reduced adsorption to the

screening-enhanced adsorption regime with increasing segment charge w a s

experimentally found by D u r a n d et al. [8] for the a d s o r p t i o n of cationic Polyacrylamide on montmorillonite. In figure 5, where t h e surface charge density is varied, the s a m e t r e n d s c a n be observed a s in figure 4. Now the

screening-reduced adsorption regime e m e r g e s for t h e h i g h e s t surface

charge density (o0> t ' L , with Go in elementary c h a r g e s / l a t t i c e site) a n d

the screening-enhanced adsorption regime for t h e lower surface charges. At high s a l t c o n c e n t r a t i o n t h e a d s o r b e d a m o u n t s move t o w a r d s t h e adsorbed a m o u n t of t h e u n c h a r g e d polymer, b u t they do n o t r e a c h t h i s value completely. T h e a d s o r b e d a m o u n t again i n c r e a s e s linearly with i n c r e a s i n g s u r f a c e c h a r g e d e n s i t y . T h e effects of e l e c t r o s t a t i c a n d nonelectrostatic attraction are additive, a s w a s also found before by van der Schee a n d Lyklema [4], Papenhuijzen et al. [5] a n d Evers et al. [29] in t h e i r m o d e l c a l c u l a t i o n s . T h i s l i n e a r i n c r e a s e i s c o n f i r m e d b y experiments, for i n s t a n c e by B o n e k a m p [3, 30].

2 . 2 . 4 The boundaries of the regimes

In t h i s section we will explore t h e b o u n d a r i e s of t h e regimes more systematically. As we have seen before, t h e screening-reduced adsorption regime occurs if %s<0 for all values of t a n d Go- Neglecting charge reversal,

t h e screening-reduced adsorption regime o c c u r s for %s>0, i n first

approximation, if i < o o / n „ ( w i t h oo in elementary c h a r g e s / lattice site). In figure 6 t h e b o u n d a r i e s b e t w e e n t h e r e g i m e s a r e s h o w n for t h r e e different values of Xs a n d various values for x a n d Go. T h e first diagram is for Xs=0.29, w h i c h is a p p r o x i m a t e l y e q u a l to t h e critical v a l u e xs c,

n e c e s s a r y to m a k e a n u n c h a r g e d polymer a d s o r b a t all, w h e r e a s for Xs values larger t h a n 4 t h e adsorbed a m o u n t of a n u n c h a r g e d polymer hardly increases anymore. T h e r e a s o n is t h a t if t h e layer closest to t h e surface is completely filled with s e g m e n t s , t h e a d s o r b e d a m o u n t (at fixed c h a i n

0.5 0.5 0.02 0.04 0.06 0.08 0.1 a (C/m2) 0 1 = 0 . 6 screening enhanced 7

A

V////7/////

Figure 6. Values for z and oo for different Xs (as indicated in the figure) where the screening-reduced adsorption regime and screening-enhanced adsorption regime occur for a

length) c a n n o t increase anymore [17]). From figure 6 it is clear t h a t t h e

screening-reduced adsorption regime will emerge for a broad range of x if

Xs is small or if ao is large, w h e r e a s for large %s or small Go it comes o u t

only for very small x.

It now becomes clear why the screening-reduced adsorption regime w a s not found in earlier calculations b a s e d on t h e m e a n field model [4, 5, 6]. Only t h e i n f l u e n c e of t h e s a l t c o n c e n t r a t i o n for h i g h l y c h a r g e d polyelectrolytes (x=-l) a n d %s>0 (usually %s=l) h a d b e e n calculated. We

also u n d e r s t a n d b e t t e r why, in experimental s y s t e m s , t h e adsorption is more often t h a n not found to increase with increasing salt concentration. Many e x p e r i m e n t s are done with highly c h a r g e d polyelectrolytes. The

screening-reduced adsorption regime for s u c h a s y s t e m would only be

found if t h e a t t r a c t i o n between polyelectrolyte a n d surface is (almost) p u r e l y e l e c t r o s t a t i c , a n d it is r a t h e r likely t h a t a t l e a s t s o m e nonelectrostatic affinity between polyelectrolyte a n d surface exists.

2.2.5 Specific adsorption of counterfoils

So far we have considered the salt ions a s solvent molecules, except for t h e i r c h a r g e . However, it is well k n o w n t h a t s a l t i o n s m a y a d s o r b specifically, which, in t e r m s of t h i s model, implies t h a t their %s is larger

t h a n zero. We will investigate the effect of specifically adsorbing salt ions having t h e s a m e charge a s the polyelectrolyte, n a m e l y t h e c o u n t e r i o n s . The m o s t interesting effect c a n be expected for t h e screening-enhanced

adsorption regime, since the trend for the screening-reduced adsorption

regime will n o t c h a n g e w h e n the salt ions have a d s o r p t i o n energy (the decrease of the adsorption with increasing salt concentration will only be more p r o n o u n c e d ) . Since t h e Xs of t h e polyelectrolyte is positive, t h e adsorbed a m o u n t will initially increase with increasing salt concentration. Then, a t higher salt c o n c e n t r a t i o n the salt cations win t h e competition a n d s t a r t displacing the polyelectrolyte. The result of t h e s e two t r e n d s is a maximum in the adsorbed a m o u n t a s a function of the salt concentration (figure 7). The larger the nonelectrostatic interaction of the salt cations C with t h e surface (the more positive their ^sc) the more effective they act a s displacers, so t h a t the m a x i m u m becomes less p r o n o u n c e d a n d moves towards lower c o n c e n t r a t i o n s . A m a x i m u m in the adsorbed a m o u n t a s a function of salt concentration h a s occasionally been found experimentally. For i n s t a n c e by B o n e k a m p [3, 30] for polylysine on silica, by Lindström & W â g b e r g [31] a n d T a n a k a et al. [25] for r e s p e c t i v e l y , c a t i o n i c Polyacrylamides a n d polyDMDAAC (DiMethyl-DiAllylAmmonium Chloride) on cellulose fibers, a n d by v a n de Steeg (chapter 4 of t h i s thesis) for cationic amylopectin adsorbing on microcrystalline cellullose.

Figure 7. The adsorbed amount T as a

function of the salt concentration cs (M) for a polyelectrolyte of 100 segments with x=0.2 and Xs=0-6, on an oppositely charged surface (-0.01 C / m2) . The s h o r t - r a n g e , nonelectrostatic inter-action of the salt cation C+ with the surface, XsC is varied. 0.75 0.5 0.25 t=0 . 1=0.035 ~ " ~ - ^v 1=0.1 ^^-" 1-0.2 -• i=0.4 /= 1 -, —J , W

V.

Figure 8. The adsorbed amount r as a

function of the salt concentration cs (M) for a polyelectrolyte with £s=0.6 and a specifically adsorbing salt cation C+ with ZsC= 1-5. The segment charge x of t h e p o l y e l e c t r o l y t e is v a r i e d , o0=-0.01 C/m2. 0.6 r 0.4 0.2 -. — -0.05 C/m* -0.025 C/ffl2 "~ X --0.005 C/m2. - ^ ^ ' " ' 0 C / m i _ - - - " " " — "" . \ \ \ \ \\

A

Figure 9. The adsorbed amount r as a function of the salt concentration cs (M) for various surface charge densities, T=0.2, ZS= 0 . 6 and XsC=l-5.

In figure 8 the segment charge x is varied at constant surface charge density, %s and %sc- Surprisingly, the critical salt concentration decreases

with increasing segment charge. This effect is opposite to what has been found when only electrostatics play a role (for instance figure la, see also equation 2). The reason is that specifically adsorbing salt ions are localized in the first layer, because otherwise they cannot gain the extra adsorption energy. A polyelectrolyte with a high segment charge also has a preference for the first layer (see figure Id), so that the displacement of