Chapter 2
Polymer Behaviour at Clay and Solid Surfaces 2.1. INTRODUCTION Since polymer adsorption holds the key to an understanding of the formation and properties of clay–polymer complexes, it seems appropriate to sketch out the outlines of this process. Many of the underlying mechanisms have come to light as a result of experimental and theoretical studies carried out over the past four decades in response to the actual and potential applications of the clay–polymer interaction in agriculture and industry. Perhaps the single, most important recent development in this area relates to the synthesis and characterization of polymer–clay nanocomposites, described in Chapter 7. Although difficulties still exist in matching experiment with theory, a self-consistent picture of polymer behaviour at solid/solution interfaces has emerged. We might add that the majority of the experimental data refer to polymer adsorption from nonaqueous solvents whereas most processes involving clay minerals and soils occur in an aqueous environment. For this reason, the role of water must be borne in mind if we are to extrapolate such data to aqueous systems. Water will compete strongly with the polymer for adsorption sites on the solid surface, particularly when hydrogen bonding can occur. Since water can act as both hydrogen bond donor and acceptor, its presence at the mineral surface may either promote or inhibit polymer adsorption. In this connection, we should mention that the basal oxygens of the tetrahedral sheet, making up the siloxane surface, are weak electron donors (Lewis bases). Thus, 2:1 layer silicates that have no isomorphous substitution in their structure, such as talc and pyrophyllite (cf. Figure 1.4), are essentially hydrophobic. Here, the water molecules interact more with each other than with the surface (Malandrini et al., 1997; Michot et al., 1994; Nulens et al., 1998; Schoonheydt and Johnston, 2006; Schrader and Yariv, 1990). However, the basal aluminol surface of 1:1 phyllosilicates, such as kaolinite (cf. Figure 1.3), can form hydrogen bonds with water molecules. By contrast, 2:1 phyllosilicates that have a negative surface charge, notably montmorillonite, are hydrophilic in character because of the presence of charge-balancing inorganic cations (cf. Figure 1.9). Having appreciable Developments in Clay Science, Vol. 4. DOI: 10.1016/B978-0-444-53354-8.00002-5 # 2012 Elsevier B.V. All rights reserved.
47
48
Formation and Properties of Clay-Polymer Complexes
enthalpies of hydration, ranging from 300 to 1500 kJ/mol (Atkins and de Paula, 2002), these counterions attract water molecules many of which must be desorbed in order to accommodate a single polymer molecule. As illustrated in Figure 2.1, the translational entropy so gained by the system provides the driving force for polymer adsorption. Entropy effects are also partly responsible for the very strong attachment of polymers because the enthalpy change for polymer adsorption is small although the measurements by Chen and Evans (2005), using dehydrated (heat-treated) montmorillonite, would suggest otherwise (cf. Chapter 3). Comprehensive theories on the behaviour of uncharged linear flexible homopolymers at a flat plate (plane) surface have been proposed (Cohen Stuart et al., 1986; Fleer et al., 1993; Scheutjens and Fleer, 1979, 1980; Silberberg, 1962a). By comparison, the theoretical basis for the adsorption of compact macromolecules, copolymers, and polyelectrolytes has not been well developed (Dobrynin and Rubinstein, 2005; Kawaguchi and Takahashi, 1992). This situation reflects the inherent complexity of such systems rather
A
B
External (bulk) solution Loops
Tail
Interface
Clay surface
Trains
Key: Water molecule Exchangeable cation Negative surface charge
Polymer in solution (random coil) Polymer adsorbed (train–loop–tail)
FIGURE 2.1 Diagram showing the series of events when an uncharged, flexible polymer adsorbs at a clay mineral surface from a dilute aqueous solution. (A) Polymer in solution adopting a random coil conformation; (B) on adsorption, the polymer chain uncoils and adopts a train– loop–tail conformation, displacing relatively ordered water molecules from the interface into the external (bulk) solution.
Chapter
2
Polymer Behaviour at Clay and Solid Surfaces
49
than a lack of interest. By the same token, relatively little attention has been paid to adsorption on other types of surfaces although some attempt has been made to analyse the behaviour of polymers between two plane surfaces (Di Marzio and Rubin, 1971; Scheutjens and Fleer, 1982, 1985) and in a pore (Pouchly, 1970). The principles behind the interactions of small organic compounds with clay minerals are now fairly well understood and provide a basis for interpreting clay–polymer complex formation. Uncharged polar organic molecules are largely adsorbed by interaction of their functional groups with the inorganic counterions at the silicate surface, while positively charged organic species are essentially taken up by cation exchange with the counterions. Adsorption is normally exothermic and increases with the molecular weight of the organic solute due to the enhanced contribution of van der Waals forces to the overall adsorption energy (Lagaly et al., 2006; Mortland, 1970; Theng, 1974; Yariv and Cross, 2002). The interactions of organic polymers with clay and solid surfaces differ in some important respects from those of simple, nonpolymeric compounds (Ash, 1973; Burchill et al., 1983). This is because polymer molecules are long, flexible, and often polyfunctional. The importance of entropy effects in relation to chain length has already been remarked on. Further, chain flexibility and polyfunctionality enable the polymer to adopt various conformations, allowing it to be attached to the solid surface by numerous segment– surface bonds or ‘trains’ as shown in Figure 2.1. A complete quantitative description of the clay–polymer interaction would therefore require understanding of polymer behaviour in solution as well as at the clay/solution interface, a condition that is not often met in practice.
2.2. ADSORPTION ISOTHERMS The determination of adsorption isotherms is perhaps the single, most useful means of characterizing the properties of polymer solutions in the presence of an adsorbing surface. Hughes and von Frankenberg (1963) have likened the solid (adsorbent) surface to a probe that, on insertion into a polymer solution, is capable of ‘scanning’ the thermodynamic condition of the system. Adsorption isotherms, however, can only yield a limited amount of information about the state of the adsorbed layer. Thus, supplementary measurements need to be carried out if we wish to gain some insight into the conformation of adsorbed polymers. A feature of polymer adsorption is that equilibrium conditions may take some considerable time (>102 s) to become established. This is particularly true for porous adsorbents, such as clay minerals. Equilibrium is normally assumed to have been attained when the amount of polymer in solution remains sensibly constant with time. As Cohen Stuart et al. (1986) have
50
Formation and Properties of Clay-Polymer Complexes
pointed out, time-dependent studies of polymer adsorption are a necessary, but not sufficient, indication of equilibrium. The reversibility of the process ðPolymerÞb , ðPolymerÞs
ð2:1Þ
where the quantities in brackets refer to concentration and the subscripts b and s denote the solution (bulk) and surface (adsorbed) phases, respectively, has only rarely been examined (Cosgrove and Fergie-Woods, 1987; Koral et al., 1958). It is generally assumed, however, that equilibrium (2.1) is shifted far to the right as indicated by the small temperature effect of the process and the shape of the isotherm, described below. By the same token, the rate of desorption on dilution is very small and adsorption is often considered to be irreversible (Bolto and Gregory, 2007; Breen, 1999; de Bussetti and Ferreiro, 2004; Deng et al., 2006; Greenland, 1972; Gregory, 1978; Seybold, 1994; Tekin et al., 2006). This observation may be ascribed to the ‘octopus effect’ in that it is statistically improbable that all train segments in a given polymer chain can detach simultaneously from the surface and remain so sufficiently long for the polymer to move away from the interface (Podoll et al., 1987). The difficulty in desorbing an adsorbed polymer as compared with a small molecule (by the same solvent and under the same conditions as used for its adsorption), however, is only one of degree. Cosgrove and Fergie-Woods (1987), for example, have reported that adsorption of low molecular weight polystyrene to carbon is reversible. Indeed, adsorbed polymers can be fully desorbed by addition of a particular solvent if the interaction between the (displacer) solvent and surface is stronger than that between polymer segment and surface. Adsorbed polymers may also be displaced by other solutes and polymers (Blockhaus et al., 1997; Chiellini et al., 2000; Kawaguchi, 1990; Klumpp et al., 1998; Pelton, 1986). In the case of micromolecules, the shape of the isotherm is diagnostic of the underlying adsorption process. On the basis of the initial slope, Giles et al. (1960) have distinguished four types of solid–solution adsorption (SSA) isotherms, referred to as S, L (for ‘Langmuir’), H (for ‘high affinity’), and C (for ‘constant partition’) (Figure 2.2). Subsequently, a theoretical basis for each type together with the corresponding experimental verification was developed using a thermodynamic approach (Giles et al., 1974a,b). S-type isotherms are rarely observed for polymer systems. These curves are found when the activation energy for removal of the adsorbed species (EA) is concentration-dependent and/or is reduced by a large negative contribution from that of the solvent (EB), or from a second solute (EC) if present. L-type curves are found when none of these energy terms is dependent on concentration. As the name suggests, C-curves are found when there is a constant partition of solute between the bulk solution and the surface phase during adsorption. H-type isotherms obtain when EAEBþEC; that is, the affinity of the solute for the solid substrate is high even at very low concentrations. They
2
51
Polymer Behaviour at Clay and Solid Surfaces
FIGURE 2.2 Diagram showing the different types of solid–solution adsorption isotherms. From Giles et al. (1960).
Equilibrium concentration of solute on adsorbent
Chapter
S
L
C
H
Equilibrium concentration of solute in solution
occur, for example, when the solute molecules, which individually may be small, are adsorbed as a relatively large unit or aggregate. Since this is the case for a single polymer chain, the SSA isotherms of most polymers are of the H-type. The initial slope may be regarded as a measure of the ease with which solute molecules can find vacant sites on the surface. The increase in slope with concentration for S-type isotherms indicates that there is a corresponding rise in the number of adsorbing sites. On the same basis, the decrease in slope with concentration for L-curves may be ascribed to increased difficulty the solute has in finding surface vacancies as its solution concentration is increased. The SSA isotherms for a number of polymers are of the L-type particularly when measured at low solute concentration and surface coverage. This might be because macromolecules can assume different conformations at the interface and show varying degrees of attachment to the surface, as adsorption progresses. The constancy in slope shown by C-type isotherms would indicate that the number of adsorbing sites does not vary with concentration. This implies that new sites are being created as adsorption progresses. Only porous adsorbents seem capable of giving rise to linear isotherms. As the solute penetrates the solid structure through a micropore, more sites become exposed and accessible to the following molecules. Interestingly, negatively charged humic and fulvic acids give rise to C-curves when they adsorb to montmorillonite from dilute solutions (Theng, 1976; Theng and Scharpenseel, 1976; cf. Chapter 12). H-curves are characterized by a long flat plateau, indicating saturation of the surface at moderate solution concentrations. Plateau adsorption values tend to increase with polymer size in that the isotherm becomes more ‘rounded’ when the molecular weight of the adsorbing polymer is sufficiently reduced (Fleer et al., 1993).
52
Formation and Properties of Clay-Polymer Complexes
If the determination of adsorption isotherms is experimentally straightforward, their interpretation is often difficult because the adsorption process, as mentioned earlier, is strongly influenced by polymer conformation. Uncharged linear flexible homopolymers in solution tend to adopt the conformation of a random coil rather than that of an extended, stretched out chain. At the solid/solution interface, however, the polymer chain adopts a conformation that allows for maximum segment–surface contacts to be established. The attachment of one segment would increase the probability of neighbouring segments to be absorbed. Since the number of segments (and/ or functional groups) in the chain is large, multiple bonding between polymer and surface is favoured. The net result is normally an interfacial conformation in which contiguous sequences of adsorbed segments or ‘trains’ alternate with free three-dimensional ‘loops’ extending away from the surface, the chain terminating at either end in two free-dangling ‘tails’ (Figure 2.1). Such a conformation may be regarded as a compromise between a random coil in solution and a randomly twisted or buckled two-dimensional surface structure of a fully collapsed chain. The extension of loops and tails defines the layer or interfacial thickness which, at high coverage, is dominated by tails (Cohen Stuart et al., 1986). The considerable amount of distortion and alteration in polymer shape accompanying adsorption leads to a loss in conformational entropy. This effect, however, is more than offset by the large increase in attraction energy due to the establishment of numerous segment–surface contacts, even though the free energy increase per contact may be quite small. In other words, all that is required for adsorption to occur is that the interaction energy per segment–surface attachment exceeds a certain critical value, usually of the order of a few tenths kT where k is the Boltzmann constant and T the absolute temperature (Section 2.3). Once this barrier is overcome, however, the excess energy per polymer chain rises rapidly, giving rise to a large increase in adsorption (Cohen Stuart et al., 1986). One consequence of the strong polymer–surface bonding is that a large amount of material can be removed even from very dilute solutions. Thus, H-type isotherms typify the adsorption from solution of polymeric compounds to solid surfaces, including clay minerals (cf. Chapter 3). Indeed, the most informative region of the isotherm corresponding to the initial rise where interactions between adsorbed chains and segments within a chain are minimal is often experimentally inaccessible because the slope here is so steep. Of the other factors influencing polymer adsorption, we may just briefly mention molecular weight, temperature, and solvency. Although there are situations where the plateau value is essentially independent of molecular weight (chain length), adsorption generally increases with chain length up to a limiting value. This is at least true for nonporous adsorbents where adsorption is restricted only by the extent of the accessible surface. The molecular weight effect extends to polydisperse systems where the high molecular
Chapter
2
Polymer Behaviour at Clay and Solid Surfaces
53
weight components are usually preferentially taken up (Chen and Evans, 2004). This behaviour might be expected on the ground that the frequency of segment–surface bonding will increase with chain length and the number of functional groups per molecule. Clay and soil systems, however, are porous, and an apparent reversal of the molecular weight effect is by no means uncommon. This is because entry into the interlayer space of a clay mineral, or the interparticle pore of a soil aggregate, may be physically impossible for polymers of a certain size. Similarly, the effect of temperature on adsorption is less than straightforward. Thus, we might expect adsorption to decrease with a rise in temperature, as is normally the case with simple, monofunctional solutes. More often than not, however, a zero or small positive temperature coefficient is observed with polymers (Israel et al., 2001; Parfitt and Greenland, 1970), and this relates to entropy effects referred to above. Since the position of equilibrium (2.1) is far to the right, this observation may also be explained in terms of the way in which temperature affects the number of attached segments or the area required per attached segment (Fontana, 1971). Theoretical considerations (Silberberg, 1962a,b) predict that train size decreases, while the number of segments contained in loops increases, with rising temperature. On the other hand, solvent effects are qualitatively easier to predict in terms of polymer–solvent and surface–solvent interactions. When the latter are weak, adsorption increases with a decrease in polymer solubility. This reflects the manner in which a given solvent influences the dimension of the polymer coils in solution. Since the macromolecular chain will be more tightly coiled in a ‘poor’ than in a ‘good’ solvent, more polymers can be packed at the surface. The solvency factor, however, does not come into the picture when only one type of solvent (e.g. water) is used. This applies to most clay and soil systems for which the role of water has already been emphasized. Here, the uncharged polymer must compete with water that is coordinated to the exchangeable cation (counterion) and, to a lesser extent, with water that is directly associated with the silicate surface. Another important parameter in the solid–polymer interaction is the thickness of the adsorbed polymer layer which again is related to the coil dimension in solution. Thicknesses between 10 and 100 nm have been reported for a variety of polymer–solvent–mineral combinations, depending on the method of measurement and solute concentrations (Cohen Stuart et al., 1986; Fontana, 1971; Stromberg, 1967). Whereas a polymer may adopt a relatively flat conformation when adsorbed from dilute solutions, the number of segment–surface contacts tends to decrease with rising concentration, while loop size increases until some maximum size is reached. However, for polymers possessing numerous functional groups capable of interacting with surface sites, no large conformational changes may occur as adsorption progresses. Using infrared (IR) spectroscopy, Fontana and Thomas (1961), for example, were able to demonstrate that the adsorption of
54
Formation and Properties of Clay-Polymer Complexes
polylauryl methacrylate (from organic solvents) onto silica occurred through hydrogen bonding between the ester carbonyl groups of the polymer and the surface silanols. This interaction gave rise to a shift in the carbonyl absorption frequency from that of the unattached segments, enabling the fraction of adsorbed segments to be determined without ambiguity. For this system, about 36% of the polymer segments were in contact with the surface, a value that was virtually invariant with molecular weight and surface coverage. Using similar techniques, Thies et al. (1967) found a value of 25% for polymethyl methacrylate, while for polystyrene and poly(4-vinyl pyridine), the fraction of attached segments decreased with increasing surface coverage. For the polyvinyl pyrrolidone/water/silica system, the bound fraction estimated by IR spectroscopy is appreciably smaller (<0.5) than the value derived from nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopic measurements (Cohen Stuart et al., 1986). Little information about adsorbed layer thickness and bound fraction is available for polymer/water/clay mineral systems. However, when intercalation can occur as it often does with montmorillonite, X-ray diffraction analysis (Francis, 1973; Greenland, 1963; Lagaly et al., 2006) and electrophoretic measurements (Hild et al., 1997; McFarlane et al., 2006; Se´quaris et al., 1999) of the clay–polymer complex can provide information about the average depth and probable conformation of the polymer in the interlayer space. Adsorbed layer thicknesses deduced in this way, however, may not apply to that portion of the polymer that adsorbs to external particle surfaces (Szczerba et al., 2010). Even if the polymer system was monodisperse, there is more scope for the molecules to form longer loops or thicker layers on external basal than interlayer surfaces. Further, different effective layer thicknesses or loop sizes may be possible for a given proportion of segments in trains.
2.3. THEORETICAL ASPECTS The adsorption of polymers from solution to solid surfaces has been the subject of many reviews. Early attempts include those by Hughes and von Frankenberg (1963), Kipling (1965), Patat et al. (1964), Stromberg (1967), Fontana (1971), and Vincent (1974), while the reviews by Cohen Stuart et al. (1986), Kawaguchi and Takahashi (1992), Fleer et al. (1993), and Dobrynin and Rubinstein (2005) represent more recent efforts. It is not intended here to give yet another comprehensive account of this topic. Rather, we will outline the main conclusions and indicate those features that may be applicable and relevant to the clay–polymer interaction. Any theory of polymer adsorption must clearly take into account the conformational properties of the adsorbed chain. In addition, theoretical treatments must be capable of predicting the effect on adsorption of such parameters as polymer volume fraction in the equilibrium solution, chain
Chapter
2
Polymer Behaviour at Clay and Solid Surfaces
55
length (number of segments), and segment–surface interaction energy (Cohen Stuart et al., 1986). Existing theories on the adsorption of uncharged, flexible homopolymers at the solid/solution interface can more or less reproduce experimental observations. Quantitative experimental verification of theoretical predictions, however, is not without difficulty because of the limited breadth of measurements, polymer polydispersity, and uncertainty about the nature (surface composition) of the adsorbent. This situation is particularly true for clay–polymer systems. In addition, the different approaches used in developing these theories have led to somewhat divergent conclusions since no single treatment gives equal weight to all aspects of polymer behaviour. Most theories consider the adsorbed polymer in isolation, neglecting interactions between chains. They further assume dilute solutions and an accessible surface whose area is much larger than that occupied by the polymer. Only the salient points and important conclusions of the various treatments will be given here. The first serious attempt to develop a theory of polymer adsorption was made by Frisch, Simha, and Eirich in the early 1950s (Frisch et al., 1953; Simha et al., 1953). Adsorption is formulated in terms of a diffusion equation, the surface being regarded as a reflecting wall and the polymer as a Gaussian coil whose segments are attached on single surface sites. The average number of adsorbed segments (v) in a chain consisting of n segments is given by v f 0:5 n0:5
ð2:2Þ
where f is an inverse function of chain flexibility. For a situation where the attached sequence comprises only one segment and solvent adsorption is absent, the Frisch–Simha–Eirich (FSE) isotherm equation is ðy=1 yÞ expð2K 1 yÞ ¼ ðKcÞ1=v
ð2:3Þ
where K1 and K are constants, K1 is a measure of the interaction energy between adsorbed segments (in excess of their interactions in the bulk phase), K is the equilibrium constant, y is the fraction of total surface covered by the polymer, and c is the polymer concentration in solution. For K1¼0 and v¼1, Equation (2.3) reduces to ðy=1 yÞ ¼ Kc
ð2:4Þ
which is the well-known Langmuir expression for the adsorption of simple (nonpolymeric) monofunctional solutes. In terms of isotherm shape, the FSE theory predicts a steeper initial rise, followed by a slower approach to a plateau value than does the Langmuir equation. More importantly, the polymer is attached to the surface by relatively few segments, the bulk being contained in loops. Further, adsorption may either increase or decrease with rising temperature. Uptake, however, would be favoured from a poor solvent since then f would be small. Similarly, Forsman and Hughes (1963) predicted that adsorption would increase with
56
Formation and Properties of Clay-Polymer Complexes
molecular weight (M) as reflected by the more rapid rise to a plateau of the isotherm with increasing n. Only at low solute concentration and for weak polymer-surface interactions would the isotherm resemble the Langmuir form when y became proportional to M0.5. On the other hand, Silberberg’s (1962a,b) treatment would predict an essentially extended (flat) surface conformation. In other words, the polymer is adsorbed with small loops and a high fraction (p) of segments in trains even when the individual segment–surface interaction energy (є) is low. Thus, for єkT (where kT is the thermal energy), p>0.7. The experimentally derived values of p, however, are generally smaller (0.25–0.4), probably due to steric factors and chain interference in the surface layer on adsorption. Only when there is a good geometrical ‘fit’ between polymer functional groups and surface sites, as might occur between polyesters and silica, does p conform closely to the theoretical prediction (Joppien, 1974). Nonetheless, uncharged linear homopolymers are apparently adsorbed with an appreciable proportion of their segments in direct contact with the surface although the magnitude of p decreases as the amount adsorbed increases (Cohen Stuart et al., 1986). Hoeve’s (1965) analysis, however, indicates that small p values, and large loops, are possible when the polymer chain is sufficiently flexible and є is small, while Roe (1974) predicts that for a given value of є, adsorption from a good solvent initially rises with increasing n and then levels off at high n. A comprehensive (self-consistent field) theory of polymer adsorption at solid/solution interfaces has been developed by Scheutjens and Fleer (1979, 1980). For monodisperse polymers, the theory predicts formation of long tails at saturation (plateau adsorption) with the number of tail segments increasing almost linearly with chain length (n). At low coverage, the polymer chain lies flat with small loops and tails, but beyond a certain threshold, the layer thickness steeply increases, especially in good solvents. At a fixed concentration, the (root mean square) layer thickness is proportional to n0.5. These points are illustrated in Figures 2.3 and 2.4. FIGURE 2.3 Diagram showing the cumulative contribution of trains, loops, and tails to the excess adsorbed amount (Gss) as a function of chain length (n) at constant polymer concentration in the bulk solution. From Cohen Stuart et al. (1986).
2.0
Tails
1.5
Loops
s
Ès 1.0
Trains
0.5
0
1
2
3
log n
Chapter
2
57
Polymer Behaviour at Clay and Solid Surfaces
FIGURE 2.4 Diagram showing the 100% distribution of segments in trains, loops, and tails as a function of chain length (n) at constant bulk concentration. From Cohen Stuart et al. (1986).
Tails
Loops
50
Trains
0 10
100
n 1000
Roefs et al. (1994) have extended the Scheutjens–Fleer (SF) theory to polydisperse polymer systems. The theory predicts that, at low solution concentrations, long-chain polymers are preferentially adsorbed over their shortchain counterparts. This is because the translational entropy per unit polymer mass is inversely proportional to chain length. Short-chain polymers, however, are preferred at high bulk concentrations because the translational entropy then becomes less important, while long chains lose more conformational entropy than short ones (Cohen Stuart et al., 1986). The question arises whether compact polymers would behave similarly to open-chain, flexible ones, described above. Silberberg’s (1973) analysis would suggest that this is so. It is perhaps surprising that the adsorption of compact polymers to solid surfaces has received relatively little attention, considering that many proteins, enzymes, and soil humic substances occur as more or less tight, globular, or spheroidal entities. This might be because biologically derived polymers are normally charged. As such, their adsorption is influenced by electrochemical factors in addition to those that come into play with uncharged polymers. Besides being charged, polyelectrolyte chains can also undergo a stretching–coiling transformation as well as swelling and shrinking in response to changes in solution pH and ionic strength. These points may be illustrated by the effect of adding sodium hydroxide on the viscosity of polyacrylic acid solutions (Figure 2.5). The initial rise in viscosity may be ascribed to a gradual uncoiling of the polyanionic chain as the number of carboxylate groups in the chain increases, leading to intramolecular charge repulsion and chain stretching. The maximum in the curve may be identified with the situation where the polymer chain is fully extended. Beyond this point, the addition of NaOH results in chain recoiling (shrinking), presumably through charge
58
Formation and Properties of Clay-Polymer Complexes FIGURE 2.5 Changes in the specific viscosity of polyacrylic acid solutions on addition of increasing amounts of NaOH as a function of the degree of polymerization (n). Curve A: n¼640. Curve B: n¼790. Curve C: n¼1000. From Flaig (1976), based on data by Staudinger (1941).
Specific viscosity
1.0
0.75
0.50
C
0.25
B A
0
0
50
100
150
Sodium ions (%)
screening at high ionic strength. These effects are important and relevant to the use of polyelectrolytes as flocculants of clay and colloidal dispersions (e.g. Michaels, 1954). The relationship between coil dimension and flocculating effectiveness will be described later. Although the adsorption of polyelectrolytes to charged surfaces has been investigated for more than three decades, an adequate theoretical analysis of the polyelectrolyte–solid interaction is yet to be developed (Cohen Stuart et al., 1986; Dobrynin and Rubinstein, 2005). An early attempt was made by Hesselink (1972) who described the driving force of adsorption (E) in terms of an electrostatic and a nonelectrostatic free energy gain. The effect of added electrolyte and pH is expressed in the dependence of E on the electrical double layer thickness (Section 2.4) and the degree of ionization of the polyelectrolyte. When the adsorbent and polymer carry the same type of charge, adsorption is predicted to decrease with an increase in charge density and to increase with salt concentration (Hesselink, 1977). The lattice theory of van der Schee and Lyklema (1984) predicts that adsorbed layers are thin because loop and tail formation is suppressed by strong charge–charge repulsion between segments. Adsorption increases and the adsorbed layer becomes thicker if this repulsion is screened by electrolyte addition. Very high ionic strengths, however, are required for adsorption to approach the behaviour of uncharged polymers. Since the net segment–surface interaction energy for polyelectrolyte adsorption to oppositely charged surfaces would be expected to exceed 1kT, the proportion of attached ‘train’ segments would be large, if not close to unity, irrespective of chain length (Dickinson and Eriksson, 1991; Higuchi, 1961). This implies a rapid collapse of the polymer chain on the solid surface, forming a thin (2–5 nm) adsorbed layer (Papenhuijzen et al., 1985). Nevertheless, polycations on montmorillonite may form short loops when the clay surface is fully occupied (Ueda and Harada, 1968). By comparison, uncharged polymers tend to form thick (6–12 nm) adsorbed layers as Rossi et al. (2002)
Chapter
2
Polymer Behaviour at Clay and Solid Surfaces
59
have reported for the adsorption of nonylphenol-polypropylene oxide-polyethylene oxide copolymers by Naþ-montmorillonite. On the other hand, polyanions are largely repelled from the basal surface of layer silicates as Parfitt and Greenland (1970) have observed for the interaction of polyuronides with Naþ-montmorillonite. Polyanions, however, may adsorb to the edge surface of clay particles by hydrogen-bonding interactions (Emerson, 1956; Kohl and Taylor, 1961; Laird, 1997), or when this surface becomes positively charged at acid pH values (Mortensen, 1962; Warkentin and Miller, 1958; Figure 1.6). Nevertheless, appreciable adsorption of polyanions to the basal surface of clay minerals can occur when the exchange sites on the surface are occupied by polyvalent cations, acting as a ‘bridge’ between the negatively charged functional groups of the polymer and the silicate surface (Breen, 1999; Laird, 1997; Theng, 1976; Theng and Scharpenseel, 1976). Indeed, the presence of polyvalent cations is generally necessary if anionic macromolecules are to adsorb to negatively charged surfaces (Gregory, 1978; Sommerauer et al., 1968; Theng, 1982). The complexation of polyelecrolytes by multivalent ions in solution has received a great deal of attention over recent years because of its importance to biological phenomena, such as DNA ‘condensation’ (Dobrynin and Rubinstein, 2005). Complexation with polyvalent cations would also decrease polyanion solubility and hence promote adsorption or deposition of the complex (Ringenbach et al., 1995).
2.4. COLLOID CHEMICAL ASPECTS Much of the information on the clay–polymer interaction relates to situations where solutions of the polymer are added to an aggregated clay system. A good example is the use of synthetic polymers, notably polyacrylamide, as ‘soil conditioners’ (cf. Chapter 6) to increase soil aggregate stability and water infiltration, reduce erosion, and promote crop growth (Carr and Greenland, 1975; De Boodt and Gabriels, 1976; Emerson, 1956; Seybold, 1994; Wallace and Terry, 1997). An increasing amount of attention, however, is being paid to the reactions of polymers with dilute aqueous solid/clay suspensions in which the particles are separated by relatively large distances. Indeed, the flocculating action of polymers, especially water-soluble polyelectrolytes, on particulate colloidal dispersions is perhaps the most important aspect of the solid–polymer interaction, being the basis of such industrial processes as mineral and food processing, water purification, sewage treatment, paper making, and brewing (Akers, 1975; Bolto, 1995; Bolto and Gregory, 2007; Dickinson and Eriksson, 1991; Dixon, 1967; Ives, 1978; La Mer and Healy, 1963; Salehizadeh and Shojaosadati, 2001; Vincent, 1974). Besides acting as a flocculant, polymers can have a dispersive or ‘protective’ effect on suspended solids when added in sufficiently large quantities (Nabzar et al., 1984; Papp and De´ka´ny, 2003). The stabilizing action of polymers may be ascribed to the formation of an adsorbed layer around the solid
60
Formation and Properties of Clay-Polymer Complexes
particles, with loops and tails extending into the external solution. As a result, the particles are sterically prevented from entering each other’s attraction sphere. The process is, therefore, referred to as ‘steric stabilization’ as against ‘charge stabilization’ due to mutual repulsion of electrical double layers around the particles (cf. Chapter 1). Theories of steric stabilization have been proposed by a number of authors (Napper, 1983; Osmond et al., 1975; Vincent, 1974). However, when very small amounts of a polymer are added to a charge-stabilized dispersion, no aggregation may occur but the particles become sensitized in that they become more susceptible to being coagulated by electrolytes. The role of (negatively charged) polymers in sensitizing and stabilizing clay mineral suspensions is further described in Chapter 4. It seems helpful at this point to define the various terms used. In the literature, ‘aggregation’, ‘coagulation’, and ‘flocculation’ are often used interchangeably. Here, we use aggregation in the generic sense, reserving coagulation for particle aggregation induced by electrolyte addition and flocculation for aggregation resulting from the linking or bridging of several particles by a polymer chain (Adachi, 1995; La Mer, 1966). These concepts are schematically illustrated in Figure 2.6. Aggregates (of kaolinite) formed by bridging flocculation are generally stronger than those produced by electrolyte-induced coagulation (Glasgow and Hsu, 1982). Polyelectrolytes bearing charges opposite in sign to that of the particles can cause aggregation, even at low solution concentration and in the absence of an inert electrolyte. In this instance, particle charge neutralization (coagulation) is more important than bridging (flocculation) by the adsorbed polymer. At high coverage by polycations, the surface charge of montmorillonite can be reversed (from negative to positive), causing charge stabilization to re-establish (Breen, 1999; Ueda and Harada, 1968) (cf. Chapter 5). A system in which hydrophobic colloidal particles, usually of <1 mm equivalent spherical diameter (e.s.d.), are homogeneously distributed in the solvent phase is referred to as a dispersion or sol. For larger particles which settle out relatively rapidly (under gravity), the term ‘suspension’ is commonly used. As van Olphen (1977) has pointed out, however, the distinction between these two states of particle division is purely arbitrary. This is particularly true for clay systems since, conventionally, clay consists of particles with an e.s.d. of <2 mm. For our purposes, ‘dispersion’ and ’suspension’ will be used interchangeably. The effect of organic polymers on the stability of dispersed solids has been discussed in a series of reviews (Adachi, 1995; Akers, 1975; Dickinson and Eriksson, 1991; Gregory, 1978, 1988; Kini, 1970; Kitchener, 1972; Kuzkin and Nebera, 1966; Pefferkorn, 1995; Vincent, 1974). Here, we shall only touch on the salient points and indicate those features that are relevant to clay mineral systems. The flocculation by polymers of colloidal dispersions, such as aqueous clay suspensions, may be induced by one of two mechanisms, namely,
Chapter
2
61
Polymer Behaviour at Clay and Solid Surfaces
A Clay dispersion, suspension, or sol Charge stabilization B Electrolyte added Coagulation
C Small amounts of polymer added Sensitization D
E
followed by electrolyte
Moderate amounts of polymer added Flocculation
F Large amounts of polymer added Steric stabilization FIGURE 2.6 Diagram showing the effects of electrolyte addition and polymer adsorption on the stability of aqueous clay mineral suspensions.
interparticle bridging and charge neutralization (Dickinson and Eriksson, 1991; Linke and Booth, 1960; Michaels, 1954; Ruehrwein and Ward, 1952). As the name suggests, interparticle bridging requires that the polymer is adsorbed to two particles at the same time (Figure 2.7A). Further, the polymer bridge needs to be compatible with the solvent; that is, the solvent has to be better than a y-solvent. For charged particles, the polymer chain must be able to span the distance of closest interparticle approach (dc). This distance may be assumed to be about twice the double layer thickness (1/k) (cf. Chapter 1); that is, dc2/k (Gregory, 1978). Thus, the necessary condition for bridging flocculation to occur is that the ‘grappling distance’, D, of the polymer (Kitchener, 1972) is greater than dc, that is, D>dc (Kashiki and Suzuki, 1986). By the same token, the presence of a small amount of electrolyte is often required to bring the particles sufficiently close for interparticle bridging to occur in aqueous dispersions (Labille et al., 2005; Lagaly, 2006). The formation
62
Formation and Properties of Clay-Polymer Complexes
B
C A FIGURE 2.7 Diagram showing the different modes of interaction between negatively charged particles (e.g. clay minerals) and polycations. (A) Interparticle bridging; (B) charge neutralization; (C) ‘patch’ adsorption. From Lagaly (2006).
of interparticle polymer bridges in different clay–polymer systems has been directly and elegantly demonstrated using electron microscopy (Audsley and Fursey, 1965; Beutelspacher, 1955; Jordine, 1963) and atomic force microscopy (Calaby-Floody et al., 2011). Charge neutralization occurs when a charged polymer adsorbs to a particle carrying charges of the opposite sign. This would apply to the interactions between polycations and clay mineral surfaces (Figure 2.7B). However, with polycations of high charge density or molecular weight, it is difficult, if not impossible, for each negatively charged surface site to be neutralized by a positively charged polymer segment. This is because the average distance between (charged) surface sites is larger than that between polymer segments. Under these conditions, the polycation chains may adsorb in ‘patches’, giving rise to regions of positive and negative charge although the amount of polycation adsorbed may be sufficient to neutralize all of the surface negative charge (Figure 2.7C). Flocculation then occurs by electrostatic attraction between positively charged patches on one particle and negatively charged (bare) regions of another particle when the particles come in contact. Aggregates produced by the electrostatic patch mechanism tend to be weaker than those formed by bridging, but stronger than those formed by (salt) coagulation (Bolto and Gregory, 2007; Gregory, 1978). The occurrence of patch–charge interactions between latex particles adsorbing poly(styrene sulphonate) has been demonstrated by Popa et al. (2009) using atomic force microscopy. According to Gregory (1978, 1988), the following five rate processes occur more or less simultaneously when a polymer solution is added to a stable suspension: (a) mixing of polymer with solid particles, (b) adsorption of polymer to particle surfaces, (c) rearrangement of adsorbed polymer to an
Chapter
2
63
Polymer Behaviour at Clay and Solid Surfaces
a
b
c
d e FIGURE 2.8 Diagram showing the different processes that take place when a polymer (flocculant) is added to a particulate suspension. Mixture of polymer and particles (a); polymer adsorption to particles (b); rearrangement of adsorbed polymer chains to an equilibrium conformation (c); collision between particles with adsorbed polymer yielding flocs/aggregates (d); floc break-up (e). Circles represent suspended particles; squiggles denote polymer chains. From Gregory (1988).
equilibrium configuration, (d) collision of particles with adsorbed polymer to form aggregates (flocs), and (e) aggregate break-up (Figure 2.8). Assuming that mixing is rapid and complete, the flocculation process may be described in terms of three characteristic time scales; ta for polymer adsorption, tr for polymer rearrangement, and tc for particle collision (Dickinson and Eriksson, 1991), ta ¼ lnð1 f Þ=k12 N0
ð2:5Þ
tc ¼ 1=k11 N0
ð2:6Þ
where N0 is the initial particle concentration, f is the fraction of added polymer adsorbed, and k12 and k11 are rate constants. Little is known about the rate of polymer rearrangement but at high particle concentrations, tc>tr. For polymers of high molecular weight, several seconds may be required for adsorbed polymers to rearrange into an equilibrium train–loop–tail conformation. During this period, the adsorbed chains are more extended, and hence can form more interparticle bridges, than in the equilibrium arrangement (Bolto and Gregory, 2007; Pelssers et al., 1990). Polymer adsorption also decreases with increasing particle concentration because adsorption sites within flocs become inaccessible to polymer molecules (Dickinson and Eriksson, 1991). This condition might explain Gill and Herrington’s (1986) observation that the adsorption of cationic polyacrylamides by kaolinite at high clay concentrations decreases with increasing polymer molecular weight. Similarly, there is little information on either floc strength or floc break-up. Flocs formed by polymer bridging are generally stronger than those produced by charge neutralization.
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Formation and Properties of Clay-Polymer Complexes
Bridged aggregates, however, do not easily reform once they are broken up (at high shear), while their charged neutralized counterparts tend to reaggregate after breakage (Gregory, 1988; Yoon and Deng, 2004). If both the polymer and particle are spherical, and transport is by diffusion, the von Smoluchowski’s (1917) equation for perikinetic coagulation (of unequal spheres) may be used to estimate the adsorption rate constant, k12 ¼ ð2kT=3Þða1 þ a2 Þ2 =a1 a2
ð2:7Þ
where k is the Boltzmann constant, T the absolute temperature, the solution viscosity, a1 the particle radius, and a2 the radius of the polymer molecules. For sheared suspensions, Equation (2.7) may be replaced by the von Smoluchowski (1917) expression for orthokinetic coagulation, k12 ¼ ð4=3ÞGða1 þ a2 Þ3
ð2:8Þ
where G is the shear rate. Assuming a particle concentration, N0¼109/cm3; a shear rate, G¼50 s1; a particle radius, a1¼1000 nm; a polymer radius, a2¼100 nm; and the fraction of added polymer adsorbed, f¼90%; Gregory (1988) calculates a perikinetic ta value of 62 s and an orthokinetic ta value of 26 s from Equations (2.5), (2.7), and (2.8). As might be expected, both polymer adsorption and particle flocculation in unstirred suspensions are much slower than when the suspensions are agitated (sheared). Recognizing that not all interparticle collisions lead to flocculation, La Mer and Smellie (1962), La Mer and Healy (1963), and La Mer (1966) proposed that the probability of bridge formation is proportional to the fraction of surface covered by the polymer, y, and to the fraction of uncovered surface, (1y). Accordingly, the collision efficiency, E, is given by E ¼ y ð 1 yÞ
ð2:9Þ
The maximum rate of flocculation occurs when y¼0.5 (half surface coverage), as Besra et al. (2002) have reported for the flocculation of kaolin suspensions by polyacrylamides. At this point, only half of the total collisions will successfully lead to flocculation. The theory of La Mer has been modified and refined by allowing for colliding particles and adsorbed polymers to adopt configurations favourable to bridging (Hogg, 1984), and the existence of actively adsorbing and nonactive sites on the particle surface (Moudgil et al., 1987). The modelling of the flocculation process has been reviewed by Thomas et al. (1999). We might add that uncharged polymers are generally poor flocculants of dilute aqueous clay suspensions since the molecules exist as random coils rather than extended chains in solution. However, such polymers are effective as soil conditioners because they can slowly spread out like a ‘coat of paint’ over adjacent clay/soil particle surfaces within aggregates, or penetrate into aggregates (Ben-Hur and Keren, 1997; Greenland, 1963).
Chapter
2
Polymer Behaviour at Clay and Solid Surfaces
65
As already remarked on, the presence of polyvalent counterions is essential for, or at least promotes, the flocculation of particles by polyelectrolytes of like charge. Both interparticle bridging by the polymer and charge reduction by the counterion are involved in the process (Levy et al., 1992). Flocculation is most effective when the polyelectrolyte chain attains maximum extension which, in turn, depends on the pH and ionic strength of the medium (Michaels, 1954; Slater et al., 1969). This is because the effect of intersegment charge repulsion on chain extension diminishes as the solution ionic strength increases. In this regard, polyelectrolytes with weakly ionized groups (COO, R3NHþ) are more sensitive to variations in solution pH (Figure 2.5) than those containing strongly ionizing sulphonate (SO3) or quaternary ammonium (R4Nþ) groups (Gregory, 1978). On the other hand, polyelectrolytes bearing charges opposite in sign to that of the particles can cause aggregation in the absence of an inert electrolyte as illustrated by the clay–polycation interaction. However, because polycations tend to collapse very rapidly over the negatively charged clay surface, and adopt a rather flat conformation, the extent of interparticle bridge formation is limited. By the same token, polycations, especially highly charged varieties, are effective coagulants of clay minerals and negatively charged colloids, in general, even at low concentrations (Black et al., 1966; Breen, 1999; Durand-Piana et al., 1987; Rebhun et al., 1969). Optimum flocculation is often observed at a polymer dosage that is just sufficient to neutralize the particle charge, or give a z potential close to zero (Bolto and Gregory, 2007). The effects of polymer addition to aqueous clay and solid suspensions may be assessed experimentally in a variety of ways. Conventional methods include sedimentation, filtration, rheology (of the suspension), and turbidity (of the supernatant), while the structure and surface properties of the aggregates (flocs) formed may be investigated by light and neutron scattering as well as electrophoretic mobility measurements (Adachi, 1995, Dickinson and Eriksson, 1991; Gill and Herrington, 1987; Gregory, 1988; Hogg, 2000; Ja¨rnstro¨m et al., 1995; Kuzkin et al., 1964; La Mer and Healy, 1963; Labille et al., 2005; Luckham and Rossi, 1999; Rossi et al., 2002; Slater and Kitchener, 1966). Only in very few instances, however, have the various methods been compared for a given system (Kuzkin et al., 1964; Slater and Kitchener, 1966; Somasundaran et al., 1984). Experimentally, the action of polymeric flocculating agents on particulate colloidal dispersions is controlled by a number of principles which Kitchener (1972) has summarized as follows (i) the polymer must be soluble in the medium and yet capable of competing effectively with solvent molecules for surface sites; (ii) although there is an optimum dosage, the concentration for effective flocculation is much less than would be needed for surface saturation (y¼0.5); (iii) at concentrations beyond the optimum, flocculation efficiency decreases until eventually the system becomes sterically stabilized; (iv) the effectiveness/dosage ratio is optimized when the polymer solution is added to the dispersion using a ‘flash mixing’ technique since this leads to
66
Formation and Properties of Clay-Polymer Complexes
Probable plane of shear
Inner layer with trains OHP Diffuse layer with loops and tails
Surface layer
OHP Probable plane of shear
a rapid, uniform distribution of polymer over the accessible surfaces; (v) flocculation is initiated by the relatively rapid aggregation of sub-micron particles through diffusional collisions (perikinetic flocculation), followed by a slower growth of supra-micron size flocs through hydrodynamic collisions (orthokinetic flocculation); (vi) in order to promote the latter process and keep the flocs in suspension until all the particles have aggregated, a ‘conditioning’ period with gentle stirring is recommended; (vii) although flocs are generally stronger than coagula, the former can be disrupted by applying a sufficiently large shearing force; the flocs so broken cannot reform to the original size on relaxing or removing the force; (viii) under steady-state conditions (low rate of shear for a sufficiently long period), the size of flocs is related to the extent and strength of interparticle bridging which, in turn, depends on the polymer chain length and the segment–surface interaction energy parameter; (ix) differences in effectiveness of a flocculant between suspensions in a similar medium reflect differences in adsorption strength whereas differences between media for the same suspension may be ascribed to changes in either polymer–surface interaction or effective chain length of the polymer. The adsorption of an uncharged homopolymer at a charged interface will clearly alter the structure of the electrical double layer around the particle. To a first approximation, we may assume that any modification of the inner (Stem) layer is due to the presence of trains in this layer, whereas that of the outer (Gouy) layer may be ascribed to loop and tail segments of the adsorbed macromolecule (Lyklema, 1976). This concept is illustrated in Figure 2.9, where the extension of the Stem layer is assumed to coincide with
Key: (Partially) dehydrated cation in inner (Stern) layer Hydrated cation Anion d
1
k
d
1
Adsorbed homopolymer k
OHP=Outer Helmholtz plane FIGURE 2.9 The effect of adsorbed uncharged homopolymers on the structure of the electrical double layer at a negatively charged (clay mineral) surface. Modified after Vincent (1974).
Chapter
2
Polymer Behaviour at Clay and Solid Surfaces
67
the outer Helmholtz plane (OHP) and the plane of shear (cf. Figure 1.20). As a consequence, both the long-range van der Waals attraction and the repulsion terms, describing the total interaction between particles, as formulated by the DLVO theory (cf. Figure 1.21), have to be modified. The presence of a homopolymer at the surface may either decrease or increase the interparticle attraction (VA). However, if the distance between the particle centres is kept constant, the net effect is to enhance VA (Vincent, 1974). The influence on VA of adsorbed layer composition and segment density in this layer has been discussed by Vincent (1973). The repulsion term (VR) in the DLVO theory (cf. Figure 1.21) is modified by the following factors: (a) changes in surface charge, (b) displacement of specifically adsorbed counterions by trains, (c) displacement of oriented water dipoles, (d) changes in dielectric constant and thickness of the inner layer by train segments, and (e) changes in the outer layer by loops and tails (Vincent, 1974). Vincent (1974) has given an equation relating the effect of (a)–(d) on the potential cd at the OHP. The effect under (e) should also be reflected in cd if the segment density in the outer layer is small as would be the case at low adsorption. For two spherical particles, an expression for VR in terms of cd, particle surface–surface separation, and Stern layer thickness, can be derived. As indicated in Figure 2.9, the magnitude of the electrokinetic or zeta (z) potential will be reduced by the presence of an adsorbed polymer, provided that changes in potential and charge distribution due to adsorption are not significant. The decrease in z may be ascribed to the physical displacement of the probable plane of shear (away from the OHP) by the adsorbed polymer (Kavanagh et al., 1975). Since the approximation cdz no longer holds, some relationship between cd and z must be established or assumed before VR can be evaluated. A different kind of approach is necessary when the segment density in the outer diffuse layer is large (Lyklema, 1976), while for polyelectrolyte adsorption, a new model would be required. The polymerinduced flocculation of colloidal suspensions through charge neutralization has been modelled by Runkana et al. (2004), using a modified DLVO theory that includes the effect of adsorbed polymer layers on van der Waals attraction. With reference to Figure 2.9, the (electrokinetic) thickness of the adsorbed polymer layer (dE) may be estimated by measuring the z potential in the absence and presence of an adsorbed (uncharged) polymer, using the following equation (Hild et al., 1997; Hunter, 1981), tanhðbz1 Þ ¼ tanhðbz2 Þ exp½kðdE dÞ
ð2:10Þ
where b¼ze*/4kT for which z is the valency, e* the electronic charge, k the Boltzmann constant, and T the absolute temperature, while 1/k is the double layer thickness (Debye length) (nm), d the Stern layer thickness (nm) (cf. Chapter 1), and z1 and z2 are the z potentials (mV) in the presence and absence of an adsorbing polymer, respectively.
68
Formation and Properties of Clay-Polymer Complexes
16 Layer thickness d E (nm)
14 12 10 8 6 4 2 0
0
0.2
0.4 0.6 0.8 Amount adsorbed (mg/m2)
1.0
1.2
FIGURE 2.10 Electrokinetic layer thickness (dE) of polyvinyl pyrrolidone adsorbed to kaolinite in 102 M NaCl at pH 5.5 in relation to the amount adsorbed and molecular weight (Mw) of the polymer: ■, Mw¼5000 Da; □, Mw¼10,000 Da; ○, Mw¼24,000 Da; ●, Mw¼44,000 Da; ▲, Mw¼245,000 Da; ♦, Mw¼400,000 Da. After Hild et al. (1997).
If the Stern layer thickness (0.40.5 nm) is neglected, the effective thickness of the adsorbed polymer layer is simply given by (Kavanagh et al., 1976), dE ¼ 2:303=k:log½tanhðbz2 Þ=tanhðbz1 Þ
ð2:11Þ
For an uncharged polyacrylamide adsorbing to montmorillonite and kaolinite, McFarlane et al. (2006) calculated an adsorbed layer thickness of 0.60.7 nm at a polymer dosage rate corresponding to <10% of plateau adsorption density, rising to 1.41.7 nm as the dosage was increased. An increase in dE values with adsorption density has also been reported for poly(vinyl alcohol) on silver iodide (Fleer et al., 1972) and gibbsite (Kavanagh et al., 1976). In the case of polyvinylpyrrolidone (PVP) adsorbing to kaolinite, Hild et al. (1997) noted a gradual increase in dE as the amount of PVP adsorbed approached surface saturation (0.6 mg/m2), beyond which the adsorbed layer thickness steeply rose. Interestingly, the extent of this increase in dE depended on the molecular weight of PVP. These observations indicate that the fraction of segments in loops (and tails) increased with polymer dosage (surface coverage) and molecular weight (Figure 2.10). Se´quaris et al. (1999) have observed similarly for complexes of Naþ-montmorillonite with PVP.
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69
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