Adsorbed Layer Thickness Results

Any fundamental study of the rheology of concentrated suspensions necessitates the use of simple systems of well-defined geometry and where the surface characteristics of the particles are well established. For that purpose well-characterized polymer particles of narrow size distribution are used in aqueous or non-aqueous systems. For interpretation of the rheological results, the inter-particle pair-potential must be well-defined and theories must be available for its calculation. The simplest system to consider is that where the pair potential may be represented by a hard sphere model. This, for example, is the case for polystyrene latex dispersions in organic solvents such as benzyl alcohol or cresol, whereby electrostatic interactions are well screened (1). Concentrated dispersions in non-polar media in which the particles are stabilized by a "built-in" stabilizer layer, may also be used, since the pair-potential can be represented by a hard-sphere interaction, where the hard sphere radius is given by the particles radius plus the adsorbed layer thickness. Systems of this type have been recently studied by Croucher and coworkers. (10,11) and Strivens (12). 

In order to be able to include a steric contribution in the interparticle energy calculation, an estimate of the adsorbed layer thickness is required. This is very difficult to access experimentally probably the only technique which might be able to provide an estimate is small-angle neutron scattering which was beyond the scope of this work. As a result, a theoretical estimation of the thickness was made, based on a few key observations. This is described below. 

Dissolved polymer molecules can be adsorbed by polymer particles via electrostatic attractive force or hydrophobic interaction. When polyelectrolyte is adsorbed on an opposite-charge particle, the polymer molecules usually have a loop-and-tail conformation and, as a result, inversion of charge occurs. For example, sulfatecarrying particles behave as cationic ones after they adsorb poly(lysine). Then poly(-styrene sulfonate) can be adsorbed on such cationic particles and reinvert the charge of particles to anionic (14). Okubo et al. pointed out that the alternate adsorption of cationic and anionic polymers formed a piled layer of polyelectrolytes on the particle, but the increment of adsorbed layer thickness was much less than expected. This was attributed to synchronized piling of two oppositely charged polyelectrolytes (15). 

A reduction in poly electrolyte charge density to 10% results in further increase in adsorbed layer thickness. The steep steric repulsion is now... 

The analysis of experimental excess adsorption isotherms using equation (2-50) had shown unusual results [22]. The adsorbed layer thickness of acetonitrile adsorbed from water on different types of reversed-phase adsorbents calculated as the ratio of adsorbed layer volume and adsorbent surface area appears to be on average equal to 14 A, which is equivalent to approximately five monolayers of acetonitrile molecules adsorbed on the hydrophobic surface. At the same time, the adsorbed layer thickness of methanol adsorbed from water on the same adsorbents is equal to only 2.5 A, which is equivalent to the monolayer-type adsorption. 

Substituting this adsorbed layer thickness into the confinement free energy [Eq. (3.51)] or into the interaction free energy [Eq. (3.66)] gives the expected result for the free energy of adsorption [Eq. (3.65)]. 

For sterically stabilised dispersions, the resulting energy-distance curve often shows a shallow minimum at particle-particle separation distance h comparable to twice the adsorbed layer thickness 5. For a given material, the depth of this minimum depends upon the particle size R, and adsorbed layer thickness S consequently, decreases with increase in S/R, as illustrated in Figure 11.4. 

The effective volume fraction increases with a relative increase of the dispersant layer thickness. Even at 10% volume fraction, a maximum packing (< = 0.67) is soon reached, with an adsorbed layer thickness that is comparable to the particle radius. In this case, overlap of the steric layers wiU result in significant increases in viscosity. Such considerations may help to explain why solids loading can be severely Hmited, especially with small particles. In practice, soUds loading curves can be used to characterize the system, and take the form of those illustrated in Figure 11.6... 

Using < p and the measured was calculated at each

using Equation (12.3), and the results are plotted in Figure 12.8. From

adsorbed layer thickness, 5, was calculated using the following equation. 

The adsorbed layer thickness of the graft copolymer on the latexes was determined using rheological measurements. Steady-state (shear stress a-y shear rate) measurements were carried out and the results were fltted to the Bingham equation to obtain the yield value and the high shear viscosity // of the suspension. 

A reasonably thick adsorbed layer. The adsorbed layer thickness of the B chains, which is usually described by a hydrodynamic value 5, (i.e., the thickness S plus any contribution from the solvation shell), should be sufficiently large to prevent the formation of a deep minimum which may result in flocculation (although reversible) and an increase in the viscosity of the suspension. A value of 5h>5 nm is usually sufficient to prevent the formation of a deep minimum. 

A decrease of the adsorbed HPAM amounts with increasing charge density is determined in this case by radioactive measurements. This is consistent with the theoretical predictions of Evers et al. [106] and their next extension by Bohmer et al. [61]. Such a decrease has been experimentally shown also in Refs. 95, 107, and 108. The thickness of the adsorbed layer for a 100% charged polyelectrolyte is found, for instance, to be 1 nm and about 3-4 nm for the 30% charged one (this volume, chapter by Claesson). The reduction in polyelectrolyte charge density to 10% results in an increase in the adsorbed layer thickness to 10-20 nm. 

Plots of G and G, versus h are illustrated in Figure 14.8. This figure shows that G increases very rapidly with decrease of h as soon as h becomes smaller than 2S (and % < 0.5). G, also increases very rapidly with decrease of h on further overlap. Combination of G , G, and G (the van der Waals attraction) results in the total Gj--h curve shown in Figure 14.8. This curve shows a minimum (G J ath — 25, but when h < 25, Gj- increases very rapidly with further decrease in h. The depth of the minimum, G , , depends on the adsorbed layer thickness. With increase of 5, G , decreases and at sufficiently high values of 5 (of the order of 5-10 nm), it reaches small values (fraction of kT units). This shows that with sterically stabilized dispersions, there is only weak attraction at relatively long distances of separation, which in most cases is overcome by the Brownian diffusion. Thus, one can say that the net interaction is repulsive, and this ensures the long-term stability of the dispersion. 

When two particles or droplets containing adsorbed polymer layers (with an adsorbed layer thickness 8) approach a distance of separation h whereby these layers begin to overlap, i.e., when h < 28, repulsion occurs as a result of two main effects (6). The first repulsive... 

The effect of droplet size and its distribution on the adsorbed layer thickness may be inferred from a comparison of the results obtained with the o/w emulsions with those recently obtained using polystyrene latex dispersions containing grafted PEO chains of (molecular weight 2000) (49). As discussed earlier, the viscoelastic behavior of the system (which reflects the steric interaction) is determined by the ratio of the adsorbed layer thickness to the particle radius (8/R). The larger this ratio, the lower the volume fraction at which the system changes from predominantly viscous to predominantly elastic response. With relatively polydisperse systems, ( )cr shifts to higher values when compared to monodisperse systems with the same mean size. 

---