Particles with Adsorbed Polymer Layers

Polyelectrolytes and non-ionic polymers are often added to stabilize a colloid. The polymer molectdes adsorb on the partitJe surface. In the case of the non-ionic polymers, the adsorbed layers provide a steric repulsion between the particles. For polyelectrolytes, the steric force is supplemented by electrostatic repulsion between the charged groups. 

In their 1997 study of the effect of neutral polymer on the ESA signal from silica, Carasso et cd. [1] used a gel layer model to derive an expression for the slip coefficient which has the form  

At high frequencies F — 1 and the slip is unaffected by the polymer. This is because the amplitudes of the back and forth displacements are so small at high frequencies that there is almost no deformation of the polymer and so there are no elastic forces to hold back the liquid. The polymer slows down the motion most at low frequencies. At intermediate frequencies there is a phase difference between the tangential field and the slip velocity, and the fluid motion leads the applied field. 

These effects become more pronounced as the polymer drag coefficient a is increased. For very large values of polymer drag coefficient, the low frequency limit of F is equal to exp (-Kd), which is equivalent to a displacement of the slipping plane by a distance d from the particle surface. In this limit the polymer is, in effect, immobile. 

The shape of the slip coefficient curves does not depend on the elastic modulus (y) of the polymer. That is, y does not affect the high and low frequency limits of the magnitude or the maximum value in the argument of F, but it does determine the absolute frequency scale. As the elastic modulus is increased (as the polymer becomes stiffer) the curves are shifted to the right along the frequency axis, but the shapes do not change. 

---

When two sterically stabilized particles with adsorbed polymer layers approach one another sufiBciently closely for the adsorbed layers to interact, two extreme cases can occur (19). 

The total interaction energy of two colloidal particles with adsorbed polymer layers is described by the equation,... 

Hereafter, we assume the polymers to form an adsorbed layer around the colloidal particles, with a typical thickness much smaller than the particle radius, such that curvature effects can be neglected. In that case, the effective interaction between the eolloidal particles with adsorbed polymer layers can be traced back to the interaction energy between two planar substrates covered with polymer adsorption layers. In the case when the approaeh of the two particles is slow and the absorbed polymers are in full equilibrium with the polymers in solution, the interaction between two opposing adsorbed layers is predominantly attractive [45, 46], mainly beeause polymers form bridges between the two siufaees. Recently, it has been shown that there is a small repulsive eomponent to the interaetion at large separations [47]. 

It is precisely the loosening of a portion of polymer to which the authors of [47] attribute the observed decrease of viscosity when small quantities of filler are added. In their opinion, the filler particles added to the polymer melt tend to form a double shell (the inner one characterized by high density and a looser outer one) around themselves. The viscosity diminishes until so much filler is added that the entire polymer gets involved in the boundary layer. On further increase of filler content, the boundary layers on the new particles will be formed on account of the already loosened regions of the polymeric matrix. Finally, the layers on all particles become dense and the viscosity rises sharply after that the particle with adsorbed polymer will exhibit the usual hydrodynamic drag. 

Fig. l. Schematic diagram describing the close approach of two colloidal particles (radius a) covered with adsorbed polymer layer of thickness 5 (a) complete penetration of free polymer into the adsorbed layer (b) polymer sheath is impenetrable to the free polymer. 

Although the average value of T would be the same as in the former case, copious aggregation occurs due to bridging. A bare particle that meets a particle with a polymer layer will immediately stick to it, because some segments of a protruding polymer chain can adsorb onto the bare surface. 

In many ceramic systems it is not possible to create a stable suspension simply by controlling pH. Large additions of acid or base can result in dissolution of the particles, or provide a too high ionic strength. Hence, addition of suitable polymeric dispersants is commonly used to create colloidally stable suspensions. These polymeric additives can induce an interparticle repulsion that prevents coagulation. Upon the close approach of two particles covered with adsorbed polymer layers, the interpenetration of the polymer layers give rise to a repulsive force, the so-called steric stabilization (10). There are some simple requirements for steric stabilization of colloidal suspensions, as follows ... 

For particles covered by an adsorbed polymer layer, it is also necessary to take into account the effect on the steric repulsive forces of the structure of the adsorbed layer. For example, for the case of separations corresponding to 8 < H < 28, the values of mix associated with linear adsorbed layer profiles may be obtained from the equation (Vincent et al, 1986) ... 

Other dimensionless groups that compare the thickness of the adsorbed polymer layer to the radius of the particle or the radius of gyration of the polymer to the particle radius in polymer/colloid mixtures can also be easily defined. We are mostly concerned with the volume fraction and the Peclet number Pe in our discussions in this chapter. However, the other dimensionless groups may appear in the equations for intrinsic viscosity of dispersions when the dominant effects are electroviscous or sterically induced. 

Consider two particles with adsorbed layers approaching each other. The adsorbed layers on the core particles first begin to overlap at the outermost extreme of the fringe, at which the surface exerts the least influence. As a first approximation, then, the initial encounter between two approaching core particles is comparable to the approach of two polymer coils in solution. In Chapter 3, Section 3.4a, we saw that the concept of excluded volume could be... 

This review indicates that good solvent conditions (in terms of either x or 0) result in a positive value for AGR. This is what would be expected from a model that assumes that the first encounter between particles with adsorbed layers is dominated by the polymers. Conversely, in a poor solvent AGR is negative and amounts to a contribution to the attraction between the core particles as far as flocculation is concerned. Under these conditions the polymer itself is at the threshold of phase separation. Van der Waals attraction between the core particles further promotes aggregation, but it is possible that coagulation could be induced in a poor solvent even if the medium decreases the effective Hamaker constant to zero. 

The most convenient of these methods is viscosity measurement of a liquid in which particles coated with a polymer are dispersed, or measurement of the flow rate of a liquid through a capillary coated with a polymer. Measurement of diffusion coefficients by photon correlation spectroscopy as well as measurement of sedimentation velocity have also been used. Hydrodynamically estimated thicknesses are usually considered to represent the correct thicknesses of the adsorbed polymer layers, but it is worth noting that recent theoretical calculations52, have shown that the hydrodynamic thickness is much greater than the average thickness of loops. 

The high precision of the disk centrifuge allowed the comparison of sedimentation velocities of colloidal particles with and without an adsorbed polymer layer, from which the hydrodynamic thickness of the adsorbed layer could be calculated (4). Here the disk centrifuge, giving complete size distributions, made the use of monodisperse samples unnecessary. 

The ability to make very precise measurements has allowed us to use the disk centrifuge to determine the thickness of adsorbed gelatin layers on silver bromide particles (4). When particles are coated with an adsorbed polymer layer, the sedimentation time reflects the size and density of the particle core as well as the thickness and density of the adsorbed layer. An apparent (incor-... 

In order to test the model used here, calculated values of the limiting free polymer concentration 0 at which phase separation occurs are compared with the experimental data [6] on the aqueous dispersions of polystyrene latex particles with adsorbed polyethylene oxide and with polyethylene oxide as the free polymer. Since no information is available regarding the thickness of the adsorbed layer, the values used by Vincent et al. [6] in their theoretical calculations are adopted. Table 1 compares the experimental values of the limiting volume fraction of the free polymer with our calculated values for two different molecular weights of the free polymer. The simple model used here gives reasonably good agreement with the experimental values. 

Two basic approaches are possible one Involves compression of a dispersion of (monodlsperse) particles canylng an adsorbed polymer layer and monitoring the pressure as a function of the volume fraction. In the second approach the force between two macroscopic surfaces with adsorbed pol5rmer layers is measured as a function of the surface separation. 

When two particles each with a radius R and containing an adsorbed polymer layer with a hydrodynamic thickness 5j, approach each other to a surface-surface separation distance h that is smaller than 25, the polymer layers interact with each other, resulting in two main situations [12] (i) the polymer chains may overlap with each other and/or (ii) the polymer layer may undergo some compression. In both cases, there will be an increase in the local segment density of the polymer chains in the interaction region. However, the real situation is perhaps in between the above two cases - that is, the polymer chains may undergo some interpenetration and some compression. 

---