Steric layers, overlap

Overlapping steric layers will result In huge viscosity increase... 

In one of the limiting cases, the free polymer is allowed to penetrate the adsorbed layer around the particles. One may note that when the free polymer and the adsorbed polymer are both present in the steric layer around the particle, the interactions between the two must be taken into account while evaluating the in-terparticle forces. However, in the absence of a detailed knowledge of the structure of the adsorbed layer, it is difficult to evaluate this contribution to the interaction potential. Then, the situation is similar to the one considered by Asakura and Oosawa (16), and the force of attraction between two bare particles of radius a in the presence of free polymer molecules of radius / can be expressed as the product of the osmotic pressure Pmm and the area of the intersection of the two overlapping volumes ... 

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... 

The first theory to recognize clearly the prime importance of the solvency of the dispersion medium in steric stabilization was that published by Fischer (1958). Fischer considered the overlap of the steric layers attached to two spheres (see Fig. 10.4). The mixing free energy change S A G ) in the small volume element dV for one of the steric layers is given by... 

One disadvantage of the approach of Fischer (1958) and Ottewill and Walker (1968) is that, as noted above, the formulae proposed by these authors are only valid for the mixing of constant segment density steric layers in the interpenetrational domain. Once the interpenetrational-plus-compressional domain is entered, no allowance is made for the elastic contribution to the free energy. The elastic interactions can become important, even paramount, when the minimum distance of separation between the surfaces of the particles (Hq) is less than the barrier layer thickness. An additional defect of the Fischer approach is apparent in this domain the overlap volume is decreased below that given by equation (12.8) because part of it is occupied by the cores of the particles. Both the Fischer and the Ottewill and Walker theories disregard this decrease in volume. Implicit in their formulae is the notion that the solid cores become equivalent to the steric barriers. This is, of course, quite unphysical. 

The essence of this theory can be grasped from Fig. 15.4. In the semidilute region, the free polymer molecules can be assumed to overlap the polymer in the steric layers. However, these unattached interpenetrated chains are displaced into the bulk phase on the close approach of two sterically stabilized particles. The free energy change that accompanies this displacement is simply... 

Surfactant. A surface active agent a chemical which reduces the surface tension of a liquid, and so improves the wetting of a surface. They are useful in dispersing powders, when surfactants adsorbed on particle surfaces produce repulsive forces between the particles when the adsorbed layers overlap (steric hindrance.)... 

Effects of finite sizes of the ions (steric effects) tend to enhance the repulsion between two surfaces. This is analogous to the increased osmotic pressure of a van der Waals gas due to finite sizes of gas molecules. In a very similar manner, finite sizes of coions and counterions contribute to enhanced repulsion. In case of coions adsorbed on the surface, the repulsion is nothing but the steric repulsion between the overlapping Stem layers. 

An exception to the mle that lowering the temperature causes transitions to phases with iacreased order sometimes occurs for polar compounds which form the smectic phase. Decreasiag the temperature causes a transition from nematic to smectic but a further lowering of the temperature produces a transition back to the nematic phase (called the reentrant nematic phase) (22). The reason for this is the unfavorable packing of the molecules ia the smectic phase due to overlap of the molecules ia the center of the layers. As the temperature is lowered, the steric iateractions overpower the attractive forces, causiag the molecules to pack much more favorably ia the nematic phase. The reentrant nematic phase can also be produced from the smectic phase by iacreasiag the pressure (23). 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

Two mechanisms of steric stabilization can be distinguished entropic stabilization and osmotic repulsion. Entropic stabilization arises when two opposing adsorbed polymer layers of adjacent particles overlap, resulting in compression and interpenetration of their... 

When the thickness of the draining film is less than twice the thickness of the adsorbed protein layer, (i.e. TLs), the approaching faces of the film experience a steric interaction because of the overlap of the adsorbed protein layers. 

In many practical instances (see Vignette 1.5), electrostatic repulsion is not a convenient option. In such cases, a suitable polymer that adsorbs on the particle surfaces may be added to the dispersion. The resulting polymer layer masks the attraction and may also provide a repulsive force, partly due to pure steric effect, when the polymer layers on two interacting particles attempt to overlap with each other. This is what is known as polymer-induced stability. Polymer-induced stability is often referred to as steric stability for the above... 

FIG. 13.13 Interaction between polymer-coated particles. Overlap of adsorbed polymer layers on close approach of dispersed solid particles (parts a and b). The figure also illustrates the repulsive interaction energy due to the overlap of the polymer layers (dark line in part c). Depending on the nature of the particles, a strong van der Waals attraction and perhaps electrostatic repulsion may exist between the particles in the absence of polymer layers (dashed line in part c), and the steric repulsion stabilizes the dispersion against coagulation in the primary minimum in the interaction potential. 

The second contribution to the steric interaction arises from the loss of configurational entropy of the chains on significant overlap. This effect is referred to as entropic, volume restriction, or elastic interaction, Gei. The latter increases very sharply with a decrease in h when the latter is less than 8. A schematic representation of the variation of Gmix, Gei, G, and Gj =G X + Gei + Ga) is given in Fig. 10. The total energy-distance curve shows only one minimum, at h 25, the depth of which depends on 5, R, and A. At a given R and A, G decreases with an increase in 5. With small particles and thick adsorbed layers (5 > 5 nm), G, becomes very small (approaches thermodynamic stability. This shows the importance of steric stabilization in controlling the flocculation of emulsions and suspensions. 

Rejection of protein adsorption to the outermost grafted surface is attributed to a steric hinderance due to the tethered chains. A grafted surface in contact with an aqueous medium, a good solvent of the chains, has been identified to have a diffuse structure [67]. Reversible deformation of tethered chains due to invasion of mobile protein molecules into the layer would lead to a repulsive force which is governed by the balance of entropic elasticity of the chains and osmotic pressure owing to the rise in the segment concentration. The overlapped repulsive force would prevent the direct contact of protein molecules with the substrate surface. 

In the theory developed by Derjaguin and Landau (24) and Verwey and Overbeek (25.) the stability of colloidal dispersions is treated in terms of the energy changes which take place when particles approach one another. The theory involves estimations of the energy of attraction (London-van der Walls forces) and the energy of repulsion (overlapping of electric double layers) in terms of inter-oarticle distance. But in addition to electrostatic interaction, steric repulsion has also to be considered. 

Adsorbed layer thickness 5 The steric interaction starts at h = 28 as the chains begin to overlap and increases as the square of the distance. Here, the important point is not the size of the steric potential but rather the distance h at which it begins. 

Steric forces arise from the overlap of the adsorbed layers and can be repulsive or attractive in nature depending on whether or not the outermost layers on the particles prefer to be in contact with the solvent. If the solvent power of the medium for the exposed portions of the exterior layer, for example, those of an adsorbed polymer layer, is satisfactory, they will be compatible with the medium and the suspension will remain stable. On the other hand, if the solvent power for the adsorbed layer is minimal, there will be a tendency for the exposed portions of the adsorbed layer on one particle to interpenetrate into those of a layer on another particle and thereby promote aggregation. 

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