Bridging attraction

3) According to the lUPAC, flocculation is a process of contact and adhesion whereby the particles of a dispersion form larger size clusters. It is synonymous with agglomeration and coagulation. 

PEO + folic acid plus 1 mM KCI (b). The rates were normalized by dividing them by the rate measured in 100 mM KCI polymer-free solution. (Adapted from Ref [1408].) 

Force versus distance experiments have revealed bridging attraction in different systems, for example, by polystyrene between mica in cyclohexane [1409] and cyclopentane [1396, 1398], or poly(ethylene oxide) between clays, glass, or silica in water [1410,1411]. Bridging by polyelectrolytes has also attracted great attention, both theoretically [1412, 1413] and experimentally [1399, 1400]. 

With the application of atomic force microscopy in measuring surface forces, it became possible to detect the bridging of individual polymer chains. In particular polyelectrolytes adsorbing to charged surfaces in aqueous medium have been studied [1414—1418]. Peeling a strongly adsorbed polyelectrolyte from a surface is similar to 

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Two Spheres. The interaction of spheres which are covered with adsorbed polymer layers is expected to follow that of macroscopic surfaces. If the surfaces of the spheres are saturated, the force between them will be repulsive, and if they are unsaturated there will be an attraction caused by bridging (2.3). However special effects are expected to arise due to the finite sizes of spheres and macromolecules. Firstly, when the spheres are small, their radii may be comparable with the range of the bridging attraction. Secondly, when the macromolecules are large, one of them may saturate two spheres then it may keep them bound to each other even though they are both saturated. 

In this range of distances, only the tails are important and as in the case of the polymer brush the tails repel each other. The force is of the order of the osmotic pressure at the midplane between the two surfaces z = hj2). At short distances b < h < ihs force still varies as 1 jh but it is attractive. In this range, the loops on both sides overlap to form bridges and the bridging attraction dominates. This equilibrium force can be measured only in cases of reversible adsorption this in general is not the case for adsorption on solid surfaces but it could be the case for adsorption on a liquid-liquid interface. 

In huntid systems (with a relative humidity of >60%), capillary condensation of the fluid in the gap between the particles in close contact may take place resulting in an attraction. The maximum attraction is achieved for two smooth spherical particles if the liquid covers the particle surfaces completely. For this case, the liquid bridge attraction force, can be calculated as follows [6] ... 

What is bridging flocculation What type of polymers are most suitable to induce bridging attraction What relative surface coverage of the polymer on the particles surface is typically optimum for flocculation ... 

The issue of critical polyelectrolyte adsorption is intimately coupled to the polymer-mediated bridging attraction between oppositely charged macro-ions immersed in a polymer solution. Moreover, electrostatically driven self-assembly of single-stranded RNA molecules on the interior of positively charged capsids, as it occurs in many spherical and rod-Uke single-stranded viruses, offers another field for potential applications of our theoretical results. The WKB method developed above has recently been implemented to weak polyelectrolyte adsorption under confined conditions [49] and to adsorption onto low-dielectric interfaces [50]. The power of the WKB approach can even be extended to more complicated adsorption situations, such as patchy surfaces, specific charged patterns on concave and convex interfaces, Janus particles, etc., and other (nearly arbitrary) potentials of polyelectrolyte-surface interactions. This might open an avenue to approach more realistic situations of polyelectrolyte adsorption and to quantitatively reproduce experimental results in the future. 

Polymer adsorption may result in bridging attraction or steric repulsion between two particles. The scaling theory of polymer adsorption that accounts for the interactiOTi between the polymer and the surface and for variation of polymer concentration near the surface [53, 54] was used for derivation of the interaction potential between two spherical colloidal particles coated by polymer [55-57] ... 

The first term within the square brackets in Eq. 23 corresponds to the short-range bridging attraction and the second term is for steric (excluded volume) repulsion. 

We report the investigation of the forces between smooth solid surfaces bearing end-grafted chains in good solvent conditions. The forces are raonotonically repulsive with a range about twice that for corresponding adsorbed chains. We observe no evidence of bridging attraction at low... 

Dynamic aspects of adsorbed layers of PS on oxidic surfaces have also been studied by surface-force measurements [73]. The effect of compression was measured for PS adsorbed on mica from cyclopentane near conditions. If compression was performed slowly the layers seemed to become irreversibly compressed as was concluded from the absence of long-range bridging attraction. Even after several days the polymer layers did not relax. 

In a later development, Somasundaran et al. ]57] developed a PBM for aggregation by polymers in shear environments. The D LVO theory was extended for this case, as discussed in the previous section, by using the modifled expression for van der Waals attraction for particles covered with polymers and the expression for bridging attraction or steric repulsion derived from the scaling theory [25]. Their model was tested qualitatively with experimental data for the flocculation of colloidal alumina suspensions in the presence of PAA and was found to reproduce the observed experimental trends [60] reasonably well. 

Bridging attraction Intersegment attraction Phase separation... 

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