Osmotic pressure, compression yield

The compression yield stress is directly comparable with the osmotic pressure for a given suspension system. The osmotic pressure has been measured by Barclay et al. (225), Rohrsetzer et al. (226), Goodwin et al. (227), and Bonnet-Gonnet et al. (228). The osmotic pressure displays the same trend as the compressive yield stress. 

One unique scaling behavior has been uncovered in this chapter for the low shear limit viscosity, equation 64, Bingham yield stress, equation 65, and the compressive yield stress-osmotic pressure, equation 74, for... 

Both Fi f and F are overestimated within this approach because self avoidance correlations are neglected. The Flory approximation is nevertheless very useful (i) It typically yields the correct equilibrium dimensions because the two overestimates cancel when the equilibrium condition is invoked, (ii) It provides a useful upper bound for Fchain- (iii) Most important, the Flory approximation is simple to apply irrespective of difficulties such as complicated geometries. While it is a good idea to use the Flory approximation as a first step in the analysis of a problem, it is important to understand its limitations. Since the free energy density is overestimated, so is the osmotic pressure. As a result erroneous results are obtained for related properties such as the force law for brush compression. The overestimate of F j f and F i can result in wrong predictions for equilibrium dimensions when F hain includes extra terms and cancellation of errors may not be relied upon. Such is the case for aggregates of block copolymers where F hain must allow for a surface energy contribution. 

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