Flat brushes

Fig. 3 Cartoon representation of an isolated grafted colloidal sphere (black core) along with the calculated monomer density profile 0(r) (for various core radii, re) [119]. The three solid lines correspond to values of the ratio of the overall particle radius R to the grafted polymer end-to-end distance of 0.5, 2 and 16, from bottom to top, respectively. The dashed line represents the self-consistent field theory calculation for the flat brush limit (r [119]. Note the depletion region...

The subscript ch refers to the chain contribution, and hereToch is the free energy per unit area of a flat brush, for which Milner and Witten obtained the expression... 

Distemper blush n. A flat brush, 5-10 in. wide, well packed, with long bristle. 

In the opposite limit Na Nb, of crewcut micelles with R = / core, the corona forms a flat brush. In this case the coronal penalty, neglecting edge effects, is independent ofp, F JkT = NAib/dy As a result d p/dp = 0 yields p = °o, indicating a tendency to form lamellae. Note that in the case of flexible diblocks of crewcut micelles exhibits a minimum at a finite p because of the core s elastic penalty. 

The sealant is introduced into the joint using a manual or compressed-air caulking gun. The surface is then smoothed using a wet flat brush. 

The internal modes of the brush may be described by an approach due to deGennes This method enables the analysis of collective, elastic deformations of brushes of various geometries. Our presentation focuses on the breathing modes of a flat brush as described by the Alexander model. In this case the layer is transitionally invariant... 

Note that kT/ qa is the diffusion coefficient of a single, impenetrable blob. Accordingly, the characteristic time associated with the longitudinal breathing modes of a flat brush is... 

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