Mushroom regime

Lipson et al. [181] performed an MC study on different types of lattices for three functional comb chains with two branched points, or H-combs, in the excluded volume regime. The variation of the branch mean size with its length follows the expected scaling law in terms of critical exponent, Rg =Nj, . This is in accordance with the expected behavior in the low branching (or mushroom) regime, and it is also in agreement with RG calculations [182]. In the Lipson et al. simulations, expansion of the different branches was analyzed by evaluating their ampHtudes in this power-law. Thus, the internal branches (backbone seg-... 

Fig.l For grafted chains, one distinguishes between a the mushroom regime, where the distance between chains, is iarger than the size of a poiymer coii and, b the... 

Such behavior has been interpreted in terms of a molecular model proposed by Brochard-Wyart and de Gennes [143] and further refined [145,146]. The first version of these models considers a solid surface bearing a few end grafted polymer chains, with a surface density, G, below the onset of the mushroom regime gAT<1, with N the polymerization index of the anchored chains). The melt chains have a polymerization index P. Both N and P are assumed to be much larger than Ne, the average number of monomers needed to form an entanglement. Thus the... 

These ideas can be used to model the flow behaviour in the presence of surface anchored chains at low surface densities ( i.e. for N chains in the "mushroom" regime of grafting... 

Cohesive slip with weak interactions. Considering that the occurrence of slip is highly dependent on the interaction developing between the polymer and the wall, Brochard and de Gennes in 1992 [10] described the case where there is only few sites of adsorption of the polymer chains at the surface of the dies. The initial situation, prevailing before flow, is called the mushroom regime and the fnction law controlling slip has been deduced theoretically ... 

We assume that v is small, i.e. v Zi a < 1. This places us in the mushroom regime, where two adjacents copolymers do not overlap. It will be seen that this is sufficient to block sliding. 

Figure 5.1 Schematic depiction of polymers grafted to an interface in a sparse fashion, (a) (mushroom regime) and (b) a dense fashion (brush regime).

In the SCF approach the isolated chains are Gaussian, while in the SCMF theory they are self-avoiding walks. Thus, the SCMF theory is a more appropriate treatment of grafted layers for the mushroom regime and the mushroom to brush transition region. ... 

In the low density, mushroom, regime the analytical approaches assume that the polymer chains do not interact with each other and that the dimensions of the chains have the same scaling characteristics as the bulk polymer chains. ... 

FIG. 9 For grafted chains, one distinguishes (a) the mushroom regime, where the distance between chains, ais larger than the size of a polymer coil, and (b) the brush regime, where the distance between chains is smaller than the unperturbed coil size. Here, the chains are stretched away from the waU due to repulsive interactions between monomers. The bmsh height h scales linearly with the pol)nnerization index, h N, and is thus larger than the unperturbed cod radius oN. ... 

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