Polymer brushes in solution

Since space is filled by the blobs the polymer volume fi action t , inside the brush must have the form 

From this we can obtain an expression for the thickness of the grafted chain h by noting that the volume of one chain, which contains N monomers, is hD, fi om which we find 

The important feature of this expression is the fact that the brush height depends on iV in a linear way, rather than as the square root, as for an ideal chain, or the 3/5 power, as it does for an isolated chain in a good solvent. This means that the chains are strongly stretched this is most easily seen by rewriting (6.1.5) in terms of the Flory radius of gyration of an isolated chain Rp and the average distance between grafting points D. This yields 

A fully close-packed brush, with the whole area of the interface taken up by the grafting sites, would have a value of a of unity and thus a volume fraction inside the brush of unity. However, this invalidates our assumption that the concentration inside the brush is in the semi-dilute regime recall that, for volume fractions of polymer greater than a crossover value 0 v/a, where V is the excluded volume parameter, we have a concentrated solution, for which 

If we equate this to the energy of attachment A we find that the coverage itself has a dependence on the relative molecular mass  

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To make further use of the azo-initiator, tethered diblock copolymers were prepared using reversible addition fragmentation transfer (RAFT) polymerization. Baum and co-workers [51] were able to make PS diblock copolymer brushes with either PMMA or poly(dimethylacrylamide) (PDMA) from a surface immobihzed azo-initiator in the presence of 2-phenylprop-2-yl dithiobenzoate as a chain transfer agent (Scheme 3). The properties of the diblock copolymer brushes produced can be seen in Table 1. The addition of a free initiator, 2,2 -azobisisobutyronitrile (AIBN), was required in order to obtain a controlled polymerization and resulted in the formation of free polymer chains in solution. 

The shape of the experimental isotherm (Fig. 3.38) is qualitatively similar to that found by van Vliet [226] with foam films from aqueous solutions of polyvinyl alcohol. It is also characteristic of the interaction energy as a function of the distance between two mica surfaces bearing grafted polymer brushes in good solvent as determined with Surface Force Apparatus (SFA) [e.g. 242],... 

The authors [228, 236] synthesized polymers of the type of so-called molecular brushes-poly(sodiumoxi) methylsylseskvioxanes (PSMSO). Molecular brushes one names comb-like polynners with high density of grafted side chains. They found anomalous low values of solutions viscosity of molecular brushes PSMSO and on this basis supposed, that at side branch length growth the qualitative changes of polymer macromolecule in solution and block occurred [228,236,237], which consisted oftran-... 

In contrast to organosoluble polymers, for most known water-based nonionic polymers, the quaUty of water as a solvent decreases upon an increase in temperature. This is known as LCST (lower critical solution temperature) behavior [144], Experimental observations of LCST behavior (thermoinduced collapse) of neutral stars or spherical polymer brushes in water are rare [145, 146], and do not yet provide systematic relationships between the LCST and the degree of branching. 

Fig. 1.9 Sketch of the total interaction potential between two spheres covered with polymer brushes in a good solvent in a solution containing non-adsorbing polymer chains...

Milner (61) addressed the energetics of polymer brushes. In this case neighboring polymer chains need to avoid one another. This volume exclusion effect provides the driving force for the chains to extend out into the solution. However, the problem is also different from the one chain bonding two particles, above, because one end of the chain is free. Milner also included a correction term for surface tension effects. He concluded that excess energies in the range of 8 to 10 kT were reasonable for many brush conformations. 

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