Brush height

Interestingly, scaling theory predicts for brushes that the density of units is independent from the distance to the surface and that the extension of the chain (or the brush height) is proportional to its contour length as if the chains were completely extended. Thus... 

An obvious aim in the simulations is to check the mean-field, and SCF theoretical approaches, which differ in some basic features. Both theories predict the same qualitative relationship for the brush height or the main chain extension in a good solvent (proportional to Np/ ). This result has been confirmed by the MC calculations of Chakrabarti and Toral [193] and Lai and Binder [194] (who... 

When the brush is immersed in poorer solvents, the theory predicts substantial changes. Thus, the chain extension and the brush height should scale as... 

The layer thickness or brush height h in a good solvent scales linear with the degree of polymerization N, as well as with the grafting density [Pg.400]

CMPE side. The maximum brush height at the CMPE edge of the sample decreases with decreasing CMPE concentration on the substrate (SI > S2 > S5). 

In Fig. 3 we show the density profiles (normalized to unity) for four different values of obtained with the full mean-field theory [52]. hi (a) the distance from the grafting surface is rescaled by the scahng prediction for the brush height, ho and in (b) it is rescaled by the imperturbed polymer radius Ro. 

Let us now turn to the thermodynamic behavior of a polymer brush. Using the Alexander scaHng model, we can calculate the free energy per chain by putting the result for the optimal brush height, Eq. 13, into the free-energy expression, Eq. 12, and obtain... 

For a theta solvent (V2 = 0) the relevant interaction is described by the third virial coefficient using a simple Alexander approach similar to the one leading to Eq. 13, the brush height is predicted to vary with the grafting density as h pa in agreement with computer simulations [65]. 

The different free energy contributions lead, upon minimization with respect to the two length scales h and d, to different behaviors. Let us first consider the weak charging limit, i.e. the situation where the counterions leave the brush, d>h.ln this case, minimization of Fion + Fint with respect to the counterion height d in the limiting case of vanishing brush height (h = 0) and monomer volume = 0) leads to... 

The scaling relations for the brush height and the crossover boundaries between the various regimes constitute the simplest approach towards charged brushes. We have already pointed out a few limitations of the presented results, which have to do with nonlinear stretching and finite-volume effects. 

In the nonlinear osmotic brush regime we combine the high-stretching (nonlinear) version of the chain elasticity in Eq. 22 with the nonhnear en-tropic effects of the counterions due to the finite volume of the polymer chains, i.e. we choose a finite effective diameter creff in Eq. 21. The final result for the equihbrium brush height is... 

Scrubber optimization is performed by adjusting the brushes and wafer rotation speeds, the DI water flow, and the brush height. The brush must be compressed 2 to 3 mm onto the wafer surface to come in direct contact... 

---