Stretching brushes

It has been mentioned in Sect. 3.1 that the molecular conformation can be altered strongly compared to that in solution if the side chains of a brush molecule are specifically adsorbed on the substrate or tend to spread on the surface to minimize the interfacial energy (Fig. 27). Moreover, the substrate changes the dimensionality of the system and breaks its symmetry [169,170]. Depending on the interfacial interactions and distribution of the side chains we can discuss a number of distinct conformations (a) stretched brush, (b) two-dimensional helix [170], and (c) globule state. 

High molecular weight polymers are principally not necessary to obtain layer thicknesses at the nm-pm scale for a stretched brush system (Fig. 9.1 (6)). 

The resolution p Rg(N) already allows us to obtain an explicit measure of the brush layer thickness L (see Fig. 36). In this case the simplest step-function profile ( )(z) with constant composition in the brush layer region is assumed (see Fig. 33). While the de Gennes-Leibler model assumes all end-attached chains to stretch at the same distance z=L from the interface, the situation with a lower free energy is conceivable [226,228] characterized by the non-uniform stretching and the total brush concentration decreasing with z. Measurements performed with higher resolution reveal [242,243,261,264] the profiles ( )(z) of the stretched brushes which might be approximated by an error function [266] ... 

To obtain useful theoretical results for the concentration profile, we need to go beyond these simple scaling arguments. Luckily, at least for the situation of relatively dense, strongly stretched, brushes, we can expect self-consistent field theories to work rather well in such a dense brush the basic mean-field assumption that any polymer chain will interact with its neighbours more than it will with itself should be well obeyed. Niunerical mean-field theories of the kind described in chapter 5 are very well suited to this kind of calculation the earliest results, due to Hirz (these results are still unpublished but some were reproduced by Milner et al. (1988)) showed profiles very different in character from those found for adsorbed chains. Rather than a concave concentration profile, the curves were notably convex, with the concentration dropping rather abruptly to zero on the outside of the brush. In fact it turns out that the profiles are rather well described by a parabolic form (see figure 6.7). It soon turned out that there was a remarkably good analytical solution to the self-consistent mean-field equations which provided an explanation for these parabolic profiles. 

Fig. 6 Schematic comparison between (a) a uniformly stretched brush, and (b) a non-uniformly stretched polymer brush similar to the Semenov scenario...

PLL-g-PEG copolymer was purchased from SuSoS AG (Dubendorf, Switzerland). The specific copolymer used, PLL(20)-g(3.6)-PEG(5), with a PLL molecular weight of 20 kDa, PEG side chains of molecular weight 5 kDa, and a grafting ratio (number of lysine units/number of PEG chains) of 3.6 shows maximum adsorption on the surface and optimum brush density to maintain a hydrated and stretched brush structure [11]. For all tribological... 

Fig. 2. The two limiting cases of a polymer brush regime, showing (a) tethered chains having the critical grafting density a = IhtR and (b) chains having a > a and forming the stretched brush. Other types of brush regime terminologies have been reported in literature. In this case, a characteristic length in the uncompressed brush (b) is given by...

Figure 3. A stretched brush comprising of chains depicted as strings of Pincus blobs. In distinction to the semi-dilute solution behavior the blobs are not close packed.

This free energy is actually valid only for brushes up to equilibrium thickness. The appropriate free energy for stretched brushes is discussed in section IX. 

Brush discharges from flexible, intermediate, bulk containers (FIBGs), plastic bags, stretch wrap, or other plastic film... 

Filament is prepared by extrusion followed by hot stretching. It may be used for brush bristles or for decorative purposes such as in the manufacture of woven lampshades. 

Inherent in the analytical SCF theory are (1) that the free ends of the chains can sample any position within the brush rather than be constrained to reside at the peripheral surface of the layer and, (2) that there is strong stretching, that is... 

A more accurate analysis of this problem incorporating renormalization results, is possible [86], but the essential result is the same, namely that stretched, tethered chains interact less strongly with one another than the same chains in bulk. The appropriate comparison is with a bulk-like system of chains in a brush confined by an impenetrable wall a distance RF (the Flory radius of gyration) from the tethering surface. These confined chains, which are incapable of stretching, assume configurations similar to those of free chains. However, the volume fraction here is q> = N(a/d)2 RF N2/5(a/d)5/3, as opposed to cp = N(a/d)2 L (a/d)4/3 in the unconfined, tethered layer. Consequently, the chain-chain interaction parameter becomes x ab N3/2(a/d)5/2 %ab- Thus, tethered chains tend to mix, or at least resist phase separation, more readily than their bulk counterparts because chain stretching lowers the effective concentration within the layer. The effective interaction parameters can be used in further analysis of phase separation processes... 

In one of several conceivable combinations of molecular weight and surface density, the binary brush forms a mixed, shorter layer and the extra length in and number of the longer chains is sufficient that these extra segments crowd one another in the outer layer and form an outer, stretched tethered layer. The Alexander analysis applied to the two-layer situation gives for the outer layer thickness of the mixture [132] ... 

In recent years, much attention has been paid to the use of controlled/ living polymerizations from flat and spherical surfaces [121,122],because this allows better control over the MW and MWD of the target polymer. By using these techniques, a high grafting density and a controlled film thickness can be obtained, as such brushes consist of end-grafted, strictly linear chains of the same length and the chains are forced to stretch away from the flat surface. Several research... 

If the backbone as well as the side chains consist of flexible units, the molecular conformation arises out of the competition of the entropic elasticity of the confined side chains and the backbone [ 153 -155]. In this case, coiling of the side chains can occur only at the expense of the stretching of the backbone. In addition to the excluded volume effects, short range enthalpic interactions may become important. This is particularly the case for densely substituted monoden-dron jacketed polymers, where the molecular conformation can be controlled by the optimum assembly of the dendrons [22-26,156]. If the brush contains io-nizable groups, the conformation and flexibility may be additionally affected by Coulomb forces depending on the ionic strength of the solvent [79,80]. 

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