Brush layer thickness

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] ... 

Figure 8.11. The dependence of the brush layer thickness normalised for the relative molecular mass of a spread film of a PDMS-PS linear diblock copolymer at the surface of ethyl benzoate. The dashed line is the scaling law prediction. After Kent et al (1995).

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] ... 

The length Do conresponds to twice the thickness of the brush layers. 

The chain dimension in the height direction was evaluated as the thickness of the brush layer, I, relative to the chain contour length, io, by atomic force microscopy (AFM). Figure 4.10 shows the solvent dependence of the conformation of the PMMA brush. Whereas the brush chain changes its conformation in response to the solvent quality at the low graft density, the high-density PMMA brush does not show... 

Salt effects in polyelectrolyte block copolymer micelles are particularly pronounced because the polyelectrolyte chains are closely assembled in the micellar shell [217]. The situation is quite reminiscent of tethered polymer brushes, to which polyelectrolyte block copolymer micelles have been compared, as summarized in the review of Forster [15]. The analogy to polyelectrolyte brushes was investigated by Guenoun in the study of the behavior of a free-standing film drawn from a PtBS-PSSNa-solution [218] and by Hari-haran et al., who studied the absorbed layer thickness of PtBS-PSSNa block copolymers onto latex particles [219,220]. When the salt concentration exceeded a certain limit, a weak decrease in the layer thickness with increasing salt concentration was observed. Similar results have been obtained by Tauer et al. on electrosterically stabilized latex particles [221]. 

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 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]

Recently, Quirk and Mathers [264] performed LASIP of isoprene on silicon wafers. A chlorodimethylsilane-functionalized diphenylefhene (DPE) was coupled onto the surface and lithiated with n-BuLi to form the initiating species. The living poly(isoprene) (PI) was end- functionalized with ethylene oxide. A brush thickness of 5 nm after two days of polymerization (9.5 nm after four days) was obtained in contrast to a polymer layer thickness of 1.9 nm by the grafting onto method using a telechelic silane functionahzed PI. 

The brash layer thickness (dry collapsed state) obtained after seven days of polymerization time and successive soxhlet extraction was found to be approx. 10 nm and very uniform ( 0.3 nm). The uniform thickness values are provided by the homogeneous initiation, polymerization and termination reaction. Meanwhile poly(2-oxazoline) homopolymers brushes with layer thicknesses of 20 to 30 nm can be obtained [275]. 

Fig. 7 Ellipsometric mapping of PBA/P2VP gradient brush, total thickness ( ), PtBA layer ( ), P2VP layer (A), (b) Fraction of PtBA versus the point coordinate on the sample (Reproduced with permission from [27])...

Fig. 10 Schematic PE brush structure. In a we show the weakly charged limit where the counterion cloud has a thickness d larger than the thickness of the brush layer, h. In b we show the opposite case of the strongly charged limit, where all counterions are contained inside the brush and a single length scale d h exists...

Surface-initiated living cationic polymerization of 2-oxazolines on planar gold substrates has been reported by Jordan et al (Fig. 9). SAMs of initiators on a planar gold substrate have been used to initiate the living cationic ringopening polymerization of 2-ethyl-2-oxazoline. The polymer chain end was functionalized with an alkyl moiety by means of a termination reaction in order to form an amphiphilic brush-type layer. The resulting layers (thickness... 

When calculating the theoretical force curves shown in Fig. 9 we used the XPS results to obtain the value of s and twice the length of the polymer brush was set to 23 nm. The anchoring points for the grafted PEO-chains were set at a distance 1.5 nm away from the mica surface. This value was chosen to be equal to the undisturbed layer thickness of the adsorbed chitosan polymer without grafted side-chains. When the prefactor is set equal to 1, the lower curve in Fig. 9 is obtained, and when a prefactor equal to two is used the upper curve is obtained. 

Fig. 3.a Schematic representation of a polymer brush. L is the layer thickness and D the average spacing between two grafting points, b The monomer density profile vs distance from the grafting plane z according to the Alexander-de Gennes model. Figure adapted from [66]... 

The most significant finding is that the plateau values at high electrolyte concentration are much larger than twice the adsorption layer thickness /iTOt > 2h (Table 3.6). This is rather unexpected since above Cw.cr, electrostatic repulsion is suppressed and steric interaction alone is expected to stabilise the film. If so, a total thickness close to the double brush thickness, i.e. /ijot 2h, would be expected. 

Both /ixot and h are very different for the two copolymer. In spite of this the thinnest films from both copolymers have the same structure two brush layers and an aqueous core of thickness - 3RF (Table 3.6). Despite some difference during their formation the equilibrium thickness of the thinnest films is probably due to the same type of stabilisation which is different from the brush-to-brush repulsion. 

However, the flow through the brush layer may be ignored in a first approximation [240], whereby the thickness h, appearing in Eq. (3.85), should be identified with the aqueous core thickness, /i2 (rather than hw) [241], The aqueous core thickness is plotted in Fig. 3.36, ( ). The dramatic influence on the interpretation is better seen in Fig. 3.37, ( ). The dependence is linear down to about /itot 90 nm. Thinner films drain faster initially and later on slower than predicted by the linear dependence, i.e. by Reynolds equation. The disjoining pressure isotherm (Fig. 3.38) is no more monotonous. 

At film thickness larger than twice the adsorption layer thickness this type of force vanishes [248], Therefore, such a mechanism is operative only at Ijtot 2Iii = 21.2 nm, i.e. hw < 28.0 nm (Table 3.5). The solid line in Fig. 3.40 is the best fit of Eq. (3.87). The van der Waals component has no practical influence on the numerical procedure. The fitted value h = 11.1 nm is in good agreement with the value of 10.6 nm used in the three layers model. Thus, de Gennes theory [248] gives a satisfactory description of the steric interactions at film thickness where brush-to-brush contact is realised. 

Consider two parallel identical plates coated with a charged polymer brush layer of intact thickness at separation h immersed in a symmetrical electrolyte solution of valence z and bulk concentration n as shown in Fig. 17. la [2]. We assume that dissociated groups of valence Z are uniformly distributed in the intact brush layer at a number density of No- We first obtain the potential distribution in the system when the two brushes are not in contact h > 2d. We take an x-axis perpendicular to the brushes with its origin 0 at the core surface of the left plate so that the region... 

FIGURE 17.1 Interaction between two identical parallel plates covered with a charged polymer brush layer and potential distribution across the brush layers, (a) Before the two brushes come into contact Qi > 2do). (b) After the two brushes come into contact (h < 2do). do is the thickness of the intact brush layer. From Ref. 2. 

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