Curved brushes

Fig. 2. Bead density profiles. Solid line Brushes, mean-field and scaling theory (step function) dashed-dotted line generalization of the Milner et al. theory for brushes in the theta state dashed-double dotted line Milner et al. theory for brushes (EV chains) dashed line EV stars dotted line EV combs. Variable r is scaled to give zero bead density for the smooth curves of brushes at r=l. The brush curves are normalized to show equal areas (same number of units). The comb and star densities are arbitrarily normalized to show similar bead density per volume unit as the step function and EV curves for brushes at the value ol r where these curves intercept...

Curves relating the corrected retention volume to the concentration of moderator (methanol) in the mobile phase [3] are shown in Figure 4. In pure water, the hydrocarbon chains of the brush phase interact with each other and collapse onto the surface in much the same way as drops of an hydrocarbon will coalesce on the... 

FIGURE 26.30 Side force coefficient S/L as function of slip angle for different loads. To fit the brush model curve, the friction coefficient had to be adjusted for load dependence according to /a = /lIo(T/To) (surface Alumina 180, speed 2 km/h). 

FIGURE 26.32 Braking and side force coefficient as function of the longitudinal slip for a set slip angle of 8° on wet asphalt at a constant speed of 30 mph, obtained with the Mobile Traction Laboratory (MIL) of the NHTSA. The curves were fitted using the brush model for composite shp with a variable friction coefficient. 

The stress curve sharply increases when the steric component appears upon compression. The initial thickness of a deformed layer is equal to be half the distance Dq obtained by extrapolating the sharpest initial increase to stress zero. The value Do is 21 1 nm, which is close the thickness of two molecular layers (19.2 nm) of the a-helix brush, calculated using the CPK model and the orientation angles obtained by FTIR analysis. We have calculated the elastic compressibility modulus Y,... 

Figure 4.7 Fluorescence anisotropy decay curves for the PMMA brush swollen in benzene (filled circles) and the free PMMA chain in benzene solution at concentrations of 0.33 (triangles) and 2.9 X 10 g (open circles). The graft density of the brush is 0.46 chains nm . The solid curve indicates the instrument response function. Reproduced with permission from the American Chemical Society.

Figure 4.8 shows the fluorescence anisotropy decay curves for PMMA brushes with various graft densities swollen in benzene and acetonitrile. Benzene and acetonitrile are good and 0 solvents for PMMA. As clearly shown in this figure. 

AC ADME ANS AUC BA/BE BBB BBM BBLM BCS BLM BSA CE CHO CMC CPC CPZ CTAB CV DA DOPC DPPC DPPH aminocoumarin absorption, distribution, metabolism, excretion anilinonaphthalenesulfonic acid area under the curve bioavailability-bioequivalence blood-brain barrier brush-border membrane brush-border lipid membrane biopharmaceutics classification system black lipid membrane bovine serum albumin capillary electrophoresis caroboxaldehyde critical micelle concentration centrifugal partition chromatography chlorpromazine cetyltrimethylammonium bromide cyclic votammetry dodecylcarboxylic acid dioleylphosphatidylcholine dipalmitoylphosphatidylcholine diphenylpicrylhydrazyl... 

Fig.22a,b. Bead density profiles in a brush of grafted chains in a theta solvent with N=200, and two different values of the grafting point densities. The smooth curves correspond to the elliptical theoretical prediction. Reprinted with permission from [199]. Copyright (1993) American Chemical Society... 

Polarization curves for Hj/Oj fuel cells at 50°C, 1 atm pressure. Curve A Nation impregnated (brush coated) PTFE-bound electrode (0.35 mg/cm Pt loading) curve B PTFE-bound catalyst layer (Pt loading 4 mg/cm ) curve C PTFE-bound electrode (Pt loading 0.35 mg/cm. (Based on Ticianelli, E. A. et al. Journal of the Electrochemical Society 1988 135 2209-2214. By permission of The Electrochemical Society.)... 

Fig. 26 Dry thickness of poly(acryl amide) as a function of the position on the silica substrate prepared by slow ( ) and fast ( ) removal of the polymerization solution by utilizing the method depicted in Fig. 24. The inset shows the dry poly(acryl amide) thickness as a function of the polymerization time. Note that both data sets collapse on a single curve at short polymerization times. Regardless of the drain speed, the brush thickness increases linearly at short polymerization times and levels off at longer polymerization times. The latter behavior is associated with premature termination of the growing polymers...

Fig.9 Typical F/R vs. D curve between the PMMA brush (L = 87nm, Mn = 121700, Mw/Mn = 1.39) and the sUica probe (attached on an AFM cantilever). The arrowheads indicate critical distances is the equilibrium thickness at which a repulsive force is detectable, and Do is the offset distance beyond which the brush was no more compressible...

The breakdown of the semi-dilute brush theory was also revealed in the force-distance curve of the high-density PMMA brush. Using the scaling approach [138], de Gennes derived the equation concerning the interaction force between two parallel plates with a semi-dilute polymer brush layer, predicting that the force-distance profiles should be scaled by plotting (F/i )... 

Fig. 17 Typical lateral force-temperature curves for the PMMA brush (Mn = 45400, Mw/Mn <1.2, a = 0.8 chains nm ) and an equivalent spin-coated film at the scanning rate of 10" nms . Reproduced with permission from [148] (Copyright 2003 The Society of Polymer Science, Japan)...

The most remarkable characteristic of candoluminescence is its temperature dependence. When a hydrogen flame is brushed over the phosphor surface, some time is required to warm up the surface before the luminescence appears. Each phosphor has a characteristic maximum in the temperature-intensity curve and at higher temperatures the intensity falls off again. Maxima for most transition metal ion- and rare earth ion-activated systems are in the range of 100 to 300 C. Candoluminescence thus occurs at much lower temperatures than the onset of purely thermal emission. 

The effect of intermolecular interactions is characterized by the Floiy-Huggins interaction parameter. For the polymer brush with 400 bonds, three values of the interaction parameter were selected in the calculations and the segment density profiles are plotted in Fig. 9. x 0 corresponds to a good solvent and x 0.5 to a poor one. With increasing value of x, the height of the polymer bmsb decreases. For the poor solvent ( =0.5), the chant segments tend to be more uniformly distributed (curve 3). 

A very effective way of stabilizing colloids is to modify the surface by grafting a polymer.1 In this manner, a high polymer density for which the chains can overlap to form a polymer bmsh can be obtained and this leads to a strong steric repulsion between the colloidal particles. In recent years,-i this-i problem-i has-i received-i attention-" both experimentally2-10 and theoretically.11-42 The theoretical investigations focused firstly on the density profile of a single brush on a flat or curved surface and secondly on the interactions between two brushes. 

Two sets of theoretical curves are plotted in Fig. 2 to examine the effect of the interaction parameter on the theoretical interaction force profile between two identical PS-X (140 K) brushes. The first set was calculated by ignoring the... 

For the PS-X (140 K) brushes and the two cases (without and with bond correlations), one can see from Fig. 2 that the theoretical force profile (solid curve 2) for the case free of bond correlations and x 0.2. and that (dashed curve 2 ) which incorporates the bond correlations and uses for x" the value 0.03 almost overlap. In addition, the theoretical curves 2 and 2 fit well the experimental data of Taunton el al.9... 

The effect of the interdigitation between the polymer chains of two brushes on the interaction force profile is plotted in Fig. 8 for three polymers PVP-PI 69-39, PVP-PI 38-69, and PS-X (140 K). The solid curves present the results in which the interdigitation was taken into account, while the dashed ones those in which the interdigitation was neglected. For the former, the chain conformational partition function [Eq. (5)] involves a 2mX2m supermatrix G for which the chain free ends can be located in any lattice layer between the two surfaces. For the latter, the conformational partition function involves a m X in supermatrix G with chains con-... 

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