Polymer brushes force curves

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 )... 

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. 

The origin of the repulsive force in high ionic strength solution was verified by comparison with theoretical curves calculated using equations derived by Kenworthy et al., based on the mean field theory of Milner et al. This theory (MWC), and the equations developed to describe the interaction energy between two opposing polymer brushes as they are compressed, make use of a parabolic segment density profile and allows a more realistic representation of the structure of tethered... 

Fig. 14 Above, interactions between oppositely charged polymer brushes during an AFM measurement. Below, force-distance curves between a surface covered with a PTMEAMA brush and a surface covered with a PSPMA brush at Ckci = 1-4 M. Reprinted from [72] with permission. Copyright 2010, American Chemical Society...

Figure 58 A binary polymer brush layer on a silicon wafer was prepared from rubbery poly(methyl acrylate) (PMA) and glassy poly (styrene-co-2,3,4,5,6-pentafluorostyrene) (PSF) using the grafting from approach. A series of force-distance curves were collected before and after the experiments to confirm the deformation was elastic, (a) The experimental loading curve (circles), fitting with the trilayered model (solid line, almost completely buried by experimental data points) and Hertzian model (dashed line), (b) Experimental depth distribution of the elastic modulus for the polymer brush layer (circles) and the best fitting with the trilayered model (solid line) showing slight increase in the elastic modulus near the surface and sharp increase in proximity to a stiff substrate. Reprinted with permission from Kovalev, A. Shulha, H. Lemieux, M. et al. J. Mater. Res. 2004,19,716. Copyright 2005 Materials Research Society.

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 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-... 

Figure 3.31. The master curve of force profiles for polystyrene brushes attached to mica surfaces and surrounded by a good solvent for the polymer. Relative molecular masses are in the range 26 500 Mi 660 000. After Taimton et al. (1990).

An extended brush-like layer is formed for the zwitterionically terminated polystyrene and comparison of force-distance curves before and after oscillatory motion showed that they were not displaced by the lubrication forces. These force-distance curves showed that the two brush-like layers interact at distances of about 2500 A. Above this separation, values of G scale with D in precisely the same manner both in the presence and in the absence of tethered polymer. The slopes of these lines, moreover, gave a viscosity (j/o) that agreed with the bulk viscosity of toluene. For the tethered pol)nner the line through these large separation data has an x axis intercept that corresponds closely to twice the polymer layer s thickness. Hence, in this region the shear plane in the system has shifted by a distance of 2Lh (Lr is hydrod5mamic layer thickness equilibrium layer thickness) and thus equation (3.4.13) becomes... 

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