Polymer segment density

Altematively, tire polymer layers may overlap, which increases tire local polymer segment density, also resulting in a repulsive interaction. Particularly on close approach, r < d + L, a steep repulsion is predicted to occur. Wlren a relatively low molecular weight polymer is used, tire repulsive interactions are ratlier short-ranged (compared to tire particle size) and the particles display near hard-sphere behaviour (e.g., [11]). 

COSGROVE ET Al.. Adsorbed Polymer Segment Density Profiles... 

It is usually assumed that the micellar corona is a continuous phase extending from the micellar core to the micellar radius Rm. The internal structure of the micelle can be described by a density profile as shown in Fig. 8. The micellar core is a homogeneous melt or glass of insoluble polymer blocks. For hydrophobic blocks in aqueous solutions, the polymer volume fraction in the micellar core is 0C 1. The micellar shell is swollen with water or aqueous salt solution and has a polymer segment density that is expected to decrease in the radial direction as 0(r) r-a as typical for star polymers or... 

In one example polymer segment density profiles of weak polyacid brushes consisting of polymethacrylic acid (PMAA) chains were investigated as a function of the pH of the environment by means of multiple-angle ellipsom-etry [68]. The polymer brushes were prepared by surface-initiated polymerization of methylacrylic acid as described above. 

FIGURE 12.5 Various conformations adapted by grafted polymer molecules sticking out in a liquid. Grafting is depicted by a dot. The local polymer segment density q> is indicated as a function of distance from the surface x. The approximate thickness of the polymer layer <5 is also indicated. 

Whilst Osmond et al. (1975) are strictly correct in drawing attention to the existence of an elastic free energy in the interpenetrational domain, the magnitude of this term is likely to be trivially small. The reason for this is that the segmental volume fraction for most polymer chains is usually quite small (< 0-05, say) and so the volume from which the incoming polymer chains are excluded is also relatively small. This conclusion is corroborated by the results of Dolan and Edwards (1975) that are reproduced in Fig. 10.2. Here the polymer segment density distribution functions both in the presence and... 

It is apparent that if the distance between the plates exceeds twice the rms end-to-end distance of the polymers (/j > 2 ) then the maximum value for the segmental volume fraction is not dramatically reduced below that in the bulk solution. The distance between the plates is clearly sufficient to permit the polymer segment density of each of the depletion layers to rise to near its bulk value, the rise length being ca . ... 

Approach of the plates to closer than twice the rms end-to-end distance of the polymers (A<2 ) results in a significant reduction in the polymer segment density compared with that in the bulk phase. At a plate separation, for example, of one rms end-to-end distance of the polymer, the maximum in the volume fraction of the polymer is less than half the bulk value. Even closer approach (/i<0-6 ) results in the polymer segment density between the plates being reduced effectively to zero. 

The mean-field approximation is expected to break down in the region near the critical point, because the fluctuations of polymer segment densities tend... 

When the polymer adsorbs in a loose train-loop-tail-like structure, as shown in Figure 15.11, the polymer segment density in the adsorbed layer is usually low, so that A3 == A2. Furthermore, as the adsorbed layer is highly solvated and (nearly) freely penetrable for counterions, the electrostatic potential at x = is relatively low. Such flexible, loopy polymer layers may protrude into the surrounding medium over a... 

The transition from dilute solution behaviour (isolated polymer coils) to semi-dilute (interpenetration of coils, uniform polymer segment density) usually occurs over a narrow range of concentration, and a critical concentration c identified. This c will, however, depend to some extent upon the particular experiment performed, e.g., solution viscosity, diffusion (cf., e.g., ref. 99) ... 

In summary, electrokinetic measurements combined with an advanced theory for soft surfaces is an effective tool for the comprehensive characterisafion of switchable hydrogel coatings. The accessible physicochemical parameters (distribution of polymer segment density, charge density, hydrodynamic softness, interphasial dilfuseness) complanent the results as obtained by techniques like ellipsometry or indenter measur ents. 

Our numerical self-consistent field (SCF) calculations are based on the model developed by Scheutjens and Fleer. In this treatment, the phase behavior of polymer systems is modeled by combining Markov chain statistics with a mean field approximation for the free energy. The equations in this lattice model are solved numerically and self-consistendy. The self-consistent potential is a function of the polymer segment density distribution and the Flory-Huggins interaction parameters, or... 

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