Segment density profiles

FIG. 12 Segment density profile as function of the distance from the wall Z for flexible (empty symbols) and semi-rigid (full symbols) living polymer chains at T = 0.4 [28]. The fractional occupancy of lattice sites by polymer segments is shown for the layers in the left half of the box. Dashed lines are guides for the eyes. 

Fig. 9. Comparison of the analytical SCF model [56] with the full numerical SCF calculation [53] for the segment density profile in flat, grafted layers at various surface densities (o is the fraction of the maximum possible surface coverage of grafted ends). The analytical profile is parabolic to its tip, while the numerical calculation shows that the density at the periphery of the layer drops off exponentially...

The theory of polymer adsorption is complicated for most situations, because in general the free energy of adsorption is determined by contributions from each layer i where the segment density is different from that in the bulk solution. However, at the critical point the situation is much simpler since the segment density profile is essentially flat. Only the layer immedia-... 

Several experimental parameters have been used to describe the conformation of a polymer adsorbed at the solid-solution interface these include the thickness of the adsorbed layer (photon correlation spectroscopy(J ) (p.c.s.), small angle neutron scattering (2) (s.a.n.s.), ellipsometry (3) and force-distance measurements between adsorbed layers (A), and the surface bound fraction (e.s.r. (5), n.m.r. ( 6), calorimetry (7) and i.r. (8)). However, it is very difficult to describe the adsorbed layer with a single parameter and ideally the segment density profile of the adsorbed chain is required. Recently s.a.n.s. (9) has been used to obtain segment density profiles for polyethylene oxide (PEO) and partially hydrolysed polyvinyl alcohol adsorbed on polystyrene latex. For PEO, two types of system were examined one where the chains were terminally-anchored and the other where the polymer was physically adsorbed from solution. The profiles for these two... 

The segment density profile obtained by s.a.n.s. is normalized in the form,... 

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

Figure 2. Experimental segment density profiles for PEO adsorbed on PS...

Segment density profiles and hydrodynamic thickness measurements have been made for polyethylene oxides adsorbed on polystyrene latex. Comparison with theoretical models shows that the hydro-dynamic thickness is determined by polymer segments (tails) at the extremity of the distribution. It is also concluded that the sensitivity of the s.a.n.s. experiment precludes the measurement of segments in this region and that the experimental segment density profiles are essentially dominated by loops and trains. 

Figure 23. Radial segment density profile through a cross-section of a highly curved spherical vesicle. The origin is at r = 0, and the vesicle radius is very small, i.e. approximately r = 25 (in units of segment sizes). The head-group units, the hydrocarbons of the tails and the ends of the hydrocarbon tails are indicated. Calculations were done on a slightly more simplified system of DPPC molecules in the RIS scheme method (third-order Markov approximation), i.e. without the anisotropic field contributions...

Integration over this segment density profile under the condition of j 0 (p r)Ajvr dr = Nfl then leads to a relationship for R as a function of N... 

---