Fraction of segments

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

The distribution of segment density normal to the surfaces is an important configurational property which serves to characterise the structure of the interfacial region. It is described in terms of the mean fraction of segments of the chain in each of... 

Hoeve44,45) extended his theory further by considering not only interactions between the train segments but also interactions among the loops, and found that the latter lead to a decrease in the number of possible conformations of adsorbed polymer chains. He assumed that the segment density distribution in any loop is uniformly expanded in one dimension by a factor of at as a result of loop-loop interactions. The volume fraction of segments at a distance z > 6 is then given by... 

Water-soluble polymers coat hydrophobic solid surfaces with multilayers and thus render the solid hydrophilic (i.e., wetting). The number of adsorbed chains (or the amount of polymer adsorbed) per surface site (or unit weight of adsorbent) is related to the volume fraction of segments in each layer. As the length of the chains increases,... 

Structural characteristics of adsorbed chains, such as the mean distance of chain ends from the surface and the fraction of segments in each layer, derive from P(i,s). The partition function and thermodynamic properties depend on the eigenvalues of W (Flory, 1969). In the limit n - oo, calculation of thermodynamic functions simplifies because one eigenvalue, denoted by A, dominates the free energy per segment,... 

Fleer and Scheutjens (1986) calculate the variation of the distribution of trains, loops, tails, and bridges with separation of the two surfaces. As one might expect, compression of the layers enhances the fractions of segments in trains and bridges at the expense of loops and tails. However, the existence and strength of attraction and repulsion have not teen correlated with the fractions of segments in the various chain configurations. 

For the determination of the fraction of segments in trains or, equivalently, the bound fraction p, one relies on features which allow differentiation between free (non-adsorbed) segments and segments in contact with the surface. In some cases, it is also possible to discriminate between parts of the solid substrate covered with polymer segments, and bare surface parts. One can then also determine the train density. 

In the two above equations, l is referred to as the component and ) k, m, and m are referred to the segments in each component, Xy is the segment-based mole fraction of segment species in component l only. The mole fractions of segments in the whole solution and in components are defined as below ... 

Zimm and Bragg showed that the fraction of segments in a helical conformation exhibits a sharp cooperative transition as s is increased, which is equivalent to increasing the interaction energy e or decreasing the temperature. The interaction energy is designed into the system based on the chemical... 

The fraction of segments in direct contact with the surface - that is the fraction of segments in trains, p (where p is the number of segments in direct contact with the surface/total number). 

As mentioned above, in order to fully characterize polymeric surfactant adsorption, three parameters must be determined (i) the adsorbed amount F (mgm or mol m ) as a function of the equihbrium concentration that is, the adsorption isotherm (ii) the fraction of segments in direct contact with the surface p (the number of segments in trains relative to the total number of segments) and (iii) the segment density distribution p(z) or the hydrodynamic adsorbed layer thickness 5. ... 

The fraction of segments in direct contact with the surface can be measured directly using spectroscopic techniques ... 

The fraction of segments p in trains can be determined using spectroscopic techniques such IR, electron spin resonance (ESR) and NMR. As discussed in Chapter 6, p depends on surface coverage, the polymer molecular weight and the solvency of the medium for the chains. 

The values of ct/Ls for different fractions of segments renormalized can be determined by the integration procedure described above. Some typical values are given in Table 12.2. In the interpenetrational domain, this form of the distribution function yields... 

Values of [Pg.254]

AGM)=ikTIVx)dV vM vi +(v2/x)ln vz+x V2Vi] (17.1) where 5 K= volume of the layer, V2 = volume fraction of segments, vi = 1 - V2, X =interaction parameter (which may be a function of V2), x=ratio of the molar volume of the polymer to that of the solvent and Ki = volume of a solvent molecule. This was summed for every layer associated with each plate, both for infinite separation and for closer approach, and their difference taken. 

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