Segment concentration, mean chains

Edwards (10) has treated the concentrated region by considering a mean field approximation. The problem is to solve the random flight or diffusion equation in a uniform field provided by the segments (from all chains). This field is proportional to p, but is independent of position. It was shown that, under these conditions, 5 is again r (i.e. a = 1, for all solvents). 

Figure 7. The distribution of chain segment density, at 8 = 0.75, in an interfacial region with M = 6. The various curves correspond to the same values of mean segment concentration as in Figure 5.

For situations of overlapping chains, where lateral fluctuations in the segment concentration become rather small, mean-field descriptions become appropriate. The most successful of this type of theoiy is the lattice model of Scheutjens and Fleer (SF-theoiy). In chapter II.5 some aspects of this model were discussed. This theory predicts how the adsorbed amount and the concentration profile 0(z) depend on the interaction parameters and x and on the chain length N. From the statistical-thermodynamic treatment the Helmholtz energy and, hence, the surface pressure ti can also be obtcdned. When n is expressed as a function of the profile 0(z), the result may be written as ... 

A polymer chain at an interface is subject to a potential t/(r), which in general is composed of two components. There is an external component that arises directly from the effects of the wall. To this must be added an internal potential which reflects the mean field experienced by one segment due to the physical presence of all other segments. In the mean field approximation, this latter potential is simply proportional to the segment concentration c(r)... 

Increasing polymer concentration affects chain scission in several ways, as it increases the bulk viscoelasticity, the stress transmission efficiency, tq, and the hydrodynamic screening. The hydrodynamic screening means the hydrodynamic interactions become negligible between chain segments whose spatial distance apart is larger than a certain value (termed hydrodynamic screen length). In both... 

So what has been gathered from the computer simulations of selfavoiding walks It appears that the conformational properties of a polymer coil are quite significantly affected by the excluded volume. The coils become looser, and the fiuctuations in the segment concentration become more severe. The mean-square size of the coil increases. Moreover, the mean-square end-to-end distance R now depends differently on the number of segments in the chain. Instead of the familiar N (which we... 

In the approximation of ideal chains being in the mean field of the potential r) owing to the presence of other chains (Edwards, 1966 de Gennes, 1979), the segment concentration near the point f given V (i ) is small falls according to... 

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