Coil-overlap region

For the coil-overlap region (where polymer coils overlap) the viscosity is... 

In the coil overlap region the argument of f(x) should be assumed to be equal to 1 (s e Equation 24) from which we get... 

A relation that fits viscosity data well in the coil overlap region is the Martin equation ... 

The geometrical problem. This involves evaluating the geometrical effect in item (2). It requires calculation of the volume of the overlapping regions as a function of d and the coil dimensions, say, r. The mathematics of this step are tedious and add little to the polymer aspects of the theory. 

Numerical results for a 10% solution of polymer [N - 1000) in Its own monomer are given in fig. 5.15 (solid curves). It is clear that long chains try to avoid the surface region because of the incurred loss of conformational entropy. The available space Is occupied by the monomer which does not suffer from these entroplcal restrictions. Hence, the polymer is depleted. It can be shown that at low (p (below coil overlap) the thickness of the depletion zone is proportional to Vw, see sec. 5.3e. At higher (as in fig. 5.15), the osmotic pressure pushes the chains closer to the surface, making the depletion layer thinner and its thickness more weakly dependent on chain length. 

The formation of a photo-reversible gel is explained as foUows. The azobenzene groups in the surface region of the polymer coil help the coil overlap. When they change to a more polar cis form, the interactions are strengthened. The change in the interpolymer interactions is responsible for the change in the gel melting temperature. 

Regions I and III are separated by the coil overlap line (Equation 22), which takes the dependence... 

A second major problem that causes error in EOR polymer intrinsic viscosity measurements concerns the uncertainty that dilute solution conditions exist during viscosity measurements. As shown by Figure 1, dilute solution conditions exist only when the overlap parameter is less than one. Extrapolation to "zero concentration reduced viscosity is linear only if viscosity data is taken in the dilute region. However, a polymer solution having an intrinsic viscosity of 30 dl/g is dilute only if the concentration is less than 1/30 g/dl (33 ppm). At concentrations higher than this, excessive coil overlap may exist. Solution reduced viscosities determined above the dilute solution region can not be easily extrapolated to zero concentration. When linear extrapolation is done, the apparent intrinsic viscosities which are obtained are larger than the true intrinsic viscosity. 

A fundamental distinction exists between dilute polymer solutions where the coils are separate (Hg. III.3a) and more concentrated solutions where the coils overlap (Hg. in.3c). At the overlap threshold (c = c ) the coils begin to be densely packed. Clearly this threshold is not sharp it is more properly defined as a region of crossover between regimes (a) and (c), but the scaling properties of c are essential. We expect c to be comparable with the local concenhation inside a single coil. In a ery good (athermal) solvent this implies ... 

Figure 8.11 The coil domains of two polymer molecules. The schematic shows by shading how the region of overlap increases as the distance between centers decreases.

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