Conformation of Single Chains in Solutions

This prediction is in excellent agreement with experimental observations in polymer melts and concentrated solutions and provides a scaling law for the dependence of the average size R of the molecular coil 

The power of the polymer volume fraction V2 in the above expression has also been verified experimentally [4] with some indication that it holds well into the concentrated regime. The transition from dilute to semi-dilute behavior occurs when the concentration of polymers is sueh that the coils begin to overlap. This concentration has been denoted in the literature as the overlap concentration, c or Vj. For high-molecular-weight polymers, this eoncentration occurs at fairly low values, V2 of the order of 0.01. Solutions are generally considered concentrated when V2 0.1. For good solvents, c scales with M [3]. Other scaling laws for polymer systans can be found in Reference 3. 

As discussed in Chapter 2, the ability of a solvent to dissolve a polymer will depend on the difference in their solubility parameters or on Flory s interaction parameter. The interaction parameter depends on temperature (see Equation 2.13), and therefore the swelling of a coil by a solvent will also depend on temperature. 

FIGURE 3.1 Illustrations of polymer chains in solutions at different concentrations. 

FIGURE 3.2 Subdivision of a chain into blobs in semi-dilute solutions. 

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