The dependence on N is obvious - the larger the polymer the more space is taken up so the smaller is φ*. The critical volume fraction φ* is calculated as: φ** is generally taken to be around 0.2-0.3 Finally at φ** the solution is "concentrated" and viscosity rises very strongly. At a critical volume fraction, φ*, the coils are touching each other so above this concentration ( "semidilute") the viscosity is increasingly strongly affected by the polymer. At low concentrations ( "dilute") the polymer coils are not touching so the viscosity is almost unchanged from the pure solvent. These formulae tell us the obvious: more monomers, N, longer chain segments, b, less and less freedom to curl back on itself (lower θ down to 0°) and a greater happiness in the solvent means a larger blob of polymer in solution.īut we also can learn more. In a very good solvent (χ=0, often called athermal) v rises to 0.59 The second is on how isolated, or not, those blobs are.Īssuming that the polymer is made of N links of chains length b where those chain segments cannot bend by more than an angle θ, and that the "happiness" of the polymer in the solvent can be measured by χ where a value of 0.5 is "neutral" then the polymer has an average end to end distance, R e and a typical radius of gyration R g given byīut what is the exponent v? For a theta solvent (χ=0.5), v is 0.5, for a very poor solvent (χ>0.75), such that the polymer curls up on itself to go from a coil to a globule,v approaches 0.33. The first is on its size if it were an isolated blob of polymer. A polymer dissolved in a solvent can be classified in two different ways.
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