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The Flory-Huggins theory for polymers

The Flory-Huggins theory for polymers. Note: Now the x is the number of repeat units = degree of polymerization. The entropy of the amorphous polymer state prior to mixing the polymer with solvent is calculated by inserting n 1 = 0 into previous equation. Entropy change per particle.

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The Flory-Huggins theory for polymers

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  1. The Flory-Huggins theory for polymers Note: Now the x is the number of repeat units = degree of polymerization

  2. The entropy of the amorphous polymer state prior to mixing the polymer with solvent is calculated by inserting n1 = 0 into previous equation

  3. Entropy change per particle = volume fraction of compound 1 ( = solvent) = volume fraction of compound 2 ( = polymer) Entropy change per mole

  4. 1. Small molecule mixtures: Phase diagrams

  5. 1. Small molecules: Binodal – coexistence curve Binodal is intersection of common tangent. Symmetrical case it is also first derivative zero points. Spinodal = unstable region, where the second derivative form Gibbsin enegry is negative. Can be calculated form the second derivative zero points. Critical point Binodal Spinodal

  6. 2. Polymer-solvent system x = number of repeat units (100% polymer) φ1 = 0 φ1 = 1 (pure solvent)

  7. 2. Polymer-solvent system

  8. 2. Polymer-solvent system Where 1: solventj1volume fraction 2: polymer, j2volume fraction, x number of repeat units Spinodal: Phase boundary where Spinodal from equation

  9. Solve 2nd degree equation If we know  parabola (opens down) Critical point ....

  10. What is corresbonding c value: Critical point ....

  11. Spinodals and critical points .... polymer/solvent oligomer/oligomer • Crital point at very low concentration • Therefore it is difficult to dissolve low polymer concentrations !! (paradox..) • Phase separation temperature • ccp is low  Tcp high • Difficult to dissolve polymers • Crital point symmetric • Phase separation temperature • ccp is high  Tcp lower • Easy to dissolve

  12. 3. Polymer-Polymer system In this example x1 = x2 Critical point Spinodal Special case when x1 = x2 = x, i.e. both has same degree of polymerization

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