Lecture18 - Polymeric Materials Polymer-Polymer...

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Unformatted text preview: Polymeric Materials Polymer-Polymer Compatibility Lecture 18 Dr. Anthony Brennan University of Florida Department of Materials Science & Department Engineering Engineering EMA 6165 Polymer Physics – AB Brennan EMA 1 Agenda • Introduction • Free Energy of Mixing – Entropic Contributions – Enthalpic Contributions • Cohesive Energy Density – Solubility Parameter • Polymer/Polymer Solubility EMA 6165 Polymer Physics – AB Brennan EMA 2 Polymer-Polymer Compatibility UCST/LCST Behavior EMA 6165 Polymer Physics – AB Brennan EMA 3 Polymer-Polymer Compatibility Structure/Property Behavior q Cahn - Hillard Relationship (metals) ∂ 2 G 2 ∂φ 4 = M ∇ ν − 2K ∇ ν 2 ∂t ∂ ν • M is a mobility Coefficient • K is an energy gradient ∇ is the gradient function for each phase EMA 6165 Polymer Physics – AB Brennan EMA 4 Polymer-Polymer Compatibility Structure/Property Behavior EMA 6165 Polymer Physics – AB Brennan EMA 5 Polymer-Polymer Compatibility Phase Separation • Consider the Hashimoto paper and our discussion of blends: • Transitions observed from spherical or Transitions columnar morphologies to lamellae or cocolumnar continuous morphologies were observed. • Using Andradi and Hellman, we will study the percolation limit for a PMMA blended with a PMMA-co-PS EMA 6165 Polymer Physics – AB Brennan EMA 6 Polymer-Polymer Compatibility Phase Separation • Critical Values for χ : χ = χc = 2 / ϕ • For a blend where ϕ For 2 • • = ϕ3 Furthermore, it is known for χ > χc : 1 1 + ∆ϕ χ ln = 2 χ c ∆ϕ 1 − ∆ϕ ' " Where: ∆ϕ = ( ϕ − ϕ ) EMA 6165 Polymer Physics – AB Brennan EMA 7 Polymer-Polymer Compatibility Structure/Property Behavior • Which defines the miscibility gap. • The spinodal range is given by: χc ∆ϕs = 1 − χ ' " where: ∆ϕs = ( ϕs − ϕs ) 2 • • q where: ϕ ’ and ϕ ’’ refer to equilibrium phases Refer to Figure 2 (Polymer (1993) 34(5), 925-932 EMA 6165 Polymer Physics – AB Brennan EMA 8 Polymer-Polymer Compatibility Structure/Property Behavior • Percolation theory predicts: ∆ψ CC = ∆ψ CC ∆ϕ = 0.67 • It is assumed that the percolation range is independent of the incompatibility term χ /χ c. • Furthermore, growth should scale with the cube root of time. EMA 6165 Polymer Physics – AB Brennan EMA 9 Polymer-Polymer Compatibility Structure/Property Behavior q Figure 3 (Polymer (1993) 34(5), 925-932 q Figure 4 (Polymer (1993) 34(5), 925-932 q Figure 5 (Polymer (1993) 34(5), 925-932 q Figure 6 (Polymer (1993) 34(5), 925-932 q Figure 13 (Polymer (1993) 34(5), 925-932 EMA 6165 Polymer Physics – AB Brennan EMA 10 Summary • Polymer - Polymer blends normally Polymer display LCST behavior. display • Phase separation behavior is a Phase function of the enthalpic term. function • Control of phase behavior is a Control function of the chemical structure. function EMA 6165 Polymer Physics – AB Brennan EMA 11 References: • Andradi, L.N. and G.P. Hellmann, The Andradi, Percolation Limits for Two-Phase Blends of PMMA and Copolymers of Styrene and MMA. Polymer, l993. 34(5): p. 925-931. MMA. 34 • Schaefer, D.W., B.C. Bunker, and J.P. Schaefer, Wilcoxon, Fractals and Phase Separation. Fractals Proc. R. Soc. Lond., l989. A423: p. 35-53. A423 • Sakurai, S., et al., Morphology Transition Sakurai, et from Cylindrical to Lamellar Microdomains of Block Copolymers. Macromolecules, of l993. 26: p. 485-9l. 26 EMA 6165 Polymer Physics – AB Brennan EMA 12 ...
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