Slide-Set-5-Phase-Behavior-Diffusion

Slide-Set-5-Phase-Behavior-Diffusion - Phase Separation...

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Unformatted text preview: Phase Separation Behavior: Phase Lecture Slide Set #5 Dr. Anthony Brennan University of Florida Tel: 352.392.6281 Email: abrennan@mse.ufl.edu EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 EMA 1 Slide Set #5 – Phase Separation Slide Behavior Behavior • Learning Objectives: – Polymerization Kinetics • Free-radical • Condensation • Chain Diffusion – Phase Separation Behavior • LCST, UCST • Spinodal and Binodal Phase Segregation EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 EMA 2 Chain Polymerization Kinetics Chain Consider the Energy: For the polymerization, For where M is the monomer, M• is the radical n is the monomer adding and n+1 indicates the chain: indicates ∆G 0 = − RT ln K Y+I R Y + * R C H C C* RH 2 Y CC C C* H n H H C C* H H RH C Y H R CC C C* H [ M n+1 •] + [ M ] ⇔ M n+1 • H HH H H RH Y R HH 2 Y H C + H R C R H * H H Y Y H RH R HH R HR CC C CC C CC H HH H HH H HH R H RH R H H R HR CC C C* CC C C +H C C CC HH H n H HH H n H H H HH Y Y n [ M n+1 •] = 1 K= = k dp [ M n •][ M ] [ M ] kp Y n Y EMA 6165 Polymer Physics – AB Brennan 3 Reaction rates and chain length Reaction Reaction rates for Reaction propagation are balanced by initiation and termination termination ki Rp = k p k t 1/ 2 [ M ][ I ] 1/ 2 Kinetic chain length is a Kinetic inversely proportional with either the competing termination and initiation rates rates ν= Rp Ri = Rp Rt EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 = kp [M ] 2( f ki kt [ I ] ) 1/ 2 4 Condensation Polymerization Kinetics Condensation [ − COOH ] + [ − OH ] ← K → [ − COO −] + [ H 2O] Reaction constant is Reaction proportional to the concentration of reactants concentration [ COO ][ H 2O] K= [ COOH ][ OH ] 1 DPn = 1− p 1+ p DPw = 1− p Where p is the fractional Where conversion and leads to the extent of reaction, chain length and f is functionality functionality 1 = 2[ M ] 0 kt + 1 2 (1 − p ) 1 Pc = 1/ 2 ( f −1) EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 5 Polymer – Polymer Phase Behavior LCST AND UCST LCST EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 6 Polymer Solubility Enthalpy of Mixing Therefore: ∆Gmix = kT ( N 1 ln υ + 1 Where N 2 ln υ ) 2 N1 = # of molecules N2 = # of segments υ= volume fraction EMA 6165 Polymer Physics – AB Brennan EMA 7 Polymer Solubility Enthalpy of Mixing ∆ S R UCST Xi= n=500 n=100 n=50 X1 Why? mole fraction of segments X2 ∆ ≠0 H Consider: London van der Waals Dipole H-bonding Acid-Base, etc. EMA 6165 Polymer Physics – AB Brennan EMA 8 Polymer Solubility Enthalpy of Mixing Use pairwise interaction energy and arguments similar to the Combinatorial Entropy Δw = 2 w1,2 −w1,1 −w2 ,2 Segment i is surrounded by zυ and 1 zυ 2 An interaction energy can be calculated for each segment and solvent molecule, w EMA 6165 Polymer Physics – AB Brennan EMA 9 UCST and LCST UCST EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 10 Polymer-Polymer Compatibility UCST/LCST Behavior EMA 6165 Polymer Physics – AB Brennan EMA 11 Spinodal Morphology Spinodal PHYSICS LETTERS, Vol114(2) A, S. Reich, 3 February 1986 EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 12 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 13 Polymer-Polymer Compatibility Structure/Property Behavior EMA 6165 Polymer Physics – AB Brennan EMA 14 Summary • Chain Chemistry defines structure. • Chain bond rotational potential Chain energies dictate properties energies • Balance of three energies defined by Balance structure/processing structure/processing • Characteristic dimensions defined by Characteristic structure and environment structure • Solubility is limited by entropy EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 EMA 15 References • Introduction to Physical Polymer Science, 4th Edition, Lesley H. Sperling, Wiley Interscience (2006) ISBN 13 978-0-471-70606-9 ISBN • Principles of Polymer Chemistry, P.J. Flory (1953) Principles Cornell University Press, Inc., New York. Cornell • The Physics of Polymers, Gert Strobl (1996) The Springer-Verlag, New York. Springer-Verlag, • Figures were reproduced from Polymer Physics, Figures (1996) Ulf Gedde, Chapman & Hall, New York. (1996) EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 EMA 16 ...
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This note was uploaded on 07/17/2011 for the course EMA 4161c taught by Professor Staf during the Fall '10 term at University of Florida.

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