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Y. H. Wen ( 溫玉合 ) and C. C. Hua ( 華繼中 )

A Theoretical and Experimental Investigation on Short - Time Stretch Relaxation of Entangled Polymer Solutions. Y. H. Wen ( 溫玉合 ) and C. C. Hua ( 華繼中 ) Department of Chemical Engineering, National Chung Cheng University. Introduction. Historical Sketch de Gennes (1971)

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Y. H. Wen ( 溫玉合 ) and C. C. Hua ( 華繼中 )

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  1. A Theoretical and Experimental Investigation on Short-Time Stretch Relaxation of Entangled Polymer Solutions Y. H. Wen (溫玉合)and C. C. Hua (華繼中) Department of Chemical Engineering, National Chung Cheng University

  2. Introduction • Historical Sketch • de Gennes (1971) • Doi and Edwards (1986) • The tube (or reptation) model and its derivatives have proven very successful, especially in describing the linear viscoelasticity of entangled polymer liquids Linear relaxation

  3. A Story about Nonlinear Viscoelasticity Chain Retraction (nonlinear relaxation) Chain Retraction (nonlinear relaxation) Orientation Relaxation (linear relaxation) • PS/DEP solution (Mw=5.5x106 g/mol; PI=1.01; Zeq=77)

  4. Application of theRouse chain in two distinct cases • Only terminal chain retraction is captured for the case of concentrated systems Rouse chain Dilute solution Concentrated solution • Objectives of the current investigation: The Rouse Model Prediction on Short-time Chain Retraction Nonlinear Stress Relaxation Data in Single-step Strain Flows • For time scales < • The impact of polymerentanglement ?

  5. Formulation ofStress Relaxation in Single-Step Strain Flows • Nonlinear stress relaxation modulus: : shear stress : tube survival probability : strain : dimensionless chain stretching : plateau modulus : D-E universal function (w/o IA assumption) • The Rouse model where and : No. of Rouse modes : No. of entanglements per chain at equilibrium

  6. Experimentally Determined Model Parameters PS/TCP solution • Number of entanglements per chain at equilibrium, φ: volume fraction of polymer • TheRouse time,

  7. Theory/Data Comparisons PS/DEP solution PS/DEP solution

  8. Self-consistently Renormalized Rouse Modes (a) t = 0 (at equilibrium) • A different number of • entanglements per chain  Nis adynamicvariable Stretching (b) t = 0+ A Renormalized Rouse model: Retraction (c) t < where

  9. PS/DEP solution PS/DEP solution

  10. Theory/Data Comparisons for Various Polymer Species PS/TCP solution PαMS/PCB solution 1,4-PB/FO solution PMMA/PCB solution

  11. Conclusions • The instantaneous entanglement property has a significant impact on short-time chain retraction of entangled polymer solutions. • Self-consistent mode renormalization leads to better agreement with experimental data. • Remaining discrepancies might result from • (a) Inaccuracy of short-time relaxation data and/or • (b) Tube pressure associated with a deformed polymer network

  12. Acknowledgements • National Science Council (93-2116-E-194-001) • Excellency Project of the Ministry of Education of ROC (91-E-FA04-2-4A)

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