A Theoretical and Experimental Investigation on ShortTime Stretch

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 n Historical Sketch n n n 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

n A Story about Nonlinear Viscoelasticity Chain Retraction (nonlinear relaxation) Orientation Relaxation (linear relaxation) § PS/DEP solution (Mw=5. 5 x 106 g/mol; PI=1. 01; Zeq=77)

n Application of the Rouse chain in two distinct cases Rouse chain Dilute solution n n Concentrated solution Only terminal chain retraction is captured for the case of concentrated systems 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 polymer entanglement ?

Formulation of Stress Relaxation in Single-Step Strain Flows n 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

n Experimentally Determined Model Parameters PS/TCP solution § Number of entanglements per chain at equilibrium, φ: volume fraction of polymer § The Rouse time,

Theory/Data Comparisons PS/DEP solution

n Self-consistently Renormalized Rouse Modes (a) t = 0 (at equilibrium) Stretching (b) t = 0+ § A different number of § entanglements per chain N is a dynamic variable A Renormalized Rouse model: Retraction (c) t < where

PS/DEP solution

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

Conclusions n n n 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

Acknowledgements n National Science Council (93 -2116 -E-194 -001) n Excellency Project of the Ministry of Education of ROC (91 -E-FA 04 -2 -4 A)