ISBN: 3-540-65181-0
TITLE: Flexible Polymer Chains in Elongational Flow
AUTHOR: Nguyen, Tuan Q.; Kausch, Hans-Henning (Eds.)
TOC:

1 Tortured Chains: An Introduction 1 
P.-G. de Gennes 
2 Polymer Solutions in Flow: A Non-Equilibrium Molecular Dynamics Approach 5 
C. Pierleoni, Y.-P. Ryckaert 
2.1 Introduction 5 
2.2 Molecular Dynamics of Dilute Solutions of Chains in Homogeneous Flow 8 
2.3 The Equilibrium Case 10 
2.3.1 Systems Studied 10 
2.3.2 The Static Structure Factor 11 
2.3.3 Polymer Longest Relaxation Time 11 
2.3.4 Dynamical Structure Factor 13 
2.4 Polymers in Shear Flow 14 
2.4.1 Phenomenological Framework for the Shear Flow Case 15 
2.4.1.1 Gyration Tensor 16 
2.4.1.2 Birefringence 17 
2.4.2 Structure of Polymers in Shear Flow 18 
2.4.2.1 Orientational Resistance 18 
2.4.2.2 A Scaling Picture at Fixed Reduced Shear Rate 20 
2.4.2.3 The Evolution of Scaling Exponents with the Reduced Shear Rate 23 
2.4.3 Internal Dynamics of Chains Under Steady Shear Flow 24 
2.4.3.1 Dynamics at Fixed beta 27 
2.4.3.2 beta-Dependence of Dynamical Properties 30 
2.5 Transient Behavior of a Nine-Bead Chain in Elongational Flow 33 
2.6 Conclusions and Perspectives 35 
List of Symbols and Abbreviations 38 
References 39 
3 Tethered Polymer Chains Under Strong Flows: Stems and Flowers 41 
F. Brochard-Wyart, A. Buguin 
3.1 Introduction 41 
3.2 Chains Immersed in a Pure Solvent 43 
3.2.1 Steady State in Uniform Flows 43 
3.2.1.1 Good Solvent (upsilon = 3/5) 43 
3.2.1.2 Ideal theta Solvent (upsilon = 1/2) 45 
3.2.2 Tethered Chains in Shear Flow 46 
3.2.2.1 Good Solvent 46 
3.2.2.2 Ideal Chains 47 
3.2.3 Relaxation processes: Stretch to Coil 48 
3.2.3.1 Good Solvent (upsilon = 3/5) 48 
3.2.3.2 Ideal q Solvent (upsilon = 1/2) 49 
3.3 Tethered Chains Immersed in a Polymer Solution 51 
3.3.1 Friction on the Test Chain (V>0) 51 
3.3.2 Deformation Under Flow 53 
3.3.2.1 Coil Regime 53 
3.3.2.2 Trumpet Regime 53 
3.3.2.3 Marginal Regime: Stem and Flower 54 
3.3.2.4 Ideal Stokes Regime 55 
3.4 Tethered Chains in Poor Solvents 56 
3.4.1 Conformation of a Single Chain in a Poor Solvent 56 
3.4.2 Force-Elongation Diagram Under Uniform Tension 57 
3.4.3 Deformation Under Solvent Flow 59 
3.4.3.1 Small Deformation: (V < V_1) 59 
3.4.3.2 "Stem and Globule": (V_1 < V < V_2) 59 
3.4.3.3 Above V2 61 
3.4.3.4 Relaxation 61 
3.5 Tethered Chains Confined in a Slit 61 
3.5.1 Good Solvent 62 
3.5.1.1 Uniform Tension 62 
3.5.1.2 Uniform Flow 62 
3.5.2 Ideal Chains 63 
3.6 Concluding Remarks 64 

References 65 
4 Osmotic Pressure in Solutions of Stretched Polymers 67 
Y. Rabin, S. Alexander 
4.1 Introduction 67 
4.2 Semi-Dilute Solution of Stretched Polymers 67 
4.3 Discussion 70 
4.3.1 Instabilities in Steady Homogeneous Flows 71 
4.3.2 Inhomogeneous Flows 71 
References 72 
5 Stretching of Polyelectrolytes in Elongational Flow 73 
O.V. Borisov, A.A. Darinskii 
5.1 Introduction 73 
5.2 Experimental Evidence 74 
5.3 Early Theoretical Approaches 78 
5.4 Equilibrium Conformation of the Polyelectrolyte Chain 80 
5.4.1 Conformation in a Salt-Free Solution 80 
5.4.2 Conformation in a Salt-Added Solution 85 
5.5 Stretching Transition in the Polyelectrolyte Chain 88 
5.5.1 Stretching in a Salt-Free Solution 88 
5.5.2 Stretching in a Salt-Added Solution 92 
5.6 Conclusions and Discussion 95 
List of Symbols and Abbreviations 97 
References 98 
6 Calculation of Flows with Large Elongational Components: CONNFFESSIT Calculation of the Flow of a FENE Fluid in a Planar 10:1 Contraction 101 
M. Laso, M. Picasso, H.C. ttinger 
6.1 Introduction 101 
6.2 CONNFFESSIT 103 
6.3 Geometry of the Planar Contraction Flow Problem 105 
6.4 The Polymeric Fluid 106 
6.5 The Time-Marching Procedure 108 
6.6 Algorithms 111 
6.6.1 Integration of the Trajectories of the Dumbbells  (External Degrees of Freedom) 111 
6.6.2 Integration of the Internal Degrees of Freedom of the Dumbbells 111 
6.6.3 Integration of the Momentum Conservation Equation 112 
6.6.4 Local Ensembles 112 
6.7 Initial and Boundary Conditions 113 
6.8 Continuum-Mechanical and Molecular Results 116 
6.9 Summary 132 
List of Symbols and Abbreviations 134 
References 135 
7 Polymer Solutions in Strong Stagnation Point Extensional Flows 137 
J.A. Odell, S.P. Carrington 
7.1 Introduction 137 
7.2 Theory and Modelling of Stretching Macromolecules 138 
7.3 Experimental Realization 139 
7.3.1 Elongational Flow Devices 139 
7.3.2 Assessment of Orientation and Stretching 142 
7.3.2.1 Birefringence Observation and Measurement 142 
7.3.2.2 Theoretical Calculations of Maximum Birefringence 143 
7.3.2.3 The RetardationBirefringence Transform for Cylindrical Symmetry 145 
7.4 Chain Stretching in Dilute Solutions 145 
7.4.1 The Coil  Stretch Transition 145 
7.4.2 The Functional Dependence of Molecular Relaxation Time (t) 146 
7.4.3 Combinations of Rotational and Extensional Flows 147 
7.4.4 The Evolution of Molecular Strain Around the Stagnation Point 148 
7.4.4.1 The Derivation of Molecular Strain from Birefringence 152 
7.4.4.2 Flow-Field Modelling 154 
7.4.4.3 Comparison of Molecular and Fluid Strain 155 
7.4.4.4 The Effect of Solvent Quality 159 
7.4.4.5 The Effect of Chain Flexibility 160 
7.4.4.6 Theoretical Simulation of Molecular Behaviour 160 
7.4.5 The Equilibrium Stretched State 160 
7.4.5.1 Light Scattering 162 
7.4.5.2 Raman Spectroscopy 163 
7.4.5.3 Direct Observation of DNA 163 
7.4.5.4 Conclusions 164 
7.4.6 Criticality and Hysteresis 164 
7.5 Semi-Dilute Solution Behaviour 166 
7.6 Extensional Viscometry 170 
7.6.1 Newtonian Fluids 170 
7.6.2 Dilute Solutions 171 
7.6.3 Semi-Dilute Solutions 173 
7.7 Thermomechanical Degradation 175 
7.7.1 Introduction 175 
7.7.2 Mechanical Scission in Dilute Solutions 176 
7.7.2.1 The TABS Theory 177 
7.7.2.2 Transient Flow Degradation 178 
7.7.2.3 Chain Scission in Simple Shear Flow 179 
7.7.3 Degradation in Semi-Dilute Solutions 180 
7.8 Conclusions 181 
References 182 
8 Birefringence of Dilute PS Solutions in Abrupt Contraction Flow 185 
T.Q. Nguyen, R. Porouchani, H.-H. Kausch 
8.1 Introduction 185 
8.2 Realization of Abrupt Contraction Flow 188 
8.2.1 Design of the Flow Cell 188 
8.2.2 Flow Field Modeling 190 
8.2.2.1 Streamlines 191 
8.2.2.2 Velocity Field 193 
8.2.2.3 Molecular Orientation 195 
8.2.2.4 Residence Time 196 
8.3 Flow Birefringence Measurements 198 
8.3.1 Principles of Optical Rheometry 198 
8.3.2 Fast Polarization Modulation Technique 201 
8.4 Experimental Results 205 
8.4.1 Experimental Conditions 205 
8.4.2 Material Characterization 205 
8.4.2.1 Chemicals 205 
8.4.2.2 Intrinsic Viscosity of PS Solutions 205 
8.4.2.3 Molecular Coil Dimensions 206 
8.4.2.4 End-to-End Chain Relaxation Time 207 
8.4.2.5 Thermodynamic Quality of the Solvents 208 
8.4.2.6 Molecular Weight Distribution 208 
8.4.3 Conversion of Retardation into Birefringence 209 
8.4.3.1 Inhomogeneity of the Birefringence Zone 210 
8.4.3.2 Numerical Inverse Abel Transform 211 
8.4.3.3 Transmission of Polarized Light at Oblique Incidence 212 
8.4.4 Extraneous Birefringence 215 
8.4.5 Probe Beam Dimensions 220 
8.4.6 Birefringence in Dilute Decalin Solutions 223 
8.4.6.1 Optical Micrography 223 
8.4.6.2 Quantitative Retardation Measurements 223 
8.4.6.3 Radial Birefringence Distribution 227 
8.4.6.4 Axial Birefringence Distribution 229 
8.4.7 Birefringence in Dilute 1-Methyl-Naphthalene Solutions 230 
8.4.8 Flow-Induced Degradation 234 
8.5 Discussion 236 
8.5.1 Affine Deformation Model 236 
8.5.1.1 Determination of Delta n_max 240 
8.5.1.2 Determination of beta 242 
8.5.2 Other Polymer Dynamics Models Relevant to Abrupt  Contraction Flow 244 
8.6 Prospects and Conclusions 246 
8.6.1 Final Words 248 
Appendix A 248 
Appendix B 250 
Appendix C 252 
List of Symbols and Abbreviations 253 
References 254 
9 The Hydrodynamics of a DNA Molecule in a Flow Field 259 
R.G. Larson, T.T. Perkins, D.E. Smith, S. Chu 
9.1 Introduction 259 
9.2 Calculation of the Drag Coefficient 261 
9.3 Stretching Experiments with Longer DNA Molecules 263 
9.4 Hydrodynamic Model for DNA 266 
9.4.1 Elastic Spring Force 267 
9.4.2 Drag Force 267 
9.4.3 Brownian Motion 269 
9.5 Simulation Results 269 
9.6 Discussion 274 
Appendix: Model Validation 276 
List of Symbols and Abbreviations 280 
References 281 
10 Single Polymers in Elongational Flows: Dynamic, Steady-State, and Population-Averaged Properties 283 
T.T. Perkins, D.E. Smith, S. Chu 
10.1 Introduction 283 
10.2 Previous Experimental Work 284 
10.3 Experimental Technique 286 
10.3.1 Direct Imaging of Single Molecules as a Measurement Technique 286 
10.3.2 DNA as a Model Polymer 288 
10.3.3 Microscope and Imaging 289 
10.3.4 Flow Cell Design 290 
10.3.5 Flow Cell Manufacture 292 
10.3.6 Pumps and Plumbing 293 
10.3.7 Flow Cell Calibration 295 
10.3.8 Solution 298 
10.3.9 Staining and DNA Preparation 300 
10.3.10 Measurement of t_1 300 
10.4 Experimental Results 302 
10.4.1 Data Reduction 302 
10.4.2 Extension vs Residency Time 304 
10.4.3 Average and Steady-State Properties; Direct Observation  of the Coil-Stretch Transition 309 
10.4.4 Steady-State Measurements Fit by the Dumbbell Model 311 
10.4.5 Conformational Dependent Dynamics at Highest Strain Rates 312 


10.4.6 Master Curves 314 
10.4.7 Affine Deformation 317 
10.4.8 Dynamic Data, Intrinsic Viscosity and the Dumbbell Model 319 
10.4.9 Comparison to Previous Experimental Work 321 
10.4.9.1 Birefringence 321 
10.4.9.2 Light Scattering 322 
10.4.9.3 Stagnation Point Flow Fracture 324 
10.4.9.4 Rheology 324 
10.4.9.5 Filament Stretching 325 
10.4.9.6 Mean Field Theories 326 
10.4.9.7 Comments on Dumbbell Model 327 
10.4.9.8 Proposed Conformations 328 
10.4.10 Limitation of Applicability 329 
10.5 Summary 329 
10.6 Future Prospects 330 
List of Symbols and Abbreviations 331 
References 332 
11 The Rheology of Polymer Solutions in Porous Media 335 
A.J. Mller, A.E. Sez 
11.1 Introduction 335 
11.2 Fluid Dynamics Characterization of Porous Media Flows 337 
11.3 Non-Newtonian Behavior in the Flow of Polymer Solutions Through Porous Media 340 
11.3.1 Review of Mechanisms Proposed to Explain Extension Thickening 343 
11.3.2 The Nature of Extension Thickening in Porous Media Flows 348 
11.3.3 Effect of Porous Media Microstructure 366 
11.3.4 Shear Thinning 371 
11.4 Flow-Induced Degradation 374 
11.5 Porous Media Flows of Polymer Blends and Cross-Linked Polymers in Solution 380 
11.5.1 Flow of Cross-Linked Polymer Solutions Through Porous Media 380 
11.5.2 Flow of Solutions of Polymer Blends Through Porous Media 383 
11.6 Concluding Remarks 389 
List of Symbols and Abbreviations 390 
References 391 
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