Flexible Polymer Chains in Elongational Flow

by Nguyen, Q. Tuan; Kausch, Hans-Henning

• ISBN13: 9783540651819
• ISBN10: 3540651810
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: Springer Verlag

Summary

The behavior of polymer solutions in elongational flow has been treated quite recently in the literature but scattered in disparate scientific journals not easily accessible. This is very surprising since elongational flow is known to be very effective on polymer chains and thus more interesting than the already wellknown shear flow. This book covers for the first time the subject from the point of view of the various disciplines. It achieves a balance between science, experiment and technology and integrates the fundamental and practical aspects.

Table of Contents

1 Tortured Chains: An Introduction	1	(4)
P.-G. de Gennes
2 Polymer Solutions in Flow: A Non-Equilibrium Molecular Dynamics Approach	5	(36)
C. Pierleoni
Y.-P. Ryckaert
2.1 Introduction	5	(3)
2.2 Molecular Dynamics of Dilute Solutions of Chains in Homogeneous Flow	8	(2)
2.3 The Equilibrium Case	10	(4)
2.3.1 Systems Studied	10	(1)
2.3.2 The Static Structure Factor	11	(1)
2.3.3 Polymer Longest Relaxation Time	11	(2)
2.3.4 Dynamical Structure Factor	13	(1)
2.4 Polymers in Shear Flow	14	(19)
2.4.1 Phenomenological Framework for the Shear Flow Case	15	(1)
2.4.1.1 Gyration Tensor	16	(1)
2.4.1.2 Birefringence	17	(1)
2.4.2 Structure of Polymers in Shear Flow	18	(1)
2.4.2.1 Orientational Resistance	18	(2)
2.4.2.2 A Scaling Picture at Fixed Reduced Shear Rate	20	(3)
2.4.2.3 The Evolution of Scaling Exponents with the Reduced Shear Rate	23	(1)
2.4.3 Internal Dynamics of Chains Under Steady Shear Flow	24	(3)
2.4.3.1 Dynamics at Fixed Beta	27	(3)
2.4.3.2 Beta-Dependence of Dynamical Properties	30	(3)
2.5 Transient Behavior of a Nine-Bead Chain in Elongational Flow	33	(2)
2.6 Conclusions and Perspectives	35	(3)
List of Symbols and Abbreviations	38	(1)
References	39	(2)
3 Tethered Polymer Chains Under Strong Flows: Stems and Flowers	41	(26)
F. Brochard-Wyart
A. Buguin
3.1 Introduction	41	(2)
3.2. Chains Immersed in a Pure Solvent	43	(8)
3.2.1 Steady State in Uniform Flows	43	(1)
3.2.1.1 Good Solvent (v = 3/5)	43	(2)
3.2.1.2 Ideal Theta Solvent (v = 1/2)	45	(1)
3.2.2 Tethered Chains in Shear Flow	46	(1)
3.2.2.1 Good Solvent	46	(1)
3.2.2.2 Ideal Chains	47	(1)
3.2.3 Relaxation processes: Stretch to Coil	48	(1)
3.2.3.1 Good Solvent (v = 3/5)	48	(1)
3.2.3.2 Ideal 8 Solvent (v = 1/2)	49	(2)
3.3 Tethered Chains Immersed in a Polymer Solution	51	(5)
3.3.1 Friction on the Test Chain (V is greater than 0)	51	(2)
3.3.2 Deformation Under Flow	53	(1)
3.3.2.1 Coil Regime	53	(1)
3.3.2.2 Trumpet Regime	53	(1)
3.3.2.3 Marginal Regime: Stem and Flower	54	(1)
3.3.2.4 Ideal Stokes Regime	55	(1)
3.4 Tethered Chains in Poor Solvents	56	(5)
3.4.1 Conformation of a Single Chain in a Poor Solvent	56	(1)
3.4.2 Force-Elongation Diagram Under Uniform Tension	57	(2)
3.4.3 Deformation Under Solvent Flow	59	(1)
3.4.3.1 Small Deformation: (V is less then V(1))	59	(1)
3.4.3.2 "Stem and Globule": (V(1) is less than V is less than V(2))	59	(2)
3.4.3.3 Above V(2)	61	(1)
3.4.3.4 Relaxation	61	(1)
3.5 Tethered Chains Confined in a Slit	61	(3)
3.5.1 Good Solvent	62	(1)
3.5.1.1 Uniform Tension	62	(1)
3.5.1.2 Uniform Flow	62	(1)
3.5.2 Ideal Chains	63	(1)
3.6 Concluding Remarks	64	(1)
References	65	(2)
4 Osmotic Pressure in Solutions of Stretched Polymers	67	(6)
Y. Rabin
S. Alexander
4.1 Introduction	67	(1)
4.2 Semi-Dilute Solution of Stretched Polymers	67	(3)
4.3 Discussion	70	(2)
4.3.1 Instabilities in Steady Homogeneous Flows	71	(1)
4.3.2 Inhomogeneous Flows	71	(1)
References	72	(1)
5 Stretching of Polyelectrolytes in Elongational Flow	73	(28)
O.V. Borisov
A.A. Darinskii
5.1 Introduction	73	(1)
5.2 Experimental Evidence	74	(4)
5.3 Early Theoretical Approaches	78	(2)
5.4 Equilibrium Conformation of the Polyelectrolyte Chain	80	(8)
5.4.1 Conformation in a Salt-Free Solution	80	(5)
5.4.2 Conformation in a Salt-Added Solution	85	(3)
5.5 Stretching Transition in the Polyelectrolyte Chain	88	(7)
5.5.1 Stretching in a Salt-Free Solution	88	(4)
5.5.2 Stretching in a Salt-Added Solution	92	(3)
5.6 Conclusions and Discussion	95	(2)
List of Symbols and Abbreviations	97	(1)
References	98	(3)
6 Calculation of Flows with Large Elongational Components: CONNFFESSIT Calculation of the Flow of a FENE Fluid in a Planar 10: 1 Contraction	101	(36)
M. Laso
M. Picasso
H.C. Ottinger
6.1 Introduction	101	(2)
6.2 CONNFFESSIT	103	(2)
6.3 Geometry of the Planar Contraction Flow Problem	105	(1)
6.4 The Polymeric Fluid	106	(2)
6.5 The Time-Marching Procedure	108	(3)
6.6 Algorithms	111	(2)
6.6.1 Integration of the Trajectories of the Dumbbells (External Degrees of Freedom)	111	(1)
6.6.2 Integration of the Internal Degrees of Freedom of the Dumbbells	111	(1)
6.6.3 Integration of the Momentum Conservation Equation	112	(1)
6.6.4 Local Ensembles	112	(1)
6.7 Initial and Boundary Conditions	113	(3)
6.8 Continuum-Mechanical and Molecular Results	116	(16)
6.9 Summary	132	(2)
List of Symbols and Abbreviations	134	(1)
References	135	(2)
7 Polymer Solutions in Strong Stagnation Point Extensional Flows	137	(48)
J.A. Odell
S.P. Carrington
7.1 Introduction	137	(1)
7.2 Theory and Modelling of Stretching Macromolecules	138	(1)
7.3 Experimental Realization	139	(6)
7.3.1 Elongational Flow Devices	139	(3)
7.3.2 Assessment of Orientation and Stretching	142	(1)
7.3.2.1 Birefringence Observation and Measurement	142	(1)
7.3.2.2 Theoretical Calculations of Maximum Birefringence	143	(2)
7.3.2.3 The Retardation-Birefringence Transform for Cylindrical Symmetry	145	(1)
7.4 Chain Stretching in Dilute Solutions	145	(21)
7.4.1 The Coil --> Stretch Transition	145	(1)
7.4.2 The Functional Dependence of Molecular Relaxation Time (Tan)	146	(1)
7.4.3 Combinations of Rotational and Extensional Flows	147	(1)
7.4.4 The Evolution of Molecular Strain Around the Stagnation Point	148	(4)
7.4.4.1 The Derivation of Molecular Strain from Birefringence	152	(2)
7.4.4.2 Flow-Field Modelling	154	(1)
7.4.4.3 Comparison of Molecular and Fluid Strain	155	(4)
7.4.4.4 The Effect of Solvent Quality	159	(1)
7.4.4.5 The Effect of Chain Flexibility	160	(1)
7.4.4.6 Theoretical Simulation of Molecular Behaviour	160	(1)
7.4.5 The Equilibrium Stretched State	160	(2)
7.4.5.1 Light Scattering	162	(1)
7.4.5.2 Raman Spectroscopy	163	(1)
7.4.5.3 Direct Observation of DNA	163	(1)
7.4.5.4 Conclusions	164	(1)
7.4.6 Criticality and Hysteresis	164	(2)
7.5 Semi-Dilute Solution Behaviour	166	(4)
7.6 Extensional Viscometry	170	(5)
7.6.1 Newtonian Fluids	170	(1)
7.6.2 Dilute Solutions	171	(2)
7.6.3 Semi-Dilute Solutions	173	(2)
7.7 Thermomechanical Degradation	175	(6)
7.7.1 Introduction	175	(1)
7.7.2 Mechanical Scission in Dilute Solutions	176	(1)
7.7.2.1 The TABS Theory	177	(1)
7.7.2.2 Transient Flow Degradation	178	(1)
7.7.2.3 Chain Scission in Simple Shear Flow	179	(1)
7.7.3 Degradation in Semi-Dilute Solutions	180	(1)
7.8 Conclusions	181	(1)
References	182	(3)
8 Birefringence of Dilute PS Solutions in Abrupt Contraction Flow	185	(74)
T.Q. Nguyen
R. Porouchani
H.-H. Kausch
8.1 Introduction	185	(3)
8.2 Realization of Abrupt Contraction Flow	188	(10)
8.2.1 Design of the Flow Cell	188	(2)
8.2.2 Flow Field Modeling	190	(1)
8.2.2.1 Streamlines	191	(2)
8.2.2.2 Velocity Field	193	(2)
8.2.2.3 Molecular Orientation	195	(1)
8.2.2.4 Residence Time	196	(2)
8.3 Flow Birefringence Measurements	198	(7)
8.3.1 Principles of Optical Rheometry	198	(3)
8.3.2 Fast Polarization Modulation Technique	201	(4)
8.4 Experimental Results	205	(31)
8.4.1 Experimental Conditions	205	(1)
8.4.2 Material Characterization	205	(1)
8.4.2.1 Chemicals	205	(1)
8.4.2.2 Intrinsic Viscosity of PS Solutions	205	(1)
8.4.2.3 Molecular Coil Dimensions	206	(1)
8.4.2.4 End-to-End Chain Relaxation Time	207	(1)
8.4.2.5 Thermodynamic Quality of the Solvents	208	(1)
8.4.2.6 Molecular Weight Distribution	208	(1)
8.4.3 Conversion of Retardation into Birefringence	209	(1)
8.4.3.1 Inhomogeneity of the Birefringence Zone	210	(1)
8.4.3.2 Numerical Inverse Abel Transform	211	(1)
8.4.3.3 Transmission of Polarized Light at Oblique Incidence	212	(3)
8.4.4 Extraneous Birefringence	215	(5)
8.4.5 Probe Beam Dimensions	220	(3)
8.4.6 Birefringence in Dilute Decalin Solutions	223	(1)
8.4.6.1 Optical Micrography	223	(1)
8.4.6.2 Qeantitative Retardation Measurements	223	(4)
8.4.6.3 Radial Birefringence Distribution	227	(2)
8.4.6.4 Axial Birefringence Distribution	229	(1)
8.4.7 Birefringence in Dilute 1-Methyl-Naphthalene Solutions	230	(4)
8.4.8 Flow-Induced Degradation	234	(2)
8.5 Discussion	236	(10)
8.5.1 Affine Deformation Model	236	(4)
8.5.1.1 Determination of (Delta)n(max)	240	(2)
8.5.1.2 Determination of Beta	242	(2)
8.5.2 Other Polymer Dynamics Models Relevant to Abrupt Contraction Flow	244	(2)
8.6 Prospects and Conclusions	246	(2)
8.6.1 Final Words	248	(1)
Appendix A	248	(2)
Appendix B	250	(2)
Appendix C	252	(1)
List of Symbols and Abbreviations	253	(1)
References	254	(5)
9 The Hydrodynamic of a DNA Molecule in a Flow Field	259	(24)
R.G. Larson
T.T. Perkins
D.E. Smith
S. Chu
9.1 Introduction	259	(2)
9.2 Calculation of the Drag Coefficient	261	(2)
9.3 Stretching Experiments with Longer DNA Molecules	263	(3)
9.4 Hydrodynamic Model for DNA	266	(3)
9.4.1 Elastic Spring Force	267	(1)
9.4.2 Drag Force	267	(2)
9.4.3 Brownian Motion	269	(1)
9.5 Simulation Results	269	(5)
9.6 Discussion	274	(2)
Appendix: Model Validation	276	(4)
List of Symbols and Abbreviations	280	(1)
References	281	(2)
10 Single Polymers in Elongational Flows: Dynamic, Steady-State, and Population-Averaged Properties	283	(52)
T.T. Perkins
D.E. Smith
S. Chu
10.1 Introduction	283	(1)
10.2 Previous Experimental Work	284	(2)
10.3 Experimental Technique	286	(16)
10.3.1 Direct Imaging of Single Molecules as a Measurement Technique	286	(2)
10.3.2 DNA as a Model Polymer	288	(1)
10.3.3 Microscope and Imaging	289	(1)
10.3.4 Flow Cell Design	290	(2)
10.3.5 Flow Cell Manufacture	292	(1)
10.3.6 Pumps and Plumbing	293	(2)
10.3.7 Flow Cell Calibration	295	(3)
10.3.8 Solution	298	(2)
10.3.9 Staining and DNA Preparation	300	(1)
10.3.10 Measurement of Tan(1)	300	(2)
10.4 Experimental Results	302	(27)
10.4.1 Data Reduction	302	(2)
10.4.2 Extension vs Residency Time	304	(5)
10.4.3 Average and Steady-State Properties; Direct Observation of the Coil-Stretch Transition	309	(2)
10.4.4 Steady-State Measurements Fit by the Dumbbell Model	311	(1)
10.4.5 Conformational Dependent Dynamics at Highest Strain Rates	312	(2)
10.4.6 Master Curves	314	(3)
10.4.7 Affine Deformation	317	(2)
10.4.8 Dynamic Data, Intrinsic Viscosity and the Dumbbell Model	319	(2)
10.4.9 Comparison to Previous Experimental Work	321	(1)
10.4.9.1 Birefringence	321	(1)
10.4.9.2 Light Scattering	322	(2)
10.4.9.3 Stagnation Point Flow Fracture	324	(1)
10.4.9.4 Rheology	324	(1)
10.4.9.5 Filament Stretching	325	(1)
10.4.9.6 Mean Field Theories	326	(1)
10.4.9.7 Comments on Dumbbell Model	327	(1)
10.4.9.8 Proposed Conformations	328	(1)
10.4.10 Limitation of Applicability	329	(1)
10.5 Summary	329	(1)
10.6 Future Prospects	330	(1)
List of Symbols and Abbreviations	331	(1)
References	332	(3)
11 The Rheology of Polymer Solutions in Porous Media	335
A.J. Muller
A.E. Saez
11.1 Introduction	335	(2)
11.2 Fluid Dynamics Characterization of Porous Media Flows	337	(3)
11.3 Non-Newtonian Behavior in the Flow of Polymer Solutions Through Porous Media	340	(34)
11.3.1 Review of Mechanisms Proposed to Explain Extension Thickening	343	(5)
11.3.2 The Nature of Extension Thickening in Porous Media Flows	348	(18)
11.3.3 Effect of Porous Media Microstructure	366	(5)
11.3.4 Shear Thinning	371	(3)
11.4 Flow-Induced Degradation	374	(6)
11.5 Porous Media Flows of Polymer Blends and Cross-Linked Polymers in Solution	380	(9)
11.5.1 Flow of Cross-Linked Polymer Solutions Through Porous Media	380	(3)
11.5.2 Flow of Solutions of Polymer Blends Through Porous Media	383	(6)
11.6 Concluding Remarks	389	(1)
List of Symbols and Abbreviations	390	(1)
References	391