Systematic development of coarse-grained polymer models Patrick ...

More documents

Recommendations

Info

3.3 DimensionlessParameters................................. 24 3.4 Force-extension Results . . . ............................... 25 3.5 PhaseSpaceVisualization................................. 27 3.6 EffectivePersistenceLength................................ 29 3.7 Fluctuations......................................... 33 3.8 LimitingBehavior ..................................... 35 3.9 FENEandFraenkelForceLaws.............................. 41 3.10Summary .......................................... 48 Chapter 4 NewSpring Force Laws 51 4.1 Justification......................................... 52 4.2 Application to Freely Jointed Chain ........................... 55 4.2.1 Equal rod lengths . ................................ 55 4.2.2 Unequal rod lengths ............................... 59 4.2.3 Approximatespringforcelaw .......................... 62 4.3 ApplicationtoWorm-likeChain.............................. 71 4.3.1 Applicationtodumbbellmodel.......................... 71 4.3.2 Exactgeneralizedmodel............................. 72 4.3.3 Useofbendingpotentials ............................ 73 4.3.4 Real continuous WLC . . . ........................... 76 4.3.5 AccuracyofMarko-Siggiaspring ........................ 77 4.3.6 New approximate force law without bending potential . . . . . . . . . . . . . 80 4.4 SummaryandOutlook................................... 84 Chapter 5 LowWeissenberg Number Response 87 5.1 Retarded-motionExpansionCoefficients......................... 87 5.1.1 FENEandFraenkelforcelaws ......................... 95 5.2 OldVersusNewForceLaws................................ 98 5.3 Influence of HI and EV . . . ............................... 99 5.4 Summary .......................................... 99 Chapter 6 High Weissenberg Number Response 101 6.1 LongestRelaxationTime .................................101 6.2 ElongationalViscosity ...................................108 6.2.1 Models of the worm-like chain . . . .......................108 6.2.2 Models of the freely jointed chain . .......................115 6.3 Influence of Hydrodynamic Interactions . . .......................120 6.4 SummaryandOutlook...................................122 Chapter 7 Nonhomogeneous Flow 123 7.1 DumbbellModel ......................................124 7.2 LongChainLimit......................................127 7.3 Finite Extensibility . . . . . . ...............................128 7.4 Summary ..........................................130
Chapter 8 Conclusions and Outlook 131 8.1 Force-extension Behavior . . ...............................131 8.2 NewForceLaws ......................................132 8.3 RheologicalResponse....................................132 8.4 NonhomogeneousFlow...................................133 8.5 Future Work . . ......................................134 Appendix A Appendices 135 A.1 Fluctuations in Force-Extension Behavior . .......................135 A.2 Retarded-motionExpansionCoefficients.........................136 A.3 ExampleoftheBehavioroftheRandomWalkSpringModel .............139 A.4 AlternativetoExactWorm-likeChain ..........................140 A.5 CalculationoftheResponseoftheToyModel......................141 Bibliography 145
Page 1: Systematic development of coarse-gr
Page 4 and 5: a number of people I met at MIT tha
Page 9 and 10: List of Figures 2.1 Sketch of the s
Page 11 and 12: 4.18 Relative error in the second m
Page 13: List of Tables 3.1 Summaryofdimensi
Page 16 and 17: 2 Abstract for other interactions b
Page 18 and 19: 4 1.2. General Polymer Physics prop
Page 20 and 21: 6 1.3. Progression of Coarse-graine
Page 22 and 23: 8 1.3. Progression of Coarse-graine
Page 24 and 25: 10 1.3. Progression of Coarse-grain
Page 26 and 27: 12 1.5. Importance of New Models So
Page 28 and 29: 14 2.2. Brownian Dynamics the effec
Page 30 and 31: 16 2.2. Brownian Dynamics where now
Page 32 and 33: 18 2.2. Brownian Dynamics Iteration
Page 34 and 35: 20 2.2. Brownian Dynamics use of a
Page 36 and 37: 22 3.2. Decoupled Springs fixed sol
Page 38 and 39: 24 3.3. Dimensionless Parameters pa
Page 40 and 41: 26 3.4. Force-extension Results 〈
Page 42 and 43: 28 3.5. Phase Space Visualization
Page 44 and 45: 30 3.6. Effective Persistence Lengt
Page 46 and 47: 32 3.6. Effective Persistence Lengt
Page 48 and 49: 34 3.7. Fluctuations 〈ˆztot〉m
Page 50 and 51: 36 3.8. Limiting Behavior α 1/2 δ
Page 52 and 53: 38 3.8. Limiting Behavior Note that
Page 54 and 55: 40 3.8. Limiting Behavior constant
Page 56 and 57:
42 3.9. FENE and Fraenkel Force Law
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
48 3.10. Summary P0 1 (1/ν) gives
Page 65 and 66:
CHAPTER 4 New Spring Force Laws Rec
Page 67 and 68:
4.1. Justification 53 fixed fixed e
Page 69 and 70:
4.2. Application to Freely Jointed
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
4.3. Application to Worm-like Chain
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
4.4. Summary and Outlook 85 freely
Page 101 and 102:
CHAPTER 5 Low Weissenberg Number Re
Page 103 and 104:
5.1. Retarded-motion Expansion Coef
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
5.3. Influence of HI and EV 99 the
Page 115 and 116:
CHAPTER 6 High Weissenberg Number R
Page 117 and 118:
6.1. Longest Relaxation Time 103 ti
Page 119 and 120:
6.1. Longest Relaxation Time 105 τ
Page 121 and 122:
6.1. Longest Relaxation Time 107 τ
Page 123 and 124:
6.2. Elongational Viscosity 109 ˆ
Page 125 and 126:
6.2. Elongational Viscosity 111 ove
Page 127 and 128:
6.2. Elongational Viscosity 113 whe
Page 129 and 130:
6.2. Elongational Viscosity 115 6.2
Page 131 and 132:
6.2. Elongational Viscosity 117 ˆ
Page 133 and 134:
6.2. Elongational Viscosity 119 pol
Page 135 and 136:
6.3. Influence of Hydrodynamic Inte
Page 137 and 138:
CHAPTER 7 Nonhomogeneous Flow In th
Page 139 and 140:
7.1. Dumbbell Model 125 consider (
Page 141 and 142:
7.2. Long Chain Limit 127 〈Xf〉/
Page 143 and 144:
7.3. Finite Extensibility 129 (L
Page 145 and 146:
CHAPTER 8 Conclusions and Outlook I
Page 147 and 148:
8.4. Nonhomogeneous Flow 133 presen
Page 149 and 150:
Appendix A Appendices A.1 Fluctuati
Page 151 and 152:
A.2. Retarded-motion Expansion Coef
Page 153 and 154:
A.3. Example of the Behavior of the
Page 155 and 156:
A.5. Calculation of the Response of
Page 157:
A.5. Calculation of the Response of
Page 160 and 161:
146 Bibliography [10] P. J. Flory,
Page 162 and 163:
148 Bibliography [57] J. S. Hur, E.
show all

Systematic development of coarse-grained polymer models Patrick ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?