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

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6.7 Comparison of the different criteria for λ and their effect on the elongational viscosity fortheMarko-Siggiaforcelaw. ..............................112 6.8 Calculation of the elongational viscosity as a function of the number of beads for constant Wi and α using the first two terms in the asymptotic expansion for the FENE force law with λ =1.................................116 6.9 Comparison of the different criteria for λ and their effect on the elongational viscosity fortheFENEforcelaw. ..................................117 6.10 Coefficient of the Pe −1/2 term, C, as a function of the number of beads with and withoutHI. .........................................121 7.1 Sketchofthesystemwithastepchangeinelectrophoreticvelocity...........124 7.2 Contours of constant stretch for the toy model as a function of the two parameters DeandWi. .........................................126 7.3 This shows a comparison of Brownian dynamics simulations in the long chain limit tothetoymodel.......................................127 7.4 Results from simulations with increasing finite extensibility. . . . . . . . . . . . . . . 128 7.5 Approach of the nonlinear bead-spring chains to full extension. . . . . . . . . . . . . 129 A.1 Relative error in extension between the real infinitely long WLC (numerical data fromBouchiatetal.)andapproximateformulas. ....................141
List of Tables 3.1 Summaryofdimensionlessparameters .......................... 24 3.2 Table of properties for models of unstained λ-phageDNA................ 31 3.3 Table of properties for models of λ-phage DNA stained with YOYO at 8 bp:1 dye molecule. .......................................... 32 3.4 Table of properties for models of λ-phage DNA stained with YOYO at 4 bp:1 dye molecule. .......................................... 32
Page 1: Systematic development of coarse-gr
Page 4 and 5: a number of people I met at MIT tha
Page 6 and 7: 3.3 DimensionlessParameters........
Page 9 and 10: List of Figures 2.1 Sketch of the s
Page 11: 4.18 Relative error in the second m
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
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48 3.10. Summary P0 1 (1/ν) gives
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CHAPTER 4 New Spring Force Laws Rec
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4.1. Justification 53 fixed fixed e
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4.2. Application to Freely Jointed
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4.3. Application to Worm-like Chain
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4.4. Summary and Outlook 85 freely
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CHAPTER 5 Low Weissenberg Number Re
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5.1. Retarded-motion Expansion Coef
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5.3. Influence of HI and EV 99 the
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CHAPTER 6 High Weissenberg Number R
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6.1. Longest Relaxation Time 103 ti
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6.1. Longest Relaxation Time 105 τ
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6.1. Longest Relaxation Time 107 τ
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6.2. Elongational Viscosity 109 ˆ
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6.2. Elongational Viscosity 111 ove
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6.2. Elongational Viscosity 113 whe
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6.2. Elongational Viscosity 115 6.2
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6.2. Elongational Viscosity 117 ˆ
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6.2. Elongational Viscosity 119 pol
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6.3. Influence of Hydrodynamic Inte
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CHAPTER 7 Nonhomogeneous Flow In th
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7.1. Dumbbell Model 125 consider (
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7.2. Long Chain Limit 127 〈Xf〉/
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7.3. Finite Extensibility 129 (L
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CHAPTER 8 Conclusions and Outlook I
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8.4. Nonhomogeneous Flow 133 presen
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Appendix A Appendices A.1 Fluctuati
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A.2. Retarded-motion Expansion Coef
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A.3. Example of the Behavior of the
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A.5. Calculation of the Response of
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A.5. Calculation of the Response of
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146 Bibliography [10] P. J. Flory,
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148 Bibliography [57] J. S. Hur, E.
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