The theory of polymer dynamics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford [u.a.]
Clarendon Press
2007
|
| Ausgabe: | Reprint. |
| Schriftenreihe: | The international series of monographs on physics
73 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016567650&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XIII, 391 S. graph. Darst. |
| ISBN: | 9780198520337 |
Internformat
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| 245 | 1 | 0 | |a The theory of polymer dynamics |c M. Doi and S. F. Edwards |
| 250 | |a Reprint. | ||
| 264 | 1 | |a Oxford [u.a.] |b Clarendon Press |c 2007 | |
| 300 | |a XIII, 391 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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Datensatz im Suchindex
| _version_ | 1819330142839767040 |
|---|---|
| adam_text | CONTENTS
1
INTRODUCTION
1
2
STATIC
PROPERTIES OF POLYMERS
8
2.1
The random flight model
8
2.1.1
The freely jointed model
8
2.1.2
General random flight models
9
2.1.3
Distribution of the end-to-end vector
11
2.2
The Gaussian chain
14
2.3
Chain conformation under an external field
17
2.3.1
The Green function
17
2.3.2
Example
—
chain confined in a box
19
2.4
Scattering function
21
2.5
Excluded volume effect
24
2.5.1
Introduction
24
2.5.2
Model of the excluded volume chain
25
2.5.3
Theoretical approaches
27
2.6
Scaling
32
Appendix
2.1
Gaussian distribution functions
35
Appendix
2.
II Differential equation for G(R,
R
;
N)
40
Appendix
2.
Ill Perturbation calculation for the excluded
volume effect
41
References
43
3
BROWNIAN MOTION
46
3.1
Introduction
46
3.2
The Smoluchowski equation
46
3.2.1
Diffusion of particles
46
3.2.2
Diffusion in phase space
50
3.2.3
Irreversibility of the Smoluchowski equation
51
3.3
The
Langevin
equation
52
3.4
Time correlation function and response function
55
3.4.1
Time correlation function
55
3.4.2
Microscopic expression for the time correlation function
56
3.4.3
Fluctuation dissipation theorem
58
3.5
Brownian motion in a harmonic potential
62
3.5.1
Smoluchowski equation
62
3.5.2
Lange vin
equation
63
3.6
Interacting Brownian particles
65
¿ii
CONTENTS
3.7
Microscopic
basis of viscoelasticity
69
3.7.1
Introduction
69
3.7.2
Constitutive equation
70
3.7.3
The Smoluchowski equation for a system in macroscopic
flow
71
3.7.4
Expression for the stress tensor
72
3.7.5
Principle of virtual work
75
3.8
Systems with rigid constraints
76
3.8.1
Introduction
76
3.8.2
The method of generalized coordinates
77
3.8.3
The method of Lagrangian multipliers
79
3.8.4
Elastic stress and viscous stress
80
3.8.5
Variational formulation
82
Appendix
3.1
Eigenfunctions of the Smoluchowski equation
83
Appendix 3.II Relationship between the
Langevin
equation
and the Smoluchowski equation
85
Appendix 3.III The
Oseen
tensor
88
References
89
DYNAMICS OF FLEXIBLE POLYMERS IN DILUTE
SOLUTION
91
4.1
The Rouse model
91
4.1.1
Dynamics of a polymer with localized interaction
91
4.1.2
Normal coordinates
94
4.2
The Zimm model
97
4.2.1
Zimm model in
θ
conditions
97
4.2.2
Zimm model in good solvent
100
4.3
Dynamical scaling
103
4.4
Dynamic light scattering
105
4.5
Viscoelasticity
108
4.5.1
Introduction
108
4.5.2
Microscopic expression for the stress tensor
110
4.5.3
Calculation of the intrinsic viscosity
112
4.5.4
Intrinsic moduli
114
4.6
Variational bounds for the transport coefficients
116
4.6.1
Introduction
116
4.6.2
Bounds for the intrinsic viscosity
116
4.6.3
Bounds for the diffusion constant
119
4.7
Birefringence
121
4.7.1
Birefringence of polymer solutions
121
4.7.2
Molecular expression for birefringence
122
4.7.3
Row birefringence
127
CONTENTS ix
Appendix
4.1 The Verdier-Stockmayer
model
129
Appendix
4.
II Derivation of the normal modes
131
Appendix
4.
Ill Dynamic structure factor
132
Appendix
4.
IV Polarizability tensor of a Gaussian chain
135
References
137
5
MANY CHAIN SYSTEMS
140
5.1
Semidilute and concentrated solutions
140
5.2
Gaussian approximation for concentration fluctuations
143
5.2.1
Collective coordinates
143
5.2.2
Pair correlation function
147
5.2.3
Osmotic pressure
148
5.2.4
Size of a single chain
149
5.3
Scaling theory
—
statics
152
5.4
Topological interaction in polymer dynamics
156
5.4.1
Entanglement effect
156
5.4.2
Rigorous approach
158
5.4.3
The tube model
160
5.5
Dynamics of concentration fluctuations
161
5.5.1
Kinetic equation
161
5.5.2
Dynamic light scattering
164
5.5.3
Form birefringence
166
5.6
Scaling theory
—
dynamics
169
5.7
Effective medium theory
172
5.7.1
Failure of the scalar field description
172
5.7.2
Hydrodynamic screening
173
5.7.3
Effective medium theory
174
5.7.4
Example
176
Appendix
5.1
Transformation to collective coordinates
180
Appendix
5.
II Osmotic pressure in concentrated solution
182
Appendix
5.
Ill Perturbation calculation of
(Jł2)
183
References
184
6
DYNAMICS OF A POLYMER IN A FIXED NETWORK
188
6.1
Tube model
188
6.1.1
Tube model in crosslinked systems
188
6.1.2
Tube model in uncrosslinked systems
189
6.2
Reptation
191
CONTENTS
IQl
6.2.1 Primitive
chain
jľí
6.2.2 Simple
application
1УЈ
6.3
Reptation
dynamics 19J
6.3.1
Stochastic equation for
reptation
dynamics
197
6.3.2
Segmental
motion
1*8
6.3.3
Correlation function of the tangent vectors
201
6.3.4
Dynamic structure factor
202
6.3.5
General time correlation function
204
6.4
Contour length fluctuation
205
6.4.1
Statistical distribution of the contour length
205
6.4.2
Dynamics of the contour length fluctuation
206
6.4.3
Effect of the contour length fluctuation on
reptation
210
6.4.4
Other small-scale fluctuations and their effects on the
segmental
motion
211
6.4.5
Branched polymers
213
Appendix
6.1
Entropy-of
a polymęr_jn_a
tube
215
References
216
MOLECULAR THEORY FOR THE VISCOELASTICITY
OF POLYMERIC LIQUIDS
218
7.1
Tube model in concentrated solutions and melts
218
7.2
Microscopic expression for the stress tensor
220
7.2.1
Stress in polymeric liquids
220
7.2.2
Stress optical law
221
7.3
Linear viscoelasticity
222
7.3.1
Background of phenomenological theory
222
7.3.2
Calculation by Rouse model
225
7.3.3
Calculation by
reptation
model
226
7.3.4
Comparison with experiments
228
7.3.5
Tube diameter in melts
230
7.3.6
Semidilute and concentrated solutions
234
7.4
Other relaxation modes
236
7.4.1
Discrepancy between the theory and experiments
236
7.4.2
Contour length fluctuation and tube reorganization
238
7.5
Stress relaxation after large step strain
239
7.5.1
Experimental setup
239
7.5.2
Calculation by Rouse model
241
7.5.3
Calculation by
reptation
model
243
7.5.4
Comparison with experimental results
249
7.5.5
Discussion
254
7.6
Nonlinear viscoelasticity
255
7.6.1
Phenomena of nonlinear viscoelasticity
255
7.6.2
Deformation gradient tensor
258
7.6.3
Constitutive equation derived from Rouse model
259
7.7
Approximate constitutive equation for
reptation
model
260
CONTENTS
xi
7.7.1 Deformation
of the primitive chain
261
7.7.2
Independent alignment approximation
262
7.7.3
Constitutive equation
264
7.7.4
Comparison with experiments
266
7.7.5
Discussion
268
7.8
Stress relaxation after double step strain
270
7.9
Rigorous constitutive equation for
reptation
model
274
7.10
Further applications
278
7.10.1
Branched polymers
278
7.10.2
Molecular weight distribution
281
7.10.3
Future problems
282
References
283
8
DILUTE SOLUTIONS OF RIGID RODLIKE
POLYMERS
289
8.1
Rodlike polymers
289
8.2
Rotational diffusion
290
8.2.1
Rotational Brownian motion
290
8.2.2
Hydrodynamics of rotational motion
291
8.2.3
Smoluchowski
equation for rotational motion
294
8.3
Translational diffusion
295
8.3.1
Hydrodynamics of translational motion
295
8.3.2
Smoluchowski
equation including both translational and
rotational diffusion
296
8.4
Brownian motion in the equilibrium state
298
8.4.1
Vector correlation function (u(t)
· «(0)) 298
8.4.2
Translational diffusion
299
8.4.3
Dynamic light scattering
300
8.5
Orientation by an electric field
303
8.5.1
The effect of an electric field
303
8.5.2
Dielectric relaxation
304
8.5.3
Electric birefringence
306
8.6
Linear viscoelasticity
307
8.6.1
Expression for the stress tensor
307
8.6.2
Calculation for weak velocity gradient
310
8.7
Nonlinear viscoelasticity
312
8.7.1
Decoupling approximation
312
8.7.2
Elongational flow
313
8.7.3
Shear flow
314
8.8
Effect of flexibility
316
Appendix
8.1
Derivation of the Smoluchowski equation by the
Kirkwood theory
318
References
322
xü CONTENTS
9 SEMIDILUTE SOLUTIONS
OF
RIGID RODLIKE
POLYMERS 324
9.1 Semidilute
and concentrated solutions of rodlike
polymers
324
9.2
Entanglement effect in rodlike polymers
326
9.2.1
Tube model
326
9.2.2
Translational diffusion
327
9.2.3
Rotational diffusion
327
9.2.4
Estimation of the tube radius and the rotational
diffusion constant
328
9.3
Brownian motion in equilibrium
330
9.3.1
Time correlation functions
330
9.3.2
Dynamic light scattering
332
9.4
Orientation by external fields
333
9.4.1
Linear regime
333
9.4.2
Nonlinear regime
—
tube dilation
334
9.4.3
Experimental study of the rotational diffusion constant
335
9.5
Viscoelasticity
336
5.
S.I Expression for the stress tensor
336
9.5.2
Linear viscoelasticity
337
9.5.3
Nonlinear viscoelasticity
339
9.6
Short time-scale motion
340
9.6.1
Chopstick model
340
9.6.2
Local equilibrium approximation
342
9.6.3
Example
343
Appendix
9.1
Tube dilation by orientational ordering
345
Appendix 9.II Effective potential for the tube
346
References
348
10
CONCENTRATED SOLUTIONS OF RIGID RODLIKE
POLYMERS
350
10.1
Introduction
350
10.2
The phase transition of rigid rods
351
10.2.1
Free energy for a given orientational distribution
function
351
10.2.2
Equilibrium distribution
354
10.3
The kinetic equation
358
10.3.1
Dynamical mean field theory
358
10.3.2
Relaxation of the order parameter
360
10.4
Pretransitional phenomena
362
10.4.1
Introduction
362
10.4.2
Magnetic birefringence
363
CONTENTS xiii
10.4.3 Viscoelasticity 365
10.5 Linear
viscosity in the
nematic
phase
366
10.5.1
Introduction
366
10.5.2
Perturbation scheme
369
10.5.3
Approximate calculation
370
10.5.4
Example—shear flow
372
10.5.5
The Leslie coefficients
374
10.6
Future problems
376
10.6.1
Nonlinear viscoelasticity in nematics
376
10.6.2
Spatial inhomogeneity and domain structure
376
10.6.3
Thermotropic liquid crystals
378
References
379
SUBJECT INDEX
381
AUTHOR INDEX
386
|
| any_adam_object | 1 |
| author | Doi, Masao 1948- Edwards, Sam F. |
| author_GND | (DE-588)1052280056 |
| author_facet | Doi, Masao 1948- Edwards, Sam F. |
| author_role | aut aut |
| author_sort | Doi, Masao 1948- |
| author_variant | m d md s f e sf sfe |
| building | Verbundindex |
| bvnumber | BV023384612 |
| classification_rvk | UV 1000 UV 4100 ZM 5000 |
| classification_tum | PHY 624f |
| ctrlnum | (OCoLC)611758436 (DE-599)HBZHT015490084 |
| dewey-full | 547.7045 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 547 - Organic chemistry |
| dewey-raw | 547.7045 |
| dewey-search | 547.7045 |
| dewey-sort | 3547.7045 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik Werkstoffwissenschaften / Fertigungstechnik |
| edition | Reprint. |
| format | Book |
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| id | DE-604.BV023384612 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:15:04Z |
| institution | BVB |
| isbn | 9780198520337 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016567650 |
| oclc_num | 611758436 |
| open_access_boolean | |
| owner | DE-703 DE-1051 DE-83 DE-92 DE-355 DE-BY-UBR DE-29 DE-573 |
| owner_facet | DE-703 DE-1051 DE-83 DE-92 DE-355 DE-BY-UBR DE-29 DE-573 |
| physical | XIII, 391 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Clarendon Press |
| record_format | marc |
| series | The international series of monographs on physics |
| series2 | The international series of monographs on physics |
| spellingShingle | Doi, Masao 1948- Edwards, Sam F. The theory of polymer dynamics The international series of monographs on physics Polimeros (Quimica) larpcal Polymères Polymérisation Polymers and polymerization Polymerlösung (DE-588)4175242-9 gnd Polymere (DE-588)4046699-1 gnd Dynamisches Verhalten (DE-588)4140475-0 gnd Viskoelastizität (DE-588)4063621-5 gnd Polymere Flüssigkeit (DE-588)4175229-6 gnd Physik (DE-588)4045956-1 gnd Dynamik (DE-588)4013384-9 gnd |
| subject_GND | (DE-588)4175242-9 (DE-588)4046699-1 (DE-588)4140475-0 (DE-588)4063621-5 (DE-588)4175229-6 (DE-588)4045956-1 (DE-588)4013384-9 |
| title | The theory of polymer dynamics |
| title_auth | The theory of polymer dynamics |
| title_exact_search | The theory of polymer dynamics |
| title_full | The theory of polymer dynamics M. Doi and S. F. Edwards |
| title_fullStr | The theory of polymer dynamics M. Doi and S. F. Edwards |
| title_full_unstemmed | The theory of polymer dynamics M. Doi and S. F. Edwards |
| title_short | The theory of polymer dynamics |
| title_sort | the theory of polymer dynamics |
| topic | Polimeros (Quimica) larpcal Polymères Polymérisation Polymers and polymerization Polymerlösung (DE-588)4175242-9 gnd Polymere (DE-588)4046699-1 gnd Dynamisches Verhalten (DE-588)4140475-0 gnd Viskoelastizität (DE-588)4063621-5 gnd Polymere Flüssigkeit (DE-588)4175229-6 gnd Physik (DE-588)4045956-1 gnd Dynamik (DE-588)4013384-9 gnd |
| topic_facet | Polimeros (Quimica) Polymères Polymérisation Polymers and polymerization Polymerlösung Polymere Dynamisches Verhalten Viskoelastizität Polymere Flüssigkeit Physik Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016567650&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000106406 |
| work_keys_str_mv | AT doimasao thetheoryofpolymerdynamics AT edwardssamf thetheoryofpolymerdynamics |