Excluded volume effects in polymer solutions as explained by the renormalization group:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 541 - 547 |
| Physical Description: | XVII, 554 S. graph. Darst. |
| ISBN: | 3540655131 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV012337807 | ||
| 003 | DE-604 | ||
| 005 | 20000817 | ||
| 007 | t | ||
| 008 | 981222s1999 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 955356474 |2 DE-101 | |
| 020 | |a 3540655131 |9 3-540-65513-1 | ||
| 035 | |a (OCoLC)40682575 | ||
| 035 | |a (DE-599)BVBBV012337807 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-703 |a DE-634 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QD381.9.S65 | |
| 082 | 0 | |a 547/.70454 |2 21 | |
| 084 | |a UV 2800 |0 (DE-625)146885: |2 rvk | ||
| 100 | 1 | |a Schäfer, Lothar |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Excluded volume effects in polymer solutions as explained by the renormalization group |c Lothar Schäfer |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XVII, 554 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 541 - 547 | ||
| 650 | 7 | |a Groupe de renormalisation |2 ram | |
| 650 | 7 | |a Polymères - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Solutions de polymère |2 ram | |
| 650 | 4 | |a Polymer solutions | |
| 650 | 0 | 7 | |a Polymerlösung |0 (DE-588)4175242-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistische Thermodynamik |0 (DE-588)4126251-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Renormierungsgruppe |0 (DE-588)4177773-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Polymerlösung |0 (DE-588)4175242-9 |D s |
| 689 | 0 | 1 | |a Statistische Thermodynamik |0 (DE-588)4126251-7 |D s |
| 689 | 0 | 2 | |a Renormierungsgruppe |0 (DE-588)4177773-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008366535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008366535 | ||
Record in the Search Index
| _version_ | 1804126965483962368 |
|---|---|
| adam_text | LOTHAR SCHAEFER EXCIUDED VOLUME EFFECTS IN POLYMER SOLUTIONS AS EXPLAINED
BY THE RENORMALIZATION GROUP WITH 117 FIGURES QM SPRINGER TABLE OF
CONTENTS 1. POWER LAWS, SCALING, UNIVERSAL CROSSOVER * A SURVEY OF
PHENOMENOLOGY 1 PART I. BASIC THEORETICAL TECHNIQUES 2. FROM A
MICROSCOPIC DESCRIPTION TO SIMPLE MODELS 13 2.1 THE MODEL 13 2.2
RELATION TO A REALISTIC MICROSCOPIC DESCRIPTION 16 3. THE NONINTERACTING
GAUSSIAN CHAIN 21 3.1 ENDPOINT CORRELATIONS 21 3.2 DENSITY CORRELATIONS
23 3.3 CALCULATION OF THE GREENSFUNCTION 26 A 3 APPENDIX 29 A 3.1 THE
5-FUNCTION 29 A 3.2 THE FOURIER TRANSFORM 30 A 3.3 THE GAUSSIAN INTEGRAL
AND INTEGRATION IN D-DIMENSIONAL SPACE 31 4. THE CLUSTER EXPANSION 33
4.1 FIRST ORDER CORRECTIONS TO ENDPOINT CORRELATIONS 35 4.2 THE FEYNMAN
RULES 38 4.3 CUMULANTS 45 4.4 AN EXAMPLE: THE SECOND VIRIAL COEFFICIENT
47 A 4 APPENDIX 49 A 4.1 FORMAL EXPRESSION FOR THE SECOND VIRIAL
COEFFICIENT 49 A 4.2 EVALUATION OF SOME SEGMENT SUMMATIONS 49 5. GRAND
CANONICAL DESCRIPTION OF SOLUTIONS AT FINITE CONCENTRATION 53 5.1 BASIC
FEATURES OF THE GRAND CANONICAL FORMALISM 56 5.1.1 DEFMITIONS 56 5.1.2
LINKED CLUSTER THEOREM AND THERMODYNAMIC LIMIT 57 X TABLE OF CONTENTS
5.1.3 DIAGRAMMATICS 58 5.1.4 CORRELATION FUNCTIONS 62 5.2 LOOP
EXPANSION, VERTEX IRREDUCIBLE GRAPHS AND SCREENED INTERACTION 65 5.2.1
THE NOTION OF LOOPS 65 5.2.2 VERTEX REDUCIBILITY 66 5.2.3 THE SCREENED
INTERACTION 69 5.3 POLYDISPERSITY: NOTATION AND BASIC FEATURES 72 5.4
TREE APPROXIMATION, SCREENING, AND A ONE LOOP EXAMPLE ... 76 5.4.1 TREE
APPROXIMATION 76 5.4.2 ANALYSIS OF THE SCREENED INTERACTION 78 5.4.3 ONE
LOOP CORRECTION TO THE FLORY-HUGGINS EQUATION 79 A 5 APPENDIX 82 A 5.1
LINKED CLUSTER THEOREM 82 A 5.2 VERTEX REDUCIBILITY FOR THE GRAND
POTENTIAL 84 A 5.3 DERIVATION OF THE LOOP EXPANSION BY FORMAL
MANIPULATION OF FUNCTIONAL INTEGRALS ... 86 A 5.3.1 THE METHOD OF
AUXILIARY FIELDS 86 A 5.3.2 FORMAL DERIVATION OF THE LOOP EXPANSION 89 A
5.4 A SHORT DISCUSSION OF THE CANONICAL FORMALISM ... 91 A 5.4.1
MANIPULATION OF CLOSED FORM EXPRESSIONS 91 A 5.4.2 DIAGRAMMATIC
PERTURBATION THEORY 94 A 5.4.3 COMPARISON TO THE GRAND CANONICAL
FORMALISM ... 96 NOTES 97 6. BREAKDOWN OF THE EXPANSIONS IN THE EXCLUDED
VOLUME REGION 99 7*. CONTINUOUS CHAIN MODEL AND NAIVE TWO PARAMETER
THEORY 103 7.1 CONTINUOUS CHAIN LIMIT AND THE EDWARDS MODEL 105 7.2
EXISTENCE OF THE CONTINUOUS CHAIN LIMIT 109 A 7 APPENDIX 118 A 7.1
FORMAL RELATION TO FIELD THEORY 118 NOTES 122 PART IL RENORMALIZATION
GROUP AND SCALING 8. THE RENORMALIZATION GROUP: FUNDAMENTAL ASPECTS ....
127 8.1 BASIC IDEAS 128 8.2 EXPLICIT CONSTRUCTION OF AN RG MAPPING 133
8.3 FLOW EQUATIONS AND CROSSOVER 136 NOTES 141 TABLE OF CONTENTS XI 9.
SCALING THEORY 143 9.1 CONCENTRATION BLOBS AND SCREENING 144 9.2 THE
TEMPERATURE-CONCENTRATION DIAGRAM 149 9.3 SOME WORDS OF CAUTION 151
NOTES 154 10*. MORE COMPLICATED INTERACTIONS AND THE GENERAL STRUCTURE
OF THE RENORMALIZATION GROUP 155 10.1 HIGHER INTERACTIONS AND ADDITIVE
RENORMALIZATION 157 10.2 THE GENERAL STRUCTURE OF THE RENORMALIZATION
GROUP 162 10.2.1 DILATATIONS 162 10.2.2 COMPARISON TO OUR PREVIOUS
RESULTS 165 10.2.3 THE GENERAL STRUCTURE OF THE RENORMALIZATION GROUP
167 10.3 FIELD THEORETIC RENORMALIZATION GROUP AND UNIVERSALITY . . .
174 NOTES 176 PART III. FIELD THEORETIC FORMULATION OF THE THEORY 11.
RENORMALIZED PERTURBATION THEORY AND FIELD-THEORETIC RENORMALIZATION
GROUP 179 11.1 ILLUSTRATION OF RENORMALIZED PERTURBATION THEORY 182 11.2
THE THEOREM OF RENORMALIZABILITY 185 11.3 RENORMALIZATION GROUP
EQUATIONS 187 11.4 GLOBAL FORM OF THE RG FLOW 189 11.5 THE NONUNIVERSAL
PARAMETERS AND TWO PARAMETER THEORY . . 192 11.6 SCALING LAWS IN THE
DILUTE LIMIT 194 11.7 RENORMALIZATION AND SCALING AT FINITE OVERLAP 197
11.7.1 RENORMALIZED EXPRESSIONS 197 11.7.2 SCALING LAWS 199 11.8 A
COMMENT ON THE UNIVERSALITY OF THE SCALING FUNCTIONS AND THE STATUS OF
OUR RESULTS 200 A 11 APPENDIX 202 A 11.1 REMARKS ON RENORMALIZABILITY
202 NOTES 205 12. DIMENSIONAL REGULARIZATION AND MINIMAL SUBTRACTION . .
207 12.1 EQUIVALENCE OF DISCRETE OR CONTINUOUS CHAINS 209 12.1.1
RENORMALIZABILITY OF THE CONTINUOUS CHAIN MODEL . 209 12.1.2 EXISTENCE
OF THE EQUIVALENT CONTINUOUS CHAIN MODEL 210 12.2 MINIMAL SUBTRACTION
212 12.3 FINAL FORM OF RENORMALIZED PERTURBATION THEORY 214 12.3.1
GENERAL PROCEDURE 214 XII TABLE OF CONTENTS 12.3.2 A SIMPLE EXAMPLE 216
12.4 PERTURBATION THEORY IN THREE DIMENSIONS VS E-EXPANSION . . 218
12.4.1 VIRTUES AND DISADVANTAGES OF THE E-EXPANSION ... 218 12.4.2
DIRECT EVALUATION IN THREE DIMENSIONS 221 NOTES 223 13. QUANTITATIVE
FORM OF THE RENORMALIZATION GROUP MAPPING 225 13.1 THE RENORMALIZATION
GROUP MAPPING IN THREE DIMENSIONS . . 226 13.2 CHOICE OF THE
RENORMALIZED LENGTH SCALE 228 13.2.1 QUALITATIVE CONSIDERATIONS 228
13.2.2 DETERMINATION OF THE THEORETICAL PARAMETERS .... 230 13.2.3 SOME
WARNING 232 13.3 THE RG MAPPING IN DIFFERENT REGIONS OF PARAMETER SPACE
. . 233 13.3.1 GENERAL FORM (D = 3) 233 13.3.2 SPECIAL LIMITS 234 13.3.3
CROSSOVER DIAGRAM FOR / 1 236 13.3.4 THE STRONG COUPLING REGION 238 A
13 APPENDIX 240 A 13.1 ELIMINATION OF 6*(1) 240 A 13.2 PARAMETER
DEPENDENCE OF RENORMALIZED PERTURBATION THEORY 241 A 13.2.1 CHOICE OF Q
0 241 A 13.2.2 CHOICE OF C 0 242 NOTES 243 14. THE RENORMALIZED TREE
APPROXIMATION: A SIMPLE ILLUSTRATION OF THE THEORY 245 14.1 DENSITY
AUTOCORRELATIONS 246 14.1.1 GENERAL EXPRESSION 246 14.1.2 RADIUS OF
GYRATION 246 14.1.3 MOMENTUM DEPENDENCE 249 14.2 OSMOTIC PRESSURE 251
14.3 DENSITY CUMULANT 253 14.4 SUMMARY OF IMPORTANT ASPECTS 256 PART IV.
ONE LOOP APPROXIMATION: DETAILED RESULTS AND COMPARISON TO EXPERIMENT
15. DILUTE LIMIT: DENSITY CORRELATIONS, VIRIAL COEFFICIENTS, AND
INTERPENETRATION RATIO 259 15.1 THE RADIUS OF GYRATION 261 15.1.1
GENERAL EXPRESSIONS 261 15.1.2 EXCLUDED VOLUME LIMIT 262 TABLE OF
CONTENTS XIII 15.1.3 WEAK COUPLING REGION 264 15.1.4 STRONG COUPLING
REGION 265 15.2 MOMENTUM DEPENDENCE OF THE SCATTERING FORM FACTOR ....
267 15.2.1 GENERAL EXPRESSIONS 267 15.2.2 THE REGION OF SMALL MOMENTA
268 15.2.3 THE LIMIT OF LARGE MOMENTA 270 15.2.4 CROSSOVER IN MOMENTUM
AND EXCLUDED VOLUME STRENGTH 272 15.3 THE SECOND VIRIAL COEFFICIENTS 274
15.3.1 GENERAL RESULTS 274 15.3.2 EXCLUDED VOLUME LIMIT 276 15.3.3 WEAK
COUPLING REGION 276 15.3.4 STRONG COUPLING REGION 277 15.4 THE
INTERPENETRATION RATIO 278 15.4.1 EXCLUDED VOLUME LIMIT 279 15.4.2
CROSSOVER BEHAVIOR 280 15.4.3 SOME COMMENT ON THE CHOICE OF TIQ 280 15.5
COMPARISON TO EXPERIMENT 281 15.5.1 SOME REMARKS ON DATA ANALYSIS 281
15.5.2 A? A 2 .,TP: 0-SOLVENTS 284 15.5.3 A*,A 2 ,-IL : GOOD SOLVENTS
288 15.5.4 MOMENTUM DEPENDENCE OF THE SCATTERING FUNCTION 291 A 15
APPENDIX 293 A 15.1 FORMAL RESULTS ON POLYDISPERSITY DEPENDENCE .... 293
A 15.2 ONE-LOOP CALCULATION OF 1^ (Q) 295 A 15.3 FURTHER PERTURBATIVE
RESULTS 299 A 15.3.1 SMALL MOMENTUM BEHAVIOR OF JD (Q, N) 299 A 15.3.2
LARGE MOMENTUM BEHAVIOR OF JD (Q, N) 300 A 15.3.3 THE SECOND VIRIAL
COEFFICIENTS 300 NOTES 302 16. DILUTE LIMIT: DETAILS ON THE INTERNAL
STRUCTURE OF ISOLATED COILS 305 16.1 ENDPOINT CORRELATIONS 311 16.1.1
END-TO-END DISTANCE 311 16.1.2 THE SHAPE OF THE END-TO-END CORRELATION
FUNCTION . 313 16.2 INTERNAL CORRELATIONS 316 16.2.1 GENERAL RESULTS 316
16.2.2 EXCESS SWELLING OF INTERNAL CORRELATIONS 318 16.2.3 TEMPERATURE
BLOBS AND HYDRODYNAMIC RADIUS . . . 320 16.3 DENSITY DISTRIBUTIONS 323
16.3.1 DISTRIBUTION FUNCTION FOR SPECIFIC SEGMENTS 323 16.3.2
DISTRIBUTION FUNCTION OF THE TOTAL SEGMENT DENSITY 324 16.3.3 THE SHAPE
OF A POLYMER COIL 325 16.4 THE SECOND VIRIAL COEFFICIENT OF TWO COILS OF
DIFFERENT SIZE . . 328 TABLE OF CONTENTS 16.4.1 ANALYTICAL RESULTS 328
16.4.2 THE EXPERIMENTAL SITUATION 330 16.5 THE FREE ENERGY EXCESS OF
INTERPENETRATING COILS 331 A 16 APPENDIX 334 A 16.1 E-EXPANSION RESULTS
334 A 16.1.1 INTERNAL CORRELATIONS 334 A 16.1.2 DENSITY DISTRIBUTIONS
335 A 16.2 AN EXPRESSION FOR THE HYDRODYNAMIC RADIUS 336 A 16.3 FREE
ENERGY, INTERNAL ENERGY, OR ENTROPY OF A SINGLE CHAIN 337 A 16.4 THE
FLORY ARGUMENT 340 NOTES 342 THERMODYNAMIC QUANTITIES FOR FINITE OVERLAP
345 17.1 THERMODYNAMIC SCALING FUNCTION AND GENERAL THERMODYNAMIC
RELATIONS 346 17.2 GENERAL ONE-LOOP RESULTS 350 17.3 THE VIRIAL
EXPANSION 352 17.3.1 DEFINITIONS 352 17.3.2 GENERAL FEATURES OF THE
VIRIAL EXPANSION 353 17.3.3 THE THIRD VIRIAL COEFFICIENT 354 17.4
EVALUATION FOR LARGER OVERLAP 356 17.4.1 THE SEMIDILUTE LIMIT 356 17.4.2
THE CONCENTRATION CROSSOVER 359 17.5 COMPARISON TO EXPERIMENT 361 17.5.1
THE DILUTE RAENGE 361 17.5.2 THE CONCENTRATION CROSSOVER 368 A 17
APPENDIX 371 A 17.1 PERTURBATIVE CALCULATION OF V 371 A 17.2 ONE-LOOP
RESULTS FOR V OR I D , C () 372 A 17.2.1 THE THERMODYNAMIC SCALING
FUNCTION 372 A 17.2.2 ONE-LOOP RESULTS FOR J C (0) 374 A 17.3 CHEMICAL
POTENTIAL AND FREE ENERGY EXCESS 375 A 17.3.1 THE CHEMICAL POTENTIAL 375
A 17.3.2 FREE ENERGY EXCESS AND RELATED QUANTITIES 376 A 17.4 RELATION
TO THE FLORY-HUGGINS PARAMETER 376 NOTES 378 DENSITY AUTOCORRELATIONS AT
FINITE OVERLAP 381 18.1 DEFINITION AND SCALING PROPERTIES OF 7 18.2 THE
RADIUS OF GYRATION . 384 18.3 MOMENTUM DEPENDENCE 386 18.3.1 THE
SEMIDILUTE LIMIT 387 18.3.2 GENERAL OVERLAP 389 TABLE OF CONTENTS XV
18.4 THE EXPERIMENTAL SITUATION 391 A 18 APPENDIX 395 A 18.1 FUELL
ONE-LOOP RESULTS 395 A 18.2 EVALUATION AND PARAMETERIZATION IN THREE
DIMENSIONS 398 A 18.2.1 RADIUS OF GYRATION 398 A 18.2.2 MOMENTUM
DEPENDENCE 399 NOTES 400 19. THE DENSITY CUMULANT 401 19.1 FORMAL
EXPRESSIONS AND GENERAL ONE-LOOP RESULTS 404 19.1.1 DEFINITIONS AND
SCALING LAWS 404 19.1.2 LOOP EXPANSION 405 19.2 THE DENSITY CORRELATION
LENGTH 407 19.2.1 EXCLUDED VOLUME LIMIT 407 19.2.2 CROSSOVER OUTSIDE THE
EXCLUDED VOLUME LIMIT .... 410 19.3 SCREENING LENGTH 411 19.4 MOMENTUM
DEPENDENCE 414 19.4.1 RANGE QR G = 0(1) 414 19.4.2 RANGE QI D = 0(1) 415
19.4.3 RANGE Q^D ~3 1, AND OVERALL BEHAVIOR OF J C 417 19.4.4
CORRECTIONS TO THE LEADING G~-^ -BEHAVIOR 418 19.5 THE EXPERIMENTAL
SITUATION 420 19.5.1 HEURISTIC METHODS OF DATA ANALYSIS 420 19.5.2
COMPARISON BETWEEN THEORY AND EXPERIMENT .... 423 A 19 APPENDIX 425 A
19.1 FUELL ONE-LOOP RESULTS 425 A 19.2 EVALUATIONS AND PARAMETERIZATIONS
IN THREE DIMENSIONS 428 A 19.2.1 DENSITY CORRELATION LENGTH 428 A 19.2.2
M C (Q, W) FO R D = 3 429 NOTES 430 20. SUMMARIZING OVERVIEW 431 PART V.
SPECIAL TOPICS 21. THE -REGION 437 21.1 RENORMALIZATION PROPERTIES 441
21.1.1 MODEL AND ADDITIVE RENORMALIZATION 441 21.1.2 MULTIPLICATIVE
RENORMALIZATION AT T = 0 445 21.1.3 RENORMALIZATION IN THE 0-REGION 446
21.2 RENORMALIZATION GROUP MAPPING AND SCALING LAWS 447 21.2.1 GENERAL
FORM OF THE RG MAPPING 447 TABLE OF CONTENTS 21.2.2 LOW ORDER
APPROXIMATION OF THE RG-MAPPING . . . 451 21.2.3 GENERAL SCALING LAWS
452 21.3 THE DILUTE LIMIT 453 21.3.1 THE RG-MAPPING 453 21.3.2 SINGLE
CHAIN RADII 455 21.3.3 THE VIRIAL COEFFICIENTS 456 21.3.4 BINARY
CONTACTS WITHIN A SINGLE CHAIN 457 21.3.5 CRITICAL DISCUSSION 459 21.4
THE EXPERIMENTAL SITUATION: DILUTE LIMIT 460 21.5 FINITE OVERLAP 462
21.5.1 RG-MAPPING 463 21.5.2 THE OSMOTIC PRESSURE 465 21.5.3 DENSITY
CORRELATIONS 466 21.6 THE EXPERIMENTAL SITUATION: CONCENTRATION
CROSSOVER 467 A 21 APPENDIX 467 A 21.1 RESULTS OF UNRENORMALIZED
PERTURBATION THEORY .. 467 A 21.1.1 SINGLE CHAIN PARTITION FUNCTION 467
A 21.1.2 TWO-CHAIN CUMULANT 469 A 21.1.3 THREE-CHAIN CUMULANT 470 A
21.1.4 END-TO-END DISTANCE OF A SINGLE CHAIN 472 A 21.2 MULTIPLICATIVE
RENORMALIZATION 473 A 21.2.1 RENORMALIZATION FACTORS OF THE MINIMAL
SUBTRACTION SCHEME 473 A 21.2.2 RENORMALIZED SCALING FUNCTIONS 475 A
21.3 CONSTRUCTION OF THE LOOP EXPANSION 476 NOTES 477 MULTICOMPONENT
SOLUTIONS 479 22.1 UNRENORMALIZED THEORY 483 22.1.1 THE MODEL 483 22.1.2
LOOP EXPANSION 484 22.1.3 TREE APPROXIMATION 487 22.2 RENORMALIZATION
AND SCALING BEHAVIOR 489 22.2.1 GENERAL CONSIDERATIONS 489 22.2.2 RG
FLOW AND FIXED POINTS 491 22.2.3 SCALING LAWS 497 22.2.4 CHOICE OF THE
RENORMALIZED LENGTH SCALE 500 22.3 TREE APPROXIMATION 502 22.3.1 THE
DENSITY CUMULANT: GENERAL CONSIDERATIONS . . . 503 22.3.2 THE DENSITY
CUMULANT: SPECIAL CASES 508 22.3.3 AUTOCORRELATIONS 516 22.3.4 THE
OSMOTIC PRESSURE 517 22.4 THE SPINODAL 520 22.4.1 BASIC EXPRESSIONS 520
22.4.2 FIXED POINT BEHAVIOR 521 TABLE OF CONTENTS XVII 22.5 THE
EXPERIMENTAL SITUATION 526 A 22 APPENDIX 531 A 22.1 FLOW OF THE TERNARY
COUPLING 531 A 22.2 EVALUATION AT AN UNSYMNIETRIC FIXED POINT 533 A 22.3
THE SPINODAL IN FIXED POINT REGION S 535 A 22.3.1 GENERAL SCALING
BEHAVIOR 535 A 22.3.2 TREE APPROXIMATION 537 NOTES 539 REFERENCES 541
FREQUENTLY OCCURRING SYMBOLS 54 9 SUBJECT INDEX 553
|
| any_adam_object | 1 |
| author | Schäfer, Lothar |
| author_facet | Schäfer, Lothar |
| author_role | aut |
| author_sort | Schäfer, Lothar |
| author_variant | l s ls |
| building | Verbundindex |
| bvnumber | BV012337807 |
| callnumber-first | Q - Science |
| callnumber-label | QD381 |
| callnumber-raw | QD381.9.S65 |
| callnumber-search | QD381.9.S65 |
| callnumber-sort | QD 3381.9 S65 |
| callnumber-subject | QD - Chemistry |
| classification_rvk | UV 2800 |
| ctrlnum | (OCoLC)40682575 (DE-599)BVBBV012337807 |
| dewey-full | 547/.70454 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 547 - Organic chemistry |
| dewey-raw | 547/.70454 |
| dewey-search | 547/.70454 |
| dewey-sort | 3547 570454 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01827nam a2200469 c 4500</leader><controlfield tag="001">BV012337807</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20000817 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">981222s1999 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">955356474</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540655131</subfield><subfield code="9">3-540-65513-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)40682575</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012337807</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QD381.9.S65</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">547/.70454</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UV 2800</subfield><subfield code="0">(DE-625)146885:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Schäfer, Lothar</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Excluded volume effects in polymer solutions as explained by the renormalization group</subfield><subfield code="c">Lothar Schäfer</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 554 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 541 - 547</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Groupe de renormalisation</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Polymères - Modèles mathématiques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Solutions de polymère</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polymer solutions</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Polymerlösung</subfield><subfield code="0">(DE-588)4175242-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Statistische Thermodynamik</subfield><subfield code="0">(DE-588)4126251-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Renormierungsgruppe</subfield><subfield code="0">(DE-588)4177773-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Polymerlösung</subfield><subfield code="0">(DE-588)4175242-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Statistische Thermodynamik</subfield><subfield code="0">(DE-588)4126251-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Renormierungsgruppe</subfield><subfield code="0">(DE-588)4177773-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008366535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008366535</subfield></datafield></record></collection> |
| id | DE-604.BV012337807 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:25:50Z |
| institution | BVB |
| isbn | 3540655131 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008366535 |
| oclc_num | 40682575 |
| open_access_boolean | |
| owner | DE-703 DE-634 DE-11 DE-188 |
| owner_facet | DE-703 DE-634 DE-11 DE-188 |
| physical | XVII, 554 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| spelling | Schäfer, Lothar Verfasser aut Excluded volume effects in polymer solutions as explained by the renormalization group Lothar Schäfer Berlin [u.a.] Springer 1999 XVII, 554 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 541 - 547 Groupe de renormalisation ram Polymères - Modèles mathématiques ram Solutions de polymère ram Polymer solutions Polymerlösung (DE-588)4175242-9 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Renormierungsgruppe (DE-588)4177773-6 gnd rswk-swf Polymerlösung (DE-588)4175242-9 s Statistische Thermodynamik (DE-588)4126251-7 s Renormierungsgruppe (DE-588)4177773-6 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008366535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schäfer, Lothar Excluded volume effects in polymer solutions as explained by the renormalization group Groupe de renormalisation ram Polymères - Modèles mathématiques ram Solutions de polymère ram Polymer solutions Polymerlösung (DE-588)4175242-9 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Renormierungsgruppe (DE-588)4177773-6 gnd |
| subject_GND | (DE-588)4175242-9 (DE-588)4126251-7 (DE-588)4177773-6 |
| title | Excluded volume effects in polymer solutions as explained by the renormalization group |
| title_auth | Excluded volume effects in polymer solutions as explained by the renormalization group |
| title_exact_search | Excluded volume effects in polymer solutions as explained by the renormalization group |
| title_full | Excluded volume effects in polymer solutions as explained by the renormalization group Lothar Schäfer |
| title_fullStr | Excluded volume effects in polymer solutions as explained by the renormalization group Lothar Schäfer |
| title_full_unstemmed | Excluded volume effects in polymer solutions as explained by the renormalization group Lothar Schäfer |
| title_short | Excluded volume effects in polymer solutions as explained by the renormalization group |
| title_sort | excluded volume effects in polymer solutions as explained by the renormalization group |
| topic | Groupe de renormalisation ram Polymères - Modèles mathématiques ram Solutions de polymère ram Polymer solutions Polymerlösung (DE-588)4175242-9 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Renormierungsgruppe (DE-588)4177773-6 gnd |
| topic_facet | Groupe de renormalisation Polymères - Modèles mathématiques Solutions de polymère Polymer solutions Polymerlösung Statistische Thermodynamik Renormierungsgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008366535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schaferlothar excludedvolumeeffectsinpolymersolutionsasexplainedbytherenormalizationgroup |