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Polymer Analysis Polymer Theory pp 171–282Cite as

Generalized Gaussian Structures: Models for Polymer Systems with ComplexTopologies

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Part of the book series: Advances in Polymer Science ((POLYMER,volume 182))

Abstract

A fundamental and long-standing problem in polymer physics is to deduce the relationship between the topology of a polymer and its dynamics. Generalized Gaussian structures (GGS), originating from the familiar Rouse model, represent a valuable tool for this purpose. This review summarizes theoretical efforts that have been undertaken in studying the dynamics of polymer systems with complex internal topologies by employing the GGS approach. The dynamic properties of a wide range of polymeric structures (ranging from polymer networks to dendritic and hybrid polymers) are discussed, while emphasizing systems that can be treated analytically (or semi-analytically). These studies provide considerable insight into the problem of relating the structure of a polymer to its dynamics. In many cases the GGS-treatment represents a first step in understanding the dynamics of polymers, and it may serve as a reference point for the development of more realistic models.

An erratum to this chapter is available at http://dx.doi.org/10.1007/12_045.

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References

  1. Rouse PE (1953) J Chem Phys 21:1272

    Article  CAS  Google Scholar 

  2. Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon, Oxford

    Google Scholar 

  3. Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, New York

    Google Scholar 

  4. de Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, Ithaca, NY

    Google Scholar 

  5. Zimm BH (1956) J Chem Phys 24:269

    Article  CAS  Google Scholar 

  6. Sommer J-U, Blumen A (1995) J Phys A–Math Gen 28:6669

    Article  CAS  Google Scholar 

  7. Schiessel H (1998) Phys Rev E 57:5775

    Article  CAS  Google Scholar 

  8. Friedrich Ch, Schiessel H, Blumen A (1999). In: Siginer DA, DeKee D, Chhabra RP (eds) Advances in the flow and rheology of non-Newtonian fluids. Elsevier, Amsterdam, p 429

    Chapter  Google Scholar 

  9. Schiessel H, Friedrich Ch, Blumen A (2000). In: Hilfer R (ed) Applications of fractional calculus in physics. World Scientific, Singapore, p 331

    Chapter  Google Scholar 

  10. Eichinger BE, Martin JE (1978) J Chem Phys 69:4595

    Article  CAS  Google Scholar 

  11. Graessley WW (1980) Macromolecules 13:372

    Article  CAS  Google Scholar 

  12. Kloczkowski A, Mark JE, Frisch HL (1990) Macromolecules 23:3481

    Article  CAS  Google Scholar 

  13. Biswas P, Kant R, Blumen A (2001) J Chem Phys 114:2430

    Article  CAS  Google Scholar 

  14. Hansen DR, Shen M (1975) Macromolecules 8:343

    Article  CAS  Google Scholar 

  15. Hall WF, De Wames RE (1975) Macromolecules 8:349

    Article  CAS  Google Scholar 

  16. Stockmayer WH, Kennedy JW (1975) Macromolecules 8:351

    Article  CAS  Google Scholar 

  17. Wang FW, DiMarzio EA (1975) Macromolecules 8:356

    Article  CAS  Google Scholar 

  18. Wang FW (1975) Macromolecules 8:364

    Article  CAS  Google Scholar 

  19. Man VF, Schrag JL, Lodge TP (1991) Macromolecules 24:3666

    Article  CAS  Google Scholar 

  20. Denneman AIM, Jongschaap RJJ (1996) J Rheol 40:589

    Article  CAS  Google Scholar 

  21. Satmarel C, Gurtovenko AA, Blumen A (2003) Macromolecules 36:486

    Article  CAS  Google Scholar 

  22. Yamakawa H (1971) Modern theory of polymer solutions. Harper and Row, New York

    Google Scholar 

  23. Peterlin A (1967) J Polym Sci Pol Phys 5:179

    Article  CAS  Google Scholar 

  24. Gotlib YY, Gurtovenko AA (1997) Macromol Theor Simul 6:523

    Article  CAS  Google Scholar 

  25. Gurtovenko AA, Gotlib YY (2000) Macromolecules 33:6578

    Article  CAS  Google Scholar 

  26. Tschoegl NW (1989) The phenomenological theory of linear viscoelastic behavior. Springer, Berlin Heidelberg New York

    Book  Google Scholar 

  27. Williams G (1972) Chem Rev 72:55

    Article  CAS  Google Scholar 

  28. Stockmayer WH, Baur ME (1964) J Am Chem Soc 86:3485

    Article  CAS  Google Scholar 

  29. Stockmayer WH (1967) Pure Appl Chem 15:539

    Article  Google Scholar 

  30. Gotlib YY, Gurtovenko AA (1996) Macromol Theory Simul 5:969

    Article  CAS  Google Scholar 

  31. Gurtovenko AA, Blumen A (2002) Macromolecules 35:3288

    Article  CAS  Google Scholar 

  32. Blumen A, Gurtovenko AA, Jespersen S (2002) J Non-Cryst Solids 305:71

    Article  CAS  Google Scholar 

  33. Biswas P, Kant R, Blumen A (2000) Macromol Theor Simul 9:56

    Article  CAS  Google Scholar 

  34. Perkins TT, Smith DE, Larson RG, Chu S (1995) Science 268:83

    Article  CAS  PubMed  Google Scholar 

  35. Wirtz D (1995) Phys Rev Lett 75:2436

    Article  CAS  PubMed  Google Scholar 

  36. Quake SR, Babcock H, Chu S (1997) Nature 388:151

    Article  CAS  PubMed  Google Scholar 

  37. Amblard F, Maggs AC, Yurke B, Pergellis AN, Leibler S (1996) Phys Rev Lett 77:4470

    Article  CAS  PubMed  Google Scholar 

  38. Kargin VA, Slonimskii GL (1948) Dokl Akad Nauk SSSR 62:239

    CAS  Google Scholar 

  39. Bueche F (1954) J Chem Phys 22:603

    Article  CAS  Google Scholar 

  40. Gotlib YY, Darinsky AA, Svetlov YE (1986) Physical kinetics of macromolecules. Khimiya, Leningrad

    Google Scholar 

  41. Grosberg AY, Khokhlov AR (1994) Statistical physics of macromolecules. AIP, New York

    Google Scholar 

  42. Edwards SF, Freed KF (1974) J Chem Phys 61:1189

    Article  CAS  Google Scholar 

  43. Freed KF, Edwards SF (1974) J Chem Phys 61:3626

    Article  CAS  Google Scholar 

  44. de Gennes PG (1976) Macromolecules 9:594

    Article  Google Scholar 

  45. Ahlrichs P, Everaers R, Dünweg B (2001) Phys Rev E 64:040501(R)

    Article  CAS  Google Scholar 

  46. Richter D, Binder K, Ewen B, Stühn (1984) J Phys Chem 88:6618

    Article  CAS  Google Scholar 

  47. Ewen B, Richter D (1997) Adv Polym Sci 134:1

    Article  CAS  Google Scholar 

  48. Kremer K, Grest GS (1990) J Chem Phys 92:5057

    Article  CAS  Google Scholar 

  49. Paul W, Smith GD, Yoon DY (1997) Macromolecules 30:7772

    Article  CAS  Google Scholar 

  50. Mondello M, Grest GS (1997) J Chem Phys 106:9327

    Article  CAS  Google Scholar 

  51. Harmandaris V, Mavrantzas VG, Theodorou DN (1998) Macromolecules 31:7934

    Article  CAS  Google Scholar 

  52. Padding JT, Briels WJ (2001) J Chem Phys 114:8685

    Article  CAS  Google Scholar 

  53. Lyulin AV, Balabaev NK, Michels MAJ (2002) Macromolecules 35:9595

    Article  CAS  Google Scholar 

  54. Paul W, Smith GD, Yoon DY, Farago B, Rathgeber S, Zirkel A, Willner L, Richter D (1998) Phys Rev Lett 80:2346

    Article  CAS  Google Scholar 

  55. McLeish TCB (2002) Adv Phys 51:1379

    Article  CAS  Google Scholar 

  56. Rubinstein M, Colby RH (1988) J Chem Phys 89:5291

    Article  CAS  Google Scholar 

  57. Paul W, Binder K, Heermann DW, Kremer K (1991) J Chem Phys 95:7726

    Article  CAS  Google Scholar 

  58. Pütz M, Kremer K, Grest GS (2000) Europhys Lett 49:735

    Article  Google Scholar 

  59. Harmandaris VA, Mavrantzas VG, Theodorou DN, Köger M, Ramirez J, Öttinger HC, Vlassopoulos D (2003) Macromolecules 36:1376

    Article  CAS  Google Scholar 

  60. Gotlib YY, Volkenshtein MV (1953) Dokl Akad Nauk SSSR 89:821

    CAS  Google Scholar 

  61. Mooney M (1959) J Polym Sci 34:599

    Article  Google Scholar 

  62. Gotlib YY (1981) Pure Appl Chem 53:1531

    Article  CAS  Google Scholar 

  63. Gotlib Y, Golovachev G (1994) J Non-Cryst Solids 172:850

    Article  Google Scholar 

  64. Denneman AIM, Jongschaap RJJ, Mellema J (1998) J Eng Math 34:75

    Article  Google Scholar 

  65. Denneman AIM, Jongschaap RJJ, Mellema J (1999) J Rheol 43:327

    Article  CAS  Google Scholar 

  66. Gurtovenko AA, Gotlib YY (1998) Macromolecules 31:5756

    Article  CAS  Google Scholar 

  67. Ronka G, Allegra G (1975) J Chem Phys 63:4104

    Article  Google Scholar 

  68. Gotlib YY, Gurtovenko AA (2000) Macromol Theor Simul 9:407

    Article  CAS  Google Scholar 

  69. Gurtovenko AA, Gotlib YY (2000) Macromol Theor Simul 9:416

    Article  CAS  Google Scholar 

  70. Chompff AJ, Duiser JA (1966) J Chem Phys 45:1505

    Article  CAS  Google Scholar 

  71. Gotlib YY, Salikhov KM (1963) Akust Zh (Acoustic J) 9:301

    Google Scholar 

  72. Ham JS (1957) J Chem Phys 26:625

    Article  CAS  Google Scholar 

  73. Gurtovenko AA, Blumen A (2001) J Chem Phys 115:4924

    Article  CAS  Google Scholar 

  74. Gurtovenko AA, Markelov DA, Gotlib YY, Blumen A (2003) J Chem Phys 119:7579

    Article  CAS  Google Scholar 

  75. Kittel C (1986) Introduction to solid state physics, 6th edn. Wiley, New York

    Google Scholar 

  76. Ashcroft NW, Mermin ND (1981) Solid state physics. Sanders College, Philadelphia, PA

    Google Scholar 

  77. Ziman JM (1972) Principles of the theory of solids, 2nd edn. Cambridge University Press, Cambridge

    Book  Google Scholar 

  78. Gurtovenko AA, Gotlib YY, Blumen A (2002) Macromolecules 35:7481

    Article  CAS  Google Scholar 

  79. Scher H, Lax M (1973) Phys Rev B 7:4491

    Article  CAS  Google Scholar 

  80. Scher H, Lax M (1973) Phys Rev B 7:4502

    Article  CAS  Google Scholar 

  81. Scher H, Montroll EW (1975) Phys Rev B 12:2455

    Article  CAS  Google Scholar 

  82. Shlesinger MF (1984) J Stat Phys 36:639

    Article  Google Scholar 

  83. Zumofen G, Blumen A, Klafter J, Shlesinger MF (1989) J Stat Phys 54:1519

    Article  Google Scholar 

  84. Schiessel H, Oshanin G, Blumen A (1995) J Chem Phys 103:5070

    Article  CAS  Google Scholar 

  85. Blumen A (2001) Philos Mag B 81:1021

    Article  CAS  Google Scholar 

  86. Klafter J, Blumen A, Shlesinger MF (1987) Phys Rev A 35:3081

    Article  CAS  Google Scholar 

  87. Montroll EW, Weiss GH (1965) J Math Phys 6:167

    Article  Google Scholar 

  88. Blumen A, Klafter J, White BS, Zumofen G (1984) Phys Rev Lett 53:1301

    Article  Google Scholar 

  89. Schnörer H, Haarer D, Blumen A (1988) Phys Rev B 38:8097

    Article  Google Scholar 

  90. Blumen A, Zumofen G, Klafter (1989) Phys Rev A 40:3964

    Article  CAS  Google Scholar 

  91. Blumen A, Schnörer H (1990) Angew Chem 102:158

    Article  CAS  Google Scholar 

  92. Blumen A, Schnörer H (1990) Angew Chem Int Edit 29:113

    Article  Google Scholar 

  93. Hilfer R (ed) (2000) Applications of fractional calculus in physics. World Scientific, Singapore

    Google Scholar 

  94. Metzler R, Klafter J (2000) Phys Rep 339:1

    Article  CAS  Google Scholar 

  95. Sokolov IM, Klafter J, Blumen A (2002) Physics Today 55:48

    Article  CAS  Google Scholar 

  96. Blizard RB (1951) J Appl Phys 22:730

    Article  CAS  Google Scholar 

  97. Schiessel H, Blumen A (1993) J Phys A–Math Gen 26:5057

    Article  Google Scholar 

  98. Heymans N, Bauwens J-C (1994) Rheol Acta 33:210

    Article  CAS  Google Scholar 

  99. Schiessel H, Metzler R, Blumen A, Nonnenmacher TF (1995) J Phys A–Math Gen 28:6567

    Article  CAS  Google Scholar 

  100. Schiessel H, Blumen A (1995) Macromolecules 28:4013

    Article  CAS  Google Scholar 

  101. Chambon F, Winter HH (1987) J Rheol 31:683

    Article  CAS  Google Scholar 

  102. Winter HH, Morganelli P, Chambon F (1988) Macromolecules 21:532

    Article  CAS  Google Scholar 

  103. Scanlan JC, Winter HH (1991) Macromolecules 24:47

    Article  CAS  Google Scholar 

  104. Blumen A, Jurjiu A (2002) J Chem Phys 116:2636

    Article  CAS  Google Scholar 

  105. Cosenza MG, Kapral R (1992) Phys Rev A 46:1850

    Article  CAS  PubMed  Google Scholar 

  106. Jurjiu A, Friedrich Ch, Blumen A (2002) Chem Phys 284:221

    Article  CAS  Google Scholar 

  107. Cates ME (1984) Phys Rev Lett 53:926

    Article  Google Scholar 

  108. Cates ME (1985) J Phys (Paris) 46:1059

    Article  CAS  Google Scholar 

  109. Sommer J-U, Vilgis TA, Heinrich G (1994) J Chem Phys 100:9181

    Article  Google Scholar 

  110. Marconi UMB, Petri A (1997) J Phys A–Math Gen 30:1069

    Article  CAS  Google Scholar 

  111. Vilgis TA, Stapper M (1998) Eur Phys J B 2:69

    Article  CAS  Google Scholar 

  112. Zilman AG, Granek R (1998) Phys Rev E 58:R2725

    Article  CAS  Google Scholar 

  113. Licinio P (2001) Physica A 294:51

    Article  CAS  Google Scholar 

  114. Mandelbrot BB (1982) The fractal geometry of nature. W.H. Freeman and Co., San Francisco, CA

    Google Scholar 

  115. Dhar D (1977) J Math Phys 18:577

    Article  Google Scholar 

  116. Jurjiu A, Koslowski Th, Blumen A (2003) J Chem Phys 118:2398

    Article  CAS  Google Scholar 

  117. Blumen A, Jurjiu A, Koslowski Th (2003) Macromol Symp 191:141

    Article  CAS  Google Scholar 

  118. Brotzman RW, Eichinger BE (1981) Macromolecules 14:1445

    Article  CAS  Google Scholar 

  119. Neuburger NA, Eichinger BE (1988) Macromolecules 21:3060

    Article  CAS  Google Scholar 

  120. Zhao Y, Eichinger BE (1992) Macromolecules 25:6988

    Article  CAS  Google Scholar 

  121. Gottlieb M, Gaylord RJ (1984) Macromolecules 17:2024

    Article  CAS  Google Scholar 

  122. McKenna GB, Flynn KM, Chen YH (1989) Macromolecules 22:4507

    Article  CAS  Google Scholar 

  123. Crissman JM, McKenna GB (1992) Polym Mater Sci Eng 67:487

    CAS  Google Scholar 

  124. McKenna GB, Crissman JM (1993) Polym Mater Sci Eng 68:280

    CAS  Google Scholar 

  125. Bastide J, Leibler L, Prost J (1990) Macromolecules 23:1821

    Article  CAS  Google Scholar 

  126. Mendes E, Lindner P, Buzier M, Boué F, Bastide J (1991) Phys Rev Lett 66:1595

    Article  CAS  PubMed  Google Scholar 

  127. Martin JE, Eichinger BE (1978) J Chem Phys 69:4588

    Article  CAS  Google Scholar 

  128. Martin JE, Eichinger BE (1980) Macromolecules 13:626

    Article  CAS  Google Scholar 

  129. Watts DJ, Strogatz SH (1998) Nature (London) 393:440

    Article  CAS  PubMed  Google Scholar 

  130. Watts DJ (1999) Small worlds: The dynamics of networks between order and randomness. Princeton University Press, Princeton, NJ

    Book  Google Scholar 

  131. Newman MEJ, Watts DJ (1999) Phys Rev E 60:7332

    Article  CAS  Google Scholar 

  132. Barthélémy M, Amaral LAN (1999) Phys Rev Lett 82:3180

    Article  Google Scholar 

  133. Monasson R (1999) Eur Phys J B 12:555

    Article  CAS  Google Scholar 

  134. Newman MEJ, Moore C, Watts DJ (2000) Phys Rev Lett 84:3201

    Article  CAS  PubMed  Google Scholar 

  135. Jespersen S, Sokolov IM, Blumen A (2000) Phys Rev E 62:4405

    Article  CAS  Google Scholar 

  136. Jespersen S, Sokolov IM, Blumen A (2000) J Chem Phys 113:7652

    Article  CAS  Google Scholar 

  137. Vilgis TA, Heinrich G (1994) Phys Rev E 49:2167

    Article  CAS  Google Scholar 

  138. Vilgis TA, Heinrich G (1994) Macromol Theor Simul 3:271

    Article  CAS  Google Scholar 

  139. Deam RT, Edwards SF (1976) Philos T Roy Soc A 280:317

    CAS  Google Scholar 

  140. Vilgis TA (1992) Macromolecules 25:399

    Article  CAS  Google Scholar 

  141. Vilgis TA, Boué F (1988) J Polym Sci Pol Phys 26:2291

    Article  CAS  Google Scholar 

  142. Sommer J-U (1991) J Chem Phys 95:1316

    Article  CAS  Google Scholar 

  143. Glatting G, Winkler RG, Reineker P (1995) Macromolecules 28:5906

    Article  CAS  Google Scholar 

  144. Schultz M, Sommer J-U (1992) J Chem Phys 96:7102

    Article  Google Scholar 

  145. Thirion P, Chasset R (1968) Rev Gen Caout Plast 45:859

    CAS  Google Scholar 

  146. McKenna GB, Gaylord RJ (1988) Polymer 29:2027

    Article  CAS  Google Scholar 

  147. Weiss N, van Vliet T, Silberberg A (1981) J Polym Sci Pol Phys 19:1505

    Article  CAS  Google Scholar 

  148. Wun KL, Prins W (1974) J Polym Sci Pol Phys 12:533

    Article  CAS  Google Scholar 

  149. Hecht AM, Duplessix R, Geissler E (1985) Macromolecules 18:2167

    Article  CAS  Google Scholar 

  150. Lindemann B, Schröder UP, Oppermann W (1997) Macromolecules 30:4073

    Article  CAS  Google Scholar 

  151. Gurtovenko AA, Gotlib YY (2001) J Chem Phys 115:6785

    Article  CAS  Google Scholar 

  152. Friedrich C, Heymann L (1988) J Rheol 32:235

    Article  CAS  Google Scholar 

  153. te Nijenhuis K, Winter HH (1989) Macromolecules 22:411

    Article  Google Scholar 

  154. Izuka A, Winter HH, Hashimoto T (1992) Macromolecules 25:2422

    Article  CAS  Google Scholar 

  155. Alfrey T, Doty P (1945) J Appl Phys 16:700

    Article  CAS  Google Scholar 

  156. Cohen MH, Grest GS (1981) Phys Rev B 24:4091

    Article  CAS  Google Scholar 

  157. Degiorgio V, Bellini T, Piazza R, Mantegazza F, Goldstein RE (1990) Phys Rev Lett 64:1043

    Article  CAS  PubMed  Google Scholar 

  158. Blumen A, Klafter J, Zumofen G (1986) In: Zschokke I (ed) Optical spectroscopy of glasses. Reidel,Dordrecht, p 199

    Chapter  Google Scholar 

  159. Bunde A, Havlin Y, Klafter J, Gräff G, Shehter A (1997) Phys Rev Lett 78:3338

    Article  CAS  Google Scholar 

  160. Gurtovenko AA, Gotlib YY, Kilian H-G (2000) Macromol Theor Simul 9:388

    Article  CAS  Google Scholar 

  161. Broderix K, Löwe H, Müller, Zippelius A (2001) Physica A 302:279

    Article  Google Scholar 

  162. Broderix K, Aspelmeier T, Hartmann AK, Zippelius A (2001) Phys Rev E 64:021404

    Article  CAS  Google Scholar 

  163. Chompff AJ (1970) J Chem Phys 53:1577

    Article  CAS  Google Scholar 

  164. Doi M (1974) Polym J 6:108

    Article  CAS  Google Scholar 

  165. Chompff AJ (1970) J Chem Phys 53:1566

    Article  CAS  Google Scholar 

  166. Ronca G (1980) J Chem Phys 72:48

    Article  CAS  Google Scholar 

  167. Graessley WW (1975) Macromolecules 8:186

    Article  CAS  Google Scholar 

  168. Graessley WW (1975) Macromolecules 8:865

    Article  CAS  Google Scholar 

  169. Kloczkowski A (2002) Polymer 43:1503

    Article  CAS  Google Scholar 

  170. Kloczkowski A, Mark JE, Erman B (1989) Macromolecules 22:1423

    Article  CAS  Google Scholar 

  171. Abramowitz M, Stegun IE (1964) Handbook of mathematical functions. National Bureau of Standards,Washington DC

    Google Scholar 

  172. Tomalia DA, Naylor AM, Goddard WA (1990) Angew Chem Int Edit 29:138

    Article  Google Scholar 

  173. Hawker CJ, Fréchet JMJ (1990) J Am Chem Soc 112:7638

    Article  CAS  Google Scholar 

  174. Fréchet JMJ (1994) Science 263:1710

    Article  PubMed  Google Scholar 

  175. NewKome GR (1996) Advances in dendritic macromolecules. JAI, London

    Book  Google Scholar 

  176. de Gennes PG, Hervet H (1983) J Phys (Paris) 44:L351

    Article  Google Scholar 

  177. Biswas P, Cherayil BJ (1994) J Chem Phys 100:3201

    Article  CAS  Google Scholar 

  178. Boris D, Rubinstein M (1996) Macromolecules 29:7251

    Article  CAS  Google Scholar 

  179. Cai C, Chen ZY (1997) Macromolecules 30:5104

    Article  CAS  Google Scholar 

  180. La Ferla R (1997) J Chem Phys 106:688

    Article  Google Scholar 

  181. Chen ZY, Cai C (1999) Macromolecules 32:5423

    Article  CAS  Google Scholar 

  182. Ganazzoli F, La Ferla R (2000) J Chem Phys 113:9288

    Article  CAS  Google Scholar 

  183. Ganazzoli F, La Ferla R, Terragni G (2000) Macromolecules 33:6611

    Article  CAS  Google Scholar 

  184. Ganazzoli F, La Ferla R, Raffaini G (2001) Macromolecules 34:4222

    Article  CAS  Google Scholar 

  185. Lescanec RL, Muthukumar M (1990) Macromolecules 23:2280

    Article  CAS  Google Scholar 

  186. Mansfield ML, Klushin LI (1992) J Phys Chem 96:3994

    Article  CAS  Google Scholar 

  187. Mansfield ML, Klushin LI (1993) Macromolecules 26:4262

    Article  CAS  Google Scholar 

  188. Murat M, Grest GS (1996) Macromolecules 29:1278

    Article  CAS  Google Scholar 

  189. Chen ZY, Cui SM (1996) Macromolecules 29:7943

    Article  CAS  Google Scholar 

  190. Lyulin AV, Davies GR, Adolf DB (2000) Macromolecules 33:3294

    Article  CAS  Google Scholar 

  191. Lyulin SV, Evers LJ, van der Schoot P, Darinskii AA, Lyulin AA, Michels MAJ (2004) Macromolecules37:3049

    Article  CAS  Google Scholar 

  192. Sheng YJ, Jiang S, Tsao HK (2002) Macromolecules 35:7865

    Article  CAS  Google Scholar 

  193. Ganazzoli F (2002) Macromol Symp 190:55

    Article  CAS  Google Scholar 

  194. Kant R, Biswas P, Blumen A (2000) Macromol Theor Simul 9:608

    Article  CAS  Google Scholar 

  195. McLeish TCB, Milner ST (1999) Adv Polym Sci 143:195

    Article  CAS  Google Scholar 

  196. Gotlib YY, Markelov DA (2002) Polymer Sci A (translated from Vysokomol Soedin, Russia) 44:1341

    Google Scholar 

  197. Satmarel C, Gurtovenko AA, Blumen A (2004) Macromol Theor Simul 13:487

    Article  CAS  Google Scholar 

  198. Yin R, Zhu Y, Tomalia DA, Ibuki H (1998) J Am Chem Soc 120:2678

    Article  CAS  Google Scholar 

  199. Percec V, Ahn CH, Ungar G, Yeardly DJP, Möller M, Sheiko SS (1998) Nature 391:161

    Article  CAS  Google Scholar 

  200. Jahromi S, Coussens B, Meijerink N, Braam AWM (1998) J Am Chem Soc 120:9753

    Article  CAS  Google Scholar 

  201. Jahromi S, Palmen JHM, Steeman PAM (2000) Macromolecules 33:577

    Article  CAS  Google Scholar 

  202. Roovers J (ed) (1999) Branched Polymers I. Adv Polym Sci 142:1

    Google Scholar 

  203. Roovers J (ed) (1999) Branched Polymers II. Adv Polym Sci 143:1

    Google Scholar 

  204. Newkome GR, Morefield CN, Vögtle F (1996) Dendritic macromolecules: concepts, syntheses,perspectives. VCH, Weinheim

    Book  Google Scholar 

  205. Freire JJ (1999) Adv Polym Sci 143:35

    Article  CAS  Google Scholar 

  206. Ganazzoli F, Allegra G (1990) Macromolecules 23:262

    Article  CAS  Google Scholar 

  207. Dondos A, Papanagopoulos D (1997) Polymer 38:6255

    Article  CAS  Google Scholar 

  208. Shida K, Ohno K, Kawazoe Y, Nakamura Y (2004) Polymer 45:1729

    Article  CAS  Google Scholar 

  209. Lyulin AV, Adolf DB, Davies GR (2001) Macromolecules 34:3783

    Article  CAS  Google Scholar 

  210. Blumen A, Jurjiu A, Koslowski Th (2004) Macromol Symp 210:301

    Article  CAS  Google Scholar 

  211. Milner ST, McLeish TCB (1997) Macromolecules 30:2159

    Article  CAS  Google Scholar 

  212. Milner ST, McLeish TCB (1998) Macromolecules 31:7479

    Article  CAS  Google Scholar 

  213. Blackwell RJ, Harlen OG, McLeish TCB (2001) Macromolecules 34:2579

    Article  CAS  Google Scholar 

  214. Bishko G, McLeish TCB, Harlen OG, Larson RG (1997) Phys Rev Lett 79:2352

    Article  CAS  Google Scholar 

  215. McLeish TCB, Larson RG (1998) J Rheol 42:81

    Article  CAS  Google Scholar 

  216. von Ferber Ch, Blumen A (2002) J Chem Phys 116:8616

    Article  CAS  Google Scholar 

  217. Kim Y, Harris AB (1985) Phys Rev B 31:7393

    Article  CAS  Google Scholar 

  218. Rodgers GJ, Bray AJ (1988) Phys Rev B 37:3557

    Article  CAS  Google Scholar 

  219. Jasch F, von Ferber Ch, Blumen A (2003) Phys Rev E 68:051106

    Article  CAS  Google Scholar 

  220. Grimmet G (1989) Percolation. Springer, Berlin Heidelberg New York

    Book  Google Scholar 

  221. Fisher ME, Essam JW (1961) J Math Phys 2:609

    Article  Google Scholar 

  222. Ben-Avraham D, Havlin S (2000) Diffusion and reactions in fractals and disordered systems. Cambridge University Press, Cambridge, UK

    Book  Google Scholar 

  223. Mezard M, Parisi G, Virasoro MA (1986) Spin glass theory and beyond. World Scientific, Singapore

    Book  Google Scholar 

  224. Schulz M, Reineker P, Möller M (1995) J Chem Phys 103:10701

    Article  CAS  Google Scholar 

  225. Burioni R, Cassi D, Blumen A (2002) Chem Phys 282:409

    Article  CAS  Google Scholar 

  226. Vicsek T (1989) Fractal growth phenomena. World Scientific, Singapore

    Book  Google Scholar 

  227. Jayanthi CS, Wu SY, Cocks J (1992) Phys Rev Lett 69:1955

    Article  CAS  PubMed  Google Scholar 

  228. Jayanthi CS, Wu SY (1993) Phys Rev B 48:10188

    Article  CAS  Google Scholar 

  229. Jayanthi CS, Wu SY (1993) Phys Rev B 48:10199

    Article  CAS  Google Scholar 

  230. Jayanthi CS, Wu SY (1994) Phys Rev B 50:897

    Article  CAS  Google Scholar 

  231. Blumen A, Jurjiu A, Koslowski T, von Ferber Ch (2003) Phys Rev E 67:061103

    Article  CAS  Google Scholar 

  232. Blumen A, von Ferber Ch, Jurjiu A, Koslowski T (2004) Macromolecules 37:638

    Article  CAS  Google Scholar 

  233. Koslowski T, Jurjiu A, Blumen A (2004) J Phys Chem B 108:3283

    Article  CAS  Google Scholar 

  234. Lach C, Müller P, Frey H, Mülhaupt R (1997) Macromol Rapid Commun 18:253

    Article  CAS  Google Scholar 

  235. Frey H, Lach C, Schlenk C, Pusel T (2000) Polym Prepr 41:568

    CAS  Google Scholar 

  236. Möck A, Burgath A, Hanselmann R, Frey H (2001) Macromolecules 34:7692

    Article  CAS  Google Scholar 

  237. Burgath A, Möck A, Hanselmann R, Frey H (1999) Polym Mater Sci Eng 80:126

    CAS  Google Scholar 

  238. Möck A, Burgath A, Hanselmann R, Frey H (1999) Polym Mater Sci Eng 80:173

    Google Scholar 

  239. Lambert C, Nöll G (1999) J Am Chem Soc 121:8434

    Article  CAS  Google Scholar 

  240. Lambert C, Gaschler W, Schmälzlin E, Meerholz K, Bräuchle C (1999) J Chem Soc Perk T2:577

    Article  Google Scholar 

  241. Lambert C, Nöll G (2002) Chem Eur J 8:3467

    Article  CAS  PubMed  Google Scholar 

  242. Bronstein IN, Semendjajev KA (1985) Taschenbuch der Mathematik (Handbook of mathematics). Naukaand Teubner, Moscow and Leipzig, Ch 2.4.2

    Google Scholar 

  243. Schwalm WA, Schwalm MK, Giona M (1997) Phys Rev E 55:6741

    Article  CAS  Google Scholar 

  244. Jahromi S, Litvinov V, Coussens B (2001) Macromolecules 34:1013

    Article  CAS  Google Scholar 

  245. Kriesel JW, Tilley TD (1999) Chem Mater 11:1190

    Article  CAS  Google Scholar 

  246. Jang WD, Jiang DL, Aida T (2000) J Am Chem Soc 122:3232

    Article  CAS  Google Scholar 

  247. Gröhn F, Kim G, Bauer BJ, Amis EJ (2001) Macromolecules 34:2179

    Article  CAS  Google Scholar 

  248. Gitsov I, Zhu C (2002) Macromolecules 35:8418

    Article  CAS  Google Scholar 

  249. Dvornic PR, Li J, de Leuze-Jallouli AM, Reeves SD, Owen MJ (2002) Macromolecules 35:9323

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Biophysics and Soft Matter Group, Laboratory of Physics and Helsinki Institute of Physics, Helsinki University of Technology, P.O.Box 1100, 02015, Helsinki, Finland

    Andrey A. Gurtovenko

  2. Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoi Prospect 31, V.O., 199004, St. Petersburg, Russia

    Andrey A. Gurtovenko

  3. Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Str. 3, 79104, Freiburg, Germany

    Alexander Blumen

Authors
  1. Andrey A. Gurtovenko
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  2. Alexander Blumen
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Correspondence to Andrey A. Gurtovenko .

Editor information

Editors and Affiliations

  1. Yokohama, Japan

    Akihiro Abe

  2. Prague, Czech Republic

    Karel Dušek

  3. Sakyo-ku, Japan

    Shiro Kobayashi

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Gurtovenko, A.A., Blumen, A. (2005). Generalized Gaussian Structures: Models for Polymer Systems with ComplexTopologies. In: Abe, A., Dušek, K., Kobayashi, S. (eds) Polymer Analysis Polymer Theory. Advances in Polymer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b135561

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