Skip to main content
SpringerLink
Log in

Multiscale modeling of polymer materials using field-theoretic methodologies: a survey about recent developments

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

Understanding the chemistry and physics of polymer systems challenges scientists from a wide spectrum of research areas, ranging from polymer science to molecular electronic structure theory. One of the characteristic features of polymer systems is that their physics involve a multitude of different length and time scales, which generally render the determination of their structure and physical properties on a detailed level computationally exhaustive. To overcome this difficulty, novel field-theoretic methodologies based on the mean field approximation have emerged recently and have proven to deliver useful results in the calculation of mesoscopic polymer models in the regime of high monomer concentrations. In this review we demonstrate that the field-theoretic approach is not only an useful formalism for treating highly concentrated polymer systems on the mesoscopic level of description, but that it is also a promising theoretical tool, to solve the multiscale problems arising in the calculation of physical properties of a wide variety of neutral and charged polymer materials. To this end, we show that the field-theoretic approach possesses the advantageous property to enable the treatment of all levels of description, spanning from the quantum to the continuum scale, within an unified theoretical framework. On the example of the coupling of the mesoscopic and continuum scale, we show that this specific feature constitutes a crucial advantage of field-theoretic approaches with regard to current state-of-the-art particle-based simulation methodologies for connecting different levels of description. Another major benefit relates to their favorable approximation characteristics, which permit to devise efficient approximation strategies for evaluating sophisticated polymer solution models in the low to moderate regime of monomer concentrations in a reliable way. To show this, we present novel low-cost approximation strategies beyond the mean field level of approximation using effective renormalization concepts, originating from the domain of quantum field theory, and demonstrate their usefulness in the calculation of structure and physical properties of several polymer models, described at various levels of description.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hawker C.J., Bosman A.W., Harth E.: Chem. Rev. 101, 3661 (2001)

    CAS  Google Scholar 

  2. Kaminsky W., Tran P.-D., Weingarten U.: Macromol. Symp. 193, 1 (2003)

    CAS  Google Scholar 

  3. Kaminsky W., Albers I., Vathauer M.: Des. Monomers Polym. 5, 155 (2002)

    CAS  Google Scholar 

  4. Kaminsky W.: Macromol. Symp. 174, 269 (2001)

    CAS  Google Scholar 

  5. Baschnagel J., Binder K., Doruker P., Gusev A.A., Hahn O., Kremer K., Mattice W.L., Müller-Plathe F., Murat M., Paul W., Santos S., Suter U.W., Tries V., Abe A.: Adv. Polym. Sci. 152, 41 (2000)

    CAS  Google Scholar 

  6. Theodorou D.N.: Comput. Phys. Commun. 169, 82 (2005)

    CAS  Google Scholar 

  7. Ulherr A., Theodorou D.N.: Curr. Opin. Solid State Mater. Sci. 3, 544 (1998)

    Google Scholar 

  8. Kremer K., Müller-Plathe F.: MRS Bull. 26, 205 (2001)

    CAS  Google Scholar 

  9. Kremer K., Müller-Plathe F.: Mol. Simul. 28, 729 (2002)

    CAS  Google Scholar 

  10. Müller-Plathe F.: Chem. Phys. Chem. 3, 754 (2002)

    Google Scholar 

  11. Müller-Plathe F.: Soft Mater. 1, 1 (2003)

    Google Scholar 

  12. Baeurle S.A., Hotta A., Gusev A.A.: Polymer 46, 4344 (2005)

    CAS  Google Scholar 

  13. Yakushevich L.V.: Nonlinear Physics of DNA. Weinheim, Wiley-VCH (2004)

    Google Scholar 

  14. Das R., Mills T.T., Kwok L.W., Maskel G.S., Millet I.S., Doniach S., Finkelstein K.D., Herschlag D., Pollack L.: Phys. Rev. Lett. 90, 188103 (2003)

    CAS  Google Scholar 

  15. Tomic S., Vuletic T., Dolanski Babic S., Krca S., Ivankovic D., Griparic L., Podgornik R.: Phys. Rev. Lett. 97, 098303 (2006)

    CAS  Google Scholar 

  16. Kottke T., Dick B., Fedorov R., Schlichting I., Deutzmann R., Hegemann P.: Biochemistry 42, 9854 (2003)

    CAS  Google Scholar 

  17. Crosson S., Moffat K.: Proc. Natl. Acad. Sci. 98, 2995 (2001)

    CAS  Google Scholar 

  18. Praprotnik M., Kremer K., Delle Site L.: Phys. Rev. E 75, 017701 (2007)

    Google Scholar 

  19. Rottler J., Barsky S., Robbins M.O.: Phys. Rev. Lett. 89, 148304 (2002)

    Google Scholar 

  20. Hotta A., Clarke S.M., Terentjev E.M.: Macromolecules 35, 271 (2002)

    CAS  Google Scholar 

  21. Olson G.B.: Science 277, 1237 (1997)

    CAS  Google Scholar 

  22. Jensen F.: Introduction to Computational Chemistry. Wiley, Chichester (1999)

    Google Scholar 

  23. Parr R.G., Yang W.: Density-Functional Theory of Atoms and Molecules. Oxford University, New York (1989)

    Google Scholar 

  24. Hohenberg P., Kohn W.: Phys. Rev. 136, B864 (1964)

    Google Scholar 

  25. Allen M.P., Tildesley D.J.: Computer Simulation of Liquids. Clarendon, Oxford (1996)

    Google Scholar 

  26. Frenkel D., Smit B.: Understanding Molecular Simulation. Academic, San Diego (1996)

    Google Scholar 

  27. Binder K., Heermann D.W.: Monte Carlo Simulation in Statistical Physics: An Introduction. Springer, Berlin (2002)

    Google Scholar 

  28. Barthel J.M.G., Krienke H., Baumgärtel H., Kunz W.: Physical Chemistry of Electrolyte Solutions: Modern Aspects. Springer, Darmstadt (1998)

    Google Scholar 

  29. Baeurle S.A.: J. Comput. Phys. 184, 540 (2003)

    Google Scholar 

  30. Redondo A., LeSar R.: Annu. Rev. Mater. Res. 34, 279 (2004) and references therein

    CAS  Google Scholar 

  31. Aoyagi T., Honda T., Doi M.: J. Chem. Phys. 117, 8153 (2002)

    CAS  Google Scholar 

  32. Stevens M.J., Kremer K.: Phys. Rev. Lett. 71, 2228 (1993)

    CAS  Google Scholar 

  33. Baeurle S.A., Kroener J.: J. Math. Chem. 36, 409 (2004) and references therein

    CAS  Google Scholar 

  34. Fredrickson G.H.: The Equilibrium Theory of Inhomogeneous Polymers. Clarendon, Oxford (2006) and references therein

    Google Scholar 

  35. Kadau K., Germann T.C., Lomdahl P.S.: Int. J. Mod. Phys. C 17, 1755 (2006)

    CAS  Google Scholar 

  36. Baeurle S.A., Martonak R., Parrinello M.: J. Chem. Phys. 117, 3027 (2002)

    CAS  Google Scholar 

  37. Baeurle S.A.: Comput. Phys. Commun. 157, 201 (2004)

    CAS  Google Scholar 

  38. Doi M., Edwards S.F.: The Theory of Polymer Dynamics. Oxford University, New York (1986)

    Google Scholar 

  39. Faller R.: Polymer 45, 3869 (2004)

    CAS  Google Scholar 

  40. Binder K.: Monte Carlo and Molecular Dynamics Simulations in Polymer Sciences. Oxford University, New York (1995)

    Google Scholar 

  41. Schmid F.: J. Phys. Condens. Matter 10, 8105 (1998)

    CAS  Google Scholar 

  42. Matsen M.W.: J. Phys. Condens. Matter 14, R21 (2002)

    CAS  Google Scholar 

  43. Caillol J.-M., Patsahan O., Mryglod I.: Physica A 368, 326 (2006)

    Google Scholar 

  44. Fredrickson G.H., Ganesan V., Drolet F.: Macromolecules 35, 16 (2002)

    CAS  Google Scholar 

  45. Terzis A.F., Theodorou D.N., Stroeks A.: Macromolecules 35, 508 (2002)

    CAS  Google Scholar 

  46. Terzis A.F., Theodorou D.N., Stroeks A.: Macromolecules 33, 1385 (2000)

    CAS  Google Scholar 

  47. Terzis A.F., Theodorou D.N., Stroeks A.: Macromolecules 33, 1397 (2000)

    CAS  Google Scholar 

  48. Valavala P.K., Odegard G.M.: Rev. Adv. Mater. Sci. 9, 34 (2005) and references therein

    CAS  Google Scholar 

  49. Gusev A.A.: J. Mech. Phys. Solids 45, 1449 (1997)

    Google Scholar 

  50. Gusev A.A.: Macromolecules 34, 3081 (2001)

    CAS  Google Scholar 

  51. Zienkiewicz O.C., Taylor R.L.: The Finite Element Method, vol. 1: The Basis. Butterworth-Heinemann, Oxford (2000)

    Google Scholar 

  52. Eischen J.W., Torquato S.: J. Appl. Phys. 74, 159 (1993)

    CAS  Google Scholar 

  53. Banerjee P.K.: The Boundary Element Methods in Engineering. McGraw-Hill, London (1994)

    Google Scholar 

  54. Baeurle S.A., Fredrickson G.H., Gusev A.A.: Macromolecules 37, 5784 (2004)

    CAS  Google Scholar 

  55. Folkes M.J., Keller A.: Polymer 12, 222 (1971)

    CAS  Google Scholar 

  56. Takayanagi M., Harima H., Iwata Y.: Mem. Fac. Eng. Kyushu Univ. 23, 41 (1963)

    Google Scholar 

  57. Whitney J.M., Riley M.B.: Am. Inst. Aeronaut. Astronaut. J. 4, 1537 (1966)

    CAS  Google Scholar 

  58. Hashin Z.: J. Mech. Phys. Solids 13, 119 (1965)

    Google Scholar 

  59. Hill R.: J. Mech. Phys. Solids 12, 199 (1964)

    Google Scholar 

  60. Hashin Z., Rosen B.W.: Trans. ASME 31, 223 (1964)

    Google Scholar 

  61. Rosen B.W.: Proc. Roy. Soc. Lond. Ser. A 319, 79 (1970)

    Google Scholar 

  62. Van Fo Fy G.A., Savin G.N.: Polym. Mech. 1, 106 (1965)

    Google Scholar 

  63. Chamis C.C., Sendeckyj G.P.: J. Compos. Mater. 2, 332 (1968)

    Google Scholar 

  64. Doi M.: Macromol. Symp. 195, 101 (2003)

    CAS  Google Scholar 

  65. Glotzer S.C., Paul W.: Annu. Rev. Mater. Res. 32, 401 (2002)

    CAS  Google Scholar 

  66. Delle Site L., Abrams C.F., Alavi A., Kremer K.: Phys. Rev. Lett. 89, 156103 (2002)

    CAS  Google Scholar 

  67. Delle Site L., Leon S., Kremer K.: J. Am. Chem. Soc. 126, 2944 (2004)

    CAS  Google Scholar 

  68. Delle Site L., Kremer K.: Int. J. Quantum Chem. 101, 733 (2005)

    CAS  Google Scholar 

  69. Neri M., Anselmi C., Cascella M., Maritan A., Carloni P.: Phys. Rev. Lett. 95, 218102 (2005)

    Google Scholar 

  70. Villa E., Balaeff A., Mahadevan L., Schulten K.: Multiscale Model. Simul. 2, 527 (2004)

    CAS  Google Scholar 

  71. Rafii-Tabar H., Hua L., Cross M.: J. Phys.: Condens. Matter 10, 2375 (1998)

    CAS  Google Scholar 

  72. Smirnova J.A., Zhigilei L.V., Garrison B.J.: Comput. Phys. Commun. 118, 11 (1999)

    CAS  Google Scholar 

  73. O’Connell S.T., Thompson P.A.: Phys. Rev. E 52, R5792 (1995)

    Google Scholar 

  74. Hadjiconstantinou N.G.: Phys. Rev. E 59, 2475 (1999)

    Google Scholar 

  75. Li J., Liao D., Yip S.: Phys. Rev. E 57, 7259 (1998)

    CAS  Google Scholar 

  76. Flekkoy E.G., Wagner G., Feder J.: Europhys. Lett. 52, 271 (2000)

    CAS  Google Scholar 

  77. Delgado-Buscalioni R., Coveney P.V.: Phys. Rev. E 67, 046704 (2003)

    CAS  Google Scholar 

  78. Broughton J.Q., Abraham F.F., Bernstein N., Kaxiras E.: Phys. Rev. B 60, 2391 (1999)

    CAS  Google Scholar 

  79. Laio A., Van de Vondele J., Röthlisberger U.: J. Chem. Phys. 116, 6941 (2002)

    CAS  Google Scholar 

  80. Csanyi G., Albaret T., Payne M.C., De Vita A.: Phys. Rev. Lett. 93, 175503 (2004)

    Google Scholar 

  81. Ghosh S.K.: Bull. Mater. Sci. 26, 3 (2003)

    CAS  Google Scholar 

  82. Baeurle S.A., Nogovitsin E.A.: Polymer 48, 4883 (2007)

    CAS  Google Scholar 

  83. Edwards S.F.: Proc. Phys. Soc. 85, 613 (1965)

    CAS  Google Scholar 

  84. Rom N., Charutz D.M., Neuhauser D.: Chem. Phys. Lett. 270, 382 (1997)

    CAS  Google Scholar 

  85. Baer R., Head-Gordon M., Neuhauser D.: J. Chem. Phys. 109, 6219 (1998)

    CAS  Google Scholar 

  86. Baeurle S.A.: Int. J. Theor. Phys. 41, 1915 (2002)

    Google Scholar 

  87. Baeurle S.A.: J. Math. Chem. 34, 29 (2003) and references therein

    CAS  Google Scholar 

  88. Aranson I.S., Kalatsky V.A., Vinokur V.M.: Phys. Rev. Lett. 85, 118 (2000)

    CAS  Google Scholar 

  89. Baeurle S.A., Charlot M., Nogovitsin E.A.: Phys. Rev. E 75, 011804 (2007)

    Google Scholar 

  90. Orkoulas G., Panagiotopoulos A.Z.: Fluid Phase Equilib. 83, 223 (1993) and references therein

    CAS  Google Scholar 

  91. Negele J.W., Orland H.: Quantum Many-Particle Systems. Perseus Books, Reading (1998)

    Google Scholar 

  92. Goldenfeld N.: Lectures on Phase Transitions and the Renormalization Group. Addison-Wesley, New York (1992)

    Google Scholar 

  93. Amit D.J.: Field Theory, the Renormalization Group and Critical Phenomena. World Scientific, Singapore (1984)

    Google Scholar 

  94. Kaku M.: Quantum Field Theory. Oxford University, New York (1993)

    Google Scholar 

  95. Noolandi J., Davison T.S., Völkel A.R., Nie X.-F., Kay C., Arrowsmith C.H.: Proc. Natl. Acad. Sci. 97, 9955 (2000)

    CAS  Google Scholar 

  96. Helfand E., Tagami Y.: J. Polym. Sci. Polym. Lett. 9, 741 (1971)

    CAS  Google Scholar 

  97. Spontak R.J., Patel N.P.: Curr. Opin. Colloid Interface Sci. 5, 334 (2000)

    CAS  Google Scholar 

  98. M.J. Folkes, A. Keller, in Block and Graft Copolymers, ed. by J.J. Burke, V. Weiss (Syracuse University, Syracuse, 1973), 87 pp

  99. Ruzette A.-V., Leibler L.: Nature Mater. 4, 19 (2005)

    CAS  Google Scholar 

  100. Balazs A.C., Emrick T., Russell T.P.: Science 314, 1107 (2006)

    CAS  Google Scholar 

  101. Thompson R.B., Ginzburg V.V., Matsen M.W., Balazs A.C.: Science 292, 2469 (2001)

    CAS  Google Scholar 

  102. Cheng J.-Y., Ross C.A., Thomas E.L., Smith H.I., Vancso G.J.: Adv. Mater. 15, 1599 (2001)

    Google Scholar 

  103. Krishnamoorthy S., Hinderling C., Heinzelmann H.: Mater. Today 9, 40 (2006)

    CAS  Google Scholar 

  104. Wang X.-Y., Prabhu R.N., Schmehl R.H., Weck M.: Macromolecules 39, 3140 (2006)

    CAS  Google Scholar 

  105. Sun S., Fan Z., Wang Y., Haliburton J.: J. Mater. Sci. 40, 1429 (2005)

    CAS  Google Scholar 

  106. Sun S.-S.: Sol. Energy Mater. Sol. Cells 79, 257 (2003)

    CAS  Google Scholar 

  107. Adams M.L., Lavasanifar A., Kwon G.S.: J. Pharm. Sci. 92, 1343 (2003)

    CAS  Google Scholar 

  108. Jeong B., Bae Y.H., Lee D.S., Kim S.W.: Nature 388, 860 (1997)

    CAS  Google Scholar 

  109. Kakizawa Y., Kataoka K.: Adv. Drug Deliv. Rev. 54, 203 (2002)

    CAS  Google Scholar 

  110. Lavik E., Langer R.: Appl. Microbiol. Biotechnol. 65, 1 (2004)

    CAS  Google Scholar 

  111. Diamant J., Williams M.C., Soane D.S.: Polym. Eng. Sci. 28, 207 (1988)

    CAS  Google Scholar 

  112. Holden G., Bishop E.T., Legge R.: J. Polym. Sci. Part C 26, 37 (1969)

    Google Scholar 

  113. Pukánszky B.: Eur. Polym. J. 41, 645 (2005)

    Google Scholar 

  114. Sperling L.H.: Introduction to Physical Polymer Science. Wiley, New York (2001)

    Google Scholar 

  115. Read D.J., Duckett R.A., Sweeney J., McLeish T.C.B.: J. Phys. D Appl. Phys. 32, 2087 (1999)

    Google Scholar 

  116. Drozdov A.D., Christiansen C.: Int. J. Eng. Sci. 44, 205 (2006)

    Google Scholar 

  117. Arridge R.G.C., Folkes M.J.: J. Phys. D: Appl. Phys. 5, 344 (1972)

    CAS  Google Scholar 

  118. Odell J.A., Keller A.: Polym. Eng. Sci. 17, 8 (1977)

    Google Scholar 

  119. Allan P., Arridge R.G.C., Ehtaiatkar F., Folkes M.J.: J. Phys. D Appl. Phys. 24, 1381 (1991)

    CAS  Google Scholar 

  120. T.L. Smith, in Block Polymers, ed. by S.L. Aggarwal (Plenum, New York, 1970), 137 pp

  121. R. Chasset, P. Thirion, in Proc. Conf. Phys. Non-Cryst. Solids, ed. by J.A. Prins (North-Holland, Amsterdam, 1965), 345 pp

  122. Curro J.G., Pincus P.: Macromolecules 16, 559 (1983)

    CAS  Google Scholar 

  123. Ferry J.D.: Viscoelastic Properties of Polymers. Wiley, New York (1970)

    Google Scholar 

  124. Curro J.G., Pearson D.S., Helfand E.: Macromolecules 18, 1157 (1985)

    CAS  Google Scholar 

  125. McKenna G.B., Gaylord R.J.: Polymer 29, 2027 (1988)

    CAS  Google Scholar 

  126. Gurtovenko A.A., Gotlib Y.Y.: J. Chem. Phys. 115, 6785 (2001) and references therein

    CAS  Google Scholar 

  127. Ngai K.L.: J. Phys. Condens. Matter 12, 6437 (2000)

    CAS  Google Scholar 

  128. Inoue T., Moritani M., Hashimoto T., Kawai H.: Macromolecules 4, 500 (1971)

    Google Scholar 

  129. Drzal P.L., Shull K.R.: Macromolecules 36, 2000 (2003)

    CAS  Google Scholar 

  130. Landau L.D., Lifshitz E.M.: Statistical Physics Part I, Volume 5 of Course of Theoretical Physics, pp. 333. Pergamon, Oxford (1980)

    Google Scholar 

  131. Baeurle S.A., Usami T., Gusev A.A.: Polymer 47, 8604 (2006)

    CAS  Google Scholar 

  132. Dair B.J., Avgeropoulos A., Hadjichristidis N., Thomas E.L.: J. Mater. Sci. 35, 5207 (2000)

    CAS  Google Scholar 

  133. Henderson C.P., Williams M.C.: Polymer 26, 2021 (1985)

    CAS  Google Scholar 

  134. Henderson C.P., Williams M.C.: Polymer 26, 2026 (1985)

    CAS  Google Scholar 

  135. Morèse-Séguéla B., St-Jacques M., Renaud J.M., Prud’homme J.: Macromolecules 13, 100 (1980)

    Google Scholar 

  136. Kraus G., Rollmann K.W.: J. Polym. Sci. Polym. Phys. Ed. 14, 1133 (1976)

    CAS  Google Scholar 

  137. Kumler P.L., Keinath S.E., Boyer R.F.: Polym. Eng. Sci. 17, 613 (1977)

    CAS  Google Scholar 

  138. Stöppelmann G., Gronski W., Blume A.: Polymer 31, 1838 (1990)

    Google Scholar 

  139. Huy T.A., Hai L.H., Adhikari R., Weidisch R., Michler G.H., Knoll K.: Polymer 44, 1237 (2003)

    CAS  Google Scholar 

  140. Baeurle S.A., Hotta A., Gusev A.A.: Polymer 47, 6243 (2006)

    CAS  Google Scholar 

  141. Gibbs J.H., Di Marzio E.A.: J. Chem. Phys. 28, 373 (1958)

    CAS  Google Scholar 

  142. Gibbs J.H.: J. Chem. Phys. 25, 185 (1956)

    CAS  Google Scholar 

  143. Di Marzio E.A., Gibbs J.H.: J. Chem. Phys. 28, 807 (1958)

    CAS  Google Scholar 

  144. Di Marzio E.A., Yang A.J.M.: J. Res. Natl. Inst. Stand. Technol. 102, 135 (1997)

    CAS  Google Scholar 

  145. Eyring H., Ree T.: Proc. Natl. Acad. Sci. 47, 526 (1961)

    CAS  Google Scholar 

  146. Hsu C.C., Eyring H.: Proc. Natl. Acad. Sci. 69, 134 (1972)

    Google Scholar 

  147. Cicerone M.T., Blackburn F.R., Ediger M.D.: Macromolecules 28, 8224 (1995)

    CAS  Google Scholar 

  148. Merabia S., Sotta P., Long D.: Eur. Phys. J. E 15, 189 (2004)

    CAS  Google Scholar 

  149. Sides S.W., Fredrickson G.H.: Polymer 44, 5859 (2003)

    CAS  Google Scholar 

  150. Beecher J.F., Marker L., Bradford R.D., Aggarwal S.L.: J. Polym. Sci. Part C 26, 117 (1969)

    Google Scholar 

  151. R.A. Robinson, E.F.T. White, in Block Polymers, ed. by S.L. Aggarwal (Plenum, New York, 1970), 123 pp

  152. Park C.H., Kim J.H., Ree M., Sohn B.H., Jung J.C., Zin W.C.: Polymer 45, 4507 (2004)

    CAS  Google Scholar 

  153. Griffith A.A.: Philos. Trans. R. Soc. London A 221, 163 (1921)

    Google Scholar 

  154. Shen M., Cirlin E.H., Kaelble D.H.: J. Polym. Sci. Polym. Lett. Ed. 8, 149 (1970)

    CAS  Google Scholar 

  155. Leary D.F., Williams M.C.: J. Polym. Sci. Polym. Lett. Ed. 8, 335 (1970)

    CAS  Google Scholar 

  156. Helfand E., Wassermann Z.R.: Polym. Eng. Sci. 17, 582 (1977)

    CAS  Google Scholar 

  157. Diamant J., Williams M.C.: Polym. Eng. Sci. 29, 227 (1989)

    CAS  Google Scholar 

  158. Hara M.: Polyelectrolytes: Science and Technology. Marcel Dekker, New York (1993)

    Google Scholar 

  159. Dautzenberg H., Jaeger W., Kotz J., Philipp B., Seidel Ch., Stscherbina D.: Polyelectrolytes: Formation, Characterization and Application. Hanser Gardner, Munich (1994)

    Google Scholar 

  160. Konieczky M., Likos C.N., Löwen H.: J. Chem. Phys. 121, 4913 (2004)

    Google Scholar 

  161. von Solms N., Chiew Y.C.: J. Chem. Phys. 118, 4321 (2003)

    Google Scholar 

  162. Wang L., Bloomfield V.A.: Macromolecules 23, 804 (1990) and references therein

    CAS  Google Scholar 

  163. Wang Q., Taniguchi T., Fredrickson G.H.: J. Phys. Chem. B 108, 6733 (2004)

    CAS  Google Scholar 

  164. Vlachy V., Haymet A.D.J.: J. Chem. Phys. 84, 587 (1986)

    Google Scholar 

  165. Chang R., Yethiraj A.: Macromolecules 38, 607 (2005)

    CAS  Google Scholar 

  166. Förster S., Abetz V., Müller A.H.E.: Adv. Polym. Sci. 166, 173 (2004)

    Google Scholar 

  167. Kimerling A.S., Rochefort W.E., Bhatia S.R.: Ind. Eng. Chem. Res. 45, 6885 (2006)

    CAS  Google Scholar 

  168. de Gennes P.-G.: Phys. Lett. 38A, 339 (1972)

    Google Scholar 

  169. Matsen M.W.: J. Phys. Condens. Matter 14, R21 (2002)

    CAS  Google Scholar 

  170. Reister E., Müller M., Binder K.: Phys. Rev. E 64, 041804 (2001)

    CAS  Google Scholar 

  171. Matsen M.W., Griffiths G.H., Wickham R.A., Vassiliev O.N.: J. Chem. Phys. 124, 024904 (2006)

    CAS  Google Scholar 

  172. Müller M., Schmid F.: Adv. Polym. Sci. 185, 1 (2005)

    Google Scholar 

  173. Müller M., Katsov K., Schick M.: Phys. Rep. 434, 113 (2006)

    Google Scholar 

  174. Daoulas K.C., Müller M.: J. Chem. Phys. 125, 184904 (2006)

    Google Scholar 

  175. Frusawa H.: J. Phys. Condens. Matter 17, L241 (2005)

    CAS  Google Scholar 

  176. Netz R.R., Andelman D.: Phys. Rep. 380, 1 (2003)

    CAS  Google Scholar 

  177. Tsonchev S., Coalson R.D., Duncan A.: Phys. Rev. E 60, 4257 (1999)

    CAS  Google Scholar 

  178. Baeurle S.A.: Phys. Rev. Lett. 89, 080602 (2002)

    Google Scholar 

  179. Baeurle S.A.: Comput. Phys. Commun. 154, 111 (2003)

    CAS  Google Scholar 

  180. Moreira A.G., Baeurle S.A., Fredrickson G.H.: Phys. Rev. Lett. 91, 150201 (2003)

    Google Scholar 

  181. Ganesan V., Fredrickson G.H.: Europhys. Lett. 55, 814 (2001)

    CAS  Google Scholar 

  182. Alexander-Katz A., Moreira A.G., Fredrickson G.H.: J. Chem. Phys. 118, 9030 (2003)

    CAS  Google Scholar 

  183. Klauder J.R.: J. Phys. A: Math. Gen. 16, L317 (1983)

    Google Scholar 

  184. Gausterer H., Klauder J.R.: Phys. Lett. B 164, 127 (1985)

    Google Scholar 

  185. Lee S.: Nucl. Phys. B 413, 827 (1994)

    CAS  Google Scholar 

  186. Gausterer H., Lee S.: J. Stat. Phys. 73, 147 (1993)

    Google Scholar 

  187. Gausterer H.: J. Phys. A: Math. Gen. 27, 1325 (1994)

    Google Scholar 

  188. Gausterer H., Thaler H.: J. Phys. A: Math. Gen. 31, 2541 (1998)

    Google Scholar 

  189. Moriconi L., Moriconi M.: Phys. Rev. E 72, 016125 (2005)

    CAS  Google Scholar 

  190. Adami C., Koonin S.E.: Phys. Rev. C 63, 034319 (2001)

    Google Scholar 

  191. Shirkov D.V.: CERN Courier 41, 14 (2001)

    Google Scholar 

  192. Weinberg S.: The Quantum Theory of Fields. Cambridge University, Cambridge (1995)

    Google Scholar 

  193. Wilson K.G.: Phys. Rev. B 4, 3184 (1971)

    Google Scholar 

  194. Wilson K.G., Kogut J.: Phys. Rep. C 12, 75 (1974)

    Google Scholar 

  195. Chaikin P.M., Lubensky T.C.: Principles of Condensed Matter Physics. Cambridge University, Cambridge (1995)

    Google Scholar 

  196. Efimov G.V., Nogovitsin E.A.: Physica A 234, 506 (1996)

    Google Scholar 

  197. Efimov G.V., Nogovitsin E.A.: Russ. J. Phys. Chem. 76, 1877 (2002)

    Google Scholar 

  198. Y.G. Yi, arXiv:physics/0010080 v13 (2002) 15 Dec

  199. Efimov G.V., Ganbold G.: Phys. Stat. Sol. 168, 165 (1991)

    Google Scholar 

  200. Dineykhan M., Efimov G.V., Ganbold G., Nedelko S.N.: Oscillator Representation in Quantum Physics, pp. 280. Springer, Berlin (1995)

    Google Scholar 

  201. Baeurle S.A., Efimov G.V., Nogovitsin E.A.: Europhys. Lett. 75, 378 (2006)

    CAS  Google Scholar 

  202. Baeurle S.A., Efimov G.V., Nogovitsin E.A.: J. Chem. Phys. 124, 224110 (2006)

    Google Scholar 

  203. Louis A.A., Bolhuis P.G., Hansen J.P.: Phys. Rev. E 62, 7961 (2000)

    CAS  Google Scholar 

  204. Likos C.N.: Phys. Rep. 348, 267 (2001)

    CAS  Google Scholar 

  205. Stillinger F.H., Weber T.A.: J. Chem. Phys. 68, 3837 (1978)

    CAS  Google Scholar 

  206. Stillinger F.H., Stillinger D.K.: Physica A 244, 358 (1997)

    CAS  Google Scholar 

  207. Massiera G., Ramos L., Ligoure C., Pitard E.: Phys. Rev. E 68, 021803 (2003)

    Google Scholar 

  208. Ligoure C.: J. Phys. Condens. Matter 17, S2911 (2005)

    CAS  Google Scholar 

  209. Liverpool T.B., Stapper M.: Europhys. Lett. 40, 485 (1997)

    CAS  Google Scholar 

  210. Derjaguin B.V.: Kolloid Z. 69, 155 (1934)

    Google Scholar 

  211. Derjaguin B.V., Landau L.D.: Acta Physicochim. URSS 14, 633 (1941)

    Google Scholar 

  212. Verwey E.J., Overbeek J.T.G.: Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdam (1948)

    Google Scholar 

  213. Norman G.E., Filinov V.S.: High Temp. (USSR) 7, 216 (1969)

    Google Scholar 

  214. Martyna G.J., Tuckerman M.E., Tobias D.J., Klein M.L.: Mol. Phys. 87, 1117 (1996)

    CAS  Google Scholar 

  215. Robbins M.O., Kremer K., Grest G.S.: J. Chem. Phys. 88, 3286 (1988) and references therein

    CAS  Google Scholar 

  216. Dijkstra M., van Roij R.: J. Phys. Condens. Matter 10, 1219 (1998)

    CAS  Google Scholar 

  217. Mezei M.: Mol. Phys. 40, 901 (1980)

    CAS  Google Scholar 

  218. Shroll R.M., Smith D.E.: J. Chem. Phys. 110, 8295 (1999) and references therein

    CAS  Google Scholar 

  219. Cagin T., Pettitt B.M.: Mol. Simul. 6, 5 (1991)

    Google Scholar 

  220. Cagin T., Pettitt B.M.: Mol. Phys. 72, 169 (1991)

    CAS  Google Scholar 

  221. Ji J., Cagin T., Pettitt B.M.: J. Chem. Phys. 96, 1333 (1992)

    CAS  Google Scholar 

  222. Attard P.: J. Chem. Phys. 107, 3230 (1997)

    CAS  Google Scholar 

  223. Weerasinghe S., Pettitt B.M.: Mol. Phys. 82, 897 (1994)

    CAS  Google Scholar 

  224. Odijk T.: Macromolecules 12, 688 (1979)

    CAS  Google Scholar 

  225. de Gennes P.-G., Pincus P., Velasco R.M., Brochard F.: J. Phys. (Paris) 37, 1461 (1976)

    Google Scholar 

  226. de Gennes P.-G.: Scaling Concepts in Polymer Physics. Cornell University, Ithaca (1979)

    Google Scholar 

  227. Gouy G.: J. Phys. 9, 457 (1910)

    CAS  Google Scholar 

  228. Chapman D.L.: Philos. Mag. 25, 475 (1913)

    Google Scholar 

  229. Hansen J.-P., Löwen H.: Annu. Rev. Phys. Chem. 51, 209 (2000)

    CAS  Google Scholar 

  230. Stern O.: Z. Elektrochem. 30, 508 (1924)

    CAS  Google Scholar 

  231. Alexander S., Chaikin P.M., Grant P., Morales P.J., Pincus P., Hone D.: J. Chem. Phys. 80, 5776 (1984)

    CAS  Google Scholar 

  232. Stevens M.J., Kremer K.: J. Phys. II France 6, 1607 (1996)

    CAS  Google Scholar 

  233. Manning G.S.: J. Chem. Phys. 51, 924 (1969)

    CAS  Google Scholar 

  234. Liao Q., Dobrynin A.V., Rubinstein M.: Macromolecules 36, 3386 (2003)

    Google Scholar 

  235. Stevens M., Kremer K.: J. Chem. Phys. 103, 1669 (1995)

    CAS  Google Scholar 

  236. des Cloizeaux J.: J. Phys. (Paris) 36, 281 (1975)

    CAS  Google Scholar 

  237. des Cloizeaux J.: J. Phys. (Paris) 36, 1199 (1975)

    Google Scholar 

  238. Janata J., Josowicz M.: Nature Mater. 2, 19 (2003) and references therein

    CAS  Google Scholar 

  239. Mezzenga R., Schurtenberger P., Burbidge A., Michel M.: Nature Mater. 4, 729 (2005)

    CAS  Google Scholar 

  240. Mezzenga R., Lee W.B., Fredrickson G.H.: Trends Food Sci. Technol. 17, 220 (2006)

    CAS  Google Scholar 

  241. Adhikari R., Michler G.H., An Huy T., Ivan’kova E., Godehardt R., Lebek W., Knoll K.: Macromol. Chem. Phys. 204, 488 (2003)

    CAS  Google Scholar 

  242. Oman S.: Makromol. Chem. 178, 475 (1977)

    CAS  Google Scholar 

  243. Vesnaver G., Skerjanc J.: J. Phys. Chem. 90, 4673 (1986)

    CAS  Google Scholar 

  244. Chu P., Marinsky J.A.: J. Phys. Chem. 71, 4352 (1967)

    CAS  Google Scholar 

  245. Reddy M., Marinsky J.A.: J. Phys. Chem. 74, 3884 (1970)

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry & Pharmacy, Institute of Physical & Theoretical Chemistry, University of Regensburg, 93053, Regensburg, Germany

    S. A. Baeurle

Authors
  1. S. A. Baeurle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Baeurle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baeurle, S.A. Multiscale modeling of polymer materials using field-theoretic methodologies: a survey about recent developments. J Math Chem 46, 363–426 (2009). https://doi.org/10.1007/s10910-008-9467-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-008-9467-3

Keywords

Search

Navigation