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Classical Density Functional Theory of Polymer Fluids

  • Jan ForsmanEmail author
  • Clifford E. Woodward
Chapter
  • 1.8k Downloads
Part of the Molecular Modeling and Simulation book series (MMAS)

Abstract

We introduce a classical density functional (DFT) description of polymer solutions, initially focusing on systems containing flexible and monodisperse chains. The theory is used to describe excluded volume effects by utilizing the so-called “Generalized Flory-Dimer” (GFD) equation of state. We also describe efficient computational approaches to numerical solutions. We then extend our treatment to describe semiflexible polymers and polydispersity. Here, the polydispersity, in combination with the well-known Schultz-Flory-Zimm molecular weight distribution, allows a different formulation for the free energy minimization. An interesting, and perhaps counterintuitive, result is that the resulting computational effort depends on the width of the molecular weight distribution, but not the average chain length. Finally, we show how the DFT can be adapted to charged oligomeric fluids displaying more complex molecular architecture. In particular, we show that the essential non-uniform structures of a model room temperature ionic liquid are accurately captured in a DFT that accounts for non-trivial bond connectivity and strongly coupled steric and electrostatic correlations.

Keywords

Molecular Weight Distribution Site Density Room Temperature Ionic Liquid Configurational Entropy Excess Free Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)MathSciNetCrossRefGoogle Scholar
  2. 2.
    N.D. Mermin, Phys. Rev. 127, A1441 (1965)MathSciNetCrossRefGoogle Scholar
  3. 3.
    D. Chandler, J.D. McCoy, S.J. Singer, J. Chem. Phys. 85, 5971 (1986)CrossRefGoogle Scholar
  4. 4.
    L. Pratt, D. Chandler, J. Chem. Phys. 66, 147 (1977)CrossRefGoogle Scholar
  5. 5.
    C.E. Woodward, J. Chem. Phys. 94, 3183 (1991)CrossRefGoogle Scholar
  6. 6.
    Y. Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)CrossRefGoogle Scholar
  7. 7.
    Y.X. Yu, J. Wu, J. Chem. Phys. 117, 2368 (2002)CrossRefGoogle Scholar
  8. 8.
    Z. Li, D. Cao, J. Wu, J. Chem. Phys. 122(17), 174708 (2005)CrossRefGoogle Scholar
  9. 9.
    R. Roth, J. Phys.: Condens. Matter 22(6), 063102 (2010)Google Scholar
  10. 10.
    X. Xu, D. Cao, J. Wu, Soft Matter 6(19), 4631 (2010)CrossRefGoogle Scholar
  11. 11.
    S. Lamperski, M. Kaja, L.B. Bhuiyan, J. Wu, D. Henderson, J. Chem. Phys. 139(5), 054703 (2013)CrossRefGoogle Scholar
  12. 12.
    C.E. Woodward, A. Yethiraj, J. Chem. Phys. 100, 3181 (1994)CrossRefGoogle Scholar
  13. 13.
    J. Forsman, C.E. Woodward, B.C. Freasier, J. Chem. Phys. 117, 1915 (2002)CrossRefGoogle Scholar
  14. 14.
    J. Forsman, C.E. Woodward, Phys. Rev. Lett. 94, 118301 (2005)CrossRefGoogle Scholar
  15. 15.
    E. Kierlik, M.L. Rosinberg, J. Chem. Phys. 97, 9222 (1992)CrossRefGoogle Scholar
  16. 16.
    G.J. Fleer, M.A.C. Stuart, J.M.H.M. Scheutjens, T. Cosgrove, B. Vincent, Polymers at Interfaces (Chapman and Hall, London, 1993)Google Scholar
  17. 17.
    J.Z. Wu, Aiche J 52(3), 1169 (2006)CrossRefGoogle Scholar
  18. 18.
    J.Z. Wu, Z. Li, Annu. Rev. Phys. Chem. 58, 85 (2007)CrossRefGoogle Scholar
  19. 19.
    S. Nordholm, M. Johnson, B.C. Freasier, Aust. J. Chem. 33, 2139 (1980)CrossRefGoogle Scholar
  20. 20.
    S. Nordholm, Aust. J. Chem. 37, 1 (1984)CrossRefGoogle Scholar
  21. 21.
    S. Nordholm, Chem. Phys. Lett. 105, 302 (1984)CrossRefGoogle Scholar
  22. 22.
    J.M. Wichert, H.S. Gulati, C.K. Hall, J. Chem. Phys. 105, 7669 (1996)CrossRefGoogle Scholar
  23. 23.
    A. Yethiraj, C.E. Woodward, J. Chem. Phys. 102, 5499 (1995)CrossRefGoogle Scholar
  24. 24.
    J. Forsman, C.E. Woodward, J. Chem. Phys. 120, 506 (2004)CrossRefGoogle Scholar
  25. 25.
    J. Forsman, C.E. Woodward, Macromol. 39, 1261 (2006)CrossRefGoogle Scholar
  26. 26.
    B.C. Freasier, C.E. Woodward, S. Nordholm, J. Chem. Phys. 90, 5657 (1989)CrossRefGoogle Scholar
  27. 27.
    T. Åkesson, C.E. Woodward, B. Jönsson, J. Chem. Phys. 91(4), 2461 (1989)CrossRefGoogle Scholar
  28. 28.
    R. Tuinier, A. Petukhov, Macromol. Theory Simul. 11, 975 (2002)CrossRefGoogle Scholar
  29. 29.
    J. van der Gucht, N.A.M. Besseling, Phys. Rev. E 65, 051801 (2002)CrossRefGoogle Scholar
  30. 30.
    J. van der Gucht, N.A.M. Besseling, G.J. Fleer, J. Chem. Phys. 119, 8175 (2003)CrossRefGoogle Scholar
  31. 31.
    J. van der Gucht, N.A.M. Besseling, J. Phys.: Condens. Matter. 15, 6627 (2003)Google Scholar
  32. 32.
    J. van der Gucht, N.A.M. Besseling, G.J. Fleer, Macromol. 37, 3026 (2004)CrossRefGoogle Scholar
  33. 33.
    S.P.F.M. Roefs, J.M.H.M. Scheutjens, G.J. Fleer, Macromol. 27, 4180 (1994)CrossRefGoogle Scholar
  34. 34.
    S.F. Edwards, Proc. Phys. Soc. 85, 613 (1965)MathSciNetCrossRefGoogle Scholar
  35. 35.
    P.G. deGennes, Rep. Prog. Phys. 32, 187 (1969)Google Scholar
  36. 36.
    P.G. deGennes, Macromol. 15, 492 (1982)Google Scholar
  37. 37.
    S.W. Sides, G.H. Fredrickson, J. Chem. Phys. 121, 4974 (2004)CrossRefGoogle Scholar
  38. 38.
    M.W. Matsen, Eur. Phys. J. E 21, 199 (2006)CrossRefGoogle Scholar
  39. 39.
    D.M. Cooke, A.C. Shi, Macromol. 39, 6661 (2006)CrossRefGoogle Scholar
  40. 40.
    S. Yang, H. Tan, D. Yan, E. Nies, A.C. Shi, Phys. Rev. E 75, 061803 (2007)CrossRefGoogle Scholar
  41. 41.
    C.E. Woodward, J. Forsman, Phys. Rev. Lett. 100, 098301 (2008)CrossRefGoogle Scholar
  42. 42.
    K.G. Honnell, C.K. Hall, J. Chem. Phys. 95, 4481 (1991)CrossRefGoogle Scholar
  43. 43.
    J. Forsman, C.E. Woodward, Macromol. 39, 1269 (2006)CrossRefGoogle Scholar
  44. 44.
    C.E. Woodward, J. Forsman, Phys. Rev. E 74, 010801 (2006)CrossRefGoogle Scholar
  45. 45.
    M. Turesson, J. Forsman, T. Åkesson, Phys. Rev. E 76, 021801 (2007)CrossRefGoogle Scholar
  46. 46.
    M. Turesson, C.E. Woodward, T. Åkesson, J. Forsman, J. Phys. Chem. B 112, 9802 (2008)CrossRefGoogle Scholar
  47. 47.
    B.V. Derjaguin, Kolloid Zeits. 69, 155 (1934)Google Scholar
  48. 48.
    J. Forsman, C.E. Woodward, J. Chem. Phys. 131, 044903 (2009)CrossRefGoogle Scholar
  49. 49.
    J. van der Gucht, N.A.M. Besseling, J. van Male, M.A. Cohen-Stuart, J. Chem. Phys. 113, 2886 (2000)CrossRefGoogle Scholar
  50. 50.
    J. Forsman, C.E. Woodward, M. Trulsson, J. Phys. Chem. B 115, 4606 (2011)CrossRefGoogle Scholar
  51. 51.
    J.Z. Wu, T. Jiang, D.E. Jiang, Z.H. Jin, D. Henderson, Soft Matter 7(23), 11222 (2011)CrossRefGoogle Scholar
  52. 52.
    I. Krossing, J.M. Slattery, C. Daguenet, P.J. Dyson, A. Oleinikova, H. Weingartner, J. Am. Chem. Soc. 128(41), 13427 (2006)CrossRefGoogle Scholar
  53. 53.
    M.V. Fedorov, A.A. Kornyshev, Chem. Rev. 114(5), 2978 (2014)CrossRefGoogle Scholar
  54. 54.
    N.V. Plechkova, K.R. Seddon, Chem. Soc. Rev. 37(1), 123 (2008)CrossRefGoogle Scholar
  55. 55.
    R.D. Rogers, K.R. Seddon, Science 302(5646), 792 (2003)CrossRefGoogle Scholar
  56. 56.
    D. Zhao, M. Wu, Y. Kou, E. Min, Catal Today 74(1), 157 (2002)CrossRefGoogle Scholar
  57. 57.
    R.P. Swatloski, S.K. Spear, J.D. Holbrey, R.D. Rogers, J. Am. Chem. Soc. 124(18), 4974 (2002)CrossRefGoogle Scholar
  58. 58.
    G. Wei, Z. Yang, C. Chen, Anal. Chim. Acta 488(2), 183 (2003)CrossRefGoogle Scholar
  59. 59.
    M. Turesson, R. Szparaga, K. Ma, C.E. Woodward, J. Forsman, Soft Matter 10(18), 3229 (2014)CrossRefGoogle Scholar
  60. 60.
    D. Bedrov, O. Borodin, Z. Li, G.D. Smith, J. Phys. Chem. B 114(15), 4984 (2010)CrossRefGoogle Scholar
  61. 61.
    G. Feng, P.T. Cummings, J. Phys. Chem. Lett. 2(22), 2859 (2011)CrossRefGoogle Scholar
  62. 62.
    G. Feng, D.E. Jiang, P.T. Cummings, J. Chem. Theory Comput. 8(3), 1058 (2012)CrossRefGoogle Scholar
  63. 63.
    G. Feng, S. Li, J.S. Atchison, V. Presser, P.T. Cummings, J. Phys. Chem. C 117(18), 9178 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Theoretical ChemistryChemical CentreLundSweden
  2. 2.School of Physical Environmental and Physical Sciences University CollegeUniversity of New South WalesKensingtonAustralia

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