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Critical to Mean Field Crossover in Polymer Blends

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Phase Behaviour of Polymer Blends

Part of the book series: Advances in Polymer Science ((POLYMER,volume 183))

Abstract

Crossover phenomena due to thermal composition fluctuations play a multifarious role in polymer blends. This is demonstrated in this article by describing results from small angle scattering experiments in particular with neutrons. Scattering methods are a direct tool to measure the strength and correlation length of composition fluctuations. We will review the effects of thermal fluctuations in binary (A/B) polymer blends under various conditions of external temperatures and pressures and additives, such as non-selective solvents and (A-B) diblock copolymers, and will give an interpretation with the corresponding crossover theories. General conclusions are that the effects from thermal composition fluctuations have to be more seriously considered in polymer blends and that the more sophisticated crossover theories are needed for a precise determination of the Flory--Huggins interaction parameter and the phase boundaries. In addition, we discuss observations of crossover to other universality classes such as the 3D-Ising case, namely the transition to the renormalized Ising case when the composition of a third component starts to fluctuate and to the isotropic Lifshitz critical behavior when an (A-B) diblock copolymer is added.

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References

  1. Utracki LA (1989) Polymer Alloys and Blends. Hanser, München

    Google Scholar 

  2. Flory PJ (1971) Principles of Polymer Chemistry. Cornell University Press, Ithaca, New York

    Google Scholar 

  3. deGennes PG (1979) Scaling Concepts in Polymer Physics, chap x. Cornell University Press, Ithaca, New York

    Google Scholar 

  4. Binder K (1994) Adv Polym Sci 112:181

    Google Scholar 

  5. Schwahn D, Mortensen K (2000) Thermal Composition Fluctuations in Polymer Blends studied with Small Angle Neutron Scattering. In: Brown W, Mortensen K (eds) Scattering in Polymeric and Colloidal Systems. Gordon & Breach Science Publishers, Amsterdam

    Google Scholar 

  6. Higgins JS, Benoit H (1994) Polymers and Neutron Scattering. Clarendon Press, Oxford

    Google Scholar 

  7. Roe RJ (2000) Methods of X-Ray and Neutron Scattering in Polymer Science. Oxford University Press, New York, Oxford

    Google Scholar 

  8. Koningsveld R, Chermin HAG, Gordon M (1970) Proc R Soc London Ser A 319:331

    Google Scholar 

  9. For example: Uzunov DI (1993) Theory of Critical Phenomena. World Scientific, Singapore

    Google Scholar 

  10. v. Sengers J (1994) In: Kiran E, Sengers J, Levelt MH (eds) Supercritical fluids: Fundamentals for application. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  11. Lifshitz M , Dudowicz J, Freed KF (1994) J Chem Phys 100:3957

    Article  Google Scholar 

  12. Dudowicz J, Lifshitz M, Freed KF, Douglas JF (1993) J Chem Phys 99:4804

    Article  Google Scholar 

  13. Fredrickson GH, Ganesan V, Drolet F (2002) Macromolecules 35:16

    Article  Google Scholar 

  14. Wang ZG (2002) J Chem Phys 117:481

    Article  Google Scholar 

  15. Bates FS, Fredrickson GH (1994) Macromolecules 27:1065; Fredrickson GH, Liu AJ, Bates FS (1994) Macromolecules 27:2503

    Article  Google Scholar 

  16. Sariban A, Binder K (1987) J Chem Phys 86:5859

    Article  Google Scholar 

  17. Deutsch HP, Binder K (1993) J Phys II (France) 3:1049

    Article  Google Scholar 

  18. Schwahn D, Mortensen K, Yee-Madeira H (1987) Phys Rev Lett 58:1544

    Article  PubMed  Google Scholar 

  19. Schwahn D, Mortensen K, Springer T, Yee-Madeira H, Thomas R (1987) J Chem Phys 87:6078

    Article  Google Scholar 

  20. Bates FS, Rosedale JH, Stepanek P, Lodge TP, Wiltzius P, Fredrickson GH, Hjelm RP (1990) Phys Rev Lett 65:1893

    Article  PubMed  Google Scholar 

  21. Hair DW, Hobbie EK, Douglas J, Han CC (1992) Phys Rev Lett 68:2476

    Article  PubMed  Google Scholar 

  22. Hair DW, Hobbie EK, Nakatani AI, Han CC (1992) J Chem Phys 96:9133

    Article  Google Scholar 

  23. Chou B, Ying Q, Linliu K, Xie P, Gao T, Li Y, Nose T, Okada M (1992) Macromolecules 25:7382

    Article  Google Scholar 

  24. Janßen S, Schwahn D, Springer T (1992) Phys Rev Lett 68:3180

    Article  PubMed  Google Scholar 

  25. Meier G, Momper B, Fischer EW (1992) J Chem Phys 97:5884

    Article  Google Scholar 

  26. Theobald W, Meier G (1995) Phys Rev E 51:5776

    Article  Google Scholar 

  27. Belyakov MY, Kiselev SB (1992) Physica A 190:75

    Article  Google Scholar 

  28. Anisimov MA, Kiselev SB, Sengers JV, Tang S (1992) Physica A 188:487

    Article  Google Scholar 

  29. Anisimov MA, Povodyrev AA, Kulikov VD, Sengers JV (1995) Phys Rev Lett 75:3146

    Article  PubMed  Google Scholar 

  30. Anisimov MA (2000) J Phys: Condens Matter 12:A451

    Google Scholar 

  31. Schwahn D, Meier G, Mortensen K, Janßen S (1994) J Phys II 4:837; Meier G, Schwahn D, Mortensen K, Janßen S (1993) Europhys Lett 22:577

    Google Scholar 

  32. Schwahn D, Frielinghaus H, Willner L (2002) J Chem Phys 116:2229

    Article  Google Scholar 

  33. Patterson D, Robard A (1978) Macromolecules 11:690

    Article  Google Scholar 

  34. Janßen S, Schwahn D, Mortensen K, Springer T (1993) Macromolecules 26:5587

    Article  Google Scholar 

  35. Hammouda B, Bauer BJ (1995) Macromolecules 29:4505

    Article  Google Scholar 

  36. Schwahn D, Schmackers T, Mortensen K (1995) Phys Rev E 52:R1288

    Article  Google Scholar 

  37. Frielinghaus H, Schwahn D, Willner L (2001) Macromolecules 34:1751

    Article  Google Scholar 

  38. Schwahn D, Frielinghaus H, Mortensen K, Almdal K (2001) Macromolecules 34:1694

    Article  Google Scholar 

  39. Frielinghaus H, Schwahn D, Dudowicz J, Freed KF, Foreman KW (2001) J Chem Phys 114:5016

    Article  Google Scholar 

  40. Frielinghaus H, Schwahn D, Willner L, Freed KF (2002) J Chem Phys 116:2241

    Article  Google Scholar 

  41. Lefebvre AA, Lee JH, Balsara NP, Hammouda B, Krishnamoorti, Kumar S (1999) Macromolecules 32:5460

    Article  Google Scholar 

  42. Beiner M, Fytas G, Meier G, Kumar SK (1998) Phys Rev Lett 81:594; (2002) J Chem Phys 116:1185

    Article  Google Scholar 

  43. Schwahn D, Frielinghaus H, Mortensen K, Almdal K (2001) Macromolecules 34:1694

    Article  Google Scholar 

  44. Miyashita N, Nose T (1995) Macromolecules 28:4433

    Article  Google Scholar 

  45. Nose T, Miyashita N (2000) Critical Behavior in Polymer Blend Solutions. In: Brown W, Mortensen K (eds) Scattering in Polymeric and Colloidal Systems. Gordon & Breach Publishers, Amsterdam

    Google Scholar 

  46. Bates FS, Maurer W, Lodge TP, Schulz MF, Matsen MW, Almdal K, Mortensen K (1995) Phys Rev Lett 75:4429

    Article  PubMed  Google Scholar 

  47. Bates FS, Maurer WW, Lipic PM, Hillmyer MA, Almdal K, Mortensen K, Fredrickson GH, Lodge TP (1997) Phys Rev Lett 79:849

    Article  Google Scholar 

  48. Schwahn D, Mortensen K, Frielinghaus H, Almdal K (1999) Phys Rev Lett 82:5056

    Article  Google Scholar 

  49. Schwahn D, Mortensen K, Frielinghaus H, Almdal K, Kielhorn L (2000) J Chem Phys 112:5454

    Article  Google Scholar 

  50. Hillmyer MA, Maurer WW, Lodge TP, Bates FS, Almdal K (1999) J Phys Chem 103:4814

    Google Scholar 

  51. Morkved TL, Chapman BR, Bates FS, Lodge TP, Stepanek P, Almdal K (1999) Faraday Discuss 112:335

    Article  Google Scholar 

  52. Pipich V, Schwahn D, Willner L (2004) Physica B 350:e897

    Google Scholar 

  53. Brazovskii SA (1975) JETP 41:8552

    Google Scholar 

  54. Holyst R, Schick M (1992) J Chem Phys 96:7728

    Article  Google Scholar 

  55. Broseta D, Fredrickson GH (1990) J Chem Phys 93:2927

    Article  Google Scholar 

  56. Kielhorn L, Muthukumar M (1997) J Chem Phys 107:5588

    Article  Google Scholar 

  57. Kudlay A, Stepanow S (2002) Macromol Theory Simul 11:16

    Article  Google Scholar 

  58. Alefeld B, Schwahn D, Springer T (1989) Nucl Inst in Physical Research A 274:210

    Article  Google Scholar 

  59. Schwahn D, Meier G, Springer T (1991) J Appl Cryst 24:568

    Article  Google Scholar 

  60. Wignall GD, Bates FS (1987) J Appl Cryst 20:28

    Article  Google Scholar 

  61. Schwahn D, Hahn K, Streib J, Springer T (1987) J Chem Phys 93:8383

    Article  Google Scholar 

  62. Tabulated values in (1992) Neutron News 2:29

    Google Scholar 

  63. Flory PJ (1970) Disc Faraday Soc 49:7

    Article  Google Scholar 

  64. Schwahn D, Willner L (2002) Macromolecules 35:239

    Article  Google Scholar 

  65. Schwahn D, Mortensen K, Janssen S (1994) Phys Rev Lett 73:1452

    Article  PubMed  Google Scholar 

  66. Le Guillon JC, Zinn-Justin J (1992) Phys Rev Lett 39:95; Zinn-Justin J (1981) J Physique 42:783; LeGuillon JC, Zinn-Justin J (1987) J Physique 48:19

    Google Scholar 

  67. Melnichenko YB, Anisimov MA, Povodyrev AA, Wignall GD, Sengers JV, Van Hook WA (1997) Phys Rev Lett 79:5266

    Article  Google Scholar 

  68. Melnichenko YB, Wignall GD, Schwahn D (2002) Phys Rev E 65:061802

    Article  Google Scholar 

  69. ten Brinke G, Karasz FE, MacKnight WJ (1983) Macromolecules 16:1827

    Article  Google Scholar 

  70. Paul DR, Barlow JW (1984) Polymer 25:487

    Article  Google Scholar 

  71. Dudowicz J, Freed KF (2000) Macromolecules 33:3467

    Article  Google Scholar 

  72. Dudowicz J, Freed KF (2000) Macromolecules 33:9777

    Article  Google Scholar 

  73. Bates FS, Wignall GD, Koehler WC (1985) Phys Rev Lett 55:2425

    Article  PubMed  Google Scholar 

  74. Graessley WW, Krisnamoorti K, Balsara NP, Fetters LJ, Lohse DJ, Schulz DN, Sissano JA (1993) Macromolecules 26:1137

    Article  Google Scholar 

  75. Jinnai H, Hasegawa H, Hashimoto T, Han CC (1992) Macromolecules 25:6078

    Article  Google Scholar 

  76. Tang H, Freed KF (1991) Macromolecules 24:958

    Article  Google Scholar 

  77. Coleman MM, Serman CJ, Bhagwagar DE, Painter PC (1990) Polymer 31:1187

    Article  Google Scholar 

  78. For example: Ma SK (1982) Statistical Mechanics. World Scientific, Singapore, p 264

    Google Scholar 

  79. Fredrickson GH, Leibler L (1989) Macromolecules 22:1238

    Article  Google Scholar 

  80. Broseta D, Leibler L, Joanny JF (1987) Macromolecules 20:1935

    Article  Google Scholar 

  81. Schwahn D, Takeno H, Willner L, Hasegawa H, Jinnai H, Hashimoto T, Imai M (1994) Phys Rev Lett 73:3427

    Article  PubMed  Google Scholar 

  82. Anisimov A, Voronel AV, Gorodetskii EE (1971) Sov Phys JETP 33:605

    Google Scholar 

  83. Fisher ME (1968) Phys Rev 176:257

    Article  Google Scholar 

  84. Pipich V, Schwahn D, Willner (2005) Phys Rev Lett 94:117801

    Article  PubMed  Google Scholar 

  85. Müller M, Gompper G (2002) Phys Rev E 66:041805

    Article  Google Scholar 

  86. Nicoll JF, Tuthill GF, Chang TS, Stanley HE (1977) Physica 86–88B:618

    Google Scholar 

  87. Kielhorn L, Muthukumar M (1999) J Chem Phys 110:4079

    Article  Google Scholar 

  88. Narayanan T, Kumar A, Gopal ESR (1990) Phys Lett A144:371; Prafulla BV, Narayanan T, Kumar A (1992) Phys Rev A 45:1266

    Google Scholar 

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  1. Institut für Festkörperforschung, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany

    Dietmar Schwahn

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  1. Dietmar Schwahn
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Correspondence to Dietmar Schwahn .

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K. F. Freed

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Schwahn, D. Critical to Mean Field Crossover in Polymer Blends. In: Freed, K.F. (eds) Phase Behaviour of Polymer Blends. Advances in Polymer Science, vol 183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b135882

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