Abstract
The current state of understanding for solution conformations of flexible polymers and their linear viscoelastic response is reviewed. Correlation length, tube diameter, and chain size of neutral polymers in good solvent, neutral polymers in θ-solvent, and polyelectrolyte solutions with no added salt are compared as these are the three universality classes for flexible polymers in solution. The 1956 Zimm model is used to describe the linear viscoelasticity of dilute solutions and of semidilute solutions inside their correlation volumes. The 1953 Rouse model is used for linear viscoelasticity of semidilute unentangled solutions and for entangled solutions on the scale of the entanglement strand. The 1971 de Gennes reptation model is used to describe linear viscoelastic response of entangled solutions. In each type of solution, the terminal dynamics, reflected in the terminal modulus, chain relaxation time, specific viscosity, and diffusion coefficient are reviewed with experiment and theory compared. Overall, the agreement between theory and experiment is remarkable, with a few unsettled issues remaining.
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References
Adam M, Delsanti M (1983) J Phys France 44:1185
Adam M, Delsanti M (1984) J Phys France 45:1513
Agarwal PK, Garner RT, Graessley WW (1987) J Polym Sci, Polym Phys 25:2095
Alexander-Katz A, Leibler L (2009) Soft Matter 5:2198
Berry GC, Fox TG (1968) Adv Polym Sci 5:261
Bohdanecky M, Kovar J (1982) Viscosity of polymer solutions. Elsevier, New York
Bordi F, Cametti C, Colby RH (2004) J Phys: Condens Matt 16:R1423
Bordi F, Cametti C, Tan JS, Boris DC, Krause WE, Plucktaveesak N, Colby RH (2002) Macromolecules 35:7031
Boris DC, Colby RH (1998) Macromolecules 31:5746
Chen SP, Archer LA (1999) J Polym Sci, Polym Phys 37:825
Colby RH, Rubinstein M (1990) Macromolecules 23:2753
Colby RH, Boris DC, Krause WE, Dou S (2007) Rheol Acta 46:569
Colby RH, Fetters LJ, Funk WG, Graessley WW (1991) Macromolecules 24:3873
Cohen J, Priel Z, Rabin Y (1988) J Chem Phys 88:7111
Cotton JP, Nierlich M, Boué F, Daoud M, Farnoux B, Jannink G, Duplessix R, Picot C (1976) J Chem Phys 65:1101
Daoud M, Cotton JP, Farnoux B, Jannink G, Sarma G, Benoit H, Duplessix R, Picot C, de Gennes PG (1975) Macromolecules 8:804
de Gennes PG (1971) J Chem Phys 55:572
de Gennes PG (1976a) Macromolecules 9:587
de Gennes PG (1976b) Macromolecules 9:594
de Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, Ithaca
de Gennes PG, Pincus P, Velasco RM, Brochard F (1976) J Phys (Paris) 37:1461
DiCola E, Plucktaveesak N, Waigh TA, Colby RH, Tan JS, Pyckhout-Hintzen W, Heenan RK (2004) Macromolecules 37:8457
Dobrynin AV, Rubinstein M (2005) Prog Polym Sci 30:1049
Dobrynin AV, Colby RH, Rubinstein M (1995) Macromolecules 28:1859
Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford University Press, New York
Donnan PG, Guggenheim EA (1934) Z Phys Chem 162:364
Dou S, Colby RH (2006) J Polym Sci Polym Phys 44:2001
Dou S, Colby RH (2008) Macromolecules 41:6505
Dragan S, Mihai M, Ghimici L (2003) Eur Polym J 39:1847
Drifford M, Dalbiez JP (1984) J Phys Chem 88:5368
Edwards SF (1966) Proc Phys Soc 88:265
Essafi W, Lafuma F, Baigl D, Williams CE (2005) Europhys Lett 71:938
Fernandez Prini R, Lagos AE (1964) J Polym Sci A-2:2917
Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, New York
Flory PJ, Daoust H (1957) J Polym Sci 25:429
Fuoss RM (1948) J Polym Sci 3:603
Fuoss RM (1951) Disc Faraday Soc 11:125
Fuoss RM, Strauss UP (1948) J Polym Sci 3:246
Geissler E, Mallam S, Hecht AM, Rennie AR, Horkay F (1990) Macromolecules 23:5270
Graessley WW (1974) Adv Polym Sci 16:1
Graessley WW (1980) Polymer 21:258
Graessley WW (2003) Polymeric liquids and networks: structure and properties. Garland Science, New York
Graessley WW (2008) Polymeric liquids and networks: dynamics and rheology. Garland Science, New York
Hair DW, Amis EJ (1989) Macromolecules 22:4528
Hara M, Wu JL, Lee AH (1988) Macromolecules 21:2214
Higgins JS, Benoit HC (1994) Polymers and neutron scattering. Oxford University Press, New York
Higgins JS, Roots JE (1985) J Chem Soc Faraday Trans 81:757
Hodgson DF, Amis EJ (1991) J Chem Phys 94:4581
Johnson RM, Schrag JL, Ferry JD (1970) Polym J 1:742
Jousset S, Bellissent H, Galin JC (1998) Macromolecules 31:4520
Kaji K, Urakawa H, Kanaya T, Kitamaru R (1988) J Phys France 49:993
Katchalsky A (1971) Pure Appl Chem 26:327
Kim MW, Peiffer DG (1988) Europhys Lett 5:321
King JS, Boyer W, Wignall GD, Ullman R (1985) Macromolecules 18:709
Krause WE, Tan JS, Colby RH (1999) J Polym Sci, Polym Phys 37:3429
Kulicke WM, Kniewske R (1984) Rheol Acta 23:75
Kulicke WM, Griebel Th, Bouldin M (1991) Polymer News 16:39
Lodge TP, Schrag JL (1982) Macromolecules 15:1376
Marcus RA (1955) J Chem Phys 23:1057
McKee MG, Hunley MT, Layman JM, Long TE (2006) Macromolecules 39:575
McKee MG, Wilkes GL, Colby RH, Long TE (2004) Macromolecules 37:1760
Nierlich M, Boue F, Lapp A, Oberthur R (1985) J Phys (Paris) 46:649
Nierlich M, Williams CE, Boué F, Cotton JP, Daoud M, Farnoux B, Jannink G, Picot C, Moan M, Wolff C, Rinaudo M, de Gennes PG (1979) J Phys (Paris) 40:701
Onogi S, Masuda T, Kitagawa K (1970) Macromolecules 3:109
Onogi S, Kimura S, Kato T, Masuda T, Miyanaga N (1966) J Polym Sci C15:381
Oosawa F (1971) Polyelectrolytes. Marcel Dekker, New York
Oostwal MG, Blees MH, de Bleijser J, Leyte JC (1993) Macromolecules 26:7300
Pearson DS (1987) Rubb Chem Tech 60:439
Pedersen JS, Schurtenberger P (2004) J Polym Sci, Polym Phys 42:3081
Pfeuty P (1978) J Phys (Paris) Colloq C2:149
Plucktaveesak N, Konop AJ, Colby RH (2003) J Phys Chem B 107:8166
Richter D, Farago B, Butera R, Fetters LJ, Huang JS, Ewen B (1993) Macromolecules 26:795
Rosser RW, Nemoto N, Schrag JL, Ferry JD (1978) J Polym Sci, Polym Phys 16:1031
Rouse PE (1953) J Chem Phys 21:1272
Rubinstein M, Colby RH (2003) Polymer physics. Oxford University Press, New York
Semenov AN (1988) J Phys France 49:175, 1353
Strauss UP, Smith EH (1953) J Am Chem Soc 75:6186
Tao H, Huang C, Lodge TP (1999) Macromolecules 32:1212
Takahashi A, Kato N, Nagasawa M (1970) J Phys Chem 74:944
Takahashi Y, Iio S, Matsumoto N, Noda I (1996) Polym Int 40:269
Takahashi Y, Yamaguchi M, Sakakura D, Noda I (1991) Nihon Reoroji Gakkaishi 19:39
Takahashi Y, Sakakura D, Wakutsu M, Yamaguchi M, Noda I (1992) Polym J 24:987
Teraoka I (2002) Polymer solutions. Wiley, New York
Terayama H, Wall FT (1955) J Polym Sci 16:357
van’t Hoff JH (1887) Z Physik Chemie 1:481
Xu Z, Qian R, Hadjichristidis N, Fetters LJ (1984) J China Univ Sci Tech 14:228
Zebrowski BE, Fuller GG (1985) J Rheol 29:943
Zimm BH (1956) J Chem Phys 24:269
Acknowledgements
The author thanks the National Science Foundation for support of this research, through DMR-0705745. William Graessley and Michael Rubinstein provided many useful comments on this paper. David Boris, Wendy Krause, Nop Plucktaveesak and Shichen Dou are the students that have worked on polyelectrolyte solutions and the author thanks them for their hard work.
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Dedicated to the memory of Professor Pierre-Gilles de Gennes; gourou magnifique et inspiration éternelle.
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Colby, R.H. Structure and linear viscoelasticity of flexible polymer solutions: comparison of polyelectrolyte and neutral polymer solutions. Rheol Acta 49, 425–442 (2010). https://doi.org/10.1007/s00397-009-0413-5
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DOI: https://doi.org/10.1007/s00397-009-0413-5