CHARGED POLYMERS

We have recently developed a new scaling theory for polyelectrolyte solution rheology. The theory is intriguing because it simultaneously explains three anomalous observations in the literature. The first is the empirical Fuoss Law for the viscosity of salt-free polyelectrolytes, which predicts that viscosity scales as the square root of concentration. Secondly, the relaxation time () of polyelectrolytes is predicted to decrease as concentration (c) increases (relaxation time varies inversely with the square root of concentration). Both predictions are in semi-quantitative agreement with experiments, and are predicted to hold when the polyelectrolyte chains overlap each other, but are not yet entangled. The third explained observation is the fact that this semidilute unentangled regime spans 3-4 decades of polymer concentration.

The fact that this overlapping but unentangled regime is much more important for charged polymer solutions than for uncharged polymer solutions is explained by two important aspects of the configuration of polyelectrolyte chains in solution. Owing to charge repulsion, the dilute configuration is rod-like, making the overlap concentration very low. Also, the charge repulsion is screened as the chains overlap, causing the size of the polyelectrolyte (determined by its end-to-end distance, R) to shrink rapidly with concentration, R~c-1/4 .This shrinking defers the entanglement concentration to a concentration much greater than the overlap concentration.

Our current work focusses on quantitative testing of the predictions of this scaling theory. Membrane osmometry and conductivity measurements are used to unambiguously determine the charge on the chain and the amount of salt present in the solutions. Steady shear rheometry determines both the viscosity and the relaxation time. Figure 1 shows the shear rate dependence of viscosity for several solutions of sulfonated polystyrene with M=1.2 x 106. The viscosity is the low shear rate limit, and the relaxation time is the reciprocal of the shear rate where shear thinning starts. Our results indicate quantitative agreement for viscosity over a part of the concentration range covered (see Figure 2), but the viscosity is systematically above the predictions for nearly two decades of concentration. Similarly, the relaxation time decreases more strongly with concentration ( ~c-1/2 is predicted, whereas, ~c-4/5 is observed). Clearly, these systems are rich with new physics that we are just beginning to explore!


Figure 1

Figure 2

Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research.
 

PUBLICATIONS

  1. L. Leibler, M. Rubinstein and R.H. Colby "Dynamics of Reversible Networks" Macromolecules, 24, 4701 (1991).
     
  2. L. Leibler, M. Rubinstein and R.H. Colby "Dynamics of Telechelic Ionomers. Can Polymers Diffuse Large Distances Without Relaxing Stress?" J. Phys II France, 3, 1581 (1993).
     
  3. M. Rubinstein, R.H. Colby and A.V. Dobrynin "Dynamics of Semidilute Polyelectrolyte Solutions" Phys. Rev. Lett., 73 , 2776 (1994).
     
  4. A.V. Dobrynin, R.H. Colby and M. Rubinstein "Scaling Theory of Polyelectrolye Solutions" Macromolecules, 28, 1859 (1995).
     
  5. M. Rubinstein, R.H. Colby, A.V. Dobrynin and J.F. Joanny "Elastic Modulus and Equilibrium Swelling of Polyelectrolyte Gels" Macromolecules, 29, 398 (1996).
      
  6. D.C. Boris and R.H. Colby "Shear Viscosity of Polyelectrolyte Solutions," in Proceedings of The XIIth International Congress on Rheology (A. Ait-Kadi, J.M. Dealy, D.F. James and M.C. Williams, editors) Canadian Rheology Group (Quebec City, 1996), p. 256.
     
  7. R.H. Colby, D.C. Boris, W.E. Krause and J.S. Tan "Polyelectrolyte Conductivity" J. Polym. Sci., Polym. Phys. Ed., 35, 2951 (1997).
     
  8. R.H. Colby, X.Zheng, M.Rafailovich, J. Sokolov, D.G. Peiffer, S.A. Schwarz, Y. Strzhemechny and D. Nguyen "Dynamics of lightly Sulfonated Polystyrene Ionomers" Phys. Rev. Lett., 81, 3876 (1998).
     
  9. D.C. Boris and R.H. Colby "Rheology of Sulfonated Polystyrene Solutions" Macromolecules, 31, 5746 (1998).
     
  10. A.J. Konop and R.H. Colby, "Role of Condensed Counterions in the Thermodynamics of Surfactant Micelle Formation with and without Oppositely Charged Polyelectrolytes" Langmuir, 15, 58 (1999).
     
  11. A.J. Konop and R. H. Colby, "Polyelectrolyte Charge Effects on Solution Viscosity of Poly(acrylic acid)," Macromolecules, 32, 2803 (1999).
      
  12. J.R. Gillmor, R.W. Connelly, R.H. Colby and J.S. Tan "Effect of Sodium Poly(styrene sulfonate) on Thermoreversible Gelation of Gelatin," J. Polym. Sci., Polym. Phys. Ed., 37, 2287 (1999).
     
  13. W.E. Krause, J.S. Tan and R.H. Colby,"Semidilute Solution Rheology of Polyelectrolytes with No Added Salt," J. Polym. Sci., Polym. Phys. Ed., 37, 3429 (1999).
     
  14. L. Bromberg, M. Temchenko and R.H. Colby, "Interactions among Hydrophobically Modified Polyelectrolytes and Surfactants of the Same Charge," Langmuir, 16, 2609 (2000).
     
  15. R.H. Colby, "Polyelectrolyte Interactions with Surfactants and Proteins", in Proceedings of the XIIIth International Congress on Rheology, 1, 414 (2000).
     
  16. N. Plucktaveesak, L.E. Bromberg and R.H. Colby, "Effects of Surfactants on the Gelation Threshold Temperature in Aqueous Solutions of a Hydrophobically Modified Prolyelectroyte", in Proceedings of the XIIIth International Congress on Rheology, 3, 307 (2000).
     
  17. R.H. Colby, N. Plucktaveesak and L.E. Bromberg, "Critical Incorporation Concentration of Surfactants added to Micellar Solutions of Hydrophobically Modified Polyelectrolytes of the Same Charge", Langmuir, 17, 2937 (2001).
     
  18. W. E. Krause, E. G. Bellomo and R. H. Colby, "Rheology of Sodium Hyaluronate under
    Physiological Conditions", Biomacromolecules, 2, 65 (2001).
     
  19. F. Bordi, R. H. Colby, C. Cametti, L. DeLorenzo and T. Gili, "Electrical Conductivity of Polyelectrolyte Solutions in the Semidilute and Concentrated Regime" The Role of Counterion Condensation", J. Phys. Chem B, 106, 6887 (2002).
     
  20. F. Bordi, C. Cametti, T. Gili and R. H. Colby, "Dielectric Relaxations in Aqueous Polyelectrolyte Solutions: A Scaling Approach and the Role of the Solvent Quality Parameter", Langmuir, 18, 6404 (2002).
     
  21. F. Bordi, C. Cametti, J. S. Tan, D. C. Boris, W. E. Krause, N. Plucktaveesak and R. H. Colby, "Determination of Polyelectrolyte Charge and Interaction with Water Using Dielectric Spectroscopy", Macromolecules 35(18), 7031 (2002).
     
  22. N. Plucktaveesak, A. J. Konop and R. H. Colby, "Viscosity of Polyelectrolyte Solutions with Oppositely Charged Surfactant" J. Phys. Chem. B 107, 8166 (2003).
     
  23. L. Guo, R. H. Colby, C. P. Lusignan and T. H. Whitesides, "Kinetics of Triple Helix
    Formation in Semidilute Gelatin Solutions", Macromolecules 36, 9999 (2003).
     
  24. L. Guo, R. H. Colby, C. P. Lusignan and A. M. Howe, "Physical Gelation of Gelatin
    Studied with Rheo-Optics", Macromolecules 36, 10009 (2003).

  25. A. V. Dobrynin, R. H. Colby and M. Rubinstein, "Polyampholytes", J. Polym. Sci., Polym. Phys. 42, 3513 (2004).
     
  26. E. Sauvage, D. A. Amos, B. Antalek, K. M. Schroeder, J. S. Tan, N. Plucktaveesak and R. H. Colby, "Amphiphilic Maleic Acid-Containing Alternating Copolymers 1. Dissociation Behavior and Compositions", J. Polym. Sci., Polym. Phys. 42, 3571 (2004).

  27. E. Sauvage, N. Plucktaveesak, R. H. Colby, D. A. Amos, B. Antalek, K. M. Schroeder and J. S. Tan, "Amphiphilic Maleic Acid-Containing Alternating Copolymers 2. Dilute Solution Characterization by Light Scattering, Intrinsic Viscosity and PGSE NMR Spectroscopy", J. Polym. Sci., Polym. Phys. 42, 3584 (2004).

    28.
  28. E. Di Cola, N. Plucktaveesak, T. A. Waigh, R. H. Colby, J. S. Tan, W. Pyckhout-Hintzen and R. K. Heenan, "Structure and Dynamics in Aqueous Solutions of Amphiphilic Sodium Maleate-Containing Alternating Copolymers" Macromolecules 37, 8457 (2004).


  29. F. Bordi, C. Cametti and R. H. Colby, "Dielectric Spectroscopy and Conductivity of Polyelectrolyte Solutions", J. Phys.: Condens. Matt. 16, R1423 (2004).
     
  30. F. Bordi, C. Cametti, T. Gili, S. Sennato, S. Zuzzi, S. Dou and R.H. Colby, "Conductometric properties of linear polyelectrolytes in poor solvent condition: The necklace model" J. Chem. Phys. 122, 234906 (2005)
     
  31. F. Bordi, C. Cametti, T. Gili, S. Sennato, S. Zuzzi, S. Dou and R.H. Colby, "Solvent quality influence on the dielectric properties of polyelectrolyte solutions: A scaling approach" Phys. Rev. E 72, 031806 (2005)
     
  32. Shihai Zhang, Shichen Dou, Ralph H. Colby and James Runt, "Glass transition and ionic conduction in plasticized and doped ionomers" J. Non-Crys. Solids 351, 2825 (2005)
     
  33. R. J. Klein, S. Zhang, S. Dou, B. H. Jones, R. H. Colby and J. Runt, Modeling Electrode Polarization in Dielectric Spectroscopy: Ion Mobility and Mobile Ion Concentration of Single-Ion Polymer Electrolytes, J. Chem. Phys. 124, 144903 (2006).
     
  34. S. Dou and R. H. Colby, Charge Density Effects in Polyelectrolyte Solution Rheology, J. Polym. Sci., Polym. Phys. 44, 2001 (2006).
     
  35. F. Bordi, C. Cametti, S. Sennato, S. Zuzzi, S. Dou and R. H. Colby, Dielectric Scaling in Polyelectrolyte Solutions with Different Solvent Quality in the Dilute Concentration Regime, Phys. Chem. Chem. Phys. 8, 3653 (2006).
     
  36. S. Dou, S. Zhang, R. J. Klein, J. Runt and R. H. Colby, Synthesis and Characterization of Poly(ethylene glycol)-based Single-Ion Conductors, Chem. Mat. 18, 4288 (2006).