STRUCTURED FLUIDS

In many cases, polymer dynamics are controlled exclusively by the motion of individual chains. In these cases, on time scales greater than the time it takes for molecules to diffuse a distance equal to their size, the material flows like a simple liquid. However, when there is large-scale structure present in the liquid (such as in liquid crystalline polymers or in surfactant solutions), viscoelastic response is evident on time scales much greater than the molecular diffusion time.

An example of this phenomenon is shown in Fig. 1, which shows oscillatory shear data for a liquid crystalline polymer. In this experiment, the frequency of mechanical oscillation is varied, so as to probe the response of the polymer on various time scales. The arrow indicates the frequency corresponding to the reciprocal of the molecular diffusion time. In the nematic phase (solid curves), the viscoelastic response is liquid-like at frequencies smaller than the frequency for molecular diffusion (reflected in the fact that the loss modulus G" dominates the response at low frequencies).

Figure 1

In contrast, the smectic phase (open symbols) is still highly viscoelastic on time scales much longer than the frequency for molecular diffusion (since the storage modulus G' is comparable to the loss modulus G'' at low frequencies. The smectic structure gives rise to the viscoelastic response of this polymer on long time scales.

Another example of a structured fluid is the diblock copolymer. At low temperatures the diblock copolymer forms a lamellar structure because the two blocks have sufficient repulsive energies. Fig. 2 shows the apparent viscosity in steady shear as a function of shear rate, and also the magnitude of the complex viscosity as a function of frequency, in the lamellar phase after extensive alignment in steady shear. The empirical Cox-Merz rule equates the complex viscosity at a given frequency to the apparent viscosity at a shear rate which is numerically equal to the frequency; apparently, the Cox-Merz rule applies to structured fluids, provided that the structure remains identical in both experiments. Once again, the arrow indicates the frequency corresponding to the reciprocal of the molecular diffusion time. The diblock copolymer is viscoelastic over time scales four orders of magnitude longer than this molecular diffusion time.

Figure 2

We are in the process of trying to relate the defect structure to the viscoelastic response of these fluids. When quenched to a glassy state, the defect structure of these polymeric structured fluids can be probed by electron microscopy and various scattering techniques.

PUBLICATIONS

1. R.H. Colby, S. McNamee, A. Delvin and C.K Ober "Chemical Heterogeneity in LC Polyesters," in 'Liquid Crystalline Polymers' (C.K. Ober and R.A. Weiss, eds.) ACS Symp. Ser., 435, 220 (1990).
    
2. E. Hall, C.K. Ober, E.J. Kramer, R.H. Colby, J.R. Gillmor and G. Galli, "Melt Diffusion in Model Liquid Crystalline Polymers," in 'Complex Fluids,' (E.B. Sirota, D. Weitz, T. Witten, and J. Israelachvilli, eds.) Materials Research Society (Pittsburgh, 1992), p. 113.
    
R.H. Colby "Viscoelasticity of Structured Fluids," in Theoretical and Applied Rheology, (P. Moldenaers and R. Keunings, eds.) Vol. 2, Elsevier (New York, 1992), p. 519.
 
4. K.A. Koppi, M. Tirrell, F.S. Bates, K. Almdal and R.H. Colby "Lamellae Orientation in Dynamically Sheared Diblock Copolymer Melts," J. Phys. 2 France, 2, 1941 (1992).
    
5. R.H. Colby, J.R. Gillmor, G. Galli, M. Laus, C.K. Ober and E. Hall, "Linear Viscoelasticity of Side Chain Liquid Crystal Polymers" Liquid Crystals, 13, 233 (1993). Errata 15, 563 (1993).
    
6. E. Hall, C.K. Ober, E.J. Kramer, R.H. Colby and J.R. Gillmor, "Diffusion and Melt Viscosity of a Main-Chain Liquid Crystalline Polyether," Macromolecules, 26, 3764 (1993).
    
7. J.R. Gillmor, R.H. Colby, E. Hall and C.K. Ober, "Viscoelastic Properties of a Main-Chain Liquid Crystalline Polyether," J. Rheology, 38, 1623 (1994).
    
8. R.H. Colby "Block Copolymer Dynamics," Curr. Opin. Coll. Int. Sci., 1, 454 (1996).
    
9. R.H. Colby, C.K. Ober, J.R. Gillmor, R.W. Connelly, T. Duong, G. Galli and M. Laus, "Smectic Rheology," Rheol. Acta, 46, 498 (1997).
    
10. S.R. Clingman, G. Mao, C.K. Ober, R.H. Colby, M. Brehmer, R. Zentel, M. Bignozzi, M. Laus, A. Angeloni, and J.R. Gillmor, "Effect of Polymer Architecture on Self-Diffusion of LC Polymers," J. Polym. Sci., Polym. Phys. Ed., 37, 405 (1999).
     
11. S. Ge, L. Guo, M.H. Rafailovich, J. Sokolov, D.G. Peiffer, S.A. Schwarz, R.H. Colby and W.D. Dozier, "Surface-Induced Ordering in Graft Copolymer Thin Films," Langmuir, 15, 2911 (1999).
     
12. L. Guo, R.H. Colby and E.L. Paulsen, "Rheology of Pluronic Solutions mixed with a Non-Ionic Diol Surfactant, in Proceedings of the XIIIth International Congress on Rheology, 3, 304 (2000).
     
13. R.H. Colby, L.M. Nentwich, S.R. Clingman and C.K. Ober, "Defect-mediated creep of structured materials", Europhys. Lett., 54, 269 (2001).
     
14. R.H. Colby, "Melt Rheology of Block Copolymers", in Encyclopedia of Materials: Science and Technology, p. 727, Elsevier (2001).
     
15. L. Guo, R.H. Colby, M.Y. Lin and G.P. Dado, "Micellar Structure Changes Changes in Aqueous Mixtures of Non-Ionic Surfactants:, J. Rheol., 45, 1223 (2001).
     
16. N. Plucktaveesak, A. J. Konop and R. H. Colby, "Viscosity of Polyelectrolyte Solutions with Oppositely Charged Surfactant" J. Phys. Chem. B 107, 8166 (2003).



17. M.-P. Nieh, S. K. Kumar, R. H. Fernando, R. H. Colby and J. Katsaras, "Effect of the Hydrophilic Size on the Structural Phases of Aqueous Nonionic Gemini Surfactant Solutions" Langmuir 20, 9061 (2004).
    
    
18. R. Bandyopadhyay, D. Liang, R. H. Colby, J. L. Harden and R. L. Leheny, "Enhanced Elasticity and Soft Glassy Rheology of a Smectic in a Random Porous Environment" Phys. Rev. Lett. 94, 107801 (2005).