Skip to main content Accessibility help
×
Home
  • Print publication year: 2011
  • Online publication date: August 2012

16 - Phenomenology

Summary

Introduction

In previous chapters, a range of experiments on aspects of polymer solution dynamics, from electrophoretic mobility to single-chain diffusion to linear viscoelasticity, has been treated(1). The previous chapter described results that were found with each method. What do these types of measurement tell us about how polymer molecules move through solution? The answers to this question come in a substantial number of parts and pieces, best treated separately before being assembled into final conclusions. There are undoubtedly other parts and pieces that might have been discussed, such as the consequences of changing the relative size of matrix and probe polymers, or the consequences of polymer topology. This chapter stays with answers most central to our purpose.

Comparison with scaling and exponential models

We began in Section 1.2 by observing that the large number of theoretical models could with a modest number of exceptions be partitioned into two major phenomenological classes, based on whether themodels predicted scaling (power-law) or exponential dependences of transport coefficients on polymer concentration, molecular weight, or other properties. What do the data say about the relative merit of these classes of theoretical model?

An obvious first question is whether the precision of experimental measurement, as viewed through the lens of our data analysis methods, is adequate to say whichmodels are acceptable. Can we distinguish between power laws and stretched exponentials? The answer is unambiguously in the affirmative.

References
[1] The author has sought to achieve completeness, but is sufficiently conscious of his fallibility to assume that some significant method has been overlooked.
[2] J., Skolnick and A., Kolinski. Dynamics of dense polymer systems. Computer simulations and analytic theories. Adv. Chem. Phys., 78 (1989), 223–278.
[3] T. P., Lodge, N. A., Rotstein, and S., Prager. Dynamics of entangled polymer liquids. Do entangled chains reptate?Adv. Chem. Phys., 79 (1990), 1–132.
[4] H., Tao, T. P., Lodge, and E. D., von Meerwall. Diffusivity and viscosity of concentrated hydrogenated polybutadiene solutions. Macromolecules, 33 (2000), 1747–1758.
[5] V. E., Dreval, A. Ya., Malkin, and G. O., Botvinnik. Approach to generalization of concentration dependence of zero-shear viscosity in polymer solutions. J. Polymer Sci.: Polymer Phys. Ed., 11 (1973), 1055–1066.
[6] P.-G., GennesScaling Concepts in Polymer Physics, Third Printing, (Ithaca, NY: Cornell UP, 1988).
[7] W. W., Graessley. The entanglement concept in polymer rheology. Adv. Polym. Sci., 16 (1974), 1–179.
[8] C., Konak and W., Brown. Coupling of density to concentration fluctuations in concentrated solutions of polystyrene in toluene. J. Chem. Phys., 98 (1993), 9014–9017.
[9] T., Koch, G., Strobl, and B., Stuehn. Light-scattering study of fluctuations in concentration, density, and local anisotropy in polystyrene-dioxane mixtures. Macromolecules, 25 (1992), 6255–6261.
[10] J., Roovers. Concentration dependence of the relative viscosity of star polymers. Macromolecules, 27 (1994), 5359–5364.
[11] M., Antonietti, T., Pakula, and W., Bremser. Rheology of small spherical polystyrene microgels: A direct proof for a new transport mechanism in bulk polymers besides reptation. Macromolecules, 28 (1995), 4227–4233.
[12] M., Sedlak. Real-time monitoring of the origination of multimacroion domains in a polyelectrolyte solution. J. Chem. Phys., 122 (2005), 151102 1–3, and references therein.
[13] M., Delsanti, J., Chang, P., Lesieur, and B., Cabane. Dynamic properties of aqueous dispersions of nanometric particles near the fluid–solid transition. J. Chem. Phys., 105 (1996), 7200–7209.
[14] X., Shi, R. W., Hammond, and M. D., Morris. DNAconformational dynamics in polymer solutions above and below the entanglement limit. Anal. Chem., 67 (1995), 1132–1138.
[15] D. M., Heuer, S., Saha, and L. A., Archer. Electrophoretic dynamics of large DNA stars in polymer solutions and gels. Electrophoresis, 24 (2003), 3314–3322.
[16] A., Einstein. Ueber die von der molekularkinetischen Theorie der Warme geforderte Bewegung von in ruhenden Flussigkeiten suspendierten Teilchen. Annalen der Physik, 322 (1905), 549–560.
[17] L., Mitnik, L., Salome, J. L., Viovy, and C., Heller. Systematic study of field and concentration effects in capillary electrophoresis of DNAin polymer solutions. J. Chromatogr. A, 710 (1995), 309–321.
[18] C. W., Oseen. Hydrodynamik. Akademische Verlagsgesellschaft, M. B. H. Leipzig. 1927.
[19] G. J., Kynch. The slow motion of two or more spheres through a viscous fluid. J. Fluid Mech., 5 (1959), 193–208.
[20] J. G., Kirkwood and J., Riseman. The intrinsic viscosities and diffusion constants of flexible macromolecules in solution. J. Chem. Phys., 16 (1948), 565–573.
[21] J. C., Crocker. Measurement of the hydrodynamic corrections to the Brownian motion of two colloidal spheres. J. Chem. Phys., 106 (1997), 2837–2840.
[22] J.-C., Meiners and S. R., Quake. Direct measurement of hydrodynamic cross correlations between two particles in an external potential. Phys. Rev. Lett., 82 (1999), 2211–2214.
[23] P. M., Cotts and J. C., Selser. Polymer–polymer interactions in dilute solution. Macromolecules, 23 (1990), 2050–2057.
[24] M., Tokuyama and I., Oppenheim. On the theory of concentrated hard-sphere suspensions. Physica A, 216 (1995), 85–119.
[25] J. C., Crocker, M. T., Valentine, E. R., Weeks, et al.Two-point microrheology of inhomogeneous soft materials. Phys. Rev. Lett., 85 (2000), 888–891.
[26] M. L., Gardel, M. T., Valentine, J. C., Crocker, A. R., Bausch, and D. A., Weitz. Microrheology of entangled F-actin solutions. Phys. Rev. Lett., 91 (2003), 158302 1–4.
[27] D. T., Chen, E. R., Weeks, J. C., Crocker, et al.Rheological microscopy: local mechanical properties from microrheology. Phys. Rev. Lett., 90 (2003), 108301 1–4.
[28] J. G., Kirkwood. Theory of solutions of molecules containing widely separated charges with special application to zwitterions. J. Chem. Phys., 2 (1934), 351–361.
[29] J. E., Martin. Configurational diffusion in semidilute solutions. Macromolecules, 19 (1986), 1278–1281.
[30] B. H., Zimm. Dynamics of polymer molecules in dilute solution: Viscosity, flow birefringence and dielectric loss. J. Chem. Phys., 24 (1956), 269–278.
[31] P. E., Rouse Jr., A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys., 21 (1953), 1272–1280.
[32] A. R., Altenberger, J. S., Dahler, and M., Tirrell. On the theory of dynamic screening in macroparticle solutions. Macromolecules, 21 (1988), 464–469.
[33] C. W. J., Beenakker and P., Mazur. Diffusion of spheres in a concentrated suspension – resummation of many-body hydrodynamic interactions. Physics Lett. A, 98 (1983), 22–24.
[34] P. G., Gennes. Dynamics of entangled polymer solutions. II. Inclusion of hydrodynamic interactions. Macromolecules, 9 (1976), 594–598.
[35] K. F., Freed and S. F., Edwards. Polymer viscosity in concentrated solutions. J. Chem. Phys., 61 (1974), 3626–3633.
[36] K. F., Freed and A., Perico. Consideration on the multiple scattering representation of the concentration dependence of the viscoelastic properties of polymer systems. Macromolecules, 14 (1981), 1290–1298.
[37] J., Won, C., Onyenemezu, W. G., Miller, and T. P., Lodge. Diffusion of spheres in entangled polymer solutions: a return to Stokes–Einstein behavior. Macromolecules, 27 (1994), 7389–7396.
[38] T., Chang, C. C., Han, L. M., Wheeler, and T. P., Lodge. Comparison of diffusion coefficients in ternary polymer solutions measured by dynamic light scattering and forced Rayleigh scattering. Macromolecules, 21 (1988), 1870–1872.
[39] A., Goodman, Y., Tseng, and D., Wirtz. Effect of length, topology, and concentration on the microviscosity and microheterogeneity of DNA solutions. J. Mol. Bio., 323 (2002), 199–215.
[40] M. G., Brereton and A., Rusli. Fluctuation–dissipation relations for polymer systems. I. The molecular weight dependence of the viscosity. Chemical Physics, 26 (1977), 23–28.
[41] J., Gao and J. H., Weiner. Excluded-volume effects in rubber elasticity. 4. Nonhydro-static contribution to stress. Macromolecules, 22 (1989), 979–984.
[42] A. E., Likhtman. Whither tube theory: From believing to measuring. J. Non-Newtonian Fluid Mech. (2009), 128–161.
[43] S. A., Rice and P., Gray. The Statistical Mechanics of Simple Liquids: an Introduction to the Theory of Equilibrium and Non-equilibrium Phenomena, (New York: Interscience, 1965).