The thermophoresis of a linear polymer chain in a solvent is examined theoretically and is shown to be due to the action of two forces. The first one is Waldmannʼs thermophoretic force (stemming from the departure of the molecular-velocity distribution from Maxwellʼs equilibrium distribution), which here is extrapolated to a dense medium by using scaling considerations. The second force is due to the fact that the viscous friction varies with position owing to the temperature gradient, which brings a zeroth-order correction to the Stokes law of friction. The present scaling theory is compared with recent experiments and is found to account for: (i) the existence of both signs of the thermodiffusion coefficient; (ii) the absolute magnitude of the coefficient; (iii) the fact that it is independent of the chain length in the high-polymer limit; and (iv) the dependence on solvent viscosity. The variation of the coefficient for short chains is also examined.
@article{CRMECA_2011__339_5_349_0,
author = {Eric Bringuier},
title = {Thermophoresis of linear polymer chains},
journal = {Comptes Rendus. M\'ecanique},
pages = {349--354},
publisher = {Elsevier},
volume = {339},
number = {5},
year = {2011},
doi = {10.1016/j.crme.2011.03.013},
language = {en},
}
Eric Bringuier. Thermophoresis of linear polymer chains. Comptes Rendus. Mécanique, Volume 339 (2011) no. 5, pp. 349-354. doi : 10.1016/j.crme.2011.03.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.03.013/
[1] Diffusion, thermodiffusion, and thermal diffusion of polystyrene in solution, J. Polymer Sci., Volume 57 (1962), pp. 227-239
[2] Characterization of thermal diffusion in polymer solutions: Dependence on polymer and solvent parameters, J. Polymer Sci. B, Volume 27 (1989), pp. 1317-1332
[3] Determination of thermodiffusion parameters from thermal field-flow fractionation retention data (W. Köhler; S. Wiegand, eds.), Thermal Nonequilibrium Phenomena in Fluid Mixtures, Springer, Berlin, 2002, pp. 250-284
[4] From small molecules to high polymers: Investigation of the crossover of thermal diffusion in dilute polystyrene solutions, Macromol., Volume 41 (2008), pp. 6205-6208
[5] Thermal diffusion of dilute polymer solutions: The role of chain flexibility and the effective segment size, Macromol., Volume 42 (2009), pp. 9147-9152
[6] Effet Soret des macromolécules flexibles, C. R. Acad. Sci. Paris (Sér. II), Volume 293 (1981), pp. 1025-1027
[7] On the reciprocal relations of Onsager, J. Chem. Phys., Volume 33 (1960), pp. 28-31
[8] On the notion of thermophoretic velocity, Phil. Mag., Volume 87 (2007), pp. 873-883
[9] Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, 1979
[10] Kinetic theory of colloid thermodiffusion, Physica A, Volume 385 (2007), pp. 9-24 The factor of 4 in the cross section in Eq. (22) should be removed
[11] Statistical Physics, Oxford, Pergamon, 1959 (Section 151)
[12] Mechanics of the Cell, Cambridge University Press, Cambridge, 2002 (Chapter 2)
[13] The Theory of Polymer Dynamics, Oxford University Press, Oxford, 1986 (Chapter 8)
[14] Simulation of a single polymer chain in solution by combining lattice Boltzmann and molecular dynamics, J. Chem. Phys., Volume 111 (1999), pp. 8225-8239
[15] Dynamics of entangled polymer solutions II: The Rouse model, Macromol., Volume 9 (1976), pp. 594-598
[16] Lattice Boltzmann simulations of soft-matter systems, Adv. Polymer Sci., Volume 14 (2007), pp. 259-264
[17] Stochastic Processes in Physics and Chemistry, Elsevier, Amsterdam, 2007 (Chapters 7 and 8)
[18] Colloid thermophoresis as a non-proportional response, J. Non-Equilib. Thermodyn., Volume 32 (2007), pp. 221-229 (selected papers from the 7th International Meeting on Thermodiffusion, Donostia-San Sebastián, Spain, June 2006)
[19] Zur Theorie der Radiometerkräfte, Z. Phys., Volume 27 (1924), pp. 1-4
[20] Theory of thermophoresis I: General considerations and mode-coupling analysis, Phys. Rev. A, Volume 27 (1983), pp. 1616-1634
[21] , Z. Naturforschung A (L. Talbot, ed.) (On the motion of spherical particles in nonhomogeneous gases, Rarefied Gas Dynamics), Volume 14, Academic, New York, 1959, pp. 589-599
[22] Anatomy of particle diffusion, Eur. J. Phys., Volume 30 (2009), pp. 1447-1470
[23] Simple procedure for correcting equations of evolution, Phys. Rev. E, Volume 56 (1997), pp. 5123-5127
[24] Colloidal Hydrodynamics, Academic, London, 1989
[25] Handbook of Chemistry and Physics, CRC, Boca Raton, 1995
[26] Statistical structure of soluble conjugated polymers, I. Conformation and electronic properties, J. Chem. Phys., Volume 92 (1990), pp. 4548-4556
Cité par Sources :
Commentaires - Politique
Internal degrees of freedom, molecular symmetry and thermodiffusion
Semen N. Semenov; Martin E. Schimpf
C. R. Méca (2011)