×

A kinetic theory and benchmark predictions for polymer-dispersed, semi-flexible macromolecular rods or platelets. (English) Zbl 1208.82085

The paper proposes a hydrodynamic theory for homogeneous, incompressible mixtures of dilute polymer chains and nano-rods or nano-platelets, which take accounts of the polymer-particle surface interactions, the semi-flexibility of the nano-rods, and the conformational dynamics of flexible polymer chains. One first presents the kinetic theory for monodomains of PNCs (polymer-particulate nano-composites), then one derives a closure model for the blend of flexible polymer chains, and lastly one solves the closure model for equilibrium and sheared dynamics of the coupled rank 2, symmetric tensors for the polymer configuration and nano-particle orientation. The theory is developed with the Rouse free energy and transport equation.

MSC:

82D60 Statistical mechanics of polymers
35Q55 NLS equations (nonlinear Schrödinger equations)
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
76A05 Non-Newtonian fluids
76T30 Three or more component flows

Software:

AUTO; AUTO-07P
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Liquid Crystalline Polymers, Report of the Committee on Liquid Crystalline Polymers (1990), National Academic Press
[2] Brostow, W.; Dziemianowicz, T.; Hess, M.; Kosfeld, R., Blending of polymer liquid crystals with engineering polymers: the importance of phase diagrams, (Weiss, R. A.; Ober, C. K., Liquid Crystalline Polymers (1990), American Chemical Society: American Chemical Society Washington, DC), 402-415
[3] (Vaia, R.; Krishnamoorti, R., Polymer Nanocomposites (2001), American Chemical Society)
[4] Koo, J., (Polymer Nanocomposites: Processing, Characterization and Applications. Polymer Nanocomposites: Processing, Characterization and Applications, Nanoscience and Technology Series (2006), McGraw-Hill)
[5] (Crawford, G.; Zummer, S., Liquid Crystals in Complex Geometries Formed by Polymer and Porous Networks (1996), Taylor & Francis: Taylor & Francis London)
[6] Vaia, R.; Wagner, H. D., Framework for nanocomposites, Mater. Today, 7, 11, 32-37 (2004)
[7] Wagner, H. D.; Vaia, R., Nanocomposites: issues at the interface, Mater. Today, 7, 11, 38-42 (2004)
[8] R. Vaia, Polymer nanocomposites open a new dimension for plastics and composites, Report, 2005.; R. Vaia, Polymer nanocomposites open a new dimension for plastics and composites, Report, 2005.
[9] Vaia, R., Nanocomposites: remote-controlled actuators, Nat. Mater., 4, 6, 429-430 (2005)
[10] Winey, K.; Vaia, R., Polymer nanocomposites, MRS Bull., 32, 4, 314-322 (2007)
[11] Mirau, P.; Serres, J.; Jacobs, D.; Garrett, P.; Vaia, R., Structure and dynamics of surfactant interfaces in organically modified clays, J. Phys. Chem. B, 112, 34, 10544-10551 (2008)
[12] Dzenis, Y., Materials science: structural nanocomposites, Science, 319, 5862, 419-420 (2008)
[13] Meli, L.; Arceo, A.; Green, P. F., Control of the entropic interactions and phase behavior of athermal nanoparticle/homopolymer thin film mixtures, Soft Matter, 5, 3, 533-537 (2009)
[14] Rey, A.; Denn, M., Dynamical phenomena in liquid-crystalline materials, Annu. Rev. Fluid Mech., 34, 233-266 (2002) · Zbl 1047.76008
[15] Liu, A.; Fredrickson, G., Phase separation kinetics of rod/coil mixtures, Macromolecules, 29, 8000-8009 (1996)
[16] Muratov, C.; E, W., Theory of phase separation kinetics in polymer-liquid crystal systems, J. Chem. Phys., 116, 11, 4723-4734 (2002)
[17] Forest, M. G.; Wang, Q., Hydrodynamic theories for mixtures of polymers and rod-like liquid crystalline polymers, Phys. Rev. E, 72, 041805: 1-17 (2005)
[18] Hess, S., Fokker-Planck-equation approach to flow alignment in liquid crystals, Z. Naturforsch., 31a, 1034-1037 (1976)
[19] Doi, M.; Edwards, S. F., The Theory of Polymer Dynamics (1986), Oxford University Press: Oxford University Press UK
[20] Feng, J.; Sgalari, G.; Leal, L. G., A theory for flowing nematic polymers with orientational distortion, J. Rheol., 44, 5, 1085 (2000)
[21] Wang, Q., A hydrodynamic theory of nematic liquid crystalline polymers of different configurations, J. Chem. Phys., 116, 9120-9136 (2002)
[22] Dhont, J.; Briels, W., Stresses in inhomogeneous suspensions, J. Chem. Phys., 117, 8, 3992-3999 (2002)
[23] Dhont, J.; Briels, W., Inhomogeneous suspensions of rigid rods in flow, J. Chem. Phys., 118, 3, 1466-1478 (2003)
[24] Dhont, J.; Briels, W., Viscoelasticity of suspensions of long, rigid rods, Colloids Surf. A, 213, 131-156 (2003)
[25] Batchelor, G., The stress system in a suspension of force-free particles, J. Fluid Mech., 41, 3, 545-570 (1970) · Zbl 0193.25702
[26] Forest, M. G.; Wang, Q., Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows, Rheol. Acta, 42, 20-46 (2003)
[27] Bird, R.; Armstrong, R.; Hassager, O., Dynamics of Polymeric Liquids, vol. 2 (1987), John Wiley and Sons
[28] Rajabian, M.; Dubois, C.; Grmela, M., Suspensions of semiflexible fibers in polymeric fluids: rheology and thermodynamics, Rheologica Acta, 44, 5, 521-535 (2005)
[29] Eslami, H.; Grmela, M.; Bousmina, M., A mesoscopic rheological model of polymer/layered silicate nanocomposites, J. Rheol., 51, 6, 1189-1222 (2007)
[30] Khokhlov, A.; Semenov, A., Liquid-crystalline ordering in solutions of semiflexible macromolecules with rotational-isomeric flexibility, Macromolecules, 17, 2678-2685 (1984)
[31] Levine, A.; Lubensky, T., Two-point microrheology and the electrostatic analogy, Phys. Rev. E, 65, 11501 (2001)
[32] Chen, D.; Weeks, E.; Crocker, J.; Islam, M.; Verma, R.; Gruber, J.; Levine, A.; Lubensky, T.; Yodh, A., Phys. Rev. Lett., 90, 108301 (2003)
[33] Levine, A.; Lubensky, T., Response function of a sphere in a viscoelastic two-fluid medium, Phys. Rev. E, 63, 41510 (2001)
[34] Hohenegger, C.; Forest, M. G., Two-point microrheology: modeling protocols, Phys. Rev. E, 78, 031501 (2008)
[35] Wang, Q.; E, W.; Liu, C.; Zhang, P., Kinetic theories for flows of nonhomogeneous rodlike liquid crystalline polymers with a nonlocal intermolecular potential, Phys. Rev. E, 65, 5, 051504 (2002)
[36] Larson, R. G., Constitutive Equations for Polymer Melts and Solutions (1988), Butterworths: Butterworths Boston
[37] Forest, M. G.; Wang, Q., Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows, Rheol. Acta, 42, 20-46 (2003)
[38] Forest, M. G.; Wang, Q.; Zhou, R., Symmetries of the Doi kinetic theory for nematic polymers of finite and infinite aspect ratio: at rest and in linear flows, Phys. Rev. E, 66, 3, 031712 (2003)
[39] E.J. Doedel, B.E. Oldeman, AUTO-07P: continuation and bifurcation software for ordinary differential equations, Concordia University Montreal, Canada, 2009.; E.J. Doedel, B.E. Oldeman, AUTO-07P: continuation and bifurcation software for ordinary differential equations, Concordia University Montreal, Canada, 2009.
[40] Ozdilek, C.; Mendes, E.; Picken, S., Nematic phase formation of boehmite in polyamide-6 nanocomposites, Polymer, 47, 2189-2197 (2006)
[41] Pesin, Y. B., Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys, 32, 4, 55-114 (1977) · Zbl 0383.58011
[42] Forest, M. G.; Zhou, R.; Wang, Q., Chaotic boundaries of nematic polymers in mixed shear and extensional flows, Phys. Rev. Lett., 93, 8, 088301-088305 (2004)
[43] Forest, M. G.; Wang, Q.; Zhou, R., The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates, Rheol. Acta, 44, 1, 80-93 (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.