Photonic crystals in biology - NanoTR-VI

Poster Session, Thursday, June 17Theme F686 - N1123A Rheological Model For Determining Degree Of Exfoliation In Polymer/Clay Nanocomposites1 Hossein Ebrahimiand Ahmad Ramazani S. 21 Islamic Azad University ( South Tehran Branch), Tehran,Iran2 Department of Chemical and Petroleum Engineering, Sharif University of Technology,Tehran,IranAbstract— We present a conformational based model for prediction rheological behavior of nanocomposite. The EVA/clayand EVA/PE/clay nanocomposites with different nanoclay contents were prepared by melt mixing. The model calculations forthe start-up viscosity are compared with experimental result. Then, a relation for determining degree of exfoliation ofnanoparticles in polymeric matrix was derived.The degree of exfoliation, intercalation and dispersion ofpolymer/clay nanocomposites traditionally characterized byX-ray diffraction (XRD) and transmission electronmicroscopy(TEM); while both are effective tools, they are stilllimited in that they only probe a small volume of the sampleand can be costly for routine characterization ofnanocomposites. Further, XRD nor TEM alone cannotaccuracy describe the level of clay dispersion and polymernanocomposite structure. Rheologyical investigation givesimportant information about the structure formation during thesynthesis of polymer/clay nanocomposites.In this study, a conformational based model for predictionrheological behavior of nanocomposite was presented. Theconformational rheological models relate the stress tensor tothe molecular conformation change concept during andso it seems that these models can be extendedphenomenologically for a system, which includes polymer andparticles. In this model two micro structural state variablecalled conformation tensor c and orientation tensor show thestate of deformation of polymer molecules and orientation ofparticles during flow, respectively.For a non-compressible polymer fluid with amicrostructure represented by a second order symmetrictensor, c, the Poisson bracket formalism leads to the followingequations for the time evolution of c [1, 2 and 3]:c1 . . 1 ( . cc. ) ( cc. ) :t2 2c2( c. )cIn wich is a fourth-order tensor, called the mobilitytensor, is the rate of strain tensor, is the vorticity tensor , stress tensor, and is the Helmholtz free energy.To derive the time evolution equations for orientation tensor , nanoparticles will be modeled inside the framework of thetime evolution equation for the fiber orientation tensor byFolgar and Tucker, 1984; Advani and Tucker 1987[4]:d a , 1 1 . . . . ( a a. . a a. 2 : aa) 2cI ( 0a)dt2 , 2 , ,.in wich and are respectively the rate-of-strain tensor andthe vorticity tensor. is related to the aspect ratio of the fibers.( =[(l/d) 2 - 1]/[(l/d) 2 +1], l and d represent respectively thefiber length and diameter, 0 is a constant equal to 3 for a 3Dorientation and 2 for a 2D orientation introduced in order tosatisfy the constraint tr a = 1. C I is the interaction coefficientparameter. With some modification in the above equations,we derive a new class of equations that can analyze the effectsof different parameters to model. This model developed forintercalate and exfoliated systems.To prove the model, the EVA/clay and EVA/PE/claynanocomposites with different nanoclay contents wereprepared by melt mixing. The model calculations for the startupviscosity are reasonably in agreement with theexperimental results both in exfoliated and intercalatedsystems. Comparing experimental results and modelcalculation was derived a relation that determineapproximately degree of exfoliation of system.*Corresponding author: ebrahimi_h@yahoo.com[1] H. Eslami, A. Ramazani S. A., H. A. Khonakdar, Macromol. TheorySimul. 12, 524-530(2004).[2] A. Ramazani, M.Grmela, A. Kadi, J. Rheol. 3, 51(1999).[3] A. Ramazani, A. Ait-Kadi, M. Grmela, J. Non-Newtonian Fluid Mech. 73,241(1997).[4] J.S. Cintra, Jr and C.L. Tuker III, J. Rheol. 39(6), 1095, (1995).[5] R. Guenette and M. Grmela, J. Non-Newtonian Fluid Mech. 45,187(1992).[6] M. Grmela, P. J. Carreau, J. Non-Newtonian Fluid Mech. 23, 271(1987).[7] A.N.Beris,B.J.Edwards, Thermodynamics of flowing systems, 1 st edition,OxfordUniversityPress,NewYork(1994).[8] R.B. Bird, R.C. Armstrong and O. Hassager, Dynamics of PolymericLiquids: vol. 1, Fluid Mechanics, 2 st edition, Wiley-VCH, New York (1987).[9] A. Ramazani, A. Ait-Kadi, M. Grmela, J. Non-Newtonian Fluid Mech.73,241(1997).[10] M. Rajabian, C. Dubois, M. Grmela and P.J. Carreau, Rheol. Acta 47,701 (2008).6th Nanoscience and Nanotechnology Conference, zmir, 2010 723