Sharma, Rati and Cherayil, Binny J (2010) Polymer melt dynamics: Microscopic roots of fractional viscoelasticity. In: Physical Review E, 81 (2, Par).
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The rheological properties of polymer melts and other complex macromolecular fluids are often successfully modeled by phenomenological constitutive equations containing fractional differential operators. We suggest a molecular basis for such fractional equations in terms of the generalized Langevin equation (GLE) that underlies the renormalized Rouse model developed by Schweizer [J. Chem. Phys. 91, 5802 (1989)]. The GLE describes the dynamics of the segments of a tagged chain under the action of random forces originating in the fast fluctuations of the surrounding polymer matrix. By representing these random forces as fractional Gaussian noise, and transforming the GLE into an equivalent diffusion equation for the density of the tagged chain segments, we obtain an analytical expression for the dynamic shear relaxation modulus G(t), which we then show decays as a power law in time. This power-law relaxation is the root of fractional viscoelastic behavior.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to The American Physical Society.|
|Department/Centre:||Division of Chemical Sciences > Inorganic & Physical Chemistry|
|Date Deposited:||24 Mar 2010 09:02|
|Last Modified:||19 Sep 2010 05:57|
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