Rotational and translational relaxation times of quasi-elastic and rigid dumbbells elastically bound to polymer network junctions

• Published in: Polymer science. Series A, Chemistry, physics Chemistry, physics, 2006-05, Vol.48 (5), p.498-508
• Main Authors: Gotlib, Yu. Ya, Lezova, A. A., Torchinskii, I. A.
• Format: Article
• Language: English
• Subjects: Dynamic tests; Equations of motion; Mathematical analysis; Mathematical models; Networks; Projection; Relaxation time; Translational motion
• ISSN: 0965-545X; 1555-6107
• DOI: 10.1134/S0965545X06050075

The dynamics of a rigid rod located between fixed junctions of a polymer network is studied. Three approaches are used in the solution of this problem. The first is based on the viscoelastic model, where a rigid rod is simulated by an elastic dumbbell with a fixed average length; the second includes solution of equations of motion for projections of the rigid rod using the Lagrangian multipliers under the constraint condition; and the third involves solution of the diffusion equation in the presence of an elastic potential. The second and third approaches allow calculation of orientational relaxation times for rod projections under the action of a strong orienting field. The dependences of the relaxation times of orientational and translational motions of the rod projections on the coordinate axes and the orientational relaxation times of mean-square rod projections on the model parameters (the distances between fixed polymer network junctions, the length of the rigid rod, and the elastic coefficient characterizing the binding between the rod and the network) are found.