The elastic trumbbell model for dynamics of stiff chains

Abstract

The dynamical behavior of the elastic trumbbell model was discussed. Two relaxation modes, the slowest one (λ₁) associated to rotation and the faster one (λ₂) to bending, dominate the relaxation spectrum of viscoelasticity and Kerr Effect. As the stiffness of the spring increases, the slowest relaxation mode Ψ₁ becomes dominant in the Kerr Effect case (K₁ ≫ K₂), and the decay curves fit nearly single exponentials if Z ≥ 0.75. This, however, does not mean that substantial bending is not present. The effect of bending is apparent in the fact that the end-over-end relaxation rate λ₁ is faster than the rigid rod limit λ_R (30% faster for Z = 0,75). Viscoelasticity, on the other hand, shows a large contribution from the internal bending mode Ψ₂ to the storage modulus G ^′_r . The bimodal character of the curve is more pronounced the stiffer the chain. Viscoelastic measurements of very stiff macromolecules (q/L > 2) are, however, difficult to perform. In most cases [6,7,21,22], however, the elastic trumbbell model has failed to reproduce the high frequency behavior of these semistiff molecules because higher bending modes appear to contribute [6] to the relaxation spectrum.

Previous theoretical work related to the dynamics of semi-stiff molecules used models that assumed small departures from rigid-body behavior [4,20,23]. Since most stiff molecules that have been investigated, on the other hand, possess 4 < λ₂/λ₁ < 15 (LMM is exceptionally rigid with λ₂/λ₁ ≈ 26), these models appear to be inadequate. It is clear that models with more degrees of freedom than the trumbbell must be tackled. The Kirkwood method that we have used here provides an exact treatment, but this method is too difficult for any but a few simple cases. A five beads model [24] (Pentabbell) is probably tractable with methods similar to the ones presented here. A different approach that it is being developed consists of performing dynamic simulations of multibead models [25,26]. Finally, the most challenging approach to this problem would be to solve the dynamics of the worm-like chain in the presence of external fields. Fixman [27] has recently proposed new ideas towards a solution of this problem.