Effect of Inertia on Linear Viscoelasticity of Harmonic Dumbbell Model

Abstract

The overdamped (inertialess) dumbbell model is widely utilized to study rheological properties of polymers or other soft matters. In most cases, the effect of inertia is merely neglected because the momentum relaxation is much faster than the bond relaxation. We theoretically analyze the effect of inertia on the linear viscoelasticity of the harmonic dumbbell model. We show that the momentum and bond relaxation modes are kinetically coupled and the inertia can affect the bond relaxation if the momentum relaxation is not sufficiently fast. We derive an overdamped Langevin equation for the dumbbell model, which incorporates the weak inertia effect. Our model predicts the bond relaxation dynamics with the weak inertia effect correctly. We discuss how the weak inertia affects the linear viscoelasticity of a simple harmonic dumbbell model and the Rouse model.

arXiv comment17 pages, 3 figures, to appear in Nihon Reoroji Gakkaishi (J. Soc. Rheol. Jpn.)

References in corpus (2)

• Relaxation Functions of Ornstein-Uhlenbeck Process with Fluctuating Diffusivity
• Kinetic models for polymers with inertial effects

Cited by in corpus (6)

• A reduction scheme for coupled Brownian harmonic oscillators
• Linear Viscoelasticity of Dumbbells Interacting via Gaussian Soft-Core Potential
• Dissipation in Langevin Equation and Construction of Mobility Tensor from Dissipative Heat Flow
• Stress Tensor of Single Rigid Dumbbell by Virtual Work Method
• Linear Response Theory of Scale-Dependent Viscoelasticity for Overdamped Brownian Particle Systems
• Finite-inertia effects in Langevin dynamics of a lopsided elastic dumbbell using exponential-time differencing schemes