Internal dissipation of a polymer

The dynamics of flexible polymer molecules are often assumed to be governed by hydrodynamics of the solvent. However there is considerable evidence that internal dissipation of a polymer contributes as well. Here we investigate the dynamics of a single chain in the absence of solvent to characterize the nature of this internal friction. We model the chains as freely hinged but with localized bond angles and threefold symmetric dihedral angles. We show that the damping is close but not identical to Kelvin damping, which depends on the first temporal and second spatial derivative of monomer position. With no internal potential between monomers, the magnitude of the damping is small for long wavelengths and weakly damped oscillatory time dependent behavior is seen for a large range of spatial modes. When the size of the internal potential is increased, such oscillations persist, but the damping becomes larger. However underdamped motion is present even with quite strong dihedral barriers for long enough wavelengths.

Figure 1

(Color online) Correlation functions for a freely hinged chain in a vacuum for $N=64$ for the lowest two modes, shown by the solid triangles. The line going through them are fits using Eq. (6).

Figure 2

(Color online) The parameters for fits of the time autocorrelation function, Eq. (6). to a damped harmonic oscillator are shown for a freely hinged chain with $N=256$. The upper line represents the mass $k^{2}M/K$ of each mode, and the lower curve represents that damping $\nu /K$.

Figure 3

(Color online) Time autocorrelation functions where bond angle is now restricted for $N=64$. Data for the first three modes is shown by the solid triangles. The lines going through it is a fit using Eq. (6).

Figure 4

(Color online) The parameters for fits of the time autocorrelation function, Eq. (6), to a damped harmonic oscillator are shown for the same data as in Fig. 3. The upper curve is a measure of the mass $k^{2}M/K$, and the lower curve is measure of the damping $\nu /K$.

Figure 5

(Color online) The distribution of dihedral bond angles for two different heights of the dihedral potential, $V_d=3$ (circles) and $V_d=4$ (triangles). Here $U_b=10$ and $N=64$.

Figure 6

(Color online) The natural logarithm of the dihedral angle distribution maximum to minimum as a function of potential amplitude $V_d$ with $U_b=10$.

Figure 7

(Color online) Time autocorrelation functions where bond angle and a dihedral potential for $N=64$, $U_b=10$. Data for the first three modes are shown by the solid triangles. The lines going through it is a fit using Eq. (6). (a) with $V_d=2$ and (b) with $V_d=3$.

Figure 8

(Color online) The damping as a function of mode number for a range of dihedral potentials with $N=64$. The bottom curve shown by the triangles is $V_d=0$, the next highest, $V_d=1$ (squares), then $V_d=2$ (diamonds), and $V_d=3$ (crosses).