Ideal linear-chain polymers with fixed angular momentum

The statistical mechanics of a linear noninteracting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This result is then compared to simulations done with a large number of noninteracting rigid links at fixed angular momentum. The simulation agrees with the theory up to finite-size corrections. The simulations are also used to investigate the anisotropic nature of a spinning polymer. We find universal scaling of the polymer size along the direction of the angular momentum, as a function of rescaled angular momentum.

Figure 1

Plot of $\frac{R_g^2}{N{l}^2}$ along with simulation results using a chain length $N=128$. The inset is a section from $L^{\prime }=5.5$ to 7 showing the exact solution as a solid line along with results from simulations done with $N=32$ (farthest from line) and $N=64$.

Figure 2

Plot of $P\left(L^{\prime }\right)$, with clear non-Gaussian behavior for high $L^{\prime }.$

Figure 3

Plot of the deviations in $R_g^2$ as a function of chain size $N$. The dashed line is the best-fit curve with $\alpha =0.436$.

Figure 4

Plot of the simulated radius of gyration in the direction of angular momentum as a function of rescaled $L$, for chain sizes $N=32$, 64, and 128.