Polymers in a Vacuum

In a variety of situations, isolated polymer molecules are found in a vacuum, and here we examine their properties. Angular momentum conservation is shown to significantly alter the average size of a chain and its conservation is only broken slowly by thermal radiation. For an ideal chain, the time autocorrelation for monomer position oscillates with a period proportional to chain length. The oscillations and damping are analyzed in detail. Short-range repulsive interactions suppress oscillations and speed up relaxation, but stretched chains still show damped oscillatory correlations.

Figure 1

The variation of the size of a chain versus its angular momentum for a ideal ring chain (increasing curve). The log of the thermal distribution for different angular momenta (decreasing curve).

Figure 2

The autocorrelation function $g(t)$ as defined in Eq. (2) for a chain of 128 monomers. Double horizontal lines give the very small error bars. The inset shows the beginning of the plot at a higher magnification, where the initial linear increase and cusps are apparent. The time unit is 1,000.

Figure 3

The scaled autocorrelation function $g(t)/⟨R^2⟩$ versus $t/N^p$, for three chain lengths, $N=32$, 64, and 128 with short-range repulsive interactions. The inset shows $g(t)$ for an $N=32$ chain with equal charges at both ends that cause it to stretch. Here $l=1$.