Knots can spontaneously form in polymers. How knotting affects polymer behavior depends on polymer knotting probability, p knot. An intriguing result about p knot in recent studies is that p knot exhibits a non-monotonic dependence on the bending stiffness and is maximized at L p ≈ 8a, where L p is the persistence length and a is the hardcore diameter of the monomer. In this work, we propose a new explanation for the non-monotonic behavior of p knot based on the fact that polymer knots are typically localized. We find that the non-monotonic behavior results from the competition of a special entropic effect arising from the variation in the sizes of localized knots and an effect arising from the variation in the free-energy cost of forming a localized knot on a fragment of a polymer. The first effect refers to the situation that shrinking the knot size for a polymer with a fixed length essentially increases the number of “slots” for knot formation and enhances p knot. Based on this explanation, we derive an approximate analytic equation that captures the non-monotonic behavior of p knot. Overall, this work provides new insights into p knot beyond previous studies, in particular, unifying the effect of the knot size on p knot and the effect of the polymer length on p knot. The results can be applied to understand DNA knotting, considering that the effective L p/a for DNA can be widely varied by the ionic strength.
Neopentyl glycol (NPG) is a promising next-generation environment-friendly refrigerant, because NPG can release huge latent heat during a solid-phase transition from a plastic crystal phase to a true crystal phase. However, NPG has a very low thermal conductivity, which restricts its applications. In this paper, we investigated the mechanisms of thermal transport of an NPG crystal by performing atomistic molecular dynamics (MD) simulations. Our simulation results obtained the thermal conductivities of 0.50, 0.32, and 0.33 W m–1 K–1 at 298.15 K along the a*, b*, and c* directions, respectively, which agree with the experimental results ranging from 0.15 to 0.42 W m–1 K–1. The anisotropy of the thermal conductivity along the three directions is caused by the hydrogen-bond network in NPG. We reveal the reasons for the low thermal conductivity: the large gap between the low-frequency region and the high-frequency region in the phonon spectrum and the ultrashort phonon mean free path (MFP). The effective MFPs are only 1.28, 5.47, and 2.22 nm along the a*, b*, and c* directions, respectively. In addition, we find that the thermal conductivity is insensitive to the temperature from 218.15 to 298.15 K, probably because the ultrashort MFP is insensitive to the temperature. Furthermore, we find that vacancy defects affect the thermal conductivity in an intriguing manner. When the defect concentrations are 2 and 4%, the thermal conductivities along the b* and c* directions increase abnormally with the increase in temperature, which is related to the re-orientation of hydroxyl groups upon the change in temperature. Overall, this work reveals the molecular mechanism of the thermal transport of NPG, which should provide valuable insights in enhancing the thermal conductivity of NPG for the application as an environment-friendly refrigerant.
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