Diffusion of a ring polymer in good solution via the Brownian dynamics

Diffusion constants D_{R} and D_{L} of ring and linear polymers of the same molecular weight in a good solvent, respectively, have been evaluated through the Brownian dynamics with hydrodynamic interaction. The ratio $C=D_{R}/D_{L}$, which should be universal in the context of the renormalization group, has been estimated as $C= 1.11 \pm 0.01$ for the large-N limit. It should be consistent with that of synthetic polymers, while it is smaller than that of DNAs such as $C \approx 1.3$. Furthermore, the probability of the ring polymer being a nontrivial knot is found to be very small, while bond crossings may occur at almost all time steps in the present simulation that realizes the good solvent conditions.Comment: 11 pages, 4 figure

Universality in the diffusion of knots

We have evaluated a universal ratio between diffusion constants of the ring polymer with a given knot $K$ and a linear polymer with the same molecular weight in solution through the Brownian dynamics under hydrodynamic interaction. The ratio is found to be constant with respect to the number of monomers, $N$, and hence the estimate at some $N$ should be valid practically over a wide range of $N$ for various polymer models. Interestingly, the ratio is determined by the average crossing number ($N_{AC}$) of an ideal conformation of knotted curve $K$, i.e. that of the ideal knot. The $N_{AC}$ of ideal knots should therefore be fundamental in the dynamics of knots.Comment: 8 pages, 14 figure

On the Limits of Analogy Between Self-Avoidance and Topology-Driven Swelling of Polymer Loops

The work addresses the analogy between trivial knotting and excluded volume in looped polymer chains of moderate length, $N<N_0$, where the effects of knotting are small. A simple expression for the swelling seen in trivially knotted loops is described and shown to agree with simulation data. Contrast between this expression and the well known expression for excluded volume polymers leads to a graphical mapping of excluded volume to trivial knots, which may be useful for understanding where the analogy between the two physical forms is valid. The work also includes description of a new method for the computational generation of polymer loops via conditional probability. Although computationally intensive, this method generates loops without statistical bias, and thus is preferable to other loop generation routines in the region $N<N_0$.Comment: 10 pages, 5 figures, supplementary tex file and datafil

Phase separation in mixtures of colloids and long ideal polymer coils

Colloidal suspensions with free polymer coils which are larger than the colloidal particles are considered. The polymer-colloid interaction is modeled by an extension of the Asakura-Oosawa model. Phase separation occurs into dilute and dense fluid phases of colloidal particles when polymer is added. The critical density of this transition tends to zero as the size of the polymer coils diverges.Comment: 5 pages, 3 figure

Self-assembly in solution of a reversible comb-shaped supramolecular polymer

We report a single step synthesis of a polyisobutene with a bis-urea moiety in the middle of the chain. In low polarity solvents, this polymer self-assembles by hydrogen bonding to form a combshaped polymer with a central hydrogen bonded backbone and polyisobutene arms. The comb backbone can be reversibly broken, and consequently, its length can be tuned by changing the solvent, the concentration or the temperature. Moreover, we have proved that the bulkiness of the side-chains have a strong influence on both the self-assembly pattern and the length of the backbone. Finally, the density of arms can be reduced, by simply mixing with a low molar mass bis-urea

A near 90-year record of the evolution of El Morado Glacier and its proglacial lake, Central Chilean Andes

Using an ensemble of close- and long-range remote sensing, lake bathymetry and regional meteorological data, we present a detailed assessment of the geometric changes of El Morado Glacier in the Central Andes of Chile and its adjacent proglacial lake between 1932 and 2019. Overall, the results revealed a period of marked glacier down wasting, with a mean geodetic glacier mass balance of −0.39 ± 0.15 m w.e.a−1 observed for the entire glacier between 1955 and 2015 with an area loss of 40% between 1955 and 2019. We estimate an ice elevation change of −1.00 ± 0.17 m a−1 for the glacier tongue between 1932 and 2019. The increase in the ice thinning rates and area loss during the last decade is coincident with the severe drought in this region (2010–present), which our minimal surface mass-balance model is able to reproduce. As a result of the glacier changes observed, the proglacial lake increased in area substantially between 1955 and 2019, with bathymetry data suggesting a water volume of 3.6 million m3 in 2017. This study highlights the need for further monitoring of glacierised areas in the Central Andes. Such efforts would facilitate a better understanding of the downstream impacts of glacier downwasting

Topological effects in ring polymers: A computer simulation study

Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for chains with up to N=512 statistical segments at a volume fraction \Phi=0.5 and show that rings in the melt are more compact than gaussian chains. A careful finite size analysis of the average ring size R \propto N^{\nu} yields an exponent \nu \approx 0.39 \pm 0.03 in agreement with a Flory-like argument for the topologica interactions. We show (using the same algorithm) that the dynamics of molten rings is similar to that of linear chains of the same mass, confirming recent experimental findings. The diffusion constant varies effectively as D_{N} \propto N^{-1.22(3) and is slightly higher than that of corresponding linear chains. For the ring sizes considered (up to 256 statistical segments) we find only one characteristic time scale \tau_{ee} \propto N^{2.0(2); this is shown by the collapse of several mean-square displacements and correlation functions onto corresponding master curves. Because of the shrunken state of the chain, this scaling is not compatible with simple Rouse motion. It applies for all sizes of ring studied and no sign of a crossover to any entangled regime is found.Comment: 20 Pages,11 eps figures, Late

The composition of the protosolar disk and the formation conditions for comets

Conditions in the protosolar nebula have left their mark in the composition of cometary volatiles, thought to be some of the most pristine material in the solar system. Cometary compositions represent the end point of processing that began in the parent molecular cloud core and continued through the collapse of that core to form the protosun and the solar nebula, and finally during the evolution of the solar nebula itself as the cometary bodies were accreting. Disentangling the effects of the various epochs on the final composition of a comet is complicated. But comets are not the only source of information about the solar nebula. Protostellar disks around young stars similar to the protosun provide a way of investigating the evolution of disks similar to the solar nebula while they are in the process of evolving to form their own solar systems. In this way we can learn about the physical and chemical conditions under which comets formed, and about the types of dynamical processing that shaped the solar system we see today. This paper summarizes some recent contributions to our understanding of both cometary volatiles and the composition, structure and evolution of protostellar disks.Comment: To appear in Space Science Reviews. The final publication is available at Springer via http://dx.doi.org/10.1007/s11214-015-0167-