Single-molecular systems are a test bed to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. Isometric and isotensional single-molecule stretching experiments and their theoretical interpretations have shown the lack of a thermodynamic limit at those scales and the nonequivalence between their corresponding statistical ensembles. This disparity between thermodynamic results obtained in both experimental protocols can also be observed in entropy production, as previous theoretical results have shown. In this work, we present results from molecular dynamics simulations of stretching of a typical polymer, polyethylene-oxide, where this framework is applied to obtain friction coefficients associated with stretching at the two different statistical ensembles for two different system sizes, from which the entropy production follows. In the smallest system, they are different up to a factor of 2, and for the bigger system, the difference is smaller, as predicted. In this way, we provide numerical evidence that a thermodynamic description is still meaningful for the case of single-molecule stretching.
Single-molecular polymers can be used to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. We have recently verified using molecular-dynamics simulations that isometric and isotensional stretching of a small polymer result in Helmholtz and Gibbs stretching energies, which are not related to a Legendre transform, as they are for sufficiently long polymers. This disparity has also been observed experimentally. Using molecular dynamics simulations of polyethylene-oxide, we document for the first time that the Helmholtz and Gibbs stretching energies can be related by a Legendre–Fenchel transform. This opens up a possibility to apply this transform to other systems which are small in Hill’s sense.
We investigate the dissolution mechanism of cellulose using molecular dynamics simulations in both water and a mixture solvent consisting of water with Na$$^+$$
+
, OH$$^-$$
-
and urea. As a first computational study of its kind, we apply periodic external forces that mimic agitation of the suspension. Without the agitation, the bundles do not dissolve, neither in water nor solvent. In the solvent mixture the bundle swells with significant amounts of urea entering the bundle, as well as more water than in the bundles subjected to pure water. We also find that the mixture solution stabilizes cellulose sheets, while in water these immediately collapse into bundles. Under agitation the bundles dissolve more easily in the solvent mixture than in water, where sheets of cellulose remain that are bound together through hydrophobic interactions. Our findings highlight the importance of urea in the solvent, as well as the hydrophobic interactions, and are consistent with experimental results.
Graphical abstract
By comparing the evolution of the local and equal load sharing fiber bundle models, we point out the paradoxical result that stresses seem to make the local load sharing model stable when the equal load sharing model is not. We explain this behavior by demonstrating that it is only an apparent stability in the local load sharing model, which originates from a statistical effect due to sample averaging. Even though we use the fiber bundle model to demonstrate the apparent stability, we argue that it is a more general feature of fracture processes.
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