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1. Inside and out: Surface thermodynamics from positive to negative curvature

   https://doi.org/10.1063/5.0099295  

   Martin, Seth C.; Hansen-Goos, Hendrik; Roth, Roland; Laird, Brian B. (August 2022, The Journal of Chemical Physics)

   To explore the curvature dependence of solid–fluid interfacial thermodynamics, we calculate, using Grand Canonical Monte Carlo simulation, the surface free energy for a 2d hard-disk fluid confined in a circular hard container of radius R as a function of the bulk packing fraction η and wall curvature C̄=−1/R. (The curvature is negative because the surface is concave.) Combining this with our previous data [Martin et al., J. Phys. Chem. B 124, 7938–7947 (2020)] for the positive curvature case (a hard-disk fluid at a circular wall, C̄=+1/R), we obtain a complete picture of surface thermodynamics in this system over the full range of positive and negative wall curvatures. Our results show that γ is linear in C̄ with a slope that is the same for both positive and negative wall curvatures, with deviations seen only at high negative curvatures (strong confinement) and high density. This observation indicates that the surface thermodynamics of this system is consistent with the predictions of so-called morphometric thermodynamics at both positive and negative curvatures. In addition, we show that classical density functional theory and a generalized scaled particle theory can be constructed that give excellent agreement with the simulation data over most of the range of curvatures and densities. For extremely high curvatures, where only one or two disks can occupy the container at maximum packing, it is possible to calculate γ exactly. In this limit, the simulations and density functional theory calculations are in remarkable agreement with the exact results. 

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2. An experimentally informed continuum grain boundary model

   https://doi.org/10.1177/10812865231223921  

   Ansari, S Syed; Acharya, Amit; Alankar, Alankar (August 2024, Mathematics and Mechanics of Solids)

   A continuum grain boundary model is developed, which uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a one-dimensional (1D) grain array. The model uses a continuum representation of the misorientation in terms of spatial gradients of the orientation as a fundamental field. The grain boundary energy density employed is non-convex in this orientation gradient, based on physical grounds. Simple gradient descent dynamics of the energy are utilized for idealized microstructure evolution, which requires higher-order regularization of the energy density for the model to be well set; the regularization is physically justified. Microstructure evolution is presented using two plausible energy density functions, both defined from the same experimental data: a “smooth” and a “cusp” energy density. Results of grain boundary equilibria and microstructure evolution representing grain reorientation in 1D are presented. The different shapes of the energy density functions representing a common data set are shown to result in different overall microstructural evolution of the system. Mathematically, the constructed energy functional formally is of the Aviles–Giga/Cross–Newell type but with unequal well depths, resulting in a difference in the structural feature of solutions that can be identified with grain boundaries, as well as in the approach to equilibria from identical initial conditions. This study also investigates the metastability of grain boundaries. It supports the general thermodynamics belief that they persist for extended periods before eventually vanishing due to the lowest energy configuration favored by fluctuations over infinite time. 

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3. Further insights into the thermodynamics of the Kitaev honeycomb model

   https://doi.org/doi.org/10.1103/PhysRevB.102.224402  

   Kexin Feng, Natalia B. (December 2020, PRB)

   null (Ed.)

   Here we revisit the thermodynamics of the Kitaev quantum spin liquid realized on the honeycomb lattice. We address two main questions: First, we investigate whether there are observable thermodynamic signatures of the topological Majorana boundary modes of the Kitaev honeycomb model. We argue that for the time-reversal invariant case the residual low-temperature entropy is the primary thermodynamic signature of these Majorana edge modes. Using large-scale Monte Carlo simulations, we verify that this residual entropy is present in the full Kitaev model. When time-reversal symmetry is broken, the Majorana edge modes are potentially observable in more direct thermodynamic measurements such as the specific heat, though only at temperatures well below the bulk gap. Second, we study the energetics, and the corresponding thermodynamic signatures, of the flux excitations in the Kitaev model. Specifically, we study the flux interactions on both cylinder and torus geometries numerically and quantify their impact on the thermodynamics of the Kitaev spin liquid by using a polynomial fit for the average flux energy as a function of flux density and extrapolating it to the thermodynamic limit. By comparing this model to Monte Carlo simulations, we find that flux interactions have a significant quantitative impact on the shape and the position of the low-temperature peak in the specific heat. 

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4. Toward an Automated-Algebra Framework for High Orders in the Virial Expansion of Quantum Matter

   https://doi.org/10.3390/condmat7010013  

   Czejdo, Aleks J.; Drut, Joaquin E.; Hou, Yaqi; Morrell, Kaitlyn J. (March 2022, Condensed Matter)

   The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order n requires analyzing (if not solving) the quantum n-body problem. In this work, we present a comprehensive review of automated algebra methods, which we developed to calculate high-order virial coefficients. The methods are computational but non-stochastic, thus avoiding statistical effects; they are also for the most part analytic, not numerical, and amenable to massively parallel computer architectures. We show formalism and results for coefficients characterizing the thermodynamics (pressure, density, energy, static susceptibilities) of homogeneous and harmonically trapped systems and explain how to generalize them to other observables such as the momentum distribution, Tan contact, and the structure factor. 

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5. NMR and computational studies of ammonium ion binding to dibenzo-18-crown-6

   Shope B, Magers DB (July 2022, Structural chemistry)

   Dibenzo-18-crown-6 (DB18C6) is a single-crown ether that can act as a host for a guest ion. In an effort to illuminate the relationships among structure, dynamics, and thermodynamics of ligand binding in a simple model for understanding the affinity and specificity of ligand interactions, nuclear magnetic resonance (NMR) experiments and density functional theory (DFT) were used to study the interaction of DB18C6 with ammonium ion. 1H-NMR was used to follow the titration of DB18C6 with ammonium chloride in deuterated methanol, a solvent chosen for its amphipathic character. Ammonium ion binds strongly to DB18C6 with a dissociation equilibrium constant at least as low as ~ 10 - 6 M. DFT calculations were used to identify optimized conformations of bound and free DB18C6 and to estimate its binding energy with ammonium ion in implicit solvent. An approach is described that accounts for geometry relaxation in addition to solvation correction and basis set superposition error; to our knowledge, this is the first such report that includes the energy difference from optimizing species geometry. The lowest-energy conformer of free DB18C6 in implicit methanol acquires an open, W-shaped structure that is also the lowest-energy conformer found for the DB18C6-ammonium ion complex. These results form a foundation for further studies of this system by molecular dynamics simulations. 

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