Spatial Correlation Functions and Thermodynamic Routes

The structure and thermodynamics of strongly coupled dusty plasmas are investigated with the soft mean spherical approximation. This integral theory approach is analytically solvable for Yukawa pair interactions yielding a closed-form solution for the direct correlation function. The pair correlation function, the structure factor, and basic thermodynamic quantities are calculated for a wide range of parameters. Exact consistency between the "energy"-"virial" thermodynamic routes and approximate consistency between the "energy"-"compressibility" paths is demonstrated. Comparison with extensive molecular dynamics results is carried out and a remarkable agreement from the Coulomb limit to the strongly screened limit is revealed. The soft mean spherical approximation is concluded to be particularly well suited for the study of dusty plasma liquids, uniquely combining simplicity and accuracy.

The vanadium redox flow battery (VRFB) is one of the promising electrical energy storage technologies in providing stable electricity supply from the primary solar and wind enery sources.1 For practical operation, it is critical to understand the electrolyte ion behavior within the VRFB membrane separator to gain insight into the ion permeation process. Here, we report our recent molecular dynamics (MD) investigations on the structure and interaction between hydrated Nafion membrane and the ionic species of the electrolyte solution: V2+, V3+, and HSO4 –. Classical MD simulations were undertaken on the following systems: Nafion/H2O/H3O+; Nafion/H2O/H3O+/HSO4 –; Nafion/H2O/H3O+/V2+; Nafion/H2O/H3O+/V3+; Nafion/H2O/H3O+/HSO4 –/V2+; and Nafion/H2O/H3O+/HSO4 –/V3+ at hydration levels (i.e., λ) of 6, 12, and 18 H2O/SO3H. The Nafion was modeled as a 15-mer ionomer with the system consisting of 64 macromolecules. A complete description of our methodology is detailed in recent manuscripts and is similar to our earlier work.2 The molecular potential models are described in prior publications.2-6 Figure 1(a) shows the spatial pair correlation function (PCF) between S-atom of the SO3 – group of Nafion with the H-atom of H3O+ and the cumulative H-atom number of H3O+ around each SO3 – (inset) for the Nafion/H2O/H3O+/HSO4 – system. The obtained first layer H3O+ numbers are: 1.18 (λ = 6); 0.72 (λ = 12); and 0.46 (λ = 18). The dashed line corresponds to the case of full association, i.e., each SO3 – has one H3O+ within the first hydration shell. Apparently, for λ = 6 the H-atom number is slightly larger than the full hydration, due to the correlation between sulfur atoms of Nafion and the H3O+ orientation. At high hydration level the H3O+in the first layer is significantly reduced due to the screening effect of water. Figure 1(b) displays PCFs between S-atom of the SO3 – group of Nafion with the H-atom of HSO4 – and the cumulative H-atom number of HSO4 - around the SO3 –. The dashed line at 0.052 indicates that all HSO4 - are in the first hydration shell of the sulfonate groups. Compare to H3O+ the H-atom number in the first layer at λ = 6 is below full hydration but still fairly high for an anion. We attribute this to the spatial limitation near the SO3 –sites due to the small size of the water cluster, among other factors. Figures 1(c) and (d) show the PCF of the sulfur atom of Nafion SO3 – with the V2+ and V3+, respectively, for the Nafion/H2O/H3O+/V2+ and Nafion/H2O/H3O+/V3+ systems. The PCFs exhibit a pronounced peak at about 2.70 and 2.40 Å for V2+ and V3+, respectively. For both ions, peak height significantly decreases with hydration level. The insets in Figures 1(c) and (d) show the cumulative number of vanadium cations around a SO3 –. At λ = 6, the number of V2+ ions is about 0.25. This number is significantly reduced at high hydration. Comparison of the two vanadium ions reveals that, the higher valence cations interact less directly with the sulfonate groups, with the number of V3+ 5 times smaller than V2+at λ = 6, and decreasing essentially to zero at λ = 18. This is probably due to the tight hydration shell of vanadium ions, which weakens the interaction between the sulfonate groups and the vanadium cations. Figures 1(e) and (f) plot the PCF between V2+, V3+ and the O2-atom (the three oxygen without bonded hydrogen) of HSO4 – in the Nafion/H2O/H3O+/HSO4 –/V2+, and Nafion/H2O/H3O+/HSO4 –/V3+ system, respectively. Comparing the PCFs for V2+ and V3+, it shows that the oxygen atom can make direct contact with the V2+ at λ = 6. The peak is missing at higher hydration levels λ = 12 and 18 due to the screening effect of water. The peak for the first layer is completely missing for V3+because of its tight water hydration layers. Acknowledgments The authors would like to thank the Navy for the support of this work through Grant N00014-12-1-0887 “Research Support for Naval Energy Needs.” 1. A. Z. Weber, M. M. Mench, J. P. Meyers, N. Philip, P. N. Ross, J. T. Gostick, and Q. Liu, Journal of Applied Electrochemistry 41, 1137 (2011). 2. S. T. Cui, J. Liu, M. E. Selvan, S. J. Paddison, and D. J. Keffer, Journal of Physical Chemistry C 112, 13273 (2008). 3. H. H. Loeffler, I. J. Yague, and B. M. Rode, Chemical Physics Letters 363, 367 (2002). 4. C. Kritayakornupong, Journal of Computational Chemistry 30, 2777 (2009). 5. C.-G. Ding, T. Taskila, K. Laasonen, A. Laaksonen, Chemical Physics 287, 7 (2003). 6. C. R. I. Chisholm, Y. H. Jang, S. M. Haile, and W. A. Goddard III, Physical Review B 72, 134103 (2005). Figure 1

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients B(j) are expressed in terms of the solution of a set of (d-1)/2 coupled algebraic equations which become nonlinear for d>/=5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d>/=5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2eta(1/d), where eta is the packing fraction, is wholly consistent with the limiting value of 1 for d-->infinity. Finally, the values for B(j) predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)].

The structural and thermodynamic properties of the argon fluid were investigated by means of a modification of the optimised random phase approximation (ORPA) theory and the square-well (SW) potential. The results were obtained at the SW potential values 1.25 < λ < 2, and along different isotherms at a wide range of densities. The radial distribution function, g(r), was calculated, and the results obtained were extrapolated to give the appropriate contact values g(σ), g(λσ −) and g(λσ +). The results were compared with the simulation and experimental data available in the literature. The results calculated for the Helmholtz free energy (A) and internal energy (E) are in good agreement with the experimental data at the sub- and super-critical temperatures. The ORPA version considered here provided good results for the compressibility factor Z from the Virial route with the SW attractive range λ = 1.7 at high temperatures and low densities.

Ni-Co bimetallic nanoparticles with core-shell, alloyed, and Janus structures explored by MD simulation

It is well established that water-alcohol mixtures exhibit anomalous properties at very low as well as at very high alcohol concentrations. Almost all the studies in this regard intend to link these anomalies to the microscopic structural changes as water (or alcohol) concentration increases in the mixture. However, it is important to note that the nature of these structural changes could be different at the water- and TBA-rich concentrations. In this article, our goal is to address such structural change overs, if really present, in the mixtures of water and tert-butanol (TBA) by using simulated X-ray scattering structure function, S(q), real space radial and spatial distribution functions and heterogeneity order parameter. By using a judicial partitioning scheme, we show that structural characteristic of pure water is qualitatively retained for X TBA < 0.1. The simulated S(q) peaks at around q = 2 and q = 2.8 Å−1, which correspond to water oxygen correlations, begin to fade away only after X TBA ≥ 0.1. This is a clear indication of microscopic structural transition at X TBA ≈ 0.1. Beyond X TBA = 0.1, the TBA structural features begin to take over to that of water. The peak at q =1.3 Å−1 which primarily corresponds to nonpolar-nonpolar correlations in pure TBA begin to rise at X TBA ≈ 0.1. However, the pre-peak at around q = 0.75 Å−1, which is due to polar-polar and nonpolar-polar correlations in pure TBA, seems to appear at lower q value only at the equi-molar concentration of the mixture. From the solvent cage surrounding the TBA molecules, we observe that while the aggregation of TBA alkyl groups, due to hydrophobic interaction, is maximum at 10% TBA, the intervening hydrogen bonding interactions between water and TBA molecules tend to lower the hydrophobic interactions between the alkyl groups of alcohol with increasing concentration of TBA. In addition to this, we also observe dimers and small clusters of water molecules in the TBA-rich regime. The computed heterogeneity order parameters for the individual components of the mixture reveal enhanced non-uniform distribution of the TBA molecules near X TBA≈ 0.1 to 0.3. These results are also supported by the radial distribution functions and nearest neighbour coordination numbers of water and TBA oxygen atoms around TBA oxygen.

Ab initio generation of amorphous semiconducting structures. The case of a-Si

We investigate the Emery model on several ladder-like lattices including two legs of copper d orbitals and various numbers of oxygen p orbitals. Pair binding energy, pair spatial structure, density distribution, and pairing correlation functions are calculated using the density-matrix renormalization group (DMRG). We show that a Luther-Emery phase with enhanced pairing correlations can be found for hole doping as well as for electron doping with realistic model parameters. Ladder properties depend sensitively on model parameters, the oxygen p orbitals taken into account, and boundary conditions. The pair binding energy is a more reliable quantity than correlation functions for ascertaining the occurrence of pairing in ladders. Overall, our results for two-leg Emery ladders support the possibility of superconductivity in the hole-doped 2D model. The issue is rather to determine which of the various ladder structures and model parameters are appropriate to approximate the two-dimensional cuprates. Published by the American Physical Society 2025

The setting up of relations between the radial distribution function and some thermodynamic quantities is continued in this chapter. That of interest, here, is the isothermal compressibility coefficient. During the course of the reasoning mentioned in this chapter, a new function is introduced. It is the function G which, in turn, is itself a function of the radial distribution function \( \overline{g} \)(R). The name of G is spatial pair correlation function or Kirkwood–Buff’s integral. Another relation, which relates the fluctuations of the numbers of molecules to the isothermal compressibility factor, is also set up. All these quantities are linked together. These relations are, actually, the starting theoretical basis of Kirkwood–Buff’s theory which is very interesting for the study of activities.

The Vlasov equation is not applicable for those turbulent plasmas in which certain higher-order correlation functions may play just as important a part as the single-particle distribution function. We construct the many-particle distribution functions by summing certain selected products of the single-particle distribution functions and the pair correlation functions, and show that, in the Rostoker-Rosenbluth fluid limit, those distribution functions satisfy the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy and enable us to truncate it at the second equation. The resulting equations contain an asymmetric feature in that the single-particle distribution function develops in time with inclusion of the correlation effects in the collision term, while the time evolution of the pair correlation function is governed by a solution of the linearized Vlasov equation. It is shown explicitly that those kinetic equations become identical to the quasilinear equations without mode coupling if the contribution of the growing plasma oscillation is singled out in the pair correlation function.

Water plays a critical role in the structure and function of proteins, although the experimental properties of water around protein structures are not well understood. The water can be classified by the separation from the protein surface into bulk water and hydration water. Hydration water interacts closely with the protein and contributes to protein folding, stability, and dynamics, as well as interacting with the bulk water. Water potential functions are often parametrized to fit bulk water properties because of the limited experimental data for hydration water. Therefore, the structural and energetic properties of the hydration water were assessed for 105 atomic resolution (<or=1.0 A) protein crystal structures with a high level of hydration water by calculating the experimental water-protein radial distribution function or surface distribution function (SDF) and water radial distribution function (RDF). Two maxima are observed in SDF: the first maximum at a radius of 2.75 A reflects first shell and hydrogen bond interactions between protein and water, and the second maximum at 3.65 A reflects second shell and van der Waals interactions between water and nonpolar atoms of protein-forming clathrate-hydrate-like structures. Thus, the two shells do not overlap. The RDF showed the features of liquid water rather than solid ice. The first and second maxima of RDF at 2.75 and 4.5 A, respectively, are the same as for bulk water, but the peaks are sharper, indicating hydration water is more stable than bulk water. Both distribution functions are inversely correlated with the distribution of B factors (atomic thermal factors) for the waters, suggesting that the maxima reflect stable positions. Therefore, the average water structure near the protein surface has experimentally observable differences from bulk water. This analysis will help improve the accuracy for models of water on the protein surface by providing rigorous data for the effects of the apparent chemical potential of the water near a protein surface.

Copulas have become an important analytic tool for characterizing multivariate distributions and dependence. One is often interested in simulating data from copula estimates. The process can be analytically and computationally complex and usually involves steps that are unique to a given parametric copula. We describe an alternative approach that uses \probability{proportional{to{size" (PPS) random sampling with weights formed from the copula likelihood function. The method is flexible and can be applied to parametric and nonparametric marginal density estimates. The precision of the simulation can be calibrated by adjusting the density of the multidimensional grid used in the simulation process. The approach is fully transparent to any copula function with continuous random variables. An example evaluates a number of goodness-of-fit criteria and provides strong support for the validity and practicality of the method.

For the next-generation polarizable force field, atom-bond electronegativity equalization fluctuating charge force field (ABEEM/MM), and quantum chemistry method, an accurate Mn2+-H2O potential function was constructed, and its parameters were determined via fitting to quantum chemistry results. Then the potential function was employed to calculate the structure and binding energies of the hydrated manganous ionic clusters Mn2+(H2O) n ( n =1-12). The results were in good agreement with those from quantum chemistry. Furthermore, the structural properties of the Mn2+ aqueous solution were simulated using ABEEM/MM molecular dynamics. This includes the radial distribution function (RDF), angular distribution function (ADF), water structure, and charge distribution. The first and second peaks of Mn2+-O RDF are located at 0.218 nm and 0.435 nm. The coordination numbers for the first and second hydration shells, which were integrated from the RDF, are 7.03 and 17.74. The first and second peaks of the O-Mn2+-O ADF are located at 80° and 140°. These results are consistent with those from experimental measurements and other theoretical simulations. The water molecules in the first hydration shell were polarized by the Mn2+ ions, and their bond lengths were stretched, but their bond angles were reduced. Mn2+ does not measurably affect the structures of the water molecules outside the first hydration shell. Our analysis of the charge distributions showed that, compared with ABEEM-7P liquid water, the charges of the H atom and lone pairs vary more in the Mn2+ aqueous solution. Moreover, there was evident charge transfer between the Mn2+ ions and their adjacent water molecules.

According to feasibility of Gaussian peaks decomposing distribution function (DF) 4πrρ(r), radial distribution function (RDF) 4πr 2ρ(r) of simple liquids also is possibly decomposed into Gaussian peaks withr in the size of several atoms. Experimental structure parameters of pure liquid Al and Si were obtained by θ-θ X-ray diffraction measurements and following data processing. Based on Gaussian decomposing liquid aluminum’s DF 4πrρ(r), liquid aluminum and silicon’s radial distribution function (RDF) 4πr 2ρ(r), it is shown that RDF of simple liquids is able to be decomposed in Gaussian function, compared with decomposing of DF, supplying more physical meaning and better indicating the short range order of liquids, which draws a clearer structure picture of simple liquids.

The coupling parameter expansion in thermodynamic perturbation theory of simple fluids is generalized to include the derivatives of bridge function with respect to coupling parameter. We applied seventh order version of the theory to Square-Well (SW) and Lennard-Jones (LJ) fluids using Sarkisov Bridge function. In both cases, the theory reproduced the radial distribution functions obtained from integral equation theory (IET) and simulations with good accuracy. Also, the method worked inside the liquid-vapor coexistence region where the IETs are known to fail. In the case of SW fluids, the use of Carnahan-Starling expression for Helmholtz free energy density of Hard-Sphere reference system has improved the liquid-vapor phase diagram (LVPD) over that obtained from IET with the same bridge function. The derivatives of the bridge function are seen to have significant effect on the liquid part of the LVPD. For extremely narrow SW fluids, we found that the third order theory is more accurate than the higher order versions. However, considering the convergence of the perturbation series, we concluded that the accuracy of the third order version is a spurious result. We also obtained the surface tension for SW fluids of various ranges. Results of present theory and simulations are in good agreement. In the case of LJ fluids, the equation of state obtained from the present method matched with that obtained from IET with negligible deviation. We also obtained LVPD of LJ fluid from virial and energy routes and found that there is slight inconsistency between the two routes. The applications lead to the following conclusions. In cases where reference system properties are known accurately, the present method gives results which are very much improved over those obtained from the IET with the same bridge function. In cases where reference system data is not available, the method serves as an alternative way of solving the Ornstein-Zernike equation with a given closure relation with the advantage that solution can be obtained throughout the phase diagram with a proper choice of the reference system.