The Radial Distribution Function and the Isothermal Compressibility Coefficient of a System

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 system of 64 water molecules with a TIPS2 intermolecular pair potential was studied by the NPT-ensemble Monte Carlo method at 773 K and 100, 1000, and 3000 MPa. The values of enthalpy, specific volume, isobaric heat capacity, isothermal compressibility, and thermal expansion coefficients were obtained and found to be in good agreement with estimates from two equations of state of water. Computed atom-atom radial distribution functions agree well with recent high-temperature X-ray diffraction data. The effect of temperature and density increases on the O-O, O-H, and H-H correlations in water was analyzed. A quantitative comparison was made between thermodynamic properties and radial distribution functions of dense supercritical water and the simple Lennard-Jones fluid. The convergence rate was noted to increase under the conditions studied in comparison with Monte Carlo simulations of liquid water at normal temperature and pressure.

Compressibilities and Volume Fluctuations of Archaeal Tetraether Liposomes

Identifying and quantifying spatial correlation are important aspects of studying the collective behavior of multiagent systems. Pair correlation functions (PCFs) are powerful statistical tools that can provide qualitative and quantitative information about correlation between pairs of agents. Despite the numerous PCFs defined for off-lattice domains, only a few recent studies have considered a PCF for discrete domains. Our work extends the study of spatial correlation in discrete domains by defining a new set of PCFs using two natural and intuitive definitions of distance for a square lattice: the taxicab and uniform metric. We show how these PCFs improve upon previous attempts and compare between the quantitative data acquired. We also extend our definitions of the PCF to other types of regular tessellation that have not been studied before, including hexagonal, triangular, and cuboidal. Finally, we provide a comprehensive PCF for any tessellation and metric, allowing investigation of spatial correlation in irregular lattices for which recognizing correlation is less intuitive.

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 experimental density and speed of ultrasound measurements, along with literature data, were used to calculate adiabatic and isothermal compressibility coefficients, the specific heat ratio, and isobaric thermal expansion coefficients for the binaries of 1-butanol with hexane and cyclohexane. They were also used to determine Beyer’s parameter of nonlinearity, B/A, and free intermolecular lengths, L. The free intermolecular lengths, L, calculated according to the Jacobson equation, were compared with values estimated from thermoacoustical parameters.

The effect of particle correlations in a classical system of charged particles moving in a static uniform background is investigated by means of a dielectric theory developed by Singwi et al. for a completely degenerate electron gas. In this theory, the short-range correlations arising from the Coulomb interaction is taken into account through a local-field correction depending on the pair correlation function. In a first approximation (I), the pair correlation function is chosen to be time independent. The extension of allowing also the pair correlation function to adjust itself to the external field results in a screening of the Coulomb potential entering the local field. The effect of this screening has been investigated for the cases of a static random-phase-approximation (RPA) dielectric function (II) and a static fully self-consistent dielectric function (III). Numerical self-consistent calculations have been carried out for the cases I-III in order to determine the static structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$. From $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ thus obtained, the Helmholtz free energy, the correlation energy, the pair correlation functions, and the isothermal compressibility have been calculated numerically, The plasma dispersion and the compressibility sum rule have also been investigated. The present method can be regarded as a rather natural extension of the RPA. Considerable improvement upon the simple Debye-H\"uckel (or, equivalently, classical RPA) is also found. The results of the present calculations are also compared with the results of other elaborate methods.

This chapter introduces the reduced (or marginal) distribution functions describing groups of s particles. The fundamental one is the pair configurational distribution function, from which the radial distribution function g(r) is defined as a key quantity in the statistical-mechanical description of liquids. Most of the chapter is devoted to the derivation of thermodynamic quantities in terms of integrals involving g(r). Apart from the conventional compressibility, energy, and virial routes, the less known chemical-potential and free-energy routes are worked out.

Quantized vortices in liquid 4He at finite temperatures are treated by first principles theory that extends results presented in paper I of this two-part set. Then the possible role of thermally excited quantized vortices in accounting for the λ transition is studied. This study indicates that vortices are probably not the dominant mechanism responsible for the λ transition, but that they may account for some minor effects near Tλ. A model that identifies critical fluctuations with quantized isothermal fourth sound waves is developed and used to derive formulas for specific heat in He II and He I. Logarithmic divergence of the constant volume specific heat is found. Numerical calculations using those formulas produce close agreement with experimental data. A formula for the radial distribution function near Tλ in He II and He I is derived and numerically evaluated. A formula for the correlation length is derived and numerically evaluated and physical characteristics of the correlation length are discussed. Numerical calculations based on that formula for correlation length are compared with experimental results. Long-range order in the liquid exhibited in the radial distribution function and correlation length is shown not to involve a Bose-Einstein condensate in this theory. The isothermal compressibility is found by integration of the radial distribution function and the result shows that isothermal compressibility is unchanged by critical fluctuations of isothermal fourth sound.

We report results for the electronic, structural and dynamical properties of liquid GaAs simulated by using ab initio molecular dynamics. Results for the total and partial structure factors, self-diffusion properties, pair correlation and angular distribution functions, and the electronic density of states are presented. Our calculated structure factor and pair correlation functions are in good agreement with available experimental data. A “common neighbor” cluster analysis is used to examine the structure of the liquid.

Wide angle X-ray scattering (WAXS) study of “two-line” ferrihydrite structure: Effect of arsenate sorption and counterion variation and comparison with EXAFS results

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

Unified SAFT-VR theory for simple and chain fluids formed of square-well, triangular-well, Sutherland and Mie segments