This work presents the derivations of basic thermodynamic properties and activity coefficients equations from linearised Poisson–Boltzmann equation. We consider two main approaches, first one is based in classical thermodynamics, which has been used original Debye Hückel, leading to model an important cornerstone electrolyte thermodynamics since its publication 1923. The second approach relies on more modern statistical mechanics, so-called charging approaches. Both derivation routes have...

This work presents a comparison between numerical solution of the Poisson–Boltzmann equation and analytical its linearized version through Debye–Hückel equations considering both size-dissimilar common ion diameters approaches. In order to verify limits in which is capable satisfactorily reproduce nonlinear Poisson–Boltzmann, we calculate mean ionic activity coefficients for different types electrolytes as various temperatures. The divergence full higher lower molalities, solutions tend...

This work discusses the introduction of concentration dependency relative permittivity in context activity coefficient models at different stages derivation models. We evaluate an experimental correlation and Michelsen–Mollerup–Breil model for order to assess impact using these both Debye–Hückel Born equations. Our results show that effects introducing levels are significant quantitative. Using as early before deriving Helmholtz free energy has best overall performance. derive a general...

The Born equation is a seminal model to study the solvation process of ions in solution, devised originally for at infinite dilution. Diverse modifications have been proposed literature since publication original work by Max 1920, with varying degrees success. In this work, we analyze and discuss various equation. We verify their performance Gibbs Free Energy, Enthalpy, Entropy using data from comprehensive database 143 charges −4 +4 26 different solvents. show how radius natural consequence...

In this work we present Hückel's original derivation and considerations, verifying the approximations that were done in his paper. More complex equations are obtained by not applying some of approximations, these compared to Hückel equation. We explore use both a linear an experimental concentration dependency relative permittivity represent data. show equation, as known today its semi-empirical form, is full model or even approximate author had derived work, being only approximation...

Indium tin oxide nanoparticles were synthesized in two different sizes by a nonhydrolytic sol-gel method. These powders then transformed into ITO via an intermediate metastable state at between 300 and 600 ºC. The presence of characteristic O-In-O O-Sn-O bands 480 670 cm-1 confirmed the formation ITO. X-ray diffraction patterns indicated preferential hexagonal phase (corundum type) as opposed to cubic when reflux time was less than 3 h heat treatment temperature below Particle morphology...

The Debye and Güntelberg Charging Processes are essential tools for deriving electrolyte solutions' activity coefficient models. Debye–Hückel, Born, Mean Spherical Approximation among some famous theories derived via charging processes. How they relate to each other, or if both processes equivalent, even consistent, has been a matter of discussion in the literature many years. In this work, we evaluate results from using Debye–Hückel Born equations, different dependencies relative...

We propose an alternative approach to calculate viscosity, based on the Rosenfeld scaling theory, which can be applied pure components and their mixtures in a wide range of temperatures, pressures, compositions. The Helmholtz (A-scaling) applies Chapman–Enskog relation, Ansatz function, PCP-SAFT equation state predict viscosity. Although it was implemented with EoS, A-scaling has potential coupled other EoS. Substances from n-alkanes, alcohols, aromatics, ethers, chlorofluorocarbons, carbon...

In this work, we demonstrate how the ion association constant can be attributed to difference between full Poisson–Boltzmann equation and its linearized version in very dilute solutions. We follow a pragmatic approach first by deriving an analytical approximated solution equation, then calculating respective Helmholtz free energy activity coefficient, finally comparing it contribution from mass action law principle. The final result is Ebeling constant. conclude that electrostatic ion–ion...

The concept of uncertainty in an isotopic analysis is not uniform the scientific community worldwide and can compromise risk false compliance assessment applied to carbon analyses natural gas exploratory evaluation. In this work, we demonstrated a way calculate one main sources uncertainty, which underestimated most studies focusing on analysis: δ13C calculation itself primarily based raw analytical data. composition methane, ethane, propane, CO2 was measured. After detailed mathematical...

Resumo-Este artigo aborda a análise de oscilações baixa frequência em sistemas elétricos potência utilizando os algoritmos VMD (Variational Mode decomposition) e Prony.As podem causar instabilidade ao sistema elétrico comprometer sua operação confiabilidade.O algoritmo é usado para decompor o sinal seus componentes modais atenuar ruído.O Prony modelar resultantes determinar parâmetros do

ADVERTISEMENT RETURN TO ISSUEPREVAddition/CorrectionNEXTORIGINAL ARTICLEThis notice is a correctionCorrection to "Helmholtz Scaling: An Alternative Approach Calculate Viscosity with the PCP-SAFT Equation of State"Cliff I. S. GonçalvesCliff GonçalvesMore by Cliff Gonçalveshttps://orcid.org/0000-0002-6547-0041, Gabriel M. SilvaGabriel SilvaMore Silvahttps://orcid.org/0000-0002-7247-9888, Papa NdiayePapa NdiayeMore Ndiayehttps://orcid.org/0000-0003-4961-7768, and Frederico W. Tavares*Frederico...

Calculation of thermodynamic properties such as vapor-liquid phase behavior with equations state is largely and successfully employed in chemical engineering applications. However, the proximities critical point, different density-fluctuation scales inherent to phenomena introduce significant changes these properties, which classical are not prepared deal. Aiming at correcting this failure, we apply a renormalization-group methodology CPA equation order improve description vicinity points....