Multiple linear regression and thermodynamic fluctuations are equivalent for computing thermodynamic derivatives from molecular simulation

Rahbari, Ahmadreza; Josephson, Tyler R.; Sun, Yangzesheng; Moultos, Othonas A.; Dubbeldam, David; Siepmann, J. Ilja; Vlugt, Thijs J. H.

doi:10.1016/j.fluid.2020.112785

Cited by 14 publications

(12 citation statements)

References 46 publications

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“…57 Note that it is assumed that partial molar properties for water are composition-independent in the composition range selected for water. 33 This will be validated in section 3 . Pure liquid water was also simulated in the NPT ensemble using the same water model (PCFF parameters) to compute the molar volume of water at atmospheric pressure and at T = 330 K and T = 360 K. Every simulation box contained 1000 water molecules.…”

Section: Model and Simulation Detailsmentioning

confidence: 88%

Electro-osmotic Drag and Thermodynamic Properties of Water in Hydrated Nafion Membranes from Molecular Dynamics

et al. 2022

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One of the important parameters in water management of proton exchange membranes is the electro-osmotic drag (EOD) coefficient of water. The value of the EOD coefficient is difficult to justify, and available literature data on this for Nafion membranes show scattering from in experiments and simulations. Here, we use a classical all-atom model to compute the EOD coefficient and thermodynamic properties of water from molecular dynamics simulations for temperatures between 330 and 420 K, and for different water contents between λ = 5 and λ = 20. λ is the ratio between the moles of water molecules to the moles of sulfonic acid sites. This classical model does not capture the Grotthuss mechanism; however, it is shown that it can predict the EOD coefficient within the range of experimental values for λ = 5 where the vehicular mechanism dominates proton transfer. For λ > 5, the Grotthuss mechanism becomes dominant. To obtain the EOD coefficient, average velocities of water and ions are computed by imposing different electric fields to the system. Our results show that the velocities of water and hydronium scale linearly with the electric field, resulting in a constant ratio of ca. 0.4 within the error bars. We find that the EOD coefficient of water linearly increases from 2 at λ = 5 to 8 at λ = 20 and the results are not sensitive to temperature. The EOD coefficient at λ = 5 is within the range of experimental values, confirming that the model can capture the vehicular transport of protons well. At λ = 20, due to the absence of proton hopping in the model, the EOD coefficient is overestimated by a factor of 3 compared to experimental values. To analyze the interactions between water and Nafion, the partial molar enthalpies and partial molar volumes of water are computed from molecular dynamics simulations. At different water uptakes, multiple linear regression is used on raw simulation data within a narrow composition range of water inside the Nafion membrane. The partial molar volumes and partial molar excess enthalpies of water asymptotically approach the molar volumes and molar excess enthalpies of pure water for water uptakes above 5. This confirms the model can capture the bulklike behavior of water in the Nafion at high water uptakes.

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Section: Model and Simulation Detailsmentioning

confidence: 88%

Electro-osmotic Drag and Thermodynamic Properties of Water in Hydrated Nafion Membranes from Molecular Dynamics

et al. 2022

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“…This study allowed them to demonstrate that the former approach worked better than the latter in predicting GDP growth in African economies (Chuku et al, 2019). In their work, other researchers have found the equivalence of multiple linear regression and thermodynamic fluctuations approaches for the calculation of thermodynamic derivatives from molecular simulation (Ahmadreza et al, 2020). Some, on the other hand, worked on a Normal least squares Vector Support Machine (NLS-SVM) and its classification learning algorithm to demonstrate after simulations on artificial and real data that NLS-SVM outperformed LS-SVM on the results obtained (Xinjun et al, 2009).…”

Section: Introductionmentioning

confidence: 92%

Predicting Budget Revenues of the Republic of Congo: Multiple Linear Regression Approach

Kaito¹

2021

IJEF

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Alongside political, legal and financial suggestions, prognosticating as part of a state's budget planning process endures a substantial element. An act that furnishes for and authorizing what the State hopes to recover as earnings along with what it intends to bear as expenditure for a calendar year and, however, which may be subject to revision during its implementation in reaction to the current economic situation; the state budget remains tactic for the extant, quality, functioning and organization of its Administration. As an oil-producing country, the Republic of Congo, which must, among other things, have the financial means to meet these ambitions, does not escape, like other countries selling hydrocarbons, the preponderance of revenues from this sector in its budget forecasts. In view of the unpredictability of international oil markets on which government revenues are largely dependent, the use of artificial intelligence would disclose ornaments in data volumes and model interdependent systems to generate outcomes synonymous with enhanced decision-making efficiency and value for money. In this article, we will have to use Machine Learning to create the prediction model using secondary data from international organizations and official annals of the Government of the Republic of Congo, that is, the annual price of a barrel of oil and the budget foresees of state incomes and expenditures entered in various initial and altering finance laws between the years 1980-2019. This representation is based on the multiple linear retrogression algorithms that will ascertain the linear relationship between a dependent variable and independent or explanatory variables. This will also concede us to approximate the foretell of the value “state revenues” from the values “oil prices” and “state expenses”. As a result of the evaluation, the coefficient of determination (R2) of the performance of the dummy based on the test data is 99%. Finally, the stereotype will be practiced on a web interface granting users to enter the new independent data and then click a button to illustrate the result of the predictions of the dependent value.

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“…57,59,60 These thermodynamic derivatives are directly obtained from ensemble fluctuations at constant composition. 56,58,61,62 Lagache et al 58 showed that the derivative of an extensive property X with respect to β = 1/(k B T) (in which k B is the Boltzmann constant and T the absolute temperature) in the NPT ensemble can be obtained from the ensemble fluctuations as follows…”

Section: Thermodynamic Properties Of Mixturesmentioning

confidence: 99%

“…To compute thermodynamic properties of compressed hydrogen with and without traces of water using molecular simulations, we use derivatives of volume, internal energy, and enthalpy with respect to temperature and pressure. These derivatives are required to calculate properties such as thermal expansivity, heat capacity, and the Joule–Thomson coefficient. ,, These thermodynamic derivatives are directly obtained from ensemble fluctuations at constant composition. ,,, Lagache et al showed that the derivative of an extensive property X with respect to β = 1/( k B T ) (in which k B is the Boltzmann constant and T the absolute temperature) in the NPT ensemble can be obtained from the ensemble fluctuations as follows where Ĥ = U + PV is the configurational enthalpy of the system, P is the imposed pressure, and U is the potential energy of the system consisting of an intermolecular contribution U ext and an intramolecular contribution U int . The mathematical proof for this is provided in the Supporting Information.…”

Section: Thermodynamic Properties Of Mixtures Obtained From Ensemble ...mentioning

confidence: 99%

Effect of Water Content on Thermodynamic Properties of Compressed Hydrogen

Rahbari

Garcia-Navarro²,

Ramdin

et al. 2021

J. Chem. Eng. Data

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Force field-based molecular simulations were used to calculate thermal expansivities, heat capacities, and Joule− Thomson coefficients of binary (standard) hydrogen−water mixtures for temperatures between 366.15 and 423.15 K and pressures between 50 and 1000 bar. The mole fraction of water in saturated hydrogen−water mixtures in the gas phase ranges from 0.004 to 0.138. The same properties were calculated for pure hydrogen at 323.15 K and pressures between 100 and 1000 bar. Simulations were performed using the TIP3P and a modified TIP4P force field for water and the Marx, Vrabec, Cracknell, Buch, and Hirschfelder force fields for hydrogen. The vapor−liquid equilibria of hydrogen−water mixtures were calculated along the melting line of ice Ih, corresponding to temperatures between 264.21 and 272.4 K, using the TIP3P force field for water and the Marx force field for hydrogen. In this temperature range, the solubilities and the chemical potentials of hydrogen and water were obtained. Based on the computed solubility data of hydrogen in water, the freezing-point depression of water was computed ranging from 264.21 to 272.4 K. The modified TIP4P and Marx force fields were used to improve the solubility calculations of hydrogen− water mixtures reported in our previous study et al. J. Chem. Eng. Data 2019, 64, 4103−4115] for temperatures between 323 and 423 K and pressures ranging from 100 to 1000 bar. The chemical potentials of ice Ih were calculated as a function of pressure between 100 and 1000 bar, along the melting line for temperatures between 264.21 and 272.4 K, using the IAPWS equation of state for ice Ih. We show that at low pressures, the presence of water has a large effect on the thermodynamic properties of compressed hydrogen. Our conclusions may have consequences for the energetics of a hydrogen refueling station using electrochemical hydrogen compressors.

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Multiple linear regression and thermodynamic fluctuations are equivalent for computing thermodynamic derivatives from molecular simulation

Cited by 14 publications

References 46 publications

Electro-osmotic Drag and Thermodynamic Properties of Water in Hydrated Nafion Membranes from Molecular Dynamics

Electro-osmotic Drag and Thermodynamic Properties of Water in Hydrated Nafion Membranes from Molecular Dynamics

Predicting Budget Revenues of the Republic of Congo: Multiple Linear Regression Approach

Effect of Water Content on Thermodynamic Properties of Compressed Hydrogen

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