Partial molar properties from molecular simulation using multiple linear regression

Abstract

Partial molar volumes, energies, and enthalpies can be computed from N pT -Gibbs ensemble simulations through a post-processing procedure that leverages fluctuations in composition, total volume, and total energy of a simulation box. By recording the instantaneous box volumes V and instantaneous number of molecules Ni of each of n species for M frames, a large M × n matrix N is constructed, as well as the M × 1 vector V. The 1 × n vector of partial molar volumesV may then be solved using N •V = V. A similar construction permits calculation of partial molar energies using M instantaneous measurements of the total energy of the simulation box, and N •Ū = U. Partial molar enthalpies may be derived fromŪ,V, and pressure p. These properties may be used to calculate enthalpy and entropy of transfer (absorption, extraction, and adsorption) for species in complex mixtures. The method is demonstrated on three systems in the N pT -Gibbs ensemble: a highly compressible natural gas condensate of methane, n-butane, and n-decane, the liquid-phase adsorption of 1,5-pentanediol and ethanol onto the MFI zeolite, and a relatively incompressible mixture of ethanol, n-dodecane, and water at liquid-liquid equilibrium. Property predictions are compared to those from numerical differentiation of simulation data sequentially changing the composition and from equations of state. The method can also be extended to reaction equilibria in a closed system and is applied to a reactive first-principles Monte Carlo simulation of compressed nitrogen/oxygen.

Recent advances in the continuous fractional component Monte Carlo methodology

“…Partial molar volumes and enthalpies are first-order derivatives of the chemical potential at constant pressure. Similar to chemical potentials, these properties cannot be sampled directly as a function of momenta or coordinates of a single configuration in the phase space [125,149,[159][160][161]. It is possible to compute partial molar enthalpies from h i = (∂(bm i )/∂b) P,N j=i in which b = 1/(k B T) and partial molar volumes y i = (∂m i /∂P) T,N j=i either by deriving expressions based on statistical mechanics or by numerical differentiation of the chemical potential as a function of T and P. In 1987, Sindzingre, Frenkel and Ciccotti [159] derived expressions to directly calculate partial molar enthalpies and partial molar volumes based on an extension of the WTPI method.…”

“…With this, derivatives from non-uniformly distributed data points can be obtained accurately. ; 2 instantaneous values of an extensive property X as a function of the instantaneous number of molecules of each component [161,171]. This method requires a simulation in an open ensemble; (4) The difference method.…”

Competitive Adsorption of Xylenes at Chemical Equilibrium in Zeolites

“…The IAST predictions are computed using pyIAST software. 141 Multiple linear regression 142,143 is used to compute changes in enthalpy and entropy due to the transfer of one xylene molecule from the bulk phase to the zeolite framework. Details about these calculations can be found in the Supporting Information.…”

Effect of Water Content on Thermodynamic Properties of Compressed Hydrogen

“…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…”

“…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.…”