Particle fluctuations within sub-regions of an -particle, three-dimensional fluid: Finite-size effects and compressibility

Salacuse, J. J.

doi:10.1016/j.physa.2008.01.094

Cited by 8 publications

(7 citation statements)

References 10 publications

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“…The possibility of including effect in scaling equations has been explored to a large extent in the literature. 35 , 37 , 46 , 48 , 55 , 56 One such equation was proposed by Strøm et al 29 and is given by …”

Section: Resultsmentioning

confidence: 99%

Chemical Potential Differences in the Macroscopic Limit from Fluctuations in Small Systems

Bråten

Wilhelmsen

Schnell

2021

J. Chem. Inf. Model.

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We present a new method for computing chemical potential differences of macroscopic systems by sampling fluctuations in small systems. The small system method, presented by Schnell et al. [Schnell et al., J. Phys. Chem. B, 2011, 115 , 10911], is used to create small embedded systems from molecular dynamics simulations, in which fluctuations of the number of particles are sampled. The sampled fluctuations represent the Boltzmann distributed probability of the number of particles. The overlapping region of two such distributions, sampled from two different systems, is used to compute their chemical potential difference. Since the thermodynamics of small systems is known to deviate from the classical thermodynamic description, the particle distributions will deviate from the macroscopic behavior as well. We show how this can be utilized to calculate the size dependence of chemical potential differences and eventually extract the chemical potential difference in the thermodynamic limit. The macroscopic chemical potential difference is determined with a relative error of 3% in systems containing particles that interact through the truncated and shifted Lennard-Jones potential. In addition to computing chemical potential differences in the macroscopic limit directly from molecular dynamics simulation, the new method provides insights into the size dependency that is introduced to intensive properties in small systems.

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Section: Resultsmentioning

confidence: 99%

Chemical Potential Differences in the Macroscopic Limit from Fluctuations in Small Systems

Bråten

Wilhelmsen

Schnell

2021

J. Chem. Inf. Model.

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“…We recall here that extrapolations of thermodynamic properties from finite-size computer simulations of single-component systems have been obtained in the past. Examples include the calculation of the compressibility of the Ising lattice gas [14] and hard disk fluids [22,29], and the investigation of the gas-liquid transition in two-dimensional Lennard-Jones fluids [16,18], as well as the calculation of the elastic constants of model solids [20].…”

Section: Simple Liquidsmentioning

confidence: 99%

“…In Figure 9 we report these results in the interval 0,0.20 using triangles. We have obtained the shifted chemical potential of urea as a function of mole fraction using Equation (29) and plot the results using the data for the mole fraction x U = 0.13 (C U = 6.03) as a reference state point (circles). The two data points are in excellent agreement.…”

Section: Multicomponent Systemsmentioning

confidence: 99%

Finite-size integral equations in the theory of liquids and the thermodynamic limit in computer simulations

et al. 2018

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We present an efficient method to obtain bulk isothermal compressibilities (κ T) and Kirkwood-Buff (KB) integrals of single-and multicomponent liquids using fluctuations of the number of molecules obtained from small-sized molecular dynamics simulations. We write finite-size versions of the Ornstein-Zernike and the KB integral equations and include there finite size effects related to the statistical ensemble and the finite integration volumes required in computer simulations. Consequently, we obtain analytical expressions connecting κ T and the KB integrals in the thermodynamic limit (TL) with density fluctuations in the simulated system. We validate the method by calculating various thermodynamic quantities, including the chemical potentials of SPC/E water as a function of the density, and of aqueous urea solutions as a function of the mole fraction. The reported results are in excellent agreement with calculations obtained by using the best computational methods available, thus validating the method as a tool to compute the chemical potentials of dense molecular liquids and mixtures. Furthermore, the present method identifies conditions in which computer simulations can be effectively considered in the TL.

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“…The SBA method has been proposed as a more efficient alternative where only one system is examined and then subdivided into blocks of different size from which the data are extracted. The method is rather general since it was originally proposed to study the critical behavior of Ising systems [ 14 , 15 ] and then extended to study liquids [ 16 , 17 , 18 , 19 , 20 , 21 ] and even the elastic constants of model solids [ 22 ].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we examine the SBA method focusing on the extrapolation of bulk thermodynamic properties of simple liquids. We use prototypical liquids and mixtures described by truncated and shifted Lennard–Jones (TSLJ) potentials to discuss the original ideas [ 16 , 17 ] and explore the background [ 20 , 21 , 23 , 24 , 25 , 26 ] for the most recent developments [ 6 , 7 , 9 ] of the method. The simple examples presented here, in addition to the results available in the literature [ 6 ], suggest that the method is suitable for the calculation of trends in the chemical potential of complex liquids in a wide range of density/concentration conditions.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method

Heidari

Kremer

Potestio

et al. 2018

Entropy

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Abstract:The spatial block analysis (SBA) method has been introduced to efficiently extrapolate thermodynamic quantities from finite-size computer simulations of a large variety of physical systems. In the particular case of simple liquids and liquid mixtures, by subdividing the simulation box into blocks of increasing size and calculating volume-dependent fluctuations of the number of particles, it is possible to extrapolate the bulk isothermal compressibility and Kirkwood-Buff integrals in the thermodynamic limit. Only by explicitly including finite-size effects, ubiquitous in computer simulations, into the SBA method, the extrapolation to the thermodynamic limit can be achieved. In this review, we discuss two of these finite-size effects in the context of the SBA method due to (i) the statistical ensemble and (ii) the finite integration domains used in computer simulations. To illustrate the method, we consider prototypical liquids and liquid mixtures described by truncated and shifted Lennard-Jones (TSLJ) potentials. Furthermore, we show some of the most recent developments of the SBA method, in particular its use to calculate chemical potentials of liquids in a wide range of density/concentration conditions.

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Particle fluctuations within sub-regions of an -particle, three-dimensional fluid: Finite-size effects and compressibility

Cited by 8 publications

References 10 publications

Chemical Potential Differences in the Macroscopic Limit from Fluctuations in Small Systems

Chemical Potential Differences in the Macroscopic Limit from Fluctuations in Small Systems

Finite-size integral equations in the theory of liquids and the thermodynamic limit in computer simulations

Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method

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