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Polonius S, Lehrner D, González L, Mai S. Resolving Photoinduced Femtosecond Three-Dimensional Solute-Solvent Dynamics through Surface Hopping Simulations. J Chem Theory Comput 2024; 20:4738-4750. [PMID: 38768386 PMCID: PMC11171268 DOI: 10.1021/acs.jctc.4c00169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2024] [Revised: 04/22/2024] [Accepted: 05/07/2024] [Indexed: 05/22/2024]
Abstract
Photoinduced dynamics in solution is governed by mutual solute-solvent interactions, which give rise to phenomena like solvatochromism, the Stokes shift, dual fluorescence, or charge transfer. Understanding these phenomena requires simulating the solute's photoinduced dynamics and simultaneously resolving the three-dimensional solvent distribution dynamics. If using trajectory surface hopping (TSH) to this aim, thousands of trajectories are required to adequately sample the time-dependent three-dimensional solvent distribution functions, and thus resolve the solvent dynamics with sub-Ångstrom and femtosecond accuracy and sufficiently low noise levels. Unfortunately, simulating thousands of trajectories with TSH in the framework of hybrid quantum mechanical/molecular mechanical (QM/MM) can be prohibitively expensive when employing ab initio electronic structure methods. To tackle this challenge, we recently introduced a computationally efficient approach that combines efficient linear vibronic coupling models with molecular mechanics (LVC/MM) via electrostatic embedding [Polonius et al., JCTC 2023, 19, 7171-7186]. This method provides solvent-embedded, nonadiabatically coupled potential energy surfaces while scaling similarly to MM force fields. Here, we employ TSH with LVC/MM to unravel the photoinduced dynamics of two small thiocarbonyl compounds solvated in water. We describe how to estimate the number of trajectories required to produce nearly noise-free three-dimensional solvent distribution functions and present an analysis based on approximately 10,000 trajectories propagated for 3 ps. In the electronic ground state, both molecules exhibit in-plane hydrogen bonds to the sulfur atom. Shortly after excitation, these bonds are broken and reform perpendicular to the molecular plane on timescales that differ by an order of magnitude due to steric effects. We also show that the solvent relaxation dynamics is coupled to the electronic dynamics, including intersystem crossing. These findings are relevant to advance the understanding of the coupled solute-solvent dynamics of solvated photoexcited molecules, e.g., biologically relevant thio-nucleobases.
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Affiliation(s)
- Severin Polonius
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
- Vienna
Doctoral School in Chemistry (DoSChem), University of Vienna, Währinger Str. 42, 1090 Vienna, Austria
| | - David Lehrner
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
| | - Leticia González
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
- Vienna
Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Sebastian Mai
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
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2
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Guo C, Yang K, Qin H, Zhu Y, Chen M, Lü Y. Abnormal condensation of water vapour at ambient temperature. Phys Chem Chem Phys 2024; 26:8784-8793. [PMID: 38420852 DOI: 10.1039/d3cp05628g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/02/2024]
Abstract
The homogeneous condensation of water vapor at ambient temperature is studied using molecular dynamics simulation. We reveal that there is a droplet size at the nanoscale where water droplets can be stabilized in the condensation process. Our simulations show that the growth of water droplets is dominated by collision and coagulation between small water droplets after nucleation. This process is found to be accompanied by exceptionally fast evaporation such that droplet growth is balanced by evaporation when water droplets grow to a critical size, approximately 12.5 Å in radius, reaching a stable size distribution. The extremely high evaporation rate is attributed to the curvature dependence of surface tension. Surface tension shows a significant decrease with decreasing droplet size below 20 Å, which causes the total free energy of nanoscaled water droplets to rise after collision and coagulation. Consequently, water droplets have to shrink via fast evaporation. The curvature dependence of surface tension is related to the dielectric ordering of water molecules near the surface of water droplets. Owing to fast evaporation, secondary condensation occurs, and many small water clusters form, ultimately exhibiting a bimodal distribution of water-droplet size.
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Affiliation(s)
- Chenchen Guo
- School of Physics, Beijing Institute of Technology, Beijing 100081, China.
- Changping School Attached to Beijing Normal University, Beijing 102206, China
| | - Kun Yang
- School of Physics, Beijing Institute of Technology, Beijing 100081, China.
| | - Hairong Qin
- School of Physics, Beijing Institute of Technology, Beijing 100081, China.
| | - Yong Zhu
- Science and Technology on Electromagnetic Scattering Laboratory, Beijing 100854, China
| | - Min Chen
- Department of Engineering Mechanics, Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
| | - Yongjun Lü
- School of Physics, Beijing Institute of Technology, Beijing 100081, China.
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3
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Dong W. Nanoscale thermodynamics needs the concept of a disjoining chemical potential. Nat Commun 2023; 14:1824. [PMID: 37005406 PMCID: PMC10067931 DOI: 10.1038/s41467-023-36970-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 02/21/2023] [Indexed: 04/04/2023] Open
Abstract
Disjoining pressure was discovered by Derjaguin in 1930's, which describes the difference between the pressure of a strongly confined fluid and the corresponding one in a bulk phase. It has been revealed recently that the disjoining pressure is at the origin of distinct differential and integral surface tensions for strongly confined fluids. Here we show how the twin concept, disjoining chemical potential, arises in a reminiscent way although it comes out eighty years later. This twin concept advances our understanding of nanoscale thermodynamics. Ensemble-dependence (or environment-dependence) is one hallmark of thermodynamics of small systems. We show that integral surface tension is ensemble-dependent while differential surface tension is not. Moreover, two generalized Gibbs-Duhem equations involving integral surface tensions are derived, as well as two additional adsorption equations relating surface tensions to adsorption-induced strains. All the results obtained in this work further evidence that an approach alternative of Hill's nanothermodynamics is possible, by extending Gibbs surface thermodynamics instead of resorting to Hill's replica trick. Moreover, we find a compression-expansion hysteresis without any underlying phase transition.
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Affiliation(s)
- W Dong
- Laboratoire de Chimie, CNRS, UMR 5182, Ecole Normale Supérieure de Lyon, 46, Allée d'Italie, 69364, Lyon, Cedex 07, France.
- State Key Laboratory of Chem/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, 410082, Changsha, China.
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4
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Bråten V, Zhang DT, Hammer M, Aasen A, Schnell SK, Wilhelmsen Ø. Equation of state for confined fluids. J Chem Phys 2022; 156:244504. [DOI: 10.1063/5.0096875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fluids confined in small volumes behave differently than fluids in bulk systems. For bulk systems, a compact summary of the system’s thermodynamic properties is provided by equations of state. However, there is currently a lack of successful methods to predict the thermodynamic properties of confined fluids by use of equations of state, since their thermodynamic state depends on additional parameters introduced by the enclosing surface. In this work, we present a consistent thermodynamic framework that represents an equation of state for pure, confined fluids. The total system is decomposed into a bulk phase in equilibrium with a surface phase. The equation of state is based on an existing, accurate description of the bulk fluid and uses Gibbs’ framework for surface excess properties to consistently incorporate contributions from the surface. We apply the equation of state to a Lennard-Jones spline fluid confined by a spherical surface with a Weeks–Chandler–Andersen wall-potential. The pressure and internal energy predicted from the equation of state are in good agreement with the properties obtained directly from molecular dynamics simulations. We find that when the location of the dividing surface is chosen appropriately, the properties of highly curved surfaces can be predicted from those of a planar surface. The choice of the dividing surface affects the magnitude of the surface excess properties and its curvature dependence, but the properties of the total system remain unchanged. The framework can predict the properties of confined systems with a wide range of geometries, sizes, interparticle interactions, and wall–particle interactions, and it is independent of ensemble. A targeted area of use is the prediction of thermodynamic properties in porous media, for which a possible application of the framework is elaborated.
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Affiliation(s)
- Vilde Bråten
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Daniel Tianhou Zhang
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Morten Hammer
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
- Gas Technology, PoreLab, SINTEF Energy Research, Trondheim NO-7465, Norway
| | - Ailo Aasen
- Gas Technology, PoreLab, SINTEF Energy Research, Trondheim NO-7465, Norway
| | - Sondre Kvalvåg Schnell
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Øivind Wilhelmsen
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
- Gas Technology, PoreLab, SINTEF Energy Research, Trondheim NO-7465, Norway
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5
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Bruch D, Balzer C, Wang ZG. Thermodynamics of Electrolyte Solutions Near Charged Surfaces: Constant Surface Charge vs. Constant Surface Potential. J Chem Phys 2022; 156:174704. [DOI: 10.1063/5.0089260] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational---that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson--Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.
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Affiliation(s)
- Dorian Bruch
- Chemistry and Chemical Engineering, California Institute of Technology Division of Chemistry and Chemical Engineering, United States of America
| | | | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, United States of America
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6
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Bråten V, Bedeaux D, Wilhelmsen Ø, Schnell SK. Small size effects in open and closed systems: What can we learn from ideal gases about systems with interacting particles? J Chem Phys 2021; 155:244504. [PMID: 34972373 DOI: 10.1063/5.0076684] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Small systems have higher surface area-to-volume ratios than macroscopic systems. The thermodynamics of small systems therefore deviates from the description of classical thermodynamics. One consequence of this is that properties of small systems can be dependent on the system's ensemble. By comparing the properties in grand canonical (open) and canonical (closed) systems, we investigate how a small number of particles can induce an ensemble dependence. Emphasis is placed on the insight that can be gained by investigating ideal gases. The ensemble equivalence of small ideal gas systems is investigated by deriving the properties analytically, while the ensemble equivalence of small systems with particles interacting via the Lennard-Jones or the Weeks-Chandler-Andersen potential is investigated through Monte Carlo simulations. For all the investigated small systems, we find clear differences between the properties in open and closed systems. For systems with interacting particles, the difference between the pressure contribution to the internal energy, and the difference between the chemical potential contribution to the internal energy, are both increasing with the number density. The difference in chemical potential is, with the exception of the density dependence, qualitatively described by the analytic formula derived for an ideal gas system. The difference in pressure, however, is not captured by the ideal gas model. For the difference between the properties in the open and closed systems, the response of increasing the particles' excluded volume is similar to the response of increasing the repulsive forces on the system walls. This indicates that the magnitude of the difference between the properties in open and closed systems is related to the restricted movement of the particles in the system. The work presented in this paper gives insight into the mechanisms behind ensemble in-equivalence in small systems, and illustrates how a simple statistical mechanical model, such as the ideal gas, can be a useful tool in these investigations.
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Affiliation(s)
- Vilde Bråten
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Dick Bedeaux
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Øivind Wilhelmsen
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Sondre Kvalvåg Schnell
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
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7
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Klein T, Piszko M, Kankanamge CJ, Kasapis G, Fröba AP. Fick Diffusion Coefficient in Binary Mixtures of [HMIM][NTf 2] and Carbon Dioxide by Dynamic Light Scattering and Molecular Dynamics Simulations. J Phys Chem B 2021; 125:5100-5113. [PMID: 33960781 DOI: 10.1021/acs.jpcb.1c01616] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Dynamic light scattering (DLS) experiments and equilibrium molecular dynamics (EMD) simulations were performed in the saturated liquid phase of the binary mixture of 1-hexyl-3-methylimidazolium bis(trifluormethylsulfonyl)imide ([HMIM][NTf2]) and carbon dioxide (CO2) to access the Fick diffusion coefficient (D11). The investigations were performed within or close to saturation conditions at temperatures between (298.15 and 348.15) K and CO2 mole fractions (xCO2) up to 0.81. The DLS experiments were combined with polarization-difference Raman spectroscopy (PDRS) to simultaneously access the composition of the liquid phase. For the first time in an electrolyte-based system, D11 was directly calculated from EMD simulations by accessing the Maxwell-Stefan (MS) diffusion coefficient and the thermodynamic factor. Agreement within combined uncertainties was found between D11 from DLS and EMD simulations for CO2 mole fractions up to 0.5. In general, an increasing D11 with increasing xCO2 could be observed, with a local maximum present at a CO2 mole fraction of about 0.75. The local maximum could be explained by an increasing MS diffusion coefficient with increasing xCO2 over the entire studied composition range and a decreasing thermodynamic factor at xCO2 above 0.7. Finally, PDRS and EMD simulations were combined to investigate the influence of the fluid structure on the diffusive process.
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Affiliation(s)
- Tobias Klein
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany
| | - Maximilian Piszko
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany
| | - Chathura J Kankanamge
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany
| | - Georgios Kasapis
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany.,Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, Robert Stevenson Road, Edinburgh EH9 3FB, U.K
| | - Andreas P Fröba
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany
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8
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Bråten V, Wilhelmsen Ø, Schnell SK. Chemical Potential Differences in the Macroscopic Limit from Fluctuations in Small Systems. J Chem Inf Model 2021; 61:840-855. [PMID: 33566592 PMCID: PMC8023585 DOI: 10.1021/acs.jcim.0c01367] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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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Affiliation(s)
- Vilde Bråten
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Øivind Wilhelmsen
- SINTEF Energy Research, Trondheim NO-7465, Norway.,Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim NO-7491, Norway
| | - Sondre Kvalvåg Schnell
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim N-7491, Norway
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9
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Strøm BA, Bedeaux D, Schnell SK. Adsorption of an Ideal Gas on a Small Spherical Adsorbent. NANOMATERIALS 2021; 11:nano11020431. [PMID: 33572075 PMCID: PMC7915188 DOI: 10.3390/nano11020431] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Revised: 02/04/2021] [Accepted: 02/06/2021] [Indexed: 11/16/2022]
Abstract
The ideal gas model is an important and useful model in classical thermodynamics. This remains so for small systems. Molecules in a gas can be adsorbed on the surface of a sphere. Both the free gas molecules and the adsorbed molecules may be modeled as ideal for low densities. The adsorption energy, Us, plays an important role in the analysis. For small adsorbents this energy depends on the curvature of the adsorbent. We model the adsorbent as a sphere with surface area Ω=4πR2, where R is the radius of the sphere. We calculate the partition function for a grand canonical ensemble of two-dimensional adsorbed phases. When connected with the nanothermodynamic framework this gives us the relevant thermodynamic variables for the adsorbed phase controlled by the temperature T, surface area Ω, and chemical potential μ. The dependence of intensive variables on size may then be systematically investigated starting from the simplest model, namely the ideal adsorbed phase. This dependence is a characteristic feature of small systems which is naturally expressed by the subdivision potential of nanothermodynamics. For surface problems, the nanothermodynamic approach is different, but equivalent to Gibbs’ surface thermodynamics. It is however a general approach to the thermodynamics of small systems, and may therefore be applied to systems that do not have well defined surfaces. It is therefore desirable and useful to improve our basic understanding of nanothermodynamics.
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Affiliation(s)
- Bjørn A. Strøm
- Department of Materials Science and Engineering, Faculty of Natural Sciences, Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway;
- Correspondence:
| | - Dick Bedeaux
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway;
| | - Sondre K. Schnell
- Department of Materials Science and Engineering, Faculty of Natural Sciences, Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway;
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10
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Thermodynamics of interfaces extended to nanoscales by introducing integral and differential surface tensions. Proc Natl Acad Sci U S A 2021; 118:2019873118. [PMID: 33452136 DOI: 10.1073/pnas.2019873118] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
As a system shrinks down in size, more and more molecules are found in its surface region, so surface contribution becomes a large or even a dominant part of its thermodynamic potentials. Surface tension is a venerable scientific concept; Gibbs defined it as the excess of grand potential of an inhomogeneous system with respect to its bulk value per interface area [J. W. Gibbs, "The Collected Works" in Thermodynamics (1928), Vol. 1]. The mechanical definition expresses it in terms of pressure tensor. So far, it has been believed the two definitions always give the same result. We show that the equivalence can break down for fluids confined in narrow pores. New concepts of integral and differential surface tensions, along with integral and differential adsorptions, need to be introduced for extending Gibbs thermodynamics of interfaces. We derived two generalized Gibbs adsorption equations. These concepts are indispensable for an adequate description of nanoscale systems. We also find a relation between integral surface tension and Derjaguin's disjoining pressure. This lays down the basis for measuring integral and differential surface tensions from disjoining pressure by using an atomic force microscope.
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11
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Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore. NANOMATERIALS 2021; 11:nano11010165. [PMID: 33440819 PMCID: PMC7827573 DOI: 10.3390/nano11010165] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Revised: 01/01/2021] [Accepted: 01/06/2021] [Indexed: 01/28/2023]
Abstract
We have described for the first time the thermodynamic state of a highly confined single-phase and single-component fluid in a slit pore using Hill's thermodynamics of small systems. Hill's theory has been named nanothermodynamics. We started by constructing an ensemble of slit pores for controlled temperature, volume, surface area, and chemical potential. We have presented the integral and differential properties according to Hill, and used them to define the disjoining pressure on the new basis. We identified all thermodynamic pressures by their mechanical counterparts in a consistent manner, and have given evidence that the identification holds true using molecular simulations. We computed the entropy and energy densities, and found in agreement with the literature, that the structures at the wall are of an energetic, not entropic nature. We have shown that the subdivision potential is unequal to zero for small wall surface areas. We have showed how Hill's method can be used to find new Maxwell relations of a confined fluid, in addition to a scaling relation, which applies when the walls are far enough apart. By this expansion of nanothermodynamics, we have set the stage for further developments of the thermodynamics of confined fluids, a field that is central in nanotechnology.
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12
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Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be 6B 11- Flux-Ional Cluster. MATERIALS 2020; 14:ma14010112. [PMID: 33383889 PMCID: PMC7796227 DOI: 10.3390/ma14010112] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/27/2020] [Revised: 12/23/2020] [Accepted: 12/24/2020] [Indexed: 02/06/2023]
Abstract
The starting point to understanding cluster properties is the putative global minimum and all the nearby local energy minima; however, locating them is computationally expensive and difficult. The relative populations and spectroscopic properties that are a function of temperature can be approximately computed by employing statistical thermodynamics. Here, we investigate entropy-driven isomers distribution on Be6B11− clusters and the effect of temperature on their infrared spectroscopy and relative populations. We identify the vibration modes possessed by the cluster that significantly contribute to the zero-point energy. A couple of steps are considered for computing the temperature-dependent relative population: First, using a genetic algorithm coupled to density functional theory, we performed an extensive and systematic exploration of the potential/free energy surface of Be6B11− clusters to locate the putative global minimum and elucidate the low-energy structures. Second, the relative populations’ temperature effects are determined by considering the thermodynamic properties and Boltzmann factors. The temperature-dependent relative populations show that the entropies and temperature are essential for determining the global minimum. We compute the temperature-dependent total infrared spectra employing the Boltzmann factor weighted sums of each isomer’s infrared spectrum and find that at finite temperature, the total infrared spectrum is composed of an admixture of infrared spectra that corresponds to the spectra of the lowest-energy structure and its isomers located at higher energies. The methodology and results describe the thermal effects in the relative population and the infrared spectra.
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13
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Strøm BA, He J, Bedeaux D, Kjelstrup S. When Thermodynamic Properties of Adsorbed Films Depend on Size: Fundamental Theory and Case Study. NANOMATERIALS 2020; 10:nano10091691. [PMID: 32867403 PMCID: PMC7558047 DOI: 10.3390/nano10091691] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Revised: 08/18/2020] [Accepted: 08/19/2020] [Indexed: 01/07/2023]
Abstract
Small system properties are known to depend on geometric variables in ways that are insignificant for macroscopic systems. Small system considerations are therefore usually added to the conventional description as needed. This paper presents a thermodynamic analysis of adsorbed films of any size in a systematic and general way within the framework of Hill’s nanothermodynamics. Hill showed how to deal with size and shape as variables in a systematic manner. By doing this, the common thermodynamic equations for adsorption are changed. We derived the governing thermodynamic relations characteristic of adsorption in small systems, and point out the important distinctions between these and the corresponding conventional relations for macroscopic systems. We present operational versions of the relations specialized for adsorption of gas on colloid particles, and we applied them to analyze molecular simulation data. As an illustration of their use, we report results for CO2 adsorbed on graphite spheres. We focus on the spreading pressure, and the entropy and enthalpy of adsorption, and show how the intensive properties are affected by the size of the surface, a feature specific to small systems. The subdivision potential of the film is presented for the first time, as a measure of the film’s smallness. For the system chosen, it contributes with a substantial part to the film enthalpy. This work can be considered an extension and application of the nanothermodynamic theory developed by Hill. It provides a foundation for future thermodynamic analyses of size- and shape-dependent adsorbed film systems, alternative to that presented by Gibbs.
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Affiliation(s)
- Bjørn A. Strøm
- Department of Structural Engineering, Faculty of Engineering Science and Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway;
- Correspondence:
| | - Jianying He
- Department of Structural Engineering, Faculty of Engineering Science and Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway;
| | - Dick Bedeaux
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway; (D.B.); (S.K.)
| | - Signe Kjelstrup
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway; (D.B.); (S.K.)
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14
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Tripathy M, Bharadwaj S, B. SJ, van der Vegt NFA. Characterizing Polymer Hydration Shell Compressibilities with the Small-System Method. NANOMATERIALS 2020; 10:nano10081460. [PMID: 32722500 PMCID: PMC7466400 DOI: 10.3390/nano10081460] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Revised: 07/21/2020] [Accepted: 07/22/2020] [Indexed: 12/03/2022]
Abstract
The small-system method (SSM) exploits the unique feature of finite-sized open systems, whose thermodynamic quantities scale with the inverse system size. This scaling enables the calculation of properties in the thermodynamic limit of macroscopic systems based on computer simulations of finite-sized systems. We herein extend the SSM to characterize the hydration shell compressibility of a generic hydrophobic polymer in water. By systematically increasing the strength of polymer-water repulsion, we find that the excess inverse thermodynamic correction factor (Δ1/Γs∞) and compressibility (Δχs) of the first hydration shell change sign from negative to positive. This occurs with a concurrent decrease in water hydrogen bonding and local tetrahedral order of the hydration shell water. The crossover lengthscale corresponds to an effective polymer bead diameter of 0.7 nm and is consistent with previous works on hydration of small and large hydrophobic solutes. The crossover lengthscale in polymer hydration shell compressibility, herein identified with the SSM approach, relates to hydrophobic interactions and macromolecular conformational equilibria in aqueous solution. The SSM approach may further be applied to study thermodynamic properties of polymer solvation shells in mixed solvents.
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Gavriil V, Chatzichristidi M, Christofilos D, Kourouklis GA, Kollia Z, Bakalis E, Cefalas AC, Sarantopoulou E. Entropy and Random Walk Trails Water Confinement and Non-Thermal Equilibrium in Photon-Induced Nanocavities. NANOMATERIALS (BASEL, SWITZERLAND) 2020; 10:E1101. [PMID: 32498312 PMCID: PMC7353189 DOI: 10.3390/nano10061101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Revised: 05/18/2020] [Accepted: 05/22/2020] [Indexed: 01/18/2023]
Abstract
Molecules near surfaces are regularly trapped in small cavitations. Molecular confinement, especially water confinement, shows intriguing and unexpected behavior including surface entropy adjustment; nevertheless, observations of entropic variation during molecular confinement are scarce. An experimental assessment of the correlation between surface strain and entropy during molecular confinement in tiny crevices is difficult because strain variances fall in the nanometer scale. In this work, entropic variations during water confinement in 2D nano/micro cavitations were observed. Experimental results and random walk simulations of water molecules inside different size nanocavitations show that the mean escaping time of molecular water from nanocavities largely deviates from the mean collision time of water molecules near surfaces, crafted by 157 nm vacuum ultraviolet laser light on polyacrylamide matrixes. The mean escape time distribution of a few molecules indicates a non-thermal equilibrium state inside the cavity. The time differentiation inside and outside nanocavities reveals an additional state of ordered arrangements between nanocavities and molecular water ensembles of fixed molecular length near the surface. The configured number of microstates correctly counts for the experimental surface entropy deviation during molecular water confinement. The methodology has the potential to identify confined water molecules in nanocavities with life science importance.
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Affiliation(s)
- Vassilios Gavriil
- National Hellenic Research Foundation, Theoretical and Physical Chemistry Institute, 48 Vassileos Constantinou Avenue, 11635 Athens, Greece; (V.G.); (Z.K.); (E.B.); (A.-C.C.)
- School of Chemical Engineering and Physics Laboratory, Faculty of Engineering, Aristotle University of Thessaloniki, University Campus, 54124 Thessaloniki, Greece; (D.C.); (G.A.K.)
| | - Margarita Chatzichristidi
- Department of Chemistry, Laboratory of Industrial Chemistry, Panepistimiopolis Zografou, National and Kapodistrian University of Athens, 15771 Athens, Greece;
| | - Dimitrios Christofilos
- School of Chemical Engineering and Physics Laboratory, Faculty of Engineering, Aristotle University of Thessaloniki, University Campus, 54124 Thessaloniki, Greece; (D.C.); (G.A.K.)
| | - Gerasimos A. Kourouklis
- School of Chemical Engineering and Physics Laboratory, Faculty of Engineering, Aristotle University of Thessaloniki, University Campus, 54124 Thessaloniki, Greece; (D.C.); (G.A.K.)
| | - Zoe Kollia
- National Hellenic Research Foundation, Theoretical and Physical Chemistry Institute, 48 Vassileos Constantinou Avenue, 11635 Athens, Greece; (V.G.); (Z.K.); (E.B.); (A.-C.C.)
| | - Evangelos Bakalis
- National Hellenic Research Foundation, Theoretical and Physical Chemistry Institute, 48 Vassileos Constantinou Avenue, 11635 Athens, Greece; (V.G.); (Z.K.); (E.B.); (A.-C.C.)
- Dipartimento di Chimica “G. Giamician” University di Bologna, Via F. Selmi 2, 40126 Bologna, Italy
| | - Alkiviadis-Constantinos Cefalas
- National Hellenic Research Foundation, Theoretical and Physical Chemistry Institute, 48 Vassileos Constantinou Avenue, 11635 Athens, Greece; (V.G.); (Z.K.); (E.B.); (A.-C.C.)
| | - Evangelia Sarantopoulou
- National Hellenic Research Foundation, Theoretical and Physical Chemistry Institute, 48 Vassileos Constantinou Avenue, 11635 Athens, Greece; (V.G.); (Z.K.); (E.B.); (A.-C.C.)
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Dawass N, Krüger P, Schnell SK, Moultos OA, Economou IG, Vlugt TJH, Simon JM. Kirkwood-Buff Integrals Using Molecular Simulation: Estimation of Surface Effects. NANOMATERIALS 2020; 10:nano10040771. [PMID: 32316368 PMCID: PMC7221661 DOI: 10.3390/nano10040771] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Revised: 04/06/2020] [Accepted: 04/13/2020] [Indexed: 11/24/2022]
Abstract
Kirkwood-Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard–Jones (LJ) and Weeks–Chandler–Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.
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Affiliation(s)
- Noura Dawass
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands
| | - Peter Krüger
- Graduate School of Engineering and Molecular Chirality Research Center, Chiba University, Chiba 263-8522, Japan
| | - Sondre K Schnell
- Department of Materials Science and Engineering, NTNU, N-7491 Trondheim, Norway
| | - Othonas A Moultos
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands
| | - Ioannis G Economou
- National Center for Scientific Research Demokritos, Institute of Nanoscience and Nanotechnology, Molecular Thermodynamics and Modelling of Materials Laboratory, GR 153 10 Aghia Paraskevi Attikis, Greece
- Chemical Engineering Program, Texas A&M University at Qatar, Education City, PO Box 23874 Doha, Qatar
| | - Thijs J H Vlugt
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands
| | - Jean-Marc Simon
- ICB, UMR 6303 CNRS - Université de Bourgogne, F-21078 Dijon, France
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17
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Rauter MT, Galteland O, Erdős M, Moultos OA, Vlugt TJH, Schnell SK, Bedeaux D, Kjelstrup S. Two-Phase Equilibrium Conditions in Nanopores. NANOMATERIALS 2020; 10:nano10040608. [PMID: 32224924 PMCID: PMC7221961 DOI: 10.3390/nano10040608] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/25/2020] [Revised: 03/20/2020] [Accepted: 03/21/2020] [Indexed: 11/16/2022]
Abstract
It is known that thermodynamic properties of a system change upon confinement. To know how, is important for modelling of porous media. We propose to use Hill's systematic thermodynamic analysis of confined systems to describe two-phase equilibrium in a nanopore. The integral pressure, as defined by the compression energy of a small volume, is then central. We show that the integral pressure is constant along a slit pore with a liquid and vapor in equilibrium, when Young and Young-Laplace's laws apply. The integral pressure of a bulk fluid in a slit pore at mechanical equilibrium can be understood as the average tangential pressure inside the pore. The pressure at mechanical equilibrium, now named differential pressure, is the average of the trace of the mechanical pressure tensor divided by three as before. Using molecular dynamics simulations, we computed the integral and differential pressures, p ^ and p, respectively, analysing the data with a growing-core methodology. The value of the bulk pressure was confirmed by Gibbs ensemble Monte Carlo simulations. The pressure difference times the volume, V, is the subdivision potential of Hill, ( p - p ^ ) V = ϵ . The combined simulation results confirm that the integral pressure is constant along the pore, and that ϵ / V scales with the inverse pore width. This scaling law will be useful for prediction of thermodynamic properties of confined systems in more complicated geometries.
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Affiliation(s)
- Michael T. Rauter
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway; (O.G.); (D.B.); (S.K.)
- Correspondence:
| | - Olav Galteland
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway; (O.G.); (D.B.); (S.K.)
| | - Máté Erdős
- Engineering Thermodynamics, Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands; (M.E.); (O.A.M.); (T.J.H.V.)
| | - Othonas A. Moultos
- Engineering Thermodynamics, Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands; (M.E.); (O.A.M.); (T.J.H.V.)
| | - Thijs J. H. Vlugt
- Engineering Thermodynamics, Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands; (M.E.); (O.A.M.); (T.J.H.V.)
| | - Sondre K. Schnell
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway;
| | - Dick Bedeaux
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway; (O.G.); (D.B.); (S.K.)
| | - Signe Kjelstrup
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway; (O.G.); (D.B.); (S.K.)
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18
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Hill’s nano-thermodynamics is equivalent with Gibbs’ thermodynamics for surfaces of constant curvatures. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.07.031] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Photons Probe Entropic Potential Variation during Molecular Confinement in Nanocavities. ENTROPY 2018; 20:e20080545. [PMID: 33265634 PMCID: PMC7513070 DOI: 10.3390/e20080545] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Revised: 07/20/2018] [Accepted: 07/21/2018] [Indexed: 12/02/2022]
Abstract
In thin polymeric layers, external molecular analytes may well be confined within tiny surface nano/microcavities, or they may be attached to ligand adhesion binding sites via electrical dipole forces. Even though molecular trapping is followed by a variation of the entropic potential, the experimental evidence of entropic energy variation from molecular confinement is scarce because tiny thermodynamic energy density diverseness can be tracked only by sub-nm surface strain. Here, it is shown that water confinement within photon-induced nanocavities in Poly (2-hydroxyethyl methacrylate), (PHEMA) layers could be trailed by an entropic potential variation that competes with a thermodynamic potential from electric dipole attachment of molecular adsorbates in polymeric ligands. The nano/microcavities and the ligands were fabricated on a PHEMA matrix by vacuum ultraviolet laser photons at 157 nm. The entropic energy variation during confinement of water analytes on the photon processed PHEMA layer was monitored via sub-nm surface strain by applying white light reflectance spectroscopy, nanoindentation, contact angle measurements, Atomic Force Microscopy (AFM) imaging, and surface and fractal analysis. The methodology has the potency to identify entropic energy density variations less than 1 pJm−3 and to monitor dipole and entropic fields on biosurfaces.
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20
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Krüger P, Vlugt TJH. Size and shape dependence of finite-volume Kirkwood-Buff integrals. Phys Rev E 2018; 97:051301. [PMID: 29906830 DOI: 10.1103/physreve.97.051301] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2018] [Indexed: 11/07/2022]
Abstract
Analytic relations are derived for finite-volume integrals over the pair correlation function of a fluid, the so-called Kirkwood-Buff integrals. Closed-form expressions are obtained for cubes and cuboids, the system shapes commonly employed in molecular simulations. When finite-volume Kirkwood-Buff integrals are expanded over an inverse system size, the leading term depends on shape only through the surface area-to-volume ratio. This conjecture is proved for arbitrary shapes and a general expression for the leading term is derived. From this, an extrapolation to the infinite-volume limit is proposed, which converges much faster with system size than previous approximations and thus significantly simplifies the numerical computations.
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Affiliation(s)
- Peter Krüger
- Graduate School of Engineering and Molecular Chirality Research Center, Chiba University, 1-33 Yayoi-cho, Inage, Chiba 263-8522, Japan
| | - Thijs J H Vlugt
- Engineering Thermodynamics, Process & Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
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21
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Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method. ENTROPY 2018; 20:e20040222. [PMID: 33265313 PMCID: PMC7512739 DOI: 10.3390/e20040222] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Revised: 03/21/2018] [Accepted: 03/22/2018] [Indexed: 12/04/2022]
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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22
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Affiliation(s)
- Noura Dawass
- Process & Energy Laboratory, Delft University of Technology, Delft, The Netherlands
| | - Peter Krüger
- Graduate School of Science and Engineering, Chiba University, Chiba, Japan
| | | | - Thijs J. H. Vlugt
- Process & Energy Laboratory, Delft University of Technology, Delft, The Netherlands
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23
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Dawass N, Krüger P, Schnell SK, Bedeaux D, Kjelstrup S, Simon JM, Vlugt TJH. Finite-size effects of Kirkwood–Buff integrals from molecular simulations. MOLECULAR SIMULATION 2017. [DOI: 10.1080/08927022.2017.1416114] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- N. Dawass
- Process & Energy Laboratory, Delft University of Technology, Delft, The Netherlands
| | - P. Krüger
- Graduate School of Science and Engineering, Molecular Chirality Research Center, Chiba University, Chiba, Japan
- ICB, UMR 6303 CNRS – Université de Bourgogne, Dijon, France
| | - S. K. Schnell
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim, Norway
| | - D. Bedeaux
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim, Norway
| | - S. Kjelstrup
- Process & Energy Laboratory, Delft University of Technology, Delft, The Netherlands
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim, Norway
| | - J. M. Simon
- ICB, UMR 6303 CNRS – Université de Bourgogne, Dijon, France
| | - T. J. H. Vlugt
- Process & Energy Laboratory, Delft University of Technology, Delft, The Netherlands
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