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Bakhshandeh A, Levin Y. Titration in Canonical and Grand-Canonical Ensembles. J Phys Chem B 2023; 127:9405-9411. [PMID: 37852244 DOI: 10.1021/acs.jpcb.3c05700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2023]
Abstract
We discuss problems associated with the notion of pH in heterogeneous systems. For homogeneous systems, standardization protocols lead to a well-defined quantity, which, although different from Sørensen's original idea of pH, is well reproducible and has become accepted as the measure of the "hydrogen potential". On the other hand, for heterogeneous systems, pH defined in terms of the chemical part of the electrochemical activity is thermodynamically inconsistent and runs afoul of the Gibbs-Guggenheim principle that forbids splitting of the electrochemical potential into separate chemical and electrostatic parts, since only the sum of two has any thermodynamic meaning. The problem is particularly relevant for modern simulation methods which involve charge regulation of proteins, polyelectrolytes, nanoparticles, colloidal suspensions, and so forth. In this paper, we show that titration isotherms calculated using semigrand canonical simulations can be very different from the ones obtained using canonical reactive Monte Carlo simulations.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul 91501-970, Brazil
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul 91501-970, Brazil
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Levin Y, Bakhshandeh A. A new method for reactive constant pH simulations. J Chem Phys 2023; 159:111101. [PMID: 37721322 DOI: 10.1063/5.0166840] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 08/29/2023] [Indexed: 09/19/2023] Open
Abstract
We present a simulation method that allows us to calculate the titration curves for systems undergoing protonation/deprotonation reactions-such as charged colloidal suspensions with acidic/basic surface groups, polyelectrolytes, polyampholytes, and proteins. The new approach allows us to simultaneously obtain titration curves both for systems in contact with salt and acid reservoir (semi-grand canonical ensemble) and for isolated suspensions (canonical ensemble). To treat the electrostatic interactions, we present a new method based on Ewald summation-which accounts for the existence of both Bethe and Donnan potentials within the simulation cell. We show that the Donnan potential dramatically affects the pH of a suspension. Counterintuitively, we find that in suspensions with a large volume fraction of nanoparticles and low ionic strength, the number of deprotonated groups can be 100% larger in an isolated system, compared to a system connected to a reservoir by a semi-permeable membrane-both systems being at exactly the same pH.
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Affiliation(s)
- Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
| | - Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
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Bakhshandeh A, Levin Y. Widom insertion method in simulations with Ewald summation. J Chem Phys 2022; 156:134110. [PMID: 35395875 DOI: 10.1063/5.0085527] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
We discuss the application of the Widom insertion method for calculation of the chemical potential of individual ions in computer simulations with Ewald summation. Two approaches are considered. In the first approach, an individual ion is inserted into a periodically replicated overall charge neutral system representing an electrolyte solution. In the second approach, an inserted ion is also periodically replicated, leading to the violation of the overall charge neutrality. This requires the introduction of an additional neutralizing background. We find that the second approach leads to a much better agreement with the results of grand canonical Monte Carlo simulation for the total chemical potential of a neutral ionic cluster.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
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Bakhshandeh A, Frydel D, Levin Y. Reactive Monte Carlo simulations for charge regulation of colloidal particles. J Chem Phys 2022; 156:014108. [PMID: 34998334 DOI: 10.1063/5.0077956] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
| | - Derek Frydel
- Department of Chemistry, Universidad Técnica Federico Santa María, Campus San Joaquin, 7820275 Santiago, Chile
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
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Landsgesell J, Hebbeker P, Rud O, Lunkad R, Košovan P, Holm C. Grand-Reaction Method for Simulations of Ionization Equilibria Coupled to Ion Partitioning. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c00260] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Jonas Landsgesell
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, D-70569 Stuttgart, Germany
| | - Pascal Hebbeker
- Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 2030, 128 43 Prague, Czech Republic
| | - Oleg Rud
- Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 2030, 128 43 Prague, Czech Republic
| | - Raju Lunkad
- Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 2030, 128 43 Prague, Czech Republic
| | - Peter Košovan
- Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 2030, 128 43 Prague, Czech Republic
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, D-70569 Stuttgart, Germany
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Hatch HW, Hall SW, Errington JR, Shen VK. Improving the efficiency of Monte Carlo simulations of ions using expanded grand canonical ensembles. J Chem Phys 2019; 151:144109. [PMID: 31615250 PMCID: PMC7254863 DOI: 10.1063/1.5123683] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software.
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Affiliation(s)
- Harold W. Hatch
- Chemical Informatics Research Group, Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8380, USA
| | - Steven W. Hall
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, SC 29634, USA
| | - Jeffrey R. Errington
- Department of Chemical and Biological Engineering, University at Buffalo, Buffalo, NY 14260, USA
| | - Vincent K. Shen
- Chemical Informatics Research Group, Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8380, USA
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Moucka F, Bratko D, Luzar A. Electrolyte pore/solution partitioning by expanded grand canonical ensemble Monte Carlo simulation. J Chem Phys 2015; 142:124705. [DOI: 10.1063/1.4914461] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Filip Moucka
- Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23221, USA
- Faculty of Science, J. E. Purkinje University, 400 96 Ústí nad Labem, Czech Republic
| | - Dusan Bratko
- Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23221, USA
| | - Alenka Luzar
- Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23221, USA
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