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Scher Y, Lauber Bonomo O, Pal A, Reuveni S. Microscopic theory of adsorption kinetics. J Chem Phys 2023; 158:094107. [PMID: 36889971 DOI: 10.1063/5.0121359] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023] Open
Abstract
Adsorption is the accumulation of a solute at an interface that is formed between a solution and an additional gas, liquid, or solid phase. The macroscopic theory of adsorption dates back more than a century and is now well-established. Yet, despite recent advancements, a detailed and self-contained theory of single-particle adsorption is still lacking. Here, we bridge this gap by developing a microscopic theory of adsorption kinetics, from which the macroscopic properties follow directly. One of our central achievements is the derivation of the microscopic version of the seminal Ward-Tordai relation, which connects the surface and subsurface adsorbate concentrations via a universal equation that holds for arbitrary adsorption dynamics. Furthermore, we present a microscopic interpretation of the Ward-Tordai relation that, in turn, allows us to generalize it to arbitrary dimension, geometry, and initial conditions. The power of our approach is showcased on a set of hitherto unsolved adsorption problems to which we present exact analytical solutions. The framework developed herein sheds fresh light on the fundamentals of adsorption kinetics, which opens new research avenues in surface science with applications to artificial and biological sensing and to the design of nano-scale devices.
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Affiliation(s)
- Yuval Scher
- School of Chemistry, Center for the Physics and Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
| | - Ofek Lauber Bonomo
- School of Chemistry, Center for the Physics and Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
| | - Shlomi Reuveni
- School of Chemistry, Center for the Physics and Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
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Ha J, Kim M, Lee S. Excluded Volume Effects on the Kinetics of Diffusion-influenced Reversible Bimolecular Reactions: A + B ⇄ C + B. B KOREAN CHEM SOC 2016. [DOI: 10.1002/bkcs.10870] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Jimin Ha
- Department of Chemistry; Seoul National University; Seoul 151-747 South Korea
| | - Minjung Kim
- Department of Chemistry; Seoul National University; Seoul 151-747 South Korea
| | - Sangyoub Lee
- Department of Chemistry; Seoul National University; Seoul 151-747 South Korea
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Agmon N. The residence probability: single molecule fluorescence correlation spectroscopy and reversible geminate recombination. Phys Chem Chem Phys 2011; 13:16548-57. [PMID: 21860864 DOI: 10.1039/c1cp20907h] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Noam Agmon
- The Fritz Haber Research Center, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel.
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Affiliation(s)
- Soohyung Park
- Institute of Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
| | - Noam Agmon
- Institute of Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
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Markovitch O, Agmon N. The distribution of acceptor and donor hydrogen-bonds in bulk liquid water. Mol Phys 2008. [DOI: 10.1080/00268970701877921] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Reversible Excited-State Proton Transfer: Effect of the Switching of Interaction Potential by Reaction. B KOREAN CHEM SOC 2006. [DOI: 10.5012/bkcs.2006.27.2.197] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Nonequilibrium Distribution Function Theory of Many-Particle Effects in the Reversible Reactions of the Type A+B ↔ C+B. B KOREAN CHEM SOC 2005. [DOI: 10.5012/bkcs.2005.26.12.1986] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Popov AV, Agmon N. Three-dimensional simulations of reversible bimolecular reactions. III. The pseudo-unimolecular ABCD reaction. J Chem Phys 2003. [DOI: 10.1063/1.1570816] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Popov AV, Agmon N. Three-dimensional simulations of reversible bimolecular reactions. II. The excited-state target problem with different lifetimes. J Chem Phys 2002. [DOI: 10.1063/1.1496455] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Affiliation(s)
- Noam Agmon
- Department of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel
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Popov AV, Agmon N. Three-dimensional simulations of reversible bimolecular reactions: The simple target problem. J Chem Phys 2001. [DOI: 10.1063/1.1412609] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gopich IV, Agmon N. Rigorous derivation of the long-time asymptotics for reversible binding. PHYSICAL REVIEW LETTERS 2000; 84:2730-2733. [PMID: 11017311 DOI: 10.1103/physrevlett.84.2730] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/1999] [Indexed: 05/23/2023]
Abstract
Using an iterative solution in Laplace-Fourier space, we supply a rigorous mathematical proof for the long-time asymptotics of reversible binding in one dimension. The asymptotic power law and its concentration dependent prefactor result from diffusional and many-body effects which, unlike for the corresponding irreversible reaction and in classical chemical kinetics, play a dominant role in shaping the approach to equilibrium.
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Affiliation(s)
- IV Gopich
- Department of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel
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Agmon N, Gopich IV. Exact long-time asymptotics for reversible binding in three dimensions. J Chem Phys 2000. [DOI: 10.1063/1.480860] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Gopich IV, Agmon N. Excited-state reversible geminate reaction. III. Exact solution for noninteracting partners. J Chem Phys 1999. [DOI: 10.1063/1.478974] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gopich IV, Solntsev KM, Agmon N. Excited-state reversible geminate reaction. I. Two different lifetimes. J Chem Phys 1999. [DOI: 10.1063/1.477827] [Citation(s) in RCA: 77] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Sung J, Shin KJ, Lee S. Relaxation kinetics of diffusion-influenced reactions of the type A+B⇄C perturbed by flash photolysis. J Chem Phys 1998. [DOI: 10.1063/1.477466] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yang M, Lee S, Shin KJ. Kinetic theory of bimolecular reactions in liquid. III. Reversible association–dissociation: A+B⇄C. J Chem Phys 1998. [DOI: 10.1063/1.476353] [Citation(s) in RCA: 60] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Yang M, Lee S, Shin KJ. Kinetic theory of bimolecular reactions in liquid. II. Reversible reaction A+B⇄C+B. J Chem Phys 1998. [DOI: 10.1063/1.476285] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sung J, Shin KJ, Lee S. Many-particle effects on the relaxation kinetics of fast reversible reactions of the type A+B⇄C. J Chem Phys 1997. [DOI: 10.1063/1.475239] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Molski A, Boens N. Convolution Kinetics with Generation and Decay for Reversible Excited-State Processes. J Phys Chem A 1997. [DOI: 10.1021/jp9630075] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andrzej Molski
- Department of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Poznań, Poland
| | - Noël Boens
- Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200F, 3001 Heverlee, Belgium
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Abstract
We investigate the various reactivity patterns possible when several transmitter molecules, released at one side of a synaptic gap, diffuse and bind reversibly to a single receptor at the other end. In the framework of a one-dimensional approximation, the complete time, reactivity, concentration and gap-width dependence are determined, using a rigorous theoretical and computational approach to the many-body aspects of this problem. The time dependence of the survival probability is found to consist of up to four phases. These include a short delay followed by gaussian, power-law, and exponential decay phases. A rigorous expression is derived for the long-time exponent and approximate expressions are obtained for describing the short-time gaussian phase.
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Affiliation(s)
- N Agmon
- Department of Physical Chemistry, Hebrew University, Jerusalem, Israel
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Agmon N, Edelstein AL. The long‐time behavior of reversible binary reactions: Theory, Brownian simulations and experiment. J Chem Phys 1994. [DOI: 10.1063/1.466302] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Edelstein AL, Agmon N. Brownian dynamics simulations of reversible reactions in one dimension. J Chem Phys 1993. [DOI: 10.1063/1.465983] [Citation(s) in RCA: 65] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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