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Lee S. Operator algebraic methods in the theory of
diffusion‐influenced
reaction kinetics. B KOREAN CHEM SOC 2021. [DOI: 10.1002/bkcs.12448] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Sangyoub Lee
- Professor Sangyoub Lee, Department of Chemistry Seoul National University Seoul South Korea
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2
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Kipriyanov AA, Doktorov AB. Theory of reversible associative-dissociative diffusion-influenced chemical reaction. II. Bulk reaction. J Chem Phys 2013; 138:044114. [DOI: 10.1063/1.4779476] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
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3
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Doktorov AB, Kipriyanov AA, Kipriyanov AA. Accumulation and Decay of Macroscopic Correlations in Elementary Reactions Kinetics. B KOREAN CHEM SOC 2012. [DOI: 10.5012/bkcs.2012.33.3.941] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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4
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Kang HW, Zheng L, Othmer HG. A new method for choosing the computational cell in stochastic reaction-diffusion systems. J Math Biol 2011; 65:1017-99. [PMID: 22071651 DOI: 10.1007/s00285-011-0469-6] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2010] [Revised: 06/23/2011] [Indexed: 10/15/2022]
Abstract
How to choose the computational compartment or cell size for the stochastic simulation of a reaction-diffusion system is still an open problem, and a number of criteria have been suggested. A generalized measure of the noise for finite-dimensional systems based on the largest eigenvalue of the covariance matrix of the number of molecules of all species has been suggested as a measure of the overall fluctuations in a multivariate system, and we apply it here to a discretized reaction-diffusion system. We show that for a broad class of first-order reaction networks this measure converges to the square root of the reciprocal of the smallest mean species number in a compartment at the steady state. We show that a suitably re-normalized measure stabilizes as the volume of a cell approaches zero, which leads to a criterion for the maximum volume of the compartments in a computational grid. We then derive a new criterion based on the sensitivity of the entire network, not just of the fastest step, that predicts a grid size that assures that the concentrations of all species converge to a spatially-uniform solution. This criterion applies for all orders of reactions and for reaction rate functions derived from singular perturbation or other reduction methods, and encompasses both diffusing and non-diffusing species. We show that this predicts the maximal allowable volume found in a linear problem, and we illustrate our results with an example motivated by anterior-posterior pattern formation in Drosophila, and with several other examples.
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Affiliation(s)
- Hye-Won Kang
- School of Mathematics, University of Minnesota, Twin Cities, MN 55455, USA.
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Doktorov AB, Kipriyanov AA, Kipriyanov AA. Manifestation of macroscopic correlations in elementary reaction kinetics. I. Irreversible reaction A+A-->product. J Chem Phys 2010; 132:204502. [PMID: 20515095 DOI: 10.1063/1.3430641] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using an modern many-particle method for the derivation of non-Markovian binary kinetic equations, we have treated theoretically the applicability of the encounter theory (ET) (the prototype of the collision theory) concepts to the widely known diffusion assisted irreversible bulk reaction A+A-->product (for example, radical reaction) in dilute solutions. The method shows that the agreement with the ET is observed when the familiar integral ET is employed which in this method is just a step in the derivation of kinetic equations. It allows for two-particle correlations only, but fails to take account of correlation of reactant simultaneously with the partner of the encounter and the reactant in the bulk. However, the next step leading to the modified ET under transformation of equations to the regular form both extends the time range of the applicability of ET rate equation (as it was for reactions proceeding with one of the reactants in excess), and gives the equation of the generalized ET. In full agreement with physical considerations, this theory reveals macroscopic correlations induced by the encounters in the reservoir of free walks. This means that the encounters of reactants in solution are correlated on a rather large time interval of the reaction. Though any nonstationary (non-Markovian) effects manifest themselves rather weakly in the kinetics of the bimolecular reaction in question, just the existence of the revealed macroscopic correlations in the binary theory is of primary importance. In particular, it means that the well-known phenomena which are generally considered to be associated solely with correlation of particles on the encounter (for example, chemically induced dynamic nuclear polarization) may be induced by correlation in the reservoir of free random walks of radicals in solution.
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6
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Yang M. Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics. J Chem Phys 2007; 126:214503. [PMID: 17567204 DOI: 10.1063/1.2737045] [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
Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.
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Affiliation(s)
- Mino Yang
- Department of Chemistry, Chungbuk National University, Cheongju, Chungbuk 361-763, South Korea.
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7
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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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8
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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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9
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Kipriyanov A, Fedorenko S, Doktorov A. Kinetic equations for exactly solvable models of a geminate reaction in the presence of scavengers. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2005.06.022] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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10
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The analysis of the derivation principles of kinetic equations based on exactly solvable models of the bulk reaction A+B→Product. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2005.06.036] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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11
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Voituriez R, Moreau M, Oshanin G. Corrections to the law of mass action and properties of the asymptotic t=∞ state for reversible diffusion-limited reactions. J Chem Phys 2005; 122:84103. [PMID: 15836016 DOI: 10.1063/1.1849161] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
For diffusion-limited reversible A+A<==>B reactions we reexamine two fundamental concepts of classical chemical kinetics-the notion of "chemical equilibrium" and the "law of mass action." We consider a general model with distance-dependent reaction rates, such that any pair of A particles, performing standard random walks on sites of a d-dimensional lattice and being at a distance mu apart of each other at time moment t, may associate forming a B particle at the rate k+(mu). In turn, any randomly moving B particle may spontaneously dissociate at the rate k-(lambda) into a geminate pair of As "born" at a distance lambda apart of each other. Within a formally exact approach based on Gardiner's Poisson representation method we show that the asymptotic t=infinity state attained by such diffusion-limited reactions is generally not a true thermodynamic equilibrium, but rather a nonequilibrium steady state, and that the law of mass action is invalid. The classical concepts hold only in case when the ratio k+(mu)k-(mu) does not depend on mu for any mu.
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Affiliation(s)
- R Voituriez
- Laboratoire de Physique Théorique des Liquides, Université Paris 6, 4 Place Jussieu, 75252 Paris, France.
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Abstract
The absorption of a photon by a hydroxy-aromatic photoacid triggers a cascade of events contributing to the overall phenomenon of intermolecular excited-state proton transfer. The fundamental steps involved were studied over the last 20 years using a combination of theoretical and experimental techniques. They are surveyed in this sequel in sequential order, from fast to slow. The excitation triggers an intramolecular charge transfer to the ring system, which is more prominent for the anionic base than the acid. The charge redistribution, in turn, triggers changes in hydrogen-bond strengths that set the stage for the proton-transfer step itself. This step is strongly influenced by the solvent, resulting in unusual dependence of the dissociation rate coefficient on water content, temperature, and isotopic substitution. The photolyzed proton can diffuse in the aqueous solution in a mechanism that involves collective changes in hydrogen-bonding. On longer times, it may recombine adiabatically with the excited base or quench it. The theory for these diffusion-influenced geminate reactions has been developed, showing nice agreement with experiment. Finally, the effect of inert salts, bases, and acids on these reactions is analyzed.
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Affiliation(s)
- Noam Agmon
- Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel.
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Affiliation(s)
- A. V. Popov
- Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
| | - A. I. Burshtein
- Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
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15
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Popov AV, Gladkikh VS, Burshtein AI. Stern−Volmer Law in Competing Theories and Approximations. J Phys Chem A 2003. [DOI: 10.1021/jp030007d] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- A. V. Popov
- Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
| | - V. S. Gladkikh
- Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
| | - A. I. Burshtein
- Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
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Abstract
Mobility of taxol inside microtubules was investigated using fluorescence recovery after photobleaching on flow-aligned bundles. Bundles were made of microtubules with either GMPCPP or GTP at the exchangeable site on the tubulin dimer. Recovery times were sensitive to bundle thickness and packing, indicating that taxol molecules are able to move laterally through the bundle. The density of open binding sites along a microtubule was varied by controlling the concentration of taxol in solution for GMPCPP samples. With >63% sites occupied, recovery times were independent of taxol concentration and, therefore, inversely proportional to the microscopic dissociation rate, k(off). It was found that 10k(off)(GMPCPP) approximately equal k(off)(GTP), consistent with, but not fully accounting for, the difference in equilibrium constants for taxol on GMPCPP and GTP microtubules. With <63% sites occupied, recovery times decreased as approximately [Tax](-1/5) for both types of microtubules. We conclude that the diffusion of taxol inside the microtubule bundle is hindered by rebinding events when open sites are within approximately 7 nm of each other.
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Affiliation(s)
- Jennifer L Ross
- Physics Department, University of California, Santa Barbara, California 93106-9530, USA
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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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Gopich IV, Szabo A. Kinetics of reversible diffusion influenced reactions: The self-consistent relaxation time approximation. J Chem Phys 2002. [DOI: 10.1063/1.1482701] [Citation(s) in RCA: 82] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Naumann W. Association–dissociation in solution/Long-time relaxation prediction by a mode coupling approach. J Chem Phys 2002. [DOI: 10.1063/1.1477929] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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22
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Solntsev KM, Huppert D, Agmon N. Challenge in Accurate Measurement of Fast Reversible Bimolecular Reaction. J Phys Chem A 2001. [DOI: 10.1021/jp004569y] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Kyril M. Solntsev
- School of Chemistry, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv 69978, Israel
| | - Dan Huppert
- School of Chemistry, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv 69978, Israel
| | - Noam Agmon
- The Fritz Haber Research Center, Department of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel
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Kwac K, Yang M, Shin KJ. Excited-state reversible association–dissociation reaction: Renormalized kinetic theory in configuration space. J Chem Phys 2001. [DOI: 10.1063/1.1344612] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Moro GJ, Severin MG. Bimolecular kinetics according to a stochastic analysis of reactant dynamics. J Chem Phys 2001. [DOI: 10.1063/1.1346634] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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26
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Kim H, Joe Shin K. On the diffusion-influenced reversible trapping problem in one dimension. J Chem Phys 2000. [DOI: 10.1063/1.481436] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [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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Sung J, Lee S. Nonequilibrium distribution function formalism for diffusion-influenced bimolecular reactions: Beyond the superposition approximation. J Chem Phys 1999. [DOI: 10.1063/1.479367] [Citation(s) in RCA: 52] [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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Kim H, Yang M, Shin KJ. Dynamic correlation effect in reversible diffusion-influenced reactions: Brownian dynamics simulation in three dimensions. J Chem Phys 1999. [DOI: 10.1063/1.479297] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gopich IV, Kipriyanov AA, Doktorov AB. A many-particle treatment of the reversible reaction A+B⇔C+B. J Chem Phys 1999. [DOI: 10.1063/1.479001] [Citation(s) in RCA: 41] [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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Kim H, Yang M, Shin KJ. Long time behavior of reversible diffusion-influenced reaction perturbed by photolysis: Brownian dynamics simulation. J Chem Phys 1999. [DOI: 10.1063/1.478273] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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33
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Naumann W. Fluorescence quenching by reversible excitation transfer: Application of a hierarchy approach to a pseudo first-order model. J Chem Phys 1999. [DOI: 10.1063/1.478247] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [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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37
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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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