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Nekrasov VM, Polshchitsin AA, Yurkin MA, Yakovleva GE, Maltsev VP, Chernyshev AV. Brownian aggregation rate of colloid particles with several active sites. J Chem Phys 2014; 141:064309. [DOI: 10.1063/1.4892163] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vyacheslav M. Nekrasov
- Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk, Russia
- Physics Department, Novosibirsk State University, Pirogova 2, 630090 Novosibirsk, Russia
| | - Alexey A. Polshchitsin
- Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk, Russia
- JSC “VECTOR-BEST”, PO BOX 492, Novosibirsk 630117 Russia
| | - Maxim A. Yurkin
- Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk, Russia
- Physics Department, Novosibirsk State University, Pirogova 2, 630090 Novosibirsk, Russia
| | | | - Valeri P. Maltsev
- Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk, Russia
- Physics Department, Novosibirsk State University, Pirogova 2, 630090 Novosibirsk, Russia
- Department of Preventive Medicine, Novosibirsk State Medical University, Krasny Prospect 52, 630091 Novosibirsk, Russia
| | - Andrei V. Chernyshev
- Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk, Russia
- Physics Department, Novosibirsk State University, Pirogova 2, 630090 Novosibirsk, Russia
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Klein HCR, Schwarz US. Studying protein assembly with reversible Brownian dynamics of patchy particles. J Chem Phys 2014; 140:184112. [DOI: 10.1063/1.4873708] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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Strieder W. Effects of electrostatic potential and shape on diffusion-controlled reaction at an elliptic site. J Chem Phys 2011; 134:044529. [DOI: 10.1063/1.3529941] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ivanov KL, Lukzen NN. Diffusion-influenced reactions of particles with several active sites. J Chem Phys 2008; 128:155105. [DOI: 10.1063/1.2898091] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Shushin AI. Non-Markovian stochastic Liouville equation and its Markovian representation: Extensions of the continuous-time random-walk approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031130. [PMID: 18517352 DOI: 10.1103/physreve.77.031130] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2007] [Revised: 09/10/2007] [Indexed: 05/26/2023]
Abstract
Some specific features and extensions of the continuous-time random-walk (CTRW) approach are analyzed in detail within the Markovian representation (MR) and CTRW-based non-Markovian stochastic Liouville equation (SLE). In the MR, CTRW processes are represented by multidimensional Markovian ones. In this representation the probability density function (PDF) W(t) of fluctuation renewals is associated with that of reoccurrences in a certain jump state of some Markovian controlling process. Within the MR the non-Markovian SLE, which describes the effect of CTRW-like noise on the relaxation of dynamic and stochastic systems, is generalized to take into account the influence of relaxing systems on the statistical properties of noise. Some applications of the generalized non-Markovian SLE are discussed. In particular, it is applied to study two modifications of the CTRW approach. One of them considers cascaded CTRWs in which the controlling process is actually a CTRW-like one controlled by another CTRW process, controlled in turn by a third one, etc. Within the MR a simple expression for the PDF W(t) of the total controlling process is obtained in terms of Markovian variants of controlling PDFs in the cascade. The expression is shown to be especially simple and instructive in the case of anomalous processes determined by the long-time tailed W(t) . The cascaded CTRWs can model the effect of the complexity of a system on the relaxation kinetics (in glasses, fractals, branching media, ultrametric structures, etc.). Another CTRW modification describes the kinetics of processes governed by fluctuating W(t) . Within the MR the problem is analyzed in a general form without restrictive assumptions on the correlations of PDFs of consecutive renewals. The analysis shows that fluctuations of W(t) can strongly affect the kinetics of the process. Possible manifestations of this effect are discussed.
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Affiliation(s)
- A I Shushin
- Institute of Chemical Physics, Russian Academy of Sciences, 117977, GSP-1, Kosygin Street 4, Moscow, Russia
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Traytak SD, Price WS. Exact solution for anisotropic diffusion-controlled reactions with partially reflecting conditions. J Chem Phys 2008; 127:184508. [PMID: 18020650 DOI: 10.1063/1.2786452] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate a generalization of the model of Solc and Stockmayer to describe the diffusion-controlled reactions between chemically anisotropic reactants taking into account the partially reflecting conditions on two parts of the reaction surface. The exact solution of the relevant mixed boundary-value problem was found for different ratios of the intrinsic rate constants. The results obtained may be used to test numerical programs that describe diffusion-controlled reactions in real systems of particles with anisotropic reactivity.
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Affiliation(s)
- Sergey D Traytak
- Institute of Applied Mechanics, Russian Academy of Sciences, 32a Lenin Avenue, GSP-1, 119991 Moscow, Russia
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Berezhkovskii AM, Barzykin AV. Simple formulas for the trapping rate by nonspherical absorber and capacitance of nonspherical conductor. J Chem Phys 2007; 126:106102. [PMID: 17362091 DOI: 10.1063/1.2711177] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- A M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.
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Crowell RA, Lian R, Shkrob IA, Bartels DM, Chen X, Bradforth SE. Ultrafast dynamics for electron photodetachment from aqueous hydroxide. J Chem Phys 2004; 120:11712-25. [PMID: 15268207 DOI: 10.1063/1.1739213] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Charge-transfer-to-solvent reactions of hydroxide induced by 200 nm monophotonic or 337 and 389 nm biphotonic excitation of this anion in aqueous solution have been studied by means of pump-probe ultrafast laser spectroscopy. Transient absorption kinetics of the hydrated electron, e(aq) (-), have been observed, from a few hundred femtoseconds out to 600 ps, and studied as function of hydroxide concentration and temperature. The geminate decay kinetics are bimodal, with a fast exponential component ( approximately 13 ps) and a slower power "tail" due to the diffusional escape of the electrons. For the biphotonic excitation, the extrapolated fraction of escaped electrons is 1.8 times higher than for the monophotonic 200 nm excitation (31% versus 17.5% at 25 degrees C, respectively), due to the broadening of the electron distribution. The biphotonic electron detachment is very inefficient; the corresponding absorption coefficient at 400 nm is <4 cm TW(-1) M(-1) (assuming unity quantum efficiency for the photodetachment). For [OH(-)] between 10 mM and 10 M, almost no concentration dependence of the time profiles of solvated electron kinetics was observed. At higher temperature, the escape fraction of the electrons increases with a slope of 3x10(-3) K(-1) and the recombination and diffusion-controlled dissociation of the close pairs become faster. Activation energies of 8.3 and 22.3 kJ/mol for these two processes were obtained. The semianalytical theory of Shushin for diffusion controlled reactions in the central force field was used to model the geminate dynamics. The implications of these results for photoionization of water are discussed.
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Affiliation(s)
- Robert A Crowell
- Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.
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Chekunaev N. Calculation of the rate constants of diffusion-controlled chemical reactions for reagents of arbitrary shape. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2004.02.008] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Shushin AI. Influence of hydrodynamic interaction on the diffusion-controlled reaction kinetics of molecules with highly anisotropic reactivity. J Chem Phys 2003. [DOI: 10.1063/1.1528184] [Citation(s) in RCA: 9] [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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Shushin AI, Barzykin AV. Effect of local molecular shape and anisotropic reactivity on the rate of diffusion-controlled reactions. Biophys J 2001; 81:3137-45. [PMID: 11720980 PMCID: PMC1301774 DOI: 10.1016/s0006-3495(01)75950-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022] Open
Abstract
The role of distance-dependent anisotropic reactivity and molecular geometry in the vicinity of localized reaction centers in influencing the rate of bimolecular diffusion-controlled reactions is analyzed in detail, both analytically and numerically. The effect of local molecular shape is considered within the model of reflective hemispheres of small radius l(h) on the surfaces of otherwise spherical molecules of radius R (l(h) << R). The distance-dependent reactivity is modeled by reactive hemispheres of radius l(r) on top of the reflective hemispheres (l(r) << R). It is shown that the presence of the reflective hemispheres leads to a markedly large increase of the reaction rate. The maximum effect is ~R/l(h) >> 1 times, as described by the ratio of local to average molecular curvature. It is observed for l(h) approximately R(l(r)/R)(1/2) >> l(r). The effect of thickness of the reaction regions is described within the model of reactive cylinders of height l(r) and angular radius theta << 1. It is shown that the characteristic parameter in the expansion of the reaction rate as a function of l(r)/R is l(r)/(Rtheta(2)), and therefore, even for small relative thickness d = l(r)/theta, its effect on the rate is very strong, i.e., the conventional model of reactive patches, which assumes zero thickness of the reaction region, may considerably underestimate the reaction rate.
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Affiliation(s)
- A I Shushin
- Institute of Chemical Physics, Russian Academy of Sciences, GSP-1, Moscow 117977, Russia
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Barzykin AV, Shushin AI. Effect of anisotropic reactivity on the rate of diffusion-controlled reactions: comparative analysis of the models of patches and hemispheres. Biophys J 2001; 80:2062-73. [PMID: 11325710 PMCID: PMC1301399 DOI: 10.1016/s0006-3495(01)76180-2] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
A comparative analysis of two models of anisotropic reactivity in bimolecular diffusion-controlled reaction kinetics is presented. One is the conventional model of reactive patches (MRP), where the surface of a molecule is assumed to be reactive over a certain region (circular patch) with the rest of the surface being inert. Another one is the model of reactive hemispheres (MRH), assuming that a molecule is reactive within a certain distance from a point on its surface. The accuracy of the known and newly derived simple analytical expressions for the reaction rate is tested by comparison with the simulation results obtained by the original Brownian dynamics method. These formulas prove to be quite accurate in the practically important limit of strong anisotropy corresponding to small size of the reactive patches or hemispheres. Numerical calculations confirm earlier predictions that the MRP rates are much smaller than the MRH rates for the same radii of the reactive regions, especially in the case where both reacting molecules are anisotropic.
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Affiliation(s)
- A V Barzykin
- National Institute of Materials and Chemical Research, Tsukuba, Ibaraki 305-8565, Japan.
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Barzykin AV, Seki K, Tachiya M. Kinetics of diffusion-assisted reactions in microheterogeneous systems. Adv Colloid Interface Sci 2001; 89-90:47-140. [PMID: 11215811 DOI: 10.1016/s0001-8686(00)00053-1] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.
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Affiliation(s)
- A V Barzykin
- National Institute of Materials and Chemical Research, Tsukuba, Ibaraki, Japan.
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Shushin AI. The effect of anisotropic reactivity and interaction potential on the kinetics of diffusion controlled reactions. J Chem Phys 2000. [DOI: 10.1063/1.1288187] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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