我们回顾了扩散控制反应理论长达一个世纪发展中的里程碑。从认识到扩散在化学反应中重要性的 von Smoluchowski 的开创性工作出发，我们讨论了完美与不完美表面反应、其微观起源及底层数学框架。介绍了单分子反应方案、反常体扩散、可逆结合/解结合动力学及许多其他扩展。引入了基于相遇的替代方法，强调其优势与潜在应用。概述了一些开放问题与未来展望。
英文摘要：
We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the underlying mathematical framework. Single-molecule reaction schemes, anomalous bulk diffusions, reversible binding/unbinding kinetics and many other extensions are presented. An alternative encounter-based approach to diffusion-controlled reactions is introduced, with emphasis on its advantages and potential applications. Some open problems and future perspectives are outlined.
We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g., a signal transduction proceeds via a series of consecutive "messengers": the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, r…
Electrostatic reaction inhibition in heterogeneous catalysis emerges if charged reactants and products are adsorbed on the catalyst and thus repel the approaching reactants. In this work, we study the effects of electrostatic inhibition on the reaction rate of unimolecular reactions catalyzed on the surface of a spherical model nanoparticle by using particle-based reaction-diffusion simulations. Moreover, we derive closed rate equations based on approximate Debye-Smoluchowski rate theory, valid for diffusion-controlled reactions, and a modified Langmuir adsorption isotherm, relevant for reacti…
It has long been appreciated that transport properties can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target -- the first-passage time (FPT). Although essential to quantify the kinetics of reactions on all time scales, determining the FPT distribution was deemed so far intractable. Here, we calculate analytically this FPT distribution and show that transport processes as various as regular diffusion, anomalous diffusion, diffusion in disordered media and in fractals fall into the same universality classes. Beyond this theore…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional settings, the behavior of the macroscopic reaction rate and its dependence on geometric parameters are not yet understood. Modeling the geometric setup by a capped cylinder with a concentric disk-like reactive region on one of the lateral surfaces, we provide an exact semi-analytical solution of the steady-state diffusion equation and compute the diffusive flu…
We study diffusion of particles on the surface of a sphere toward a partially reactive circular target with partly reversible binding kinetics. We solve the coupled diffusion-reaction equations and obtain the exact expressions for the time-dependent concentration of particles and the total diffusive flux. Explicit asymptotic formulas are derived in the small target limit. This study reveals the strong effects of reversible binding kinetics onto diffusion-mediated reactions that may be relevant for many biochemical reactions on cell membranes.
The desorption kinetics was modelled with the both interface- and surface reactions as rate-controlling steps. It has been shown analytically, that in the model of 'shrinking core' desorption, the finite hydride-decomposition-rate causes a modified slope of kinetics. The dependence of desorption time on the powder particle size has the same power of order as for the surface controlled desorption.
This chapter aims at emphasizing the crucial role of partial reactivity of a catalytic surface or a target molecule in diffusion-controlled reactions. We discuss various microscopic mechanisms that lead to imperfect reactions, the Robin boundary condition accounting for eventual failed reaction events, and the construction of the underlying stochastic process, the so-called partially reflected Brownian motion. We show that the random path to the reaction event can naturally be separated into the transport step toward the target, and the exploration step near the target surface until reaction. …
This perspective on laser control provides a quick overview over different schemes for coherent control of chemical reactions and photophysical processes. It originally appeared in Bunsen Magazin 1, 13 - 23 (2012).
Direct real time studies of reacting individual atoms in technologically important gold and platinum nanocatalysts in controlled reducing and oxidising gas environments and operating temperatures using novel environmental scanning transmission electron microscopy (ESTEM) with single atom sensitivity are presented. The direct in situ observations provide new insights into the dynamic behaviour of single atoms which may be important as catalytic active sites as well as migrating as part of deactivation mechanisms. The single atom dynamics reveal that the primary role of nanoparticles in the cata…
Achieving control over chemical reaction's rate and stereoselectivity realizes one of the Holy Grails in chemistry that can revolutionize chemical and pharmaceutical industries. Strong light-matter interaction in optical or nanoplasmonic cavities might provide the knob to reach such control. In this work, we demonstrate the catalytic and selectivity control of an optical cavity for two selected Diels-Alder cycloaddition reactions using the quantum electrodynamics coupled cluster (QED-CC) method. Herein, we find that by changing the molecular orientation with respect to the polarization of the …
Ultracold molecules offer remarkable opportunities to study chemical reactions at nearly zero temperature. Although significant progresses have been achieved in exploring ultracold bimolecular reactions, the investigations are usually limited to measurements of the overall loss rates of the reactants. Detection of the reaction products will shed new light on understanding the reaction mechanism and provide a unique opportunity to study the state-to-state reaction dynamics. Here we report on the direct observation of an exoergic atom-exchange reaction in an ultracold atom-dimer mixture. Both th…
We propose a general theoretical description of chemical reactions occurring on a catalytic surface with heterogeneous reactivity. The propagator of a diffusion-reaction process with eventual absorption on the heterogeneous partially reactive surface is expressed in terms of a much simpler propagator toward a homogeneous perfectly reactive surface. In other words, the original problem with general Robin boundary condition that includes in particular mixed Robin-Neumann condition, is reduced to that with Dirichlet boundary condition. Chemical kinetics on the surface is incorporated as a matrix …
Metallic nanoparticles embedded in stimuli-responsive polymers can be regarded as nanoreactors since their catalytic activity can be changed within wide limits: the physicochemical properties of the polymer network can be tuned and switched by external parameters, e.g. temperature or pH, and thus allows a selective control of reactant mobility and concentration close to the reaction site. Based on a combination of Debye's model of diffusion through an energy landscape and a two-state model for the polymer, here we develop an analytical expression for the observed reaction rate constant $k_{\rm…
Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, that has typically different physical properties than the reactant species, has been disregarded so far. Here we study the effects of reactant-product and product-product interactions as well as asymmetric diffusion properties on the rate of diffusion-controlled reactions in the classical Smoluchowski-setup for chemical transformations at a perfect catalytic sphere. …
We present an overview of the role of quantum coherence in influencing nonadiabatic processes in the condensed phase. Equations of motion for mixed quantum-classical dynamics are derived from the Consistent Histories interpretation of quantum mechanics. Application of the methods toward computing the excited state lifetime of an excess electron in water and heavy water provides a unique demonstration of our method.
An important physical process unique to neutral-ion systems is the charge-transfer (CT) reaction. Here, we present measurements of and models for CT processes between co-trapped ultracold Ca atoms and Yb ions under well-controlled conditions. The theoretical analysis reveals the existence of three reaction mechanisms when lasers from a magneto-optical trap (MOT) and an additional catalyst laser are present. Besides the direct CT involving existent excited Ca population in the MOT, the second pathway is controlled by MOT-induced CT, whereas the third one mostly involves the additional red-detun…
The Diels-Alder cycloaddition, in which a diene reacts with a dienophile to form a cyclic compound, counts among the most important tools in organic synthesis. Achieving a precise understanding of its mechanistic details on the quantum level requires new experimental and theoretical methods. Here, we present an experimental approach that separates different diene conformers in a molecular beam as a prerequisite for the investigation of their individual cycloaddition reaction kinetics and dynamics under single-collision conditions in the gas phase. A low- and high-level quantum-chemistry-based …
In the study of rare events in complex systems with many degrees of freedom, a key element is to identify the reaction coordinates of a given process. Over recent years, a number of methods and protocols have been developed to extract the reaction coordinates based on limited information from molecular dynamics simulations. In this review, we provide a brief survey over a number of major methods developed in the past decade, some of which are discussed in greater detail, to provide an overview of the problems that are partially solved and challenges that still remain. A particular emphasis has…
Molecular motions and chemical reactions occurring in constrained space play key roles in many catalysis and energy storage applications. However, its understanding has been impeded by difficulty in detection and lack of reliable model systems. In this work, we report geometric and chemical manipulation of O2 diffusion and ensuing O2-mediated charge transfer (CT) that occur in the 2D space between single-layer transition metal dichalcogenides (TMDs) and dielectric substrates. As a sensitive real-time wide-field imaging signal, charge-density-dependent photoluminescence (PL) from TMDs was used.…
Control over various fragmentation reactions of a series of polyatomic molecules (acetylene, ethylene, 1,3-butadiene) by the optical waveform of intense few-cycle laser pulses is demonstrated experimentally. We show both experimentally and theoretically that the responsible mechanism is inelastic ionization from inner-valence molecular orbitals by recolliding electron wavepackets, whose recollision energy in few-cycle ionizing laser pulses strongly depends on the optical waveform. Our work demonstrates an efficient and selective way of pre-determining fragmentation and isomerization reactions …
For a theoretical understanding of the reactivity of complex chemical systems, relative energies of stationary points on potential energy hypersurfaces need to be calculated to high accuracy. Due to the large number of intermediates present in all but the simplest chemical processes, approximate quantum chemical methods are required that allow for fast evaluations of the relative energies, but at the expense of accuracy. Despite the plethora of benchmark studies, the accuracy of a quantum chemical method is often difficult to assess. Moreover, a significant improvement of a method's accuracy (…
We present a quantum mechanical / molecular mechanics (QM/MM) to tackle chemical reactions with substantial molecular reorganization. For this, molecular dynamics simulations with smoothly switched interaction models are used to suggest suitable product states, whilst a Monte Carlo algorithm is employed to assess the reaction likeliness subject to energetic feasibility. As a demonstrator, we study the cross-linking of bisphenol F diglycidyl ether (BFDGE) and 4,6-diethyl-2-methylbenzene-1,3-diamine (DETDA). The modeling of epoxy curing was supplemented by Differential Scanning Calorimetry (DSC)…
