Mass transport and energy equilibration in heavy ion collisions

The lack of mass drift observed in Kr-induced collisions is explained assuming energy and particle transfer from the light to the heavy fragment during the equilibration stage in asymmetric heavy-ion reactions. Transferred energy and particle number can be estimated from the interfragment thermal equilibrium distribution provided the initial partition is known which we calculate within a semiclassical theory based on TDHF. The experimental findings are consistent with the theoretical predictions. In particular, the experimental mass drift as function of total kinetic energy loss is quantitatively described within a modified diffusion model which takes into account the mass exchange prior to the transport stage.     

Theory of gel point in real polymer solutions

We develop a new theory of gelation which takes into account (i) delay of the gel point and (ii) change of functionality due to ring formation. We show that the problem of finding the gel point in real polymer solutions reduces to the problem of calculating the total ring concentration and the extent of reaction of intermolecular reaction at the gel point. In this paper, we solve a special case of this problem, on the basis of the independence assumption between intermolecular reaction and cyclization which takes into account only (i) the delay of the gel point: making use of the asymptotic equality of the total ring concentration, we acquire an approximate solution for the gel point D_c as a function of the inverse concentration , the relative frequency of cyclization and dimension d. Applying the observed values of in linear polyesters, the theoretical result reproduces well the Wile and the Gordon-Scantlebury observations, showing the existence of a critical dilution beyond which gelation can not occur, and an asymptote . As the classical gel point is approached, the present theory reduces to the linear equation, which makes one-to-one correspondence with the real slope , suggesting the inequality which is just what polymer chemists have quested for so far, with the physical meaning having remained unknown. Receveid: 30 December 1997 / Revised: 28 May 1998 / Accepted: 12 June 1998     

Pattern formation in the reaction with anisotropic lateral adsorbate-adsorbate interactions

We present Monte Carlo simulations of the formation of (1×2) islands in the case of the 2 A + B ₂ → 2 AB reaction occurring via the Langmuir-Hinshelwood mechanism on a square lattice under steady-state conditions. The model employed takes into account the effect of anisotropic lateral B-B interactions on the rates of B diffusion and elementary reaction events. The results obtained with qualitatively realistic ratio of the rate of elementary reaction steps indicate that the average island size depends on the details of diffusion and reaction dynamics in a similar way as in the earlier studied case of the simplest A + B reaction running via the Eley-Rideal mechanism. Received 4 January 2002 and Received in final form 2 April 2002 Published online 25 June 2002     

High pressure studies of elementary chemical dynamics

Abstract

Studies of chemical reactions over large density ranges provide a simple access to a variety of static and dynamic interactions between reactants and solvents. The interpretation of the observed “activation volumes” by transition state theory is shown to be inadequate. Kramers-Smoluchowski theory provides a more suitable starting point of the analysis. However, multidimensional barrier and cluster effects also have to be taken into account. Viscoelastic effects describe the transition into the solid phase. Photoisomerization studies of diphenylpolyenes illustrate barrier crossing processes. The effects of cage dynamics and diffusion control are demonstrated with bromine and iodine photolysis experiments.     

Computing reaction paths of a bifurcation reaction: an action wave-front-based perspective

Application of Hamilton–Jacobi (HJ) equation to reaction systems which involve energy barrier(s) leading to the product is relatively new. Such problems are described by a new class of HJ equation, called the generalised HJ equation. This new HJ equation renders an anisotropic propagation for the wave front. In this paper, we describe the adaptation of the fast marching method (FMM) and the generalised HJ equation to understand a new class of reaction process where the energy barrier does not lead to the product; instead, a new class of states are detected along the reaction path of such reactions. These states are valley-ridge inflection point, branching point and potential energy ridge. Such reactions are characterised as bifurcation reactions. We have identified a new classical wave front, called the reaction action front (RAF) which distinctly separates the reaction system into a reactant zone and a product zone connected by a third zone, called ‘neck’. The RAF is an important tool to understand the bifurcation reaction and the associated reaction paths. We have also introduced a convenient way to compute the reaction path force (RPF) using the FMM. The RPF for a bifurcation reaction significantly differs from the reactions with energy barrier, and so, the RPF provides vital information about the occurrence of branching of a path. The method has been tested for the isomerisation reaction of methoxy radical (H₃C) to hydroxymethylene radical (H₂?OH).     

A DFT-based microkinetic theory for Fe2O3 reduction by CO in chemical looping

Redox kinetics of oxygen carrier in chemical looping is an important component for material preparation, reactor design and process demonstration. How to bridge the gap between the microscale density functional theory (DFT) and the macroscale redox kinetics and develop a first-principle-based theoretical model is still a challenge in the field of chemical looping. This study addresses this challenge and proposes a DFT-based microkinetic rate equation theory to calculate the heterogeneous kinetics of Fe₂O₃ reduction by CO in chemical looping. Firstly, the DFT calculation is adopted to search the reaction pathways and to obtain the energy barriers of elementary reactions. Secondly, the DFT results are introduced into the transition state theory (TST) to calculate the reaction rate constants and build the rate equations of elementary surface reactions. Finally, by considering the bulk diffusion, a rate equation is developed to bridge the gap between the elementary surface reactions and the grain conversion. In the theory, the reaction mechanism obtained from DFT and kinetic rate constants obtained from TST are directly implemented into the rate equation to predict the reduction kinetics of oxygen carriers without fitting experimental data. The accuracy of the developed theory is validated by experimental data of two Fe₂O₃ oxygen carriers obtained from the thermogravimetric analyzer (TGA). The microkinetic rate equation theory is based on the first principles calculation and can predict directly the redox kinetics of oxygen carriers without depending on the experimental kinetic data, therefore, it provides a powerful theoretical tool to screen the oxygen carrier materials and optimize the microstructure of oxygen carriers.     

Reaction rate theory for supramolecular kinetics: application to protein aggregation

ABSTRACT

Probing reaction mechanisms of supramolecular processes in soft and biological matter, such as protein aggregation, is inherently challenging. This is because these processes involve multiple molecular mechanisms that are associated with the rearrangement of large numbers of weak bonds, resulting in complex free energy landscapes with many kinetic barriers. Reaction rate measurements at different temperatures can offer unprecedented insights into the underlying molecular mechanisms. However, to be able to interpret such measurements, a key challenge is to establish which properties of the complex free energy landscapes are probed by the reaction rate. Here, we present a reaction rate theory for supramolecular kinetics based on Kramers theory of diffusive reactions over multiple kinetic barriers. We find that reaction rates for protein aggregation are of the Arrhenius–Eyring type and that the associated activation energies probe only one relevant barrier along the respective free energy landscapes. We apply this advancement to interpret, in experiments and in coarse-grained computer simulations, reaction rates of amyloid aggregation in terms of molecular mechanisms and associated thermodynamic signatures. These results suggest a practical extension of the concept of rate-determining steps for complex supramolecular processes and establish a general platform for probing the underlying energy landscape using kinetic measurements.     

Grain Growth Kinetics of BaTiO3 Nanocrystals During Calcining Process

以醋酸钡和钛酸四丁酯为原料,采用溶胶-凝胶法合成了纳米BaTiO3粉体;运用差示/热重、X射线衍射及透射电镜对前驱体凝胶和产物进行了表征,并根据XRD结果,研究了纳米BaTiO3的晶格常数、晶格畸变度和晶粒尺寸随焙烧温度及时间的变化。结果表明,焙烧温度与时间对纳米BaTiO3晶格常数的影响不明显;随焙烧温度或时间的延长,纳米BaTiO3的晶格畸变度减小,晶粒尺寸增大,但晶格畸变度和晶粒尺寸更敏感于焙烧温度. 基于扩散控制机理的传统模型探讨了焙烧过程纳米BaTiO3晶粒生长动力学,得出其晶粒生长指数为7,晶粒生长活化能为75.49 kJ/mol. 将基于扩散与反应共同控制机理的新型等温模型应用于本研究中,结果表明,新型等温模型更能真实地反映纳米BaTiO3焙烧过程中的晶粒生长行为,说明纳米BaTiO3晶粒生长过程同时受溶质扩散和表面反应控制,其藕合晶粒生长活化能为27.23 kJ/mol.     

Unimolecular reactions of the resonance-stabilized cyclopentadienyl radicals and their role in the polycyclic aromatic hydrocarbon formation

Resonance-stabilized cyclopentadienyl radicals are important intermediate species in the combustion of transportation fuels. It not only serves as precursors for polycyclic aromatic hydrocarbon (PAH) formation, but also involves in the formation of fundamental PAH precursors such as propargyl and acetylene. In this work, the unimolecular reactions of the cyclopentadienyl radicals are theoretically studied based on high-level quantum chemistry and RRKM/master equation calculations. Stationary points on the potential energy surface (PES) are calculated at the CCSD(T)/CBS//M06–2X/6–311++(d,p) level of theory. The branching ratios of unimolecular reactions of the cyclopentadienyl radicals are analyzed for a broad temperature range from 500 to 2500 K and pressures from 0.01 to 100 atm. It is found that the isomerization reaction of the cyclopentadienyl radical via 1,2-hydrogen transfer dominates at low temperatures and high pressures, while the well-skipping decomposition reaction which forms propargyl and acetylene is important at high temperatures and low pressures. Both the decomposition reaction of the cyclopentadienyl radicals and its reverse reaction show pronounced pressure dependence, and their reaction rate constants are compared against available low-pressure experimental measurements and theoretical studies. The temperature- and pressure-dependent rate coefficients for important reactions involved on the C₅H₅ PES are calculated and updated in a chemical kinetic model. Impacts of the unimolecular reactions of the cyclopentadienyl radicals on the PAH formation are explored by the numerical modeling of a low-pressure cyclopentene counterflow diffusion flame.     

A theoretical study on the bimolecular reactions encountered in the pyrolysis of acetamide

Bimolecular reactions of acetamide with acetamide itself, acetimidic acid and acetic acid are investigated to account for the formation of the three major experimental products from the pyrolysis of acetamide, namely ammonia, acetic acid and acetonitrile. This mechanism involves bimolecular deammonation reactions to form acetamide anhydride, acetic anhydride and N‐acetyl acetamide, and the subsequent fragmentation of these intermediates into acetic acid and acetonitrile. It is found that the overall reaction barrier for the formation of the three major experimental products from the bimolecular reaction of acetamide with its enol form (acetimidic acid) amount to a 36.1 kcal/mol barrier. This barrier is in excellent agreement with the corresponding experimental data from the self‐condensation of acetamide. This finding stresses on the role of acetimidic acid as a major intermediate in the pyrolysis of acetamide. The calculated activation barriers for the two available pathways in the bimolecular reaction of acetamide and acetic acid into imide and N‐acetyl acetamide (36.3 kcal/mol and 24.0 kcal/mol) is in accord with the corresponding experimental activation energy of 30.1 kcal/mol for the autocatalytic reaction of acetamide with the acetic acid. Reaction rate constants are obtained for all plausible reactions. Kinetic data presented herein should be instrumental in building a robust model for the decomposition of N‐alkylated amides, that is, a major structural entity in biomass. Copyright © 2011 John Wiley & Sons, Ltd.     

Recombination of a coulomb plasma and nonbinary interaction effects

A theory has been constructed for the recombination of a Coulomb plasma with allowance for the anomalous nature of diffusion along the energy axis in the negative energy region of Coulomb particles. These anomalies, which were revealed earlier by first-principles numerical simulation, are due to the dynamic memory of a classical Coulomb plasma. Two kinetic models are presented. The first takes random collisions with a hypothetical gas of two-level atoms into account. Comparison of the results of this model with first-principles calculations shows that the characteristic of the diffusion coefficients is missing. The second model takes the discrete nature of bound states into account. Calculations show that for an electron-hole plasma the recombination rate deviates substantially from the results of conventional theory only when either the recombination time is very short or the effect is masked by radiative recombination. For ion-ion plasma, the deviations from conventional recombination theory run to several orders of magnitude. This is of interest in relation to ball lightning.Institute of General Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 68–89, January, 1993.     

Vibrational control of molecular electron transfer reactions

ABSTRACT

Vibrational motions promote molecular electron transfer (ET) reactions by bringing electron donor and electron acceptor electronic states to fleeting resonance, and by modulating the donor-to-acceptor electronic coupling. The main experimental signature of molecular motion effects on the ET rate is the temperature dependence of the rate, which gives information about the overall free energy activation barrier for the ET reaction. Another approach to probing the vibrational control of ET reactions is to excite specific electron-transfer-active vibrational motions by external infrared (IR) fields. This type of experimental probe is potentially more specific than thermal excitation and recent experiments have shown that molecular ET rates can be perturbed by mode-specific IR driving. We review the theory and experiments of vibrational control of ET rates, and discuss future challenges that need to be tackled in order to achieve the mode-specific tuning of rates.     

Modeling of certain nonuniform processes in semiconductor technology

In this paper two problems are formulated and solved: the problem of diffusion in a two-phase system with a moving boundary, and the problem of taking into account the finite reaction rate for formation of the new phase. A numerical solution is found by a variational method, which has a number of practical advantages. Zh. Tekh. Fiz. 68, 75–82 (April 1998)     

Classical simulations of heavy-ion fusion reactions and weakly-bound projectile breakup reactions

Heavy-ion collision simulations in various classical models are discussed. Heavy-ion reactions with spherical and deformed nuclei are simulated in a classical rigid-body dynamics (CRBD) model which takes into account the reorientation of the deformed projectile. It is found that the barrier parameters not only on the initial orientations of the deformed nucleus, but also on the collision energy and the moment of inertia of the deformed nucleus. Maximum reorientation effect occurs at near- and below-barrier energies for light deformed nuclei. Calculated fusion cross-sections for ²⁴Mg + ²⁰⁸Pb reaction are compared with a static-barrier-penetration model (SBPM) calculation to see the effect of reorientation. Heavy-ion reactions are also simulated in a 3-stage classical molecular dynamics (3S-CMD) model in which the rigid-body constraints are relaxed when the two nuclei are close to the barrier thus, taking into account all the rotational and vibrational degrees of freedom in the same calculation. This model is extended to simulate heavy-ion reactions such as⁶Li + ²⁰⁹Bi involving the weakly-bound projectile considered as a weakly-bound cluster of deuteron and ⁴He nuclei, thus, simulating a 3-body system in 3S-CMD model. All the essential features of breakup reactions, such as complete fusion, incomplete fusion, no-capture breakup and scattering are demonstrated.     

Molecular photodynamics involved in multi-photon excitation fluorescence microscopy

We present a simple model for calculating the fluorescence generated by the multi-photon excitation (MPE) of molecules in solution. The model takes into account internal molecular dynamics such as ground-state depletion due to inter-system crossing (ISC), as well as external molecular dynamics associated with diffusion into and out of an excitation volume confined in 3-dimensions. Internal and external molecular dynamics are combined by using a technique of linearization of a modified diffusion equation which takes into account the possibility of concentration depletion due to photobleaching. In addition, we discuss the phenomenon of pulse saturation which effectively limits the molecular excitation rate constant in the case of short pulsed excitation. Our results are specifically applied in the context of fluorescence autocorrelation functions and single-molecule detection. In the latter case, we discuss some consequences of high-order multi-photon photobleaching. Finally, we include three appendices to rigorously define the temporal and spatial profiles of an arbitrary excitation beam, and also to discuss some properties of an exact evaluation of concentration depletion due to photobleaching. Received: 9 March 1998 / Accepted: 20 April 1998     

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged It? stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.     

State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis

ABSTRACT

The rate of nucleation processes such as the freezing of a supercooled liquid or the condensation of supersaturated vapour is mainly determined by the height of the nucleation barrier and the diffusion coefficient for the motion across it. Here, we use a Bayesian inference algorithm for Markovian dynamics to extract simultaneously the free energy profile and the diffusion coefficient in the nucleation barrier region from short molecular dynamics trajectories. The specific example we study is the nucleation of vapour bubbles in liquid water under strongly negative pressures, for which we use the volume of the largest bubble as a reaction coordinate. Particular attention is paid to the effects of discretisation, the implementation of appropriate boundary conditions and the optimal selection of parameters. We find that the diffusivity is a linear function of the bubble volume over wide ranges of volumes and pressures, and is mainly determined by the viscosity of the liquid, as expected from the Rayleigh–Plesset theory for macroscopic bubble dynamics. The method is generally applicable to nucleation processes and yields important quantities for the estimation of nucleation rates in classical nucleation theory.     

On the mechanism of effective chemical reactions with turbulent mixing of reactants and finite rate of molecular reactions

A generalization of the theory of chemical transformation processes under turbulent mixing of reactants and arbitrary values of the rate of molecular reactions is presented that was previously developed for the variant of an instantaneous reaction [13]. The use of the features of instantaneous reactions when considering the general case, namely, the introduction of the concept of effective reaction for the reactant volumes and writing a closing conservation equation for these volumes, became possible due to the partition of the whole amount of reactants into “active” and “passive” classes; the reactants of the first class are not mixed and react by the mechanism of instantaneous reactions, while the reactants of the second class approach each other only through molecular diffusion, and therefore their contribution to the reaction process can be neglected. The physical mechanism of reaction for the limit regime of an ideal mixing reactor (IMR) is revealed and described. Although formally the reaction rate in this regime depends on the concentration of passive fractions of the reactants, according to the theory presented, the true (hidden) mechanism of the reaction is associated only with the reaction of the active fractions of the reactants with vanishingly small concentration in the volume of the reactor. It is shown that the rate constant of fast chemical reactions can be evaluated when the mixing intensity of reactants is much less than that needed to reach the mixing conditions in an IMR.     

Ehrlich-Schwoebel barrier controlled slope selection in epitaxial growth

We examine the step dynamics in a 1+1-dimensional model of epitaxial growth based on the BCF-theory. The model takes analytically into account the diffusion of adatoms, an incorporation mechanism and an Ehrlich-Schwoebel barrier at step edges. We find that the formation of mounds with a stable slope is closely related to the presence of an incorporation mechanism. We confirm this finding using a solid-on-solid model in 2+1 dimensions. In the case of an infinite step edge barrier we are able to calculate the saturation profile analytically. Without incorporation but with inclusion of desorption and detachment we find a critical flux for instable growth but no slope selection. In particular, we show that the temperature dependence of the selected slope is solely determined by the Ehrlich-Schwoebel barrier which opens a new possibility in order to measure this fundamental barrier in experiments. Received 11 May 1999 and Received in final form 6 November 1999