Molecular dynamics simulations kinetic theory

The theory was very similar to that described earlier, but was simplified in view of the complexity of the problem. A number of reaction intermediates were considered explicitly, and the corresponding signals were calculated by molecular dynamics simulation. Kinetic equations governing the reaction sequence were established and were solved numerically. The main simplification of the theory is that, when calculating A5[r, r], the lower limit of the Fourier integral was shifted from 0 to a small value q. The authors wrote [59]... 

The theory was very similar to that described earlier but was simplified in view of the complexity of the problem. A number of reaction intermediates were considered explicitly, and the corresponding signals were calculated by molecular dynamics simulation. Kinetic equations governing the reaction... 

By contrast, few such calculations have as yet been made for diffusional problems. Much more significantly, the experimental observables of rate coefficient or survival (recombination) probability can be measured very much less accurately than can energy levels. A detailed comparison of experimental observations and theoretical predictions must be restricted by the experimental accuracy attainable. This very limitation probably explains why no unambiguous experimental assignment of a many-body effect has yet been made in the field of reaction kinetics in solution, even over picosecond timescale. Necessarily, there are good reasons to anticipate their occurrence. At this stage, all that can be done is to estimate the importance of such effects and include them in an analysis of experimental results. Perhaps a comparison of theoretical calculations and Monte Carlo or molecular dynamics simulations would be the best that could be hoped for at this moment (rather like, though less satisfactory than, the current position in the development of statistical mechanical theories of liquids). Nevertheless, there remains a clear need for careful experiments, which may reveal such effects as discussed in the remainder of much of this volume. 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

The solvated electron is a transient chemical species which exists in many solvents. The domain of existence of the solvated electron starts with the solvation time of the precursor and ends with the time required to complete reactions with other molecules or ions present in the medium. Due to the importance of water in physics, chemistry and biochemistry, the solvated electron in water has attracted much interest in order to determine its structure and excited states. The solvated electrons in other solvents are less quantitatively known, and much remains to be done, particularly with the theory. Likewise, although ultrafast dynamics of the excess electron in liquid water and in a few alcohols have been extensively studied over the past two decades, many questions concerning the mechanisms of localization, thermalization, and solvation of the electron still remain. Indeed, most interpretations of those dynamics correspond to phenomenological and macroscopic approaches leading to many kinetic schemes but providing little insight into microscopic and structural aspects of the electron dynamics. Such information can only be obtained by comparisons between experiments and theoretical models. For that, developments of quantum and molecular dynamics simulations are necessary to get a more detailed picture of the electron solvation process and to unravel the structure of the solvated electron in many solvents. 

The kinetic theory of liquids has been worked on intensively in this century. The activated-state theories of Eyring (29) and co-workers were the first entry into the field. Later Bom and Green (30, 31), Kirkwood and his collaborators (32), and others developed rigorous kinetic theories. Because of the complexity of the rigorous theories and the diflBculty of getting numerical results from them, attention in recent years has turned to molecular dynamics simulation (33). 

The physics of motion in a layer adjacent to the solid surface is quite different from the bulk motion described by the Stokes equation. This generates effective slip at a microscopic scale comparable with intermolecular distances. The presence of a slip in dense fluids it is confirmed by molecular dynamics simulations [17, 18] as well as experiment [19]. The two alternatives are shp conditions of hydrodynamic and kinetic type. The version of the slip condition most commonly used in fluid-mechairical theory is a linear relation between the velocity component along the solid surface and the shear stress... 

The validity of the viscoelastic model (5.32) has been tested against experimental and molecular dynamics simulation results [26, 27, 28]. The detailed comparison has established that the viscoelastic model works remarkably well for wavenumbers k km, where km denotes the first peak position of the static structure factor S k). However, it has also been found that the situation is not so satisfactory for smaller wavenumbers, where the viscoelastic model is shown in some circumstances to yield even qualitatively incorrect results. This failure was attributed to the fact that the single relaxation time model (5.31) cannot describe both the short-time behavior of the memory function, dominated by the so-called binary collisions, and in particular the intermediate and long-time behavior where in the liquid range additional slow processes play an important role (see the next subsection). It is obvious that these conclusions demand a more rigorous consideration of the memory function, which lead to the development of the modern version of the kinetic theory. Nevertheless, the viscoelastic model provides a rather satisfactory account of the main features of microscopic collective density fluctuations in simple liquids at relatively large wavenumbers, and its value should not be undervalued. 

Although it turned out that a number of essential features concerning dynamics of molecular liquids can be well captured by the theory of the previous subsection (see Secs. 3 and 5), an intense investigation through experimental, theoretical, and molecular-dynamics simulation studies for simple liquids has revealed that the microscopic processes underlying various time-dependent phenomena cannot be fully accounted for by a simplified memory-function approach [18, 19, 20]. In particular, the assumption that the decay of memory kernels is ruled by a simple exponential-type relaxation must be significantly revised in view of the results of the kinetic framework developed for dense liquids (see Sec. 5.1.4). This motivated us to further improve the theory for dynamics of polyatomic fluids. 

The purpose of this chapter is to selectively summarize recent advances in the molecular modeling of anode and cathode electrocatalytic reactions employing different computational approaches, ranging from first-principles quantum-chemical calculations (based on density functional theory, DFT), ab initio and classical molecular dynamics simulations to kinetic Monte Carlo simulations. Each of these techniques is associated with a proper system size and timescale that can be adequately treated and will therefore focus on different aspects of the reactive system under consideration. 

Gas transport in nano-confinements can significantly deviate from the kinetic theory predictions due to surface force effects. Kinetic theory-based approaches based on the assumption of dynamic similarity between nanoscale confined and rarefied flows in low-pressure environments by simply matching the Knudsen and Mach numbers are incomplete. Molecular dynamics simulations of nanoscale gas flows in the early transition and free-molecular flow regimes reveal that the wall force field penetration depth should be considered as an important length scale in nano-confined gas flows, in addition to the channel dimensions and gas mean free path. 

The basic, macroscopic theories of matter are equilibrium thermodynamics, irreversible thermodynamics, and kinetics. Of these, kinetics provides an easy link to the microscopic description via its molecular models. The thermodynamic theories are also connected to a microscopic interpretation through statistical thermodynamics or direct molecular dynamics simulation. Statistical thermodynamics is also outlined in this section when discussing heat capacities, and molecular dynamics simulations are introduced in Sect 1.3.8 and applied to thermal analysis in Sect. 2.1.6. The basics, discussed in this chapter are designed to form the foundation for the later chapters. After the introductory Sect. 2.1, equilibrium thermodynamics is discussed in Sect. 2.2, followed in Sect. 2.3 by a detailed treatment of the most fundamental thermodynamic function, the heat capacity. Section 2.4 contains an introduction into irreversible thermodynamics, and Sect. 2.5 closes this chapter with an initial description of the different phases. The kinetics is closely link to the synthesis of macromolecules, crystal nucleation and growth, as well as melting. These topics are described in the separate Chap. 3. 

The theoretical methods to investigate the evolution kinetics of ordered microdomain structures are those in the atomic-scale including molecular dynamics simulations, Monte Carlo simulations, dynamic SCFT, dynamic density functional theory (DDFT), and those in the meso-scale including dissipative particle dynamics (DPD) simulations, etc. More details of these approaches can be found in the literatures. 

The temperature instability of a two-dimensional reactive fluid of N hard disks bounded by heat conducting walls has been studied by molecular dynamics simulation. The collision of two hard disks is either elastic or inelastic (exothermic reaction), depending on whether the relative kinetic energy at impact exceeds a prescribed activation barrier. Heat removal is accomplished by using a wall boundary condition involving diffuse and specular reflection of the incident particles. Critical conditions for ignition have been obtained and the observations compared with continuum theory results. Other quantities which can be studied include temperature profiles, ignition times, and the effects of local fluctuations. 

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