Fluctuation-induced chemical reaction

To analy2e premixed turbulent flames theoretically, two processes should be considered (/) the effects of combustion on the turbulence, and (2) the effects of turbulence on the average chemical reaction rates. In a turbulent flame, the peak time-averaged reaction rate can be orders of magnitude smaller than the corresponding rates in a laminar flame. The reason for this is the existence of turbulence-induced fluctuations in composition, temperature, density, and heat release rate within the flame, which are caused by large eddy stmctures and wrinkled laminar flame fronts. 

It has been suggested that weak interactions could be responsible for driving racemates towards homochirality via a deterministic process. However, it is difficult to deduce conclusions regarding the role played by these forces in chemical reactions for ensembles of molecules, since they induce a chiral bias of only 106 molecules per mole six orders of magnitude lower than the stochastic fluctuations present in a racemate. 

The equivalent of induced fit vs. conformational selection for the case of a motor protein is power stroke (a force-generating conformational change driven by a chemical reaction) vs. diffusion and catch (thermal fluctuation, even against an external force, followed by stabilization by chemical reaction). As we have discussed above, the distinction is meaningful only kinetically. For protein machines, the energy involved is not much greater than the thermal energy, and hence one cannot expect that one of the two processes overwhelms the other. 

First, there are terms of the form <5S(12)[z —0L (12 z)] 5S(12)>o. From its definition in (9.12), we see that 55(12) is the deviation of the reactive operator from its velocity average. The correlation function above characterizes the time evolution (Laplace transformed) of these fluctuations. If the chemical reaction is slow, we expect that perturbations of the velocity distribution induced by the reaction will be small hence such contributions may be safely neglected in this limit. This argument may be made more formal using limiting procedures analogous to those described in Section V. In principle, one may also use this term to introduce a modification to in S(/- 2) due to velocity relaxation effects. This will lead to some effective reactive collision frequency in place of k p. 

When the chemical reactions take place in fluid phases, concentration fluctuations may also result from the coupling with convective motion induced for example by local temperature gradients, surface effects like evaporative cooling and Marangoni effects or even by stirring memory. Due to the extreme sensitivity of the phase dynamics to fIuctuations,this coupling is very likely to affect the overall behaviour of the system and should be Incorporated in Its description. 

The previous results as well as numerical simulations 8 J suggest that a non-equilibrium bistable reactive system may evolve by nucleation process, in agreement with the theory of nucleation-induced transitions [ 9 3and with experimental observations 10 ]], If the whole system is initially in the metastable state a, in such conditions that the lifetime of a is of the order of the observation time, spontaneous local fluctuations may form a microdroplet of the stable state y then the chemical reaction tends to extend its volume, whereas the diffusion tends to reduce it. The deterministic theory shows L J if the radius of the droplet happens to exceed a... 

In many practical devices and many natural phenomena, chemical reactions and convection are playing together in addition, the velocity of the flow is most often such that turbulence takes place. In such cases, the study and prediction of reaction rates need some type of "modelling" of the macroscopic randomness due to the turbulence indeed the fluctuations induced by the turbulence have generally a first order influence on the non linearity of the chemical rates. 

For two fluctuating species new varieties of instabilities may occur, indeed even intrinsically stable chemical reactions may induce mechanical instabilities by coupling with hydrodynamics... 

Hydrogen bond (HB) networks play a relevant role on the dynamics of chemical and biochemical reactions in solution. The structure of HB network is determined by many-body energy cooperativity associated with polarization effects. Electronic density fluctuations induced by thermal effects or photoexcitation, assist and drive energy transfer processes in solution [46]. An interesting aspect related to the formation of HB networks is the role that they may have played in the origin of self-organized structures associated with life [47]. Therefore, the stmcture, dynamics and more recently, the electronic properties of these complex HB networks have been the subject of several fundamental investigations. In this section, we review recent applications of MBE decomposition schemes to the calculation of the electronic absorption spectra of liquid water and HCN. 

The space-time density fluctuations in polar liquid and their coupling widi a variety of chemical processes have attracted much attention in recent years. The photo-induced electric excitation of a solute and the thermal electron transfer reaction are among most well studied examples in such chemical processes. In this brief note, we report our recent effort to build theoretical tools for investigating such phenomena based on the integral equation method in die statistical mechanics of liquids. ... 

In this chapter, the focus will be on how information can be extracted, utilizing the second category described earlier (Fig. 8.1b). In its general form, the normalized autocorrelation function of the detected fluorescence fluctuations will show a complex dependence on the reaction rates and the coeflicients of the translational diffusion, and cannot be expressed in an analytical form. Fortunately, for a rather broad range of molecular reactions the reaction-induced fluorescence fluctuations can be treated separately from those due to translational diffusion [19]. If diffusion is much slower than the chemical relaxation time(s) and/or the diffusion coeflicients of all fluorescent species are equal, then the time-dependent fluorescence correlation function can be separated into two factors. The first factor, Gd( ), depends on transport properties (diffusion or flow) and the second, R t), depends only on the reaction rate constants ... 

Furthermore, it has recently been found that the discrete nature of a molecule population leads to qualitatively different behavior than in the continuum case in a simple autocatalytic reaction network [29]. In a simple autocatalytic reaction system with a small number of molecules, a novel steady state is found when the number of molecules is small, which is not described by a continuum rate equation of chemical concentrations. This novel state is first found by stochastic particle simulations. The mechanism is now understood in terms of fluctuation and discreteness in molecular numbers. Indeed, some state with extinction of specific molecule species shows a qualitatively different behavior from that with very low concentration of the molecule. This difference leads to a transition to a novel state, referred to as discreteness-induced transition. This phase transition appears by decreasing the system size or flow to the system, and it is analyzed from the stochastic process, where a single-molecule switch changes the distributions of molecules drastically. 

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