Kramers problem for nonequilibrium current-induced chemical reactions

We discuss the use of tunneling electron current to control and catalyze chemical reactions. Assuming the separation of time scales for electronic and nuclear dynamics we employ Langevin equation for a reaction coordinate. The Langevin equation contains nonconservative current-induced forces and gives nonequilibrium, effective potential energy surface for current-carrying molecular systems. The current-induced forces are computed via Keldysh nonequilibrium Green's functions. Once a nonequilibrium, current-depended potential energy surface is defined, the chemical reaction is modeled as an escape of a Brownian particle from the potential well. We demonstrate that the barrier between the reactant and the product states can be controlled by the bias voltage. When the molecule is asymmetrically coupled to the electrodes, the reaction can be catalyzed or stopped depending on the polarity of the tunneling current.     

A microscopic model of chemical reactions with reorganization. High-energy approximation

A dynamical model of a chemical reaction, accompanied by reorganization of the immediate environment of the isolated chemical subsystem, is proposed. The model enables studying the emergence of nonequilibrium distribution functions as a combined result of the interaction within the dynamical subsystem and the energy exchange with a subsystem of inactive degrees of freedom (thermal bath). The study is based on the quasiclassical high-energy approximation for nonadiabatic effects in the energy exchange within the dynamical subsystem, for strong and weak coupling of the oscillator mode with the thermal bath. Such an approximation allows for the important statement that nonequilibrium effects in thermal reactions are absent if the initial translational distribution along the reaction coordinate and the initial vibrational distribution in transversal degrees of freedom are Boltzmann-like with the same temperature. The results obtained in the absence of the initial equilibrium distribution have been used for interpreting the kinetics of endothermic plasmochemical reactions proceeding under nonequilibrium conditions.     

非平衡性引起的对质量作用定律的偏离

在化学反应动力学中,质量作用定律占有重要的地位,通常认为,该定律仅适用于理想的反应体系,并假定,一旦反应在平衡条件下遵循质量作用定律,那么在非平衡条件下也应遵循该定律,但根据最近的研究结果,平衡条件下的理想反应体系,在非平衡条件下可能变成非理想体系,换言之,非平衡性可能引起非理想性,这表明,非平衡条件下的(基元)反应并不总是遵守质量作用定律,本文利用文献的一些结果,并结合1个具体反应模型,研究了山非平衡性引起对质量作用定律的偏离,结果表明,非平衡性本身对反应动力学规律有重要影响,对化学反应动力学的研究亦具有一定启发作用。     

Extension of solution‐reaction‐surface description to examination of nonequilibrium solvation effect for microsolvated reaction

A microscopic method to examine a nonequilibrium solvation effect is reported. The solution reaction is simplified as a barrier‐crossing reaction within a solution reaction surface that corresponds to a two‐dimensional space determined by solute and solvent reactive coordinates. For this simplification, the motions within the space spanned by nonreactive coordinates are frozen. We derive three rate constant expressions: (1) in the nonadiabatic solvation limit, (2) in the equilibrium solvation limit, and (3) of the transition‐state theory. This method was applied to the examination of the contact‐ion‐pair formation of t‐BuCl in four waters. We found that the nonadiabatic solvation picture overestimates the nonequilibrium solvation effect. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 791–796, 2000     

Open-system nonequilibrium steady state: statistical thermodynamics, fluctuations, and chemical oscillations

Gibbsian equilibrium statistical thermodynamics is the theoretical foundation for isothermal, closed chemical, and biochemical reaction systems. This theory, however, is not applicable to most biochemical reactions in living cells, which exhibit a range of interesting phenomena such as free energy transduction, temporal and spatial complexity, and kinetic proofreading. In this article, a nonequilibrium statistical thermodynamic theory based on stochastic kinetics is introduced, mainly through a series of examples: single-molecule enzyme kinetics, nonlinear chemical oscillation, molecular motor, biochemical switch, and specificity amplification. The case studies illustrate an emerging theory for the isothermal nonequilibrium steady state of open systems.     

Exact solutions for the entropy production rate of several irreversible processes

We investigate thermal conduction described by Newton's law of cooling and by Fourier's transport equation and chemical reactions based on mass action kinetics where we detail a simple example of a reaction mechanism with one intermediate. In these cases we derive exact expressions for the entropy production rate and its differential. We show that at a stationary state the entropy production rate is an extremum if and only if the stationary state is a state of thermodynamic equilibrium. These results are exact and independent of any expansions of the entropy production rate. In the case of thermal conduction we compare our exact approach with the conventional approach based on the expansion of the entropy production rate near equilibrium. If we expand the entropy production rate in a series and keep terms up to the third order in the deviation variables and then differentiate, we find out that the entropy production rate is not an extremum at a nonequilibrium steady state. If there is a strict proportionality between fluxes and forces, then the entropy production rate is an extremum at the stationary state even if the stationary state is far away from equilibrium.     

Reachability,persistence, and constructive chemical reaction networks (part I): reachability approach to the persistence of chemical reaction networks

For a chemical reaction network, persistence is the property that no species tend to extinction if all species are initially present. We investigate the stronger property of vacuous persistence: the same asymptotic feature with a weaker requirement on initial states, namely that all species be implicitly present. By implicitly present, we mean for instance that if only water is present and the reaction network incorporates the information that water is made of hydrogen and oxygen, then hydrogen and oxygen are implicitly present. Persistence is inherently interesting and has implications for the global asymptotic stability of equilibrium states. Our main tools are the work of A. I. Vol’pert on the nullity and positivity of species concentrations, and the enabling notion of reachability. The main result states that a reaction network is vacuously persistent if and only if the set of all species is the only set of species that both is closed with respect to reachability and causes the implicit presence of all species. This paper is the first in a series of three articles. Two sequel papers introduce additional formalisms and use them to describe two large classes of reaction networks that are used as models in biochemistry and are vacuously persistent.     

Shear thinning and shear dilatancy of liquid n-hexadecane via equilibrium and nonequilibrium molecular dynamics simulations: Temperature, pressure, and density effects

Equilibrium and nonequilibrium molecular dynamics (MD) simulations have been performed in both isochoric-isothermal (NVT) and isobaric-isothermal (NPT) ensemble systems. Under steady state shearing conditions, thermodynamic states and rheological properties of liquid n-hexadecane molecules have been studied. Between equilibrium and nonequilibrium states, it is important to understand how shear rates (gamma) affect the thermodynamic state variables of temperature, pressure, and density. At lower shear rates of gamma<1 x 10(11) s(-1), the relationships between the thermodynamic variables at nonequilibrium states closely approximate those at equilibrium states, namely, the liquid is very near its Newtonian fluid regime. Conversely, at extreme shear rates of gamma>1 x 10(11) s(-1), specific behavior of shear dilatancy is observed in the variations of nonequilibrium thermodynamic states. Significantly, by analyzing the effects of changes in temperature, pressure, and density on shear flow system, we report a variety of rheological properties including the shear thinning relationship between viscosity and shear rate, zero-shear-rate viscosity, rotational relaxation time, and critical shear rate. In addition, the flow activation energy and the pressure-viscosity coefficient determined through Arrhenius and Barus equations acceptably agree with the related experimental and MD simulation results.     

Some consequences of thermodynamic feasibility for chemical reaction networks

Power law dynamics is used to describe the stability behavior in metabolic networks such as chemical reaction networks (CRN’s). These systems allow multiple steady states within a single stoichiometric class. On the other side thermodynamic constraints such as loop-less fluxes represented by the Gorban theorem of alternatives applied to these networks reveal considerable restrictions to their dynamics by eliminating multistability of CRN’s in general. Thermodynamic feasible CRN’s are contained in the class of injective CRN’s. We can give an alternative proof of the detailed balance with Brewer’s Fixed Point Theorem. Furthermore we can derive by the loop-less principle the extended detailed balance. This paper establishes a link between recent research in CRN theory and thermodynamic basics. The result has also consequences for the picture of multiple steady states as assumed for cell differentiation and regulation. CRN’s provide from their perspective not enough means to maintain multistability without regulation or external control.

     

Nonoscillation in closed reversible chemical systems

For a closed reversible chemical system obeying mass action kinetics, we prove that structurally stable closed orbits do not exist if there are no more reaction steps than reactants. We derive this using an appropriate Lyapunov function for a special case in which the number of reaction steps equals the number of reactants and a stationary point is shown to be unique and asymptotically stable.     

Theory of chemical reactions in solids. Part I

The adiabatic approximation is used to derive the probability of an elementary chemical reaction in a lattice, which resembles the production of a defect and transition of an impurity between two equilibrium positions. The process is shown to be of quasiactivation type at high temperatures.     

Simulating the relaxation dynamics of microwave-driven zeolites

We have performed equilibrium and nonequilibrium molecular dynamics simulations to study how microwave (MW)-heated zeolite systems relax to thermal equilibrium. We have simulated the relaxation of both ionic and dipolar phases in FAU-type zeolites, finding biexponential relaxation in all cases studied. Fast-decay times were uniformly below 1 ps, while slow-decay times were found to be as long as 14 ps. Fast-decay times increase with an increase in the initial temperature difference between MW-heated ions/dipoles and the equilibrium system. Slow-decay times were found to be relatively insensitive to the details of the MW-heated nonequilibrium state. Velocity, force, and orientational correlation functions, calculated at equilibrium to explore the natural dynamics of energy transfer, decay well before 1 ps and show little evidence of biexponential decay. In contrast, kinetic energy correlation functions show strong biexponential behavior with slow-decay times as long as 14 ps. We suggest a two-step mechanism involving initial, efficient energy transfer mediated by strongly anharmonic zeolite-guest forces, followed by a slower process mediated by weakly anharmonic couplings among normal modes of the zeolite framework. In addition to elucidating relaxation from MW-heated states, we expect that these studies will shed light on energy transfer in other contexts, such as adsorption and reaction in zeolites, which often involve significant heat release.     

Relative Boltzmann entropy, evolution equations for fluctuations of thermodynamic intensive variables, and a statistical mechanical representation of the zeroth law of thermodynamics

Generalized thermodynamics or extended irreversible thermodynamics presumes the existence of thermodynamic intensive variables (e.g., temperature, pressure, chemical potentials, generalized potentials) even if the system is removed from equilibrium. It is necessary to properly understand the nature of such intensive variables and, in particular, of their fluctuations, that is, their deviations from those defined in the extended irreversible thermodynamic sense. The meaning of temperature is examined by means of a kinetic theory of macroscopic irreversible processes to assess the validity of the generalized (or extended) thermodynamic method applied to nonequilibrium phenomena. The Boltzmann equation is used for the purpose. Since the relative Boltzmann entropy has been known to be intimately related to the evolution of the aforementioned fluctuations in the intensive thermodynamic variables, we derive the evolution equations for such fluctuations of intensive variables to lay the foundation for investigating the physical implications and evolution of the relative Boltzmann entropy, so that the range of validity of the thermodynamic theory of irreversible processes can be elucidated. Within the framework of this work, we examine a special case of the evolution equations for the aforementioned fluctuations of intensive variables, which also facilitate investigation of the molecular theory meaning of the zeroth law of thermodynamics. We derive an evolution equation describing the relaxation of temperature fluctuations from its local value and present a formula for the temperature relaxation time.     

Comparison of Accuracy and Convergence Rate between Equilibrium and Nonequilibrium Alchemical Transformations for Calculation of Relative Binding Free Energy

Estimation of protein-ligand binding affinity within chemical accuracy is one of the grand challenges in structure-based rational drug design. With the efforts over three decades, free energy methods based on equilibrium molecular dynamics (MD) simulations have become mature and are nowadays routinely applied in the community of computational chemistry. On the contrary, nonequilibrium MD simulation methods have attracted less attention, despite their underlying rigor in mathematics and potential advantage in efficiency. In this work, the equilibrium and nonequilibrium simulation methods are compared in terms of accuracy and convergence rate in the calculations of relative binding free energies. The proteins studied are T4-lysozyme mutant L99A and COX-2. For each protein, two ligands are studied. The results show that the nonequilibrium simulation method can be competitively as accurate as the equilibrium method, and the former is more efficient than the latter by considering the convergence rate with respect to the cost of wall clock time. In addition, Bennett acceptance ratio, which is a bidirectional post-processing method, converges faster than the unidirectional Jarzynski equality for the nonequilibrium simulations.     

Equilibrium calculations of viscosity and thermal conductivity across a solid-liquid interface using boundary fluctuations

We calculate viscosity and thermal conductivity in systems of Lennard-Jones particles consisting of coexisting solid and liquid with different interface wetting properties using the recently developed equilibrium boundary fluctuation theory. We compare the slip length and equivalent liquid length obtained from these calculations with those obtained from nonequilibrium molecular dynamics. The equilibrium and nonequilibrium calculations of the slip length and the sum of the thermal equivalent lengths are in good agreement. We conclude that for both interfacial properties, the nonequilibrium simulations were probing the linear response. The significant dependence of the intrinsic equivalence length on the interfacial temperature difference used to generate the thermal gradient is explained as a consequence of the different thermodynamic states of the two interfaces.     

Validated computing approach for high-pressure chemical and multiphase equilibrium

For the computation of chemical and phase equilibrium at constant temperature and pressure, there have been proposed a wide variety of problem formulations and numerical solution procedures, involving both direct minimization of the Gibbs energy and the solution of equivalent nonlinear equation systems. Still, with very few exceptions, these methodologies may fail to solve the chemical and phase equilibrium problem correctly. Nevertheless, there are many existing solution methods that are extremely reliable in general and fail only occasionally. To take good advantage of this wealth of available techniques, we demonstrate here an approach in which such techniques can be combined with procedures that have the power to validate results that are correct, and to identify results that are incorrect. Furthermore, in the latter case, corrective feedback can be provided until a result that can be validated as correct is found. The validation procedure is deterministic, and provides a mathematical and computational guarantee that the global minimum in the Gibbs energy has been found. To demonstrate this validated computing approach to the chemical and phase equilibrium problem, we present several examples involving reactive and nonreactive components at high pressure, using cubic equation-of-state models.     

Experiments on temporal and spatial chemical patterns

Two examples of bifurcation sequences observed in experiments on nonequilibrium reactions in continuous flow stirred reactors are discussed: one experiment demonstrates that bifurcation diagrams can serve as a tool for elucidating chemical mechanisms, and another experiment illustrates that even very complex bifurcation sequences need not include chaotic states. A discussion of chemical spatial patterns emphasizes the need for the development of spatially extended reactors in which patterns can be maintained indefinitely. Three such recently developed reactors are described.