On the perturbation of the vibrational equilibrium distribution of reactant molecules by chemical reactions

There are now many examples in various fields where the behaviour of ‘particles' as exhibited by their transition from one state to another is described by a multidimensional stochastic process. The linear migration model in which particles move independently of one another through a number of states has been dealt with by Bartlett (1949). This process has been used by Siegert (1949) in considering the approach to equilibrium of non-interacting gas molecules and by Krieger and Gans (1960) and Gans (1960) to examine the distribution of a multicomponent system disturbed from its equilibrium distribution and relaxing by first-order processes to another equilibrium. The correspondence between the deterministic model based on the principle of mass action and the stochastic model has been discussed by Darvey and Staff (1966) in the context of unimolecular multicomponent chemical reactions.

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Equilibrium distributions for systems of chemical reactions with applications to the theory of molecular adsorption

Journal of Applied Probability ◽

10.2307/3212098 ◽

1969 ◽

Vol 6 (3) ◽

pp. 505-515 ◽

Cited By ~ 8

Author(s):

J. Orriss

Keyword(s):

Chemical Reactions ◽

Equilibrium Distribution ◽

The Other ◽

Molecular Adsorption ◽

Reaction Equation ◽

Reversible Chemical Reaction ◽

Different Types ◽

Equilibrium Distributions ◽

Set Up ◽

Reaction Equations

SummaryIn this paper a stochastic model is set up for a certain type of reversible chemical reaction and a solution given for the equilibrium distribution; this solution is then extended to deal with any system of chemical reactions.Three different types of reaction are considered:(1) Several substances Ai react together and give a set of substances Bj. The reaction is reversible, with the substances Ai appearing only on one side of the reaction equation and the substances Bj only on the other.(2) Several different reactions involving the substances Ai and Bj take place simultaneously, but in each reaction equation the substances Ai can appear only on one side and the Bj only on the other.(3) The restriction of the sets Ai and Bj to different sides of the reaction equations is removed: any reaction involving any of the substances Aiand Bj on either side of the equation is permissible.The paper concludes with some applications of the results to problems of molecular adsorption.

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Equilibrium distributions for systems of chemical reactions with applications to the theory of molecular adsorption

Journal of Applied Probability ◽

10.1017/s0021900200026577 ◽

1969 ◽

Vol 6 (03) ◽

pp. 505-515 ◽

Cited By ~ 2

Author(s):

J. Orriss

Keyword(s):

Chemical Reactions ◽

Equilibrium Distribution ◽

The Other ◽

Molecular Adsorption ◽

Reaction Equation ◽

Reversible Chemical Reaction ◽

Different Types ◽

Equilibrium Distributions ◽

Set Up ◽

Reaction Equations

Summary In this paper a stochastic model is set up for a certain type of reversible chemical reaction and a solution given for the equilibrium distribution; this solution is then extended to deal with any system of chemical reactions. Three different types of reaction are considered: (1) Several substances Ai react together and give a set of substances Bj. The reaction is reversible, with the substances Ai appearing only on one side of the reaction equation and the substances Bj only on the other. (2) Several different reactions involving the substances Ai and Bj take place simultaneously, but in each reaction equation the substances Ai can appear only on one side and the Bj only on the other. (3) The restriction of the sets Ai and Bj to different sides of the reaction equations is removed: any reaction involving any of the substances Ai and Bj on either side of the equation is permissible. The paper concludes with some applications of the results to problems of molecular adsorption.

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First-Order Conservative Processes with Multiple Latent Roots

Journal of Applied Probability ◽

10.2307/3212285 ◽

1969 ◽

Vol 6 (1) ◽

pp. 186-194 ◽

Cited By ~ 4

Author(s):

J. Radcliffe ◽

P. J. Staff

Keyword(s):

Stochastic Process ◽

Stochastic Model ◽

Chemical Reactions ◽

Equilibrium Distribution ◽

Deterministic Model ◽

Multicomponent System ◽

Mass Action ◽

Approach To Equilibrium ◽

First Order ◽

Gas Molecules

There are now many examples in various fields where the behaviour of ‘particles' as exhibited by their transition from one state to another is described by a multidimensional stochastic process. The linear migration model in which particles move independently of one another through a number of states has been dealt with by Bartlett (1949). This process has been used by Siegert (1949) in considering the approach to equilibrium of non-interacting gas molecules and by Krieger and Gans (1960) and Gans (1960) to examine the distribution of a multicomponent system disturbed from its equilibrium distribution and relaxing by first-order processes to another equilibrium. The correspondence between the deterministic model based on the principle of mass action and the stochastic model has been discussed by Darvey and Staff (1966) in the context of unimolecular multicomponent chemical reactions.

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Surface reactions observed by photoemission electron microscopy (PEEM)

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100121831 ◽

1992 ◽

Vol 50 (1) ◽

pp. 286-287

Author(s):

H.H. Rotermund

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Work Function ◽

Chemical Reactions ◽

Reaction Diffusion ◽

Dynamic Processes ◽

Clean Surface ◽

Crystal Surfaces ◽

Single Crystal Surfaces ◽

Photoemission Electron

Chemical reactions at a surface will in most cases show a measurable influence on the work function of the clean surface. This change of the work function δφ can be used to image the local distributions of the investigated reaction,.if one of the reacting partners is adsorbed at the surface in form of islands of sufficient size (Δ>0.2μm). These can than be visualized via a photoemission electron microscope (PEEM). Changes of φ as low as 2 meV give already a change in the total intensity of a PEEM picture. To achieve reasonable contrast for an image several 10 meV of δφ are needed. Dynamic processes as surface diffusion of CO or O on single crystal surfaces as well as reaction / diffusion fronts have been observed in real time and space.

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Microwaves: Application in Electron Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100158248 ◽

1990 ◽

Vol 48 (3) ◽

pp. 140-141

Author(s):

Anthony S-Y Leong ◽

David W Gove

Keyword(s):

Electron Microscopy ◽

Light Microscopy ◽

Chemical Reactions ◽

Electromagnetic Waves ◽

Tissue Fixation ◽

Primary Method ◽

Dipolar Molecules ◽

Wide Range ◽

Time Required ◽

Cryostat Sections

Microwaves (MW) are electromagnetic waves which are commonly generated at a frequency of 2.45 GHz. When dipolar molecules such as water, the polar side chains of proteins and other molecules with an uneven distribution of electrical charge are exposed to such non-ionizing radiation, they oscillate through 180° at a rate of 2,450 million cycles/s. This rapid kinetic movement results in accelerated chemical reactions and produces instantaneous heat. MWs have recently been applied to a wide range of procedures for light microscopy. MWs generated by domestic ovens have been used as a primary method of tissue fixation, it has been applied to the various stages of tissue processing as well as to a wide variety of staining procedures. This use of MWs has not only resulted in drastic reductions in the time required for tissue fixation, processing and staining, but have also produced better cytologic images in cryostat sections, and more importantly, have resulted in better preservation of cellular antigens.

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Fine structure and properties of defects in naturally occurring silicates and oxides

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100175430 ◽

1990 ◽

Vol 48 (4) ◽

pp. 460-461

Author(s):

David R. Veblen

Keyword(s):

Chemical Reactions ◽

High Resolution Electron Microscopy ◽

Extended Defects ◽

Single Chain ◽

Naturally Occurring ◽

Resolution Electron ◽

Fine Structures ◽

Image Simulations ◽

Similar Crystal Structure

Extended defects and interfaces control many processes in rock-forming minerals, from chemical reactions to rock deformation. In many cases, it is not the average structure of a defect or interface that is most important, but rather the structure of defect terminations or offsets in an interface. One of the major thrusts of high-resolution electron microscopy in the earth sciences has been to identify the role of defect fine structures in reactions and to determine the structures of such features. This paper will review studies using HREM and image simulations to determine the structures of defects in silicate and oxide minerals and present several examples of the role of defects in mineral chemical reactions. In some cases, the geological occurrence can be used to constrain the diffusional properties of defects.The simplest reactions in minerals involve exsolution (precipitation) of one mineral from another with a similar crystal structure, and pyroxenes (single-chain silicates) provide a good example. Although conventional TEM studies have led to a basic understanding of this sort of phase separation in pyroxenes via spinodal decomposition or nucleation and growth, HREM has provided a much more detailed appreciation of the processes involved.

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