Collisional mechanisms

An important class of luminescence sensors are those based on the decrease of luminescence intensity and lifetime of the probes as function of analyte concentration. Assume that the probe intensity decays by a single exponential with an unquenched lifetime tq. If quenching occurs only by a dynamic (collisional) mechanism, then the ratio to/t is equal to Fq/F and is described by the classic Stern-Volmer equation... 

The electron relaxation is usually field dependent and the main mechanism for electron relaxation is the modulation of transient ZFS caused by collisions with solvent molecules. Small static ZFS have been estimated for several manganese(II) and gadolinium(III) proteins, and somewhat larger ones for iron(III) compounds. In such low symmetry systems, it is reasonable to expect the magnitude of transient ZFS to be related to that of the static ZFS, as the former can be seen as a perturbation of the latter. As a consequence, systems with increasing static ZFS experience faster electron relaxation rates. Modulation of static ZFS by rotation could be an additional mechanism for relaxation, which may coexist with the collisional mechanism. 

In this chapter, two simple cases of stereomechanical collision of spheres are analyzed. The fundamentals of contact mechanics of solids are introduced to illustrate the interrelationship between the collisional forces and deformations of solids. Specifically, the general theories of stresses and strains inside a solid medium under the application of an external force are described. The intrinsic relations between the contact force and the corresponding elastic deformations of contacting bodies are discussed. In this connection, it is assumed that the deformations are processed at an infinitely small impact velocity and for an infinitely long period of contact. The normal impact of elastic bodies is modeled by the Hertzian theory [Hertz, 1881], and the oblique impact is delineated by Mindlin s theory [Mindlin, 1949]. In order to link the contact theories to collisional mechanics, it is assumed that the process of a dynamic impact of two solids can be regarded as quasi-static. This quasi-static approach is valid when the impact velocity is small compared to the speed of the elastic... 

The book contains two parts each part comprises six chapters. Part I deals with basic relationships and phenomena of gas-solid flows while Part II is concerned with the characteristics of selected gas-solid flow systems. Specifically, the geometric features (size and size distributions) and material properties of particles are presented in Chapter 1. Basic particle sizing techniques associated with various definitions of equivalent diameters of particles are also included in the chapter. In Chapter 2, the collisional mechanics of solids, based primarily on elastic deformation theories, is introduced. The contact time, area, and... 

Let us first discuss a system which is traditional for optical pumping in the Kastler sense [106, 224, 226], namely an optically oriented alkali atom A (see Fig. 1.1) in a noble gas X buffer surrounding. It is important to take into account the fact that in alkali atoms, owing to hyperfine interaction, nuclear spins are also oriented. However, in a mixture of alkali vapor with a noble gas alkali dimers A2 which are in the 1SJ electronic ground state are always present. There exist two basic collisional mechanisms which lead to orientation transfer from the optically oriented (spin-polarized) atom A to the dimer A2 (a) creation and destruction of molecules in triple collisions A + A + X <—> A2 + X (6) exchange atom-dimer reaction... 

So far we have considered various radiational and collisional mechanisms of polarization of molecules. There exist earlier methods applying the action of an external stationary magnetic, later of an external electrostatic, field to beam molecules for producing anisotropic distribution of the angular momentum J and of the molecular axis. 

From the point of view of an elementary reactive collisional act, two limiting cases of collisional mechanisms can be distinguished. They are intimately connected with the type of the potential energy surface on which the reaction takes place. 

Most of our present understanding of the dynamics and of the collisional mechanisms of elementary chemical reactions comes from classical approaches, from simple classical models, and from quasiclassical trajectory studies. More recently, quantum mechanical results on the dynamics of directmode reactions have become available. 

The statistical theories provide a relatively simple model of chemical reactions, as they bypass the complicated problem of detailed single-particle and quantum mechanical dynamics by introducing probabilistic assumptions. Their applicability is, however, connected with the collisional mechanism of the process in question, too. The statistical phase space theories, associated mostly with the work of Light (in Ref. 6) and Nikitin (see Ref. 17), contain the assumption of a long-lived complex formation and are thus best suited for the description of complex-mode processes. On the other hand, direct character of the process is an implicit dynamical assumption of the transition-state theory. 

If a collision between two species that can form a stable molecule is to result in recombination, there must be some mechanism by which the intermediate can lose energy—either transfer to a third body or emission of light. For association directly into the ground electronic state, only the collisional mechanism is possible. It may be represented by the reaction sequence... 

In the rarefied flow regime, all of these collisional mechanisms can also occur. Due to the reduced number of intermolecular collisions, however, all of the energy distributions may be in a state of nonequilibrium. This means that the rates of the kinetic processes cannot be described by the temperature-dependent forms usually employed in continuum models. Instead, models are required that describe these processes at the individual collision level. 

Increasing theoretical and experimental attention has been paid to the vibrational relaxation and predissociation of vibrationally excited vdW molecules 195.203-205) Efficient vibrational relaxation takes place through the collisional mechanism ... 

The values of t (i.e., the critical exponent for electrical conductivity versus fluence), obtained from the slope of logftr) versus log(4> - j) linear dependences for various ion-implanted polymers (polyacrylonitrile [11], polyimide [87], poly-2,6-dimethyl-polyphenyleneoxide [11], perylene derivatives [12]), are 4-5 when the energy is deposited predominantly by the collisional mechanism and 7-8 when electronic stopping prevails. These values of the critical exponent for conductivity are substantially higher than those observed for metal nanoparticles in a dielectric matrix [88], which can be apparently explained by the effects of the conducting phase ordering during the implantation. 

CoLLisiONAL Mechanisms Using Nonreactive Gases AND Kinetic Energy Discrimination... 

The limitations of the earlier designs restricted their use for real-world samples because there appeared to be no way to effectively focus the ions, and therefore there was very little control over the collision process. So, even though the addition of a collision/reaction gas helped reduce plasma-based spectral interferences, it did virtually nothing for matrix-induced spectral interferences. In addition, there was no way to carry out KED in the interface region and, as a result, it made it very difficult to take advantage of collisional mechanisms using an inert gas such as helium. 

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