Disordered kinetics

There are systems in which rate coefficients may vary randomly according to some probability distribution. Consider an amorphous solid in which an active intermediate is formed by radiation chemistry. The rate of reaction of that intermediate depends on the specific immediate surroundings of the intermediate, which may vary with location in the amorphous solid. The rate coefficients vary in space in the sample but not in time and such a system is said to have static disorder. 

---

Zema M., Domeneghetti M.C., and Tazzoli V. (1999) Order-disorder kinetics in orthopyroxene with exsolution products. Am. Mineral. 84, 1895-1901. 

The theory can be extended to reaction systems with disordered kinetics, for which the rate coefficients are random. There are two different cases (1) static disorder, for which the rate coefficients are random variables selected from certain probability laws and (2) dynamic disorder, for which the rate coefficients are random functions of time. For details see [5]. Here we give the expression of the average probability density of the lifetime for stationary systems with static disorder ... 

The response law (12.22) can be extended to disordered kinetics with static or dynamic disorder [5]. For stationary systems with static disorder the response law is... 

Ale] Electron diffraction, nuclear gamma resonance Order-disorder kinetics in Co-Fe equiatomic alloys + V... 

Nes] Neutron diffraction Order-disorder kinetics of Fe-Co-2 mass% V... 

In the usual mass action chemical kinetics the rate coefficients are parameters with fixed values these values may change with temperatme, pressme, and possibly ionic strength for reactions among ions. In the field of disordered kinetics we broaden the study to systems in which the rate coefficients may vary. For some prior reviews on disordered kinetics, see [15]. 

In both cases the late stages of kinetics show power law domain growth, the nature of which does not depend on the mitial state it depends on the nature of the fluctuating variable(s) which is (are) driving the phase separation process. Such a fluctuating variable is called the order parameter for a binary mixture, tlie order parameter o(r,0 is tlie relative concentration of one of the two species and its fluctuation around the mean value is 5e(/,t) = c(r,t) - c. In the disordered phase, the system s concentration is homogeneous and the order... 

Some of the distinctions that we shall have to examine in more detail before proceeding much further are the considerations of order versus disorder, solid versus liquid, and thermodynamics versus kinetics. These dualities are taken up in the next section. With those distinctions as background, we shall examine both the glassy and crystalline states from both the experimental and modelistic viewpoint. 

Radiation Damage. It has been known for many years that bombardment of a crystal with energetic (keV to MeV) heavy ions produces regions of lattice disorder. An implanted ion entering a soHd with an initial kinetic energy of 100 keV comes to rest in the time scale of about 10 due to both electronic and nuclear coUisions. As an ion slows down and comes to rest in a crystal, it makes a number of coUisions with the lattice atoms. In these coUisions, sufficient energy may be transferred from the ion to displace an atom from its lattice site. Lattice atoms which are displaced by an incident ion are caUed primary knock-on atoms (PKA). A PKA can in turn displace other atoms, secondary knock-ons, etc. This process creates a cascade of atomic coUisions and is coUectively referred to as the coUision, or displacement, cascade. The disorder can be directiy observed by techniques sensitive to lattice stmcture, such as electron-transmission microscopy, MeV-particle channeling, and electron diffraction. 

In photoluminescence one measures physical and chemical properties of materials by using photons to induce excited electronic states in the material system and analyzing the optical emission as these states relax. Typically, light is directed onto the sample for excitation, and the emitted luminescence is collected by a lens and passed through an optical spectrometer onto a photodetector. The spectral distribution and time dependence of the emission are related to electronic transition probabilities within the sample, and can be used to provide qualitative and, sometimes, quantitative information about chemical composition, structure (bonding, disorder, interfaces, quantum wells), impurities, kinetic processes, and energy transfer. 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

---