Solids molecular kinetic theory

A correlation between surface and volume processes is described in Section 5. The atomic-molecular kinetic theory of surface processes is discussed, including processes that change the solid states at the expense of reactions with atoms and molecules of a gas or liquid phase. The approach reflects the multistage character of the surface and volume processes, each stage of which is described using the theory of chemical kinetics of non-ideal reactive systems. The constructed equations are also described on the atomic level description of diffusion of gases through polymers and topochemical processes. 

You can t understand gases without understanding the movement of gas particles. Remember from your study of the kinetic-molecular theory in Chapter 13 that gas particles behave differently than those of liquids and solids. The kinetic theory provides a model that is used to explain the properties of solids, liquids, and gases in terms of particles that are always in motion and the forces that exist between them. The kinetic theory assumes the following concepts about gases are true. 

Fig. 15. Variation of the contact angle with the velocity for glycerol/water displacing air on a PET surface. Solid line corresponds to molecular-kinetic theory and dotted line to Cox model. " ...

The role of adhesion and surface energetics on polymer friction has been critically examined by Lee. The application of molecular kinetic theory to adhesion and friction of elastomers has been carried out by Lavrentev , and molecular interaction for solids at contact have been reviewed . 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic theory of gases, and their interrelationship through A, and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests that this should be a dependence on T1/2, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to r3/2 for the case of molecular inter-diffusion. The Arrhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, then an activation enthalpy of a few kilojoules is observed. It will thus be found that when the kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation enthalpy will be a few kilojoules only (less than 50 kJ). 

The success of kinetic theories directed toward the measurements of surface areas depends upon their ability to predict the number of adsorbate molecules required to exactly cover the solid with a single molecular layer. Equally important is the cross-sectional area of each molecule or the effective area covered by each adsorbed molecule on the surface. The surface area then, is the product of the number of molecules in a completed monolayer and the effective cross-sectional area of an adsorbate molecule. The number of molecules required for the completion of a monolayer will be considered in this chapter and the adsorbate cross-sectional area will be discussed in Chapter 6. 

According to kinetic theory, the molecules of any substance are in a constant state of motion at all temperatures above absolute zero. The molecules of a solid are restricted in their movement by attractive forces which hold them near a fixed position so that the motion corresponds to a molecular vibration rather than to actual movement of the molecules. This is true to a lesser extent in liquids in which the molecules both vibrate and move around. 

After the formulation of defect thermodynamics, it is necessary to understand the nature of rate constants and transport coefficients in order to make practical use of irreversible thermodynamics in solid state kinetics. Even the individual jump of a vacancy is a complicated many-body problem involving, in principle, the lattice dynamics of the whole crystal and the coupling with the motion of all other atomic structure elements. Predictions can be made by simulations, but the relevant methods (e.g., molecular dynamics, MD, calculations) can still be applied only in very simple situations. What are the limits of linear transport theory and under what conditions do the (local) rate constants and transport coefficients cease to be functions of state When do they begin to depend not only on local thermodynamic parameters, but on driving forces (potential gradients) as well Various relaxation processes give the answer to these questions and are treated in depth later. 

Uranium hexafluoride is probably the most interesting of the uranium fluorides. Under ordinary conditions, it is a dense, white solid with a vapor pressure of about 120 hull ai room temperature. It can readily be sublimed or distilled, and it is by far the most volatile uranium compound known. Despite its high molecular weight, gaseous UFg is almost a perfect gas, and many of the properties of the vapor can be predicted from kinetic theory. 

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or solid. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (5) the intramolecular vibrations are considered identical for molecules in either the gas or liquid phases, and (4) the potential energy of a collection of molecules is a function of only the various intermolecular distances. 

The physical condition of the kinetic theory of gases can be described by elastic collisions of monodispersed spheres with the Maxwellian velocity distribution in an infinite vacuum space. Therefore, for an analogy between particle-particle interactions and molecular interactions to be directly applicable, the following phenomena in gas-solid flows should not be regarded as significant in comparison to particle-particle interactions the gas-particle... 

In the condensed phase the AC permanently interacts with its neighbors, therefore a change in the local phase composition (as were demonstrated on Figs. 8.1 and 8.2) affects the activation barrier level (Fig. 8.6). Historically the first model used for surface processes is the analogy of the collision model (CM) [23,48,57]. This model uses the molecular-kinetic gas theory [54]. It will be necessary to count the number of the active collisions between the reagents on the assumption that the molecules represent solid spheres with no interaction potential between them. Then the rate constant can be written down as follows (instead of Eq. (6)) ... 

Except the kinetic equations, now various numerical techniques are used to study the dynamics of surfaces and gas-solid interface processes. The cellular automata and MC techniques are briefly discussed. Both techniques can be directly connected with the lattice-gas model, as they operate with discrete distribution of the molecules. Using the distribution functions in a kinetic theory a priori assumes the existence of the total distribution function for molecules of the whole system, while all numerical methods have to generate this function during computations. A success of such generation defines an accuracy of simulations. Also, the well-known molecular dynamics technique is used for interface study. Nevertheless this topic is omitted from our consideration as it requires an analysis of a physical background for construction of the transition probabilities. This analysis is connected with an oscillation dynamics of all species in the system that is absent in the discussed kinetic equations (Section 3). 

Even with an adequate description of molecular velocities near the particle surface, it is not possible to completely establish all variables influencing thermal force. This is because there also exists a so-called thermal slip flow or creep flow at the particle surface. Reynolds (see Niven, 1965) and others have pointed out that as a consequence of kinetic theory, a gas must slide along the surface of a solid from the colder to the hotter portions. However, if there is a flow of gas at the surface of the particle up the temperature gradient, then the force causing this flow must be countered by an opposite force acting on the particle, so that the particle itself moves in an opposite direction down the temperature gradient. This is indeed the case, known as thermal creep. Since the velocity appears to go from zero to some finite value right at the particle surface, this phenomenon is often described as a velocity jump. A temperature jump also exists at the particle surface. 

Thermodynamics and kinetics of the positron and Ps have been developed to a certain extent, mainly in liquids. It is interesting to observe that the positron and Ps are in fact localized in the bubble or the defect sites of molecular media [17], Therefore, the motion of the positron and Ps in molecular media is always coupled with the surrounding molecules, i.e. never in the form of a free particle in liquids or solids. Most existing theories... 

Because the molecular theory of gases is so much more extensively developed than that of liquids or solids, the kinetics of gas reactions have been heavily emphasized relative to solutions and solids. The extensive... 

Metals form a class of solids with characteristic macroscopic properties. They are ductile, have a silver-white luster, and they conduct electricity and heat remarkably well. An early, but still relevant microscopic model aimed at explaining the electrical conductivity, heat conductivity, and optical properties was proposed by Drude [10]. His model incorporates two important successes of modem science the discovery of the electron in 1887 by J. J. Thomson, and the molecular kinetic gas theory put forward by Boltzmann and Maxwell in the second half of the 19th century. 

The concept of solid angle, commonly used in kinetic theory, radiation and other scattering problem descriptions, is defined before the molecular scattering process is described in further details in the subsequent section. 

Petrov and Petrov (1998) developed a molecular hydrodynamic theory of film deposition during removal. Their theory correctly assumes a flow pattern - which we identified as a split streamline - between the solid substrate and the monolayer in Figure 10.5 (c). This pattern is indeed the necessary pattern for successful deposition during removal, but it is not the only flow pattern for solid removal at all dynamic contact angles. Petrov and Petrov (1998) address the kinetics of water removal between the solid and the monolayer and the formation of wet or dry monolayers depending on the amount of water entrained. 

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