Materials kinetics homogeneous

In deterministic theory we started with the definition of a compartment as a kinetically homogeneous amount of material. The equivalent definition in stochastic theory is that the probability of a unit participating in a particular transfer out of a compartment, at any time, is the same for all units in the compartment. 

Compartmental models are the mathematical result of such lumping. A com-partment is an amount of material that is kinetically homogeneous. Kinetic homogeneity means that material introduced into a compartment mixes instantaneously, and that each particle in the compartment has the same probability as all other particles in the compartment of leaving the compartment along the various exit pathways from the compartment. A compartmental model consists of a finite number of compartments with specified interconnections, inputs, and losses. 

A homogeneous kinetic process is one which occurs in a single phase, while a heterogeneous kinetic process involves several (two or more) distinct regions or phases. Almost all solid-state kinetic processes are heterogeneous because almost all solid-state systems manifest heterogeneity. Therefore, the field of materials kinetics mainly confronts heterogeneous kinetic processes. 

Let us start with some definitions. A compartment is an amount of material that acts as though it is well-mixed and kinetically homogeneous. A compartmental model consists of a finite number of compartments with specified interconnections among them. The interconnections represent fluxes of material which physiologically represent transport from one location to another or a chemical transformation, or both, or control signals. An example of a simple two-compartment model is Ulustrated in Figure 9.1 where the compartments are represented by circles and the interconnections by arrows. 

Much of the basic theory of reaction kinetics presented in Sec. 7 of this Handbook deals with homogeneous reaclions in batch and continuous equipment, and that material will not be repeated here. Material and energy balances and sizing procedures are developed for batch operations in ideal stirred tanks—during startup, continuation, and shutdown—and for continuous operation in ideal stirred tank batteries and plug flow tubulars and towers. 

It has also been recognized that micro-structured components, because of their low mass and thermal inertia, are able to offer short response times for unsteady state periodic operations. Micro-reactors have been used successfully for fluorination, oxidations and both heterogeneous [63-65] and homogeneous hydrogenations [66]. A review on gas-liquid micro-structured reactors has been published [67]. The very small material inventory when using micro devices offers another advantage, notably as a laboratory tool for screening applications, kinetics determination and process data acquisition, where the main concern is... 

The types of explosions that may occur depend on the confinement of the reactive material, its energy content, its kinetic parameters, and the mode of ignition (self-heating or induced by external energy input). Explosions are characterized as physical or chemical explosions, and as homogeneous or heterogeneous as described in Figure 2.2. 

The present procedure involving homogeneous catalysis is operationally simple and takes advantage of the easy availability of 2-(l -hydroxyalkyl )-acrylic esters. A two-step procedure Involving kinetic resolution of the racemic starting material with an optically active hydrogenation catalyst, followed by a further reduction with an achiral catalyst, leads to diastereomerically pure products in 4. 97t ee. 

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