Neutrality condition, reaction-diffusion process

In the literature on diffusion and diffusion-controlled reactions or processes one encounters many different terms that describe the diffusional behaviour under different experimental conditions tracer and self-diffusion of atoms and ions, diffusion of defects, chemical diffusion, ambipolar diffusion, a.o. Many of these are used for treating diffusion in compounds, and in the following chapters these phenomena and terms will be described in more detail. Here we will start out with a few simple phenomenological descriptions, and for simplicity we look only at diffusion of neutral, independent particles. 

A much more detailed and time-dependent study of complex hydrocarbon and carbon cluster formation has been prepared by Bettens and Herbst,83 84 who considered the detailed growth of unsaturated hydrocarbons and clusters via ion-molecule and neutral-neutral processes under the conditions of both dense and diffuse interstellar clouds. In order to include molecules up to 64 carbon atoms in size, these authors increased the size of their gas-phase model to include approximately 10,000reactions. The products of many of the unstudied reactions have been estimated via simplified statistical (RRKM) calculations coupled with ab initio and semiempirical energy calculations. The simplified RRKM approach posits a transition state between complex and products even when no obvious potential barrier... 

A possible reconciliation of these seemingly conflicting results lies in the lifetimes of the individual radical cations under the different experimental conditions. In the PET experiment the lifetime is dictated by the rate of intersystem crossing, a hyperfine induced process, which often falls into the range 10-9 to 10-8 sec. The aminium salt catalyzed rearrangement is a free radical cation chain reaction. Under these conditions the radical cation lifetime is determined by the diffusion-limited encounter with a neutral molecule, which may be quite slow at the low temperatures of these experiments. Although any barrier to isomerization is larger at the lower temperatures, it is well-known that the barriers to many radical cation reactions are reduced drastically. 

By far the most commonly exploited polymerization of heterocycles is the oxidative polymerization, which can be carried out using chemical or electrochemical oxidation conditions. Chemical oxidative polymerization is advantageous in that the reactions are fast and simple, using relatively mild conditions (94), and polymers could presumably be mass-produced at a reasonable cost (95). Oxidation potentials depend upon the electron density of the monomers the more electron-rich a monomer is, the easier it is to oxidize. The oxidative polymerization of thiophene is shown in Figure 3 this mechanism is equally applicable to other heterocycles. The mechanism is thought to involve a one-electron oxidation of the monomer to form a resonance-stabilized radical cation. This can couple with a molecule of starting material to form a radical cation dimer, which loses another electron to form the dicationic dimer, or the radical cation can couple with another radical cation to form a dicationic dimer. The dicationic dimer then loses two protons to form the neutral dimer, and the entire process is repeated to form polymer. The fundamental polymerization mechanism is the same for both chemical and electrochemical polymerization, although there are additional factors (diffusion, scan rate, electrode characteristics, etc) that must be considered for electrochemical polymerization. 

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