Reaction of a single grain

Two-process model with surface nucleation-radial anisotropic growth 10.4.1. Reaction of a single grain 

On the other hand, the law that gives the rate according to the fractional extent is identical to that obtained in the one-process model of instantaneous nucleation and the corresponding curves are identical. 

Nucleation on a grain being random, the latency time is not reproducible from one experiment to another in the same conditions the obtained kinetic curves are translated with each other. This result was observed in the decomposition of a monocrystal of lithium monohydrate sulfate [BOU 98]. 

Two-process model with nucleation and anisotropic growth 

We assume that the reactivity of growth and the specific frequency of nucleation are independent of time (pseudo-steady state modes at constant tenperature and partial pressures). We will thus refer to relations [10.16] and [10.18], but in this case, a nucleus corresponds to a grain we can thus reveal in these expressions the space function of growth of a grain. 

---

Figure 10.2. Reaction of a single grain with slow germination and very fast growth...

Figure 2.15. The temperature change along the cross section of the sample in the case of a dynamic heating program. T, temperature space coordinate t, time A T. temperature drop. 1, Furnace 2, sample holder 3, sample 4. thermoelement 5, a single grain of the sample. Time and temperature of the beginning (/, Ts), maximum rate (tj, T6), and end (f4, 7"0) of an endo-thermal reaction. Heat transfer between furnace and sample surface (U), surface and center of the sample (F), surface and center of a single grain (Z) (114).

The simple experiments of Kuchinskii and Ershler have provided great insights into the nature of the Ni(OH)2/NiOOH reaction [88,89]. They investigated oxidation and reduction of a single grain of Ni(OH)2 with a platinum point contact On charge, the Ni(OH)2 turned black and oxygen was evolved preferentially on the... 

The influence of crystalline orientation and surface structure on water reactivity was clearly shown in a study performed by ESCA, LEED, and STM on NiO thin films [123], After oxidation at 300 K at low oxygen pressure of a single crystal of Ni(lll), the thin film, three to four layers thick, consists mainly of NiO( 111) grains in parallel epitaxy with the substrate. This film, otherwise unstable, is stabilized by a complete layer of OH formed by reaction with the residual water contained in oxygen gas. The hydroxyl groups are ionic (OH ) and singly bonded to the surface metal atoms that terminate the polar NiO(l 11) plane [124]. The ionic character of the hydroxyl groups would compensate at least partially the repulsive interaction between Ni cations in the outermost plane of NiO [124], A further exposure (150 L) at room temperature to water leads to the formation of a nearly complete layer of nickel hydroxide with the terminal sequence OH-Ni-OH. 

For example, it was shown [129] that the introduction of a single 1-mm-diameter grain of Pt/Zr02 catalyst at 850 °C into a methane—oxygen flow with a ratio of [CH4]/[02] = 2 (corresponding to the maximum reaction rate) affects not only the conversion of reactants. 

To check the model, a reaction of decomposition is carried out with a single grain. 

If we cany out the experiment with a single grain, this evolves from one moment to, which varies from one ejqteriment to the other and which represents the age of birth of the nucleus because we know that a grain is attacked uniformly on the whole surface. As we study a reaction of decomposition, the development of the layer of the solid B is necessarily an inward one. 

In conclusion, we see that many laws are available to account for the function space, which is the rate variation over time in isothermal and isobaric conditions. While it is still difficult to attribute a model to a particular family of reactions, we notice that all the oxidation reactions of a metal (such as [14.R4]) are modeled by single process, which is perfectly logical because it is extremely difficult to carry out experiments in areas that are completely free of metal oxide traces. We also notice that the reactions between solids, such as [14.R5], are also frequently modeled in a single process, since in this case there is fast diffusion on the surface of the grains that are in contact with each other. On the other hand, most decomposition reactions, such as [14.R2], are modeled with two processes although in some cases the maximum rate of curve 14.2c is quite near to the origin. 

Steinfeld et al. [133] demonstrated the technical feasibility of solar decomposition of methane using a reactor with a fluidized bed of catalyst particulates. Experimentation was conducted at the Paul Scherrer Institute (PSI, Switzerland) solar furnace delivering up to 15 kW with a peak concentration ratio of 3500 sun. A quartz reactor (diameter 2 cm) with a fluidized bed of Ni (90%)/Al2O3 catalyst and alumina grains was positioned in the focus of the solar furnace. The direct irradiation of the catalyst provided effective heat transfer to the reaction zone. The temperature was maintained below 577°C to prevent rapid deactivation of the catalyst. The outlet gas composition corresponded to 40% conversion of methane to H2 in a single pass. Concentrated solar radiation was used as a source of high-temperature process heat for the production of hydrogen and filamentous... 

It is important to keep in mind that, in the development of the sensitive layer as a whole, we are dealing with an ensemble of reaction units where reaction may or may not proceed in a parallel fashion among the many units. Under certain conditions the kinetics of development of a typical single grain can be inferred directly from a measurement of the overall rate of formation of silver, but this is not true as a general proposition. Studies of development of the individual grains are of fundamental importance, since the grain is the real unit of development. 

It should be noted that solid explosives may be detonated in any condition from a coarse powder to a single crystal (Ref 6, p 166). Heterogeneous polycrystalline mixtures can be termed "solid only by convention phenomena such as grain erosion in the detonation reaction zone are of dominant importance. They depend in a complex way on the intercrystalline free space and on a free space more strictly defined, the difference between the volume of the crystals and the volume of the ions therein... 

---