Solid-state reactions rate constants

Thus, expression (59) enables us to describe the solid-state reaction rate constant dependence on the parameters of the potential barrier and medium properties in a wide temperature range, from liquid helium temperatures when the reaction runs by a tunneling mechanism to high temperatures (naturally, not exceeding the melting point) when the transition is of the activation type. 

Figure 16. Illustration of change of solid-state reaction rate constant in phase transition. Soft-mode splitting out occurs at point equalling 0,7i/4a, njla, 3 t/4o and n/a for curves 1-5, respectively. K( T) jump at Kq = 0 determined by difference in amplitude in two phases.

The boundary kinetics (stages 2-4) may result in changing the constant of solid-state reaction rate and deviation from the parabolic law of phase growth controlled by stages 1 and 5 [8]. 

The Pb02/PbOx border slowly penetrates into the metal, but only at a very slow rate as a solid-state reaction. Cracks are formed when the oxide layer exceeds a given thickness, on account of the growth in volume when lead becomes converted into lead dioxide (Table 7). Underneath the cracks the corrosion process starts again and again. As a whole, the corrosion proceeds at a fairly constant rate. It never comes to a standstill, and a continually flowing anodic current, the corrosion current is required to re-establish the corrosion layer. 

In the solid state reaction depicted, A begins to decompose to B at Ti and the reaction temperature for decomposition is T2, with a weight loss of Wi Likewise, the reaction of B to form C begins at T3 and the reaction temperature (where the rate of reaction is maximum) is T4. Note that the weight loss becomes constant as each reaction product is formed and the individual reactions are completed. If we program the temperature at 6 °C/min., we would obtain the results in 7.3.4. This is called d3mamic thermogravimetry. 

These rate equations C2in be used for quite complicated reactions, but a specific method or approach is needed. Many authors have tried to devise methods for obtaining rate constants and orders of reaction for given solid state reactions. None have been wholly successful, except for Freeman and Carroll (1948). 

Gomes, W. (1961). "Definition of Rate Constant and Activation Energy in Solid State Reactions," Nature (London) 192, 965. An article discussing the difficulties associated with interpreting activation energies for reactions in solids. 

An XRPD system equipped with a heatable sample holder has been described, which permitted highly defined heating up to 250°C [55]. The system was used to study the phase transformation of phenan-threne, and the dehydration of caffeine hydrate. An analysis scheme was developed for the data that permitted one to extract activation parameters for these solid-state reactions from a single non-isothermal study run at a constant heating rate. 

The authors [1] studied kinetics of poly (amic acid) (PAA) solid-state imidization both in the presence of nanofiller (layered silicate Na+-montmorillonite) and without it. It was found, that temperature imidization 1] raising in range 423-523 K and nanofiller contents Wc increase in range 0-7 phr result to essential imidization kinetics changes expressed by two aspects by essential increase of reaction rate (reaction rate constant of first order k increases about on two order) and by raising of conversion (imidization) limiting degree Q im from about 0,25 for imidization reaction without filler at 7 i=423 K up to 1,0 at Na -montmorillonite content 7... 

In Eqs. (3.58) and (3.59), the kt are the reaction rate constants. We will see in Chapter 4 that many solid-state ceramic processes involve simultaneous mass transport (diffusion), thermal transport, and reaction. 

By extrapolating Dto 1000 °C, we can calculate the parabolic rate constant kp (see Eqn. (6.30)) and compare it with the experimental value derived from Figure 16-10 b. From this comparison, it seems as if Fe2+ is the rate determining cation for the formation of fayalite by solid state reaction. Since we conclude from Section 15.2.2 that n natural olivines, it is most unlikely (in view of the... 

Although more complex models have been proposed to describe the process [57, 85, 86], involving the Ps bubble state and its shrinking upon reaction, the equations based on a reversible reaction with a forward and reverse reaction rate constants as in scheme (X) enables the fitting of the data perfectly, as shown by the solid line in Figure 4.9. The kinetic equations corresponding to such a scheme are tedious to derive, particularly as concerns the intensities (still more when a magnetic field is applied). However, they do not present insuperable mathematical difficulties and should be used instead of the approximate expressions that have appeared casually (e.g., "steady state" treatment of the reversible reaction). From scheme (X), it is not expected that the variation of X3 with C be linear, but the departure from linearity may be rather small, so that the shape of the X3 vs C plots may not be taken as a criterion to ascribe the nature of the reaction. 

Such an "anomalous" variation of R(B) with B [90] is shown in Figure 7 the solid line is the fit to the data on the basis of the above-mentioned statements. Qualitatively, the rapid variation of R(B) with B is easily understood as B increases, the (m=0) bound-state decay rate constant, A.C(B), also increases, in accordance with eq.(ll). This increase is very rapid, because of the high sensitivity of A.C(B) to B, due to the low hyperfine splitting of the bound-state [89-91], which corresponds to having an efficient leak towards the right of reaction (X). Thus, the overall reaction rate constant is greatly increased, resulting in the rapid decrease of R(B) with B [90],... 

The current status of the models of fluctuational and deformational preparation of the chemical reaction barrier is discussed in the Section 3. Section 4 is dedicated to the quantitative description of H-atom transfer reactions. Section 5 describes heavy-particle transfer models for solids, conceptually linked with developing notions about the mechanism of low-temperature solid-state chemical reactions. Section 6 is dedicated to the macrokinetic peculiarities of solid-state reactions in the region of the rate constant low-temperature plateau, in particular to the emergence of non-thermal critical effects determined by the development of energetic chains. 

The kinetics of even the elementary solid-state reactions is normally nonexponential this indicates the existence of a set of configurations characterized by different values of rate constants. The existence of this set of configurations distinguishes the glasslike state from the crystalline one. 

The kinetics associated with the thermally induced phase transformations of phenanthrene and caffeine monohydrate were studied using hot-state quantitative XRPD.29 Using a single non-isothermal experiment conducted at a constant heating rate, it was possible to obtain the activation parameters for the solid-state reactions. In another study, quantitative XRPD was used to study the tetrahydrate to monohydrate transition of the sodium salt of 5-(4-oxo-phenoxy-4H-quinolizine-3-carboxamide)-tetra-zolate.30... 

Simulated data are shown in Figure 1 with solid lines and the parameter values that best fit experimental data in Table 1. The specific reaction rate constant x(l) has the same value for all cases and this is consistent with the fact that each deactivation run was done starting with fi esh catalyst. On the other hand, parameter x(2) reflects some type of equilibrium state reached for free active catalytic sites. It takes very small values for a poison as pyridine, intermediate values for an inhibitor like CS2, and values close to one for pure n-octane and for n-octane mixed with the smallest amount of benzene. In larger amounts, benzene seems to act as coke inhibitor, which is consistent with the fact that it does not change activity in a significant manner but it does change the distribution of reaction products. 

---