Reactant depletion

Thus the progress curve for product formation is the mirror image of reactant depletion. 

Running an exothermal reaction under adiabatic conditions leads to a temperature increase, and therefore to acceleration of the reaction, but at the same time, the reactant depletion leads to a decreasing reaction rate. Hence, these two effects act in an opposite way the temperature increase leads to an exponential increase of the rate constant and therefore of the reaction rate. The reactant depletion slows... 

Since the accumulation is determined by a balance between feed rate and reaction rate (reactant depletion), it can be influenced by using different feed rates or different temperatures. This offers the possibility of optimizating the process conditions (discussed in Section 7.9). 

Then we consider a reaction presenting a given accumulation corresponding to a known adiabatic temperature rise. In the case of cooling failure, the reaction proceeds under adiabatic conditions it is accelerated by the temperature increase, but at the same time, the reactant depletion decreases the reaction rate. Thus, the reaction rate passes a maximum, as described in Figure 10.7 (see also section 10.6.2.1). For the design of the relief system, the maximum heat release rate at... 

Starting from process temperature (Tp), the reaction is accelerated by the temperature increase to MTT following Arrhenius Law. But, at the same time reactants are converted, which results in a depletion of the reactant concentration and consequently in reduction of the reaction rate. Thus, two antagonistic factors play at the same time acceleration with temperature and slowing down by the reactant depletion. Both effects may be summarized in an acceleration factor (facc) that multiplies the heat release rate. Thus ... 

In this equation, the conversion term for a first-order reaction (1-X) is expressed as a function of the characteristic temperature levels of the scenario. First-order is a conservative approximation, since for higher reaction orders the reactant depletion is even higher. Zero-order would even be more conservative, but is generally unrealistic. 

At the pressures at which this system is run, deposition is diffusion controlled. Therefore, the flow patterns set up and boundary layer thicknesses are important to the goal of uniform deposition on all wafers. As noted in Chapter 3, the narrowing flow passage in the flow direction compensates for reactant depletion. 

From equation (44) we see that the reactant concentration decreases monotonically with time from its initial value C (0), while that of the product increases monotonically. The concentration of the chain carrier exhibits a more complicated behavior, according to equation (45). If — 0 initially, then there is a linear increase of with time at early times by initiation. If /Cj > (a — l)kpCj (0) (which applies, for example, to straight-chain reactions), then dc /dt decreases continually with time, and after a sufficient amount of reactant depletion and carrier buildup, begins to decrease and eventually decays exponentially through termination with a time constant /c that is, Cq However, there are other ranges of parameters in... 

If losses are negligible, then addition of cy times equation (54) to equation (53) reveals that eyO -h (p remains constant, that is, (p = — ey(6 — 6q), which may be used in / in equation (54) to obtain a single differential equation for 0(t) under these conditions. Since yc 1, often reactant depletion is negligible except in late stages of the process, and / = 1 may be employed in equation (54). Since 6 1, in a first approximation, equation... 

FIGURE B.4. Schematic illustration of nondimensional temperature-time histories for thermal explosions for the simplified Frank-Kamenetskii model (main graph) and for a more complete model that includes reactant depletion (inset). 

The infinite 0 at a finite r is contradictory to equation (54) and is a consequence of the approximations that lead to equation (56). Even if reactant depletion is neglected, retention of the factor (1 -h 0)" in the exponential in the rate term of equation (56) would cause the generation rate to level off at a value for very large values of 0, as illustrated schematically... 

In the absence of reactant depletion gradients, that is film growth under charge transfer control, and absent significant electrocrystallization anisotropy, a uniform... 

Rather than because of promotion by a product or intermediate, the rate may accelerate because a reactant that acts as inhibitor is consumed. For example, a small amount of inhibitor present initially may depress the rate of a chain reaction until used up (see Section 10.8). More interesting are reactions inhibited by one of the principal reactants (called substrate-inhibited in biochemistry parlance). An example is hydroformylation, in which CO is a reactant with negative reaction order (see Example 6.2 in Section 6.3). There is a subtle but important difference between product-promoted and reactant-inhibited reactions The rate of a product-promoted reaction builds up to a maximum and then declines as reactant depletion overpowers product promotion. In contrast, the rate of a reactant-inhibited reaction keeps escalating, possibly catastrophically, until the respective reactant is almost completely exhausted. Typically, some other mechanism then takes over. [The negative apparent reaction order of the respective reactant arises from an additive denominator term in a one-plus rate equation, but the other terms may be small or insignificant by comparison.] Possible mass-transfer implications of such behavior will be examined in Section 13.3. 

---