Five-step model

Since Eqs. 11 and 12 are not of the same type, the reaction evidently is nonelemen-tary. Consequently, let us try various mechanisms and see which gives a rate expression similar in form to the experimentally found expression. We start with simple two-step models, and if these are unsuccessful we will try more complicated three-, four-, or five-step models. 

Figure 7 Five-step model for mass transfer through crystal membranes. Srep / adsorption from the gas phase to the external surface. Step 2 transport from the external surface into the pores. Step 3 intracrystalline diffusion. Step 4 transport out of the pores to the external surface. Step 5 desorption from the external surface into the gas phase. (From Ref. 35.)...

Barrer proposed a qualitative model of single-gas transport through microporous materials [62]. A five-step model can qualitatively describe the transport through a microporous membrane at moderate temperatures (see Figure 10.14) ... 

Purpose Generate data sets using mixed deterministic/stochastic models with N = 1. .. 1000. These data sets can be used to test programs or to do Monte Carlo studies. Five different models are predefined sine wave, saw tooth, base line, GC-peaks, and step functions. Data file SIMl.dat was... 

The methodology described below outlines five steps I through V to establish the model balances. The first task is to define the system by choosing the balance or control region. This is done using the following procedure ... 

Oscillations are familiar phenomena in mechanical systems and in electric circuits. Noyes and Field discussed the possibilities for concentration oscillations in closed systems and illustrated the principles by means of Oregonator model consists of the following five steps ... 

This model was first developed by Yagi and Kunii (1955, 1961), who visualized five steps occurring in succession during reaction (see Fig. 25.4). 

The above five steps are repeated until the results for the heterogeneous model are very closely agreeing with the industrial data. 

A FIVE-STEP PLANNING MODEL. . YOUR PLAN WILL BE DIFFERENT. ... 

The pharmacophore generation module in Phase generates pharmacophore models using a four to five step procedure described below. 

The intercalation process has been the subject of extensive thermodynamic studies [3,4], providing free energy, entropy and enthalpy differences between the intercalated and free states of various drug molecules. On the other hand, dynamic studies are far less common. Some different aspects of the intercalating molecules have been studied using ultrafast methods [5]. Kinetic studies of drug intercalation are few in number, and a consensus on the mechanism has not been reached [6,7]. Thus, Chaires et al. [6] have proposed a three step model for daunomycin intercalation from the stopped flow association, while Rizzo et al. [7] have proposed a five step kinetic model. 

The computational procedures for the numerical calculations of the TBI model for specific systems were described in several previous publications (Tan and Chen, 2005, 2008a). Here, we summarize the general computational procedure using a 12-nt DNA duplex as an example. We assume temperature T = 25 °C, dielectric constant e = 78 for solvent and 20 for the nucleic acid interior, and the radii of the (hydrated) ions 4.5 A for Mg2"1" and 3.5 A for Na+. The numerical calculations of the TBI model involve the following five steps ... 

It has been also reported a study on the threading process of a a - cyclodextrin (a-CD) and polyethylene glycol (PEG), as a function of temperature and solvent composition. This reaction produces a polyrotaxane that eventually precipitates and forms a thick gel. Ceccato et al. [46] have proposed a molecular model for the interpretation of the temperature and solvent composition effect on the threading process. According of this model, the reaction can be depicted as a five - step phenomenon that mainly depend on the threading and sliding of a-CD and PEG. The transition... 

Based on this postulate and the pronounced effect of agitation on particle incorporation Buelens et al7X77 proposed a five-step mechanism for composite deposition. In the first step particles in the bulk of the electrolyte obtain an ionic cloud by adsorbing ions from the electrolyte. In the second and third step the particles are transported by bath agitation to the hydrodynamic boundary layer and by diffusion through the diffusion layer to the cathode surface. Finally, the particles adsorb on the cathode surface still surrounded by their ionic cloud and are incorporated by the reduction of some of the adsorbed ions. A model for the calculation of the weight percent of incorporated particles was developed consistent with this mechanism. The basic hypothesis of the model is that a certain amount, x, out ofX ions adsorbed on a particle must be reduced at the... 

A general model for transport through porous crystal membranes was described by Barter [35]. The model involves five steps (Fig. 7) ... 

Jiang et al. [225] fitted a five-step global mechanism to a detailed methane oxidation mechanism. They identified the dominant reactions in the detailed mechanism and determined the rate expressions for the steps of the global mechanisms on the basis of the rate of the corresponding reaction rates of the detailed model. The reduced model was also tested in reactive shock calculations. 

Fig. 7.19. Use of five-step parrot model, in conjunction with engine model, in post-processing of end gas reactions to show the influence of spark advance on autoignition. Values of pressure, temperature, mass fraction burned, and chain carrier mole fraction, C, computed from engine cycle model without end gas chemistry (broken curves) and with end gas chemistry (full curves). Spark advance before top centre with 90 octane number fuel (a) 10°, non-autoigniting cycle, (b) 20°, autoignition indicated by asterisk.

The process of forming the salt sodium chloride can be broken down into five steps as shown in Figure 9 on the following page. Keep in mind that these steps do not really take place in this order. However, these steps, do model what must happen for an ionic bond to form between sodium cations and chloride anions. 

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