First-order model double

Figure 5. Comparison of single first-order and double first-order models to 0co mixing-cell data.

Table V. Double First- Order Model Parameters and Fit Variance ...

The model fit variances are given in Table IV and calculated rate parameters for the two reactions in Table V. In nearly all cases an improvement in model fit was observed. This is typified by the comparison between the fit gg a single first-order and double first-order (DFO) model to the 0 Co data, as shown in Figure 5. Although the DFO model shows considerable improvement over single-site models, residual plots indicate a small systematic deviation at higher concentrations. This is discussed further in the following section. 

With the possible exception of selenium, a two-site, double first-order (DFO) model shows an improvement over single site-models for describing sorption of the radionuclides studied. The dependence of sorption on alteration history in the majority of cases indicates that experiments with systems representative of well-weathered fracture systems are necessary to obtain data applicable to actual disposal vault conditions. 

The approach taken in the development of an analytical model for the combustion of double-base propellants has been based on the decomposition behavior of the two principal propellant ingredients, nitrocellulose and nitroglycerin. The results of several studies reviewed by Huggett (HI2) and Adams (Al) show that nitrocellulose undergoes exothermic decomposition between 90° and 175°C. In this temperature range, the rate of decomposition follows the simple first-order expression... 

The initial rate of the model reaction follows a first-order dependence for the activated catalyst, the Michael donor, and the Michael acceptor. The rate determining step is not the C-C bond formation or protonolysis but the decomplexation of the bidentate product. This was evidenced by the relationship between the initial conversion and the reaction time. Extrapolation to fg = 0 h provides a positive intercept. In other words, upon addition of the reagents, the C-C bond formation occurs almost instantaneously. The amount of product at fo correlates within the experimental error to the double precatalyst loading since the dimeric precatalyst forms two active monomeric catalyst species. 

On the other hand, isomerization of sil-trans P-carotene was found to be comparatively faster in a model containing methyl fatty acid and chlorophyll heated at 60°C (Table 4.2.6), resulting in 13-cw-P-carotene as the predominant isomer. The first-order degradation rate of P-carotene significantly decreased with the increased number of double bonds in the methyl fatty acid, probably due to competition for molecular oxygen between P-carotene and the fatty acid. Since the systems were maintained in the dark, although in the presence of air, the addition of chlorophyll should not catalyze the isomerization reaction. 

The equations used in these models are primarily those described above. Mainly, the diffusion equation with reaction is used (e.g., eq 56). For the flooded-agglomerate models, diffusion across the electrolyte film is included, along with the use of equilibrium for the dissolved gas concentration in the electrolyte. These models were able to match the experimental findings such as the doubling of the Tafel slope due to mass-transport limitations. The equations are amenable to analytic solution mainly because of the assumption of first-order reaction with Tafel kinetics, which means that eq 13 and not eq 15 must be used for the kinetic expression. The different equations and limiting cases are described in the literature models as well as elsewhere. 

Newson (1975) was among the first to develop a pore plugging model of demetallation to predict catalyst life. By using the pore structure model of Wheeler (1951), the pellet was assumed to have N pores of identical length but with a specified distribution of pore radii. Metal deposition was assumed to be a first-order reaction over an outer fraction of the pore length and to have a uniform thickness. This model showed that the broadness of the size distribution had little effect on the catalyst life for the same average radii, but that increasing the radii from 45 to 65 A more than doubled the catalyst life. The restricted form of the diffusivity (see Section IV,B,5) was not employed in this model. 

Brown (1999b) reported formaldehyde and VOC emissions from new, unfinished particleboard and MDF (both using urea formaldehyde resins) in Ausbalia. Formaldehyde emissions over the first three weeks exhibited first-order decay behavior that predicted little to no formaldehyde emission after 6 months. However, further emission measurements at 8 months showed the products sbll emitted formaldehyde at approximately one-half the new product rate (also further unpublished measurement at 2 years showed the same emission rate as at 8 months). It was concluded that the wood-based panels emitted formaldehyde by a double-exponen-ttal model, the early- to late-term emissions including the free formaldehyde in the products but the long-term emissions consisbng of only the formaldehyde... 

Monte Carlo techniques were first applied to colloidal dispersions by van Megen and Snook (1975). Included in their analysis was Brownian motion as well as van der Waals and double-layer forces, although hydrodynamic interactions were not incorporated in this first study. Order-disorder transitions, arising from the existence of these forces, were calculated. Approximate methods, such as first-order perturbation theory for the disordered state and the so-called cell model for the ordered state, were used to calculate the latter transition, exhibiting relatively good agreement with the exact Monte Carlo computations. Other quantities of interest, such as the radial distribution function and the excess pressure, were also calculated. This type of approach appears attractive for future studies of suspension properties. 

When the oxidizing species, an electron acceptor, and the electron donor are both embedded within a biological macromolecule (e.g., in a protein or DNA molecules), the reaction kinetics are entirely different from those in solution in which both species can diffuse freely and encounter one another in order to undergo chemical reaction. An example of such intramolecular processes is the one-electron oxidation of guanine (G) by a 2AP neutral radical, both site-specifi-cally positioned within a DNA duplex [28]. Here, both reaction partners are fixed within a DNA helix and the bimolecular reaction model is not suitable for describing the reaction kinetics (4.16). Instead, the kinetics of oxidation of G by 2AP(-H) radicals in double-stranded DNA follow first-order kinetics with the magnitudes... 

Fig. /. The four-state model used for the description of triplet energy transfer in the RC according to Angerhofer (1997). For detailed explanation, see text. The filled arrows denote the rates that have been observed and described in the literature. The broken arrows depict rates that are either unknown (from and to BS) or speculative (k3 -i for bypass reaction, and k4 -2 for tunneling). The rates defined by arrows between different molecules (P, B, and Car) are in reality second order rates, i.e. they depend on the ground state concentrations of the molecule the excited state of which they point to. In the case of low excitation densities, i.e., when double excitation of the RCs can be neglected these rates can be assumed to be first order as for example done by Frank et al. (1996b).

Examples of double porosity models applied to stable isotope transport in regional and contact metamorphism are given by Bowman et al. (1994) (see discussion of Alta contact aureole below), though this is not explicitly stated. Curves calculated for onedimensional transport using a first order rate law were fitted to observed profiles with a... 

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