Apparent parameters

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

The immobilization procedure may alter the behavior of the enzyme (compared to its behavior in homogeneous solution). For example, the apparent parameters of an enzyme-catalyzed reaction (optimum temperature or pH, maximum velocity, etc.) may all be changed when an enzyme is immobilized. Improved stability may also accrue from the minimization of enzyme unfolding associated with the immobilization step. Overall, careful engineering of the enzyme microenvironment (on the surface) can be used to greatly enhance the sensor performance. More information on enzyme immobilization schemes can be found in several reviews (7,8). 

The simplest kinetic model applied to describe lipase catalyzed reactions is based on the classic Michaelis-Menten mechanism [10] (Table 3). To test this model Belafi-Bakd et al. [58] studied kinetics of lipase-catalyzed hydrolysis of tri-, di-, and mono-olein separately. All these reactions were found to obey the Michaelis-Menten model. The apparent parameters (K and V ) were determined for global hydrolysis. 

In our previous work [63], we studied the hydrolysis kinetics of lipase from Mucor javanicus in a modified Lewis cell (Fig. 4). Initial hydrolysis reaction rates (uri) were measured in the presence of lipase in the aqueous phase (borate buffer). Initial substrate (trilinolein) concentration (TLj) in the organic phase (octane) was between 0.05 and 8 mM. The presence of the interface with octane enhances hydrolysis [37]. Lineweaver-Burk plots of the kinetics curve (1/Uj.] = f( /TL)) gave straight lines, demonstrating that the hydrolysis reaction shows the expected kinetic behavior (Michaelis-Menten). Excess substrate results in reaction inhibition. Apparent parameters of the Michaelis equation were determined from the curve l/urj = f /TL) and substrate inhibition was determined from the curve 1/Uj.] =f(TL) ... 

Catalytic activity of solid acids in hydrocarbon conversions is often correlated with their acidity. Problems arise from the difficulty to bridge the gap between the equilibrium thermodynamic concept of acidity and the composite kinetic concept of catalytic activity [1], The correlation is meaningful if connected parameters are related to each other, namely, intrinsic activities are correlated with intrinsic acidities or relationship is established between corresponding apparent parameters. 

The flow rate curve L is unaffected by reversibility it still shows a linear dependence on the extent of reaction 1 — ass with a gradient determined by the inverse of the residence time. The reaction rate curve R now depends upon two parameters, /S0 and Ke (the third apparent parameter aeq is uniquely determined by these). We will examine the effects of these separately below, but may note some general features here. 

This result means that if the mass transfer kinetics follows the liquid film linear driving force model, the breakthrough curve can be fitted to the Thomas model [23], provided that the apparent parameter given by Eq. 14.85 be used. Again, the apparent rate parameter is concentration dependent. 

When the (one-substrate) Michaelis-Menten equation is applied at saturation of B the following apparent parameters are obtained for the sequential mechanism ... 

A convenient way of expressing rate equations for reactions subjected to inhibition is in terms of apparent parameters ... 

If kinetic rate data from an immobilized enzyme are collected directly, as presented in section 3.2.2, only effective (apparent) parameters are obtained that do not reflect the actual behavior of the enzyme. This information, though useful, is valid only at the precise conditions at which the experiment was performed. Eor design... 

The apparent parameters and are available by a typical Michae-lis-Menten evaluation. Once determined, it is in addition possible to determine the values for and V+ since the apparent parameters are themselves also of the Miehaelis-Menten form depending on [XO]. For a detailed description of how to perform such analyses, see the respective publication. ... 

Resonance energy transfer (RET) can also result in deci which have varions powers of time in the exponent Depending on whether RCT occurs in one, two, or three dimensions, r can appear with powers of I, or I, respectively, Hence we see that intensity deroys can late a number of forms depending on the underlying moleeular phenomenon. In our opinion, it is essential to analyze each deciqr with the model which correctly describes the samples. Use of an incorrect modd, such as use of the multiexponential modd to describe transient effects, results in apparent parameter values (Oh and xi) which cannot be... 

The effect of diffusion on the shape of the frequency response can be judged by the Xa values. The data were fit to the model which allows D-A diffusion and to the same model with the diffusion coefficient set equal to zero (Thble 14.3). When D = 0, the values of x< increase at higher temperatures, indicating that the donor decay has become more like asingle exponential. In fact, the tendency toward a single exponential can be seen from the recovered values of the half-width. These apparent hw values become smaller at higher temperature. As described in Section I4.5.D, the trend in apparent parameter values can yield useful information about the behaidor of complex systems. 

It is worth pointing out that Eqns (4.13)—(4.20) are for the ORR on a smooth planar electrode or catalyst surface rather than in a porous matrix catalyst layer. It is expected that the situation in the catalyst layer may be more complicated than on the planar surface. However, it is believed that with modification using the apparent parameters as well as the real electrochemical active surface, the equations are still valid for quantitative treatment of experimental data. 

Determination of the inhibition kinetic parameter follows the same approach as simple Michaelis-Menten kinetics, discussed earlier, using the linearization approach. Thus, it is better to express Equations 4.33, 4.35, and 4.37 in terms of apparent parameters, as shown in Equation 4.38. This is compatible with a simple Michaelis-Menten relationship. 

Electrode Kinetic and Mass Transfer for Fuel Cell Reactions For the reaction occurring inside a porous three-dimensional catalyst layer, a thin-film flooded agglomerate model has been developed [149, 150] to describe the potential-current behavior as a function of reaction kinetics and reactant diffusion. For simplicity, if the kinetic parameters, such as flie exchange current density and diffusion limiting current density, can be defined as apparent parameters, the corresponding Butler-Volmer and mass diffusion relationships can be obtained [134]. For an H2/air (O2) fuel cell, considering bofli the electrode kinetic and the mass transfer, the i-rj relationships of the fuel cell electrode reactions within flie catalyst layer can be expressed as Equations 1.130 and 1.131, respectively, based on Equation 1.122. The i-rj relationship of the catalyzed cathode reaction wifliin the catalyst layer is... 

Equation 1.11 applied for correlation of the experimental data [P P]eq - temperature (for both bulk and solvent process) allowed, eventually, an estimation to be made of the absolute thermodynamic parameters of polymerization AHp = -0.64 k) mol and ASp = -5.8Jmol K (cf. the apparent parameters in Table 1.1) (44). 

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