Model-free kinetic analysis

Model-free kinetic analysis of nonsteady-state reactions is a recent development that began with the thin zone microreactor configuration [82, 88, 89]. A model-free kinetic method known as the Y-procedure has been used to extract the nonsteady-state rate of chemical transformation from reaction-diffusion data with no assumptions regarding the kinetic model the reader is referred to [90] for more details describing this procedure. 

Model-free kinetic analysis of nonsteady-state reactions was recently introduced, allowing extraction of the nonsteady-state rate from reaction-diffusion data without assuming a particular kinetic model. Details about the so-called Y-procedure are reported by Yablonsky et al. [3]. 

Ramani, R. and Alam, S., Composition optimization of PEEK/PEI blend nsing model-free kinetics analysis, Thermochim. Acta, 511 (1-2), 179-188 (2010) DOl 10.1016/j.tca.2010.08.012. 

In order to assess the activation energy for development of a reasonable model for kinetic analysis of pristine PE and PE-n-MMT thermal degradation processes, a few evaluations by model-free methods have been done as the starting point. As an example, the results of a model-free Friedman analysis for thermal degradation of PE, where the activation energy is a function of partial mass loss change [24], are shown in Figure 5. 

Model-free kinetics software employs numerical integration methods to measure activation energy versus conversion from cure exotherms at three or more heating rates, or from isothermal data at three or more temperatures. In both cases a minimum of four runs is recommended. Predictions like conversion-time plots and calculated DSC curves are made using Eq. (3.31). An advanced version of MFK software allows analysis of data from arbitrary heating programs, such as combined ramp and isothermal. A drawback of the commercial software is that a discrete mathematical relationship is not produced that can be exported and incorporated into cure models. 

Five percent random error was added to the error-free dataset to make the simulation more realistic. Data for kinetic analysis are presented in Table 6.4.3 (Berty 1989), and were given to the participants to develop a kinetic model for design purposes. For a more practical comparison, participants were asked to simulate the performance of a well defined shell and tube reactor of industrial size at well defined process conditions. Participants came from 8 countries and a total of 19 working groups. Some submitted more than one model. The explicit models are listed in loc.cit. and here only those results that can be graphically presented are given. 

The kinetics of the CTMAB thermal decomposition has been studied by the non-parametric kinetics (NPK) method [6-8], The kinetic analysis has been performed separately for process I and process II in the appropriate a regions. The NPK method for the analysis of non-isothermal TG data is based on the usual assumption that the reaction rate can be expressed as a product of two independent functions,/ and h(T), where f(a) accounts for the kinetic model while the temperature-dependent function, h(T), is usually the Arrhenius equation h(T) = k = A exp(-Ea / RT). The reaction rates, da/dt, measured from several experiments at different heating rates, can be expressed as a three-dimensional surface determined by the temperature and the conversion degree. This is a model-free method since it yields the temperature dependence of the reaction rate without having to make any prior assumptions about the kinetic model. 

The vapor-layer model developed in Section IV.A.2 is based on the continuum assumption of the vapor flow. This assumption, however, needs to be modified by considering the kinetic slip at the boundary when the Knudsen number of the vapor is larger than 0.01 (Bird, 1976). With the assumption that the thickness of the vapor layer is much smaller than the radius of the droplet, the reduced continuity and momentum equations for incompressible vapor flows in the symmetrical coordinates ( ,2) are given as Eqs. (43) and (47). When the Knudsen number of the vapor flow is between 0.01 and 0.1, the flow is in the slip regime. In this regime, the flow can still be considered as a continuum at several mean free paths distance from the boundary, but an effective slip velocity needs to be used to describe the molecular interaction between the gas molecules and the boundary. Based on the simple kinetic analysis of vapor molecules near the interface (Harvie and Fletcher, 2001c), the boundary conditions of the vapor flow at the solid surface can be given by... 

Hinrichsen, Muhler, and co workers—micro kinetic analysis parameterized by redox model. Hinrichsen et al.317 investigated the elementary steps by micro kinetic analysis by applying temperature and concentration-programmed experiments over Cu/Zn0/Al203, and modeling the data with the simplified redox mechanism in the spirit of Ovesen, Topsoe, and coworkers.303 This included 3 steps (1) dissociative adsorption of H2 on Cu metallic surface (2) dissociative adsorption of H20 leading to an adsorbed H2 molecule and an O adatom and a reduction step by CO to form gas phase C02 and a free active site (see Scheme 71). 

An important group of methods relies on the inherent order of the data, typically time in kinetics or chromatography. These methods are often based on Evolving Factor Analysis and its derivatives. Another well known family of model-free methods is based on the Alternating Least-Squares algorithm that solely relies on restrictions such as positive spectra and concentrations. 

In many applications, such as chromatography, equilibrium titrations or kinetics, where series of absorption spectra are recorded, the individual rows in Y, C and R correspond to a solution at a particular elution time, added volume or reaction time. Due to the evolutionary character of these experiments, the rows are ordered and this particular property will be exploited by important model-free analysis methods described in Chapter 5, Model-Free Analyses. 

Model-based nonlinear least-squares fitting is not the only method for the analysis of multiwavelength kinetics. Such data sets can be analyzed by so-called model-free or soft-modeling methods. These methods do not rely on a chemical model, but only on simple physical restrictions such as positiveness for concentrations and molar absorptivities. Soft-modeling methods are discussed in detail in Chapter 11 of this book. They can be a powerful alternative to hard-modeling methods described in this chapter. In particular, this is the case where there is no functional relationship that can describe the data quantitatively. These methods can also be invaluable aids in the development of the correct kinetic model that should be used to analyze the data by hard-modeling techniques. 

This equation states that the change in the free energy of the critical germ with the chemical potential per molecule of species / in the original phase (i.e., the mother liquor) equals the negative of the excess number An of molecules of type i in the nucleus over that present in the same volume of original space. The nucleation theorem is independent of the model and of the transition it holds true for classical nucleation theory, density functional theory, or cluster kinetic analysis and for gas-to-liquid or liquid-to-solid conversions. 

The goal of a complete kinetic analysis is to define the rate and free energy change of each step in the reaction. Because the rates of each reaction in an enzymic pathway are comparable, the measurable events are kinetically linked and sometimes difficult to separate. Therefore, solution of an enzyme mechanism must include a fitting of all experiments to the complete model, including all steps in the pathway. Ideally one should measure each reaction in a sequence and then provide one additional measurement as a check for internal consistency. The two important checks on an enzyme reaction sequence are (1) measurement of the overall free energy change for the reaction in solution and (2) comparison of the predicted and measured steady-state kinetic constants. 

Separation of the trapped radicals showed that the vapor phase of smoke from each cigarette type produced a unique set of free radicals (four to ten distinct peaks). Vapor mixtures used to model tobacco smoke consisted of NO, air, isoprene, and methanol. The model systems produced a set of free radicals that consisted of four major and several minor peaks, two of which matched peaks in tobacco smoke chromatograms. Quantities of free radicals trapped from cigarettes tested varied from 54 + 2 nmol to 66 + 9 mnol. The cigar tested produced 185 + 9 mnol of free radicals. In their experiments, oxygen competed with the nitroxide trap for MSS vapor-phase radicals. A kinetic analysis of the O2 competition shows that actual radical concentrations in the smoke were approximately 100-fold higher than measured. 

Kinetic analysis according to the model-free approach by Kissinger-Akahira-Sunose [25, 26] was performed with the computer program Excel. For kinetic analysis according to the advanced Vyazovkin method [27], the STAR software... 

To illustrate more clearly the nature of free radical polymerization, it is instructive to examine the values of the individual rate constants for the propagation and termination steps. A number of these rate constants have been deduced, generally using nonstationary-state measurements such as rotating sector techniques and emulsion polymerization [26]. Recently, the lUPAC Working Party on Modeling of kinetics and processes of polymerization has recommended the analysis of molecular weight distributions of polymers produced in pulsed-laser-initiated polymerization (PLP) to determine values of... 

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