Intrinsic parameters

In the previous sections the theoretical relations describing the strength of a polymer fibre as a function of the intrinsic parameters, such as the chain modulus, the modulus for shear between adjacent chains, the orientation distribution and the chain length distribution, have been discussed. In this section the dependence of the strength on the time and the temperature will be investigated. 

The passage from one control to the other is pictured in Figure 2.5 for the cathodic peak potential and the peak width as a function of the scan rate and of the intrinsic parameters of the system. We note that increasing the scan rate tends to move the kinetic control from the follow-up reaction to the electron transfer step. It thus appears that the overall reaction may well be under the kinetic control of electron transfer, even if this is intrinsically fast, provided that the follow-up reaction is irreversible and fast. The reason is that the follow-up reaction prevents the reverse electron transfer from operating, thus making the forward electron transfer the rate-determining step. 

The procedure to be followed, then, is to estimate the parameters K within each reaction-rate model by some appropriate technique (K8). The intrinsic parameter A can then be estimated by linear least squares. Owing to experimental error in the data, this estimate of A will typically be neither plus nor minus one-half. Hence the remaining portion of the analysis is to estimate the... 

An intrinsic parameter is one that is inherently present in or arises naturally from a reaction-rate model. These parameters, which are of a simpler functional form than the entire rate model, facilitate the experimenter s ability to test the adequacy of a proposed model. Using these intrinsic parameters, this section presents a method of preparing linear plots for high conversion data, which is entirely analogous to the method of the initial-rate plots discussed in Section II. Hence, these plots provide a visual indication of the ability of a model to fit the high conversion data and thus allow a more... 

When any hyperbolic model is written in terms of fractional conversions instead of partial pressures, two groupings of terms inherently arise within the denominator These two groupings will be called the intrinsic parameters Cx and C2. For example, when data are taken for the olefinic dehydration of a pure alcohol feed to a reactor, Eq. (80) becomes... 

Consider again the 500°F data for the alcohol dehydration just discussed. Equations (84)—(88) arose from Eq. (80). A similar set of equations can be generated from Eq. (81) (K5). Let us examine the two models through an analysis of their intrinsic parameters. 

The development of an adequate mathematical model representing a physical or chemical system is the object of a considerable effort in research and development activities. A technique has been formalized by Box and Hunter (B14) whereby the functional form of reaction-rate models may be exploited to lead the experimenter to an adequate representation of a given set of kinetic data. The procedure utilizes an analysis of the residuals of a diagnostic parameter to lead to an adequate model with a minimum number of parameters. The procedure is used in the building of a model representing the data rather than the postulation of a large number of possible models and the subsequent selection of one of these, as has been considered earlier. That is, the residual analysis of intrinsic parameters, such as Cx and C2, will not only indicate the inadequacy of a proposed model (if it exists) but also will indicate how the model might be modified to yield a more satisfactory theoretical model. 

Ci An observed value of an intrinsic parameter, which collects all denominator terms J... 

The intrinsic parameter, characterizing the type of interactions, is the Frumkin interaction parameter a, which is positive for attractive forces and negative for repulsive forces. In addition, 9 = is the fraction of the electrode covered with deposited material, and f ax is the maximal surface coverage. Combining (2.93) and (2.94) with (2.102), the following integral equation is obtained as a general solution ... 

Finally, as previously emphasized, solid/gas biocatalysis, because of its peculiarities, leads to a more accurate approach to the study of the effect of the microenvironment on enzymatic activity and stability. This allows access to intrinsic parameters of enzymes, thus providing a better molecular understanding of enzyme catalysis in general. 

Each atomic nucleus - as well as each particle - is characterised by a number of intrinsic parameters, including the spin I. This vector quantity, which has a preferential direction, is introduced in quantum mechanics and has no classical equivalent. It explains, among other things, the behaviour of atoms in media where there is a preferential direction. The spin of the nucleus can be related to the kinetic moment L using classical mechanics and it has the same dimensions (J - s). Thus an atom, placed in a magnetic field, will sense the orientation of the magnetic field. The spin is defined by the spin quantum number, /, which is dependent on the individual nucleus considered, and is always a positive multiple of 1/2, including zero. 

Since the appearance of the 6-th WR Catalog (van der Hucht et ai. 1981) the galactic distribution of WR stars has been studied by many authors (Hidayat et al. 1981. 1984 Meylan and Maeder. 1983 Conti et al. 1983). Recently the membership of 42 WR stars in open clusters and associations has been reassessed (Lundstrom and Stenholm, 1984) and improved photometry (Massey. 1984) and new classifications have become available for a considerable fraction of the 157 known galactic WR stars. This allows a redetermination of the intrinsic parameters (b-v)Q and My of WR stars and their photometric distances. 

It has to be emphasized that x2 is an intrinsic parameter of the network. Its value should be the same in the unswollen state and in the presence of any swelling solvent. 

The term PdVa disappears, because the ideal interface has no volume. We integrate the expression keeping the intrinsic parameters T,/Zj, and 7 constant.2 This integration is allowed because it represents, in principle, a feasible process, e.g., through simply increasing the surface area of the system. This can be realized by, for instance, tilting a sealed test tube which is partially filled with a liquid. Result ... 

The second term indicates the work required to bring dQ from one plate to the other at a potential U. Assuming we have a homogeneous system, an integration at constant intrinsic parameters 7 and U results in... 

Pros The choice of targets or objective functions is rather wide, depending on the reaction and application envisioned. Possibly, one easily accessible objective function such as CO conversion can be replaced by another more intrinsic parameter like the OSC for the Selox reaction, subject to a preliminary mechanistic investigation that clearly demonstrates the equivalence of the two parameters for evaluating performance. For the WGS reaction, selectivity is not a problem, except for methane and methanol side formation. For the Selox reaction, selectivity towards CO oxidation rather than towards H2 oxidation becomes a priority objective function. 

To further characterize the mobility of the IRE loop, time-resolved isotropic fluorescence emission decay components of the IRE RNAs were determined as a function of temperature. Some details of the measurements and data assessment will be necessary here to appreciate both the utility of the information and caveats about its literal interpretation. Considering first the TCSPC instrument itself, some uncertainty in the measurements arise from its intrinsic parameters. With 300 nm incident light, the IRF of the photomultiplier tube ranged from 190 to 276 ps full-width at half-height (FWHH). The width of the IRF and the time resolution (32.5 ps/channel) limit the short components that can be reliably extracted from the fit, and certainly those <200 ps will have large errors on their amplitudes and lifetimes. Fluorescence emission decay components as short as 9—20 ps (Larsen et al., 2001) and 30—70 ps (Guest el al., 1991) (and much shorter by Wan et al., 2000) have been measured for 2AP in a stacked conformation, but in our instrument, a fit to such a short lifetime would be inaccurate. 

Quantitative Predictions. In this section we use the riser data to determine intrinsic activity and coking parameters (kj, Aj) in the model, and then predict MAT and FFB conversion and coke yields. Typically, we will have either the MAT or FFB activity and coke information and the task is to predict the riser performance. As the models use intrinsic parameters, it is immaterial which test information is available. The intrinsic parameters can be easily extracted by fitting the data to the appropriate reactor model. We will use the riser data as it gives the intrinsic information directly. The fitted rate parameters are summarized in Table III. The other model parameters, such as the activation energies, heats of reaction, the coke deactivation exponent, n, (also given in Table III), were estimated independently. The details of parameter estimates are described in the Appendix. 

The conversions are predicted quite accurately over a wide range of coke levels (from 0.7 to 2.7 wt %). There are some minor discrepancies in the coke predictions. However, these predictions are within the experimental accuracies of the tests. The FFB conversions are reproducible within 2 numbers, with 20% accuracy for coke yields. Similarly, the MAT data are reproducible within 3 numbers with 30% accuracy for coke yields. These comparisons suggest that the models could be used to fit the catalyst intrinsic parameters (kj, A,) from the transient tests and then predict the steady state riser performance. Indeed, we have done this exercise and we predict a reverse ranking for catalysts A and C in going from transient tests to the riser performance, as observed in the riser experimental data. 

An important conclusion from these simulations is that neither the FFB nor the MAT test simulates riser behavior, since neither of these tests reflects the intrinsic catalyst activity and decay. These intrinsic parameters are masked by backmixing in the FFB test and by a high temperature drop in the adiabatic MAT unit. In addition, the time averaged values of the long contact time FFB and MAT tests overemphasize the low catalyst activity at long contact times, while the short contact time riser is only exposed to initial activity and catalyst decay. 

Non-metallic rare-earth compounds studied under high pressure. In almost all cases the energy level shifts as a function of pressure have been determined. The second column gives details concerning the measurements and evaluations made. In particular the following abbreviations are used L Luminescence-, A Absorption-, E Excitation-, S Site-selective spectroscopy, O Other methods, EPC Electron-Phonon Coupling, Int Intensities, LT Lifetime, CFP Crystal-Field Parameters, FIP Free-Ion Parameters, IP Intrinsic Parameters, ET Energy Transfer... 

The intrinsic parameters Bk depend only on the distance Rj and on the kind of ligand j located at (Rj, j,geometrical factors can be calculated once the structural changes under pressure have been determined for example by X-ray diffraction experiments. For the distance dependence of the intrinsic parameters Bk a simple power law is commonly assumed ... 

The quantities B (Rq) and are treated as adjustable parameters and Rq is a reference distance that can be chosen arbitrarily. In principle, the number of ligand shells considered for the calculation of intrinsic parameters is not limited, however, it is usually assumed that only the nearest neighbors of the rare-earth ion contribute significantly to the crystal-field potential. Thus, especially long-range interactions like electrostatic interactions are not accounted for explicitly. Because these interactions are most important for k = 2 parameters, in many cases only the k = 4, 6 intrinsic parameters have been considered. 

The systems that have been studied in detail under pressure are LaCl3 doped with Pr3+, Nd3+ (Troster et al., 1995), and U3+ (Troster et al., 1995), / OCl (R = La, Pr, Gd) doped with Pr3+ (Bungenstock et al., 2000b), and MFC1 (M = Ba, Ca, Sr) doped with Sm2+ (Shen and Holzapfel, 1995c, 1995d). In the case of LaCb only one type of ligands exists and thus only one set of intrinsic parameters has to be determined. The results for this system for the intrinsic parameters (/Jq1) and r 1 for Pr3+, Nd3+ and U3+ are summarized in table 6. 

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