Fundamental influence coefficients

Alternatively, fundamental parameter methods (FPM) may be used to simulate analytical calibrations for homogeneous materials. From a theoretical point of view, there is a wide choice of equivalent fundamental algorithms for converting intensities to concentrations in quantitative XRF analysis. The fundamental parameters approach was originally proposed by Criss and Birks [239]. A number of assumptions underlie the application of theoretical methods, namely that the specimens be thick, flat and homogeneous, and that, for calibration purposes, the concentrations of all the elements in the reference material be known (having been determined by alternative methods). The classical formalism proposed by Criss and Birks [239] is equivalent to the fundamental influence coefficient formalisms (see ref. [232]). In contrast to empirical influence coefficient methods, in which the experimental intensities from reference materials are used to compute the values of the coefficients, the fundamental influence coefficient approach calculates... 

Quantitative XRF analysis has developed from specific to universal methods. At the time of poor computational facilities, methods were limited to the determination of few elements in well-defined concentration ranges by statistical treatment of experimental data from reference material (linear or second order curves), or by compensation methods (dilution, internal standards, etc.). Later, semi-empirical influence coefficient methods were introduced. Universality came about by the development of fundamental parameter approaches for the correction of total matrix effects... 

XRF nowadays provides accurate concentration data at major and low trace levels for nearly all the elements in a wide variety of materials. Hardware and software advances enable on-line application of the fundamental approach in either classical or influence coefficient algorithms for the correction of absorption and enhancement effects. Vendors software packages, such as QuantAS (ARL), SSQ (Siemens), X40, IQ+ and SuperQ (Philips), are precalibrated analytical programs, allowing semiquantitative to quantitative analysis for elements in any type of (unknown) material measured on a specific X-ray spectrometer without standards or specific calibrations. The basis is the fundamental parameter method for calculation of correction coefficients for matrix elements (inter-element influences) from fundamental physical values such as absorption and secondary fluorescence. UniQuant (ODS) calibrates instrumental sensitivity factors (k values) for 79 elements with a set of standards of the pure element. In this approach to inter-element effects, it is not necessary to determine a calibration curve for each element in a matrix. Calibration of k values with pure standards may still lead to systematic errors for unknown polymer samples. UniQuant provides semiquantitative XRF analysis [242]. 

Unlike thermally developing flow, the superposition method cannot be applied directly to the simultaneously developing flow because of the dependence of the velocity profile on the axial locations. However, certain influence coefficients are introduced to determine the local Nusselt number for simultaneous developing flow in concentric annuli with thermal boundary conditions that are different from the four fundamental conditions the influence coefficients 0 through 0 2, determined by Kakacj and Yiicel [104] are listed in Tables 5.24 and 5.25. 

Several examples of the application of the influence coefficients and fundamental solutions are detailed in the following paragraphs. 

The third example is for the case of uniform heat flux at the outer wall and uniform temperature on the inner wall, that is, qZ = qZ at r = r0 and Tw=TtdXr= r,. The local Nusselt numbers at the two walls are determined from the fundamental solutions of the third and fourth kinds from Tables 5.22 and 5.23 and the influence coefficients from Table 5.25, which are given as... 

TABLE 5.24 Influence Coefficients from Fundamental Solutions of the Third and Fourth Kinds for Simultaneously Developing Flow in Concentric Annular Ducts for Pr = 0.7 [104]... 

Q f, influence coefficients derived from the fundamental solutions of the second... 

The most complex case is the analysis of all, or most, of the elements in a sample about which little or nothing is known. In this case a full qualitative analysis would be required before any attempt is made to quantify the matrix elements. Once the qualitative composition of the sample is known, again, one of three general techniques is typically applied use of type standardization, use of an influence coefficient method, or use of a fundamental parameter technique. 

To determine major and minor elements in complex samples, more elaborate matrix correction algorithms need to be appHed. They can be roughly divided into two categories the influence coefficient methods and the fundamental parameter method. 

Multiple element Type standardization Use of influence coefficients Fundamental parameter techniques... 

Both the influence coefficient and fundamental parameter technique require a computer for their application. 

The simplest quantitative analysis situation to handle is the determination of a single element in a known matrix. In this instance, a simple calibration curve of analyte concentration versus line intensity is sufficient for quantitative determination. A slightly more difficult case might be the determination of a single element where the matrix is unknown. Three basic methods are commonly employed in this situation use of internal standards, addition of standards, and use of a scattered line from the X-ray source. The most complex case is the analysis of all, or most, of the elements in a sample, about which little or nothing is known. In this case a full qualitative analysis would be required before any attempt is made to quantitate the matrix elements. Once the qualitative composition of the sample is known, one of three general techniques is typically applied type standardization, influence coefficient methods, or fundamental parameter techniques. Both the influence coefficient and fundamental parameter techniques require a computer for their application. 

Alternatively, standardless fundamental parameter (FP) techniques are based on built-in mathematical algorithms that describe the physics of the detector response to pure elements. In this case, the typical composition of a sample must be known, while the calibration model may be verified and optimized by one single standard sample. The techniques include the fundamental parameter method,the influence coefficient method, and the empirical coefficient method. 

Isotherm Subtraction. A second method (7) of determining the net proton coefficient from adsorption data is an adaptation of the thermodynamics of linked functions as applied to the binding of gases to hemoglobin (19). The net proton coefficient determined by this method is designated, Xp- The computational procedure makes a clear distinction between the influence of adsorption density and pH on the magnitude of the net proton coefficient. The fundamental equation used in the calculation of Xp is... 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

Bacterial inactivation is achieved by CO2 absorption in the liquid phase, even though the reason why it happens is still not clear. In this respect, batch- and semi-continuous operating modes are substantially different. In the batch system the residence time, i.e., the time of contact between gas- and liquid phase, must be sufficient to allow the diffusion of CO2 in the liquid, and is therefore a fundamental parameter to assure a desired efficiency. In the semi-continuous system the contact between the phases is localized in the surface of the moving micro-bubbles. In this second case, the efficiency of the process is influenced by temperature, pressure, gas flux, bubble diameter, and other parameters that modify the value of the mass-transfer coefficient. Therefore, it is not correct to use the residence time as a key parameter in the semi-continuous process. In fact, a remarkable microbial inactivation is reached even with an exposure time of 0 min (i.e., pressurizing and immediately depressurizing the system) these two steps are sufficient to allow CO2 to diffuse through the liquid phase. 

In connection with Kokochashvili s observations there arises an important fundamental question about the stability of normal propagation of a continuous plane flame front. We must analyze the influence of convexity and concavity of the flame front on the propagation velocity. In mixtures in which the diffusion coefficient is equal to or less than the thermal diffusivity, a convexity (in the direction of propagation) decreases and a concavity increases the flame velocity. The increase in the velocity is explained by the fact that the mixture, enveloped by the concave flame from all sides, heats up more rapidly.12... 

A fundamental concept in all theories for determining activity coefficients is that ionic interactions are involved. These interactions cause a deviation in the free energy associated with the ions from what it would be if they did not occur. Consequently, at the limit of an infinitely dilute solution, activity coefficients go to 1 because there are no ionic interactions. This basic consideration also leads to the idea that as the concentration of ions increases, their extent of interaction must also increase. Ionic strength is a measure of the overall concentration of ions in a solution and the fact that more highly charged ions exert a greater influence on ionic interactions. It is calculated as ... 

Reaction of dissolved gases in clouds occurs by the sequence gas-phase diffusion, interfacial mass transport, and concurrent aqueous-phase diffusion and reaction. Information required for evaluation of rates of such reactions includes fundamental data such as equilibrium constants, gas solubilities, kinetic rate laws, including dependence on pH and catalysts or inhibitors, diffusion coefficients, and mass-accommodation coefficients, and situational data such as pH and concentrations of reagents and other species influencing reaction rates, liquid-water content, drop size distribution, insolation, temperature, etc. Rate evaluations indicate that aqueous-phase oxidation of S(IV) by H2O2 and O3 can be important for representative conditions. No important aqueous-phase reactions of nitrogen species have been identified. Examination of microscale mass-transport rates indicates that mass transport only rarely limits the rate of in-cloud reaction for representative conditions. Field measurements and studies of reaction kinetics in authentic precipitation samples are consistent with rate evaluations. 

Linear nonequilibrium thermodynamics has some fundamental limitations (i) it does not incorporate mechanisms into its formulation, nor does it provide values for the phenomenological coefficients, and (ii) it is based on the local equilibrium hypothesis, and therefore it is confined to systems in the vicinity of equilibrium. Also, properties not needed or defined in equilibrium may influence the thermodynamic relations in nonequilibrium situations. For example, the density may depend on the shearing rate in addition to temperature and pressure. The local equilibrium hypothesis holds only for linear phenomenological relations, low frequencies, and long wavelengths, which makes the application of the linear nonequilibrium thermodynamics theory limited for chemical reactions. In the following sections, some of the attempts that have been made to overcome these limitations are summarized. 

Hydrophobicity (or lipophilicity) characterizes the readiness of a molecule to escape or to prefer the water environment. It plays a fundamental role in biochemical processes and influences the fate of a molecule in the environment. Thus, hydrophobic descriptors play an important role in QSAR modeling that is used in drug research and for risk characterization. The most widely used hydrophobic descriptor is the octanol-water partition coefficient (log P) proposed by Hansh [49]. P is a quotient between solubihties in octanol and water. It is defined by following equation ... 

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