Chemical component independent

The contact angles of water and adhesive resin on wood are higher in the case of freshly harvested wood compared to stored chips. This means that the surface of particles from this fresh wood is more hydrophobic. This influences the wetting and the penetration negatively and with this the gluability. Reason for this lower wettability of freshly harvested wood is a higher content of some wood chemical components, or wood extractives, as has been determined by water extraction. This result, however, must not be confused with the better wettability of a freshly cut surface, independently if it is freshly harvested or stored wood. 

Biological-physiological detection The methods involved here take account of the biological activity of the separated components independent of their physical or chemical properties [12]. 

Here, B ls = K (KK )" is the final qxp matrix of regression coefficients for converting a spectral measurement into concentration estimates. For KK (pxp) to be invertible K should be of full rank. A first requirement for this is that pchemical components should not exceed the number of wavelengths. Furthermore, the set of pure spectra in K should be independent, i.e. no pure spectrum may be an exact linear combination of the other pure spectra. 

At this point we can derive a set of governing equations that fully describes the equilibrium state of the geochemical system. To do this we will write the set of independent reactions that can occur among species, minerals, and gases in the system and set forth the mass action equation corresponding to each reaction. Then we will derive a mass balance equation for each chemical component in the system. Substituting the mass action equations into the mass balance equations gives a set... 

We have considered a large number of values (including the molality of each aqueous species, the mole number of each mineral, and the mass of solvent water) to describe the equilibrium state of a geochemical system. In Equations 3.32-3.35, however, this long list has given way to a much smaller number of values that constitute the set of independent variables. Since there is only one independent variable per chemical component, and hence per equation, we have succeeded in reducing the number of unknowns in the equation set to the minimum possible. In addition,... 

It is noted that all systems in turmoil tend to subside spontaneously to simple states, independent of previous history. It happens when the effects of previously applied external influences damp out and the systems evolve toward states in which their properties are determined by intrinsic factors only. They are called equilibrium states. Experience shows that all equilibrium states are macroscopically completely defined by the internal energy U, the volume V, and the mole numbers Nj of all chemical components. 

In the preceding section we have set up the canonical ensemble partition function (independent variables N, V, T). This is a necessary step whether one decides to use the canonical ensemble itself or some other ensemble such as the grand canonical ensemble (p, V, T), the constant pressure canonical ensemble (N, P, T), the generalized ensemble of Hill33 (p, P, T), or some form of constant pressure ensemble like those described by Hill34 in which either a system of the ensemble is open with respect to some but not all of the chemical components or the system is open with respect to all components but the total number of atoms is specified as constant for each system of the ensemble. We now consider briefly the selection of the most convenient formalism for the present problem. 

Let us define the chemical components as the building blocks describing all the possible chemical species present in the system (Morel and Hering, 1993). The chemical components are the minimal set of atoms, species, or ions that may describe the entire attainable stoichiometry of the system. A desirable property is that these components be independent of each other, i.e., that they form an orthonormal set in composition space. 

Percent Variance Table (Model Diagnostic) Table 5.21 displays the concentration and spectral percent variance explained for the MCB models using from 1 to 10 factors. After four factors, 99-69% of the concentration variance and 99.93% of the spectral variance are explained. The spectral variance explained per factor decreases smoothly and there does not appear to be anything unusual about these results. A four-factor model is reasonable given that three would be the minimum with four chemical components varying. (Tlie concentrations of the four components sum to unity for each sample. Therefore, one degree of freedom is lost and only three independent sources of variability are present in this system.)... 

Multivariate models have been successful in identifying source contributions in urban areas. They are not independent of Information on source composition since the chemical component associations they reveal must be verified by source emissions data. Linear regressions can produce the typical ratio of chemical components in a source but only under fairly restrictive conditions. Factor and principal components analysis require source composition vectors, though it is possible to refine these source composition estimates from the results of the analysis (6.17). 

The use of the "closed system" to describe the assemblages in these closed basins seems justified in that frequently, most always, in fact, the number of clay minerals present in the sediments discussed above is two or more. The omnipresence of amorphous silica or chert raises the total number of phases to three. In an essentially three-component system, Mg-Si-Al or possibly four if H+ is considered, this indicates that the chemical components of the minerals are present in relatively fixed quantities in the chemical system which produces the mineral assemblages. None of the first three components is "mobile", i.e., its activity is independent of its relative mass in the solids or crystals present. However, there are sediments which present a monophase assemblage where only one variable need be fixed. Under these conditions sepiolite can be precipitated from solution and pre-existing solid phases need not be involved. 

To prove (5.30), let us begin by writing the known fundamental equation for entropy in the more general form S = S(U, Xh X2,...) to focus on its dependence on U, where 2Q are the remaining extensive arguments (e.g., V, N, N2,..., Nc for a system with c independent chemical components). By the chain rule, the differential variations dS can be written as... 

Equation (6.35b) shows that the new intensive variable, chemical potential pi, as introduced in this chapter, is actually superfluous for the case c = 1, because its variations can always be expressed in terms of the old variations dT dP. Thus, as stated in Inductive Law 1 (Table 2.1), only two degrees of freedom (independently variable intensive properties) suffice to describe the thermodynamic variability of a simple c = 1 system. This confirms (as expected) that chemical potential pu only becomes an informative thermodynamic variable when chemical change is possible, that is, for c > 2 chemical components. 

In the definition of c, one must generally assume that any chemical component is free to penetrate into any phase, even if the partitioning between phases varies strongly from component to component. Hence, c is the number of independent chemical components found in any phase, to account for the limiting case in which different chemical components partition completely (within limits of experimental detection) into different phases. 

The number of independent chemical components c can generally be determined from the equation... 

Problem Determine the number of independent chemical components, c, for each of the following systems ... 

For chemical purposes, the internal energy (8.71) must include chemical work terms, one for each of the c independent chemical components participating in active equilibria. Together with the usual extensities XL for heat (S) and pres sure-volume work (V), the arguments of the internal energy function must be extended to include c additional chemical extensities (such as the mole numbers n2,. .., nc, with conjugate chemical potentials ... 

For thermodynamic purposes, the dimensionality of a system with c independent chemical components and p distinct phases is determined by the Gibbs phase rule (8.89) ... 

From the chosen (/-based starting point (M = M(t/)), each possible state S = S(Q of a single-phase system of c independent chemical components can be parametrized by the numerical values ( ) of the c + 2 extensive variables XL in S ... 

Solid state reactions occur mainly by diffusional transport. This transport and other kinetic processes in crystals are always regulated by crystal imperfections. Reaction partners in the crystal are its structure elements (SE) as defined in the list of symbols (see also [W. Schottky (1958)]). Structure elements do not exist outside the crystal lattice and are therefore not independent components of the crystal in a thermodynamic sense. In the framework of linear irreversible thermodynamics, the chemical (electrochemical) potential gradients of the independent components of a non-equilibrium (reacting) system are the driving forces for fluxes and reactions. However, the flux of one independent chemical component always consists of the fluxes of more than one SE in the crystal. In addition, local reactions between SE s may occur. 

Nevertheless, the chemical potentials of SE s are frequently used instead of the chemical potentials of (independent) components of a crystalline system. Obviously, a crystal with its given crystal lattice structure is composed of SE s. They are characterized much more specifically than the crystal s chemical components, namely with regard to lattice site and electrical charge. The introduction of these two additional reference structures leads to additional balanced equations or constraints (beside the mass balances) and, therefore, SE s are not independent species in the sense of chemical thermodynamics, as are, for example, ( - 1) chemical components in an n-component system. 

Since the state of a crystal in equilibrium is uniquely defined, the kind and number of its SE s are fully determined. It is therefore the aim of crystal thermodynamics, and particularly of point defect thermodynamics, to calculate the kind and number of all SE s as a function of the chosen independent thermodynamic variables. Several questions arise. Since SE s are not equivalent to the chemical components of a crystalline system, is it expedient to introduce virtual chemical potentials, and how are they related to the component potentials If immobile SE s exist (e.g., the oxygen ions in dense packed oxides), can their virtual chemical potentials be defined only on the basis of local equilibration of the other mobile SE s Since mobile SE s can move in a crystal, what are the internal forces that act upon them to make them drift if thermodynamic potential differences are applied externally Can one use the gradients of the virtual chemical potentials of the SE s for this purpose ... 

The results of the discussion on the phenomenological thermodynamics of crystals can be summarized as follows. One can define chemical potentials, /jk, for components k (Eqn. (2.4)), for building units (Eqn. (2.11)), and for structure elements (Eqn, (2.31)). The lattice construction requires the introduction of structural units , which are the vacancies V,. Electroneutrality in a crystal composed of charged SE s requires the introduction of the electrical unit, e. The composition of an n component crystal is fixed by n- 1) independent mole fractions, Nk, of chemical components. (n-1) is also the number of conditions for the definition of the component potentials juk, as seen from Eqn. (2.4). For building units, we have (n — 1) independent composition variables and n-(K- 1) equilibria between sublattices x, so that the number of conditions is n-K-1, as required by the definition of the building element potential uk(Xy For structure elements, the actual number of constraints is larger than the number of constraints required by Eqn. (2.18), which defines nk(x.y This circumstance is responsible for the introduction of the concept of virtual chemical potentials of SE s. 

An extension of linear regression, MLR involves the use of more than one independent variable. Such a technique can be very effective if it is suspected that the information contained in a single independent variable (X) is insufficient to explain the variation in the dependent variable (Y). For example, it is suspected that a single integrated absorbance of the NIR water band at 1920 nm is insufficient to provide accurate concentrations of water contents in process samples. Such a situation can occur for several reasons, such as the presence of other varying chemical components in the sample that interfere with the 1920-nm band. In such cases, it is necessary to use more than one band in the spectrum to build an effective calibration model, so that the effects of such interferences can be compensated. 

To illustrate the MLR method, the SMLR calibration method is used to build a model for the czs-butadiene content in the polymers. In this case, four variables are specified for selection, based on prior knowledge that there are four major chemical components that are varying independently in the calibration samples. The SMLR method chooses the four X-variables 1706, 1824, 1670, and 1570 nm, in that order. These four selected variables are then used to build an MLR regression model for czs-butadiene content, the fit of which is shown in Figure 8.13. Table 8.5 lists the variables that were chosen by the SMLR method,... 

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