Quantity-Intensity Relationships

Availability of nutrients such as K+ and Ca2+ to plants in soil systems is related to the quantity and form of these nutrients in the solid phase. The quantity and form of the nutrients are related to their chemical potential (Beckett, 1964). However, it is not possible to directly measure the chemical potential of an ion in the solid phase, but it is possible to measure the difference in the chemical potential between two ions in the solution phase at equilibrium with the solid phase. The latter can then be related to the chemical potential difference of the two ions in the solid phase (Beckett, 1964,1972 Nye and Tinker, 1977). 

AExK -- Quantity factor (Q) and represents changes [gains (+) or losses (-) of exchangeable K+] 

This relationship (Fig. 4.32) implies that the ability of a soil system to maintain a certain concentration of a cation in solution is determined by the total amount of the cation present in readily available forms (exchangeable and soluble) and the intensity by which it is released to the soil solution. 

The Q/I relationship can be demonstrated as follows Consider the exchange reaction given by Reaction 4.38 and replacing Na+ by K+, the Gapon expression is 

For most agricultural soils under K-fertilization, ExK ExCa,/2 and Equation 4.59 then becomes a linear equation where ExK is the dependent variable, CRK is the independent variable, and KG[ExCa1/2] is the slope. This slope can also be expressed as the derivative of ExK with respect to CRK  

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Evangelou, V. P. 1986. The influence of anions on potassium quantity-intensity relationships. Soil Sci. Soc. Am. J. 50 1182-1188. 

Lumbanraja, J., and V. P. Evangelou, 1992. Potassium quantity-intensity relationships in the presence and absence of NH4 for three Kentucky soils. Soil Sci. 154 366-376. 

Quantity/intensity relationships are often used to describe soil capacity to buffer phosphorus concentration in soil pore water. The quantity (0 refers to the amount of phosphorus adsorbed on soil surface, whereas intensity (/) refers to the concentration of P in soil pore water. This ratio can also be viewed as partition coefficient (K ), as indicated by liner sorption isotherms. The ratio expressed as either QII or is influenced by various physicochemical properties of soils, including clay content, high concentration of Fe and Al oxides, CaCOj content, organic matter content, pH, and redox potential. 

Evangelou, V. R, J. Wang, and R. E. Phillips. 1994. New developments and perspectives on soil potassium quantity/intensity relationships. In Advances in Agronomy, ed. D. L. Sparks, 52 173-227. New York Academic Press, http //www.sciencedirect.com/science/article/ B7CSX 987WV-9/2/2dl 14c45add9280c27d84f69cf710871. 

It can be said that the relationship between the intensity of sensation and the stimulus has nearly the same feature as that between the absolute quantity and the human experience for quantity. The relationship shown in Figure 1.2 almost corresponds to the Weber-Fechner law. 

Nanocrystalline systems display a number of unusual features that are not fully understood at present. In particular, further work is needed to clarify the relationship between carrier transport, trapping, inter-particle tunnelling and electron-electrolyte interactions in three dimensional nan-oporous systems. The photocurrent response of nanocrystalline electrodes is nonlinear, and the measured properties such as electron lifetime and diffusion coefficient are intensity dependent quantities. Intensity dependent trap occupation may provide an explanation for this behaviour, and methods for distinguishing between trapped and mobile electrons, for example optically, are needed. Most models of electron transport make a priori assumptions that diffusion dominates because the internal electric fields are small. However, field assisted electron transport may also contribute to the measured photocurrent response, and this question needs to be addressed in future work. 

An approach often used to predict the relative chemical potential of K+ in soils is the quantity-intensity (Q/I) relationship. A typical Q/l plot for a binary cation system is shown in Figure 4.32 with the following components ... 

Section BT1.2 provides a brief summary of experimental methods and instmmentation, including definitions of some of the standard measured spectroscopic quantities. Section BT1.3 reviews some of the theory of spectroscopic transitions, especially the relationships between transition moments calculated from wavefiinctions and integrated absorption intensities or radiative rate constants. Because units can be so confusing, numerical factors with their units are included in some of the equations to make them easier to use. Vibrational effects, die Franck-Condon principle and selection mles are also discussed briefly. In the final section, BT1.4. a few applications are mentioned to particular aspects of electronic spectroscopy. 

To overcome these matrix influences, other calibration strategies can be used (Danzer et al. [1998]). According to one of them, a specialized three-dimensional calibration model, the relation between signal intensity and both sample weight and content is evaluated. The relationship between the three quantities, y = f(x,w) is demonstrated in Fig. 6.12 by the example of Zn determination represented above. 

The analogue to one-component thermodynamics applies to the nature of the variables. So Ay S, U and V are all extensive variables, i.e. they depend on the size of the system. The intensive variables are n and T -these are local properties independent of the mass of the material. The relationship between the osmotic pressure and the rate of change of Helmholtz free energy with volume is an important one. The volume of the system, while a useful quantity, is not the usual manner in which colloidal systems are handled. The concentration or volume fraction is usually used ... 

When this happens the adsorption phenomenon follows the so-called Langmuir isotherm and the current intensity at the maximum of the forward peak is correlated with the parameter To (that represents the quantity of Ox, in mol m-2, initially adsorbed on the electrode surface) and with the scan rate according to the relationship ... 

The existence of a linear dynamic range for a given detection method or process indicates that there is a direct relationship between the signal intensity and the actual quantity of the material being detected. This direct relationship enables accurate quantitation and the elimination of overexposure and saturated signals as well as the signals, which, although detectable, are below the minimum level of quantification. 

The expression for the contribution to the spin-orbit induced MCD intensity from perturbation of the ground state is somewhat reminiscent of an expression for the Ag quantity of EPR spectroscopy. The similarity lies in the paramagnetic term, Agp. This term is composed of integrals of a spin-orbit operator over molecular orbitals similar to the expression for the perturbation of the ground state in the presence of spin-orbit coupling (Eqs. 52-56). The paramagnetic contribution to Ag dominates for blue copper proteins and it was suspected that the MCD parameters and Amay have some sort of relationship. It was found that many of the terms that make large contributions to AgP do play a role in the MCD intensity but no simple relationship was found (160). 

The compositional and two-phase morphological relationships of "A-B" blocks, the "A-B-A" and starblocks have been studied intensively. It has been demonstrated that there is a substantial difference between random copolymers and block polymers, and this difference is based solely on the architectural arrangement of the monomeric units. One of the most important differences is that one Tg is observed in the random copolymer, which is related to the overall composition of the polymer. The block polymer has been shown to have two Tg s - one for polystyrene and one for the polydiene segment, and that these Tg s are not affected by the composition of the block copolymer. Since we can now synthesize large quantities of these pure block polymers, more detailed physical studies can be carried out. The two Tg s observed in... 

Diffuse reflectance R is a function of the ratio K/S and proportional to the addition of the absorbing species in the reflecting sample medium. In NIR practice, absolute reflectance R is replaced by the ratio of the intensity of radiation reflected from the sample and the intensity of that reflected from a reference material, that is, a ceramic disk. Thus, R depends on the analyte concentration. The assumption that the diffuse reflectance of an incident beam of radiation is directly proportional to the quantity of absorbing species interacting with the incident beam is based on these relationships. Like Beer s law, the Kubelka-Munk equation is limited to weak absorptions, such as those observed in the NIR range. However, in practice there is no need to assume a linear relationship between NIRS data and the constituent concentration, as data transformations or pretreatments are used to linearize the reflectance data. The most used linear transforms include log HR and Kubelka-Munk as mathemati-... 

Two important quantities relating to fluorescent solutions are the mean life of the excited state and the quantum yield. In the ideal case where every excited molecule loses its energy by radiation the emission intensity decays exponentially with time, and the time to drop to 1/e of the original intensity is called the radiational mean life. If only a fraction F of the molecules radiate, the remainder being degraded in some other competitive way, then the actual life, as would be found by measurement, is smaller by the fraction F. This relationship, however, would not be true if some of the molecules were almost instantly degraded by solvent molecules after excitation. Direct determinations of mean lives require special apparatus, sometimes of doubtful accuracy, because of the short times, 10-7 to 10 9 sec., involved. Although much work has been done in this field with scintillator crystals and solutions, there are... 

The mass-average molar mass of the block copolymer solute, M , and the second virial coefficient, A2, can be obtained from SLS. These quantities can be determined from the concentration dependence of the scattered light intensity using the relationship (cf. Section 1.4.10)... 

Lucifer Yellow probes are water-soluble to at least 1.5%. The absorbance maximum of the derivatives occurs at about 426—428 nm with an emission peak at about 530—535 nm, in the yellow region of the spectrum. The quantum yield of Lucifer dyes is about 0.25. The good intensity of luminosity from these dyes makes possible detection of small quantities of labeled molecules intracellularly. The fluorescent conjugates are readily visible in living cells at concentrations that are nontoxic to cell viability. The low molecular weight and water solubility of these dyes allow passage of labeled compounds from one cell to another, potentially revealing molecular relationships... 

Searching for the next most critical determinant of the vanadium distribution revealed a relationship between vanadium and the quantity of zeolite in each particle, as measured using the La+Ce intensity value. 

Hankin J, Murphy R (2010) Relationship between MALDI IMS intensity and measured quantity of selected phospholipids in rat brain sections. Anal Chem 82 8476-8484. doi 10.1021/ acl01079v... 

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