Type Relations

Langmuir-Type Relations For systems composed of solutes that individually follow Langmuir isotherms, the traditional multi-component Langmuir equation, obtained via a kinetic derivation, is 

To satisfy the Gibbs adsorption isotherm for unequal monolayer capacities, explicit isotherms can be obtained in the form of a series expansion [LeVan and Vermeulen,/. Phys. Chem., 85,3247 (1981)]. A two-term form is 

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M refer to the density and molecular weight of /, and R is the gas constant. For simplicity, we assume each component to be monodisperse mote complex expressions result when polydispersity is considered (6). This model also assumes the heat of mixing pet unit volume follows a van Laar-type relation where B is... 

Isosteric Heat of Adsorption The most useful heat of adsorption for fixed-bed calculations is the Isosteric heat of adsorption, which is given by the Clausius-Clapeyron type relation... 

FreundlicVi-Type Relations A binary Freundlich isotherm, obtained from the ideal adsorbed solution theoiy in loading-explicit closed form [Crittenden et al.. Environ. Sci. TechnoL, 19, 1037 (1985)], is... 

C-type, related to the fluorite strueture but with one-quarter of the anions removed in sueh a way as to reduee the metal eoordination number from 8 to 6 (but not oetahedral) favoured by the middle and heavy lanthanides. 

The problems encountered in any attempt to treat the transmission of the effects of one substituent in a disubstituted heterocycle through the heterocyclic nucleus to a reaction site in the other substituent (i.e. the side-chain) are enormous, and it is consequently not surprising that relatively little work has been done in this area. First, while in benzene derivatives there are three positions, i.e. three relations between substituent and reacting side-chain to be considered, the number of complexities is much greater in heterocycles. Thus, e.g., in pyridine alone, after elimination of the orientations involving a vicinal relationship between substituent R and the side-chain Y to which no Hammett-type relation is likely to be applicable, the following cases should be considered ... 

In the cases 6-R-3-Y and 5-R-2-Y, the relation of R to Y corresponds to the para relation in benzene. When Y is in the 4-position, only meta-type (2-R or 6-R) substituents are possible. With R in the 2-position, aside from the one para-type relation (5-R-2-Y), two different metatype relations (4-R- and 6-R-2-Y) are possible, and the reactivity need not be the same for these two. Two ways suggest themselves to overcome this difficulty One might attempt to define separate a-values for substituents, depending not only on the relative position with respect to the side-chain, as in and Op, but also in relation to the heteroatom ... 

For catalytic reactions and systems that are related through Sabatier-type relations based on kinetic relationships as expressed by Eqs. (1.5) and (1.6), one can also deduce that a so-called compensation effect exists. According to the compensation effect there is a linear relation between the change in the apparent activation energy of a reaction and the logarithm of its corresponding pre-exponent in the Arrhenius reaction rate expression. 

Type Assignment Assign the concept type related to a concept identifier. 

Both the frequency of the well and its depth cancel, so that the free energy of activation is determined by the height of the maximum in the potential of mean force. The height of this maximum varies with the applied overpotential (see Fig. 13). To a first approximation this dependence is linear, and a Butler-Volmer type relation should hold over a limited range of potentials. Explicit model calculation gives transfer coefficients between zero and unity there is no reason why they should be close to 1/2. For large overpotentials the barrier disappears, and the rate will then be determined by ion transport. 

The interactions between bare mica surfaces in 10 and 10 M KNO solutions were determined at pH = 3.5. In both cases an exponential type relation F(D) = 0-lcD was indicated, with decay lengths 1/k = 1.4 nm and 8 nm for the two salt concentrations, respectively, but with an effective surface potential tp = 40 mV, considerably lower than its value at the higher pH used in the PEO experiments (figure 6a, curve (a)). The lower value of p is probably the result of a lower net degre of ionization of the mica surface in the presence of the large H1" concentration (the low pH was used to ensure full ionization and polyelectrolyte). 

The most popular system in mechanistic and model studies as well as in analytical applications (clinical, food, environmental) appears to be that of firefly luciferin and luciferin-type-related model luminescence [3, 5,23, 57], The luciferase from Photinus pyralis, Photinus luciferin 4-monooxygenase (ATP-hydrolyzing), EC 1.13, 12.7, is a hydrophobic enzyme that catalyzes the air oxidation of luciferin in the presence of ATP and magnesium ions to yield light emission ... 

Soil-related data (HM and BC content in soil parent materials) were included in calculations to account the values of HM weathering. Also we considered the influence of soil types on forest biomass productivity. Runoff data (at scale 0.5 x 0.50 were directly used to get input data on drainage water fluxes, Qie. Forest-type-related data (wood biomass growth and HM content in wood biomass) inserted into our database were subdivided depending on either coniferous, deciduous or mixed forests. 

Figure 8. Forest-type-related cartographic data on the left—Land use map (IGBP Map ofEDC DAAC, 1997, see de Vries et al., 2002) applied in calculations 2002 on the right-fragment of the map of forest tree dominants (National Atlas, 2003, see Priputina, 2004b).

AlB2-type variants and derivative structures. A number of A1B2-type related structures are here presented in order to emphasize the role that structural characteristics such as those present in the A1B2 type may play in a variety of intermetallic phases and to illustrate an example of a structure family containing numerous members interrelated by various kind of more or less large deformations or substitutions. Reference to a seminal paper by Gladyshevskii et al. (1992) will especially be made. 

We may Ixanp all of the temperature effects into a van t Hoff-type relation by writing the characteristic time in the form... 

Steady state shear viscosity measurements indicate a power-law type relation for the variation of the shear viscosity with shear rate even in the lower shear rate range between 10"1 to 1 sec"l. The results at higher shear rates were questionable due to the slip between the sample and cone and plate fixtures. 

There are Cauchy-Schwarz-type relations between the diagonal and nondiagonal elements of f2, 1/2, and 2-... 

Historically, Saletu (1976) performed a series of EP experiments in health subjects to stud the action of several antipsychotics, antidepressants, anxiolytics and psychostimulants. Similar to Fink and Itil for the pharmaco-EEG, he reported on systematic, drug-type-related changes in EP latencies after somatosensoiy stimulation of his subjects. 

Existence of a high degree of orientational freedom is the most characteristic feature of the plastic crystalline state. We can visualize three types of rotational motions in crystals free rotation, rotational diffusion and jump reorientation. Free rotation is possible when interactions are weak, and this situation would not be applicable to plastic crystals. In classical rotational diffusion (proposed by Debye to explain dielectric relaxation in liquids), orientational motion of molecules is expected to follow a diffusion equation described by an Einstein-type relation. This type of diffusion is not known to be applicable to plastic crystals. What would be more appropriate to consider in the case of plastic crystals is collision-interrupted molecular rotation. 

For all Sb-Se compositions nsed in this stndy, the dark DC conductivity can be expressed in the temperatnre range considered by an Arrhenins-type relation... 

Industry funding of cost-effectiveness evaluation officials could be resisted as potentially creating a client-type relation with regulators which compromises objectivity. 

For weak quenching, the expression reduces to the Stern-Volmer type relation,... 

Figure 13.9 Relationship between orthorhombic H-MoN and L-MoN unit cells and hexagonal - WC type related - 6-MoN sublattice.

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