Inden model

The Inden model [20] is frequently used to describe second-order magnetic order-disorder transitions. Inden assumed that the heat capacity varied as a logarithmic function of temperature and used separate expressions above and below the magnetic order-disorder transition temperature (TtIS) in order to treat the effects of both long- and short-range order. Thus for z = (T/TtIS) < 1 ... 

The two coefficients KL and Ks are derived empirically. They are related through the entropy of transition and constrained to reproduce the total enthalpy and entropy increments accompanying the phase transition. Since, the Inden model demands a series expansion in order to calculate the entropy, a simpler related equation by Hillert and Jarl [21] is used in many computer programs. 

The cluster site approximation, CSA, has the great advantage that the required number of equations to handle the necessary variables is given by the product Cn (Oates and Wentl 1996) as compared to the exponential value C" aassociated with a full CVM treatment (Inden and Pitsch 1991). The CSA is a variant of the quasichemical model proposed by Li as early as 1949, where the number of clusters that are considered to contribute to the entropy are reduced by excluding all clusters that share edges or bonds. Kikuchi (1977) has deduced the consequential changes in entropy for an f.c.c. structure (Eqs 7.32 and 7.33), which places CSA intermediate... 

Integration of experimental Cp data with temperature can be used to bypass the plethora of models described in the previous sections, as it provides both the critical ordering temperature and the ratio of sro to Iro. This route has been extensively used to describe magnetic transformations (Inden 1977a, Hillert and Jarl 1978, Nishizawa et al. 1979) and generalised through the develq)ment of a series of approximate... 

The model of Inden. This approach was pioneered by Inden (1976) who developed the following empirical equations ... 

S.4.3.2 Model of Hillert and Jarl. In his original treatment, Inden (1976) used a complicated but closed expression for the enthalpy, but had to use a series expansion in order to calculate the entropy. Hillert and Jarl (1978) therefore decided to convert the Cp expression directly through a series expansion which substantially simplifies the overall calculation and leads to a maximum error of only 1-2 J/mol at the Curie temperature of Fe. The equivalent equations to those used by Inden (1976) are given by... 

Kitamura, K., Shibata, R., Tsuji, Y., Shimano, M., Inden, Y., and Murohara, T. (2011). Eicosapentaenoic acid prevents atrial fibrillation associated with heart failure in a rabbit model. Am. J. Physiol. Heart Circ. Physiol. 300, H1814-H1821. 

We will take a semiempirical approach using numerous molecules, models, assumptions, and estimates rather than doing new calorimetric experiments and/or quantum chemical calculations. Indeed, we will also test what is probably the simplest assumption - that (4n + 2) n electrons found within a conjugated ring species is expected to result in enhanced stability and that this compound is called aromatic. We will consider the dihydroindene (indane) skeleton composed of a benzene ring fused to a nonaromatic five-membered ring that lacks additional double bonds, and will use this carbocyclic hydrocarbon with X = Y = Z = CH2 as a paradigm for many heterocyclic derivatives for which the possible aromaticity is of relevance to the current chapter. Similarly we use indene with -X-Y- = -CH=CH-, Z = CH2 for a variety of unsaturated heterocycles of interest here. 

Nishio et al. <2002HCA2383> performed a photochemical [2+2] cyclization reaction between jV-a 1 koxycarbony 1 -benzo-l,3-oxazol-2-thione 108 and a noncyclic alkene 109. The reaction led to the formation of spiro-thietanes 110, in most cases in high yields (Table 8). They also reported <2003HCA3255> that when in a similar reaction a cycloalkene was used, the reaction led to the formation of compounds 111 and iminothietanes 112. Cyclopentene and indene were used as model cycloalkenes (Scheme 17). 

By combining thermodynamically-based monomer partitioning relationships for saturation [170] and partial swelling [172] with mass balance equations, Noel et al. [174] proposed a model for saturation and a model for partial swelling that could predict the mole fraction of a specific monomer i in the polymer particles. They showed that the batch emulsion copolymerization behavior predicted by the models presented in this article agreed adequately with experimental results for MA-VAc and MA-Inden (Ind) systems. Karlsson et al. [176] studied the monomer swelling kinetics at 80 °C in Interval III of the seeded emulsion polymerization of isoprene with carboxylated PSt latex particles as the seeds. The authors measured the variation of the isoprene sorption rate into the seed polymer particles with the volume fraction of polymer in the latex particles, and discussed the sorption process of isoprene into the seed polymer particles in Interval III in detail from a thermodynamic point of view. 

Many of the steps used in this synthesis were first tested using model compounds. The Diels-Alder addition leading to (52) is based on the known behaviour of indenes in that reaction (E. Wenkert et al., J. org. Chem., 1967, 3, 1126) the procedure for its decarboxylation/decarbonylation is noteworthy of. B. M. Trost and F. Chen, Tetrahedron Letters,... 

A typical example of an effective bioprecursor prodrug is given by the anti-inflammatory drug sulindac. Sulindac, di-5-fluoro-2-methyl-l-[p-(methylsulfinyl) benzylidene] indene-3 acetic acid is a non-steroidal anti-inflammatory agent having a broad spectrum of activity in animal models and in man. The two quantitatively significant biotransformations undergone by sulindac in laboratory species and... 

Styrene and d-limonene are included in the table since they are monomers for some resins. Tetralin is used as a model for indene for which no parameter values are available. 

A final test of the intracellular fluxes determined by metabolite balancing was provided through comparison with the predictions of a first-order kinetic model describing the oxidation of pulsed [ C]-indene to all detectable indene derivatives in steady state cells. Assuming Michaelis-Menten kinetics for a typical reaction depicted in Fig. 4, the rate of labeled metabolite conversion by that reaction can be expressed as... 

In all of the radiolabeled tracer experiments conducted, the concentrations of the corresponding indene metabolites were found to be constant so that the linear model with respect to the radiolabeled tracer is justified. However, for the mass balance on radiolabeled indene, the total metabolite concentration is not constant and the first-order kinetic model is only satisfied when the total concentration is sufficiently low such that for that respective enzyme. 

Fig. 6. Comparison of kinetic model predictions with experimental measurements of C-in-dene metabolites for Rhodococcus KYI cells obtained from a chemostat at steady state obtained with a dilution rate of 0.065 h and 100 ppm indene air feed concentration. Reaction rate constants used in the kinetic model were determined from flux estimates as described in the text...

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