Capacity factor temperature dependence

Normal alkanes or fatty acid methyl esters are generally used as the standard homologous compounds. The column separation number is dependent on the nature of the stationary phase, the column length, column temperature, and carrier gas flow rate [42-44]. Referring to Figure 1.2, at a sufficiently high capacity factor value either n, N, or SN provides a reasonable value for comparing... 

When a model for a CUORICINO detector (see Section 15.3.2) was formulated and the pulses simulated by the model were compared with those detected by the front-end electronics, it was evident that a large difference of about a factor 3 in the pulse rise time existed. This discrepancy was mainly attributed to the uncertainty in the values of carrier-phonon decoupling parameter. For the thermistor heat capacity, a linear dependence on temperature was assumed down to the lowest temperatures. As we shall see, this assumption was wrong. 

For capacity measurements, several techniques are applicable. Impedance spectroscopy, lock-in technique or pulse measurements can be used, and the advantages and disadvantages of the various techniques are the same as for room temperature measurements. An important factor is the temperature dependent time constant of the system which shifts e.g. the capacitive branch in an impedance-frequency diagram with decreasing temperature to lower frequencies. Comparable changes with temperature are also observed in the potential transients due to galvanostatic pulses. 

Since the results of zone refining depend on the interaction of momentum, heat and mass transfer in the system, all the basic factors affecting these three processes, both molecular and convective, have to be taken into consideration. These basic factors are concentration W, Density f, viscosity /i, heat capacity Cp, temperature den-sification coefficient, thermal conductivity k, molecular dif-fusivity D, zone diameter d, zone length L, zone travel speed u, temperature difference in zone A T and acceleration g. The concentration W may affect, JJi, Cp,, k, and D as well as the properties of the P.S.Z. (mushy region). Aside from the concentration W, all... 

Trithiolane is a stable compound at room temperature, although it will polymerize eventually and is best kept cool and sealed from the atmosphere. Separation of cisjtrans mixtures of 3,5-dialkyl-1,2,4-trithiolanes is possible on alumina. Reverse-phase HPLC has been used to separate cyclic methylene sulfides, and tellurides with retention times and capacity factors dependant in a systematic way on ring size, number and type of chalcogens and the number of heteronuclear bonds within the ring. 

This competition between electrons and the heat carriers in the lattice (phonons) is the key factor in determining not only whether a material is a good heat conductor or not, but also the temperature dependence of thermal conductivity. In fact, Eq. (4.40) can be written for either thermal conduction via electrons, k, or thermal conduction via phonons, kp, where the mean free path corresponds to either electrons or phonons, respectively. For pure metals, kg/kp 30, so that electronic conduction dominates. This is because the mean free path for electrons is 10 to 100 times higher than that of phonons, which more than compensates for the fact that C <, is only 10% of the total heat capacity at normal temperatures. In disordered metallic mixtures, such as alloys, the disorder limits the mean free path of both the electrons and the phonons, such that the two modes of thermal conductivity are more similar, and kg/kp 3. Similarly, in semiconductors, the density of free electrons is so low that heat transport by phonon conduction dominates. 

For the fresh and the specifically aged catalyst materials, the dependence of the normalized NOx storage capacity on temperature could be kept the same (Giithenke et al, 2007b). This minimized the number of parameters to be re-adapted for two catalysts with different ageing level. Thus, only the maximum NOx storage capacity and the pre-exponential factors for the reactions R1-R22 had to be re-evaluated, cf. Table III and Eq. (36). 

Standard heat capacities of transfer can be derived from the temperature dependence of standard enthalpies of solution (8). While this technique can give general trends in the transfer functions from water to mixed solvents (9), it is not always sufficiently precise to detect the differences between similar cosolvents, and the technique is rather laborious. Direct measurements of the difference between heat capacities per unit volume of a solution and of the solvent a — gq can be obtained with a flow microcalorimeter (10) to 7 X 10 5 JK 1 cm-3 on samples of the order of 10 cm3. A commercial version of this instrument (Picker dynamic flow calorimeter, Techneurop Inc.) has a sensitivity improved by a factor oi about two. 

The FDS5 pyrolysis model is used here to qualitatively illustrate the complexity associated with material property estimation. Each condensed-phase species (i.e., virgin wood, char, ash, etc.) must be characterized in terms of its bulk density, thermal properties (thermal conductivity and specific heat capacity, both of which are usually temperature-dependent), emissivity, and in-depth radiation absorption coefficient. Similarly, each condensed-phase reaction must be quantified through specification of its kinetic triplet (preexponential factor, activation energy, reaction order), heat of reaction, and the reactant/product species. For a simple charring material with temperature-invariant thermal properties that degrades by a single-step first order reaction, this amounts to -11 parameters that must be specified (two kinetic parameters, one heat of reaction, two thermal conductivities, two specific heat capacities, two emissivities, and two in-depth radiation absorption coefficients). 

Because of the occurrence of the excess quantities hEand sE in eqn.(3.9), the coefficients in eqn.(3.10) for the temperature dependence of the retention are a function of the stationary phase. Hence, every stationary phase may be expected to yield a different optimum temperature, at which the capacity factors of all sample components fall in the optimum range. Therefore, to make a fair comparison between two different stationary phases for a given separation problem, the (potentially different) optimum temperature should be established for each of them and the resulting chromatograms should be compared. The common practice of characterizing (and consequently comparing) stationary phases at a standard temperature is a very convenient one. Nevertheless, it may give rise to erroneous conclusions in some cases. 

The radiative losses can be calculated using the conventional equations [11]. The temperature rise dependence contains terms for the electric field strength, dielectric loss factor, heat capacity, and emissivity, and many of these are also temperature dependent. As a result, the complete theoretical analysis of dielectric heating is mathematically very complex [1],... 

As is evident from the preceding discussion, the retention behavior of a polypeptide or protein P- expressed in terms of the capacity factor k is governed by thermodynamic considerations. Peak dispersion, on the other hand, arises from time-dependent kinetic phenomena, which are most conveniently expressed in terms of the reduced plate height he, . When no secondary effects, i.e., when no temperature effects, conformational changes, slow chemical equilibrium, pH effects, etc. occur as part of the chromatographic distribution process, then the resolution Rs, that can be achieved between adjacent components separated under these equilibrium or nearequilibrium conditions can be expressed as... 

When a volatile compound is introduced into the carrier gas and carried into the column, it is partitioned between the gas and stationary phases by a dynamic countercurrent distribution process. The compound is carried down the column by the carrier gas, retarded to a greater or lesser extent by sorption and desorption in the stationary phase. The elution of the compound is characterized by the partition ratio, k, a dimensionless quantity also called the capacity factor. It is equivalent to the ratio of the time required for the compound to flow through the column (the retention time) to the retention time of a nonretarded compound. The value of the capacity factor depends on the chemical nature of the compound the nature, amount, and surface area of the liquid phase and the column temperature. Under a specified set of experimental conditions, a characteristic capacity factor exists for every compound. Separation by gas chromatography occurs only if the compounds concerned have different capacity factors. 

Once in the column, compounds in the test mixture are separated by virtue of differences in their capacity factors, which in turn depend on their vapor pressure and degree of interaction with the stationary phase. The capacity factor, which governs resolution and retention times of components of the test mixture, is also temperature dependent. The use of temperature-programmable column ovens takes advantage of this dependence to achieve efficient separation of compounds differing widely in vapor pressure. 

Fig. 7. Dependence of the capacity factor of the protonated peptides on the concentration of D-camphor-10 sulphonate (A) and -hexyl sulfonate (B) in the mobile phase. Column /i.-Bondapak Cig flow rate 2 ml/min temperature 20°C, mobile phase 507c methanol-50% water-50 mM NaHiP04 with HjPOi added to pH 3.0, containing various concentrations of the ion-pairing reagents. The protonated peptides were as follows 1, Arg-Phe 2, Arg-Phe-Ala 3, Met-Arg-Phe 4, Met-Arg-Phe-Ala 5, Leu-Trp 6, Leu-Trp-Met-Arg 7, Leu-Trp-Met 8, Leu-Trp-Met-Arg-Phe. Reproduced from Hearn and Grego (34).

Fig. 4,3. Differences in the effect of temperature on the number of theoretical plates and of the amount of chromatographed substance on the retention of template molecules and their enantiomers, (a) Temperature dependence of the number of theoretical plate Wh) in the resolution of D-la and L-la on a polymer imprinted with 1 [21]. (b) Dependence of the capacity factor k on the amount of chromatographed substance in the resolution of l- and of D-phenylalanine anilide on a polymer imprinted with L-phenylalanine anilide [49],...

Pace RJ and Datyner A. The temperature dependence of Langmuir capacity factor in glassy polymers. J Polym Sci 1981 B19(10) 1657-1658. 

The dependence of the capacity factor on temperature is given by the Van t Hoff equation ... 

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