Constant series

Alkene Series Constants from equation 4 Constants from equation 7 Experimental AHhyd (g)f... 

Crystal 300 Series Constant voltage or constant current, positive or negative (identical with PrinCE pressure, simultaneous pressure and voltage. 10-400°C max. System) Pressure -180 - 250 mbar, 1 mbar increments. 

The dimensions of the silicalite which is crystallized are strongly influenced by changes in reactant concentrations (Fig. 2 and 3, Table 3). These differences are most pronounced in the aspect ratios (i.e. length/width) of crystals synthesized. Aspect ratios were found to differ considerably for the S- and T-series where the alkalinity was varied over an extensive range. For constant alkalinity, a rather constant aspect ratio is observed (B-series). Constant values of aspect ratios were observed for batches with identical alkalinities but where the source of silica was changed from precipitated silica to Ludox. High aspect ratios have been reported previously for silicalite crystallized at low alkalinities (19,20). 

In the direct method two series of aliquots are formed from a solution of the labeled counterpart of the substance to be analyzed (which is not radioactive). The first series is formed by increasing volumes of this solution containing cyi. y .. ..tya amounts of the labeled substance. The second series is formed by increasing, but times lower amounts of the same solution. To the aliquots of the second series constant amounts of the substance to be analyzed (in nonradioactive form) are added. After establishing the same separation conditions for all aliquots of both series, the separation is performed. The evaluation of the analytical results is identical to that in the reverse method. 

Polymer 5 of the third series underwent sc-CO treatment under the same conditions as polymer 3 of the third series constant pressure of 250 bar, and various temperatures, of 60°C, 80°C, and 100°C. Its characteristic ratio is lower (0.59) than that (0.771) of pol5Tner 3 and its glass transition temperature (205°C) is also lower than that (225°C) of polymer 3. Its free volume increased less than that of polymer 3, from 0.2068 to 0.4798, which means an increase of 132% compared to 222.2% increase of polymer 3. The dielectric constant decreased but not very significantly, from 3.28 to 2.87 (Table 3.8). 

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

When subjected to an electron bombardment whose energy level is much higher than that of hydrocarbon covalent bonds (about 10 eV), a molecule of mass A/loses an electron and forms the molecular ion, the bonds break and produce an entirely new series of ions or fragments . Taken together, the fragments relative intensities constitute a constant for the molecule and can serve to identify it this is the basis of qualitative analysis. 

The method implies injection of a mixture of 3 radioactive tracers each being distributed into one of the 3 phases. The tracers must show such differences in the emitting y-radiation energy spectra that they can be simultaneously detected by on line y-spectrometry. Candidate tracers are Br-82 as bromobenzene for oil, Na-24 or La-140 for water, and Kr-85 for gas. The tracers are injected simultaneously at a constant rate into the flow in the pressurised pipe, and the concentration is detected as series of instantaneous measurements taken downstream as illustrated in figure 2. 

As discussed in Chapter III, the progression in adsoiptivities along a homologous series can be understood in terms of a constant increment of work of adsorption with each additional CH2 group. This is seen in self-assembling monolayers discussed in Section XI-IB. The film pressure r may be calculated from the adsorption isotherm by means of Eq. XI-7 as modified for adsorption from dilute solution ... 

For an ideal gas and a diathemiic piston, the condition of constant energy means constant temperature. The reverse change can then be carried out simply by relaxing the adiabatic constraint on the external walls and innnersing the system in a themiostatic bath. More generally tlie initial state and the final state may be at different temperatures so that one may have to have a series of temperature baths to ensure that the entire series of steps is reversible. 

It is detemrined experimentally an early study was the work of Andrews on carbon dioxide [1], The exact fonn of the equation of state is unknown for most substances except in rather simple cases, e.g. a ID gas of hard rods. However, the ideal gas law P = pkT, where /r is Boltzmaim s constant, is obeyed even by real fluids at high temperature and low densities, and systematic deviations from this are expressed in tenns of the virial series ... 

The exponential fiinction of the matrix can be evaluated tln-ough the power series expansion of exp(). c is the coliinm vector whose elements are the concentrations c.. The matrix elements of the rate coefficient matrix K are the first-order rate constants W.. The system is called closed if all reactions and back reactions are included. Then K is of rank N- 1 with positive eigenvalues, of which exactly one is zero. It corresponds to the equilibrium state, witii concentrations r detennined by the principle of microscopic reversibility ... 

A second detennining factor in the Femii contact mechanism is the requirement tliat the wavefrmction of the bonding orbital has a significant density at each nucleus, in order for the nuclear and the electron magnets to interact. One consequence of this is that K correlates with nuclear volume and therefore rises sharply for heavier nuclei. Thus the constants m the XFI series with X = Si, Ge, Sn and are... 

For phase encoding the phase twist is most connnonly varied by incrementing in a series of subsequent transients as tiiis results in a constant transverse relaxation attenuation of the signal at the measurement position. The signal intensity as a fiinction of G is... 

Dielectric constants of metals, semiconductors and insulators can be detennined from ellipsometry measurements [38, 39]. Since the dielectric constant can vary depending on the way in which a fihn is grown, the measurement of accurate film thicknesses relies on having accurate values of the dielectric constant. One connnon procedure for detennining dielectric constants is by using a Kramers-Kronig analysis of spectroscopic reflectance data [39]. This method suffers from the series-tennination error as well as the difficulty of making corrections for the presence of overlayer contaminants. The ellipsometry method is for the most part free of both these sources of error and thus yields the most accurate values to date [39]. 

The interactive studies were followed by a series of batch calculations in which the xenon atom was dragged at a constant rate from the cavity to a location well into the solvent (total distance of approximately 1.8 nm, depending on the starting location of the xenon atom) in fixed time intervals Ixitween 1... 

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