Density-dependent

The resulting relationship for the film density depending on the wall thickness changeAw is as following ... 

As discussed above, one may try to represent the density dependence of atom recombhiation rate coefficients k in the spirit of equation (A3.6.24) as... 

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. 

In order to probe the importance of van der Waals interactions between reactants and solvent, experiments in the gas-liqnid transition range appear to be mandatory. Time-resolved studies of the density dependence of the cage and clnster dynamics in halogen photodissociation are needed to extend earlier quantum yield studies which clearly demonstrated the importance of van der Waals clnstering at moderate gas densities [37, 111]... 

The analysis of recent measurements of the density dependence of has shown, however, that considering only the variation of solvent structure in the vicinity of the atom pair as a fiinction of density is entirely sufficient to understand tire observed changes in with pressure and also with size of the solvent molecules [38]. Assuming that iodine atoms colliding with a solvent molecule of the first solvation shell under an angle a less than (the value of is solvent dependent and has to be found by simulations) are reflected back onto each other in the solvent cage, is given by... 

Figure A3.6.13. Density dependence of die photolytic cage effect of iodine in compressed liquid n-pentane (circles), n-hexane (triangles), and n-heptane (squares) [38], The solid curves represent calculations using the diffusion model [37], the dotted and dashed curves are from static caging models using Camahan-Starling packing fractions and calculated radial distribution fiinctions, respectively [38],...

Wang Y A, Govind N and Carter E A 1999 Orbital-free kinetic-energy density functionals with a density-dependent kernel Phys. Rev. B 60 16 350... 

A. Boyum and co-workers, "Density Dependent Separation of White Blood Cells," inj. R. Harris, ed.. Blood Separation and Plasma Fractionation, Wiley-Liss, New York, 1991. 

Tap Density. Tapping a mass of loose powder, or more specifically, the appHcation of vibration to the powder mass, separates the powder particles intermittently, and thus overcomes friction. This short-time lowering of friction results in an improved powder packing between particles and in a higher apparent density of the powder mass. Tap density is always higher than apparent density. The amount of increase from apparent to tap density depends mainly on particle size and shape (see Table 4). 

The hydrolysis and polycondensation reactions initiate at numerous sites within the TMOS/H2O solution as mixing occurs. When sufficient intercoimected Si—O—Si bonds are formed in a region, the material responds cooperatively as colloidal (submicrometer) particles or a sol. The size of the sol particles and the cross-linking within the particles, ie, the density, depends on the pH and R ratio, where R = [H2 0]/[Si(0R)4]. 

The exchange current density, depends on temperature, the composition of the electrolyte adjacent to the electrode, and the electrode material. The exchange current density is a measure of the kinetic resistance. High values of correspond to fast or reversible kinetics. The three parameters, a, a. ... 

In planning cathodic protection, the specific resistivity of the water, the size of the surfaces to be protected and the required protection current densities have to be determined. The protection current density depends on the type and quality of the coating. Thermosetting resins (e.g., tar-epoxy resin coatings) are particularly effective and are mostly used today on coastal structures. They are chemically... 

Galvanic or impressed current anodes are used to protect these components. The anode material is determined by the electrolyte zinc and aluminum for seawater, magnesium for freshwater circuits. Platinized titanium is used for the anode material in impressed current protection. Potential-regulating systems working independently of each other should be used for the inlet and outlet feeds of heat exchangers on account of the different temperature behavior. The protection current densities depend on the material and the medium. 

As the air density depends on both the temperature and moisture content of the air, it is necessary to apply the general gas equation ... 

The simplest calibration procedure for a gas flow-measuring device is to connect it in series with a reference meter and allow the same flow to pass th tough both instruments. This requires a reference instrument of better metrological quality than the calibrated instrument. One fact to consider when applying this method is that the mass flow rate in the system containing both instruments is constant (assuming no leakage), but the volume flow rate is not. The volume flow rate depends on the fluid density and the density depends on the pressure and the temperature. The correct way to calibrate is to compare either the measured mass... 

Table 6.2 summarizes the low pressure intercept of observed shock-velocity versus particle-velocity relations for a number of powder samples as a function of initial relative density. The characteristic response of an unusually low wavespeed is universally observed, and is in agreement with considerations of Herrmann s P-a model [69H02] for compression of porous solids. Fits to data of porous iron are shown in Fig. 6.4. The first order features of wave-speed are controlled by density, not material. This material-independent, density-dependent behavior is an extremely important feature of highly porous materials. 

The density dependence of however, is not trivial since one must take into account the density dependence of the monomeric friction [41] given by the monomer reorientation rate W. If a scaling plot of the correct ratio DN/iyVl /N) is attempted, one again finds poor scaling in terms of the variable (Fig. 24(a)), and a good collapse of data if instead... 

Radical polymerization of diallylamine derivatives produce water-soluble polymers of low molecular weight [22,55-57]. In order to increase the molecular weight, acrylamide has been copolymerized with these diallylamine derivatives to produce cationic polymers with variable charge density depending on the content of the structural units of pyrrolidinium rings and acrylamide in polymeric chains [22,55,58-61]. 

The amorphous phase differs from the mesophase and the crystalline phase by a clearly lower value of density. The amorphous phase density depends on the internal orientation of the fiber. Us value is in the range 1.335-1.357 g/cm. In the case of a very high orientation, it can even reach the value 1.363 g/cm-. ... 

V Z V" and the measurement of the actual component volumes V becomes a difficult undertaking. In these systems, a volume change—either shrinkage or expansion—is experienced upon mixing of the components. In addition, thermal effects may accompany the formation of the mixture or solution. The volumetric composition of liquid mixtures is expected to vary with temperature owing to the density dependence on temperature. 

Crosslinking resoles in the presence of sodium carbonate or potassium carbonate lead to preferential formation of ortho-ortho methylene linkages.63 Resole networks crosslinked under basic conditions showed that crosslink density depends on the degree of hydroxymethyl substitution, which is affected by the formaldehyde-to-phenol ratio, the reaction time, and the type and concentration of catalyst (uncatalyzed, with 2% NaOH, with 5% NaOH).64 As expected, NaOH accelerated the rates of both hydroxymethyl substitution and methylene ether formation. Significant rate increases were observed for ortho substitutions as die amount of NaOH increased. The para substitution, which does not occur in the absence of the catalyst, formed only in small amounts in the presence of NaOH. 

Fig. 1.23. Density-dependence of angular momentum relaxation rate. Points correspond to experimental data presented in Fig. 1.17. The straight solid line is a binary estimation of this rate with the cross-section Oj = 3 x 10-15 cm2 and the broken curve presents the result obtained in the rough-sphere approximation used in [72, 80].

The value of the magnetic hyperfine interaction constant C = 22.00 kHz is supposed to be reliably measured in the molecular beam method [71]. Experimental data for 15N2 are shown in Fig. 1.24, which depicts the density-dependence of T2 = (27tAv1/2)-1 at several temperatures. The fact that the dependences T2(p) are linear until 200 amagat proves that binary estimation of the rotational relaxation rate is valid within these limits and that Eq. (1.124) may be used to estimate cross-section oj from... 

In both models the rotational shift of the line 5co is the same either in the static limit, where it is equal to zero, or in the case of extreme narrowing where it reaches its maximum value coq. A slight difference in its dependence on tE is observed in the intermediate region only. The experimentally observed density dependence of the shift shown in Fig. 3.5 is in qualitative agreement with theory. 

Fig. 3.13. Density-dependence of the Qo, branch line width y of methane (the dashed line is for pure vibrational dephasing, supposed to be Unear in density), (o) experimental data (with error bars) [162] Top part rotational contribution yR and its theoretical estimation in motional narrowing limit [162] (solid line) the points were obtained by subtraction of dephasing contribution y

Fig, 3.16. The density-dependence of the frequency shift of the Q-branch maximum. The y values for the curves are in the notation of Fig. 3.15. When plotting the experimental data, the cross-section found in the fitting of the density dependence of the width was employed (Fig. 3.15). 

Frenkel D., Gravestein D. J., van der Elsken J. Non-linear density dependence of rotational line-broadening of HC1 in dense argon, Chem. Phys. Lett. 40, 9-13 (1976). 

The use of SCFs as solvents influences the reacting system because it is possible to dramatically change the density of the fluid with small perturbations of temperature and pressure and, in such a way, greatly affect the density-dependent bulk properties such as the dielectric constant, solubility and diffu-sibility of these compressible fluids. 

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