Free factor, measured

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

Cathodic protection of uncoated objects in the soil is technically possible however, the high current requirement, as well as measures for the necessary uniform current distribution and for //f-free potential measurement, result in high costs. In determining the costs of cathodic protection of pipelines, it has to be remembered that costs will increase with increases in the following factors ... 

Thus for a determination of a from a g factor measurement it would be desirable to choose an ion where Z is sufficiently high to get a small uncertainty in a but the influence of higher order QED contributions is not too large. Ca19+ seems to be a good choice. If we assume the same experimental accuracy on that ion as presently obtained in C5+ we would obtain a fractional uncertainty in a of 8 10-8. This is comparable to other present determinations of a from Quantum Hall or Josephson effect. The envisaged improvement in the experimental g factor by one order of magnitude would make the a determination competitive with that extracted from the g factor of the free electron. 

The total free energy measures the factors holding the whole phase together. In this sense the vapor pressures are bulk properties reflecting the stability of the condensed phase. 

The apparatus used to determine separation factors for an adsorbed monolayer was similar to that used by Cunningham, Chapin, and Johnston 4,5) but was modified to minimize the dead space and ensure good thermal equilibrium between the feed gas and the adsorbent. The inner copper cylindrical chamber was filled with 67 grams of the same y-alumina used in the isosteric heat of adsorption experiments for the establishment of the distribution function. The y-alumina was, however, free of any paramagnetic material to permit ortho-para separation factor measurements. 

The difference in etch rate between (111) and (100) surfaces was related to the bond densities on the two surfaces in the early surface kinetics models. According to Hesketh et the etch rate difference between (100) and (111) planes is due to the difference in the surface free energy of the crystal planes which is proportional to the number of bonds on the surface. The (111) plane, which has the lowest surface free energy measured in vacuum, has the lowest bond density and thus has the lowest etch rate. They postulated that the etch rate of crystal planes is a function of the total number of bonds at the surface, that is, the sum of the in-plane, lateral bonds between atoms in the plane of the surface, and surface bonds, dangling bonds. It was recognized however, that this effect alone will not cause etch rate differences of more than a factor of two. ° ... 

The basis for the high diagnostic efficacy of plasma free metanephrines is explained by several factors (1) plasma free metanephrines are produced by metabolism of catecholamines within pheochromocytomas, a process that occurs continuously and independently of variations in catecholamine release by tumors (2) normally only small amounts of metanephrines are produced in the body, and these are relatively unresponsive to sympathoadrenal activation compared with the parent amines and (3) VMA and the metanephrines commonly measured in urine are different metabofites from the free metanephrines measured in plasma, and are produced in different parts of the body by metabolic processes not directly related to the tumor itself." ... 

Figures 2 to 5 show examples of mobility reduction factors measured in oil-free Berea cores containing high-salinity, high-hardness brines under reservoir conditions. (An explanation of surfactant names used in these figures appears in the Appendix.) Nitrogen was used as the gas phase. MRF values presented in these figures were obtained from pressure gradients measured after pseudosteady-state flow through the linear cores had...

Many hydrocarbon-miscible floods are run in reservoirs containing brines of extremely high salinity and hardness. Surfactants that may be used for mobility control foams at such conditions are commercially available. The effectiveness of foams generated with these surfactants was illustrated by way of representative mobility reductions factors measured in oil-free porous media. 

The vapor pressure of a substance is determined by two factors the gain in energy on evaporation and the ratio of phase volumes at absolute zero which are available to a molecule in the solid or gaseous state respectively. The first factor comprises the heats of vaporization whose temperature dependence is determined by the difference between specific heat in vapor and in condensate the second factor measures the a priori probability that we are concerned with a molecule in the condensed or in the free state and is proportional to the chemical constants of the particular... 

A form factor measurement by Moon and Koehler (1979) on CCq. 74Tho.26 revealed a 4f free-ion Ce form factor in the y-phase at T= 180 K and deviations from the 4f form factor at the two low-g reflections (111) and (200) in the a-phase at T= 50 K. The results at 50 K suggest that the induced moment in the a-phase has two components, one 4f-like and the other 5d-hke, as also found for CePdj and CeSnj. 

The subject of the recoil-free fraction was initially discussed in Mossbauer s original paper (Mossbauer, 1958). Since then, many books and review articles (e.g. Nussbaum, 1966) have been devoted to describing experimental measurements and theoretical calculations of the recoil-free fraction f Hence this discussion will be limited to some of the major aspects of the information obtainable from /-factor measurements. The measurement itself is relatively easy, since for thin absorbers the Mossbauer spectral area is proportional to /, and thus the relative change in / with temperature is readily obtainable. With thick absorbers one can still obtain accurate values, although the analysis requires transmission integrals (Shenoy, 1973). 

As shown in Table 1.5 for PBX-9502 and Table 1.6 for Composition B, the measured reaction zone parameters for heterogeneous explosives vary considerably with the experimental technique. The reported reaction zone thickness for PBX-9502 (95/5 TATB/Kel F, p = 1.894) varies by a factor of 8 between the metal free-surface measurement of Craig and the foil-water measurement reported by Sheffield As shown in Table 1.6, the reaction zone thickness of Composition B (64/36 RDX/TNT, p = 1.713) varies by a factor of 4 between the bromoform measurement and the conductivity measurement of Hayes . 

We start with the question of what happens to the large orbital moment of f electrons when they are hybridized with other states in solids. This question, of course, is central to understanding the unusual properties of actinide (and cerium) compounds. Form-factor measurements had shown the importance of hybridization effects in compounds such as UGej (Lander et al. 1980), but at that time no theory had been developed to handle these effects in particular the orbital contribution was known to be incorrectly treated in band-structure calculations (Brooks et al. 1984, Brooks 1985). Brooks, Johansson, and their collaborators corrected this deficiency by adding an orbital polarization term in the density-functional approximation (see the chapter by Brooks and Johansson (ch. 112) in this volume). When they made calculations on a series of intermetallic compounds, particularly those with a transition metal in the compact fee Laves phase, they found that the value of was reduced compared to the free-ion values. Loosely speaking, we can associate such a partial quenching of the /j ,-value with the fact that the 5f electrons have become partially itinerant, and we know that fully itinerant electrons (in the 3d metals, for example) have 0. 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

The applicability of the two-parameter equation and the constants devised by Brown to electrophilic aromatic substitutions was tested by plotting values of the partial rate factors for a reaction against the appropriate substituent constants. It was maintained that such comparisons yielded satisfactory linear correlations for the results of many electrophilic substitutions, the slopes of the correlations giving the values of the reaction constants. If the existence of linear free energy relationships in electrophilic aromatic substitutions were not in dispute, the above procedure would suffice, and the precision of the correlation would measure the usefulness of the p+cr+ equation. However, a point at issue was whether the effect of a substituent could be represented by a constant, or whether its nature depended on the specific reaction. To investigate the effect of a particular substituent in different reactions, the values for the various reactions of the logarithms of the partial rate factors for the substituent were plotted against the p+ values of the reactions. This procedure should show more readily whether the effect of a substituent depends on the reaction, in which case deviations from a hnear relationship would occur. It was concluded that any variation in substituent effects was random, and not a function of electron demand by the electrophile. ... 

The overall requirement is 1.0—2.0 s for low energy waste compared to typical design standards of 2.0 s for RCRA ha2ardous waste units. The most important, ie, rate limiting steps are droplet evaporation and chemical reaction. The calculated time requirements for these steps are only approximations and subject to error. For example, formation of a skin on the evaporating droplet may inhibit evaporation compared to the theory, whereas secondary atomization may accelerate it. Errors in estimates of the activation energy can significantly alter the chemical reaction rate constant, and the pre-exponential factor from equation 36 is only approximate. Also, interactions with free-radical species may accelerate the rate of chemical reaction over that estimated solely as a result of thermal excitation therefore, measurements of the time requirements are desirable. 

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