Specific mass effect

Atom Hartree-Fock energy Normal and specific mass effects Total relativistic correction... 

The isotope shifts of light elements give absolute values of the specific mass effect caused by electron momentum correlations. Studies of transitions of the type 3p" 3d-3/>" 4p in Ar II (n = 5), Cl II (n = 4), and S II ( = indicate a strong correlation of the 3d electron with the inner... 

Isotopes with 1 = 0 have no hyperfine structure, but in transitions between energy levels in a mixture of I = 0 isotopes of the same element, a line structure may still be obtained. This effect is called the isotopic shift. It has two origins and a distinction is made between the mass effect and the volume effect. The mass effect can be divided up into the normal and the specific mass effects. The normal mass effect is due to the movement of the nucleus, which is due to the fact that it is not infinitely heavy. For hydrogenic systems it is possible to take this into account by using the reduced mass fi instead of m... 

The specific mass effect is due to the interactions (correlations) between the different outer electrons. The mass effect is very prominent for hydrogen/deuterium but is quickly reduced for heavier elements. For such elements the volume effect becomes important. It is particularly prominent when the electron configuration contains unpaired s electrons. The nucleus has a charge density over a finite volume. The s electron with a charge probability distribution p (r) can penetrate the nucleus and is then no longer under the influence of the pure Coulomb field. A nucleus of mass M has a smaller radius r than one with the mass M+AM, and thus the potential begins to deviate from a Coulombic one at smaller values of r. The situation is illustrated in Fig.2.21. There will be an energy shift described by... 

The important point to note here is that the gas-phase mass-transfer coefficient fcc depends principally upon the transport properties of the fluid (Nsc) 3nd the hydrodynamics of the particular system involved (Nrc). It also is important to recognize that specific mass-transfer correlations can be derived only in conjunction with the investigator s particular assumptions concerning the numerical values of the effective interfacial area a of the packing. 

Approaches used to model ozone formation include box, gradient transfer, and trajectoty methods. Another method, the particle-in-cell method, advects centers of mass (that have a specific mass assigned) with an effective velocity that includes both transport and dispersion over each time step. Chemistry is calculated using the total mass within each grid cell at the end of each time step. This method has the advantage of avoiding both the numerical diffusion of some gradient transfer methods and the distortion due to wind shear of some trajectory methods. 

In the early 1990s, Bakker and Van den Akker (1991, 1994) introduced an approximate but effective Euler Euler approach (see also A. Bakker s PhD Thesis, 1992) on the basis of a single-phase RANS flow field calculated by FLUENT, a code named GHOST calculated local and averaged values of bubble size db, gas hold-up a, and specific mass transfer rate kfl. 

For all other conditions EF has to be determined by tests (Fig. 23-13). EF and therefore the effective vent area Aw of a non-inertia-free explosion device are smaller than the venting efficiency of an inertia-free vent device (specific mass < 0.5 kg/m2) with the same vent area. Therefore, such devices need testing to determine the mechanical strength before actual use, and the EF or the pressure rise, respectively, has to be chosen relative to the Predmax of the rupture disk of the same area. 

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

The main contribution to the hydrogen-deuterium isotope shift is a pure mass effect and is determined by the term E in (3.6). Other contributions coincide with the respective contributions to the Lamb shifts in Tables 3.2, 3.3, 3.7, 3.9, 4.1, 5.1, and 6.1. Deuteron specific corrections discussed in Subsubsect. 6 and collected in (6.16), (6.28), (6.29), and (6.37) also should be included in the theoretical expression for the isotope shift. 

Since isotopic fractionation is mass dependent, there will be a smooth relationship between effects observed in various isotopic ratios. In most cases of interest, the magnitude of fractionation and the fractional mass range are both small in an absolute sense, and to first order the degree of fractionation is approximately linear in mass 8m is proportional to dm, where 8m is a fractional measure (e.g., in per mil) of the fractionation effect between isotopes of mass m and m0 [Equation (1.1)] and 8m=m - m0. In elements of three or more isotopes, this is the signature by which fractionation is distinguished from specific isotope effects. If two or more isotopic ratios are observed to vary in this fashion appropriate for fractionation, it is usually considered that this is not an accident and that fractionation has indeed occurred (rather than two or more independent effects that depend on the nuclear identity of the isotopes in question). 

FIGURE 18.14 Effect of relative scission ratio on specific mass for combined end-chain and random scission. 

Applications in organic liquids are another suitable field for coated resonators and are much more easily performed than in aqueous surroundings. In contrast to the complex effects in aqueous phases, the main interference to the mass effect in organic liquids occurs from viscosity, which can be compensated for using a dual array with an uncoated transducer and/or a non-imprinted coated device, as in the gas phase. The best compensation for non-specific effects and temperature fluctuations is achieved with a dual/ternary electrode geometry on one quartz plate. 

---