Trapping radius

D = Da + Db, t-o is a trapping radius and nB is trap concentration) is valid only if one neglects fluctuations of the volume of the Wiener sausage. In the opposite case at long times the kinetics for mobile donors A becomes fluctuation-controlled and as t -a oo obeys finally equation (2.1.106). Of our special interest here are arguments and results for the case of mobile traps B and d 3 based on simple estimates similar to those which resulted in equation (2.1.106). 

Fig. 9.3.5 Relationships between ITMS operating pressure, field frequency, trap radius and pump capabilities [5, 6],...

In the following, we shall limit ourselves for the sake of simplicity to optical deactivation reagents X and Y are attached to two flexible chains and immersed in a liquid of the same chains. We shall also assume that the reaction occurs whenever the distance between the two centers X and Y becomes smaller than a given trapping radius b. 

If we introduce at this point (30) into (27), we arrive at an expression which is independent of the trapping radius b ... 

Figure Bl.7.14. Schematic cross-sectional diagram of a quadnipole ion trap mass spectrometer. The distance between the two endcap electrodes is 2zq, while the radius of the ring electrode is (reproduced with pennission of Professor R March, Trent University, Peterborough, ON, Canada).

Fig. 3. Schematic diagram of an ion trap where A and B represent end cap electrodes, C the ring electrode, Tq the internal radius of C, and the internal...

Consider first penetration into a cylindrical pore. An estimate of the extent of penetration can be obtained by equating the back pressure of trapped air to the capillary driving pressure. Then the distance. r penetrated into a pore of length / and radius r is then ... 

Interception A special case of impingement, in which a particle is trapped on a fiber due to the effect of Van der Waals forces rather than inertia. The interception of a particle in a particle collection device occurs when the particle follows a gas streamline round a collector at a distance less than the radius of the particle. 

Design —good design to minimise exposed dissimilar metal couples, radius sharp edges and avoid water traps. Allow for protection of mating faces. 

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

A (3 fibril formation an identifiable nucleating species has yet be isolated. Direct observation has been made difficult by the small size of the (3 peptide, which has an effective hydrodynamic radius of 4 nm [98-100], and by the apparent low abundance of nucleating species due to the low probability of their formation. Such species would be formally akin to an enzyme transition state that is usually kinetically inferred or sometimes trapped with certain kinds of inhibitor. In disaggregated, ultrafiltered (20 nm pore size) preparations, less than 1% of the molar peptide concentration is inferred to be present as seeds or nuclei determined by the kinetics of fibril formation [101]. 

Equation (2-14) provides a way to calculate the liquid temperature in equilibrium with the ready-to-grow bubble if the saturation pressure or temperature, the value of B, and the cavity radius are known (Shai, 1967). Several modified versions of nucleation criteria have since been advanced. An example is the model proposed by Lorenta et al. (1974), which takes into account both the geometric shape of the cavity and the wettability of the surface (in terms of contact angle < >). Consider an idealized conical cavity with apex angle ip, and a liquid with a flat front penetrating into it (Fig. 2.3a). Assume that once the vapor is trapped in by the liquid front, the interface readjusts to form a cap with radius of curvature rn. Conservation of vapor... 

As stated in Section 2.1, there is a waiting period between the time of release of one bubble and the time of nucleation of the next at a given nucleation site. This is the period when the thermal boundary layer is reestablished and when the surface temperature of the heater is reheated to that required for nucleation of the next bubble. To predict the waiting period, Hsu and Graham (1961) proposed a model using an active nucleus cavity of radius rc which has just produced a bubble that eventually departs from the surface and has trapped some residual vapor or gas that serves as a nucleus for a new bubble. When heating the liquid, the temperature of the gas in the nucleus also increases. Thus the bubble embryo is not activated until the surrounding liquid is hotter than the bubble interior, which is at... 

Kevan (1974) has exhaustively reviewed ein organic glasses, to which the reader s attention is drawn. He points out that the effective spur radius r for trapped electrons may be operationally given in angstroms as... 

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