Onsager radius

These are general equations that allow calculating solvatochromic shifts if we know electric characteristics of the solute (dipole moments in the ground and excited states, pg and /[Pg.211]

FL, and the difference in dipole moments determined from the plot is 2.36 D if the Onsager radius is 0.33 nm [53]. The Onsager cavity radius was obtained from molecular models where the molar volumes were calculated by CAChe WS 5.0 computer program. The simplest method to estimate the cavity radius is to assume a = (3y/47r) 3, where V is the volume of the solute. 

The course of the recombination processes in a particular system depends on several factors. One of the most important ones is the polarity of the system. Both geminate and bulk recombination processes are strongly influenced by the Coulomb attraction between electrons and cations, and the range of this interaction in condensed matter is determined by the dielectric constant e. The range of the Coulomb interaction in a particular system is usually represented by the Onsager radius, r, which is defined as the distance at which the electrostatic energy of a pair of elementary charges falls down to the thermal level kj,T. 

The signs + and are for repulsion and attraction, respectively.) L is called Onsager radius [73] at which the Coulomb interaction energy equals the thermal energy kBT. Finally, for the Coulomb attraction (see more details in Chapter 4), the effective reaction radius is [67]... 

When L rB, the effective reaction radius coincides practically with the Onsager radius,... 

If both L ro and l ro, the Arrhenius law takes place with the effective activation energy E equal to that of the Coulomb attraction just after the creation of charged pair, similar to the case of elastic interaction. Note that since the actual value of the Onsager radius L in alkali halides could be as large as L 100 A (T = 100 K, e 5, — —ee = e), only a small... 

Fig. 4.5. Effective radii of the diffusion-controlled tunnelling recombination for the Coulomb attraction (a) and repulsion (b) (after [65]). Curve 1 and 2 are results of computer calculations with parameters cr = 107s l, r = 20 A, Rd = 4 A and cr = 10l4s l, r = 2 A, Rd = 4 A respectively. L - the Onsager radius, equation (3.2.55), Ro - radius of strong tunnelling recombination, equation (4.3.7).

We do not discuss here variational estimates of the for details see the review article [33]. Note here only that radius estimates show that for a typical small-radius electron defect, the activator atom A0 and begin to deviate from the Onsager radius L at very small D values only (low temperature) when the applicability of binary approximation itself is questionable. It comes from the fact that due to small values of tq 0.5 A and e 5 the Onsager... 

The value of the parameter L entering equation (6.4.1) defines whether the Coulomb attraction or recombination is predominant as L effective recombination sphere equals the Onsager radius). 

Figure 6.39 shows the time development of particle concentrations. At long times the kinetics for a symmetric (Da = Db) and asymmetric (Da = 0) cases differ significantly in the latter case reaction proceeds more quickly. Note that the choice of the parameter L — 1 corresponds to the weak electrostatic field the Onsager radius R is small and coincides with the recombination sphere radius r0. The initial dimensionless concentration n(0) = 0.1 is not also too large it is only 10 percent of the maximum concentration which could be achieved under irradiation [12], The magnitudes of these two parameters were chosen to make our computations more time-saving. 

A semi-quantitative picture of positronium formation in a spur in a dense gas was developed by Mogensen (1982) and Jacobsen (1984, 1986). If the separation of the positron from an electron is r, and there is assumed to be only one electron in the spur (a so-called single-pair spur), then the probability of positronium formation in the spur, in the absence of other competing processes, can be written as [1 — exp(—rc/r)] here rc is the critical, or Onsager, radius (Onsager, 1938), given for a medium of dielectric constant e by... 

Here D is the coefficient of the encounter diffusion of the ions and rc = e1 /cT is the Onsager radius of the Coulomb well in solvent with dielectric constant e. By... 

The particular case of highly polar solvents is of special interest since it provides wider opportunities for analytical study of the phenomenon. If the Onsager radius is smaller than a, it can be set to zero, thus switching off the electrostatic interaction. Then for polar solvents we obtain from (3.203)... 

Coulomb interaction between the charged NCs and the ejected electron seems to be an important factor in the Physics of NCs. The Onsager radius is a measure of the strength of the interaction... 

Krauss and Brus [15] measured the dielectric constant of CdSe dots, and found a value of 8. Hence, at room temperature we find r0ns — 70 A (angstrom) (however, note that the dielectric constant of the matrix is not identical to that of the dot). Since the length scale of the dots is of the order of a few nanometers, the Coulomb interaction seems to be an important part of the problem. This according to the theory in Ref. 16 is an indication of possible deviations from the universal 1 /2 power-law behavior. It is also an indication that an ejected electron is likely to return to the dot and not escape to the bulk (since the force is attractive). In contrast, if the Onsager radius is small, an ejected electron would most likely escape to the bulk, leaving the dot in state off forever (i.e., Polya... 

The field dependence of Q0ns(F) appears in a complex manner through the parameter B which determines the expansion terms of the infinite series in Eq. (138). The expansion coefficients in Eq. (138) are governed by the so-called Onsager radius at which the Coulombian attraction is equal to the thermal energy, kT... 

Due to the lesser mobility of the solvated e s and e+s, as compared to that of the quasi-free particles, solvation sets a time limit to Ps formation in polar solvents. The absence of solvation in nonpolar solvents therefore usually results in a much higher Ps yield. Furthermore, the Onsager radius, the distance at which the attractive potential between charged particles (here, e+... 

The changes in the o-Ps lifetimes should be explainable on the basis of eq. (10) and its connection with the free volume. It is interesting to note that in sulfolan, the latter does not change at the liquid/plastic phase transition. The changes in I3 cannot yet be quantified. Changes in the dielectric constant (in the Onsager radius) should be one of the main factors to consider. 

Here, M and M are the excited singlet or triplet states of M, respectively. As shown in reaction (6-15a), a singlet radical pair is initially produced in this reaction. The ion-radicals produced in very viscous nonpolar solvents cannot leave for the bulk but recombine with the probability nearly equal to unity because the initial intercharge distance (5 to 15 nm) is less than the Onsager radius for nonpolar solvents (30 nm). The S-T conversion (reaction (6-15d)) is expected to occur though the HFCM. Thus, the S-T conversion rate should be reduced by magnetic fields. 

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