Onsager theory slope/intercept

The applicability of the Onsager theory can be determined from the field dependence of the photogeneration efficiency at low fields. From Eq. (20), the efficiency should have a linear field dependence. From plots of the efficiency versus field, the slope-to-intercept ratio is... 

In addition to three-dimensional models, there have been several onedimensional models based on the Onsager theory (Holroyd et al., 1972 Haberkom and Michel-Beyerle, 1973 Smetjek et al., 1973 Blossey, 1974 Singh and Bassler, 1975 Charle and Willig, 1978 Hong and Noolandi, 1978b Siddiqui, 1983, 1984). For the one-dimensional case, a field-independent slope-to-intercept ratio cannot be defined. One-dimensional models have been seldom used for organic materials. 

Figure 25 The low-field slope-to-intercept ratio for a dispersion of /J-F Pc for different delay times between the exposure and the application of a collection field. The exposures were 500-550 nm strobe illumination (open circles) and 532 nm laser exposures (solid circles). The solid line represents the theoretical value derived from the Onsager theory.

In all liquids, the free-ion yield increases with the external electric field E. An important feature of the Onsager (1938) theory is that the slope-to-intercept ratio (S/I) of the linear increase of free-ion yield with the field at small values of E is given by e3/2efeB2T2, where is the dielectric constant of the medium, T is its absolute temperature, and e is the magnitude of electronic charge. Remarkably S/I is independent of the electron thermalization distance distribution or other features of electron dynamics in fact, it is free of adjustable parameters. The theoretical value of S/I can be calculated accurately with a known value of the dielectric constant it has been well verified experimentally in a number of liquids, some at different temperatures (Hummel and Allen, 1967 Dodelet et al, 1972 Terlecki and Fiutak, 1972). 

For = 3.0, the ratio is 3.5 x 10-5 cni/V at 296 K. Although based on the assumption that g(r,0) is spherically symmetric, the ratio is independent of the function selected to represent the distribution of thermalized pair separations and contains no adjustable parameters. It thus provides a very critical test of the theory. Batt et al. (1968,1969) were the first to demonstrate the applicability of the Onsager formalism by use of the low-field slope-to-intercept ratio. The primary quantum yield and the thermalization distance can be determined by comparing experimental and theoretical values of the field dependence of the photogeneration efficiency at high fields, or by the temperature dependence of the zero-field quantum efficiency. The latter technique is based on the assumption that the primary quantum yield is independent of temperature. In most cases, thermalization distances and primary quantum yields have been determined from the field dependencies of photogeneration efficiencies at high fields. 

---