Perrin Model

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

The results of this study show a definite quenching of the 418 nm phosphorescence emission of DMT. One would expect that the quenching effect, in a rigid glass, would fit the Perrin model (73). A plot in In 4>0/4> versus concentration of 4,4 -BPDC yielded a straight line, the slope of which was identified with NV. The radius, R, of the active volume of quenching sphere was calculated by the following equation ... 

Thus, if E and d are taken as constants, the parallel-plate model predicts a constant capacity, i.e., one that does not change with potential. So it appears that the Helmholtz-Perrin model would be quite satisfactory for electrocapillaiy curves that are perfect parabolas (Fig. 6.56). 

However, is the electrocapillaiy curve a perfect parabola Almost, but not quite. There is always a slight asymmetry (see Fig. 6.56), and that asymmetry precludes it from having constant capacities, as the Helmholtz-Perrin model predicts. 

In the previous section it was seen that the Helmholtz-Perrin model fixes the solution charges onto a sheet parallel to the metal. I Iowcver, this model was too rigid... 

Now, the cosh function gives inverted parabolas [Fig. 6.65(b)]. Hence, according to the simple diffuse-charge theory, the differential capacity of an electrified interface should not be a constant. Rather, it should show an inverted-parabola dependence on the potential across the interface. This, of course, is a welcome result because the major weakness of the Helmholtz-Perrin model is that it does not predict any variation in capacity with potential, although such a variation is found experimentally [Fig. 6.65(b)],... 

What are the implications of Eq. (6.132) The Stem synthesis of the two models implies a synthesis of the potential-distance relations characteristic of these two models [Fig. 6.66(b)] a Z/ncar variation in the region from. v = 0 to the position of the OHP according to the Helmholtz-Perrin model (see Section 6.6.2), and an exponential potential drop in the region from OHP to the bulk of solution according to the Gouy-Chapman model (see Section 6.6.4), as shown in Fig. 6.67. 

After all this analysis, can we say that the Stem model is consistent with experimental results In other words, is the Stem model able to reproduce the differential capacity curves Under certain conditions, it is. So, to some extent, the Stem model was successful. However, what are the restrictions the model imposes Recall that in the Helmholtz-Perrin model the ions lay close to the electrode on the OHP. The condition for the Stem model to succeed is that ions not be in close proximity to the electrode they are not to be adsorbed. Thus the model proved to be valid only for electrolytes such as NaF (Graliame, 1947).45 Both of these ions, Na+ and F, are known to have a hydration layer strongly attached to them in such a way that even in the proximity of the electrode they are almost not interacting with the electrode surface. The Stem model works well representing noninteracting ions. 

In the Helmholtz-Perrin model, we found that (Section 6.6.2)... 

In a rigid system such as a glass or a polymer, the molecules M and Q are distributed at random and do not move, at least within the lifetimes of excited states. The distance distribution follows the Perrin law which is based on a very simple model. Take any excited molecule M, and ask if one quencher molecule Q happens to be within the volume of action defined by the centre-to-centre distance r. Should any molecule Q be found within this action volume, the molecule M is quenched instantaneously, but if there is no quencher Q within this space, then M emits as if no quenchers at all were present. Figure 3.39 gives a picture of the Perrin model. The mathemat-... 

The electron transfer from the photoexcited Ru(bpy)32+ to MV2+ confined in a polysiloxane film showed a complete static quenching following the Perrin model,32) and the electron transfer distance rc was 1.4 nm, which is comparable to a conventional electron transfer distance in biological systems. The presence of a tryptophan residue model, 3-methyindole (IND) enhanced much the quenching efficiency (Fig. 19.6) by lengthening the electron transfer distance, and the electron transfer distance was estimated to be 2.7 nm, almost twice that without the mediator.32 ... 

This type of static quenching requires relatively high quencher concentrations and it follows the Perrin action sphere model [64]. According to this model, each emitter molecule is surrounded by an active volume (in the general case it needs not be a sphere), such that if there is one quencher molecule at least within this volume, then quenching takes place instantly but molecules which have no quencher within the active volume emit just like those in a sample devoid of quencher. The Perrin model leads to two observable results ... 

Q.19.7 Describe the Helmholtz-Perrin model and discuss one of its fundamental problems. Draw the arrangement of counter ions and electrode as proposed by the Helmholtz-Perrin model. 

A. 19.7 The Helmholtz-Perrin model proposes a double layer of ions that exactly cancels the effects of the electrode. A fundamental problem with this proposal is that it does not include the randomizing effects of thermal diffusion as part of its model. See Fig. 20.3. 

A. 19.8 The Gouy-Chapman model replaces the double layer of the Helmholtz-Perrin model with the diffuse cloud of charge that was more concentrated near the electrode. One of its fundamental problems is that it ignores the effect of the dielectric constant of high-potential fields present at the interface. See Fig. 20.4... 

Perrin Model. At the other extreme, Perrin (16) considered the case where the donor and acceptor molecules are immobile, and energy transfer occurs Instantaneously when the two molecules lie within a critical transfer distance, R, and does not occur at all at large intermolecular separations. 

Inokuti-Hirayama Model. The Perrin model is too simplified, although it is convenient for practical use. The static triplet-triplet energy transfer between immobile chromophores dispersed in solids can be well described by the Inokuti-Hirayama theory (17). 

The Combined Stern-Volmer and Perrin Model A model has been proposed by Morishima et al. [97] which takes account of Manning s theory [98] of polyelectrolytes and introduces a modification into the Stem-Volmer equation to describe sphere-of-action (Perrin) quenching this has been termed combined Stern-Volmer and Perrin Analysis and has been adopted [95,96] in an effort to describe quenching of fluorescence from labeled PMAA by T1+ ions, for example. 

The Perrin Model describes an active sphere as the volume around a fluorophore such that a quencher present within this volume will deactivate fluorescence with unit efficiency. Quenchers outside of this zone do not influence the excited state. 

The theory is limited, however, in that the implication of a sharp spherical boundary does not in reality describe the observed more gradual falloff in quenching action as a function of donor-acceptor separation. A further obvious discrepancy is that donor lifetime is in fact a function of acceptor concentration, whereas the Perrin model predicts the complete Independence of donor lifetime upon presence of acceptor. 

The exponential decay of transfer rate indicates that the exchange interaction is very sensitive to distance. The exchange transfer prefers the nearest or the second nearest D-A pairs. Such a behavior of exchange interaction is similar to the Perrin model, in which the transfer rate is assumed to be constant if A exists within a critical distance and is zero outside the range. This model is thought to be the most applicable to the exchange interaction. In the Perrin model, the steady-state luminescence of D as a function of concentration of A is simply written as [4]... 

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