Reducing behavioral discrepancy

Confirmation of the validity of the principle of corresponding states is shown in figure 9.4A, where we see the analogies in the reduced isotherms of H2O, CO2, and N2 according to reduced pressure. However, figure 9.4B shows that the principle of corresponding states is only an approximation of actual behavior in the vicinity of the critical point in the case of H2O, there are in fact discrepancies between predicted and actual behavior. 

It may be conjectured that collective behavior implies that the surfactants that make up the mixture are not too different, the presence of an intermediate being a way to reduce the discrepancy. When the activity coefficient is calculated from non-ideal models it is often taken to be proportional to the difference in solubihty parameters [42,43], which in case of a binary is the difference (3i - if the system is multicomponent, then the dil -ference is - Sm) y which is often less, because the mean value exhibits an average lower deviation. In other terms, it means that for a ternary in which the third term is close to the average of the two first terms, then the introduction of the third component reduces the nonideahty because (5i - 53) + ( 2 - < (5i - 52) -... 

The reason for this large discrepancy between the molecular and macroscopic requirements for a description is to be found in the fact that from the latter point of view we are not at all interested in the particular behavior of each molecule but are instead interested only in the average behavior of the system as a whole. If we can adopt a similar disinterest in individual molecules, we can perhaps hope to bridge the gap. Thus if we can somehow reduce our original system of 3V second-order differential equations to a small set that describes the average behavior of the whole, we shall have some chance of relating the macroscopic behavior of the system to the microscopic description. 

The results are shown in Table 2.2. The value Bg = 20 mT obtained in this way is in reasonable agreement with the critical field derived from the C measurements regarding the error bars involved in the derivation of both values. There is, however, a large discrepancy in the value of B h obtained from the critical fields for parallel orientation. The reason for this unusual behavior is unclear. It might be an indication for the decoupling of the 2D superconducting layers. Another possible explanation would be an upper critical field Bc2 which is reduced due to the paramagnetic hmit [183]. 

While it is an open question whether the quenching reactions in multiple-pair spurs and sensitization of solute fluorescence by "dark" states can explain the discrepancies, it seems more likely that the loss of the solute luminescence is due to some irregularity in the behavior of cyclohexane holes. One possibility is that rapid electron spin-relaxation in these holes randomizes [RH +A " geminate pairs and reduces the A yield (see section 2.2). The occurrence of such randomization does not contradict the experimental estimates of fg (0.5-0.6) for recombination of secondary pairs these estimates... 

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