Lognormal distribution, pore

Fig. 9.39 Complex plane plots for lognormally distributed pores with ideally polarizable walls for constant pore volume and various standard deviations a (From Ref. [453], copyright (2011), with permission from Elsevier)...

The permeability Ps is a measure of the transport of a molecule by diffusion. The reflection coefficient a of a given component is the maximal possible rejection for that component (at infinite solvent flux). Various models have been proposed for the reflection coefficient [75-77]. In the lognormal model [78], a lognormal distribution is assumed for the pore size. No steric hindrance in the pores or hydrodynamic lag is taken into account, but it is assumed that a molecule permeates through every pore that is larger than the diameter of the molecule. Moreover, the diffusion contribution to the transport through the membrane is considered to be negligible. Therefore, the reflection curve can be expressed as ... 

Farameters derived from the size distrihiition fit (Rq Radius of tin nia.rimuiit in tin lognormal distribution a ividth of tin disti ibution A /. Vp/ yi contrnstx number density Rj/. mean radius of a single port Sjm total specific surface area ],lrn total specific micropore volume R pore radius from Cuinit.r approximation). 

It is assumed that the pore length Ip takes a lognormal distribution fix ) as follows... 

Based on the results at 85°C/80%RH/20V and 95°C/80%RH/20V, which are presented in Fig, 6, the activation energy for the migration process Is 0.15 eV, in agreement with literature values for ionic diffusion (17). The time-to-fail dependence on relative humidity is seen in Fig. 7. which best satisfies the model for an average pore size r = 17.5 nm and a lognormal-distribution a - 1.45. Figure 8 shows the humidity factor versus relative humidity (RH) calculated from the model and how well it agrees with the experimental data and the B.E.T. adsorption isotherm. 

Inversion of composite isotherms and enthalpy curves have been made using the constructed database, and assuming a lognormal form for the pore size distribution. The symmetrical distribution underlying the composite data is reproduced well Significantly however, the isotherm data underestimate the proportion of ultramicropores in the composite on the other hand, the enthalpy data do not entirely account for the fraction of wider pores present. This initial study suggests that prospects exist for a more precise characterisation of micropore distributions using a combination of enthalpy and isotherm experimental data. 

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