Pore Applications

The parallel bundle, by its nature, cannot give hysteresis or entrapment in porosimetry, and the stochastic pore network indicates that both these phenomena arise from randomness and connections amongst pores. Applications of this simple model to oil-... 

Porosity of the solid if the solid is microporous, the molecules of the liquid may be too large to penetrate into all the pores (application derivation of a micropore size distribution from the immersion energies in liquids of similar chemical nature but different molecular size). 

Jagiello J, Olivier J P (2009) A Simple Two-Dimensional NLDFT Model of Gas Adsorption in Finite Carbon Pores. Application to Pore Structure Analysis. Journal of Physical Chemistry C 113 19382-19385 Ravikovitch P I, Neimark A V (2001) Characterization of micro- and mesoporosity in SBA-15 materials from adsorption data by the NLDIT method. Journal of Physical Chemistry B 105 6817-6823 Harkins W D, Jura G (1944) Surfaces of Solids. XII. An Absolute Method for the Determination of the Area of a Finely Divided Crystalline Solid. J. Am. Chem. Soc. 66 1362-1366... 

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

Kierlik E and Rosinberg M L 1993 Perturbation density functional theory for polyatomic fluids III application to hard chain molecules in slitlike pores J Chem. Phys. 100 1716... 

Casci J L 1994 The preparation and potential applications of ultra-large pore molecular sieves a review Stud. Surf. Sc/. Catai. 85 329-56... 

For practical reasons, the application of the adsorption method to the study of surface area and porosity has to be limited to bodies which are either very finely divided or possess an extensive pore system. It is helpful to consider the case of finely divided bodies first. 

Now, in principle, the angle of contact between a liquid and a solid surface can have a value anywhere between 0° and 180°, the actual value depending on the particular system. In practice 6 is very difficult to determine with accuracy even for a macroscopic system such as a liquid droplet resting on a plate, and for a liquid present in a pore having dimensions in the mesopore range is virtually impossible of direct measurement. In applications of the Kelvin equation, therefore, it is almost invariably assumed, mainly on grounds of simplicity, that 0 = 0 (cos 6 = 1). In view of the arbitrary nature of this assumption it is not surprising that the subject has attracted attention from theoreticians. 

In using the table for pore size calculations, it is necessary to read off the values of the uptake from the experimental isotherm for the values of p/p° corresponding to the different r values given in the table. Unfortunately, these values of relative pressure do not correspond to division marks on the scale of abscissae, so that care is needed if inaccuracy is to be avoided. This difficulty can be circumvented by basing the standard table on even intervals of relative pressure rather than of r but this then leads to uneven spacings of r . Table 3.6 illustrates the application of the standard table to a specific example—the desorption branch of the silica isotherm already referred to. The resultant distribution curve appears as Curve C in Fig. 3.18. 

At the upper end of the pore size range there is no theoretical limit to the applicability of the Kelvin equation to adsorption isotherms so long as 9 < 90°. There is however a practical limitation, the nature of which may be gathered from Table 3.8 which gives the relative pressures corresponding to... 

The evaluation of pore size distribution by application of the Kelvin equation to Type IV isotherms has hitherto been almost entirely restricted to nitrogen as adsorptive. This is largely a reflection of the widespread use of nitrogen for surface area determination, which has meant that both the pore size distribution and the specific surface can be derived from the same isotherm. 

The table convincingly demonstrates how the unsuspected presence of micropores can lead to an erroneous value of the specific surface calculated from a Type II isotherm by application of the standard BET procedure. According to the foregoing analysis, the external specific surface of the solid is 114m g" the micropore volume (from the vertical separation of isotherms A and E) is 105 mm g but since the average pore width is not precisely known, the area of the micropore walls cannot be calculated. Thus the BET figure of 360m g calculated from isotherm E represents merely an apparent and not a true surface area. 

The computation of mesopore size distribution is valid only if the isotherm is of Type IV. In view of the uncertainties inherent in the application of the Kelvin equation and the complexity of most pore systems, little is to be gained by recourse to an elaborate method of computation, and for most practical purposes the Roberts method (or an analogous procedure) is adequate—particularly in comparative studies. The decision as to which branch of the hysteresis loop to use in the calculation remains largely arbitrary. If the desorption branch is adopted (as appears to be favoured by most workers), it needs to be recognized that neither a Type B nor a Type E hysteresis loop is likely to yield a reliable estimate of pore size distribution, even for comparative purposes. 

In writing the present book our aim has been to give a critical exposition of the use of adsorption data for the evaluation of the surface area and the pore size distribution of finely divided and porous solids. The major part of the book is devoted to the Brunauer-Emmett-Teller (BET) method for the determination of specific surface, and the use of the Kelvin equation for the calculation of pore size distribution but due attention has also been given to other well known methods for the estimation of surface area from adsorption measurements, viz. those based on adsorption from solution, on heat of immersion, on chemisorption, and on the application of the Gibbs adsorption equation to gaseous adsorption. 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

---