THEVOLUME AND AREA DISTRIBUTIONS IN POROUS SUBSTANCES
tide. They represent a new class of silicon compounds. 4. Dichlorodifluorosilane reacts with n-propyl-
magnesium bromide to yield mainly dipropyldifluorosilane and some dipropylchlorofluorosilane.
RECEIVED JUNE 23, 1950
[CONTRIBUTION FROM THE
MULTIPLE FELLOWSHIP O F BAUGH AND
SONSCOMPANY, MELLOX INSTITUTE]
The Determination of Pore Volume and Area Distributions in Porous Substances. I.
Computations from Nitrogen Isotherms
BY ELLIOTT BARRETT, P. LESLIE G.
PAUL HALENDA P.
Introduction This paper describes a technique for estimating the volume and area of porous adsorbents available to molecules of various sizes. This technique was developed to dealwith relatively coarsely porous adsorbents exhibiting a wide range of pore sizes, but the procedure to be described appears to be applicable to porous solids of any nature. Wheeler’ proposed a theory which is a composite of BET multilayer adsorption and capillary condensation viewpoints. This theory can be summarized by the equation
where Vs is the volume of gas adsorbed a tsaturation pressure, V is the volume of gas adsorbed a t pressure p , L(r)dr is the total length of pores whose radii fall between r and r dr. rpnis the critical radius, that is, the radius of the largest pore still completely filled with liquid adsorbate a t any particular pressure and t is the multilayer thickness which is normally built up a t pressure p . Wheeler considered the radius of the pore tobe equal to the sum of the multilayer thickness as calculated from the BET theory and the radius normally calculated from the simple Kelvin equation. He also suggested that the pore size distribution, L(r), may be approximated by a simple Maxwellian or Gaussian distribution. Shul12pointed out that the BET thicknesses become much larger than experimental thicknesses for flat surfaces in the highpressure region. Shull proposes the use of experimental data3s4taken-from nitrogen isotherms for crystalline materials, for the determination of the multilayer thickness, t, in the Wheeler theory. He then developed a simplified method for fitting the experimental data to Maxwellian or Gaussian distribution functions. Almost simultaneously Oultons proposed a method for determining the poredistribution from the isotherm without the necessity of assuming a definite form for the distribution. He corrects for physical adsorption on the walls of pores empty of capillary condensed adsorbate, hereafter termed capillary condensate] by assuming that the thickness of the physically adsorbed layer is constant and equal to that of the statistical number of
- t ) 2 L(r)dr
+monolayers a t the relative pressure of the hysteresis point. This paper will show that the assumption of a simple Gaussian or Maxwellian distribution of pore sizes is inadequate for many adsorbents. It will also show that Oulton’s assumption of constant thickness for the physically adsorbed layer, while adequate for a finely porous material such as that to which he applied i t (a cracking catalystwith a pore area maximum a t radius 26.5 A.), is inadequate to deal with more coarsely porous adsorbents. A formal analysis of the relationship between nitrogen desorption isotherms a t liquid nitrogen temperatures and the distribution of pore volume and area with respect to pore radius will be made on the assumption that equilibrium between the gas phase and the adsorbed phase during desorption isdetermined by two mechanisms: (1) physical adsorption on the pore walls (which would occur to the same extent whether the area involved constituted walls of pores or a flat surface impenetrable to nitrogen), and (2) capillary condensation in what Oulton5 has called the “inner capillary volume.” Results of the analysis will be applied to several adsorbents utilizing the experimental data used by...