Pore size determination Washburn equation

Relation 9.77 is usually called the Washburn equation [55,237], One should consider it as a special case of the fundamental Young-Laplace equation [3,9-11], Washburn was the first to propose the use of mercury for measurements of porosity. Now, it is a common method [3,8,53-55] of psd measurements for a range of sizes from several hundreds of microns to 3 to 6 nm. The lower limit is determined by the maximum pressure, which is applied in a mercury porosimeter the limiting size of rWl = 3 nm is achieved under PHg = 4000 bar. The measurements are carried out after vacuum treatment of a sample and filling the gaps between pieces of solid with mercury. Further, the hydraulic system of a device performs the gradual increase of PHg, and the appropriate intmsion of mercury in pores of the decreasing size occurs. 

The porosity of solid samples can be quantitatively studied by mercury poro-simetry. The total volume, specific surface area of the pores, bulk density, and particle size can be determined in 1.8 nm-300 pm pore size and 15 nm-3 mm particle size. The principle of the method is that there is a relationship between the pressure of mercury and the size of the pores filled with mercury. The pressure of mercury (p) required for its introduction into the pores of a given radius (r) can be expressed by Washburn s equation ... 

In this study mercury intrusion porosimetry (MIP) analyses were employed to determine the pore size distribution and pore volume over the range of approximately 100 pm down to 7.5 nm diameter, utilising CE Instruments Pascal 140/240 apparatus, on samples previously dried overnight at 150°C. The pressure/volume data were analysed by use of the Washburn Equation [14] assuming a cylindrical nonintersecting pore model and taking the mercury contact angle as 141° and surface tension as 484 mN m [10]. For the monolith... 

The method of mercury porosimetry requires evacuation of the sample and subsequent pressurization to force mercury into the pores 49). This technique was originally developed to enable pore sizes to be determined in the macropore range, where the gas adsorption method breaks down for practical reasons (6). Application of mercury porosimetry is based on the Washburn equation 62,63),... 

Mercury porosimetry is performed nearly exclusively on automatic commercial instruments that differ mainly in the highest operative pressure, which determines the size of smallest attainable pores. The highest pressure is limited by the uncertainty about the validity of the Washburn equation, which forms the basis of data evaluation. In pores with sizes similar to the mercury atom the assumption that physical properties of liquid mercury (surface tension, contact angle) are equal to bulk properties is, probably, not fully substantiated. For this reason the up-to-date instruments work with pressures up to 2000 - 4000 atm, only. 

Mercury porosimetry is a method currently used to characterize the texture of porous materials. It enables determining pore volume, specific surface area and also distributions of pore volume and surface area versus pore size. It can be applied to powders, as weU as to monolithic porous materials. The basic hypothesis usually accepted is that mercury penetrates into narrower and narrower cavities or pores as pressure increases. Data analysis is performed using the intrusion equation proposed by Washburn (1921) ... 

Mercury porosimetry is featured in many of the contributions to this volume. Indeed, it is now one of the most popular methods available for the characterization of a wide range of porous materials and the derived pore sizes are often quoted in the patent and technical literature. The method is based on the non-wetting nature of mercury and the application of the Washburn equation. The volume of mercury penetrating into a porous solid is determined as a function of the applied pressure, which is assumed to be directly related to the pore width. 

Mercury poroslmetry is widely used to determine the pore size distributions of porous solids. The relationship between pressure and intruded pore diameter is described by the Washburn equation. 

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