FEBRUARY 1979 The Analyst Vol. 104 No. 1235 Sub-micrometre Particle Size Characterisation and Distribution by Mercury Penetration Nayiand G. Stanley-Wood Postgraduate School of Studies in Powder Technology, University of Bradford, Great Horton Road, Bradford, BD7 1DP The technique of inercury porosimetry is usually regarded as a method for the determination of surface areas and the evaluation of pore size distributions in porous solids. With fine non-porous or microporous materials the initial low- pressure region of a mercury penetration graph can be used to determine the inter-particle spaces or voids in an assembly of discrete particles. A determination of the particle size and distribution of three powders, in the one micrometre and sub-micrometre size range, has been obtained from mercury porosimetry breakthrough and intrusion pressures.The mercury intrusion particle diameters and distributions are compared with values obtained by gravitational and centrifugal sedimentation methods and electron microscopy counts for particle size measurement. Keywords Particle size characterisation ; mercury penetration The high-pressure mercury intrusion technique is commonly used to characterise, in terms of the volume, number and distribution, the void or pore spaces in porous materials. The evaluation and interpretation of the volume of mercury which penetrates, under pressure, into porous solids was initially proposed by Washburn,l,2 who applied the Young - Laplace equation for capillary rise in cylindrical tubes to the measurement of the size of pores in solids: P = (--2yLccos e)lY .. .. .. .. - * (1) where P is the applied intrusion pressure, yLa the surface tension of mercury, 8 the contact angle of mercury and Y the radius of the cylindrical tube. In reality, however, the results of pore size distribution analysis obtained by use of this equation give only an indistinct image of the real situation, as the model chosen is one of a collection of perfectly cylindrical tubes open at both ends.3 The limitations of the Washburn model were recognised by de Boer,* Frevel and Kre~sley,~ Kruyers and Mayer and S t o ~ e . ~ * * Frevel and Kressley proposed an alternative model to describe the penetration of mercury or fluid under pressure into void spaces within a solid sample composed of a collection of non-porous uniform spheres.The derived mathematical relationship allowed the deter- mination and direct comparison, from the initial penetration or breakthrough pressure of mercury, P*, into this assembly of non-porous spheres, of a surface-area equivalent spherical radius, yS, with that of a mercury-porosimeter equivalent particle radius, Ym, over the porosity range 39.54-25.95y0. Later, Mayer and Stowe described, in more general terms, the breakthrough pressure required for the penetration of a fluid into a collection of non-porous, uniform, solid spheres over the extended porosity range of 47.64-25.95y0. This model was subsequently modified to evaluate the toroidal void volume between touching spheres P = -Y&'/A)/Yg . . .. .. .. * (2) where the function (L'/A) was regarded as equivalent to the breakthrough pressure P* and was calculated for all degrees of packing between the two porosities of hexagonal close- packed and cubic-packed spheres (Tables I1 and I11 in reference 7).9798 STANLEY-WOOD : SUB-MICROMETRE PARTICLE SIZE A?"ySt, VOJ. 104 Many attempts3,9,10 have been made to measure the size of irregularly shaped non-porous particles by mercury intrusion. This technique has, however, been criticised because the Frevel and Kressley and Mayer and Stowe models of an assembly of regular monosized spheres are used to characterise a random polysized assembly of particles. Agreement of the mercury particle radius, rm, calculated from the regular monosized sphere model of Mayer and Stowe, with the radii determined from other independent particle characterisation techniques is, according to Van Brake1,ll fortuitous. Svata and ZabranskylO have shown experimentally, however, that the regular sphere model of Mayer and Stowe can be used to evaluate the particle size and the size distribution of spherical and non-spherical particles.The particle size measurement by mercury porosimetry of various sized and shaped bodies of poly(methy1 methacrylate), carbonyl iron and nickel and fritted glass, all non-porous solids, showed close agreement with the particle size determined by sedimentation and microscope- count techniques. When the mercury intrusion technique is used with porous particles, there is a difficulty in separating the effect of the volume of mercury that penetrates the spaces between particles (voids) from the effect of the volume of mercury that penetrates the spaces within particles.The purpose of this investigation was to show whether mercury intrusion could be used to indicate the presence, and measure the shape of the size distribution, of micro- metre and sub-micrometre particles in porous and non-porous powders. Experiment a1 Powders Steel shot This is a plastic-coated steel shot with a mean particle size of 112 pm, as determined by sieve analysis with Endecott test sieves and shaker. The density, as determined with an air pycnometer (Beckman, Model 930) or by mercury displacement, is 7.952 x 103 or 7.615 x lo3 kg m-3, respectively. The theoretical density from the literature12 is 7.750 x 103 kg m-3 (Fig. 1, Table I).I I I I I I I I 1 10 30 50 70 90 99 99.9 99.99 P roba bi I i ty Fig. 1. Sieve and mercury intrusion size distributions for steel shot. 0, Mercury penetration 118 pm; , sieve size 112 pm. Magnesium trisilicate This is a hydrated magnesium silicate. The mean particle size by wide-angle scanning photosedimentation (WASP) is 15.1 pm by mass, with a size range of 3.0-30.0 pm. The number - length particle size obtained from electron microscope photographs at 700 x and 2600 x magnification is 1.9 pm (Fig. 2, Table I), with a size range of 0.38-19.2 pm. The density, as determined by air pycnometry, is 2.17 x lo3 kg m-3.Febmary , 1979 CHARACTERISATION AND DISTRIBUTION BY MERCURY PENETRATION 99 Barium sul$hate scanning photosedimentation technique, of 10.7 pm and a size range of 1.8541.0 pm.This fine, white, insoluble powder has a mean particle size, by mass, with the wide-angle The TABLE I PHYSICAL CHARACTERISTICS OF POWDERS Characteristic Density x 103/kg m-3 . . .. .. Specific volume of solid/cms 8-1 . . .. .. .. Mercury volume/cm3 g-l in pores Structure . . .. .. {voids .. .. .. Porosity (c) . . .. .. .. Packing anglelangular degrees . . .. (L'/A)min. = P* p.s.i.a. . . .. .. Mean particle diameter/pm . . . . WASP d,t .. .. .. .. Centrifugal d,t . . .. .. .. Microscope d, . . .. .. .. Mercury d, .. .. .. .. Steel shot 7.952 0.125 5 0.082 9 Non-porous 0.398 4.214 - 7 1-72 112 (sieve) 119.8 - - 118.0 Barium sulphate 4.36 0.229 4 0.845 0.132 Microporous 0.700 90 3.35 17.0 0.57 1.10 4.8 Magnesium trisilicate 2.17 0.460 1.596 0.066 Microporous 0.752 90 3.35 15.1 40% < 2.3 1.85 17.8 Dicalcium phosphate 2.31 0.432 9 } 0.777 Mesoporous 0.642 90 3.35 18.0 15% < 3.0 2.60 6.8 number - length particle size from electron microscope photographs at 650 x and 2600 x magnification is 1.1 pm, with a size range of 36.2-0.54 pm (Fig.3). The density, as deter- mined by air pycnometry, is 4.36 x lo3 kg m--3. Dicalcium phosphate dihydrate Dicalcium phosphate dihydrate is a white, crystalline, water-insoluble powder with a mean particle size, as determined by photosedimentation, of 18.0pm and a size range of 5.3-27.5 pm. The number - length particle size from electron microscope photographs at 650 x and 2600 x magnification is 2.5 pm with a size range of 0.57-39.1 pm (Fig. 4, Table I).100 r 0 0.1 1 10 30 50 70 90 99 99.9 99.99 Probability Fig. 2. Size distributions for magnesium trisilicate. ., WASP by mass distribution; 0. WASP by surface distribution; A, centrifuge by mass; A, centrifuge by mass (different sample mass) ; 0, mercury penetration (e = 0.75); and 0, electron microscope number count. Adsorption Isotherms Adsorption isotherms of all powders were obtained by low-temperature nitrogen adsorption. The apparatus used was similar to that described in British Standard 4359, Part I.l3 All samples were de-gassed at room.temperature (24 5 1 "C) for 16 h at a vacuum of less than100 STANLEY-WOOD : SUB-MICROMETRE PARTICLE SIZE Analyst, VOZ. IOP Torr prior to adsorption measurements being made. The temperature of adsorption was 77 K and the nitrogen gas used was research grade XX from the British Oxygen Company, Wembley, Middlesex.0 0.1 1 10 30 50 70 90 99 99.9 9 I99 Proba bi I i ty Fig. 3. Size distributions for barium sulphate. A, Mercury penetration (c = 0.70); B, WASP by mass distribution; C, electron microscope number count; D, WASP by surface distribution; and E, centrifuge by mass. Brunauer, Emmett and Teller surface area The specific surface area of the powders was calculated from the monomolecular volume of nitrogen adsorbed between the relative pressure range of 0.05-0.35 and the Brunauer, Emmett and Teller equation.14 Mesopore size range (2.0-100 nm) The nitrogen adsorption isotherms of magnesium trisilicate, barium sulphate and dicatcium phosphate dihydrate, measured over the relative pressure range 0.08-0.98, were used to E 3 10.E : FJ a - + . 5 . 0 0 - .- 1.0 L 0.1 0 0.1 1 10 30 50 70 90 99 99.9 99.99 Probability Fig. 4. Size distributions for dicalcium phosphate. A, Mercury penetration (e = 0.64) ; B. WASP by mass distribution; C, WASP by surface distribution; D, electron microscope number count: and E. centrifuge by mass.February, 1979 CHARACTERISATION AND DISTRIBUTION BY MERCURY PENETRATION 101 characterise the porous or non-porous structure of the powders in the pore size range 2.0- 100 nm (0.1 pm). From the adsorption isotherm 40 values of the amount of nitrogen adsorbed into or on to the solid surface at specific relative pressures were taken. The specific relative pressure values were taken in known, positive incremental steps and these, together with the appropriate nitrogen volumes adsorbed per gram of powder, formed the data input to a computer.The pore size and number distribution were calculated from a computer program of the modified mathematical porous model of Barrett, Joyner and Halenda.15 The computer program was written in FORTRAN for use on an ICL 1904 com- puter. The values of the Kelvin radius were calculated from the Kelvin equation and the statistical thickness of the adsorbed layer was calculated from the data of Schull.16 Micropore surface area (pore radii 1.6-2.0 nm or less) The volume of nitrogen adsorbed at specific relative pressures obtained from the experi- mental adsorption isotherms was compared with the thickness of the unimpeded adsorbed nitrogen layer at the same specific relative pressure as obtained from the Lippens and de Boer t curve.17 The resultant Va - t graph was used to measure the amount of micro- porous area within the powders.When a straight line passes through the origin of the V , - t graph the slope of the line is a measure of the non-microporous surface area : .. .. * (3) .. vi3 St = 1.547- .. t where St is the non-microporous area in m2g-l, V , is the volume of nitrogen adsorbed at specific relative pressures and a specific thickness measured in cm3 g-l and t is the statistical thickness of an unimpeded adsorbed nitrogen layer in nanometres. A convex deviation of the line with the statistical thickness axis indicates a microporous powder. A curve concave to the statistical thickness axis, at large values of layer thickness, indicates a solid with mesoporous structure (pore radii of 2.0-100 nm).Mercury Intrusion Measurement of the volume of mercury penetrating the voids and pores within the four samples were made by use of a high-pressure Micromeritics Mercury Porosimeter, Model 905-1. All of the powder samples were de-gassed at room temperature (24 & 1 "C) for at least 16 h at a vacuum of less than Torr. The steel shot was de-gassed until a vacuum of less than 10-2Torr was maintained for 1 h. The pressure on the mercury was increased incrementally from below atmospheric, 1.11 p.s.i.a. (7.5 kPa), up to 47800 p.s.i.a. (328 MPa). The particle sizes of the collection of particles were calculated from the Mayer and Stowe equation, assuming a surface tension of 0.474 N m-l and a contact angle of 130" for mercury.The particle diameter from mercury intrusion (&) in pm was calculated from .. .. - - (4) .. .. 137.5 x P* P dm = where P is the experimental pressure in p.s.i.a. and P* the reduced breakthrough pressure obtained from Table I1 of reference 7 at various powder sample porosities and mercury contact angles. Electron Microscopy Number - Length Counts Scanning electron photographs of the powders were obtained from a Cambridge Stereoscan S4-10 after coating the particles with pure gold. A total of more than 300 particles for each powder were individually measured by the Feret diameter and the particle sizes classified into different size classes in order to obtain a number - length distribution similar to that specified in British Standard 3406.18102 STANLEY-WOOD SUB-MICROMETRE PARTICLE SIZE Analyst, VOZ.I04 Pipette Centrifuge for Sub-micron Powders The size analysis of particles below approximately 5 pm is carried out in a centrifugal field by using a modified pipette centrifuge.lg The centrifugal head is a 16 cm diameter, horizontally mounted bowl in which six narrow-bore tubes, 7 cm in length, are radially attached to a hollow central shaft. The centrifugal bowl is driven by a constant-speed motor at either 750 or 1500 rev s-l and it contains an initial volume of 150 ml of a dilute suspension of powder (less than 0.1% V / V ) in 0.1% m/V Calgon dispersant. Aliquots of 10 ml are extracted from the spinning bowl through the tubes via the hollow central shaft at various time intervals.The amount of powder extracted at these known time intervals is determined gravi- metrically after being dried in a hot oven. The particle size is determined from the Stokes equation, modified for centrifugal force, and the percentage undersize of the powder evaluated for the Kamak equation.20 Results and Discussion Spherical Steel Shot The sieve size distribution of these spherical, non-porous solids is shown in Fig. 1. The mean sieve size was 112 pm. From the mercury intrusion data the total volume of mercury that penetrated the assembly of steel shot when in the high-pressure mercury sample tube was 0.0829 cm3 g-1 (Fig. 5 and Table I). The porosity of this collection of spheres, or any assembly of particles, can be calculated from the relationship Total volume of mercury penetrating the assembly of particles per gram Total volume of mercury per gram +l/density of solid € = Thus, for steel shot, the porosity of the sample in the mercury sample tube was 0.0829/ (0.0829 + 0.1255) = 0.398.The single acute angle for this packing arrangement and porosity, from Table I in reference 7, is between 71" and 72". Interpolation of the Mayer and Stowe general function (L.'/A)min. or reduced breakthrough pressure P* for "square" access openings for the above acute packing angle gives a value of 4.214 p.s.i.a. for break- through when mercury has a contact angle of 130". The particle size and distribution of non-porous spherical steel shot determined from equation (4) and the percentage of mercury penetrating the packed spherical particles is shown in Figs. 1 and 5.The over-all shape of the distribution graph determined by mercury intrusion is similar to that determined by sieve analysis. 1 .o c b, (? 0.9 5 0.8 5 0.7 2 0.6 0.5 - f 0.4 0.3 + 0.2 F g 0.1 O i l + 0 .- + 0, 1 5 10 50 100 500 1000 500010000 50000 Intrusion pressure/p.s.i .a. Fig. 5. Mercury intrusion graphs: A, Steel shot; B, barium sulphate ; C , magnesium trisilicate ; and D, dicalcium phosphate.February, 1979 CHARACTERISATION AND DISTRIBUTION BY MERCURY PENETRATION 103 Barium Sulphate The mass and surface distributions obtained by photo- and centrifugal sedimentation are shown in Fig. 3, together with the distribution obtained by a number - length electron- microscope count and the mercury intrusion technique.Nitrogen adsorption isotherm analysis by the Barrett, Joyner and Halenda method and the Lippens and de Boer V , - t method shows that barium sulphate contains a large number of pores in the size range up to 2.0nm radius. The number of pores then decreases rapidly so that barium sulphate can be regarded as having no meso- or macropores (Fig. 6). This characterisation of the non-mesoporous structure of barium sulphate is substantiated by the linearity of the Va versus t graph (Fig. 7) at nitrogen layer thicknesses greater than 1.4 nm. 0 10 20 30 40 50 60 70 350 400 450 500 Pore radius/nm Fig. 6. Nitrogen adsorption pore size distributions : A, magnesium trisilicate ; B, dicalcium phosphate; and C, barium sulphate. The mercury intrusion graph (Fig.5) indicates, however, the presence of pores, using the Washburn model, in the diameter range 160-0.0036 pm (160000-3.6 nm). The barium sulphate mercury intrusion graph can be readily divided into regions, one region in which mercury is being forced between particles and has a volume of 0.845 cm3 g-l, and another in which mercury is being forced into particles and has a volume of 0.132 cm3 g-l (Table I, Fig. 5). 120 110 100 90 80 70 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Statistical thickness of nitrogen layer ( t ) /nrn Fig. 7. Micropore Va v e m u t graphs. A, Magnesium trisilicate; R, barium sulphate ; and C, dicalcium phosphate.104 STANLEY-WOOD : SUB-MICROMETRE PARTICLE SIZE Analyst, VoZ. 104 The porosity of the collection of particles assembled in the mercury sample tube can be evaluated in a similar manner to that shown under Spherical Steel Shot.The porosity of barium sulphate is thus 0.845/(0.845 + 0.132 + 0.2294) = 0.700. This porosity value is beyond the range of porosity versus acute angle of packing studied by Mayer and Stowe. Their relationship of breakthrough pressure versus packing angle (Fig. 9 in reference 7) does show, however, a smooth function over the higher packing angles, which tends to a constant value. A measure of the distribution of sizes, although not the surface diameter size predicted by theory, can be obtained when a breakthrough pressure value of 3.35 p.s.i.a. at a 90" packing angle is taken and substituted into equation (4). The size distribution deter- mined from the percentage of mercury penetrating between these irregularly shaped poly- sized particles follows a similar distribution to that determined by a number - length count.The sub-micrometre tail of the barium sulphate is coincidental with the sub-micrometre particle size distribution determined by centrifugal sedimentation, but is not detected by the gravitational photosedimentation technique. Magnesium Trisilicate The mass and surface size distributions obtained by photosedimentation and the mass distribution from centrifugal sedimentation are shown together with the nuniber - length and mercury intrusion size distributions in Fig. 2. The nitrogen adsorption isotherm analyses by the Barrett, Joyner and Halenda and V , - t methods (Figs. 6 and 7) show that magnesium trisilicate is solely a microporous solid.The mercury volume intrusion graph (Fig. 5) falsely indicates that, like barium sulphate, magnesium trisilicate has pores in the diameter size range 160000-3.6nm. The intrusion graph can be readily divided into two regions, one in which the volume of mercury can be attributed to the filling of voids between particles (a volume of 1.596 cm3g-l), and the second attributable to the filling of pores in particles (a volume of 0.066 cm3g1). The porosity of the collection of magnesium trisilicate particles in the mercury sample tube is 0.752 and the breakthrough pressure can be taken as being 3.35 p.s.i.a. The size distribution calculated from equation (4) shows a similarly shaped distribution to that obtained by a combination of the micrometre photo- sedimentation and the sub-micrometre centrifugal sedimentation techniques, as well as that of the number - length microscope count.The particle radius or diameter predicted by the mercury intrusion theory is a surface diameter but the diameter measured by intrusion,with both magnesium trisilicate and barium sulphate, shows a closer correlation with a mass Stokes diameter than with a surface diameter. Adjustment of the experimental mercury diameter distribution to that of a surface diameter distribution would necessitate a breakthrough pressure value, at a packing range of 90" and mercury contact angle of 130°, in the region of 1.52 p.s.i.a. This breakthrough pressure value could only be achieved at a 90" pack if the contact angle between mercury and solid was in the range 110-100".Dicalcium Phosphate Dihydrate The particle size distributions obtained by photosedimentation and centrifugal sedimenta- tion techniques are shown in Fig. 4. The nitrogen adsorption isotherm analysis (Figs. 6 and 7) shows that dicalcium phosphate is non-microporous but has a mesoporous structure. The mercury volume intrusion graph (Fig. 5) cannot readily be divided into two regions; the volume of mercury filling both the voids between particles and the pores in particles is 0.777 cm3 g-l. The porosity of the collection of dicalcium phosphate particles in the mercury sample tube has been calculated to be 0.642, with a breakthrough pressure of 3.35 p.s.i.a. The shape of the calculated mercury intrusion size distribution graph bears little resemblance, at large diameters, to the sedimentation or number - length distributions. The presence of mesopores in dicalcium phosphate has destroyed the physical model upon which the mercury intrusion diameter calculations are based.After mercury has filled the mesopores within the solid, with the result that the solid can be regarded as non-porous at higher mercury pressures, the mercury size distribution obtained from the Mayer and Stowe physical model is similar to that of the centrifugal and number - length distributions.Febmary, 1979 CHARACTERISATION AND DISTRIBUTION BY MERCURY PENETRATION Conclusions 105 With non-porous spheres the mercury intrusion technique evaluates a similarly shaped distribution of particle sizes to that determined by other, more conventional, particle sizing techniques.The diameter (or radius) measured is not, however, the surface diameter (or radius) predicted by the Mayer and Stowe model. The particle sizes measured by the mercury technique are greater than the sieve sizes of spherical shot. With microporous, irregularly shaped particles, the mercury intrusion particle size tech- nique detects both micrometre and sub-micrometre particles, which can usually only be sized by two separate characterisation methods. The mercury diameter evaluated from the microporous magnesium trisilicate powder correlates with the mass Stokes diameter rather than a surface diameter. The correlation between the mercury diameter and the Stokes diameter is, however, dubious for barium sulphate, except for sub-micrometre particles. With meso- or macroporous material little correlation exists between the mercury diameter and the Stokes diameter.This result supports the observations of Van Brakel and Mayer and Stowe that the spherical model does not perfectly represent a real solid. The mercury particle size technique can, however, be used, with additional adsorption information, in order to obtain an over-all size distribution characterisation in the micrometre and sub- micrometre particle size ranges. 1. 2. 3. 4. 6. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. References Washburn, E. W., Phys. Rev., 1926, 17, 273. Washburn, E. W., Proc. Nutn. Acud. Sci. U.S.A., 1921, 7 , 116. Scholten, J. J. F., Beers, A. M., and Kiel, A. M., J . Catulysis, 1976, 36, 23. de Boer, J. H., Adv. Catalysis, 1969, 9, 139. Frevel, L. K., and Kressley, L. J., Anulyt. Chem., 1963, 35, 1492. Kruyer, S., Trans. Faraduy SOC., 1968, 54, 1768. Mayer, R. P., and Stowe, R. A., J . Colloid Sci., 1966, 20, 893. Mayer, R. P., and Stowe, R. A., J . Phys. Chem., 1960, 70, 3867. Orr, C., Powder Technol., 1969/70, 3, 117. Svata, M., and Zabransky, Z., Powder Technol., 1970, 3, 296. Van Brakel, J., Powder Technol., 1976, 11, 206. Weast, R. C., Editor, “Handbook of Chemistry and Physics,” Fifty-seventh Edition, CRC Press, British Standard 4369 : Part I : 1969. Brunauer, S., Pure A#@. Chem., 1976, 48, 401. Barrett, E. P., Joyner, L. G., and Halenda, P. O., J . Am. Chew. Soc., 1961, 73, 373. Stanley-Wood, N. G., and Johansson, M. E., Drug Dev. Ind. Pharmacy, 1978,4, 69. Lippens, B. C., and de Boer, J. H., J . Catalysis, 1966, 4, 319. British Standard 3406 : 1963. Allen, T., “Particle Size Measurement,” Second Edition, Chapman and Hall, London, 1970. Kamak, H. J., Ind. Engng Chem., Analyt. Edn, 1961, 23, 044. Cleveland, Ohio, 1976. Received July 6th, 1978 Accepted Sefltember 8th, 1978