**Introduction**

Micromeritics is the science and technology of small particles in the micrometre range. The knowledge and control of the size of particles is of importance in pharmacy and materials science. The size, and hence the surface area of a particle, can be related to the physical, chemical and pharmacologic properties of drugs. Clinically, the particle size of a drug can affect its release from dosage forms that are administered orally, parenterally, rectally and topically. The successful formulation of suspensions, emulsions and all tablets; both physical stability and pharmacologic response also depends on the particle size achieved in the product.

Particle size, surface area, pore size, material density, and active surface area are characteristics that are crucial to the understanding of a variety of materials. This knowledge is essential in the development of products, the efficient utilization of raw materials, and the understanding of many natural phenomena. Pharmacology, cosmetics, nanotechnology, paints, pigments, food science, ceramics, textiles, geological science, and polymer science are some of the areas of science and technology that rely on Micromeritics’ instruments to determine the physical characteristics of powders and solid materials.

Particle size analyzers employ laser diffraction, sedimentation, and electrozone sensing. Physical adsorption and mercury porosimetry instruments determine surface area and porosity. Chemical adsorption techniques are used to determine the active area of catalysts, metal dispersion, and surface energy.

**Applications of micromeritics**

**Release and dissolution**

Particle size and surface area influence the release of a drug from a dosage form that is administered orally, rectally parenterally and topically. Higher surface area brings about intimate contact of the drug with the dissolution fluids in vivo and increases the drug solubility and dissolution.

**Absorption & drug action**

Particle size and surface area influence the drug absorption and subsequently the therapeutic action. The higher the dissolution, the faster the absorption and hence quicker and greater the drug action.

**Physical stability**

Micromeritic properties of a particle i.e the particle size in a formulation influences the

physical stability of the suspensions and emulsions. Smaller the size of the particle, better the physical stability of the dosage form owing to the brownian movement of the particles in the dispersion.

**Dose uniformity**

Good flow properties of granules and powders are important in the manufacturing of tablets and capsules. The distribution of particles should be uniform in terms of number and weight.

**Characterization of packing geometry**

**Bulk properties**

There are a number of bulk properties of powders which are of importance because they give information on how a powder is likely to behave when it is being used in a process.

**1. Density of pharmaceutical powders**

The bulk and tapped density of pharmaceutical powders are often measured for processability.

**i) Bulk/Fluffy/Poured density**

Bulk density is a property of powders, granules and other “divided” solids, especially used in reference to pharmaceutical powder or soil. It is defined as the mass of many particles of the

material divided by the total volume they occupy. The total volume includes particle volume, inter-particle void volume and internal pore volume.

Bulk density is not an intrinsic property of a material; it can change depending on how the material is handled. For example, a powder poured in to a cylinder will have a particular bulk density; if the cylinder is disturbed, the powder particles will move and usually settle closer together, resulting in a higher bulk density. Bulk density is a measure of the weight of the sample per unit volume (g/ml), usually given on dry basis.

**Bulk density = mass of dry solid/ volume**.

The bulk density of a sample is inversely related to the porosity of the same sample. The more pore space in a sample, the lower the value for bulk density.

**ii) Tapped/Consolidated density**

The tapped density is measured for two primary purposes:

(i) the tapped value is more reproducibly measured than the bulk value, and

(ii) the flowability of a powder is inferred from the ratio of these two measured

densities.

The tapped density of a pharmaceutical powder is determined using a tapped density tester, which is set to tap the powder at a fixed impact force and frequency.

Tapped density by the USP method is determined by a linear progression of the number of taps.

**Tapped density tester for powders (Stamp volumeter)**

The Tapped Density Testers have been designed to measure the tapped density of powders, granules and similar products in accordance with USP Method 2 and EP. This technique is particularly useful in powder flowability studies and also in determining the amount of settlement during transit to optimise pack sizes e.g., washing powders, etc.

Tapped density is achieved by mechanically tapping (raising the cylinder and allowing it to drop a specified distance under its own weight) a measuring cylinder containing the sample under test.

Two versions of the tester are available dependent on the number of test stations

required (1 or 2).

**Mode of operation**

The mode of operation is identical on both models. Weigh out a predetermined amount of the sample, say 100 g +/- 0.1%, and place it in the graduated cylinder provided and note the unsettled volume. Secure the graduated cylinder to the test platform of the tester using the bayonet fitting provided for this purpose. Unless otherwise specified, set the number of taps via the touch sensitive keypad on the front of the instrument to 500 and operate the device making a note of the resulting tapped volume. Repeat this operation for a further 750 taps noting the volume once again. Continue repeating the test in increments of 1250 taps until the difference in tapped volume is less than 2%. Note the final reading.

The tapped density in grams per ml can now be calculated by dividing the sample weight by the final tapped volume. Measures of the ability of the powder to flow and its compressibility can now be given in the form of the so-called Hausner ratio (Tapped Density/Bulk Density) and the Compressibility

**Index ((Tapped Density – Bulk Density/Tapped Density) x 100).**

In a free flowing powder, inter-particulate interaction is less significant and unsettled and tapped densities will be closer in value. In poorly flowing powders, the inverse is to be expected. It follows that the closer the Hausner ratio is to one, the better the flow. Powders with poor flow generally have a ratio of greater than 1.25.

**iii) True density**

True density is obtained by using a relative density bottle (pycnometer) by non-solvent

displacement technique. Material density can also be determined by gas pycnometry.

**iv) Powder Porosity/Voidage**

The proportion of the powder which is not composed of solid i.e. it is the volume of the air spaces in between the particles. Used in material science, the porosity of a porous medium (such as rock, particle or sediment) describes the fraction of void space in the material, where the void may contain, for example, air or water. It is defined by the ratio of* Vv/VT = φ*

where VV is the volume of void-space (such as fluids) and VT is the total or bulk volume of material, including the solid and void components. Both the mathematical symbols φ and n are used to denote porosity.

Porosity is a fraction between 0 and 1, typically ranging from less than 0.01 for solid granite to more than 0.5 for peat and clay, although it may also be represented in percent terms by multiplying the fraction by 100. In pharmaceutical materials, it ranges from 10 – 90%. 10% denotes wide size range material, and 90% for fluffy/fibrous particles. A value for porosity can be calculated from the bulk density ρbulk and particle density ρparticle:

**φ = 1 – Pbulk/Particles.**

**Measuring porosity**

Several methods can be employed to measure porosity, including the volume/density method (pore volume = total volume – material volume), water saturation method (pore volume = total volume of water – unsaturated water), water evaporation method (pore volume in cubic

centimeters = weight of saturated sample in grams – weight of dried sample in grams), Mercury intrusion porosimetry (several non-mercury intrusion techniques have been

developed due to toxicological concerns, and the fact that mercury tends to form amalgams with several metals/alloys), and nitrogen gas adsorption (nitrogen gas adsorption in pores is measured either by volume or weight. This technique is suitable for materials with very fine

pores).

**Factors affecting packing geometry**

- Particle size and size distribution
- Particle shape and texture
- Surface properties- electrostatic effects
- Handling and processing conditions

**Flow properties of powders**

**Angle of repose, θ**

The so-called θ of a powder is the angle of elevation to the horizontal at which the powder commences to slide upon itself. It is determined by: θ = ADp + B.

A powder may be allowed to flow out of a funnel to form a conical heap:

The cone may be formed by placing an open cylinder on a base of the same radius, filling it with powder and then raising it slowly to leave a conical heap behind.

θ > 50o denotes unsatisfactory flow

θ < 25o

denotes very good flow properties.

θ decreases fairly regularly with particle size in the range 200 – 2000 µm and can be expressed by:

θ = ADp + B

A & B are constants for a particular material; Dp is the particle size concerned.

**Angle of friction, α**

This the angle to which a particular surface must be elevated from the horizontal before the

powder begins to slide upon it.

Most direct method is to measure the rate which the powder emerges through the orifice of a

container/hopper and using a recording flow meter.

θ, α and direct measurement are used for free flowing powders and granules.

**Methods for cohesive powders**

Powders finer than 10 µm tend to be cohesive and form agglomerates. A Jenike Shear cell is

used to study cohesive powders.

Carr’s Compressibility (% Compressibility)

This is a flowability index developed by Carr and is given by the equation:

**% Compressibility = (Dt – DB)/Db**

Dt is the tapped/consolidated density

Db is the bulk/fluffy density

**The following relationship exists between % Compressibility range and flow**

Percentage compressibility of 5 – 15 is Excellent (free flowing granules)

- 12 – 16 is good (free flowing powdered granules)
- 18 – 21 is fair (powdered granules)
- 23 – 28 is poor (very fluid powders
- 28 – 35 is poor (fluid cohesive powders)
- 35 – 38 isvVery poor (fluid cohesive powders)
- >40 is extremely poor (cohesive powders).

**Hausner ratio (HR)**

This is given by the ratio of tapped density to bulk density. This ratio relates to interparticle friction and as such could be used to predict powder flow properties.

**Improvement of powder flowability**

- Alteration of particle size and size distribution
- Alteration of particle shape or texture
- Alteration of surface forces
- Formulation additives/flow activators- glidants, which reduce adhesion and cohesion
- Alteration of process condition: use of vibration-assisted hoppers where arching and bridging occurs and use of force feeders.

**Particle size analysis**

**Different techniques**

Clearly if we look at our particle under the microscope we are looking at some 2-D projection of it and there are a number of diameters that we can measure to characterize our particle. If we take the maximum length of the particle and use this as our size, then we are really saying that our particle is a sphere of this maximum dimension. Likewise, if we use the minimum diameter or some other quantity like Feret’s diameter, this will give us another answer as to the size of our particle. Hence we must be aware that each characterization technique will measure a different property of a particle (max. length, min. length, volume, surface area etc.) and therefore will give a different answer from another technique which measures an alternative dimension.

**Dimensions**

Due to irregularities in particle shape, a solid particle is often considered to approximate to a sphere which can then be characterized by determination of its diameter. Because measurement is hypothetical, the dimension is referred to as the equivalent diameter of the particle. Equivalent diameters It is possible to generate more than one sphere which is equivalent to a given irregular particle shape.

These are different from Feret’s and Martins diameters- values are dependent on both the orientation and the shape of the particles. These are statistical diameters which are averaged over many different orientations to produce a mean value for each particle.

Feret’s diameter is determined from the mean distance between two parallel tangents to the projected particle perimeter. Martin’s diameter is the mean chord length of the projected particle perimeter, which can be considered as the boundary separating equal particle areas A & B.

Also possible to determine particle size based on spheres of for e.g. equivalent volume, sedimentation volume, mass or sieve mass of a given particle. Method used dictates the type of equivalent diameter which is measured although, inter-conversions may be possible.

**Particle size distribution**

A particle population which consists of spheres or equivalent spheres with uniform dimension is monosized- characteristic described by a single diameter. This is unusual.

Most powders contain particle with large number of different equivalent diameters. To represent this, size distribution is sub-divided into different size ranges and represented in form of histogram- better interpretation.

**Alternative to Histogram**

Sequential adding the percent frequency values, to produce a cumulative percent frequency distribution. • If the addition sequence begins with the coarsest particles, the values obtained will be cumulative percent frequency undersize; the reverse case produces a cumulative percent oversize. • Can be used to compare two more particle populations.

**Statistics**

**Mean, Median and Mode – basic statistics**

It is important to define these three terms as they are so often misused in both statistics and particle size analysis:

**MEAN**

This is some arithmetic average of the data. There are a number of means that can be calculated for particles.

**MEDIAN**

This is the value of the particle size which divides the population exactly into two equal halves i.e. there is 50% of the distribution above this value and 50% below.

**MODE**

This is the most common value of the frequency distribution i.e. the highest point of the frequency curve.

If distribution is a Normal or Gaussian distribution,the mean, median and mode will lie in exactly the same positions.

**Leptokurtic Distribution**

A leptokurtic distribution is symmetrical in shape, similar to a normal distribution, but the center peak is much higher; that is, there is a higher frequency of values near the mean. In addition, a leptokurtic distribution has a higher frequency of data. If you move scores from shoulders of a distribution into the centre and tails of a distribution, the result is a peaked distribution with thick tails.

- Thin tailed blunt peaked curves are platykurtic
- The normal distribution is mesokurtic.

**Influence of particle shape**

Techniques discussed above for representing the particle size distributions are all based on the assumption that particles could be adequately characterized by an equivalent circle or sphere. In some cases, particles deviate markedly from circularity and sphericity and the use of a single equivalent diameter measurement may be inappropriate. Particles can be: fibrous, acicular, prismatic etc.

**Methods of measurement**

From our earlier sections, we have seen that each measurement technique produces a different answer because it is measuring a different dimension of our particle. We will now discuss some of the relative advantages and disadvantages of the main different methods employed.

**Sieves**

This is an extremely old technique but has the advantage that it is cheap and is readily usable for large particles. The main disadvantages to many users are the following:

- Not possible to measure sprays or emulsions
- Measurement for dry powders under 400# (38µ) very difficult. • Cohesive and agglomerated materials e.g. clays are difficult to measure.
- Materials such as 0.3µ TiO2 are simply impossible to measure and resolve on a sieve. The method is not inherently high resolution.
- The longer the measurement, the smaller the answer as particles orientate themselves to fall through the sieve. This means that measurement times and operating methods (e.g. tapping) need to be rigidly standardised.
- A true weight distribution is not produced. Rather the method relies on measuring the second smallest dimension of the particle. This can give some strange results with rodlike materials e.g. paracetamol in the pharmaceutical industry.
- Tolerance. It is instructive to examine a table of BS sieve sizes and see the permitted tolerances on average and maximum variation.

**Sedimentation**

This has been the traditional method of measurement in the paint and ceramics. The applicable range is 2 – 50 microns. The principle of measurement is based on the Stokes’ Law equation:

Equipment can be as simple as the Andreason pipette or more complicated involving the use of centrifuges or X-rays. The end result is a Stokes diameter (DST) which is not the same as a weight diameter, and is simply a comparison of the particle’s settling rate to a sphere settling at the same rate. The main disadvantages of the technique for pigment users are the following:

- Speed of measurement. Average times are 25 minutes to 1 hour for measurement making repeat analyses difficult and increasing the chances for reagglomeration.
- Accurate temperature control. Needed to prevent temperature gradients and viscosity changes.
- Inability to handle mixtures of differing densities – many pigments are a mixture of colouring matter and extender/filler.
- Use of X-rays. Some systems use X-rays and, in theory, personnel should be monitored.
- Limited range. Below 2 µm, Brownian motion predominates and the system is inaccurate. Above 50 µm, settling is turbulent and Stokes’ Law again is not applicable.

Equivalent diameter is D.id – frictional drag diameter and D.st – Stokes diameter.

**Electrozone sensing (Coulter Counter)**

This technique was developed in the mid 1950’s for sizing blood cells which are virtually monomodal suspension in a dilute electrolyte. The principle of operation is very simple. A glass vessel has a hole or orifice in it. Dilute suspension is made to flow through this orifice and a voltage applied across it. As particles flow through the orifice the capacitance alters and this is indicated by a voltage pulse or spike. In older instruments the peak height was measured and related to a peak height of standard latex. Hence the method is not an absolute one but is of a comparative nature. Problems of particle orientation through the beam can be corrected for by measuring the area under the peak rather than the peak height. For real, industrial materials such as pigments there are a number of fundamental drawbacks:

- Difficult to measure emulsions. (Sprays not possible!) Dry powders need to be suspended in a medium so cannot be measured directly.
- Must measure in an electrolyte. For organic based materials this is difficult as it is not possible to measure in xylene, butanol and other poorly conducting solutions.
- The method requires calibration standards which are expensive and change their size in distilled water and electrolyte.
- For materials of relatively wide particle size distribution the method is slow as orifices have to be changed and there is a danger of blocking the smaller orifices.
- The bottom limit of the method is set by the smallest orifice available and it is not easy to measure below 2 µm or so. Certainly it is not possible to measure TiO2 at 0.2 µm.
- Porous particles give significant errors as the “envelope” of the particle is measured.
- Dense materials or large materials are difficult to force through the orifice as they sediment before this stage.

Equivalent diameter is dv – volume diameter.

**Microscopy**

This is an excellent technique as it allows one to directly look at the particles in question. So the shape of the particles can be seen and it can also be used to judge whether good dispersion has been achieved or whether agglomeration is present in the system. The method is relatively cheap and for some microscope systems it is possible to use image analysis to obtain lists of numbers (usually to 6 or 8 places of decimals, well beyond the resolution of the technique!). It is interesting to note that 1g of 10 µm particles (density 2.5) contains 760 x 106 particles – all these can never be examined individually by microscopy. However, it is not suitable as a quality or production control technique beyond a simple judgement of the type indicated above. Relatively few particles are examined and there is the real danger of unrepresentative sampling. Furthermore, if a weight distribution is measured the errors are magnified – missing or ignoring one 10 µm particle has the same effect as ignoring one thousand 1 µm particles. Electron microscopy has elaborate sample preparation and is slow. With manual microscopy few particles are examined (maybe 2000 in a day with a good operator) and there is rapid operator fatigue. Again there is the problem of “which dimension do we measure?” Hence there can be large operator to operator variability on the same sample. In combination with diffraction microscopy becomes a very valuable aid to the characterization of particles. Equivalent diameters are projected area diameter da, projected perimeter diameter dp, Feret’s diameter dF, and Martin’s diameter dm.

**Laser diffraction**

This is more correctly called Low Angle Laser Light Scattering (LALLS). This method has become the preferred standard in many industries for characterization and quality control. The applicable range according to ISO13320 is 0.1 – 3000 µm. Instrumentation has been developed in this field over the last twenty years or so. The method relies on the fact that diffraction angle is inversely proportional to particle size. Instruments consist of:

- A laser as a source of coherent intense light of fixed wavelength. He-Ne gas lasers (λ=0.63 µm) are the most common as they offer the best stability (especially with respect to temperature) and better signal to noise than the higher wavelength laser diodes. It is to be expected when smaller laser diodes can reach 600 nm and below and become more reliable that these will begin to replace the bulkier gas lasers.
- A suitable detector. Usually this is a slice of photosensitive silicon with a number of discrete detectors. It can be shown that there is an optimum number of detectors (16 – 32) – increased numbers do not mean increased resolution. For the photon correlation spectroscopy technique (PCS) used in the range 1nm – 1µm approximately, the intensity of light scattered is so low that a photomultiplier tube, together with a signal correlator is needed to make sense of the information.
- Some means of passing the sample through the laser beam. In practice it is possible to measure aerosol sprays directly by spraying them through the beam. This makes a traditionally difficult measurement extremely simple. A dry powder can be blown through the beam by means of pressure and sucked into a vacuum cleaner to prevent dust being sprayed into the environment. Particles in suspension can be measured by recirculating the sample in front of the laser beam.

Older instruments and some existing instruments rely only on the Fraunhofer approximation which assumes:

- Particle is much larger than the wavelength of light employed (ISO13320 defines this as being greater than 40 λ i.e. 25µm when a He-Ne laser is used).
- All sizes of particle scatter with equal efficiencies.
- Particle is opaque and transmits no light.

Equivalent diameters are area diameter da and volume diameter dv following computation in some instruments.

Laser diffraction gives the end-user the following advantages:

- The method is an absolute one set in fundamental scientific principles. Hence there is no need to calibrate an instrument against a standard – in fact there is no real way to calibrate a laser diffraction instrument. Equipment can be validated, to confirm that it is performing to certain traceable standards.
- A wide dynamic range. The best laser diffraction equipment allows the user to measure in the range from say 0.1 to 2000 microns. Smaller samples (1nm – 1µm) can be measured with the photon correlation spectroscopy technique as long as the material is in suspension and does not sediment.
- Flexibility. For example it is possible to measure the output from a spray nozzle in a paint booth. This has been used by nozzle designers, to optimise the viscosity, ∆P and hole size and layout, in order to get correct droplet size. This has found extensive application in the agricultural and pharmaceutical industries. There is now an ASTM standard for sprays using laser diffraction.
- Dry powders can be measured directly, although this may result in poorer dispersion than using a liquid dispersing medium. However, in conjunction with a suspension analysis it can be valuable in assessing the amount of agglomerated material in the dry state.

Liquid suspensions and emulsions can be measured in a recirculating cell and this gives high reproducibility and also allows dispersing agents (e.g. 0.1% Calgon, sodium hexametaphosphate solution for TiO2) and surfactants to be employed to ascertain the primary particle size. If possible the preferred method would be to measure in liquid suspension (aqueous or organics) for the reasons discussed above. - The entire sample is measured. Although samples are small (4-10g for dry powders, 12g for suspensions typically) and a representative sample must be obtained, all the sample passes through the laser beam and diffraction is obtained from all the particles.
- The method is non-destructive and non-intrusive. Hence samples can be recovered if they are valuable. A volume distribution is generated directly which is equal to the weight distribution if the density is constant. This is the preferred distribution for chemical engineers.
- The method is rapid producing an answer in less than one minute. This means rapid feedback to operating plants and repeat analyses are made very easily.
- Highly repeatable technique. This means that the results can be relied on and the plant manager knows that his product has genuinely changed and that the instrument is not “drifting”.
- High resolution. Up to 100 size classes within the range of the system can be calculated on the Malvern Mastersizer.