Determinación del Incremento de volumen

Micromeritics is the science of small particles; a particle is any unit of matter having defi ned physical dimensions. It is important to study particles because most drug dosage forms are solids, solids are not static systems, the physical state of particles can be altered by physical manipulation, and particle charac- teristics can alter therapeutic effectiveness.

Micromeritics is the study of a number of characteristics, including particle size and size distribution, shape, angle of repose, porosity, true volume, bulk volume, apparent density, and bulkiness.

PARTICLE SIZE

A number of techniques can be used to determine particle size and size distributions. Particle size deter- minations are complicated by the fact that particles are not uniform in shape. Only two relatively simple examples are provided for a detailed calculation of the average particle size of a powder mixture. Other methods are generally discussed. The techniques used include the microscopic method and the sieving method.

The microscopic method can include not fewer than 200 particles in a single plane using a calibrated ocular on a microscope. Given the following data, what is the average diameter of the particles?

SIZE OF COUNTED PARTICLES (mm) MIDDLE VALUE mm “d” NO. OF PARTICLES PER GROUP “n” “nd”

40–60 50 15 750 60–80 70 25 1,750 80–100 90 95 8,550 100–120 110 140 15,400 120–140 130 80 10,400 Σn = 355 Σnd = 36,850 Chap06.indd 186 Chap06.indd 186 10/22/2009 8:53:20 PM10/22/2009 8:53:20 PM

PHYSICAL PHARMACY CAPSULE 6.1 CONT. Σ = = = μ Σ av nd 36,850 d 103.8 m n 355

The sieving method entails using a set of U.S. standard sieves in the desired size range. A stack of sieves is arranged in order, the powder placed in the top sieve, the stack shaken, the quantity of the powder rest- ing on each sieve weighed, and this calculation performed:

SIEVE ARITHMETIC MEAN OPENING (mm) WEIGHT RETAINED (g) % RETAINED % RETAINED × MEAN OPENING (mm) 20/40 0.630 15.5 14.3 9.009 40/60 0.335 25.8 23.7 7.939 60/80 0.214 48.3 44.4 9.502 80/100 0.163 15.6 14.3 2.330 100/120 0.137 3.5 3.3 0.452 108.7 100.0 29.232 av (%retained) (ave.size) 29.232 d 0.2923mm 100 100 Σ × = = =

Another method of particle size determination entails sedimentation using the Andreasen pipet, a special cylindrical container from which a sample can be removed from the lower portion at selected intervals. The powder is dispersed in a nonsolvent in the pipette and agitated, and 20-mL samples are removed over time. Each 20-mL sample is dried and weighed. The particle diameters can be calculated from this equation:

i e 18h d ( ρ)gt η = ρ − where

d is the diameter of the particles,

h is the height of the liquid above the sampling tube orifi ce, η is the viscosity of the suspending liquid,

ρi – ρe is the density difference between the suspending liquid and the particles, g is the gravitational constant, and

t is the time in seconds.

Other methods of particle size determinations include elutriation, centrifugation, permeation, adsorp- tion, electronic sensing zone (the Coulter counter), and light obstruction. The last includes both standard light and laser methods. In general, the resulting average particle sizes by these techniques can provide the average particle size by weight (sieve method, light scattering, sedimentation method), and the average particle size by volume (light scattering, electronic sensing zone, light obstruction, air permeation, and even the optical microscope).

ANGLE OF REPOSE

The angle of repose is a relatively simple technique for estimating the fl ow properties of a powder. It can easily be determined by allowing a powder to fl ow through a funnel and fall freely onto a surface. The height and diameter of the resulting cone are measured and the angle of repose is calculated from this equation:

tan q = h/r where

h is the height of the powder cone and r is the radius of the powder cone.

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PHYSICAL PHARMACY CAPSULE 6.1 CONT.

EXAMPLE 1

A powder was poured through the funnel and formed a cone 3.3 cm high and 9 cm in diameter. What is the angle of repose?

tan θ = h/r = 3.3/4.5 = 0.73 arc tan 0.73 = 36.25°

Powders with a low angle of repose fl ow freely, and powders with a high angle of repose fl ow poorly. A number of factors, including shape and size, determine the fl ow properties of powders. Spherical parti- cles fl ow better than needles. Very fi ne particles do not fl ow as freely as large particles. In general, particles in the size range of 250 to 2,000 μm fl ow freely if the shape is amenable. Particles in the size range of 75 to 250 μm may fl ow freely or cause problems, depending on shape and other factors. With most particles smaller than 100 μm, fl ow is a problem.

POROSITY, VOID, AND BULK VOLUME

If spheres and the different ways they pack together are used as an example, two possibilities arise. The closest packing may be rhombus-triangle, in which angles of 60° and 120° are common. The space between the particles, the void, is about 0.26, resulting in porosity, as described later, of about 26%. Another packing, cubical, with the cubes packed at 90° angles to each other, may be considered. This results in a void of about 0.47, or a porosity of about 47%. This is the most open type of packing. If particles are not uniform, the smaller particles will slip into the void spaces between the larger particles and decrease the void areas.

Packing and fl ow are important, as they affect the size of the container required for packaging, the fl ow of granulations, the effi - ciency of the fi lling apparatus for making tablets and capsules, and the ease of working with the powders.

The characteristics used to describe powders include porosity, true volume, bulk volume, appar- ent density, true density, and bulkiness. The photo is a tapped density tester.

Porosity is

Void × 100

This value should be determined experimentally by measuring the volume occupied by a selected weight of a powder, V_bulk. The true volume, V, of a powder is the space occupied by the powder exclusive of spaces greater than the intramolecular space.

Void can be defi ned as

bulk bulk

V V

V −

Tapped density tester. (Courtesy of Varian Inc.)

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PHYSICAL PHARMACY CAPSULE 6.1 CONT. therefore, porosity is bulk bulk V V 100 V − _×

and the bulk volume is

True volume + porosity

APPARENT DENSITY, TRUE DENSITY, AND BULKINESS

The apparent density, ρ_a, is

bulk Weight of the sample

V

The true density, ρ, is

Weight of the sample V

The bulkiness, B, is the reciprocal of the apparent density, B = 1/ρa

EXAMPLE 2

A selected powder has a true density (ρ) of 3.5 g/cc. Experimentally, 2.5 g of the powder measures 40 mL in a cylindrical graduate. Calculate the true volume, void, porosity, apparent density, and bulkiness. True volume:

Density mass(weight) / volume

Volume mass(weight) / density

2.5 g/ (3.5 g/ cc) 0.715cc = = = = Void: − ₌ − ₌ bulk bulk V V 40mL 0.715mL 0.982 V 40mL Porosity: Void × 100 = 0.982 × 100 = 98.2% Apparent density: 2.5 g (P a) 0.0625 g/ mL 40mL = = Bulkiness: = 1 = 1/Pa 16mL/g 0.06265(g/mL)

Powders with a low apparent density and a large bulk volume are considered light, and those with a high apparent density and a small bulk volume are considered heavy.

Chap06.indd 189

size analyzers are automated and linked with computers for data processing, distribution anal- ysis, and printout.

The science of small particles is discussed further in Physical Pharmacy Capsule 6.1, Micro- meritics. Physical Pharmacy Capsule 6.2, Particle These methods and others may be used for the

analysis of particle size and shape. For some materials, a single method may be suffi cient; however, a combination of methods is frequently preferred to provide greater certainty of size and shape parameters (7). Most commercial particle

PHYSICAL PHARMACY CAPSULE 6.2