Particle size analysis -Chapter 3
Importance of PSA Size and hence surface area of particles affect: The rate of drug dissolution and release from dosage forms Flow properties of granules and powders. Proper mixing of granules and powders. Physical stability for suspensions. Grittiness for topical formulation (powder must be impalpable). Irritation of the eyes for ophthalmic suspensions (small particle must be used).
Dimensions When determining the size of large solid usually we need to measure at least three dimensions. When determining the size of a sphere, it is possible to describe the size using one dimension (diameter). If a particles of powder is perfectly spherical, than it is possible to describe the particle size by measuring the diameter of the particle.
Dimensions However, particles are often irregular and not perfectly spherical. Such irregular particles are considered to approximate to a sphere (equivalent sphere), which can then be characterized by determining its diameter. Because the measurement is based on an hypothetical sphere, which represents only an approximation to the true size of the particle, the dimension is called equivalent sphere diameter.
Equivalent sphere diameter It is possible to generate more than one sphere which is equivalent to a given irregular particle shape. Different equivalent diameters constructed around the same particle. (Aulton s 3 rd ed.)
Equivalent sphere diameter
Equivalent sphere diameter The equivalent spherical diameter, relates the size of a particle to the diameter of a sphere having the same surface area or volume or sedimentation rate or other factors. Examples of types of equivalent diameters: Surface diameter (d s ) is the diameter of a sphere having the same surface area as the particle in question. Volume diameter (d v ) is the diameter of a sphere having the same volume as the particle in question. Stokes diameter (d st ) is the diameter of a sphere undergoing sedimentation in a specific medium at the same rate as the asymmetric particle.
Two topics will be covered in this Chapter: 1. Particle size distribution. 2. Methods for particle size analysis.
Particle size distribution A powder population (a bulk of powder) which consists of spheres or equivalent spheres of the same diameter is said to be monodispersed and its characteristics can be described by a single equivalent sphere diameter. However, in pharmaceutical systems this situation is almost never encountered. Most powders contain particles with a range of different equivalent diameters, i.e. they are polydispersed.
Particle size distribution In order to be able to define the size distribution of polydisperse powder samples, the size distribution can be broken down into different size ranges, which can be presented in the form of a histogram (or curve). The histogram presentation allows also to compare the characteristics of two or more polydisperse powder samples.
# of Particles in Each Size Range PSD - Frequency distribution When the number (or weights) of particles lying within a certain size range is plotted against a size range (or mean particle size), a frequency distribution curve is obtained. 60 Such plots give a visual representation of the distribution that an average diameter cannot achieve. 50 40 30 20 10 0 0.75 1.25 1.75 2.25 2.75 3.25 3.75 Mean of Size Range (um)
PSD - Normal distribution The figure shown in the previous slide is representative of a normal distribution: the particles are symmetrically distributed about a central value. The peak frequency value (called mode) separated the normal curve in two identical halves, because the size distribution is fully symmetrical (normal). For normal distribution, mean = median =mode mean average size of a population median size where 50% of the population is below/above mode size with highest frequency
PSD - % Frequency In many cases, rather than plotting the number of particles (or weight), laying within a specific size range, the percent particles (or weight) in each size range (% frequency) can be plotted. Size Range (μm) Mean of Size Range, di (μm) Number of particles in each size range, ni % Frequency (ni/n)*100% 0.50 1.00 0.75 2 1.7 1.00 1.50 1.25 10 8.5 1.50 2.00 1.75 22 18.6 2.00 2.50 2.25 54 45.8 2.50 3.00 2.75 17 14.4 3.00 3.50 3.25 8 6.8 3.50 4.00 3.75 5 4.2 N=Σ ni= 118 100
PSD Number vs Weight distributions Number distributions imply that the data were collected by a counting technique (microscopy, Coulter counter). We are frequently interested in obtaining data based on weight (weight distribution) which can be achieved by using sedimentation or sieving techniques. We can still convert number data (i.e. obtained by microscopy) to weight data given the assumption that the general shape and density of the particles are independent of the size range of the sample.
PSD- Skewed distribution Not all particles populations are characterized by normal size distributions and the frequency distributions of such populations exhibit skewness. In this case, mean median mode.
# of Particles # of Particles Skewed distribution can sometimes be normalized by replotting the equivalent particle diameter using a logarithmic scale. This is often referred to as log-normal distribution. 70 60 50 40 30 20 10 0 PSD- Skewed distribution 0 5 10 15 20 Mean of Size Range, um 70 60 50 40 30 20 10 0 1 10 100 Mean of Size Range, um
PSD- Skewed distribution a) Normal distribution: the mode separates the curves into two symmetrical halves. b) Positively skewed: a frequency curve with an elongated tail towards the higher size range. c) Negatively skewed: a frequency curve with an elongated tail towards the lower size range. d) Bimodal: the frequency curve containing two peaks (two modes).
PSD Cumulative frequency distribution Then, % frequency can then be used to produce the cumulative percent frequency. Cumulative % oversize: The total percent of particles with size higher than the lower limit of each class interval Cumulative % undersize: The total % of particles with size lower than the upper limit of each class interval
PSD Cumulative frequency distribution
PSD - Cumulative frequency distribution The median particle diameter corresponds to the point that separates the cumulative frequency curve into two equal halves, above and below which 50% of the particles lie (point a) Just as the median divides a symmetrical cumulative size distribution curve into two equal halves, so the lower and upper quartile points at 25% (b) and 75% (c) divide the upper and lower ranges of a symmetrical curve into equal parts.
PSD - IQCS Not all particle populations are characterized by symmetrical or normal size distributions and the frequency distributions of such populations exhibit skewness. The degree of skewness can be estimated by determining the interquartile coefficient of skewness (IQCS):
PSD - IQCS IQCS ( c ( c a) a) ( a ( a b) b) a is the median diameter and b and c are lower and upper quartile points. The IQCS can take any value between 1 and +1. If the IQCS is zero then the size distribution is practically symmetrical between the quartile points
Methods of PS analysis 1. Sieve analysis method. 2. Microscopy. 3. Sedimentation in a liquid or gas. 4. Electrical sensing zone method 5. Laser light scattering
1. Sieving method The most widely used method for measuring PSD (simple, cheap, rapid and with little variability). This method uses a series of standard calibrated sieves. Sieves are generally used for grading coarser particles. ISO range (45 1000 microns) Equivalent diameter measured is the Sieve diameter (d A ): the width of the minimum square opening which the particle will pass.
1. Sieving method Sample preparation Sieve analysis is usually carried out using dry powders. For powders in liquid suspension wet sieving can be used. Also for powders which tends to agglomerates during dry sieving, wet sieving can be used.
Equipment 1. Sieving method Sieve analysis uses wire woven stainless steel meshes with known aperture diameters which form a physical barrier to particles. Most sieve analysis use a stack or nest of sieves which has the smallest mesh above a collector tray followed by meshes that become progressively coarser towards the top of the stack of sieves.
1. Sieving method Principle of measurement The sieves are mounted on a mechanical shaker. Powder is loaded on to the coarsest sieve at the top of the assembled stack and the nest is subjected to mechanical vibration. After suitable time the particles that passes through one sieve and retained on the next finer sieve are collected and weighed. Frequently the powder is assigned the size of the screen through which it passes, on which it is retained or the mean of the two values.
Limitations 1. Sieving method Sieving errors would result from a number of variables including sieve loading, intensity and time of agitation. Care must be taken to ensure that the correct techniques are employed. For materials >150 μm, a sieve analysis and particle size distribution is accurate and consistent. However, for material that is finer than <150 μm, dry sieving can be significantly less accurate. Sieve analysis assumes that all particles will be round (spherical). Less spherical particles (e.g. elongated or flat) will give less reliable results. Unsuitable for material that adheres to the sieve or forms clumps.
1. Sieving method Standards for powders based on sieving In order to characterize the particle size of a given powder, the USP uses these standards descriptive terms: very coarse, coarse, moderately coarse, fine, and very fine. These terms are related to the proportion of powder that is capable of passing through the openings of standard sieves.
1. Sieving method Standards for powders based on sieving Very coarse (No. 8): All particles pass through a No. 8 sieve and not more than 20% pass through a No. 60 sieve. Coarse (No. 20): All particles pass through a No. 20 sieve and not more than 40% pass through a No. 60 sieve. Moderately coarse (No. 40): All particles pass through a No. 40 sieve and not more than 40% pass through a No. 80 sieve. Fine (No. 60): All particles pass through a No. 60 sieve and not more than 40% pass through a No. 100 sieve Very fine (No. 80): All particles pass through a No. 80 sieve. There is no limit to greater fineness.
Microscopy 2. Microscopy Equivalent diameter: d a, d p, d F, d M can be determined Range of analysis: Light microscope: 1-1000 microns Scanning electron microscope (SEM): 0.05-1 microns Transmission electron microscope (TEM): 0.001 0.05 microns
2. Microscopy Equivalent diameter d p : perimeter diameter is based on a circle having the same perimeter as the particle. d a : projected area diameter is based on a circle of equivalent area to that of the projected image of a particle;
2. Microscopy Equivalent diameter: d F : Feret s diameter is the distance between two parallel tangents to the projected particle perimeter. d M : Martin s diameter is the is the length of a line that divides a randomly oriented particle into two equal areas. d F, d M are diameters which are averaged over many different orientations to produce a mean value for each particle diameter. d M corresponds to the dotted lines
2. Microscopy Light microscopy - procedure A suspension, diluted or undiluted, is mounted on a slide and placed on a mechanical stage. The microscope eyepiece is fitted with a micrometer by which the size of the particles can be estimated. The field can be projected onto a screen where the particles are measured more easily.
2. Microscopy Disadvantages 1. The number of particles that must be counted (300-500) to obtain a good estimation of the distribution makes the method slow and tedious. 2. The diameter is obtained from only two dimensions of the particle: length and breadth. No estimation of the depth (thickness) of the particle is ordinarily available. (E.g. for a flaky particle the size measurement might be overestimated).
2. Microscopy Advantage Microscopic examination of a sample should be undertaken even when other methods of particle size analysis are available, because the presence of agglomerates and particles of one or more than one component can be detected properly by microscopy but overlooked by other methods.
3. Sedimentation method Equivalent diameter: d st (Stokes diameter) Stokes equation: v h t d 2 st s 0 18 g d st ( 18 s h o) gt d st = (Stokes diameter) h = height or sedimentation distance η = viscosity of the medium ρ s = density of the particles ρ o = density of dispersion medium, g = acceleration due to gravity v = rate of settling t = time
3. Sedimentation method The Stoke s equation holds exactly only for spheres falling freely without hindrance and at a constant rate. The law is applicable to irregularly shaped particles of various sizes as long as one realizes that the diameter obtained is a relative particle size equivalent to that of sphere falling at the same velocity as that of the particles under consideration. (i.e. equivalent Stokes diameter). The particles must not be aggregated or clumped together in the suspension since such clumps would fall more rapidly than the individual particles, and erroneous results would be obtained (deflocculating agent may be needed).
3. Sedimentation method Range of analysis: Gravitational sedimentation: 5-1000 microns Centrifugal sedimentation: 0.5-50 microns
3. Sedimentation method Pipette method (Andreasen pipette) The Andreasen apparatus usually consists of a 550-mL vessel. In contains a 10-mL pipette sealed into a ground-glass stopper. When the pipette is in place in the cylinder, its lower tip is 20 cm below the surface of the suspension.
3. Sedimentation method Pipette method (Andreasen pipette) Particle size distribution can be determined by examining the powder as it sediments. The powder is dispersed uniformly or introduced as a thin layer in a fluid. The powder should not be soluble in the fluid, but should be easily dispersed (wetting agent might be added to the fluid).
Balance method 3. Sedimentation method The increase in weight of sedimented particles falling onto a balanced pan suspended in fluid is recorded with respect to time.
3. Sedimentation method Alternative techniques One of the limitations of gravitational sedimentation it is that it is not suitable for particles < 5 microns: in this case the test becomes too slow and less accurate. This can be minimized by increasing the driving force of sedimentation by replacing the gravitational force with a larger centrifugal force (centrifugal sedimentation).
The electrical sensing zone method of particle characterization is also known as Coulter Counter. Equivalent diameter: d V (Volume diameter) d V Diameter of the sphere having the same volume as the particle Range of analysis: 0.1-1000 microns 4. Electric sensing zone method
The change in electrical resistance between the electrodes is proportional to the volume of the particle (volume of the electrolyte solution displaced). 4. Electric sensing zone method Powder samples are dispersed in an electrolyte solution to form a very diluted suspension. The particle suspension is drawn through an orifice where electrodes are situated on either side and surrounded by electrolyte solution. As the particle travels through the orifice, it displaces its own volume of electrolyte solution.
4. Electric sensing zone method
4. Electric sensing zone method This is a very accurate method of measurement, yet very expensive and sophisticated. Moreover dispersions must be sufficiently diluted to avoid the occurrence of coincidence. Coincidence is when more than one particle is present in the orifice at any one time. This may result in two or more particles counted as one and therefore inaccurate measurement (i.e. the equivalent diameter is based on the volume of two particles rather than one).
5. Laser light scattering Low angle light scattering Equivalent diameters: d a and d V Principle of measurement: Scattering of light upon incidence with particle suspended in air or a liquid. Detection range: 0.5 to 1000 microns
Laser light is passed through a dilute suspension of the particles. The light is scattered by the particles, and is detected by detector which measures light intensity over a range of angles. 5. Laser light scattering Low angle light scattering For particles (i.e. >1 µm) that are much larger than the wavelength of light, any interaction with particles causes light to be scattered in a forward direction with only a small change in angle (Fraunhofer diffraction). The angle of scatter is inversely proportional to the particle diameter.
5. Laser light scattering Dynamic light scattering Based on the Brownian movement (random motion of small particles caused by collisions with the smaller molecules of the suspended fluids). It analyses the constantly changing patterns of laser light, scattered by particles in Brownian movement. The rate of change of scattered light can be related to the particle size. Range of analysis: 0.001 1 microns.