Particle Size Analysis PDF

Particle size Dr Pooya Davoodi [email protected] 1 Reading Aulton ME, Aulton’s Pharmaceutics: The design and manufacture of medicines, 3rd edition, 2007 Florence AT and Attwood D, Physicochemical principles of Pharmacy, 4th edition, 2006...

Particle size Dr Pooya Davoodi [email protected] 1 Reading Aulton ME, Aulton’s Pharmaceutics: The design and manufacture of medicines, 3rd edition, 2007 Florence AT and Attwood D, Physicochemical principles of Pharmacy, 4th edition, 2006 2  Learning Objectives Understand the importance of particle size in pharmaceutical applications Describe and detail various techniques involved in particle size measurements Outline the principles involved in some particle size measuring techniques Understand the correlation between particle size and sedimentation rate 3 Why is particle size measurement important? Size influences physical properties of pharmaceutical materials – Powder flow, tablet formation It tells us if a process has been successful – Milling of a solid; homogenization of emulsions Gives an indication of product stability – Emulsion droplet size on storage 4 Why is particle size important? Particle size are of importance for both the production of medicines containing particulate solids and the efficacy of such medicines following administration. 5  What is particle size? Here it’s obvious How do we measure non-spherical objects? And what do you do when you have a lot of them of varying shapes and sizes? 6 Equivalent diameters We need to find a way of defining a single size for a particle that may be irregularly shaped To do this we use the concept of equivalent diameter – the diameter of a sphere that is in some unique way similar to the particle in question Simplest to do this by volume Volume Equivalent Diameter (dV) 7  Simplest is Volume Equivalent Diameter (dV) – the diameter of a sphere that has the same volume as the irregular particle – it’s unambiguous, as particles have a well-defined volume Many other ways of specifying equivalent diameters -Surface-volume (equivalent sphere) diameter -Feret’s diameter -Hydrodynamic diameter -Martin’s diameter -Perimeter diameter - Projected area diameter 8 Distributions of particle size Suppose we have many particles, all different? Could measure them one at a time and construct a frequency histogram The height of the band tells us how many particles are within those size limits 9  Mode Median Mean Standard deviation Size with most particles is called the mode (The peak frequency value) Can also define a mean (the weighted arithmetic mean size) and a median (the size with half the particles on each side) – all 3 parameters are not usually the same! The width can be defined as the standard deviation 10 Different ways of representing distributions We understand the histogram but what is the black line? This is the percentage of particles above or below a given size rather than those at a given size – called a cumulative frequency representation It’s the same data drawn in a different way 11 Different ways of representing distributions Typical cumulative frequency distribution integral ⅆ𝐹 dF = f ( x) න ⅆ𝑥 = න𝑓 𝑥 ⅆ𝑥 = 𝐹 𝑥 dx ⅆ𝑥 This is the percentage of particles above or below a given size rather than those at a given size – called a cumulative frequency representation It’s the same data drawn in a different way 12 The distributions can be by number, surface, mass or volume (where particle density does not vary with size, the mass distribution is the same as the volume distribution) 13  Nominal Aperture Sizes 0 50 100 Sieve analysis 2000 µm 20000.1 µmg 1410 µm 14101.2 µmg 1000 µm 10006.6 µmg 710 µm 22.0 710 µmg 500 µm 49.5 500 µmg 350 µm 79.2 350 µmg Axis Title 250 µm 92.4 250 µmg 180 µm 79.2 180 µmg Sieve stack 125 µm 49.5 125 µmg 90 µm 22.0 90 µmg 60 µm 606.6 µmg 45 µm 451.2 µmg PAN 0.1 g PAN 14 Ground Salt – Sieve stack 100 90 80 70 Blue line mass of salt Mass of ground salt 60 Vertical lines – sieve sizes 50 40 30 20 10 0 0 500 1000 1500 2000 2500 Mesh size (microns) 15 Ground Salt – Sieve stack 100 90 Blue line Sieve sizes Mass of ground salt 80 mass of salt 70 factor of 60 2 50 Vertical lines – 40 sieve sizes 30 20 10 0 1 10 100 1000 10000 Mesh size (microns) Is a lognormal distribution! 16 COMMON METHODS OF DISPLAYING SIZE DISTRIBUTIONS Normal distribution (Gaussian distribution) Probability density function 1 𝒙−𝜇 2 𝑦= exp[− ] 𝜎 2𝜋 2𝜎 2 Don’t need to remember this! 𝝁 = mean 𝝈 = standard deviation 𝜋 = 3.14159 𝑒𝑥𝑝(x) = exponential function (𝑒 𝑥 ) 𝑒 = 2.71828 17 Normal distribution Probability density function 𝐊𝐞𝐲 𝐝𝐞𝐬𝐜𝐫𝐢𝐩𝐭𝐨𝐫𝐬 𝝁 = mean 𝝈 = standard deviation 𝐦𝐞𝐚𝐧 ≈ 𝐦𝐨𝐝𝐞 ≈ 𝐦𝐞𝐝𝐢𝐚𝐧 normal distribution with an arithmetic mean of 45 and standard deviation of 12 18 Normal distribution (Gaussian distribution) Log-normal distribution Probability density function 1 𝒍𝒏 𝒙 − 𝜇 2 𝑦= 𝑒𝑥𝑝 − 𝜎 2𝜋 2𝜎 2 Don’t need to remember this! 𝐊𝐞𝐲 𝐝𝐞𝐬𝐜𝐫𝐢𝐩𝐭𝐨𝐫𝐬 𝝁 = arithmetic mean of ln [x] 𝝈 = standard deviation of ln[x] 𝐦𝐞𝐚𝐧 ≠ 𝐦𝐨𝐝𝐞 ≠ 𝐦𝐞𝐝𝐢𝐚𝐧 𝜎2 Average value 𝑚𝑒𝑎𝑛 = 𝑒𝑥𝑝 𝜇 + 2 Mid value 𝑚𝑒𝑑𝑖𝑎𝑛 = 𝑒𝑥𝑝 𝜇 Most frequent value 𝒎𝒐𝒅𝒆 = 𝑒𝑥𝑝 𝜇 − 𝜎 2 20  Size distribution plotted on Size distribution plotted on linear coordinates logarithmic coordinates To check for a log-normal distribution, size analysis data are plotted on lognormal probability graph paper. Using such graph paper, a straight line will result if the data fit a log- normal distribution. 21 NORMAL PROBABILITY PAPER LOG-NORMAL PROBABILITY PAPER 22  Volume Equivalent Diameter The greatest number on the blue line is the “mode value” 100 100% Blue line frequency (not 90 Cumulative frequency 80 80% Volume weighted Mass of ground salt cumulative) 70 60 60% 50 40 40% 30 20 20% 10 0 0% 1 10 100 1000 10000 Mesh size (microns) 50% of the volume weighted cumulative frequency can be used to read off the “median value” 23  Volume Equivalent Diameter 100 100% Blue line frequency (not 90 Cumulative frequency 80 80% Volume weighted Mass of ground salt cumulative) 70 60 60% 50 40 40% 30 20 20% 10 0 0% 1 10 100 1000 10000 Mesh size (microns) The size in microns equivalent to the 90% -10% Volume Weighted Cumulative Frequency is known as “Span” - gives a measure of how wide the distribution is 24 Techniques for measuring particle size Many ways of doing this including: – Sieving – Sedimentation – Microscopy – Light scattering Choice depends on – Applicable size range for sample – Cost – Time taken – Skill required – Precision – Quantity of material needed – How much data they provide (e.g. full distribution or just an average) 25 Sieving Oldest method, inexpensive, widely available Separates fine material from course material by means of a series of woven or perforated surfaces. The proportion of different size particles are recorded and analysed. Sieves are precision-woven square mesh, from steel or bronze wire Smallest size is about 50 m – smaller particles don’t pass through readily, fine meshes are easily damaged and clogged Method defines a ‘sieve equivalent diameter’ – the size of the sphere which will pass through the square hole 26  Standard size sieves stacked into a ‘nest’ of decreasing mesh size – bottom is a closed tray (pan) Sample put in top and shaken - particles fall through until mesh size is too small – at which point the particles will be retained When shaking is completed, the amount of particles in each sieve is then weighed Since the length of the particle does not hinder its passage through the sieve apertures (unless the particle is extremely elongated), the sieve diameter is dependent on the maximum width and/or maximum thickness of the particle. 27 www.tpub.com/.../engine/14080/css/14080_127.htm Errors in sieving Errors are readily visualised with sieving. – Sieve holes may vary in size due to manufacture or damage – Powder may coat the wires leading to sieve apertures being reduced – Particles may be cohesive – stick together so that they don’t pass through the mesh – Vibration from shaking may damage the particles leading to erroneous ‘fines’ – Stack may not be shaken for long enough to get particles to their final sieve – Sieve may be overloaded – only works well for a light load – Particle shape may cause problems (e.g. needle-like particles) 28 Sedimentation - theory The rate at which suspended particles settle has long been used for size measurement The connection between particle size and settling rate or ‘sedimentation velocity’ is given by Stokes’ law v = sedimentation velocity r2 = density of particle r1 = density of fluid 2𝑟 2 𝜌2 − 𝜌1 𝑔 g = acceleration due to gravity 𝑣= r = particle radius 9𝜂 η = fluid viscosity Experimentally ‘v’ is measured and used to calculate the radius and hence particle diameter 29 Sedimentation in practice Settling velocity is not measured directly We can measure the amount of material settled in a particular time (e.g. on to an immersed balance pan) – a sedimentation balance We can measure the amount remaining in suspension vs time by passing a beam of light or x-rays through the sample Because settling can be slow under gravity, instruments usually use centrifugal sedimentation to speed things up - g in Stokes’ law is then replaced by rw2, where r is the centrifuge radius and w the angular velocity 30  Andreasen pipette Sedigraph III Insert sample and push button Remove samples over time (hours/days) and analyse for particle content; calculate size distribution 31  Microscopy and image analysis More sophisticated and expensive technologies Many different types of microscopy (e.g. Light, electron, atomic force etc). Uses very small volume of sample Measures 1 nm – millimetres depending on technique Computer thresholds image then simply counts pixels in each region, constructs histogram, computes statistics as required 10 µm (SEM) (TEM) 32  Disadvantage- Measures relatively few particles Advantage - One of the few methods of getting shape information 33 ImageJ software https://imagej.net/Welcome Download and have a play 34 Particle size analysis by light scattering Light scattering methods now account for the majority of size measurements and instruments Advantages: – Rapid – Easy to use – Wide applicability – Wide size range What is light scattering and how do we use it to measure particle size? 35 Light scattering phenomena If we shine a light through a suspension of particles, we can see its track 36 When light hits a particle, it is scattered in all directions Light If we place a screen opposite the particles, we can see a scattering or diffraction pattern 37 The diffraction pattern is determined by the particle size and shape Given the particle size, we CAN compute the scattering pattern – it’s not a simple calculation! Unfortunately, the opposite is not true – given the scattering pattern, we CANNOT directly compute the particle size! 38 If there are lots of particles in suspension (there usually are!) then we just see the scattering from each one adding up: Light And because the particles are at different sizes, the various patterns usually smear out So, the ring-like patterns on the last 2 slides may not be familiar. 39 So, there are 2 problems: Measuring the diffraction pattern Finding the particle size distribution from it Modern instrument can do both of these. How does it work? 40  Operation of a laser diffraction sizer Particles in a dilute suspension Scattering is measured from many particles Laser light source High intensity Single colour single direction Array detector Similar to digital camera sensor Measures light intensity at each point 41 How does the calculation work? It guesses the size distribution! (The ‘trial’ distribution) It calculates the scattering pattern of the trial distribution It compares the trial distribution scattering pattern with the measured scattering pattern (of course they don’t match at first) It adjusts the trial distribution Recalculates scattering pattern of trial distribution Goes round loop, adjusting trial distribution until its scattering pattern is the same as the measured scattering pattern The size measured is a representation of the hydrodynamic radius, this is defined as the size of a sphere that moves at an identical rate to the particle 42  Particle counting Problem with previous methods is that they tell you the size distribution, but do not tell you how many particles are present. For some applications, the number of particles is critical (e.g. cell counting, or particle contamination in injections). The classic instrument for this is the Coulter Counter or electrical zone sensing (EZS) technique 43  Electrical zone sensing Imagine a beaker containing a dilute suspension of particles Now let’s immerse in this a tube containing a single small hole: tube hole 44  If we now apply suction to the tube, the suspension will stream in through the hole, bringing some particles with it: suction The volume of suspension drawn through the aperture is determined by the suction potential created Now, let’s put an electrode in + - each chamber and add a battery; the only way we could pass a current through the circuit would be if it goes through the aperture: 45 (Note: that we need to dissolve a bit of electrolyte to make it carry a current)  If a particle is sucked through the aperture, it will briefly occlude the hole and stop part of the current (i.e. reducing the electrical current). We can suck a known amount of suspension (e.g. 1 ml or 10 ml) through the aperture and the instrument will count the number of times the current is blocked. From the amplitude of the pulse (current or voltage), we can also measure the size (volume) of each particle, and the instrument can build up a size distribution Sufficiently small apertures (15 micrometres is the smallest commercially supplied aperture) 46 Optical particle counting A similar particle counter can be made using optical sensing of particles Particles in dilute suspension are passed through a narrow beam of light As they pass, they cast a shadow which is measured by a photodetector This is the principle of the Hiac counter which is the method used in pharmacopoeial tests for particles in injections 47  Conclusions This lecture presents a few techniques in particle characterization Some points you might like to think about: – A lot of these techniques need to have the particles in a suspension. What can we do if the particles are water-soluble? – Try to find out the smallest size that can be measured by light diffraction, and why is it a limit (Hint – search the web for instrument manufacturers) – Particle size is really important in inhalation, so review the concepts here after you have done inhaled drug delivery – Get some idea of state of the art by reading manufacturers websites – Malvern Instruments, Sympatec, Micromeritics 48