PHAR2911 · Pharmaceutics And Professional Practice
Micromeritics & Particle Characterisation
Micromeritics is the science of small particles — their size, shape, surface area and flow — and it is the quantitative core of PHAR2911 pharmaceutics. It matters because making a powder finer raises surface area and speeds dissolution (the Noyes–Whitney lever for poorly-soluble drugs) but worsens flow and dose uniformity, and the written exam rewards you for naming the right diameter, reading a distribution (the median d50), and running the standard calculations (Stokes' law, GSD, Hatch–Choate) cleanly.
What this chapter covers
- 01Particle size as a distribution: mean vs mode vs median (d50)
- 02Six equivalent-diameter definitions (Martin's, Feret's, projected-area, equivalent-volume, Stokes', aerodynamic)
- 03Particle shape & specific surface area
- 04Stokes' law & sedimentation (Andreasen) sizing
- 05Choosing a sizing method by size range
- 06Log-normal statistics: GSD = d84/d50 = d50/d16
- 07Hatch-Choate: count median (CMD) to mass median (MMD)
- 08Powder flow indices (angle of repose, Carr's index, Hausner ratio) & effect on dissolution
Geometric standard deviation from a log-probability plot
- +1Recall the GSD identity for a log-normal powder: GSD = d84/d50 = d50/d16 (the 16% and 84% points sit one σ either side of the median).
- +1Apply the ratio with the read values: GSD = d84/d50 = 90 / 18 = 5.0.
- +1Cross-check via logs: log GSD = log d84 − log d50 = log 90 − log 18 = 1.954 − 1.255 = 0.699; antilog(0.699) = 5.0. Consistent.
- +1State the unit: GSD is a ratio of two sizes, so it is dimensionless (no µm).
Key terms
- Micromeritics
- The science of small particles — the study of the size, shape, surface area and packing/flow of powder particles. Size is reported in micrometres (µm = 10−6 m).
- Polydisperse vs monodisperse
- A polydisperse powder contains a spread (range) of particle sizes; a monodisperse powder has particles all of one size. Real pharmaceutical powders are polydisperse, so size is quoted as a distribution, not a single value.
- Median diameter (d50)
- The size that splits the population 50/50 — half the particles (by the chosen weighting) are smaller and half larger. It is the headline size statistic; distinct from the mean (arithmetic average) and the mode (most frequent size).
- Equivalent diameter
- The diameter of a sphere matched to an irregular particle on some property — e.g. equivalent-volume diameter (same volume, πd³/6), Stokes' diameter (same settling velocity), or aerodynamic diameter (a unit-density sphere with the same settling velocity). Always name which one.
- Geometric standard deviation (GSD)
- The dimensionless measure of spread for a log-normal powder: GSD = d84/d50 = d50/d16. GSD = 1 means monodisperse; larger GSD means a wider size range.
- Hatch-Choate equation
- The bridge between a count-weighted and a mass-weighted distribution of a log-normal powder: ln MMD = ln CMD + 3(ln GSD)², where CMD is the count median and MMD the mass median diameter. Because mass scales as d³, MMD exceeds CMD.
Micromeritics & Particle Characterisation FAQ
Why does smaller particle size speed up dissolution?
For a fixed mass, finer particles expose more total surface area, and dissolution rate is proportional to surface area (Noyes-Whitney). So particle-size reduction (micronisation) is the classic fix for a poorly-soluble drug. The catch: smaller, more cohesive particles flow worse, hurting mixing and dose uniformity — you have to state that trade-off.
What's the difference between the mean, mode and median particle diameter?
Mean = the arithmetic average (Σn_i d_i / Σn_i); mode = the most frequent size (tallest histogram bar); median = d50, the size that splits the population 50/50. Pharmaceutical powders are right-skewed (log-normal), so they separate as mode, then median, then mean (each larger). They coincide only for a perfectly symmetric (normal) distribution.
Why isn't a single particle-size number enough — why name the diameter and method?
Real particles are not spheres, so each instrument reports a different equivalent diameter: a microscope gives a projected-area diameter, sedimentation gives a Stokes' diameter, laser diffraction gives an equivalent-volume diameter. A result like '20 µm' is incomplete unless you state which diameter and which technique produced it.
How do you measure powder flow, and why does it matter?
Flow is judged from the angle of repose (lower cone angle = freer flowing) and from bulk vs tapped density via Carr's compressibility index and the Hausner ratio (a Hausner ratio near 1, and a low Carr's index, indicates free flow). Good flow gives uniform die-fill and consistent tablet/capsule weight and dose; cohesive fines bridge and segregate.
Is the GSD ever expressed in micrometres?
No. GSD is a ratio of two sizes (d84/d50), so it is dimensionless. Attaching 'µm' to a GSD answer is a common error that signals you've confused a size with a spread — the same applies to the Hausner ratio.
Exam move
Treat this chapter as a small toolkit and drill the moves until they are automatic. First, always name the diameter and the method before quoting any size — examiners reward this and it stops careless errors. Then memorise the four calculations and the exact form to use: sphere volume = πd³/6 (solve d³ first, then cube-root once); Stokes' d_st = √[18ηv / ((ρ_s − ρ0)g)] worked entirely in CGS units (g/cm³, poise, cm/s, g = 981) and only converted to µm at the end; GSD = d84/d50 = d50/d16 (dimensionless); and Hatch-Choate ln MMD = ln CMD + 3(ln GSD)². Finally, be ready to write one or two sentences on the central tension — reducing particle size raises surface area and speeds dissolution but worsens flow and dose uniformity — because the conceptual marks hinge on showing you understand the formulation consequence, not just the arithmetic. (Check your unit outline for how this material is assessed.)
