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I am looking for some advice regarding particle size distribution (PSD) & how this can be affected by grinding a tablet.

During an assay by HPLC, the method requires grinding of a tablet before dissolving in order to extract the active pharmaceutical ingredient (API) into solution. Of the tablet, the API is only 0.5% m/m of the tablet. I have been told that over grinding the tablets can affect extraction of the API and this is supposedly related to PSD as the API is the smallest particle found in the tablet amongst other excipients. Could someone explain how "over grinding" would cause a detremential effect? Thanks.

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    $\begingroup$ Contrary to HPLC, readers of ChemSE may be not familiar with API and PSD; some are just starting to study chemistry. Thus, if you use less common abbreviations, define them once. If API or PSD are not correctly deciphered, revert the edit. $\endgroup$
    – Buttonwood
    Feb 9, 2021 at 15:31
  • $\begingroup$ If the API is only 0.5% m/m of the total tablet, the active ingredient is not buried as a single grain into the matrix of e.g., potato starch, but finely dispersed. Thus, there is no danger that if you miss the special grain your HPLC would yield a reading of zero. But of course, the finer the grinding, the greater the surface area, which increases the rate the material may dissolve. Add information to add clarity to your question. $\endgroup$
    – Buttonwood
    Feb 9, 2021 at 15:36
  • $\begingroup$ Can you give a reference which suggests that overgrinding reduces extraction? This must be very specific to the tablet matrix (polymeric coating?) etc. $\endgroup$
    – AChem
    Feb 9, 2021 at 16:40
  • $\begingroup$ If there is such an effect, could it be due to the localized heating during grinding? Though the overall sample may not appear to get much warmer, as particles are crushed, they can be heated intensely, leading to decomposition or hastening attack by air. $\endgroup$ Feb 9, 2021 at 18:27
  • $\begingroup$ I agree with DrMoishePippik that localized heating may be part of the answer, but I'd suggest a different reason. It seems that only part of the tablet's contents are dissolved. I'd suspect that the grinding coats the active ingredient with an inactive one that doesn't dissolve. $\endgroup$
    – MaxW
    Feb 9, 2021 at 19:08

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I sort of feel this is actually more of a mathematical/statistical/modeling related question than traditional chemistry.

In essence, one argument is that the sample derived effective API concentration is impacted by possible changes in the particle size distribution due to grinding. Now, there are, in effect, known statistical distributions that address particle size distributions (PSDs), and associated methods to assess parameters of said distributions relating to sample means and variability, and changes thereto. This would seem to be a possible component of the analysis.

As background, I reference Wikipedia on the topic, which importantly notes, to quote:

The PSD of a material can be important in understanding its physical and chemical properties...It affects the reactivity of solids participating in chemical reactions, and needs to be tightly controlled in many industrial products such as the manufacture of printer toner, cosmetics, and pharmaceutical products.

as both surface area (a function of particle size) and concentration influence a reaction.

Also, some detail on PSD distributions:

  • The log-normal distribution is often used to approximate the particle size distribution of aerosols, aquatic particles and pulverized material.
  • The Weibull distribution or Rosin–Rammler distribution is a useful distribution for representing particle size distributions generated by grinding, milling and crushing operations.
  • The log-hyperbolic distribution was proposed by Bagnold and Barndorff-Nielsen[9] to model the particle-size distribution of naturally occurring sediments. This model suffers from having non-unique solutions for a range of probability coefficients.
  • The skew log-Laplace model was proposed by Fieller, Gilbertson and Olbricht[10] as a simpler alternative to the log-hyperbolic distribution.

Now, for example, in the case of the Log-normal distribution, the best estimate of the parent population mean particle size (which here can be used to estimate total concentration) is obtained by working with the log values of the sample particle sizes. Wikipedia on the Log-normal distribution notes that the sample mean (say 'm') and variance (${s^2}$) of these log-transformed values can be employed to more accurately specify the parent population (aka, the Log-normal) mean, which turns out to be ${Exp(m + 0.5*s^2)}$. Note, simply taking the straight average of the observed Log-normals size values is not recommended as a Log-normal random deviate can be very noisy being the ${Exp()}$ of a Normal random deviate, hence the use of a log-transform. The Weibull distribution is another example of where the parent population mean is a function of two of the distribution's to-be-estimated parameters.

Further, it may indeed be the case that excessive grinding affects particle size distribution and reaction rate. However, this should be verified experimentally to determine the potential impact. Perhaps using a proxy, that produces a more readily measurable product (as in gas evolution, or strongly colored compound) may be of assistance.

Finally, this educational source comments on the inter-connection between reaction rate, mass and concentration, noting an exception, to quote:

The concentration of the reactants determines the speed of the reaction. In simple reactions, an increase in the concentration of reactants accelerates the reaction. The more collisions over time, the faster the reaction can advance. The small particles have less mass and more surface area available for the collisions of other particles. However, in other more complex reaction mechanisms, this may not always hold true. This is often observed in reactions involving huge protein molecules with large masses and convoluted structures with reaction sites buried deep within them that are not easily approached by collision particles.

So, still some experimenting required here in an obviously specialty discipline with a possibly large molecule.

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