Supporting Information
Model and Experimental Results of API-Water Slurry Disproportionation
Before tackling the influence of excipients on stability, and the leap towards understanding true solidstate stability, a first step was to model a disproportionation reaction of just API in a water slurry to test
the numerical simulations. Raman spectroscopy and also pH were used as in situ probes to monitor the
disproportionation reaction of A*HCl in a water slurry. Raman spectra were collected using a Rxn1
Raman spectrometer (Kaiser Optical Systems, Inc., Ann Arbor, MI, USA) with 785-nm excitation laser
operating at 200 mW and connected to an immersion probe via fiber optics. Typical Raman spectra for
the freebase and HCl salt are given in Figure S1. A simple two point univariate calibration model was
developed using freebase and HCl slurry standards to aid in quantification of the % freebase (%Fb) in the
slurry. Note that the freebase slurry standards were formed by disproportionation of the HCl salt until
changes in the Raman spectra were no longer evident. The peak at 1580 cm-1 in the Raman spectra was
common to both the HCl salt and freebase and was used for normalization. The % salt was computed as:
𝐴𝑟𝑒𝑎 (1589𝑐𝑚−1 𝑡𝑜 1599𝑐𝑚−1 )
%𝑆𝑎𝑙𝑡 = 0.00494 ∗ 𝐴𝑟𝑒𝑎(1574𝑐𝑚−1 𝑡𝑜 1588𝑐𝑚−1 ) + 0.0046 (S1)
with second derivative and two point baseline subtraction applied. Only 0% and 100% Salt calibration
standards were used in the model and the absolute uncertainty is estimated to be < 20%. The %freebase
in the univariate model was calculated as %Fb = 100% - %Salt.
An experiment to study the disproportionation of A*HCl was initiated by slurrying 4 g A*HCl with 30
ml water. After equilibration, four successive additions of 20 ml of water were added to influence the pH,
and thus the % disproportionation. Figure S2 shows the experimental %Salt and %Fb data determined
from applying the univariate model to the Raman spectra and also the results from a 1st principle model
(smooth lines) discussed in the main article. The initial addition of water is found to result in ~30%
freebase formation and the next two additional shots of water produce ~65% and ~100% freebase. The
fourth addition of water does not show up in the Raman data as all of the salt had been converted to the
freebase after the 3rd addition. Note that as the slurry density is lessened the Raman intensity was also
considerably weakened resulting in decreasing signal to noise as the volume was increased. The fact that
the univariate model predicts ~120% freebase at this stage may also be attributed to the fact that the slurry
standards used to build the model were recorded under more concentrated conditions. Figure S3 shows
the experimental pH and also the simulated pH for the A*HCl experiment described above. After the first
addition of 30 ml water, the pH equilibrates to what should be pHmax due to the presence of both salt and
freebase solids in equilibrium with the solution. Upon spiking in the first 20 ml of water, the pH spikes
up and then equilibrates back to pHmax. This behavior illustrates that more of the salt has dissolved, and
also proportionally, more solid freebase formed. By the third addition of water, the pH no longer
equilibrates back to pHmax, illustrating that all of the solid salt has been converted to freebase, which
agrees with the Raman data shown in Figure S2.
The first principles model predictions for % disproportionation and also the simulated pH are compared
with the experimental data in Figure S2 and Figure S3 respectively. The model predictions are seen to be
in nearly quantitative agreement with experiment. It should be emphasized that there were no adjustable
parameters for freebase yield in the model other than the experimental solubilities and pKa data (which
were not varied from their literature values). The relatively small absolute difference between the
experimental and simulated pH and Raman trends given in the figures could be explained by a small
calibration error of the pH meter or small changes in the solubility and pKa data used in the simulation.
Effect of Activity coefficients on the model predictions
The solubilities of the salts in the current work are reasonably high and thus the saturated solutions would
not necessarily be considered dilute (ideal) and thus there could be an impact of the ionic strength of the
solution on the activity coefficients. To test this hypothesis activity coefficients were estimated for the
mono-salts using the empirical Davies approximation (Davies, C.W. (1962). Ion Association. London:
Butterworths. pp. 37–53) to the Debye-Hückel theory given by:
√𝐼
√
log 𝛾 = −0.51 (1+ 𝐼 − 0.2𝐼) (S2)
I is the ionic strength of the solution (mol/L). For a water slurry experiment the ionic strength was taken
as two times the observed salt solubility. The pKa of API base and salt forming acid were corrected for
the activity coefficients according to:
  H  Fb 
pK a (base)  pK  log  FbH   (S3)
 




0
a
and
  H  Cl
pK a (acid )  pK  log 
  HCl


0
a


 (S4)


The salt solubility product (Ksp) can be written as:


K sp  [ FbH  ][Cl  ] *  FbH  Cl (S5)
Thus
K sp

 FbH  Cl

was actually measured in the solubility experiments at ionic strength of two times the
solubility. Using equation S2 for calculating the activity coefficient, the Ksp could be calculated
independently such that the solubility could be predicted at any given ionic strength.
For neutral species in electrolyte solutions the activity coefficient is often assumed to depend linearly on
ionic strength as defined by the Setschenow equation:
log 𝛾 = 𝐾𝑚 ∗ 𝐼 (S6)
where Km is a Setschenow or “salting out” coefficient. The coefficients depend on the type of electrolyte
present and in an experimental study on caffeine, theophylline, and theobromine, Km was determined to
be in the range of -0.4 to 0.4 (P. Perez-Tejeda et al., J. Chem. Soc. Faraday Trans. 1, 1987, 83, 10291039). Because the nature of the electrolyte in modeling the formulation was not clear, nor the
applicability to the API presented here, simulations were simply performed for Km = -0.1 and 0.1 to see
the effects. The Setschenow equation was applied in the calculation of the activity coefficients of
freebase (γFb) and salt forming acid (γHCl).
In the experiment to determine the freebase solubility, γ was assumed to be 1, however in the modeling of
the formulation the solubility was corrected based on equation S6. In the microhydration environment of
the tablet, the ionic strength is not a well defined quantity. According to the approximation of solution
mediated disproportionation employed in the model, we assume I cannot be less than that due to the
dissolved API salt. Several of the excipients used in the prototypical formulations are electrolytes
however and may influence I. As magnesium stearate and sodium croscarmellose are known to have low
aqueous solubilities, their contribution was neglected. Sodium lauryl sulfate is highly water soluble and
given the water volumes for formulation 1 at 75% RH could contribute to ~1 mol/L of ions to the ionic
strength. Thus simulations were performed for ionic strengths of 1 mol/L.
With the corrected values of pKa and solubility, the model simulations were performed as described in the
article. The simulation results illustrated a very small difference in the predictions of %
disproportionation (less than 2% difference for intermediate levels of disproportionation for B*HCl in
F2, which is a salt with one of the highest solubilities, when comparing the γ=1 assumption and the case
where the ionic strength only comes from the salt. This difference was also observed to correlate with the
salt solubility as expected, thus predictions for salts with lower solubility were influenced even less. The
simulation results comparing the formulation with 1 mol/L ionic strength did show a larger difference in
the predictions. For B*HCl in F2 approximately +/- 10% change in the %disproportionation was
predicted. Given the uncertainties in the treatment of the activities the error introduced could be larger
however in this case all of the molecules are expected to exhibit a similar error, resulting in an absolute
shift in the % disproportionation predictions, but preserving a relative comparison.
Supporting Information Figures
2.5
Intensity (arb. units)
2
A
1.5
1
B
0.5
0
100
300
500
700
900
1100
wavenumber (cm-1)
1300
Figure S1. Typical Raman spectra for A*HCl (B) and freebase (A).
1500
1700
120
100
80
Model (% Salt)
Model (% Fb)
Exp. (% Salt)
Exp. (% Fb)
%
60
40
20
0
-20
0
10
20
30
40
50
60
70
80
Time (min)
Figure S2. Experimental and model simulations of the %A*HCl and %freebase. The steps in the
profiles are due to successive additions of water which result in disproportionation.
1.4
1.3
Model
Experiment
pH
1.2
1.1
1
0.9
0.8
0
10
20
30
40
Time (min)
50
60
70
80
Figure S3. Experimental and model simulations of the pH data for a A*HCl water slurry
experiment. The steps in the profiles are due to successive additions of water which result in some
disproportionation.