(394c) Effect of Surface Energy Evolution On Particle Nucleation Under Gas Anti-Solvent Precipitation Conditions

We address here the problem of particle nucleation and growth under so-called Gas-Anti-Solvent-Precipitation (GASP-) conditions. This complex environment is of considerable interest for  several currenttechnologies. In the  pharmaceutical industry¹ , which motivated the present work, GASP environment is used to produce the controlled precipitation of an Active Pharmaceutical Ingredient (API) from an organic  solvent, often sprayed into compressed CO₂. Of importance is the ability to predict and control the size distribution of the nucleated particles, with the usual goal of producing narrow distributions of ultrafine particles to facilitate rapid dissolution when administered. Our  theoretical model² is illustrated using the  system: phenanthrene [as API-surrogate] precipitated from liquid toluene using CO₂ as anti-solvent at ca. 60 bar and 298K). Our preliminary results demonstrate the need to  account for  the time evolution of not only the supersaturation (no surprise!) but also the surface energy of the  particle/fluid interface(remarkably, rarely considered).

In our well-mixed single droplet theoretical model² we consider the time-evolution of particle nucleation- and condensation-growth-rates, fully  coupled to the evolving environmental conditions associated with CO₂ uptake  and solution volume change. Particle nucleation rates are conveniently  approximated using Classical Nucleation Theory (CNT), and single  particle  growth rates are  based on a molecular  collision-theory-based kinetic model³, including  Gibbs-Kelvin(-Ostwald) curvature corrections for  recently born particles. However, the numerical method used to solve the Population Balance Equation governing the particle number density distribution  function (NDDF) is not restricted to any  particular choice of rate laws  for nucleation or growth, nor does it presume or restrict the mathematical form of the NDDF. Our model identifies the dependence of the characteristic  particle size and nucleation/growth time scales of the problem as a function of the control parameters in the nearly  isobaric/isothermal  GASP-environment (mainly pressure level and initial API under-saturation).  Besides revealing the relevant dimensionless groups governing  the performance of such systems, we demonstrate the importance of surface energy evolution (SEE) in determining the critical nucleus size, and  associated nucleation rates,  in this variable composition “carrier  fluid”. Our model also reveals the effects of SEE on the ultimate particle NDDF. In this regard, we find that a non-monotonic time evolution of the critical nucleus size can give rise to multi-modal size distribution functions, without the need to involve physical processes other than  particle nucleation. Our results also show that, for the system under consideration (phenanthrene precipitated from  micron-size toluene solution droplets using CO₂ as anti-solvent)  typical particle growth times are considerably longer than the corresponding characteristic nucleation times. In such cases  post-nucleation particle growth introduces only a small correction, and the finally observed precipitated particle NDDF basically betrays the integrated time history of the critical nucleus  size convoluted with log(supersaturation). As a corollary,  controlling the time evolution of  the critical nucleus size (viaboth effective surface energy and supersaturation) enables NDDF-control, which, in some cases, can even  yield (normally undesirable) multi-modal API particle populations.

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 a Yale University, Department of Chemical and Environmental Engineering,
New Haven, CT, 06520-8286, USA

 b Departmento de Física Matemática y de Fluidos, UNED, Madrid, Apdo 60141, 28080, Spain

References:

 1.  Martin, A. and Cocero, MJ, “Micronization Processes With Supercritical Fluids: Fundamentals and Mechanisms”, Advanced Drug Delivery Reviews(Elsevier),vol 60, pp 339-350(2008)

 2. Rosner, DE and Arias-Zugasti, M, “Theory of Pharmaceutical Powder‘Micronization’ Using Compressed Gas Anti-solvent (Re-) Precipitation”; Paper # WG10S1O1, *European  Aerosol Conference; Granada, Spain, September 6, 2012; J Supercritical Fluids(to be submitted) August , 2013

 3. Rosner, DE, “Collision Theory Re-Interpretation of Kinetic Data for the Growth  of Organic Crystal Surfaces; Part  I. Melt Growth; Part
 II . Physical  Vapor–Growth, Part  III. Solution–Growth; Implications for the  Precipitation of Pharmaceuticals in Trans-critical Environments?"; Crystal Growth & Design (ACS), (to be submitted); Summer  2013