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Characterizing Intermolecular Interactions from Self-Diffusion Coefficients to Locate Conditions for Spherical Crystallization

Guangwen He1, Reginald B. H. Tan2, Paul J. A. Kenis3, and Charles F. Zukoski3. (1) Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 S. Mathews Ave., Urbana, IL 61801, (2) Department of Chemical & Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore, 117576, (3) Department of Chemical & Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 S. Mathews Ave., Urbana, IL 61801

Spherical crystallization is a prominent crystal growth process in the pharmaceutical industry that produces crystal agglomerates with desired flowability and compressibility for downstream processing. This process involves quenching a concentrated solution to a point below the solubility boundary and into a region where the solution spontaneously separates into two phases - one concentrated and one dilute in the solute. Crystals nucleate in droplets of the concentrated phase resulting in the desired crystal properties. To gain more insight into the physical chemistry of spherical crystallization, we are interested in understanding the metastable phase behavior of the crystallizing solution, and thus the accessibility of the fluid/fluid phase separation. Recent studies suggest that this phase boundary is submerged below the fluid/solid phase boundary when the interaction energy between solute molecules has an attractive well of which the width is a small fraction of the molecular diameter.

In this study we measure concentration-dependent long-time self-diffusion coefficients Ds for several compounds in solutions using nuclear magnetic resonance (NMR). This concentration dependence can be described in terms of interactions between the molecules weighted by hydrodynamic interactions. In the dilute limit, Ds = D0(1+D2f) where D0 is the infinite dilution diffusivity, D2 is a function of the pair interactions, and fÉnis the solute volume fraction. Comparing measured values of D2 measured as a function of temperature with those predicted for interaction energies of different ranges but fixed strength, we are able to estimate a range and strength of attraction. Given these parameters we can predict the fluid/solid phase boundary and carry out an additional check by comparing with experimental data. Finally using equilibrium phase boundaries we are able to estimate the location of the metastable fluid/fluid phase boundary thus providing estimates of the accessibility of the conditions required for spherical crystallization. The efficacy of this method of locating the position of the fluid/fluid phase boundary will be discussed by comparing predictions with experimental results derived from several compounds.