Phase Diagrams for Cocrystals with Multiple Stoichiometries

Abstract / Introduction

Cocrystals of pharmaceutical or nutraceutical molecules are considered challenging compounds to scale up by solution crystallization due to the possibility of incongruent dissolution of the components, which can lead to the crystallization of a mixture of solid forms and/or starting materials.  Many factors should be taken into account when considering the solution behavior of cocrystals, particularly during crystallization process development:

  • ˜The equilibrium solubility of a cocrystal in a given solvent system has been shown to be dependent upon the solution concentration of each component1. The diagram below illustrates this concept, in which the solubility of a cocrystal AB (by following the concentration of component A) is plotted against the concentration of component B at a constant temperature.

  • ˜Cocrystal phase solubility diagrams have been demonstrated to be solvent dependent as well as temperature dependent2
  • While techniques such as solvent drop grinding or contact melting have been shown to facilitate cocrystal formation, solution-based crystallization techniques, such as cooling, slurry, or solvent-antisolvent, are more suitable and more commonly-used methods for scale-up.

Finding a solvent system in which the dissolution of the cocrystal is congruent is a critical step for developing an optimal scaleable solution crystallization process to ensure the desired multi-component phase, rather than a mixture of phases, is isolated from the process.

Along with the perceived difficulty in scaling up cocrystals, the stoichiometry of cocrystals is somewhat unpredictable.  Unlike the acids and bases that compose salts, which possess discrete functional groups capable of forming ionic bonds, the components of cocrystals are typically held together by hydrogen bonds or other similar non-ionic interactions, which are more difficult to predict.  In this study, two p-coumaric acid-nicotinamide cocrystals in two different stoichiometric ratios were discovered: 1:1 and 2:1 p-coumaric acid:nicotinamide.

p-Coumaric acid is a nutraceutical compound with antioxidant properties3 that exhibits poor aqueous solubility but is moderately soluble in a variety of organic solvents (e.g. alcohols, ketones, etc.).  Nicotinamide, the amide of nicotinic acid and part of the vitamin B group3, exhibits high aqueous solubility as well as moderate solubility in various organic solvents.

Herein, the ternary phase solubility diagrams for each p-coumaric acid-nicotinamide cocrystal are presented in three different solvent systems: methyl ethyl ketone (MEK), 97:3 (v/v) acetonitrile (ACN):water, and 20:80 (v/v) ethanol (EtOH):water.  The phase solubility diagrams show the equilibrium solution concentration of p-coumaric acid as a function of nicotinamide concentration as well as the solubility of the individual components.  These particular solvent systems were selected to demonstrate the variability in ternary phase solubility diagrams between congruent versus incongruent solvent systems for both stoichiometries.  Computational methods were also employed to illustrate Gibb’s free energy surfaces used in the construction of the phase diagrams.


  • ˜The purpose of this study is to illustrate the various phase solubility diagrams of the 1:1 and 2:1 p-coumaric acid-nicotinamide cocrystals in three solvent systems to exhibit the differences attributed to congruent versus incongruent dissolution of both cocrystals and how those differences relate to cocrystal stoichiometry.
  • Isothermal Gibb’s free energy surfaces are used to rationalize the stability regions for one solution phase and four solid phases for each solvent system.
  • ˜Knowledge of the thermodynamic stability of each cocrystal in each solvent system will facilitate prediction of a scaleable solution crystallization process that will yield the desired cocrystal in a single phase, rather than a mixture of solid phases.

Results and Discussion

Cocrystal Characterization and
Preliminary Solubility Assessments

  • ˜1:1 and 2:1 p-coumaric acid-nicotinamide cocrystals were confirmed to consist of unique crystalline cocrystals of given stoichiometries by XRPD and proton NMR analysis.

XRPD patterns of 1:1 and 2:1 p-coumaric acid-nicotinamide cocrystals compared with as-received nicotinamide and p-coumaric acid starting materials

  • ˜Phase uniformity was confirmed for the 1:1 cocrystal by single crystal analysis and for the 2:1 cocrystal by XRPD indexing.
  • Approximate solubility estimates and preliminary small-scale cooling or slurry experiments in a variety of solvent systems provided background information for the selection of solvent systems in which to build phase solubility diagrams.
    • Solvents were selected based, in part, on the ability to crystallize a given cocrystal in a single phase (to illustrate congruency) or in a mixture of solid phases (to illustrate incongruency).
  • ˜Equilibrium solubility values were measured for p-coumaric acid and nicotinamide as a basis for building the phase diagrams (reported as a range due to the acquisition of data from two different thermodynamic conditions).

  • ˜Mixed solvents (ACN:water and EtOH:water) treated as pseudo-single components
  • ˜Ref. States: G=0 for each component at ambient temperature and pressure
  • ˜Liquid solution free energy surface using 1st-order Redlich-Kister expansion4

  • ˜Solids treated as stoichiometric with no solvent content
  • ˜Tie lines through the solid free energy and tangent to the liquid solution indicate solid solubility loci.  These are unshaded wedge-shaped regions in phase diagrams.
  • ˜Intersections of solubility loci are eutectic points.
  • ˜One eutectic and two solids define three-phase regions, shaded in the phase diagrams.

  • ˜The free energy surfaces were fit by
    • minimizing the sum-of-square-distances from the measured solution compositions to the corresponding solubility curve
    • with respect to the solid free energies of fusion (Gifus/kT) and
    • ˜the solution excess free energy parameters (aij/kT).
  • Solvent systems for multi-gram scale-up of the cocrystals were selected based on the phase diagrams and thermodynamic stability data presented below.


  • ˜ MEK was chosen for solution crystallization of the 1:1 cocrystal
    • Highest 1:1 cocrystal solubility of the studied solvent systems
    • Congruent with respect to the 1:1 cocrystal
    • Incongruent with respect to the 2:1 cocrystal
    • 1:1 cocrystal consistently resulted in a single solid phase from cooling process
    • Successfully produced on ~7 g scale

97:3 ACN:water

  • ˜ 97:3 ACN:water was selected for crystallization of the 2:1 cocrystal
    • Cooling process consistently yielded single phase 2:1 cocrystal
    •  Phase diagram shows congruence with respect to the 1:1 cocrystal
    • 2:1 cocrystal congruence appears to be temperature dependent
      • (slightly) incongruent at ambient temperature
      • (likely) congruent at elevated temperature
    • Seeding was employed to ensure 2:1 cocrystal crystallization
    • Successfully produced on ~8 g scale

20:80 EtOH:water

  • ˜20:80 EtOH:water was not selected for cocrystal solution crystallization
    • Incongruent with respect to both cocrystals, predicted to yield a mixture of solid phases
    • The nicotinamide solubility is not well fit by the phase diagram indicating either the solution model requires higher order or the solubility determination is in error.


  • ˜Cocrystals of p-coumaric acid with nicotinamide were discovered in two stoichiometric ratios, 1:1 and 2:1.
  • Regions of thermodynamic stability for the 1:1 and 2:1 p-coumaric acid-nicotinamide cocrystals in each solvent system are presented via ternary phase diagrams, thus determining congruent or incongruent dissolution for each cocrystal.
  • ˜This information is critical for developing optimal crystallization process conditions for cocrystals of varying stoichiometries to ensure the desired multi-component phase, rather than a mixture of phases, is isolated from the process.
  • For the low-solubility solids considered here, the 1st-order Redlich-Kister expansion is sufficient to model the solution, except perhaps for nicotinamide solubility in EtOH:water.
  • ˜In neat MEK, the 1:1 cocrystal congruently dissolves and was successfully produced on ~7 g scale in a single phase by cooling.
  • ˜In 97:3 (v/v) ACN:water, the 2:1 cocrystal may congruently dissolve at elevated temperature, although dissolution is not quite congruent at ambient temperature.  The 2:1 cocrystal was successfully produced on ~8 g scale in a single phase by cooling.
  • ˜In 20:80 (v/v) EtOH:water, both cocrystals incongruently dissolve and the solubility of p-coumaric acid is limited, indicating that excess nicotinamide is needed to produce each cocrystal as a single phase.

Next Steps

  • ˜Investigation of the phase diagram in 97:3 ACN:water at elevated temperature to confirm congruence for the 2:1 cocrystal upon cooling
  • Retesting of the equilibrium solubility of nicotinamide in 20:80 EtOH:water to determine if the poor fit in the phase diagram is attributable to the solution model or the initial solubility determination
  • ˜Estimation of metastable zone width for each cocrystal in the applicable solvent system to further refine crystallization process conditions
  • ˜Solution crystallization of each cocrystal at ~1 – 2 L (or ~70 – 140 g) scale

Instrumentation and Methodology

  • ˜Equilibrium solubility values were determined for the 1:1 and 2:1 cocrystals by slurrying each cocrystal in an excess of one component for an extended period of time at ambient temperature.  Aliquots of the liquid phase were analyzed by High Performance Liquid Chromatography (HPLC) to measure the concentrations of p-coumaric acid and nicotinamide.  Solid phases before and after slurrying were analyzed by X-ray Powder Diffraction (XRPD).
  • Equilibrium solubility values were determined for the p-coumaric acid and nicotinamide starting materials by slurrying each compound for an extended period of time at ambient temperature and analyzing the liquid phase by HPLC.  The above procedure was repeated, but with the addition of a heating/cooling step prior to the ambient temperature slurry, to obtain the data from two different thermodynamic conditions.
  • ˜Three different solvent systems were used for the above solubility determinations: 20:80 (v/v) EtOH:water, 97:3 (v/v) ACN:water, and MEK.
  • ˜Ambient temperature was ~20 – 25°C.
  • Cooling crystallization experiments were conducted by combining solids of p-coumaric acid and nicotinamide in the applicable molar ratio with the appropriate solvent system (MEK for the 1:1 cocrystal and 97:3 ACN:water for the 2:1 cocrystal), heating to 76 – 78°C with stirring, cooling at 0.2°C/min to the applicable seeding temperature (69-70°C for both cocrystals), holding at the seeding temperature for 30 – 60 min., and cooling at 0.2°C/min to 10°C.
  • Multi-gram crystallization experiments were performed using a Mettler Toledo EasyMax 102 in a 100-mL reactor equipped with an overhead stirrer, temperature probe, turbidity probe, nitrogen purge, and Universal Control Box.  Software employed was Mettler Toledo iControl version 5.1.29.
  • ˜X-ray Powder Diffraction (XRPD)
    • PANalytical X’Pert Pro diffractometer, Cu Ka radiation
    • ˜XRPD indexing performed using X’Pert High Score Plus 2.2a (2.2.1)
  • ˜High Performance Liquid Chromatography (HPLC)
    • ˜Agilent 1100 series liquid chromatograph equipped with UV detection, column temperature control, degasser, quaternary pump, and an autosampler
    • HPLC column, Waters Symmetry C18, 3.5μm, 100mm x 4.6 mm or equivalent
    • ˜Isocratic method using mobile phase consisting of 10 mM sodium 1-octanesulfonate monohydrate in a mixture of 75% water, 25% methanol, and 0.1% phosphoric acid
  • ˜Solution Proton Nuclear Magnetic Resonance Spectroscopy (NMR)
    • ˜Varian UNITYINOVA-400 spectrometer
    • ˜Samples dissolved in DMSO-dcontaining tetramethylsilane (TMS)
    • ˜Spectra referenced to TMS at 0.0 ppm
  • ˜Phase diagrams
    • ˜Parameter optimization using Nelder-Mead simplex algorithm5
    • ˜Calculations performed and output rendered using Wolfram Mathematica version 7.0


  • ˜SSCI’s Analytical Resources department
  • Patrick Wheeler for HPLC support
  • ˜Jared Smit for computational support
  • ˜Dr. Patrick Tishmack and Eyal Barash for their insightful review


  1. Nehm, S., et al. 2006, Crystal Growth & Design, 6, 592-600.
  2. Chiarella, R., et al. 2007, Crystal Growth & Design, 7, 1223-1226.
  3. Wikipedia, the free encyclopedia, (accessed September 2012).
  4. Redlich, A. T., et al. 1952, Chem. Eng. Progr. Symp. Ser. No. 2, 48, 49-61.
  5. Nelder, J. A. and R. Mead 1965, Computer Journal, 7, 308-313.