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SOLUBILITY AND CRYSTAL RADIUS R nc

SOLUBILITY AND CRYSTAL RADIUS R nc. Liquid. a + b. Liquid. a + b. r. a. a. Solid. NIMESULIDE (non steroidal antiinflammatory drug) (crystal cell side = 0.87 nm). M w = 308.5. Carbon Nitrogen Oxigen Sulphur. C sinf = 10 m g/cm 3 (37°C, water).

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SOLUBILITY AND CRYSTAL RADIUS R nc

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  1. SOLUBILITY AND CRYSTAL RADIUS Rnc Liquid a + b Liquid a + b r a a Solid

  2. NIMESULIDE (non steroidal antiinflammatory drug) (crystal cell side = 0.87 nm) Mw =308.5 Carbon Nitrogen Oxigen Sulphur Csinf =10 mg/cm3 (37°C, water)

  3. NIMESULIDE RELEASE FROM CROSSLINKED PVP (water 37°C) polymer amorphous Csinf nanocrystrals

  4. a + b Liquid r a Kelvin equation9 It holds for an ideal solution gsl = solid-liquid surface tension vs = solid solute molar volume R = universal gas constant T = temperature Csnc = nanocrystal solubility Csinf = macrocrystal solubility

  5. glv Vapour Liquid drop q gsv gsl Solid substrate EQUAZIONE DI YOUNG Per sostanza pura q = 0 ===>

  6. Melting temperature and enthalpy dependence on crystal radius vapor liquid solid

  7. constants liquid-vapour surface first curvature Solid-liquid surface first curvature liquid-vapour surface second curvature solid-liquid surface second curvature solid-vapour surface second curvature solid-vapour surface first curvature gsl = solid-liquid interfacial tension gsv = solid-vapour interfacial tension glv = liquid-vapour interfacial tension Asl = solid-liquid interfacial area Asv = solid-vapour interfacial area For a sphere: Alv = liquid-vapour interfacial area rsl, rsv, rlv curvature radii

  8. Remembering that: 1) Pv Pl Young eq. for a pure substance 2) Ps Closed system thermal equilibrium chemical equilibrium

  9. Rsl Rsv V L S mechanical equilibrium

  10. Considering the Gibbs-Duhem equation 2 1 1 3 1 2 3 k = 1 ===> only one component (pure substance) From the mechanical equilibrium conditions, it follows:

  11. then: Assuming vl and vs << vv

  12. TWO LIMITING CONDITIONS Rnc Rlv Rnc Rnc Rnc Rlv ≈  Rlv ≈ Rsl =Rnc Rnc Rsv does not exist

  13. Rnc Rlv Rnc Rnc Rnc Rlv ≈  Rlv ≈ Rsl =Rnc Rnc Xncr≈ 1 Many nanocrystals Xncr≈ 0 Very few nanocrystals

  14. General equation [M. Zhang, et al., Physical Review B 62 (2000) 10548] Dhmr and Tmr dependence on Rnc and Xcnr requires an iterative solution of these equations assuming a starting value of Xcnr

  15. Numerical solution of: Dhmd (drug melt. enthalpy) Dhmix (mixture melt. enthalpy) wd(Dhr+DhT) 0 wd(drug mass fraction) 1 ? No Yes Solution: Xncr, Dhmr(Rnc), Tmr(Rnc) Xncr =Xncr1A

  16. Nanocrystals size distribution volume occupied by crystals ranging in [Rnc – (Rnc+dRnc)]

  17. Solubility dependence on crystal radius Rnc Liquid(a+b) a fugacity of pure drug in the state of under-cooled liquid at the system temperature (T) and pressure (P) thermodynamic equilibrium drug solubility

  18. 4 Under-cooled liquid drug T, P 1 Solid drug nanocrystals T, P isobaric heating isobaric cooling Isobaric-isotermic melting 2 Solid drug nanocrystals Tmr, P 3 Liquid drug Tmr, P

  19. gd is calculated knowing macro-crystal solubility in the desired solvent

  20. Case study: nimesulide + crosslinked polyvinylpyrrolidone co-ground Ratio 1:3 Co-grinding time: 1, 2 and 4 hours DSC analysis

  21. DSC analysis

  22. Nanocrystals differential size distribution

  23. Dhmr and Tmr dependence on Rnc and Xncr (crystal cell side = 0.87 nm)

  24. (crystal cell side = 0.87 nm) Nanocrystals solubility dependence on Rnc and Xncr

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