1. 0) SOLUBILITY OF NANOCRYSTALS 5,6
Liquid
Solid a
a + b
Liquid
a + b a r

2. NANOCRYSTALS MELTING: ENTHALPY and TEMPERATURE
- Surface atoms have fewer inter-atomic bonds with respect to bulk ones.
- They are characterized by higher energy contents.
- Lattice break-down on crystal surface requires less energy with respect to bulk lattice break-down.
H2O E
- This effect becomes relevant only when the number of surface atoms is not negligible compared to that of the bulk atoms (nano-crystals)2.

3. CYCLODEXTRIN POLYMER amorphous drug nanocrystals
Amorphous and nanocrystal drugs are not stable (months, years)
STABILISING AGENT
CYCLODEXTRIN
POLYMER
amorphous drug
nanocrystals

4. AMORPHOUS- NANOCRYSTALS DRUG
DRUG LOADING: solvent swelling 8
DRUG
POLYMER PARTICLES
DRUG SOLVENT
AMORPHOUS- NANOCRYSTALS DRUG
S.A.
ELIMINATION
SWELLING AGENT

5. AMORPHOUS- NANOCRYSTALS DRUG
DRUG LOADING: supercritical carbon dioxide 9
DRUG
POLYMERIC BED
SWELLING
S.C. CO2
AMORPHOUS- NANOCRYSTALS DRUG
37°C; 73 bar
PRESSURE
REDUCTION

6. AMORPHOUS- NANOCRYSTALS DRUG
DRUG LOADING: co-grinding 4
POLYMER PARTICLES
DRUG +
MECHANICAL
ENERGY
AMORPHOUS- NANOCRYSTALS DRUG
MILL

7. BIOAVAILABILITY IMPROVEMENT 10
Wistar Rats; Dose: 11 mg/kg
Cogrinding (180 min)
Vinpocetine:PVP-Cl 1:4 w/w
Physical mixture
5-fold bioavailability enhancement

8. Liquid Nucleation and Growth
2) MELTING: PHYSICAL FRAME 11 Rv
Rsl
Solid
Rlv
Liquid
Vapor
Liquid Nucleation and Growth Rv
Vapor
Rsv
Solid
Rlv
Liquid
Homogeneous Melting
Vapor
Rsl
Solid
Rlv
Liquid
Liquid Skin Melting Rv

9. Rv
Vapor
Rsv
Solid
Rlv
Liquid
Homogeneous Melting
According to this approach (HM), the solid (spherical) crystal is in equilibrium with a liquid (spherical) phase having the same mass and both are embedded in the vapor phase

10. Vapor
Rsl
Solid
Rlv
Liquid
Liquid Skin Melting Rv
This approach (LSM) assumes the formation of a thin liquid layer over the solid core. The thickness of the liquid layer remains constant up to the solid core complete melting

11. Liquid Nucleation and GrowthRv
Rsl
Solid
Rlv
Liquid
Vapor
Liquid Nucleation and Growth
According to this approach (LNG), the liquid layer thickness increases approaching the melting temperature. Accordingly, the solid core melting takes place when the liquid layer thickness is no longer negligible in comparison to the solid core radius

12. 1) GENERAL DISPOSITION OF PHASES 2) PHYSICAL DISPOSITION OF PHASES
2b) MELTING: MATHEMATICAL MODEL 5,6
CENTRAL PROBLEM IS THE DETERMINATION OF THE PROPER EXPRESSION OF THE SYSTEM INTERNAL ENERGY U
solid
liquid
vapor
1) GENERAL DISPOSITION OF PHASES
Vapor
Solid
Liquid
2) PHYSICAL DISPOSITION OF PHASES

13. 2) GENERAL DISPOSITION OF PHASES
solid
liquid
vapor
dUl
dUv
dUs
dUlv
dUls
THERMODYNAMIC EQUILIBRIUM CONDITIONS

14. 1) PHYSICAL DISPOSITION OF PHASESHM
Vapor
Solid
Liquid
dUlv
dUsv
EQUILIBRIUM CONDITIONS
dUs
dUl
dUv
LNG
dUv
Solid
Liquid
Vapor
dUl
dUsl
dUs
dUlv
LSM
dUv
Vapor
Solid
Liquid
dUl
dUs
dUsl
dUlv

15. AS THE TWO APPROACHES LEAD TO THE SAME CONCLUSIONS, THE
«GENERAL DISPOSITION OF PHASES»
ONE WILL BE DISCUSSED NOW …..
… HOWEVER, MATHEMATICAL DETAILS OF THE
«PHYSICAL DISPOSITION OF PHASES»
CAN BE FOUND IN REF 6

16. 2c) MELTING: GENERAL PHASES DISPOSITION5
solid
liquid
vapor

17. gsl = solid-liquid interfacial tension
constants
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
Solid-liquid surface first curvature
solid-liquid surface second curvature
solid-vapour surface first curvature
solid-vapour surface second curvature
rsl, rsv, rlv
curvature radii
liquid-vapour surface first curvature
liquid-vapour surface second curvature

18. 1) 2) Closed system Pl Pv Young eq. Ps for a pure substance
thermal equilibrium
chemical equilibrium
Remembering that: 1) 2)
Young eq.
for a pure substance Ps Pl Pv

19. Pure substance q = 0 ===>
YOUNG EQUATION 12
glv q
Vapour
gsv
gsl
Solid substrate
Liquid drop
Pure substance q = 0 ===>

20. mechanical equilibrium

21. 1 2 3 2 1 1 3 Considering the Gibbs-Duhem equation
k = 1 ===> only one component (pure substance) 2 1 1 3
From the mechanical equilibrium conditions, it follows:

22. Assuming vl and vs << vv
then:
Assuming vl and vs << vv

23. WORKING EQUATION
Molar terms
Dsm (J/mol K)= sl-ss
Dhm (J/mol)= hl-hs
Mass terms
DHm (J/Kg)= Hl-Hs
DSm (J/Kg K)= Sl-Ss

24. Spherical Crystals (LSM, LNG)Rv
Vapor
Rsl
Solid
Rlv
Liquid
Liquid Nucleation and Growth11
D = Rlv-Rsl >> 0
Liquid Skin Melting11
D = Rlv-Rsl ~ 0

25. SPHERICAL CRYSTALS Tolman equation13:
surface tension (g) dependence on crystal radius Rc
d = molecule diameter/3
SPHERICAL CRYSTALS

26. NO, WE HAVE TO ESTABLISH A RELATION BETWEEN Rsl and Rlv
ARE WE DONE?
NO, WE HAVE TO ESTABLISH A RELATION BETWEEN Rsl and Rlv
A POSSIBLE WAY IS TO RECALL THE CONCEPT ON CRISTALLINE FRACTION Xnc

27. (nano)crystal mass Liquid (amorphous) mass
Xnc = (nano)crystal fraction
(nano)crystal
mass
Liquid (amorphous)
mass Rc
Rlv

28. Working equation for spherical crystals
Zhang equation14 for spherical crystals.
This equation descends from a thermodynamic cycle devoted to the evaluation of the GIBBS energy variation between the state of solid nano-crystals and the state of under-cooled liquid.

29. LIQUID NUCLEATION GROWTH Y ∞
XNC
Rlv ∞
Solid
Liquid
LIQUID NUCLEATION GROWTH
Melting of very few crystals inside a huge amount of
liquid( (amorphous phase)
Rsl Y 1
XNC 1
Rlv
Rsl
Solid
Liquid
Rsl
Rlv
LIQUID SKIN MELTING
Melting of many packed crystals inside a small amount of
liquid( (amorphous phase)

30. (mixture melt. enthalpy)
Iterative determination of Xnc4, 6, 15
Xnc = Xnc1A No
Numerical solution of:
DHmd
(drug melt. enthalpy)
DHmix
(mixture melt. enthalpy)
wd(DHr+DHT) ?
wd(drug mass fraction) 1
Yes
Solution: Xnc, DHmr(Rc), Tmr(Rc)

31. Nanocrystals size distribution
dVc = volume occupied by crystals ranging in [Rc – (Rc+dRc)]
DHmr* = enthalpy of the drug/polymer mixture (J)
DHmr = specific enthalpy of the drug/polymer mixture (J/Kg)
rs = solid drug density (Kg/m3)
Q° = DSC trace (W)
v = DSC heating speed (°C/s)
P = probability of finding a crystal of radius Rc

32. c = c/a b = b/a Parallelepiped crystals (LSM, LNG) SHAPE FACTORS c’’
Solid
Liquid
Vapor b D b’
b’’ a a’
a’’ c c’
SHAPE FACTORS
c = c/a
b = b/a

33. Working equation for parllelepiped crystals. k = f(b, c, Xnc)
Zhang equation14 for parallelepiped crystals.
This equation descends from a thermodynamic cycle devoted to the evaluation of the GIBBS energy variation between the state of solid nano-crystals and the state of under-cooled liquid.

34. Cylindrical crystals (LSM, LNG)
Solid
Liquid
Vapor
L=l*Rsl D
L’= L+2D Rv
Rsl
Rlv D
SHAPE FACTOR: l = L/Rsl

35. Working equation for cylindrical crystals. k = f(l, Xnc)
Zhang equation14 for cylindrical crystals.
This equation descends from a thermodynamic cycle devoted to the evaluation of the GIBBS energy variation between the state of solid nano-crystals and the state of under-cooled liquid.

36. 3) RESULTS: THEORETICAL
NIMESULIDE
(non steroidal antiinflammatory drug)
(crystal cell side = 0.87 nm; Tm∞ = 148.7°C)
Carbon Nitrogen Oxigen Sulphur
Mw = 308.5
Csinf = 10 mg/cm3 (37°C, water)

37. Parallelepiped (square basis, b =b/a = 1, and Xnc = 0.5)
c = c/a c a
b=a

38. c = c/a

39. Parallelepipeds of equal volume Vc = a3 (cube) and different surface Sc
b = 1/c

40. Cylinder (Xnc = 0.5)
l/2

41. l/2

42. l = 2 Cylinders of equal volume Vc = 2pRc3 (cubic cylinder)
and different surface Sc
l = 2
cubic cylinder
(Hc = 2Rc

43. Comparison among SPHERE, CUBE and CUBIC CYLINDER
Xnc = 0.5
SR/V
Sphere = 3
Cylinder = 2
Cube = 3
..Surface tension effects
Tm∞ = 148.7°C

44. Effect of Xnc: SPHERE
Tm∞ = 148.7°C

45. 4) RESULTS: EXPERIMENTAL (SPHERICAL CRYSTALS)
nimesulide + crosslinked polyvinylpyrrolidone co-ground
Ratio 1:3 Co-grinding time: 1, 2 and 4 hours
DSC analysis

46. DSC analysis

47. Nanocrystals differential size distribution

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

49. 6) FINAL CONSIDERATIONS
WHICH RADIUS ARE WE REFERRING TO?
CRYSTAL
CRYSTALLITE r
PARTICLE
CRYSTALS
AMORPHOUS

50. HOW TO EVALUATE CRYSTALLITES SHAPE?
Starting from the crystal unit cell (X-rays data) it is possible determining crystallite shape by means of proper software as, for example, the free WinXMorph 16, 17 …….
NIMESULIDE
….. then, this shape can be approximated by means of the idealized structure shown (sphere, cylinder, parallelepiped)

51. 5) SOLUBILITY Kelvin equation12 Liquid It holds for an ideal solution
a + b a r
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

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

53. 1
Solid drug
nanocrystals
T, P 4
Under-cooled
liquid drug
T, P
isobaric heating
isobaric cooling
Isobaric-isotermic melting 2
Solid drug
nanocrystals
Tmr, P 3
Liquid drug
Tmr, P

54. Dcp = cpl - cps
gd can be evaluated knowing macro-crystal solubility (Xd∞) in the desired solvent and assuming it does not depend on Dhmr and Tmr

55. Nanocrystals solubility dependence on Rnc and Xnc
(Nimesulide: crystal cell side = 0.87 nm)

56. 8) REFERENCES
Medicinal Products for Human Use: Guidelines, Pharmacos 4, Eudralex Collection, 2005, p. 234
C. Lipinski, Poor aqueous solubility: an industry wide problem in drug discovery. Am. Pharm. Rev. 5(2002)
E. R. Cooper, Nanoparticles: a personal experience for formulating poorly water soluble drugs. J. Control. Release 141(2010) 300–302.
N. Coceani, L. Magarotto, D. Ceschia, I. Colombo, M. Grassi, Theoretical and experimental analysis of drug release from an ensemble of polymeric particles containing amorphous and nano-crystalline drug. Chem. Eng. Sci. 71(2012)
Hasa D., Voinovich D., Perissutti B., Grassi G., Fiorentino S. M., Farra R., Abrami M., Colombo I., Grassi M, Reduction of melting temperature and enthalpy of drug crystals: theoretical aspects. Eur. J. Pharm. Sci. 2013, 50,
D. Hasa, B. Perissutti, D. Voinovich, M. Abrami, R. Farra, S. M. Fiorentino, G. Grassi, M. Grassi. Drug Nanocrystals: theoretical background of solubility increase and dissolution rate enhancement”. Chemical and Biochemical Engineering Quarterly, 2014, 28(3), 21-32

57. Huang, W. J. , Sun, R. , Tao, J. , Menard, L. D. , Nuzzo, R. G
Huang, W.J., Sun, R., Tao, J., Menard, L.D., Nuzzo, R.G., Zuo, J.M., Coordination-dependent surface atomic contraction in nanocrystals revealed by coherent diffraction. Nature Materials 7,
Carli, F., Colombo, I., Magarotto, L., Torricelli, C., Influence of polymer characteristics on drug loading into crosspovidone. Int. J. Pharm. 33,
Kikic, I., Lora, M., Cortesi, A., Sist, P., Sorption of CO2 in Biocompatible Polymers: Experimental Data and Qualitative Interpretation. Fluid Phase Equilibria ,
Hasa D., Voinovich D., Perissutti B., Bonifacio A., Grassi M., Franceschinis E., Dall’Acqua S., Speh M., Plavec J., Invernizzi S., Multidisciplinary Approach on Characterizing a Mechanochemically Activated Composite of Vinpocetine and Crospovidone. J. Pharm. Sci. 100,
Nanda K.K., Size-dependent melting of nanoparticles: hundred years thermodynamic model. Pramana Journal of Physics 72,
Adamson, A.W. and Gast, A.P., Physical Chemistry of Surfaces, Wiley, 1997
Tolman, R.C., The effect of droplet size on surface tension. J. Chem. Phys. 17,

58. Zhang, M., Efremov, M.Y., Schiettekatte, F., Olson, E.A., Kwan, A.T., Lai, S.L., Wisleder, T., Greene, J.E., Allen, L.H., Size-dependent melting point depression of nanostructures: nanocalorimetric measurements. Physical Review B 62,
Grassi G., Hasa D., Voinovich D., Perissutti B., Dapas B., Farra R., Franceschinis E., Grassi M. Simulatenous Release and ADME processes of poorly water-soluble drugs: mathematical modelling. Molecular Pharmaceutics, 2010, 7(5),
Kaminsky W. WinXMorph: a computer program to draw crystal morphology, growth sectors and cross sections with export files in VRML V2.0 utf8-virtual reality format. Journal of Applied Crystallography, 2005, 38,
Kaminsky W. From CIF to virtual morphology using the WinXMorph program. Journal of Applied Crystallography, 2007, 40,