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

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.

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

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

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

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

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

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

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

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

Liquid Nucleation and Growth Rv 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

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

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

1) PHYSICAL DISPOSITION OF PHASES HM 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

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

2c) MELTING: GENERAL PHASES DISPOSITION5 solid liquid vapor

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

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

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

mechanical equilibrium

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:

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

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

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

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

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

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

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.

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)

(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)

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

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

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.

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

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.

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)

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

c = c/a

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

Cylinder (Xnc = 0.5) l/2

l/2

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

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

Effect of Xnc: SPHERE Tm∞ = 148.7°C

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

DSC analysis

Nanocrystals differential size distribution

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

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

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)

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

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)

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

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

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

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