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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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slide1

SOLUBILITY AND CRYSTAL RADIUS Rnc

Liquid

a + b

Liquid

a + b

r

a

a

Solid

slide2

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)

slide3

NIMESULIDE RELEASE FROM CROSSLINKED PVP

(water 37°C)

polymer

amorphous

Csinf

nanocrystrals

slide4

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

slide5

glv

Vapour

Liquid drop

q

gsv

gsl

Solid substrate

EQUAZIONE DI YOUNG

Per sostanza pura q = 0 ===>

slide7

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

slide8

Remembering that:

1)

Pv

Pl

Young eq.

for a pure substance

2)

Ps

Closed system

thermal equilibrium

chemical equilibrium

slide9

Rsl

Rsv

V

L

S

mechanical equilibrium

slide10

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:

slide11

then:

Assuming vl and vs << vv

slide12

TWO LIMITING CONDITIONS

Rnc

Rlv

Rnc

Rnc

Rnc

Rlv ≈ 

Rlv ≈ Rsl =Rnc

Rnc

Rsv does not exist

slide13

Rnc

Rlv

Rnc

Rnc

Rnc

Rlv ≈ 

Rlv ≈ Rsl =Rnc

Rnc

Xncr≈ 1

Many nanocrystals

Xncr≈ 0

Very few nanocrystals

slide14

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

slide15

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

slide16

Nanocrystals size distribution

volume occupied by crystals ranging in [Rnc – (Rnc+dRnc)]

slide17

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

slide18

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

slide20

Case study:

nimesulide + crosslinked polyvinylpyrrolidone co-ground

Ratio 1:3 Co-grinding time: 1, 2 and 4 hours

DSC analysis

slide23

Dhmr and Tmr dependence on Rnc and Xncr

(crystal cell side = 0.87 nm)

slide24

(crystal cell side = 0.87 nm)

Nanocrystals solubility dependence on Rnc and Xncr