Equilibration and thermalization of classical systems - IOPscience
Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in...
Transcript of Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in...
![Page 1: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/1.jpg)
Approaches to measure equilibrium (intrinsic) and “transient” solubility, and the
impact on dissolution and membrane transport kinetics.
Lynne S. TaylorPurdue University
![Page 2: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/2.jpg)
Outline
• Thermodynamics of solubility, crystalline and amorphous• Solubility measurement
• Experimental approaches• Media effects• Common issues in measurement
• Supersaturation – defining based on solubility measurements versus thermodynamic considerations
• Dissolution of different solid state forms and controlling factors• Factors impacting membrane transport• Supersaturation evaluation in different media and membrane transport
![Page 3: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/3.jpg)
Solubility – Conventional Definition
Thermodynamically Stable FormSaturated Solution Concentration = X mg/mL
![Page 4: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/4.jpg)
Solubility – extended definition
Saturated Solution Concentration = X mg/mL
Y mg/mLZ mg/mL
Polymorph x
Polymorph y
Amorphous z
![Page 5: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/5.jpg)
What Factors Determine Crystal Solubility?
crystal at MP
heating
liquid at RT
cooling
liquid at MP
melting
crystal at RT
+ solvent
![Page 6: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/6.jpg)
ln𝑎𝑎𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = ln 𝑥𝑥𝛾𝛾 = −∆𝐺𝐺𝑓𝑓𝑓𝑓𝑐𝑐𝑓𝑓𝑓𝑓𝑓𝑓
𝑅𝑅𝑅𝑅
ln 𝑥𝑥 = −∆𝐺𝐺𝑓𝑓𝑓𝑓𝑐𝑐𝑓𝑓𝑓𝑓𝑓𝑓
𝑅𝑅𝑅𝑅− ln 𝛾𝛾
solute-solvent interactionsSolid state properties
)298(01.0log5.0log −−−= fsolidw TPS
Simplified Thermodynamic Description
Yalkowsky’s General Solubility Equation
Jain and Yalkowsky J. Pharm. Sci. 2001
![Page 7: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/7.jpg)
-20
-15
-10
-5
0
5
Ibuprofen Griseofulvin Telaprevir Ritonavir SucroseLn
sol
ubilit
y (m
ole
fract
ion)
LN Xideal/crystallinity
LN (gamma)/Hydrophobicity
Relative Contributions of Crystal Lattice and Hydrophobicity to Aqueous Solubility
![Page 8: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/8.jpg)
Polymorph X
Polymorph Y
Amorphous Z
Concentration Free energy
Changing the Solid State Form Changes Thermodynamic Activity and Solubility
RTG
X
Z
eSS ∆
≈
(Supersaturation)
![Page 9: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/9.jpg)
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70
Atazanavir
TelaprevirRitonavir Warfarin
Obs
erve
d En
hanc
emen
t Rat
io
Predicted Enhancement Ratio
IbuprofenPhenylbutazone
Diclofenac
Griseofulvin
Sorafenib
4x
65x
Amorphous:Crystalline Solubility Ratios
Taylor, L. S.; Zhang, G. G. Z., ADDR. 2016 doi:10.1016/j.addr.2016.03.006
Large ΔGHigh Mpt
Small ΔGLow Mpt
![Page 10: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/10.jpg)
Key Points
• Solubility depends on solid properties • The solubility also depends on the solvent• The solvent does not impact the thermodynamic activity of the
crystal*
*true as long as the solvent does not mix with the crystal, e.g. solvate formation
![Page 11: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/11.jpg)
Membrane flux depends on solute activity not concentration
Twist and Zatz J. Soc. Cosmet. Chem. 1986
Increasing crystal solubility = constant flux
Saturated solutions of methyl parabens in different solvents
Large variations in concentrationSame flux value
Why?
saturated
activity solid = activity solution
3 mg/mL
300 mg/mL
![Page 12: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/12.jpg)
Solubility measurement
• Top down• Early phase solubility• Amorphous solubility• Risks
• Unknown solid form• Solvent effects• True equilibration may not be reached
• Bottom up• Crystalline solubility• Concerns
• Equilibration time• Solid phase at end of experiment• Separation of solid and supernatant• pH
Conc
entr
atio
n
Time
Top down
Bottom up
![Page 13: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/13.jpg)
conc
entr
atio
n
subsaturated (1 phase)
supersaturated(metastable, 1 phase)
Crystal solubility
L-L coexistance
(amorphous solubility)
“Fast” crystallizer
“Slow” crystallizer
Spinodal
time
supersaturated(unstable,2 phase)
LLPS
crystallization
Metastable boundary
Phase Transitions in Supersaturated Solutions
![Page 14: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/14.jpg)
Media Effects
• pH• Ionic strength• Buffer species• Solubilizing components (most commonly micelles)
![Page 15: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/15.jpg)
pH-dependent Solubility –Crystalline Drug
PosaconazolepKas: 3.6 and 4.6
)101( )( pHpKBtot
aSS −+=
Crystalline solubility
![Page 16: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/16.jpg)
pH-dependent Solubility –Amorphous Drug
PosaconazolepKas: 3.6 and 4.6
)101( )( pHpKBtot
aSS −+=
Amorphous solubility
![Page 17: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/17.jpg)
pH Solubility Profiles for Amorphous and Crystalline Posaconazole
![Page 18: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/18.jpg)
Concentration of unionized form as a function of pH
0.27
9.08
33.6x
Supersaturation is ~ 33
![Page 19: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/19.jpg)
Solubilizing Media Components
![Page 20: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/20.jpg)
Some comments about solubility measurement• Magnetic stirrers can grind material. This may reduce particle size and
allow small particles to pass through a filter. • Chemical stability in medium should be checked for equilibration
period.• Separation method should be carefully considered• Ionic strength matters! Keep constant when measuring solubility as a
function of pH.• Check pH and adjust if necessary prior to equilibration point.• Check solid state form of drug in equilibrium with solution
(polymorph, salt, free form etc).
Avdeef A, Fuguet E, Llinàs A, Ràfols C, Bosch E, Völgyi G, Verbić T, Boldyreva E, Takács-Novák K. Equilibrium solubility measurement of ionizabledrugs–consensus recommendations for improving data quality. ADMET and DMPK. 2016 Jun 29;4(2):117-78.
![Page 21: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/21.jpg)
21
Impact of solid state form on dissolution rate
Noyes-Whitney equation: ( )hCDACC
hDA
dtdM s
s
≈−=
Iopanoic acid
• Comparison of intrinsic dissolution rates of three solid forms: two polymorphs and amorphous solid
• IDRs are reflecting (apparent) solubility values of the solids
Stagner & Guillory, 1979, J Pharm Sci
![Page 22: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/22.jpg)
Amorphous Form has a Faster Dissolution Rate than Crystal
0
5
10
15
20
25
0 10 20 30 40 50 60
Itrac
onaz
ole
conc
entr
atio
n µg
/ml
Time (min)
Cryst AmoQM
( )hCDACC
hDA
dtdM s
s
≈−=
Slope of amorphous form ~ 20X crystal
Bhardwaj et al. (2018). Int J Pharm 540(1-2):106-119.
![Page 23: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/23.jpg)
Dissolution of Amorphous Solid Dispersions
23
-5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
0
10
20
30
40
50
60
70
crystalline drug controlled
Crystalline ITZ Amorphous ITZ SD HME
Rel
ativ
e D
isso
lutio
n R
ate
% Polymer
amorphous drug controlled
![Page 24: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/24.jpg)
24
Dissolution rate of drug from an ASD can be much faster than from pure amorphous drug
Itraconazole-PVPVA system0 10 20 30 40 50 60 70 80 90
0
10
20
30
40
50
60
70
crystalline drug controlled
Crystalline ITZ Amorphous ITZ SD HME
Rel
ativ
e D
isso
lutio
n R
ate
% Polymer
amorphous drug controlled
No predictive models for these systems
![Page 25: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/25.jpg)
supersaturated
activity solid < activity solute
S ∝ 𝐶𝐶𝑠𝑠𝑠𝑠𝐶𝐶𝑒𝑒𝑒𝑒
0 2 4 6 8
0.00
0.04
0.08
0.12
0.16
Flux
( µg/
min
)
C/Ceq
Flux ∝ Supersaturation
Supersaturation and Membrane Transport
![Page 26: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/26.jpg)
Defining Supersaturation
eqeqeqeq cc
cc
aaS ≈==
γγ
eqeqccS γγ ≈≈ when only valid is
We can check this relationship by performing flux measurements
![Page 27: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/27.jpg)
Supersaturation (activity based)
J is the diffusive flux across a membrane and a is activity of the solute in the solution.
D is the diffusion coefficient of the solute, h is the thickness of the membrane and γm is the activity coefficient of the solute in the membrane.
y = 0.0715x + 0.2324R² = 0.999
0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60 70 80 90 100
Conc
entr
atio
n (u
g/m
l)
Time (minutes)
Receiver Cell BufferJ = Slope
![Page 28: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/28.jpg)
Impact of Solubilizing Media on Crystalline and Amorphous Solubility
PosaconazoleMwt: 701 g/mol
Log P: 4.6pKa: 3.6 and 4.6
0
5
10
15
20
25
30
35
40
45
Blank Buffer V1 FaSSIF V1 FaSSIF V2 FaHIF Composite-FaSSIF
Solu
bilit
y (μ
g/m
L)
Crystalline Solubility Amorphous Solubility
0
5
10
15
20
25
30
Blank Buffer V1 FaSSIF V1 FaSSIF V2 FaHIF Composite-FaSSIF
Extent of increase in solubility
![Page 29: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/29.jpg)
0
5
10
15
20
25
30
35
40
45
FaSSIF Buffer 1 FaSSIF V1 FaSSIF Buffer 2 FaSSIF V2 FaHIF Composite-FaSSIF
Supe
rsat
urat
ion
ratio
Media
a/a*c/c*
Activity versus Concentration-Based Supersaturation
Flux measurements are similar for the different media. Concentration-based estimates are much lower in solubilizing media
![Page 30: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/30.jpg)
Medium Km/w at crystalline solubility Km/w at amorphous solubilityFaSSIF-V1 13.9 5.3
Composite-FaSSIF 7.4 1.9FaHIF 11.3 1.6
Explanation – Micelle-water Partition Coefficient is not Constant with Solute Concentration
![Page 31: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/31.jpg)
Supersaturation Duration Also Depends on the Medium
0
20
40
60
80
100
120
140
Buffer FaSSIF-V1 FaSSIF-V2 FaHIF
Indu
ctio
n tim
e (m
inut
es)
Posaconazole Atazanavir≈ 2.2 fold increase
≈ 4 fold increase
![Page 32: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/32.jpg)
Summary
• Solubility is dictated by the solid and the solvent properties• Many different values of solubility can be measured depending on
experimental set-up. Which value is important?• Current approach of defining supersaturation in complex medium is
unlikely to be predictive of transport behavior• Better estimates of supersaturation are also vital to understand
crystallization kinetics. Impact of media components on crystallization kinetics are not well understood.
![Page 33: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/33.jpg)
Acknowledgements
• Ahmed Elkhabaz• Dana Moseson• Anura Indulkar• Geoff Zhang• Gao Yi• Tu van Duong• Patrick Augustijns• Joachim Brouwers• Vivek Bhardwaj
• FDA• NSF• AbbVie
![Page 34: Approaches to measure equilibrium (intrinsic) and ... 1-2 Lynne Taylor.pdf• Chemical stability in medium should be checked for equilibration period. • Separation method should](https://reader035.fdocuments.net/reader035/viewer/2022071116/5ffdc792d7cce7158714f4cc/html5/thumbnails/34.jpg)
And for fun – some cool pictures!
Posaconazole crystallized from buffer and FaSSIF-V1(with polymer)
Amorphous posaconazole precipitated in HIF