1

Prediction, Crystallization and Stability of Polymorphs

E. Marti 1), E. Kaisersberger 2)

1) APCh Marti Consulting, CH-4054 Basel, Switzerland 2) NETZSCH-Gerätebau GmbH, D-95100 Selb, Germany

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Scope of the Presentation

• Introduction

• Prediction and Crystallization

• Stability

• Examples

• Conclusions

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PhandTA 12

Results of Polymorph Prediction

The Prediction Processes for the Determination of the Crystal Energy Landscape for a given Substance may give the following Suggestions: • Only one single and thermodynamically stable crystal Form is the reality. • Additional metastable polymorphic Forms are also predicted? • An important question is: Is a Borderline in the Energy Difference between the stable and the metastable Polymorphs existing for each individual Substance ?

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5

The Crystal Structure Prediction (CSP)

The Crystal Structure Prediction was initiated in the1980's. J. Maddox‘s outcry was a clear statement that the CSP project was of an unexpected complexity. Nature (London), 335, 201 (1988) The judgment for this development is the following: The methodology for the CSP was constantly improved, however, the expectations were constantly increased.

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Prediction of Polymorphs

• Our contacts in this area were limited to literature as well as to scientists as participants and lecturers of PhandTA Conferences, e.g. J. Dunitz, H.-B. Bürgi, A. Gavezzotti • In 1995, I had to evaluate as head of a project team the impact of the Prediction of Polymorphs for Drug Substances performed by the group of Prof. H. R. Karfunkel, Pharma Division, CIBA-Geigy.

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Prediction of Polymorphs for a given Chemical Substance

• 1999 J.D. Dunitz, ETH Zürich, CH: Too many crystal structures are existing within a narrow lattice band. • 2002 H.-B. Bürgi, University of Bern, CH: None of the applied schemes has succeeded to predict a set of polymorphs which appeared by crystallization.

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Prediction of Polymorphs

At the moment, we usually calculate the lattice energy landscape, an approximation to the real crystal energy at 0 K. Sarah L. Price, Phys. Chem. Chem. Phys., 2008, 10, 1996-2009 The free energy of a crystal lattice is approximated by a temperature independent energy. Martin U. Schmidt, Clariant GmbH, Frankfurt am Main

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Lattice Energy: Estimated Accuracies improved for a Prediction of Polymorphs

Lattice Energy for Drug Substances:

100 to 300 kJ• Mol -1

Accuracy of Calculation afforded for a Prediction:

Better than 1 kJ• Mol -1

Common Errors of theoretical Calculations:

Period around 2008 Period after 20091

up to 8 kJ• Mol -1 lower than 1 kJ• Mol -1 (1)

(1) M. A. Neumann and M.-A. Perrin, CrystEngComm, 2009,11, 2475

Classical Crystallization Procedures to find Polymorphs

• Classical Crystallization for the Search of Polymorphs. • Decision Tree “Investigation Tree the Need to Set Acceptance Criteria for Polymorphism in Drug Substances” see Q6A. Main Question: Are for the Substance under investigation multiple polymorphic Forms existing? • High-Throughput Procedures with Crystallization Arrays, Handling and Detection Systems.

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Is this final Set ever reached? This ever present minimal risks, is this not a gift of Nature?! Statement: W.C. McCrone Disappearing Polymorphs: J.D. Dunitz, J. Bernstein Ritonavir Polmorphs: S.R. Chemburkar et al. … Consecutive Tasks as start of a Development of a new crystalline Drug Substance Determination of a comprehensive chemical and physical Stability for all detected and relevant polymorphic Forms. We restrict our considerations to the transitions of Polymorphs as Function of Temperature.

Assumed the final Set of Polymorphs are found for a given Substance by Crystallization

with or without the support by a Crystal Structure Prediction

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Lattice Energy of Crystals

•  Determinations of the Lattice Energy of Polymorphs: • Partial Pressure Measurements • Solution Calorimetry These Procedures are performed point by point under isothermal or isobaric conditions.

• Determination of the Lattice Energy Differences of Polymorphs by the Heat of Fusion

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13

Partial Pressure Measurements

Partial Pressure Measurements allow to determine the pressure and therefore the activity of a substance. I developed in Ciba-Geigy the Transpiration or Flow method, because the transported mass could easily be purified (e.g. solvents and impurities and finally be analyzed with selected and appropriate analytical methods. See: Vapor Pressure Instrument Netzsch VPA 434 U. Griesser, M.Szelagiewicz, U.Hofmeier, C. Pitt and S. Cianferani, J. Therm. Anal. Cal., 57, (1999) 45

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Partial Pressure Measurements Phenoxyacetic acid: Polymorphic Forms: α and β

Temperature range: 60 to 100°C Mean partial pressure: 10 - 8 Bar T fus,α = 116 T fus,β = 114°C by DSC Results from partial pressure curves: Heat of Sublimation: ∆sub Hα = 153 kJ•mol-1 ∆sub Hβ = 159 kJ•mol-1

Stability information of the enantiotropic system: Transition temperature evaluated: T α, β = 105 °C Activity ratio at 60°C: pα / pβ = 1.34

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Gibbs Free Energy Function1

ΔGi (T) = ΔHi (T) - T• ΔSi (T)

with i = I, II for two known Polymorphs

• The Reference State for the Solid States of the Polymorphs of a given substance is the corresponding molten Phase.

• The higher Approximation affords the Measurement

of the Heat Capacities.

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Gibbs Free Energy Function

Driving Force for Transition

Linear Free Energy Function

III,fus

IIIfus

I,fus

Ifus

IIIfusIfusIII,trsI

TH

TH

HHTΔ

−Δ

Δ−Δ=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−=fus,iTT1iHfusΔs,iΔG

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−Δ+⎟

⎟⎠

⎞⎜⎜⎝

⎛−Δ−=ΔΔ I

fus

IfusIII

fus

IIIfus

IIII

TTH

TTHTG 11,

Transition Temperature

• E.Marti, A. Geoffroy, O. Heiber, E. Scholl, Thermodynamic Stability of Polymorphic Forms of a Substance – 5th. Int. Conf. on Chemical Thermodynamics (1977) Ronneby, Sweden • E. Marti, J. Thermal Anal. Vol. 33 (1988) 37

Non-linear Gibbs Free Energy Functions

Calculation with linear Functions of Heat Capacities of the solid and the liquid state

See Eq. (13) E.Marti, J. Thermal Anal., 33, (1988), 37- 45

 

 

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Linear and Non-linear Gibbs Free Energy Functions: Experimental Data afforded

Linear Gibbs Free Energy Functions: Melting Points and Enthalpies of Fusion for thr Polymorphs Non-linear Gibbs Free Energy Functions: In addition Heat Capacities for: 1. The Polymorphs under investigation 2. The corresponding molten Phase All thermodynamic Data should de determined with a certain Accuracy!

Accuracy Level reached for thermocynamic Data

• Melting Point Calibration of Instrument using high purity Indium. Accuracy better then 0.5 K. • Heat of Fusion Indium is also here the main Calibration Substance. Accuracy better than 0.5 kJ mol-1. • Heat Capacities Calibration Material: Sapphire Ideal Test Substance for a Validation: Polystyrene SRM 705a: Accuracy better than 1% see: E. Marti, E. Kaisersberger and E. Moukhina, J.Therm. Anal. Cal., 85, 2006, 505-525

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Heat Capacity of atactic Polystyrene

Authors Year Method Heat Capacity in Jg-1 K-1

at T in K

250 300 350 Reed, NIST SRM 705a 1990 AC 1.0139 1.2319 1.4556

Karasz et al.

as received 1965 AC 1.0125 1.2275 1.4425

Marsh IUPAC 1987 AC 1.0144 1.2310 1.4556

Abu-Isa, Dole 1965 AC 0.9865 1.2007

ATHAS, Wunderlich 1996 DSC and calc. 1.0026 1.2228 1.4574

Marti, Kaisersberger, et al. SRM 705a

2006 DSC mean of 4 measurements

1.0070 1.2237 1.4403

Marti, Kaisersberger, et al. SRM 705a

2006 TMDSC 0.9995 1.2122 1.4249

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Specific Heat Curves of Polystyrene measured by the DSC 204 Phoenix® from Netzsch, Sample: NIST SRM 705a

Temperature dependence of the specific heat of atactic PS, sample size 19.404 mg, heating rate 2.5 Kmin-1, consecutive runs (1) to (4)

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Linear Functions of the Specific Heat below the Glass Transition for atactic PS from Literature Data and

own Measurements assigned as DSC mean and TMDSC mean

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

220 230 240 250 260 270 280 290 300 310 320 330 340 350

Temperature / K

cp /

(Jg-1

K-1)

DSC mean TMDSC mean Literature mean Lit.mean +/- 2 %

± 2 %

Paracetamol: Specific Heat of Polymorphs Form I and II by Adiabatic Calorimetry

1) E. V. Boldyreva, et. al., JTAC, vol. 77 (2004) p. 620-621, tables 5 and 6 (extract) 23

Paracetamol: Specific heat of Polymorphs form I and II and the Liquid by DSC

1) M. Sacchetti, JTAC, Vol. 63 (2001) p. 348 Fig.2 (average of 4 measurements) 24

Linear Gibbs Free Energy Functions

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Linear and Non-Linear Gibbs Free Energy Functions1)

1) Boldyreva (solid cp); liquid cp from Sacchetti 26

Comparison of Data: Prediction, experimental, Gibbs for Paracetamol Polymorphs I and II

Prediction: M.A. Neumann and M.-A. Perrin, 30th July 2009 Rank as lattice energy rel. to the existing stable Form I: Form Rel. Stability / kJ mol–1 Stability I 0 stable IV – 0.36 predicted, metastable II – 0.7 metastable (lower lattice energy) 1. Experimental: Ph. Espeau et al., J. of Pharm. Sciences, 94, 3, March 2005 Diff. of Enthalpies of fusion ∆fusHII – ∆fusHI = 28.4 - 28.9 = II – I – 0.51 at 169°C 2. Stability relation acc. to Gibbs Free Energy Functions: Cp Data based on E. Boldyreva and M. Sacchetti Tfus and ∆fusH: M. Szelagiewicz et al., J. Therm. Cal., 57, 1999 ∆G = – 0.8 at 157°C Enthalpies of fusion: ∆fusHII = 26.5 ∆fusHI = 28.0 kJ mol–1

Discussion of the Enthalpies of Fusion

• Ph. Espeau et al., J. Pharm. Sciences, 94, 3, March 2005 ∆fusHI = 28.9 kJ mol–1 ∆fusHII = 28.4 kJ mol–1 Values determined by 41 Measurements: 95% confidence intervals for Polymorph II: [28.216; 28.651] Literature values reported for Polymorph II: Range: 26.4 and 33.5 kJ mol–1 • A. Burger and R. Ramberger, Mikrochim. Acta, II (1979) 273 ∆fusHI = 28.1 kJ mol–1 ∆fusHII = 26.9 kJ mol–1

• M. Szelagiewicz et al., J. Therm. Cal., 57, 1999 ∆fusHI = 28.0 kJ mol–1 ∆fusHII = 26.5 kJ mol–1

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Gibbs Free Energy Function: Carbamazepine

Modification (literature values [1,2])

I α

AII

BII

III β

IV

Tfus in °C

190

185

187

176

173

ΔfusH in kJ mol-1

26

-

≈22

31

-

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Gibbs Free Energy Function: Carbamazepine

Stability regions of Carbamazepine form I and form III

-14

-12

-10

-8

-6

-4

-2

0

273 293 313 333 353 373 393 413 433 453 473

Temperature / K

Gib

bs fr

ee e

nerg

y / k

J m

ol -1

Tfus,III =176 °C Tfus,I =190 °C

Ttrs I,III = 118 °C

I

III

III

I

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Thermodynamic Transition Temperature Tα, β for the α (I) and β (III) crystal Modification of

Carbamazepine as enantiotropic System

Tfus, α = 190 °C Tfus, β = 176 °C ∆fusHα = 26.0 kJ mol-1 ∆fusHβ = 31.0 kJ mol-1

Authors and year T α,β in °C Method

• Behme, Brook (1991) 71, 73 Solubility • Behme, Brook (1991) < 150 DSC • Krahn et al. (1987) ≈ 100 DSC • Lowes et al. (1987) ≈ 120 Thermo-Microscopy • Heiber, Marti (1980) ≈ 120 DSC: Gibbs Linear • Marti, Geoffroy (1995) 115 DSC: Gibbs nonlinear • Marti et al. (2002) 118 DSC: Gibbs nonlinear Marti, Geoffroy (2002): Kinetic transitions for both polymorphic forms in suspension in the vicinity of 118 °C executed as proof T α,β

E. Marti, E. Kaisersberger et al., NETZSCH Annual 2000, Selb/D

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Sulfathiazole, DSC

140 150 160 170 180 190 200 210 220 Temperature /°C

0

2

4

6

8

10

DSC /(mW/mg)

201 .4 °C

196 .2 °C

melting of form III crystallization of form I

melting of form II

melting of form I

173 .7 °C

29 .6 J/g 0 .6 J/g

108 .4 J/g

↓ exo

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Sulfathiazole crystal Modifications I and III: non-linear Gibbs Free Energy Functions

-8

-7

-6

-5

-4

-3

-2

-1

0

20 40 60 80 100 120 140 160 180 200 220

Temperature / °C

Gib

bs fr

ee e

nerg

y / k

J m

ol -1

Tf us,I = 201°CTf us,III = 174 °C

Ttrs I,III = 96 °C thermodynamicallystable form I

stable form III

Modification or phase, i

Melting point Enthalpy of fusion Constants for the molar heat capacity Tfus in K ΔfusH in kJ mol-1 ai,0 in J mol-1K-1 ai,1 in J mol-1K-2

I 474 28.9 16.8 0.812 III 447 33.3 55.7 0.732

liquid 226.4 0.598

2)  G. Milosovich, J. Pharm. Sci., 53,5 (1964) 484

Ttrs I,III = 94 ± 3 °C 2)

Ttrs I,III = 96 ± 6 °C 1)

1)  E. Marti, J. Therm. Anal. 33 (1988) 37

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Conclusions

Some Statements and Questions about the results of the Prediction Procedures are as follows: • The Prediction of Polymorphs is now closer at a breakthrough. • What is the Impact of the predicted Crystal Forms on the difficult task of Crystallization? • A main question, not solved today, is the quantitative Impact of the Entropy for the Prediction Procedure? • The Comparison of predicted Structures for well selected Substances with Stability Data should be enlarged in the future. • Too many thermodynamic Data are published which are not determined at the state of the art.

Acknowledgements

•  The authors are extremely thankful to Dr. Thomas Denner and

Dr. Jürgen Blumm, Erich Netzsch GmbH& Co. Holding KG, Selb, Bayern for their support of the presented work. In addition, the authors acknowledge the valuable scientific support of friends and former Coworkers, namely Martin Szelagiewicz, André Geoffroy, Solvias Ltd., Kaiseraugst, Switzerland and Michael Mutz, Novartis Pharma Ltd. Basel, Switzerland.

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Non-Linear Gibbs Free Energy Functions1)

37 1) Boldyreva (solid cp); liquid cp from Sacchetti

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First Approximations

Estimation of the Heat of Sublimation from

molecular parameters, namely the number of valence

electrons (Z) for non-hydrogen-bonding compound:

ΔsubH = 0.84 • Z + 39 kJ•Mol-1 (1) A. Gavezzotti, Acc. Chem. Res. (1994), 27, 309

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Heat of Sublimation: Approximations for Crystals with strong intermolecular Hydrogen Bonds

The mean value for the enthalpy of intermolecular hydrogen bonds is for certain Compounds (acids, alcohols, amides...) approximated by:

ΔhhH : 12 kJ•Mol-1

The number of hydrogen bonds per molecule in the crystal is nhb,

ΔsubH = 0.84 • Z + 39 + nhb • 12 kJ•Mol-1 (2) E. Marti`s enlargement of the Eq. (1) by Gavezzotti

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Heat of Sublimation: Approximations by Relationships between molecular Structure and Crystal Properties

Substance Formula Z nhb ΔsubH

Eq. 1 or 2 kJ•Mol-1

ΔsubH Lit. kJ•Mol-1

Acenaphtene C12H10 58 0 88 82

Adipic acid

C6H10O4

42 42 84

0 4 0

75 123 150

129

Caffeine

C8H10N4O2 58

58 0 2

88 112

115 form I (1)

119 form II at 25 °C

(1) U. Griesser, M. Szelagiewicz et al., J. Therm. Anal. Cal. 57, 1999, 45

Stability Determinations for Polymorphs

A scientific Documentation for the Stability Relation of Polymorphs is preferably anticipated as Functions of Temperature or Pressure. In addition to these thermodynamic functions are a rather great number of physicochemical procedures existing for such an evaluation.

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Lattice Energy by Solution Calorimetry

The lattice energy of a crystalline substance can also be determined by solution calorimetry. The enthalpy of Dissolution must be determined under identical conditions for two samples, namely one which is 100 % crystalline and one which is completely amorphous. The differences of the enthalpies of dissolutions for two polymorphs measured under equal conditions is a mass for the stability relation.

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Polymorphism:

MonotropyTfus

α = 190°CTfus

β = 166°C

-15

-13

-11

-9

-7

-5

-3

-1

0 25 50 75 100 125 150 175 200

Temperature / °C

Gib

bs fr

ee e

nerg

y / k

J m

ol-1

ΔfusHα > ΔfusH

β

ΔfusHα =36 kJ mol-1, ΔfusHβ = 31 kJ mol-1

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Polymorphism:

EnantiotropyTfus

α = 190°CTfusβ = 166°C

Ttrsα,β = 109°C

-14

-12

-10

-8

-6

-4

-2

0

0 25 50 75 100 125 150 175 200

Temperature / °C

Gib

bs fr

ee e

nerg

y / k

J m

ol-1

ΔfusHα < ΔfusHβ

ΔfusHα =23 kJ mol-1, ΔfusHβ = 31 kJ mol-1

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Paracetamol: Gibbs Free Energy values for the modifications I and II

Form I Form II ΔΔGII-ITfus = 169 °C Tfus = 157 °C

ΔfusH = 28 kJmol-1 ΔfusH = 26.5 kJmol-1

Temperature Temperature ΔGs,I ΔGs,II ΔGs,II - ΔGs,I

K °C kJmol-1 kJmol-1 kJmol-1

273 0 -10.706 -9.676 1.030283 10 -10.072 -9.059 1.013293 20 -9.439 -8.443 0.996303 30 -8.805 -7.827 0.979313 40 -8.172 -7.210 0.961323 50 -7.538 -6.594 0.944333 60 -6.905 -5.978 0.927343 70 -6.271 -5.362 0.910353 80 -5.638 -4.745 0.893363 90 -5.005 -4.129 0.875373 100 -4.371 -3.513 0.858383 110 -3.738 -2.897 0.841393 120 -3.104 -2.280 0.824403 130 -2.471 -1.664 0.807413 140 -1.837 -1.048 0.789423 150 -1.204 -0.431 0.772433 160 -0.570 0.185 0.755443 170 0.063 0.801 0.738453 180 0.697 1.417 0.721

Non-Linear Gibbs Free Energy Functions

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Paracetamol: Non-linear Gibbs Free Energy Functions  Temperature

K  

Temperature °C  

Form I delta Gs,I kJ mol-1  

Form II delta Gs,II kJ mol-1  

delta-delta Gs,II-Gs,I

kJ mol-1  

273   0   -7,4476   -6,8120   0,6356  283   10   -7,2448   -6,5989   0,6459  293   20   -7,0038   -6,3480   0,6558  303   30   -6,7267   -6,0614   0,6653  313   40   -6,4153   -5,7410   0,6744  323   50   -6,0716   -5,3885   0,6830  333   60   -5,6970   -5,0057   0,6913  343   70   -5,2933   -4,5942   0,6991  353   80   -4,8618   -4,1553   0,7065  363   90   -4,4039   -3,6905   0,7134  373   100   -3,9211   -3,2011   0,7199  383   110   -3,4144   -2,6884   0,7259  393   120   -2,8851   -2,1536   0,7315  403   130   -2,3343   -1,5977   0,7366  413   140   -1,7630   -1,0219   0,7412  423   150   -1,1724   -0,4271   0,7453  433   160   -0,5632   0,1857   0,7489  443   170   0,0634   0,8155   0,7520  453   180   0,7068   1,4615   0,7547  

442   169   0  430   157   0  

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Carbamazepine, Gibbs free energy functions and their differences ΔΔG = ΔGs,I - ΔGs,III

Form I Form III

Tfus = 190 ° C Tfus = 176 °C

ΔfusH = 26 kJ mol-1 ΔfusH = 31 kJ mol-1

Temperature K

Temperature ΔGs,I ΔGs,III ΔΔG = ΔGs,I - ΔGs,III

°C kJ mol-1 kJ mol-1 kJ mol-1

273 0 -10.670 -12.151 1.481

293 20 -9.546 -10.771 1.225

313 40 -8.423 -9.390 0.967

333 60 -7.300 -8.009 0.709

353 80 -6.177 -6.628 0.451

373 100 -5.054 -5.247 0.193

393 120 -3.931 -3.866 -0.065

413 140 -2.808 -2.486 -0.322

433 160 -1.685 -1.105 -0.580

453 180 -0.562 0.276 -0.838

473 200 0.562 1.657 -1.095

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Sulfathiazole

Melting point Enthalpy of fusion Constants for the molar heat-capacity

Modification orphase

I Tfus in K ΔfusH in kJ mol-1 ai,0 in J mol-1K-1 ai,1 in J mol-1K-2

I 474 28.9 16.8 0.812

III 447 33.3 55.7 0.732

liquid 226.4 0.598