Diversity amidst Similarity: A Multidisciplinary Approach to Polymorphs, Solvates & Phase Relations; Erice, June 2004Dr. Jan-Olav Henck Thermodynamics

Diversity amidst Similarity: A Multidisciplinary Approach to Polymorphs, Solvates & Phase Relations; Erice, June 2004 Dr. Jan-Olav Henck

Thermodynamics in Polymorphism Research

Why consider thermodynamic relationships in polymorphism research?

Why and how to draw an Energy-Temperature Diagram?

Examples


Many analytical tools are used in Polymorphism Research:

Thermomicroscopy Differential Scanning Calorimetry Thermogravimetry Microcalorimetry / Solution Calorimetry (N)IR and Raman Spectroscopy X-Ray diffraction methods Solid-state NMR spectroscopy Pycnometry ..........


...and more or less all the results derived by the methods are used to answer the following questions (I):

How many polymorphs have been crystallized from a given substance? Which crystal form is thermodynamically stable at „ambient conditions“? And how can it be obtained?


...and or more less all the results derived by the methods are used to answer the following questions (II):

If a substance is polymorphic, are the modifications enantiotropically or monotropically related? And in the case of enantiotropism: Where is the thermodynamic transition point?

Which crystal form(s) is (are) thermodynamically metastable, but durable for a significant amount of time to be considered for a (pharmaceutical) product due to special properties?


To avoid erroneous interpretation, it is useful to treat the data as part of a closed system. Is a tool available, that gives the possibility to take the results from different methods and put it in a closed system?

E

Yes, it is the semiquantitative graphical solution of the Gibbs-Helmholtz-Equation: H = G -TS

T

G0 = H0

cp

-S

G = G(T)

H = H(T)

TS


Energy/temperature diagram

Fundamental tool for the solution of complex polymorphic systems.

Graphical semiquantitative solution of the Gibbs-Helmholtz Equation for polymorphic systems.


References

Buerger, M.J. Crystallographic aspects of phase transformations. In Smoluchowski, R., Mayer, J.E. and Weyl, W.A. (eds.), Phase transformation in Solids, John Wiley and Sons, New York, 1951, pp. 183-211.

Burger, A. and Ramberger, R. On the polymorphism of pharmaceuticals and other molecular crystals. I: Theory of Thermodynamic Rules. Mikrochim. Acta II (1979) 259-271.

Burger, A. and Ramberger, R. On the polymorhism of pharmaceuticals and other molecular crystals. II: Applicability of Rhermodynamic Rules. Mikrochim. Acta II (1979) 273-316.

Grunenberg, A., Henck, J.-O. and Siesler, H.W. Theroretical and practical application of energy/temperature diagrams as an instrument in preformulation studies of polymorphic drug substances. Int.J.Pharm. 129 (1996)147-158.


Essential thermodynamic background (Approximations)

Heat Capacity and Enthalpy Each crystal form has its own heat capacity, which is a function of the enthalpy H and the temperature T. Cp

= (H / T)p

Solids show low compressibility. The heat capacity of solids at constant volume and constant pressure are about the same.

The heat capacity increases with increasing temperature since T and H are always positiv.

The H isobars of two modifications are parallel. They do not intersect. Their distance (trH, transition enthalpy) is directly

measurable (DSC).

There are no lattice vibrations of ideal crystals at absolute zero. The heat capacity at 0 K is zero.


Enthalpy isobars

Two modifications and the melt

Temperature [K]

Energy

0

Enthalpy(H)

cp

HI

HII

liq

mHI

mHII

trHII-I

mp II

tr, III

mp I


Essential thermodynamic background (Approximations)

Gibbs Free Energy and Entropy

At 0 Kelvin G = H.

The Entropy is the partial derivative of the Free Enthalpy and the Temperature. (G / T)p = -S.

Since S is always positive, G decreases with increasing temperature.

The G Isobars of two crystal forms converge and never intersect twice.

The relationship between the Enthalpy H and the Free Enthalpy G is defined by the Gibbs-Helmholtz Equation.


Free Enthalpy isobars

Two polymorphs and the melt

Temperature in K

Energy

0 K

Free Energy (G)

-S

G

G II

G I


The relative position of the G-Isobars of different modifications can be determined by solubility experiments.


I

IIsIsII m

mTRG ln)()(

Essential thermodynamic background

mII: saturation solubility of mod.II in a given solventmI: saturation solubility of mod.I in the same (as for mod.II) given solvent




Temperature in K

Energy

0 K

Free Energy (G)

-S

G

G II

G I

Zoom In




Temperature in K

Energy

0 K

Free Energy (G)

G II

G I

GT2

GT3

GT1


Enantiotropism vs Monotropism

Phase transitions of solids can be thermodynamically reversible or irreversible. Modifications, which transform

reversibly without passing the liquid or gaseous state are calld enantiotropic polymorphs. If the modifications

are not interconvertable under these conditions, the system is monotropic.


Enantiotropism

Temperature [K]

Energy

0

IH

IIH

G IIG I

mp IItr, III

trHII-I

mHII

mHI

mp I

Mod.I Mod.II


heating

cooling

endo

Mod.II Mod.I

Mod.II Mod.I


Monotropism

Temperature [K]

Energy

0

IIH

IH

G IIG I

mp II

trHII-I

mHI

mHII

mp I

Mod.II Mod.I


Phase diagram vs Energy/Temperature diagram

Henck, J.-O., Kuhnert-Brandstätter, M. J.Pharm.Sci. 88 (1999) 103-108


Burger-Ramberger RulesHeat-of-fusion rule

If the higher melting form has the lower heat of fusion the two forms are most probable enantiotropic

otherwise they are monotrotropic

Power Compensation DSC


Burger-Ramberger RulesHeat-of-transition rule

If an endothermal transition is observed at some temperature it may be assumed that there is a transition point below it, i.e. the two forms are related enantiotropically.


Burger-Ramberger RulesHeat-of-transition rule

If an exothermal transition is observed at a given temperature it may be assumed that there is no transition point below it, i.e. the two forms are related monotropically, (or the transition temperature is higher).


Burger-Ramberger RulesDensity and Infrared rule

If a modification has a lower density than another one, then it may be assumed that at absolute zero this crystal form is less stable.

If the first absorption band in the infrared spectrum of a hydrogen-bonded molecular crystal is higher for a modification than for the other one, that form may be assumed to have the larger entropy.


Data Monotropism Enantiotropism< tp > tp

Heat oftransition

exothermic exothermic endothermic

Heat offusion

I > II II > I

Heat capacity II > I I > IIEntropy II > I I > IIEntropy offusion

I > II II > I

Solubility(in a givensolvent)

II > I I > II II > I

Density I > II II > IPhysicalstability

I > II II > I I > II

Mod.I: higher melting formMod.II: lower melting form< below the thermodynamic transition point> above the thermodynamic transtion point

Enantiotropism vs Monotropism


Example: Polymorphism of Nimodipine1

1 Grunenberg, A., Keil, B. and Henck, J.-O. Int. J. Pharmaceutics 118 (1995) 11-21.

Mod.I Mod.IIMelting point [°C] 124 116Heat of fusion [kJ mol-1] 39 46True density [g cm-3] 1.27 1.30Calculated density Xray [g cm-3] 1.271 1.303 Solubility in water at 25°C [mg/100mL] 0.036 0.018

Two modifications, which can be obtained in macroscale at room temperature showing the following data:


Nimodipine

Temperature [K]

Energy

0

IH

IIH

G IIG I

mp IItr, III

trHII-I

mHII

mHI

mp I

?


Where is the thermodynamic transition point?

and

Using the following equation Tp can be estimated:

Yu, L., J. Pharm. Sci. 84 (1995) 966-974; Henck, J.-O., Ph.D.Thesis 1996

k = 0.005


Example: Polymorphism of Nimodipine1

Mod.I Mod.IIMelting point [°C] 124 116Heat of fusion [kJ mol-1] 39 46

Tpcalc. = 82 °C

Tpexp. = 88 ± 8 °C (by slurry conversion experiments)


Nimodipine

Temperature [K]

Energy

0

IH

IIH

G IIG I

mp IItr, III

trHII-I

mHII

mHI

mp I

~88°C


2 Modifications

Mod.I - Mod.II E or M

3 Modifications

Mod.I - Mod.II E E E M M E M MMod.II - Mod.III E E M M E M E MMod.I - Mod.III E M M M E E M EG-isobar intersections 3 2 1 0 2 2 1 1

?

E : EnantiotropismM : Monotropism


Temperature [K]

Energy

0

IH

IIIH

G IIIG I

mp IItr, III mp I

liqH

Mod.I - Mod.II MMod.II - Mod.III MMod.I - Mod.III E

GII

X


Temperature [K]

Energy

0

IH

IIIH

G IIIG I

mp IItr, III mp I

liqH


GII

X


Temperature [K]

Energy

0

IH

IIIH

G IIIG I

mp IItr, III mp I

liqH


GII

X


Example: Tedisamil Dihydrochloride

Henck, J.-O., Finner, E. and Burger, A., J. Pharm. Sci. 89 (2000) 1151-1159.

heating

heating

cooling

II I

IIII

III I II


Henck, J.-O., Finner, E. and Burger, A., J. Pharm. Sci. 89 (2000) 1151-1159.

Temperature [°C]

Mod.I - Mod.II EMod.I - Mod.III EMod.II - Mod.III E


Example: Sulfamethoxidiazin

Burger, A., Ramberger, R. and Schulte, K., Analyse des polymorphen Systems von Sulfamethoxidiazin. Arch. Pharm. 313 (1980) 1020-1028.


Sulfamethoxidiazin

Burger, A., Ramberger, R. and Schulte, K., Analyse des polymorphen Systems von Sulfamethoxidiazin. Arch. Pharm. 313 (1980) 1020-1028.


Summary (I)

What is necessary to draw an E/T diagram?:

- use arbitrary units for the E and T axis.

- order of relative stability of the polymorphs at 0 Kelvin.

- order of relative stability of the polymorphs at higher temperature (melting point).


Summary (II)

The E/T diagram is a useful tool to interpretdata obtained in polymorphism research, because:

- it is a graphical solution, that presents thethermodynamic relationships of polymorphsin one picture and helps to avoid erroneous interpretations.

- it is a helpful tool to design experiments to obtain a desired polymorph.


Acknowledgements

Prof. Joel Bernstein

Dr. Alfons GrunenbergDr. Arkady EllernProf. Jack DunitzProf. Roland Boese

Humboldt Foundation, Bonn (Germany)

Documents

Diversity amidst Similarity: A Multidisciplinary Approach to Polymorphs, Solvates & Phase Relations; Erice, June 2004Dr. Jan-Olav Henck Thermodynamics