Crystallization in polymorphic systems
Lian Yu
University of Wisconsin – Madison,
School of Pharmacy and
Department of Chemistry
With thanks to
PRF, NSF
Polymorphs of Carbon
Hard
Electrical insulator
Soft
Semi-metal
Soft
Conductive
Polymorphs serve two goals of chemical research:
Finding new materials
Learning structure-property relations
Polymorphs of ROY
O
N
(1) R P-1
mp 106.2 oC
= 21.7°
(4) OP P21/c
mp 112.7 oC
= 46.1°
N
O
H
N
(2) ON P21/c
mp 114.8oC
= 52.6°
C

(3) Y P21/c
mp 109.8 oC
= 104.7°
S
ROY
CH3
J. Am. Chem. Soc.
2000, 122, 585
(6) ORP Pbca
mp 97 ºC, = 39.4°
(5) YN P-1, mp 99 ºC
= 104.1°
(7) RPL
R
100 m
R05
Y04
Y04
(8) Y04
L
L
JACS 2001
R
JACS 2005a
(9) YT04 P21/c (10) R05
mp 106.9oC
 = 112.8°
JACS 2005b
“Non-polymorphic” systems
OH
COOH
HO
HO
naphthalene
benzoic acid
O
OH
O
sucrose
OH
OH
O
OH
OH
Polymorphs of drugs have different
bioavailability
Polymorphs have been used to test the third
law of thermodynamics
Westrum & McCullough (1963)
… and other structure-property relations
G. Schmidt and
workers before him
h
Solution or melt
no reaction
The problem of controlling polymorphism:
Crystallizing from the same liquid, which
polymorph “wins”?
A
B
liquid
C
This talk
Crystallization in polymorphic systems
(1) A new mechanism: Nucleation of one
polymorph by another
(2) Hidden polymorph discovered by crossnucleation
(3) Survival of the fittest polymorph: Fast
nucleater vs. fast grower
Crystallization = nucleation + growth
Crystallization in polymorphic systems
Ostwald (1897):
liquid
least stable
….
2nd least stable
most stable
Etter (1991):
Another mechanism: Nucleation of one
polymorph by another
(1)  crystallizes first
(2) nucleates on 
while  continues to grow

c

(3)  grows faster
CH2OH
c
D-mannitol
HO-C-H
HO-C-H
H-C-OH
H-C-OH
Yu, L. J. Am. Chem. Soc. 2003, 125, 6380
CH2OH
Other examples of cross-nucleation: ROY
R05
Y04
Chen, Xi, Yu JACS 2005
100 m
100 m
100 m
100 m
Other examples: Phenobarbital and
carbamazepine/nicotinamide
100 μm
Phenobarbital
Carbamazepine/Nicotinamide
The new polymorph must grow faster than
or as fast as the initial polymorph
r (m/s)
4.0
Growth Rates of ROY at 27 ºC
3.0
2.0
1.0
0.0
Y04
YT04
ON
YN
R
OP
R05
Y
Direction of cross nucleation:
Y04  R, R05; R  YN
ON, OP, YT04  Y
Crystallographic Data of ROY
Form
YT04
Y
ON
OP
R
YN
crystal sys.
monoclinic
monoclinic
monoclinic
monoclinic
triclinic
triclinic
orthorhombic
space group
description
P21 /n
yellow
prism
8.2324
11.8173
12.3121
90
102.505
90
1169.36
4
1.473
P21 /n
yellow
prism
8.5001
16.413
8.5371
90
91.767
90
1190.5
4
1.447
P21 /c
orange
needle
3.9453
18.685
16.3948
90
93.830
90
1205.9
4
1.428
P21 /n
orange
plate
7.9760
13.319
11.676
90
104.683
90
1199.9
4
1.435
P-1
red
prism
7.4918
7.7902
11.9110
75.494
77.806
63.617
598.88
2
1.438
P-1
yellow
needle
4.5918
11.249
12.315
71.194
89.852
88.174
601.85
2
1.431
Pbca
orange-red
plate
13.177
8.0209
22.801
90
90
90
2409.8
8
1.429
a, Å
b, Å
c, Å
°
 °
 °
volume, Å3
Z
Dcal, gcm-3
ORP
No apparent lattice matching exists between
cross-nucleating structures
The less stable polymorph can nucleate the
more stable () and vice versa ().
ROY
D-mannitol
2
1.2
G-G β, kJ/mole
YN
G-GY, kJ/mol
0.8
0.4
L-sc
R
ON
YT04
OP
0
L
1
0.5
Tm


Tm
OP
-0.5
340
ON
-0.4
30

0
Y
Y
1.5
Tm
50
70
T, C
90
360
380
400
420
440
T, K
L
110
Cross-nucleation rate depends on temperature
D-mannitol/PVP
115 °C
Cross-nucleation

110 °C

“Waiting
time”
105 °C
100 °C
A Poisson process: “Waiting time” to the first
success has exponential distribution
70
107 C
<> = 3.3 x 10-9 m2s
Count
60
50
40
30
20
, 10-9 m2s
10
0
70
1
0
4
8
60
16
20
24
28
109 C
<> = 27 x 10-9 m2s
Count
2
12
50
40
30
20
, 10-9 m2s
10
0
60
0
30
60
50
120
150
180
210
240
270
300
111 C
<> = 71 x 10-9 m2s
Count
40
30
1: 1st success
2: 2nd success
90
20
, 10-9 m2s
10
0
0
60
Cross-nucleation in
seeded crystallization
120
180
240
300
360
420
480
540
600
D-mannitol at 140 ºC
seed side-on
[001]
spacer (0.15 mm thick)
melt

100 m
seed
end-on

seed
[001]

fiber loop
Polymorphs identified by
Raman microscopy, XRD


100 m
Tao, J.; Yu, L. Cryst. Growth Des. 2007, 7, 2410
This talk
Crystallization in polymorphic systems
(1) A new mechanism: Nucleation of one
polymorph by another
(2) Hidden polymorph discovered by crossnucleation
(3) Survival of the fittest polymorph: Fast
nucleater vs. fast grower
Crystals of resolvable chiral molecules: a
special case of polymorphs
R
S R
S
R
R
S
R
R
S
R
S
R
S
R
R
S
rarer
S
rare
conglomerate (C)
racemate
or racemic
compound
(RC)
S
S
R
R
R
RSRSRSRS
SRSRSRSR
RSRSRSRS
S
S
common
S
racemic liquid
R = R enantiomer
S = S enantiomer
RRRR
RRRR +
RRRR
SSSS
SSSS
SSSS
AR
AS
enantiomorphs
SSRSRRRS
SRRRSRSS
RSSSRSRR
solid solution
(SS)
A hidden polymorph discovered by seeding
S
N
Liquid of
R or S
O
O
tazofelone
(chiral drug)
Liquid of R and
S (racemic)
Fast nucleation,
slow growth
enantiomorph
Slow nucleation,
fast growth
R
racemic
S compound
solid solution of R and S
Huang, Chen, Yu. JACS 2006
Crystallographic data of the racemic solid
solution of R and S tazofelone
SS-0.5
SS-0.5
AS
RCI
RCII
T/K
100
296
293
293
295
Space group (No.)
P21/n (14)
P21/n (14)
P21 (4)
P21/c (14)
Pbca (61)
Crystal system
Monoclinic
Monoclinic
Monoclinic
Monoclinic
Orthorhombic
a/Å
9.1969(9)
9.3882(14)
9.392
11.313
17.204
b/Å
10.9212(11)
10.9503(16)
10.962
17.082
11.287
c/Å
17.6758(17)
17.855(3)
17.823
19.324
18.860
β/
93.1731(18)
93.766(3)
94.29
101.11
90
V/Å3
1772.7(3)
1831.6(5)
1829.8
3665
3662.2
4
4
4
8
8
1.205
1.166
1.167
1.165
1.166
Z
ρcalc/g
cm-3
T (°C)
A Type 2 solid solution
max. mp
155
at xR = 0.5
Tm,RCI
150
Tm,A
Tm,RCII
Tm,SS-0.5
• Solid solutions of
enantiomers are
rare
145
Te,AR-RCI
Te,AR-RCII
140
• Occurrence in
racemate-forming
system is
unprecedented
135
Te,A ≈ 110°C
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
xR
Free energies of TZF solid solutions
5
intermediate
stability/solubility
4
G  GRCII (kJ/mol)
AR, AS
3
LR,LS
SS-0.85
2
L-0.85,
L-0.15
SS-0.5
1
RCI
Tm, RCII
0
-1
360
RCII
Tm, RCI
Tt
380
400
420
LRC
440
T (K)
Yu, L., Huang, J., Jones J. K. J. Phys. Chem. B 2005, 109, 19915-19922.
The solid solution could be discovered by
seeding because it grows faster than the
racemic compound, despite its slow nucleation
-4
Logr (m/s)
SS-0.5
-5
-6
RCI
-7
-8
70
90
110
130
150
T, °C
More hidden polymorphs?
This talk
Crystallization in polymorphic systems
(1) A new mechanism: Nucleation of one
polymorph by another
(2) Hidden polymorph discovered by crossnucleation
(3) Survival of the fittest polymorph: Fast
nucleater vs. fast grower
It is common to treat polymorph control as a
nucleation problem
• Seeding with a polymorph to grow the same
• The Use of Polymer Heteronuclei for Crystalline
Polymorph Selection. Lang, Grzesiak and
Matzger* J. Am. Chem. Soc. 2002, 124, 14834
• Nonphotochemical, Laser-Induced Nucleation of
Supersaturated Aqueous Glycine Produces
Unexpected Polymorph. Zaccaro, Matic,
Myerson, and Garetz. Cryst. Growth & Design
2001, 1, 5
But it is also a growth problem
R05: slow nucleater, fast grower
Y04: fast nucleater,
slow grower
Chen, Xi, Yu JACS 2005
100 m
100 m
100 m
100 m
Polymorphs can grow at very different rates
glycine grows 500 x faster than glycine in
water at the same supersaturation (10 %)
(Chew et al. Cryst. Eng. Comm. 2007)
H2
C
O
H
_C
N
O
H
+ H
 (P31 or P31)  stable
(P21/n)  metastable
Log u, (m/s)
Growth rates between ROY polymorphs can
-4
differ by 1000 times
and change with
-5
temperature
Polymorphs of ROY
O
(4) OP P21/c
mp 112.7 oC
= 46.1°
H
N
(2) ON P21/c
mp 114.8oC
= 52.6°
C
S
CH3
(3) Y P21/c
mp 109.8 oC
= 104.7°
-8
J. Am. Chem. Soc.
2000, 122, 585
(7) RPL
-9
(6) ORP Pbca
mp 97 ºC, = 39.4°
ON
R
100 m
-10
R05
Y04
Y04
(8) Y04
L
JACS 2001
-7

ROY
(5) YN P-1, mp 99 ºC
= 104.1°
YT04
N
O
N
(1) R P-1
mp 106.2 oC
= 21.7°
-6
L
R
JACS 2005a
(9) YT04 P21/c (10) R05
mp 106.9oC
 = 112.8°
JACS 2005b
T, K
-11
220 240 260 280 300 320 340 360 380
Sun, … J. Phys. Chem. B 2008, 112, 5594
No good explanations yet…
For ROY, the fast growers can transition from
diffusion-controlled to “diffusionless” growth
2
u : time required to
add one layer of
molecules to the
crystal
 : time required
for an average
molecule in the
liquid to reorient or
diffuse its diameter
Log  (s)
0
u diffusion-2
controlled
growth
u diffusionless
growth
-4
α
Tg = 259 K
-6
3
3.2
3.4
3.6
3.8
4
● ON
∆ YN
□ R05
+ YT04
xY
R
○ OP
4.2
4.4
103/T, 1/K
Center-of-mass radial distribution functions of
ROY polymorphs
3
Diffusioncontrolled
growth
1
0
4
3
4
5
6
7
8
9
10
3
4
5
6
7
8
9
10
4
5
6
7
8
9
10
4
5
6
7
8
9
10
4
5
6
7
8
9
10
4
5
6
7
8
9
10
ON
2
No. of molecules
Able to
transition to
“diffusionless”
growth
YN
2
0
4
YT04
2
0
4 3
2
Y
0
3
4
OP
2
0
2 3
1
R
0
3
r, Å
If the fast grower is not the fast nucleater, it
can still “win” by nucleating on an existing
polymorph
A nucleus
A crystal
(fast nucleater)
liquid
B nucleus
B crystal
(fast grower)
Summary
• Fast nucleater need not be fast grower
• Through cross-nucleation, a fast-growing
polymorph can dominate the product
• Cross-nucleation helps discover a rare solid
solution of enantiomers. It is the first example
for a racemate-forming system
• The relative growth rates of polymorphs is an
important unsolved (likely solvable) problem