Transcript No Slide Title

Structure determination of
triacylglycerols from powder
diffraction data
René Peschar
Laboratory for Crystallography
Universiteit van Amsterdam
The Netherlands
Overview
• Introduction
– Why structure determination of TAG’s?
– Why Powder diffraction data
• X-ray diffraction and crystals
• Powder diffraction
• Structure determination using powder
diffraction data
• Application to triacylglycerols
• Conclusion
Scheme of bloom formation on chocolate
Introduction
• Melt and crystallization behaviour of
(natural) fats and triacylglycerols
• (Natural) fats consist mainly of
triacylglycerols
• Phase transition behaviour
• Explanation at atomic level => structure
information
• In solid state: crystalline!
• X-ray diffraction (Single crystal/powder)
X-ray diffraction and crystals
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Crystal: regular 3D stacking of identical units
X-rays on crystal => diffraction (Bragg’s Law)
Single crystal (0.1 mm) : 3D diffraction pattern
Triacylglycerols single crystals difficult to
grow
• => Powder diffraction
Bragg’s Law
All waves scatterd by the planes (hkl) must be
in phase
2dhkl sin(qhkl) = n l
X-ray diffraction
• Intensity Ihkl  | Fhkl|2
• Structure factor Fhkl = | Fhkl| exp (ijhkl)
N
Fhkl   fj exp 2 (hxj  ky j  lzj )
j 1
• Atomic coordinates xj,yj,zj
• Electron density r (x,y,z)
r ( x, y , z ) 
1




   Fhkl exp[ 2i (hx  ky  lz )]
h   k   l  
• Maxima in r (x,y,z) are the xj,yj,zj
• Phase problem: jhkl unknown
Powder diffraction
– Small crystals ( <10 mm)
– Uniformly oriented sample (flat sample/capillary)
• Diffraction gives:
– ‘ID’ diffraction pattern Intensity (I) vs 2q
• Application:
– (Qualitative) identification
• e.g. Polymorphs cocoa butter or TAGs
– Crystal Structure determination
• chain packing, atomic positions)
• => 3D periodic electron density
Polymorphs
of cocoa
butter
Prerequisites for a successful structure
determination from powder data
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Sample preparation
Data collection
Pattern fitting and indexing
Choice of structure determination technique
Sample preparation
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Capillary diameter (0.3-1.5 mm)
Wavelength !
Absorption
Particle statistics (Capillary 0.3 mm)
Preferred orientation
Laboratory data collection beforehand!
Data collection
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Synchrotron (if possible) FWHM = 0.04
Wavelength (l > 0.8 Å)
Small slit size (reduce peak asymmetry at low 2q)
Data collection protocol
– Reciprocal lattice point density vs exposure time
– Total exposure time (~ 8 h)
– Start at lowest possible 2q
• 0-30
• 10-30
• 20-30
– Step size 0.005° 2q
Pattern fitting and indexing
• Extract intensity maxima
– Background
– Peak profile (e.g. Pseudo Voigt)
• Auto-indexing programs (eg ITO, TREOR, DICVOL)
• Check pattern if all maxima are covered (eg
CHEKCELL, see CCP14 home page)
• Extract reflection intensities and/or cluster intensities
Pattern indexing
E.g. orthorhombic lattice:
(1/dhkl)2 = (h/a)2 + (k/b)2 + (l/c)2
Results from powder data
Choice of structure determination technique
• ‘Traditional’ single-crystal methods
– Patterson, Direct Methods, incl. maximum
entropy/maximum likelyhood
– Reciprocal space
• No complete initial model required
• Individual reflection intensities
• Atomic resolution
• Direct space grid search methods
– Direct space
• Complete model
• Some but not all individual intensities required
– Grid search, Monte Carlo, Simulated
Annealing, Genetic algorithm
Structure of C13C13C13
Direct space grid search techniques
• Basic assumption:
– Almost complete structural model or fragment:
standard inter atomic distances and angles (or
from similar structure in data base, or via
molecular modelling)
– Structure can be expressed in terms of a set of
6+n variables (degrees of freedom):
• Position (x,y,z) of a specific atom
• Eulerian angles (q,j,y)
• n Torsian angles t1,t2,….,tn
Stereochemical model (trial model)
• Build from stereochemical descriptors in
Cartesian coordinate system
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interatomic distances
interatomic angles
dihedral angles (torsian angles)
transform model to crystallographic unit cell
• Take similar model
– e.g. from Cambridge Structural Database.
Modify wherever necessary (standard bond
lengths, angles), optionally using Molecular
Modelling (eg Cerius2TM)
Grid search direct space
• General algorithm
– Generate trial structures(s)
– Calculate powder diffraction
pattern/intensities/structure factors
– Compare with experimental data
– Accept or reject on basis of a criterion function
• Advantage: Extraction of all individual
intensities not required. Degrees of freedom
determine complexity of global optimization
problem
• Disadvantage: Model should be realistic; time
consuming
Consistency criterion
R( X )   | Xj (obs)  sXj (cal) |  Xj (obs)
j
Single (resolved) reflection
Xj(obs) = Ihkl
Cluster of overlapping reflections
Xj(obs) = S Ihkl
Correct solution: low R(X) ( < 0.5)
j
Grid search implementation
• Systematic change of variable values (pre-defined grid increments)
– Extract 50-300 low-angle individual intensities X=I
or clusters of overlapping intensities X= S I
in full pattern decomposition
– Perform rotation (steps 10-30°) and translation searches (0.5-0.6Å)
– For minima found: decrease steps to 5° - 1° and 0.1 Å
– Torsion angle searches (initially 20° => 5°)
• Advantage: minimum in criterion function R(X) not likely to be missed
• Disadvantage: Time-consumpton can become prohibitive if degrees of
freedom is large
MRIA system (local version) Zlokazov V.B. and Cherneyschev V.V. (1992) J Appl. Cryst. 25 - 447-451 (MRIA)
Chernyshev V.V. and Schenk H. (1998) Z. Kristallogr. 213, 1-3 (Grid Search)
Refinement
• Bond-restrained Rietveld refinement
– e.g. Baerlocher, 1993
• Very small parameter shifts
• Coupling Uiso
Nomenclature of some fatty acids
Chain: double bond
10:0 decanoic
12:0 dodecanoic
13:0 tridecanoic
14:0 tetradecanoic
15:0 pentadecanoic
16:0 hexadecanoic
17:0 heptadecanoic
18:0 octadecanoic
18:1 octadec-cis-9-enoic
18:1 octadec-trans-9-enoic
19:0 nonadecanoic
20:0 icosanoic
C(apric)
L(auric)
M(yristic)
P(almitic)
S(t)(earic)
O(leic)
E(laidic)
A(rachidic)
Structures of triacylglycerols on the
basis of powder-diffraction data
• b-CnCnCn (n=even; 14 =MMM, 18=SSS)
• b-CnCnCn (n=13,15,17,19)
• b’-CnCn+2Cn (n=14; MPM)
Poster: The structure of b’-PSP and b-PSP
References (ESRF beam-line used)
15.15.15; 17.17.17; 19.19.19
Helmholdt R.B., Peschar R. and Schenk H. (2002) Acta Cryst B58,
134-139 (BM16)
MMM; SSS
Van Langevelde A., Peschar, R. and Schenk, H. (2001) Acta Cryst
B57, 372-377 (BM01B, BM16)
13.13.13
Van Langevelde A., Peschar, R. and Schenk, H. (2001) Chem.
Mater. 13, 1089-1094. (BM16)
MPM; CLC (Single Crystal)
Van Langevelde, A., Van Malssen, K.F., Driessen, R., Goubitz, K.,
Hollander, F., Peschar, R., Zwart, P. and Schenk, H.. (2000) Acta
Cryst. B56, 1103-1111 (ID11, BM16)
CnCnCn (n=even) series
• Structures are homologous, Unit cell transformed
• CCC(10.10.10), LLL(12.12.12),MMM(14.14.14),PPP(16.16.16)
CnCnCn (n=even) series
• Structures are homologous, Unit cell transformed
• CCC(10.10.10), LLL(12.12.12),MMM(14.14.14),PPP(16.16.16)
Structures of triacylglycerols on the
basis of powder-diffraction data
• b-CnCnCn (n=even; 14 =MMM, 18=SSS)
• b-CnCnCn (n=13,15,17,19)
• b’-CnCn+2Cn (n=14; MPM)
Poster: The structure of b’-PSP and b-PSP
Melting point alternation
Larson (1966): melting point alternation for long-chain
compounds is caused by differences in packing densities at
the layer interface
Lutton and Fehl (1970)
Triacylglycerol cell parameters
The unit cell parameters for the b phase of the triacylglycerols C13C13C13,
C15C15C15, C17C17C17,and C19C19C19 as determined from the synchrotron
XRPD data when the acyl chains are as parallel as possible with the longest
axis
Compound
a (Å)
b (Å)
c (Å)
 ()
b ()
 ()
Volume (Å3)
Dcalc (g/cm3)
C13C13C13a
11.9438(6)
41.342(1)
5.4484(3)
71.905(4)
100.291(5)
121.824(3)
2172.5(1)
1.04
C15C15C15
11.8998(1)
46.3879(4)
5.4400(1)
72.359(1)
100.211(1)
121.125(1)
2448.9(1)
1.04
C17C17C17
11.8664(2)
51.450(1)
5.4321(1)
72.765(2)
100.095(1)
120.577(2)
2725.8(1)
1.03
a) Van Langevelde A.J. (2000), Van Langevelde et al. (2001a)
C19C19C19
11.8680(1)
56.5143(9)
5.4280(1)
73.064(1)
100.020(1)
120.084(1)
3011.8(1)
1.03
Melting point alternation
CnCnCn (Left, A: n=odd, right, B: n=even)
For n=odd packing is less dense, so a lower melting point
Structures of triacylglycerols on the
basis of powder-diffraction data
• b-CnCnCn (n=even; 14 =MMM, 18=SSS)
• b-CnCnCn (n=13,15,17,19)
• b’-CnCn+2Cn (n=14; MPM)
Poster: The structure of b’-PSP and b-PSP
The b’ structure of CLC and MPM
• Homologous
The b’ structure of CLC and MPM
• Homologous
Compound
a (Å)
b (Å)
c (Å)
 ()
b ()
 ()
Volume (Å3)
Space Group
Chem. Form.
Z
Dcalc (g/cm3)
Tdata collection (K)
b'-CLCa
22.783(2)
5.6945(6)
57.368(6)
90.0
90.0
90.0
7443(1)
Ic2a
C35H66O6
8
1.04
295
b'-LMLb
22.650(2)
5.6513(4)
67.183(6)
90.0
90.391(7)
90.0
8599.3(9)
I2
C41H78O6
8
1.03
250
b'-MPMb
22.63(1)
5.621(7)
76.21(4)
90.0
90.0
90.0
9784
Ic2a
C47H90O6
8
1.02
295
b'-MPMb
22.660(2)
5.6261(7)
76.217(8)
90.0
90.18(1)
90.0
9717(1)
I2
C47H90O6
8
1.03
250
b'-PSPb
5.5946(8)
85.48(2)
90.0
22.829(4)
90.0
10917(3)
Ic2a
C53H102O6
8
1.02
250
The b’ structures of CLC and MPM
• Bend molecules
• Orthogonal zigzag planes
Packing diagrams of b’-CLC
Top: Along the b-axis, showing the bending of the molecules
Bottom: Along the c-axis, showing the chain packing
Notice: flat methyl-end planes
b’-CnCn+2Cn vs b-CnCnCn structures
CLC (Chair I, II, III)
PPP (Tuning fork, I, III, II)
Triacylglycerol conformations
Chair
Tuning fork
Conclusion
Crystal structure determination of
triacylglycerols on the basis of powder
diffraction data is possible, provided
• Well-prepared sample
• High-resolution (synchrotron) data
• Pattern can be indexed
• Homologous model available
Acknowledgements
Laboratorium voor Kristallografie, J.B. van Mechelen
M.M. Pop
Universiteit van Amsterdam,
The Netherlands
H. Schenk
E. Sonneveld
V. Chernyshev (Moscow State
P. Zwart
University)
D.J.A. De Ridder
ESRF (Grenoble, France) Staff at
E. Dova
BM16 and BM01b
R.A.J. Driessen
NWO/CW Netherlands Foundation
for Chemical Research
K. Goubitz
STW Netherlands Technology
R.B. Helmholdt
Foundation
A. van Langevelde
Unilever
K.F. van Malssen