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
• 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 LawAll waves scatterd by the planes (hkl) must be
in phase
2dhkl sin(hkl) = n
X-ray diffraction
• Intensity Ihkl | Fhkl|2
• Structure factor Fhkl = | Fhkl| exp (ihkl)
• Atomic coordinates xj,yj,zj
• Electron density (x,y,z)
• Maxima in (x,y,z) are the xj,yj,zj
• Phase problem: hkl unknown
)(2exp1
jjjj
N
jhkl lzkyhxfF
)](2exp[1
),,( lzkyhxiFzyx hkllkh
Powder diffraction
– Small crystals ( <10 m)– Uniformly oriented sample (flat sample/capillary)
• Diffraction gives:– ‘ID’ diffraction pattern Intensity (I) vs 2
• 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
• Sample preparation
• Data collection
• Pattern fitting and indexing
• Choice of structure determination technique
Sample preparation
• Capillary diameter (0.3-1.5 mm)
• Wavelength !
• Absorption
• Particle statistics (Capillary 0.3 mm)
• Preferred orientation
• Laboratory data collection beforehand!
Data collection
• Synchrotron (if possible) FWHM = 0.04• Wavelength ( > 0.8 Å)• Small slit size (reduce peak asymmetry at low 2)
• Data collection protocol– Reciprocal lattice point density vs exposure time– Total exposure time (~ 8 h)– Start at lowest possible 2
• 0-30
• 10-30
• 20-30
– Step size 0.005° 2
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 (,,)
• n Torsian angles 1,2,….,n
Stereochemical model (trial model)
• Build from stereochemical descriptors in Cartesian coordinate system– 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)(|)()(|)( obsXcalsXobsXXR j
j
jj
j
Single (resolved) reflection
Xj(obs) = Ihkl
Cluster of overlapping reflections
Xj(obs) = Ihkl
Correct solution: low R(X) ( < 0.5)
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= 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 acidsChain: double bond10:0 decanoic C(apric)
12:0 dodecanoic L(auric)
13:0 tridecanoic
14:0 tetradecanoic M(yristic)
15:0 pentadecanoic
16:0 hexadecanoic P(almitic)
17:0 heptadecanoic
18:0 octadecanoic S(t)(earic)
18:1 octadec-cis-9-enoic O(leic)
18:1 octadec-trans-9-enoic E(laidic)
19:0 nonadecanoic
20:0 icosanoic A(rachidic)
Structures of triacylglycerols on the basis of powder-diffraction data
• -CnCnCn (n=even; 14 =MMM, 18=SSS)
• -CnCnCn (n=13,15,17,19)
• ’-CnCn+2Cn (n=14; MPM)
Poster: The structure of ’-PSP and -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
• -CnCnCn (n=even; 14 =MMM, 18=SSS)
• -CnCnCn (n=13,15,17,19)
• ’-CnCn+2Cn (n=14; MPM)
Poster: The structure of ’-PSP and -PSP
Melting point alternationLarson (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
Compound C13C13C13a C15C15C15 C17C17C17 C19C19C19
a (Å) 11.9438(6) 11.8998(1) 11.8664(2) 11.8680(1)b (Å) 41.342(1) 46.3879(4) 51.450(1) 56.5143(9)c (Å) 5.4484(3) 5.4400(1) 5.4321(1) 5.4280(1) ( ) 71.905(4) 72.359(1) 72.765(2) 73.064(1) ( ) 100.291(5) 100.211(1) 100.095(1) 100.020(1) ( ) 121.824(3) 121.125(1) 120.577(2) 120.084(1)Volume (Å3) 2172.5(1) 2448.9(1) 2725.8(1) 3011.8(1)Dcalc (g/cm3) 1.04 1.04 1.03 1.03
The unit cell parameters for the phase of the triacylglycerols C13C13C13,
C15C15C15, C17C17C17,and C19C19C19 as determined from the synchrotronXRPD data when the acyl chains are as parallel as possible with the longestaxis
a) Van Langevelde A.J. (2000), Van Langevelde et al. (2001a)
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
• -CnCnCn (n=even; 14 =MMM, 18=SSS)
• -CnCnCn (n=13,15,17,19)
• ’-CnCn+2Cn (n=14; MPM)
Poster: The structure of ’-PSP and -PSP
The ’ structure of CLC and MPM• Homologous
The ’ structure of CLC and MPM• Homologous
Compound '-CLCa '-LMLb '-MPMb '-MPMb '-PSPb
a (Å) 22.783(2) 22.650(2) 22.63(1) 22.660(2)b (Å) 5.6945(6) 5.6513(4) 5.621(7) 5.6261(7) 5.5946(8)c (Å) 57.368(6) 67.183(6) 76.21(4) 76.217(8) 85.48(2) ( ) 90.0 90.0 90.0 90.0 90.0 ( ) 90.0 90.391(7) 90.0 90.18(1) 22.829(4) ( ) 90.0 90.0 90.0 90.0 90.0Volume (Å3) 7443(1) 8599.3(9) 9784 9717(1) 10917(3)Space Group Ic2a I2 Ic2a I2 Ic2aChem. Form. C35H66O6 C41H78O6 C47H90O6 C47H90O6 C53H102O6
Z 8 8 8 8 8Dcalc (g/cm3) 1.04 1.03 1.02 1.03 1.02Tdata collection (K) 295 250 295 250 250
The ’ structures of CLC and MPM• Bend molecules
• Orthogonal zigzag planes
Packing diagrams of ’-CLCTop: Along the b-axis, showing the bending of the molecules
Bottom: Along the c-axis, showing the chain packing
Notice: flat methyl-end planes
’-CnCn+2Cn vs -CnCnCn structuresCLC (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
AcknowledgementsLaboratorium voor Kristallografie,
Universiteit van Amsterdam, The Netherlands
V. Chernyshev (Moscow State University)
D.J.A. De Ridder
E. Dova
R.A.J. Driessen
K. Goubitz
R.B. Helmholdt
A. van Langevelde
K.F. van Malssen
J.B. van Mechelen
M.M. Pop
H. Schenk
E. Sonneveld
P. Zwart
ESRF (Grenoble, France) Staff at BM16 and BM01b
NWO/CW Netherlands Foundation for Chemical Research
STW Netherlands Technology Foundation
Unilever