Structure determination of triacylglycerols from powder diffraction data René Peschar Laboratory for Crystallography Universiteit van Amsterdam The Netherlands.

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