X-ray diffraction as a tool for structural characterization of cellulosic materials

Transcription

1 X-ray diffraction as a tool for structural characterization of cellulosic materials Andreas Bohn COST-Workshop January 217 International Training School on Nanocellulose Characterization

2 Outline X-ray basic theory and data analysis Introduction X-ray diffraction in polymer science Crystal structure of cellulose Important structural parameters for characterization of polymers - degree of crystallinity - crystallite dimensiones - preferred orientation of crystallites X-ray phase analysis

3 X-ray diffraction basics How many periodic distances are there within a lattice? A lattice plane is a plane which intersects atoms of a unit cell across the whole threedimensional lattice. Threre are many ways of constructing lattice planes through a lattice The perpendicular separation between parallel planes with the same distance is called the d- spacing

4 X-ray diffraction basics and in three dimensiones!

5 X-ray diffraction basics Bragg s Law In materials with crystalline structures Bragg s law describes the conditions required for constructive interference of the X-ray Bragg s Law n λ = 2 d sin θ λ = X-ray wavelength d = distance between lattice planes θ = angle of incidence with lattice plane n = integer

6 X-ray diffraction basics The periodic lattice found in crystalline structures may act as a diffraction lattice for electromagnetic radiation with wavelength of a similar order of magnitude (1-1 m).

7 X-ray diffraction basics What for differences we will observe in the case of a single crystal and a polycrystalline powder? Single crystals - X-rays diffracted from a single crystal produce single spots which are well resolved - due to the orientation effects reflections are missing from lattice planes which are not in reflection condition (Bragg s Law) Polycrystalline powder - all orientations present -> continous Debye diffraction rings - spots are not resolved and superimposed

8 X-ray diffraction basics

9 X-ray diffraction in polymer science What can X-ray diffraction provide for structural characterization of polymers? 1. Identification of semicrystalline polymers 2. Identification of crystalline phases (polymorphism) of polymers 3. Quantitative phase analysis of chemical identical composites (eg. Cellulose I/II) 4. Degree of crystallinity: XRD is a primary technique to determine the degree of crystallinity in polymers 5. Microstructure: Crystallite sizes in polymers are usually on the scale of nanometers and can be determined using variantes of the Scherrer equation 6. Orientation: Polymers, due to their long chain structure, are highly susceptible to orientation. XRD is a primary tool for determination of the crystalline orientation of the nano-crystallites in polymers.

10 Crystal structures of native Cellulose I and regenerated Cellulose II (According to Blackwell et al.) parallel chain arrangement anti-parrallel in Cellulose II Space group P2 1 Crystal system: monoclinic Z = 2 (two chains in UC) a a Cellulose I a =.817 nm b =.786 nm c = 1.38 nm γ = 97. Cellulose I b Cellulose II b Cellulose II a =.81 nm b =.94 nm c = 1.36 nm γ =

11 Crystal structures of cellulose Supermolecular arrangement of cellulose crystallites in wood (Cellulose I) Schematic formation of cellulose microfibrils in wood (adopted from (Moon et al. 211). TC (terminal enzyme complexs).

12 WAXD Degree of crystallinity highly crystalline crystalline (2) Bacterial cellulose Cotton rel. intensity [e.u.] (11) (1-1) (4) rel. intensity [e.u.] (1-1) (11) (2) (4) diffraction angle 2θ [deg] semicrystalline amorphous diffraction angle 2θ [deg] Wood fiber MC, milled rel. intensity [e.u.] (1-1) (11) (2) rel. intensity [e.u.] (4) diffraction angle 2θ [deg] diffraction angle 2θ [deg]

13 WAXD Degree of crystallinity The fraction of the polymer that consists of regions showing long-range three-dimensional order. Two phase modell Most of the polymers are semicrystalline, consisting of crystalline and amorphous regions Crystallinity influences many of the polymer properties, e.g.: - Hardness, E-Modulus, Tensile, Stiffness, Melting Point The degree of crystallinity can be determined by several methods: Problems - X-ray diffraction - NMR-spectroscopy - Calorimetry - Density measurements - Infrared spectroscopy Fringed micelle model correct separation of the crystalline and amorphous regions imperfections in crystals are not easily distinguished from the amorphous phase various techniques may be affected to different extents by imperfections disagreement among the results of crystallinity by different methods

14 WAXD Degree of crystallinity The determination of x c implies use of a two-phase model, i.e. the sample is composed of crystals and amorphous and no regions of semi-crystalline organization. The diffraction profile is divided in two parts: Peaks are related to diffraction of crystallites broad scattering alone is related to the amorphous scattering x c = s p s s s 2 I s ds p c 2 I s ds K( s ) p s = 4π sin Θ λ I = I crystalline + I amorphous I crystalline = diffracted intensity of the crystalline phase I amorphous = diffracted intensity of the amorphous phase I c I = I c + I a I a Degree of crystallinity x c = II cccccccccccccccccccccc II cccccccccccccccccccccc + IIIIIIIIII ppppppppp

15 WAXD Degree of crystallinity XRD diffractograms of different cellulose samples Cellulose II S1: Modal fibers S2: Bacterial cellulose S3: Cotton S4: Birch craft pulp, bleached S5: Spruce dissolving pulp S6: Milled cellulose (Modo pulp) Degree of crystallinty x c determined by the Ruland- Vonk method rel. intensity [e.u.] % 62 % 58 % 51 % 52 % θ ] % amorphous

16 WAXD Microstructure: Crystallite sizes in polymers The half width of peaks (FWHM) is related to the crystallite dimensiones rel. intensity [e.u.] Bacterial cellulose (1-1) (11) (2) FWHM Full Width at Half Maximum (FWHM): the width of the diffraction peak at a height half-way between background and the peak maximum Narrow half width corresponds to bigger crystallites Bacterial cellulose: FWHM (2) : θ (PVII) Cotton diffraction angle 2θ [deg] 11 rel. intensity [e.u.] (1-1) (11) (2) FWHM Broad half width corresponds to smaller crystallites Cotton: FWHM (2) : θ (PVII) diffraction angle 2θ [deg]

17 WAXD Microstructure: Crystallite sizes in polymers Scherrer s formula: D ( hkl) = B K λ cosθ B published by Scherrer in 1918 D (hkl) = thickness of the crystallite perpendicular to the lattice plane (hkl) K = constant dependent on crystallite shape (.89) λ = X-ray wavelength B = FWHM (full width at half max) or integral breadth θ B = diffraction angle of the (hkl) reflection Assumption: Crystals exhibit uniform size and shape Other contributions to peak broadening: o o lattice distortions (strain) B strain instrumental effects B instr. B obs = B instr. + B sample = B instr. + B size + B strain

18 WAXD Microstructure: Crystallite sizes in polymers 2 18 Quartz (Sand) Bacterial cellulose Intensity [cps] Scattering angle 2θ [ ]

19 WAXD Microstructure: Crystallite sizes in polymers Degree of crystallinity and crystallite dimensions of different cellulosic fibers (Cellulose II) Kind of fibre Viscose x c [%] D 1-1 [nm] D 11 [nm] D 4 [nm] technical yarn textile yarn Lyocell Filament, 2 nd generation Carbamate

20 WAXD - Preferred orientation (texture) of crystallites (hkl) random orientation of crystallites (e.g. isotropic powder) [uvw] preferred orientation of crystallites (typical for platelike crystallites)

21 WAXD - Preferred orientation (texture) of crystallites Types of orientation random Cellulose I axial Cellulose I uniplanar (S PB) Casing, Cellulose II uniplanar (E PB) Casing, Cellulose II Preferred orientation effects on X-ray film patterns : 1. Arcs instead of rings (axial orientation) 2. Missing rings (uniplanar orientation)

22 WAXD - Preferred orientation (texture) of crystallites Types of orientation 1 C.J. Heffelfinger, R.L. Burton J. Polym. Sci. 47, 289 (196)

23 WAXD - Preferred orientation (texture) of crystallites Degree of orientation cotton jute Polypropylene, partial oriented Polypropylene, highly oriented flax flax hemp hemp Cellulose I different degree of orientation

24 WAXD - Preferred orientation (texture) of crystallites Degree of orientation Cellulose-II fiber Determination of (semi) quantitative orientation parameters from X-ray flat films Regenerated Cellulose fiber (Cellulose II) OD (1-1) =.862 FWHM = Intensity [Grey value] CLCF 92-1 FWHM flax hemp Azimuthal scan φ [deg] OD (1-1) = (18 - FWHM) / 18

25 WAXD - Preferred orientation (texture) of crystallites Degree of orientation Herman s factor f c 1 3 sin 2 2 = β (X-ray) f t = f ( n) (birefringence) f a = f ( f c, ft, xc, ρa, ρc) (calculated) flax hemp

26 WAXD - Preferred orientation (texture) of crystallites Degree of orientation Herman s factor 9 Cellulose I Cellulose II (2) rel. Intensity [e.u] 6 3 (1-1) (1-1) (11) (11) (2) perp. to cellulose chains (4) (4) Diffraction angle 2θ [ ]

27 WAXD - Preferred orientation (texture) of crystallites Degree of orientation Herman s factor norm. Intensität Distribution of the intensities of (4) lattice planes (cellulose chains) Probe 1 Probe 2 Probe 3 Probe 4 Probe 5 Sample Draw Ratio Material 1,88 regenerated Cellulose fiber 2 2,65 regenerated Cellulose fiber 3 5,3 regenerated Cellulose fiber 4 12,37 regenerated Cellulose fiber 5 14,14 regenerated Cellulose fiber Half widths FWHM, degree of orientation OD (hkl) und ODI (hkl) and Herman s orientation parameter fc Sample Draw ratio FWHM [ ] OG (4) OGI (4) fc 1,88 22,16,877,45, ,65 14,48,92,75,96 3 5,3 13,92,923,77, ,37 12,89,928,8, ,14 12,43,931,81, Azimuthaler Scan φ [ ] ODI (hkl) = I (hkl)ori / ( I (hkl)ori + I (hkl)iso ) - Determination of the 2θ-angle for the (4)- reflex at 2θ ~ 34.6 with a θ/2θ-scan - Measurement of the distribution of the (4) lattice planes at constant θ and 2 θ by a φ- spinner scan in the θ-angle range of 6-12 I (hkl)ori = Intensity of oriented lattice planes (hkl) I (hkl)iso = Intensity of isotropic lattice planes (hkl)) OD (4) = (18 - FWHM) / 18 f c = 1-3/2* <sin 2 ß> (Herman s Faktor)

28 Orientational parameters of various man-made cellulosic fibres 1,,8,6,4,2, Lyocell (1st gen.) Cord Enka Lyocell (2) Enka Viscose Carbamate 1 Carbamate 2 Carbamate 3 Carbamate 4 Carbamate 5 Carbamate 6 Orientational factors f i fc ft fa

29 X-ray texture analysis by pole figures Introduction to texture analysis Preferred orientation is usually described in terms of pole figures. A pole figure is measured at a fixed scattering angle (constant d spacing) and consists of a series of ϕ-scans (inplane rotation around the center of the sample) at different tilt or χ-angles. The pole figure data are displayed as contour plots with zero angle in the center. The pole figure of a sample with a preferred orientation will show a specific intensity distribution with maxima and minima. The recorded intensities will be uniform, if the crystallites in the sample are randomly distributed. Eulerian angles: χ Rotation around the Eulerian cradle φ Rotation around the normal of the sample surface 2θ Scattering angle

30 X-ray texture analysis by pole figures Principle of pole figure measurement M M [N] [N] N [N] [N] T N [N] [N] T Uniplanar texture type Uniplanar-axial texture type Sample fixed coordinate system, pole sphere

31 X-ray texture analysis by pole figures Uniplanar orientation of the (1-1) lattice planes Cellulose Casing M (hkl) T M [uvw] T

32 X-ray texture analysis by pole figures χ-scans of the (1-1) pole figure at const. φ Uniplanar orientation parameter were calculated from cuts through the pole figure ll M and T Density M-direction (lengthwise) 16 φ = φ = 9 15 χ Density T-direction (transverse) χ, Chi Uniplanar orientation parameter: OG = (18 - χ) / Chi M-direction: χ = 21.51, OG M =.88 T-direction: χ = 25.29, OG T =.86 OG T / OG M =

33 X-ray texture analysis by pole figures (11) pole figures in transmission (2θ ~ 2 ) - Viscofan casing No. 7 (hkl) M ϕ= [uvw] T

34 X-ray texture analysis by pole figures Evaluation of axial orientation parameter from the (11) pole figure in transmission Axial orientation parameter OD (11) = (18 - HW) / I total = I ori + I iso ODI (11) = I ori / I total OD (11) = (no axial orientation) OD (11) = 1 (perfect axial orientation) rel. Intensity.15.1 HW I ori HW I ori ODI (11) = 1 or 1 % (no isotropic background, all lattice planes are oriented) ODI (11) = (only isotropic background, no oriented lattice planes).5. I iso Azimuthal angle [ ]

35 Qualitative phase analysis Cellulose I 8 (4) Cellulose I Each different crystalline solid has a unique X-ray diffraction pattern which acts like a fingerprint Needs: Peak positions and approximate relative intensities Tools: Crystal structure bases rel. Intensität [e.u] (1) (2) (3) (5) Peak 2θ d [nm] Phases which same chemical composition have different XRD patterns and can be distinguished Beugungswinkel 2θ [ ] d 1 d 2 d 3 d 4

36 WAXD Quantitative phase analysis Problem: Determining the relative proportions of crystalline phase present in an unknown sample. Ratio of peak intensitites varies linearly as a function of weight fractions for any two phases (e.g. A and B) in a mixture Needs: I A / I B value for all phases involed Tools: Calibration with mixture of known quantitites -> fast: gives semi quantitative results

37 WAXD Quantitative phase analysis Example: Cellulose I / II Determination of quantitative phase components from a series of Cell I / Cell II reference mixtures in e.g. 1% steps 1 % Cell-I 5 % Cell-I, 5 % Cell-II 1 % Cell-II

38 WAXD Quantitative phase analysis Example: Cellulose I / II Simple Method: rel. Intensity [e.u] (1-1) (1-1) (11) (11) (2) (2) (4) Cellulose I Cellulose II - Peak height comparison of relevant peaks of cellulose I and II Advanced method: - Fit of complete diagrams using a phase analysis software (IAP): Pure cellulose I and II samples are used as reference samples in order to analyze the unknown sample using least-squares-fitting -> Problem: the reference corner samples! Diffraction angle 2θ [ ] -> Not always simple superposition of reference samples if structural parameter are not constant (e.g., alkalization process)

39 WAXD Quantitative phase analysis Example: Cellulose I / II Cell1 (2) Quantitative phase amounts of cellulose I and II of fibrous casings 12 1 Cell1 (11) Cell1 (1-1) Cell1 (4) Pr.1 - Cell-I Pr.3 Pr.4 Pr.5 Pr.7 Pr.6 Sample Cellulose I [ %] Cellulose II [ %] Deviation F rel. Intensität [e.u.] Cell2 (1-1) Beugungswinkel 2θ [ ]

40 Thank you for your attention! Questions?