X-ray diffraction in polymer science

1 1)Identification ofsemicrystalline polymers and Recognition ofcrystalline phases (polymorphism) of polymers 2)Polymers are never 100% crystalline. XRD is a primary technique to determine the degree of crystallinityin polymers. 3) Microstructure: Crystallite size in polymers is usually on the nano-scale in the thickness direction. The size of crystallites can be determined using variants of the Scherrer equation. 4) Orientation: Polymers, due to their long chain structure, are highly susceptible to orientation. XRD is a primary tool for the determination of crystalline orientation through the Hermansorientation diffraction in polymer science5 10 15 20 25 30 35 402002 = I2 (deg)PEpolyethylene1102 = 1) Identification of semicrystalline polymersPositions and Intensities of the peaks are used for identifying the =2 The diffraction of unoriented samples in transmission by using a flat filmis characterized by concentric circles called Debye Scherrer Rings Unoriented PE200(2 = )110(2 = )The diffraction of unorientedsamples in reflectionUnoriented PEX ray diffraction of semicrystalline and amorphous polymer510 15 20 25 30 35 40400310210220211( )300( )I2 (deg)110( )s-PSsyndiotattic polystyrene 510 15 20 25 30 35 40I2 (deg)

2 S-PSsyndiotactic polystyrene amorphous510152025303540__030220_421_322 _421420040410002040_111_111_101_04103102 0200510600410400210310210210010010132131 030220200210211220300110 Intensity DCE 2 (deg)_410_321301302230121401231331_11210 2210020_121111_301_321211230121212_32230 2411411210020111s-PSPosition and Relative intensities are the fingerprint of crystalline phases of polymer1) Identification of crystalline phases of polymersab 0510152025303540T = 280 CmaxT = 290 CmaxT = 300 CmaxT = 310 CmaxT = 320 Cmaxt = 5 minmax + edcbaIntensity2 (deg)s-PSIdentification of crystalline phases of polymers also if they are present in I + IIForma I + IIForma III2 (deg)Forma I(110)I(300)I(211)I(220)I(200)II(220)II( 311)IIi-PBX ray diffraction of semicrystalline polymer and inorganic compound 510 15 20 25 30 35 40400310210220211( )300( )I2 (deg)110( )s-PSsyndiotattic polystyrene inorganic compound polymer 5101520253035404550556065707580I2 (deg) ( )2 ( )What about this spectra?

3 PolimeroCarica inorganicaDiffrazione dei raggi X del campione prima TGAD iffrazione dei raggi X del campione dopo TGA amorphous / crystalline ( polymer , inorganic/organic compound) crystalline phasesThe peak positions, intensities, widths and shapesprovide important information about the structure of the material degree of crystallinity : xcamorphousecrystallinecrystallinIIIxc+= 2)XRDa primary technique to determine the degree of crystallinityin determination of the degree of crystallinity implies use of a two-phase model, the sample is composed of crystals and amorphous and no regions of semi-crystalline organization. amorphousecrystallin III+=5101520253035I2 The diffraction profile is divided in 2 parts: peaks are related to diffraction of crystallites, broad alone is related to scattering of amorphous phase.

4 AmcrcrKAAAxc+=Kis a constant related to the different scattering factors of crystalline and amorphous phases. For relative measures K= 1. PEIa= diffracted intensity of amorphous phaseIb= diffracted intensityof backgroundIc= diffracted intensity of crystalline phase IcIaIbThe assumption is that the areas are proportional to the scattering intensities of crystalline and amorphous phases2) XRD: determination of degree of crystallinityin (deg) 510152025302 (deg)IntensityThe half-width of peaks is related to crystallite to broadening can be due to lattice distortion, structural disorder as well as instrumental large correspond to smaller crystallites3) Microstructure: Crystallite size in polymersHalf-width narrow correspond to bigger crystallitesB= 2 = 2 2 2 12 (deg) = B bb= broadening instrumental = broadening due to crystallites dimensionsB= half-width of peaksIntensityImaxImax/22 22 1B2 Crystallite size in polymers:cos =KLhklScherrer s EquationLhkl= crystallite dimensions (in ) along the direction perpendicular to the crystallographic plane hkl.

5 = half-width of peak related to the crystallographic plane hkl(rad).K= constant (usually K= ) = diffraction angle of the hkl reflection. = wavelength used ( Cuk = .)bcan be measured by the half-width of a peak of crystalline compounds low molecular ) Microstructure: Crystallite size in polymers4)Orientation: Polymers, due to their long chain structure,are highly susceptible to orientationDraw directioncfiberX-rayFiberaxesX-ray diffraction of oriented polymer : fiber patternequatorl=0 (hk0)First layer l=1 (hk1)Second layerl=2 (hk2)i-PP fiber))/(( 1-Rytansencl=c= periodicity along the chain axes = wavelength used (CuK = )llll= layerx, y= distance of reflections from the center along equatorial and meridian linesR= chamber radius meridianyx = RytancosRxcoscos1- 23602 Distance from layers correspond to caxesX-ray diffraction of fibers annealed at different TTrans-planar conformationc= Helical conformationc= = 50 % = 100 % = 500 % = 200 %Oriented sPPfiber stretched at different =100(Lf-Li)/LiLf = final lengthLi = initial lengthFirst layer l=1 (hk1)equator l=0 (hk0)Azimutal scan:measuring the intensity at 2 constant, by varying the angle.

6 If = 0 for meridian reflection (00l)<cos2 00l> = 1 e fc=1 The fiber is perfected oriented: fc= 1 Orientation with respect to draw directionparameterparallelrandomperpendi cular<cos2 >f111/300-1/2 The degree of orientation can be determined from the intensity distribution of the corresponding diffraction on the Debye ring by using theHermans Orientation Function()13212 = cosfZ = draw axesabc a,Z b,Z c,Z 2 ( ) >= < = d)I(d 2/02/02222sencossenIcoscoscoshklhklhklIf the radiation is perpendicular to the fiber axesAverage cosine squared value of angleTypes of ORIENTATIONGEOMETRY(Heffelfinger& Burton)1 PREFERRED ORIENTATIONC rystallographic elementsReference elements1 Random---2 AxialCrystallographic Axes parallel to reference axescdraw axes3 PlanarCrystallographic Axes on a reference plane cfilm plane4 Planar-axialCrystallographic plane Parallel to a reference axes(100)draw axes5 UniplanarCrystallographic plane Parallel to a a reference plane (100)film plane6 Uniplanar-axialCrystallographic Axes parallel to reference axesand a Crystallographic plane Parallel to a a reference planec(100)draw axesfilm planeC.

7 J. Heffelfinger, R. L. Burton J. Polym. Sci. 47, 289 (1960). Types of Orientation in polymers510152025303540 DCE clathrate 240101150 DCBAE170111060130040110020030210 Intensity040 Figure 22 (deg)111020020010010040410030020600211 410400220300200110 230_510152025303540 DCE clathrate '' ''13104124015010100217011106014013012004 0110020 ABCDE411_321_230_030410002 Figure 1040_041031020 200510600410400210310 2102100100101321310302202002102112203001 10 Intensity2 (deg)121401231331020210020111_111302111_ 111_411322_321_420040410__Uniplanar orientation: spsfilmendedgethrough Through direction Edge direction End direction MD TD Types of Orientation in polymers010 Uniplanar orientation : (010)Rizzo, Lamberti, Albunia, Ruiz de Ballesteros, Guerra , 35, 5854 Albunia, Rizzo, Guerra Chem.

8 , 21,3370010 Film surfaceAlong the chain projections of packing of forms of s-PS showing (010) planes parallel to the film surface(010) planes correspond to rows of parallel helices with minimum interchain distances ( ) and maximuminterplanar distances( )s-PSco-crystalsChatani, Y.; Shimane, Y.; Inagaki, T.; Ijitsu, T.; Yukinari, T.; Shikuma, H. polymer , 1993, 34, 1620. De Rosa, C.; Rizzo, P.; Ruiz de Ballesteros, O.; Petraccone, V.; Guerra G. polymer , 1999, 40, nmRLa/2acbLLRRU nique feature of s-PS:three uniplanar orientationsacbLLRRS olution casting; Spin-coatingSolvent induced crystallization on amorphous filmTHF, CHCl3 Rizzo, Lamberti, Albunia, Ruiz, GuerraMacromolecules2002, 35, 5854p-xylene, dichloroethaneRizzo, Costabile, GuerraMacromolecules2004, 37, 3071Bp > 140 CRizzo, Spatola, Del Mauro, GuerraMacromolecules2005, 38, 10089Bp < 110 CRizzo, Della Guardia, GuerraMacromolecules2004, 37, 8043 Film thicknessa//c//a c//a//c Albunia, Rizzo, Tarallo, Petraccone, Guerra Macromolecules 2008,41, 8632biaxial M RIEEEEsPS Films: Orientation Upon Biaxial Balanced DrawingPaola Rizzo*, Alexandra R.

9 Albunia Macromolecular Chemistry and Physics 2011, 212,1419-26caa//c//010 Film surfacea// c// planescorrespond to rows of parallel helices with minimum interchaindistances ( ) and maximum interplanar distances ( )a//c//Planes(sPS)syndiotactic polystyrene(PET)polyethylene terephthalatebiaxial M RIEEEEBin, Y.; Oishi,K.; Yoshida, K.; Nakashima T.; Matsuo, M.; J. polymer , 2004,36,394-402(a= b= c= = =118 =112 ) triclinic lattice(100)uniplanar orientationUniplanar orientationUniplanar orientationA crystalline planepreferentiallyparallel to the film planePrimary slip-plane:-containing the chain axis- and having the highest densityPaola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia2002, 185, 53-63.(i-PP) polypropylenebiaxial M RIEEEENDMDTDTDMDMDABC(i-PP) polypropylenePaola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia2002, 185, M RIEEEEIn the Schulz reflection methodthe goniometer is set at the Bragg angle corresponding to the crystallographic planes of interest.

10 A special specimen holder tilted the sample with the horizontal axis (y rotation axis), while rotating it in its own plane about an axis normal to its surface (j rotation axis) . The y rotation can be varied from 0 to 90 , whereas the j rotation can be varied from 0 to 360 . The pole figures are plotted on a polar stereographic projection using linear intensity scale. (i-PP) polypropyleneUniplanarorientationbiaxial M RIEEEEP aola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia2002, 185, lines indicate the relativeintensity of the pole related to the maximum diffracted intensity (assumed equal to 10).The presence on the diffraction rings of the pole figures of the(110)and (130)reflectionof intensity maxima along MDindicates some preferential c-axis orientation along TD.