Improved cellulose X-ray diffraction analysis using Fourier series modeling

Abstract

This paper addresses two fundamental issues in the peak deconvolution method of cellulose XRD data analysis: there is no standard model for amorphous cellulose and common peak functions such as Gauss, Lorentz and Voigt functions do not fit the amorphous profile well. It first examines the effects of ball milling on three types of cellulose and results show that ball milling transforms all samples into a highly amorphous phase exhibiting nearly identical powder X-ray diffraction (XRD) profiles. It is hypothesized that short range order within a glucose unit and between adjacent units survives ball milling and generates the characteristic amorphous XRD profiles. This agrees well with cellulose I d-spacing measurements and oligosaccharide XRD analysis. The amorphous XRD profile is modeled using a Fourier series equation where the coefficients are determined using the nonlinear least squares method. A new peak deconvolution method then is proposed to analyze cellulose XRD data with the amorphous Fourier model function in conjunction with standard Voigt functions representing the crystalline peaks. The impact of background subtraction method has also been assessed. Analysis of several cellulose samples was then performed and compared to the conventional peak deconvolution methods with common peak fitting functions and background subtraction approach. Results suggest that prior peak deconvolution methods overestimate cellulose crystallinity.

Graphic abstract

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

References

  1. Ahvenainen P, Kontro I, Svedström K (2016) Comparison of sample crystallinity determination methods by X-ray diffraction for challenging cellulose I materials. Cellulose 23:1–14

    Article  Google Scholar 

  2. Astley OM, Chanliaud E, Donald AM, Gidley MJ (2001) Structure of acetobacter cellulose composites in the hydrated state. Int J Biol Macromol 29:193–202. https://doi.org/10.1016/S0141-8130(01)00167-2

    CAS  Article  PubMed  Google Scholar 

  3. Azubuike CP, Rodríguez H, Okhamafe AO, Rogers RD (2012) Physicochemical properties of maize cob cellulose powders reconstituted from ionic liquid solution. Cellulose 19:425–433. https://doi.org/10.1007/s10570-011-9631-y

    CAS  Article  Google Scholar 

  4. Bansal P (2011) Computational and experimental investigation of the enzymatic hydrolysis of cellulose. Georgia Institue of Technology, Atlanta

    Google Scholar 

  5. Bansal P, Hall M, Realff MJ et al (2010) Multivariate statistical analysis of X-ray data from cellulose: a new method to determine degree of crystallinity and predict hydrolysis rates. Bioresour Technol 101:4461–4471. https://doi.org/10.1016/j.biortech.2010.01.068

    CAS  Article  PubMed  Google Scholar 

  6. Barnette AL, Lee C, Bradley LC et al (2012) Quantification of crystalline cellulose in lignocellulosic biomass using sum frequency generation (SFG) vibration spectroscopy and comparison with other analytical methods. Carbohydr Polym 89:802–809. https://doi.org/10.1016/j.carbpol.2012.04.014

    CAS  Article  PubMed  Google Scholar 

  7. Bates S, Zografi G, Engers D et al (2006) Analysis of amorphous and nanocrystalline solids from their X-Ray diffraction patterns. Pharm Res 23:2333–2349. https://doi.org/10.1007/s11095-006-9086-2

    CAS  Article  PubMed  Google Scholar 

  8. Buerger M, Klein GE (1945) Correction of X-ray diffraction Intensities for Lorentz and Polarization Factors. J Appl Phys 16:408–418

    CAS  Article  Google Scholar 

  9. Ciolacu D, Ciolacu F, Popa VI (2011) Amorphous cellulose—structure and characterization. Cellul Chem Technol 45:13

    CAS  Google Scholar 

  10. Cullity BD (1978) Elements of x-ray diffraction. Addison-Wesley Pub. Co., Reading

    Google Scholar 

  11. Delhez R, De Keijser TH, Mittemeijer EJ (1982) Determination of crystallite size and lattice distortions through X-ray diffraction line profile analysis. Fresenius Z Für Anal Chem 312:1–16

    CAS  Article  Google Scholar 

  12. Delhez R, de Keijser TH, Langford JI, Louër D, Mittemeijer EJ, Sonneveld, EJ (1993) Crystal imperfection broadening and peak shape in the Rietveld method. In: Young RA (ed) The Rietveld Method. Oxford University Press, p 132

  13. Dinnebier RE (2008) Powder diffraction: theory and practice. Royal Society of Chemistry, Cambridge

    Google Scholar 

  14. Dumitriu S (2004) Polysaccharides: structural diversity and functional versatility, 2nd edn. CRC Press, Boca Raton

    Google Scholar 

  15. Fang L, Catchmark JM (2014) Structure characterization of native cellulose during dehydration and rehydration. Cellulose 21:3951–3963. https://doi.org/10.1007/s10570-014-0435-8

    CAS  Article  Google Scholar 

  16. Fawcett TG, Crowder CE, Kabekkodu SN et al (2013) Reference materials for the study of polymorphism and crystallinity in cellulosics. Powder Diffr 28:18–31

    CAS  Article  Google Scholar 

  17. Fink H-P, Philipp B, Paul D et al (1987) The structure of amorphous cellulose as revealed by wide-angle X-ray scattering. Polymer 28:1265–1270. https://doi.org/10.1016/0032-3861(87)90435-6

    CAS  Article  Google Scholar 

  18. Fourier J (1822) Theorie analytique de la chaleur, par M. Fourier. chez Firmin Didot, pere et fils

  19. French AD (2014) Idealized powder diffraction patterns for cellulose polymorphs. Cellulose 21:885–896. https://doi.org/10.1007/s10570-013-0030-4

    CAS  Article  Google Scholar 

  20. French AD, Santiago Cintrón M (2013) Cellulose polymorphy, crystallite size, and the Segal Crystallinity Index. Cellulose 20:583–588. https://doi.org/10.1007/s10570-012-9833-y

    CAS  Article  Google Scholar 

  21. Garvey CJ, Parker IH, Simon GP (2005) On the interpretation of X-Ray diffraction powder patterns in terms of the nanostructure of cellulose I fibres. Macromol Chem Phys 206:1568–1575. https://doi.org/10.1002/macp.200500008

    CAS  Article  Google Scholar 

  22. Guo J, Catchmark JM (2012) Surface area and porosity of acid hydrolyzed cellulose nanowhiskers and cellulose produced by Gluconacetobacter xylinus. Carbohydr Polym 87:1026–1037. https://doi.org/10.1016/j.carbpol.2011.07.060

    CAS  Article  Google Scholar 

  23. He J, Cui S, Wang S (2008) Preparation and crystalline analysis of high-grade bamboo dissolving pulp for cellulose acetate. J Appl Polym Sci 107:1029–1038. https://doi.org/10.1002/app.27061

    CAS  Article  Google Scholar 

  24. Hermans PH, Weidinger A (1946) On the diffusely diffracted radiation in the X-ray diagrams of cellulose fibres. Recl Trav Chim Pays-Bas 65:620–623. https://doi.org/10.1002/recl.19460650814

    CAS  Article  Google Scholar 

  25. Hult E-L, Iversen T, Sugiyama J (2003) Characterization of the supermolecular structure of cellulose in wood pulp fibres. Cellulose 10:103–110. https://doi.org/10.1023/A:1024080700873

    CAS  Article  Google Scholar 

  26. Ioelovich M, Leykin A, Figovsky O (2010) Study of cellulose paracrystallinity. BioResources 5:1393–1407. https://doi.org/10.15376/biores.5.3.1393-1407

    CAS  Article  Google Scholar 

  27. Jmol (2016) An open-source Java viewer for chemical structures in 3D. https://jmol.sourceforge.net/. Accessed 25 June 2016

  28. Ju X, Bowden M, Brown EE, Zhang X (2015) An improved X-ray diffraction method for cellulose crystallinity measurement. Carbohydr Polym 123:476–481. https://doi.org/10.1016/j.carbpol.2014.12.071

    CAS  Article  Google Scholar 

  29. Klug HP, Alexander LE (1974) X-Ray Diffraction procedures: for polycrystalline and amorphous materials, 2nd edn. Wiley, New York

    Google Scholar 

  30. Kroon-Batenburg LM, Kruiskamp PH, Vliegenthart JF, Kroon J (1997) Estimation of the persistence length of polymers by MD simulations on small fragments in solution. Application to cellulose. J Phys Chem B 101:8454–8459

    CAS  Article  Google Scholar 

  31. Langford JI, Wilson AJC (1978) Scherrer after sixty years: a survey and some new results in the determination of crystallite size. J Appl Crystallogr 11:102–113

    CAS  Article  Google Scholar 

  32. Lanson B (1997) Decomposition of experimental X-ray diffraction patterns (profile fitting); a convenient way to study clay minerals. Clays Clay Miner 45:132–146

    CAS  Article  Google Scholar 

  33. Ling Z, Wang T, Makarem M, Santiago Cintrón M, Cheng HN, Kang X, Bacher M, Potthast A, Rosenau T, King H, Delhom CD, Nam S, Edwards JV, Kim SH, Xu F, French AD (2019) Effects of ball milling on the structure of cotton cellulose. Cellulose 26:305–328

    CAS  Article  Google Scholar 

  34. Luca Lutterotti MAUD (2020) Material analysis using diffraction. https://maud.radiographema.eu/. Accessed 14 Feb 2020

  35. Madsen IC, Scarlett NVY, Kern A (2011) Description and survey of methodologies for the determination of amorphous content via X-ray powder diffraction. Z Für Krist Cryst Mater 226:944–955

    CAS  Google Scholar 

  36. McCusker LB, Von Dreele RB, Cox DE et al (1999) Rietveld refinement guidelines. J Appl Crystallogr 32:36–50

    CAS  Article  Google Scholar 

  37. Mittemeijer EJ, Welzel U (2008) The “state of the art” of the diffraction analysis of crystallite size and lattice strain. Z Für Krist 223:552–560

    CAS  Google Scholar 

  38. Nada Stubičar IŠ (1998) An X-Ray Diffraction study of the crystalline to amorphous phase change in cellulose during high-energy dry ball milling. Holzforschung 52:455–458. https://doi.org/10.1515/hfsg.1998.52.5.455

    Article  Google Scholar 

  39. Nelson ML, O’Connor RT (1964) Relation of certain infrared bands to cellulose crystallinity and crystal latticed type. Part I. Spectra of lattice types I, II, III and of amorphous cellulose. J Appl Polym Sci 8:1311–1324. https://doi.org/10.1002/app.1964.070080322

    CAS  Article  Google Scholar 

  40. Park S, Baker JO, Himmel ME et al (2010) Cellulose crystallinity index: measurement techniques and their impact on interpreting cellulase performance. Biotechnol Biofuels 3:10. https://doi.org/10.1186/1754-6834-3-10

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  41. Park S, Johnson DK, Ishizawa CI et al (2009) Measuring the crystallinity index of cellulose by solid state 13C nuclear magnetic resonance. Cellulose 16:641–647. https://doi.org/10.1007/s10570-009-9321-1

    CAS  Article  Google Scholar 

  42. Pecharsky V, Zavalij P (2008) Fundamentals of powder diffraction and structural characterization of materials, 2nd edn. Springer, Berlin

    Google Scholar 

  43. Pires L, de Figueiredo F, Ferreira F (2014) The Rietveld method as a tool to quantify the amorphous amount of microcrystalline cellulose. J Pharm Sci 103:1394. https://doi.org/10.1002/jps.23909

    CAS  Article  Google Scholar 

  44. Rodgers JL, Nicewander WA (1988) Thirteen ways to look at the correlation coefficient. Am Stat 42:59–66. https://doi.org/10.2307/2685263

    Article  Google Scholar 

  45. Schwanninger M, Rodrigues JC, Pereira H, Hinterstoisser B (2004) Effects of short-time vibratory ball milling on the shape of FT-IR spectra of wood and cellulose. Vib Spectrosc 36:23–40. https://doi.org/10.1016/j.vibspec.2004.02.003

    CAS  Article  Google Scholar 

  46. Segal L, Creely JJ, Martin AE, Conrad CM (1959) An empirical method for estimating the degree of crystallinity of native cellulose using the X-Ray diffractometer. Text Res J 29:786–794. https://doi.org/10.1177/004051755902901003

    CAS  Article  Google Scholar 

  47. Stankovic L, Dakovic M, Thayaparan T (2013) Time-frequency signal analysis with applications. Artech House Publishers, Norwood, MA

    Google Scholar 

  48. Suortti P (1993) Bragg reflection profile shape in X-ray powder diffraction patterns. In: Young RA (ed) The Rietveld method. Cambridge University Press, Cambridge, pp 167–185

    Google Scholar 

  49. Swenson HA, Schmitt CA, Thompson NS (1965) Comparison of the configuration of β-1,4 linked hexosans and wood xylan pentosans by means of the eizner-ptitsyn viscosity equations. J Polym Sci Part C Polym Symp 11:243–252. https://doi.org/10.1002/polc.5070110117

    Article  Google Scholar 

  50. Taylor LS, Zografi G (1998) The quantitative analysis of crystallinity using FT-Raman spectroscopy. Pharm Res 15:755–761. https://doi.org/10.1023/A:1011979221685

    CAS  Article  PubMed  Google Scholar 

  51. Teeäär R, Serimaa R, Paakkarl T (1987) Crystallinity of cellulose, as determined by CP/MAS NMR and XRD methods. Polym Bull 17:231–237. https://doi.org/10.1007/BF00285355

    Article  Google Scholar 

  52. Wada M, Okano T, Sugiyama J (1997) Synchrotron-radiated X-ray and neutron diffraction study of native. Cellulose 4:221–232. https://doi.org/10.1023/A:1018435806488

    CAS  Article  Google Scholar 

  53. Ward K (1950) Crystallinity of cellulose and its significance for the fiber properties. Text Res J 20:363–372. https://doi.org/10.1177/004051755002000601

    CAS  Article  Google Scholar 

  54. Warren BE (1990) X-Ray diffraction, Reprint edn. Dover Publications, New York

    Google Scholar 

  55. Watanabe K, Tabuchi M, Morinaga Y, Yoshinaga F (1998) Structural features and properties of bacterial cellulose produced in agitated culture. Cellulose 5:187–200. https://doi.org/10.1023/A:1009272904582

    CAS  Article  Google Scholar 

  56. Young RA (ed) (1995) The Rietveld Method. In: OUP/International Union of Crystallography|International Union of Crystallography Monographs on Crystallography, pp. 5

  57. Zhang Y, Inouye H, Crowley M et al (2016) Diffraction pattern simulation of cellulose fibrils using distributed and quantized pair distances. J Appl Crystallogr 49:2244–2248. https://doi.org/10.1107/S1600576716013297

    CAS  Article  Google Scholar 

  58. Zhang S, Winter WT, Stipanovic AJ (2005) Water-activated cellulose-based electrorheological fluids. Cellulose 12:135–144. https://doi.org/10.1007/s10570-004-0345-2

    CAS  Article  Google Scholar 

Download references

Acknowledgments

The research work in this paper is supported by the Center for Lignocellulose Structure and Formation, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001090, and by the National Institute of Food and Agriculture, U.S. Department of Agriculture, Pennsylvania Agricultural Experiment Station 4602 under Accession Number 1009850. We thank two colleagues at Penn State University, Liza Wilson from Department of Biology for the training of ball milling and Nichole Wonderling from Materials Research Institute for the training and discussion on XRD analysis.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jeffery M. Catchmark.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (XLSX 150 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yao, W., Weng, Y. & Catchmark, J.M. Improved cellulose X-ray diffraction analysis using Fourier series modeling. Cellulose 27, 5563–5579 (2020). https://doi.org/10.1007/s10570-020-03177-8

Download citation

Keywords

  • Amorphous cellulose
  • Ball milling
  • Crystallinity index
  • Crystal size
  • Fourier series
  • Peak deconvolution
  • X-ray diffraction