Use of Fourier Series in X-ray Diffraction (XRD) Analysis and Fourier-Transform Infrared Spectroscopy (FTIR) for Estimation of Crystallinity in Cellulose from Different Sources

Abstract

Cellulose crystallinity can be described according to the crystal size and the crystallinity index (CI). In this research, using Fourier-transform infrared spectroscopy (FTIR) and X-ray diffraction (XRD) methods, we studied the crystallinity of three different types of cellulose: banana rachis (BR), commercial cellulose (CS), and bacterial cellulose (BC). For each type of cellulose, we analyzed three different crystallization grades. These variations were obtained using three milling conditions: 6.5 h, 10 min, and unmilled (films). We developed a code in MATLAB software to perform deconvolution of the XRD data to estimate CI and full width at half-maximum (FWHM). For deconvolution, crystalline peaks were represented with Voigt functions, and a Fourier series fitted to the amorphous profile was used as the amorphous contribution, which allowed the contribution of the amorphous profile to be more effectively modeled. Comparisons based on the FTIR spectra and XRD results showed there were no compositional differences between the amorphous samples. However, changes associated with crystallinity were observed when the milling time was 10 min. The obtained CI (%) values show agreement with values reported in the literature and confirm the effectiveness of the method used in this work in predicting the crystallization aspects of cellulose samples.

Keywords: Fourier series; X-ray diffraction; cellulose; crystallinity; crystallinity index; infrared spectroscopy; peak deconvolution.

Figure 1

Flow process diagram. Cellulose from banana rachis (BR), a commercial sample (CS), and bacterial cellulose (BC) were used. Three samples were obtained from each cellulose type: an unmilled sample (film), a sample ball-milled for 10 min (P_BR_BM_10 m, P_CS_BM_10 m, and P_BC_BM_10 m), and one ball-milled for 6.5 h (P_BR_BM_6.5 h, P_CS_BM_6.5 h, and P_BC_BM_6.5 h).

Figure 2

Diagram of main steps followed in the MATLAB routine to perform deconvolution of complete XRD profile and to obtain CI and FWHM (width) of crystalline peaks.

Figure 3

Infrared spectra of cellulose samples: (a) banana rachis (BR) milled at 10 min (P_BR_BM_10 m) and 6.5 h (P_BR_BM_6.5 h), and unmilled (Film BR); (b) commercial sample (CS) milled at 10 min (P_CS_BM_10 m) and 6.5 h (P_CS_BM_6.5 h), and unmilled (Film CS); (c) bacterial cellulose (BC) milled at 10 min (P_BC_BM_10 m) and 6.5 h (P_BC_BM_6.5 h), and unmilled (Film BC); and (d) BR, CS, and BC samples at 6.5 h milling time.

Figure 4

(a) Amorphous banana rachis (BR), (b) commercial sample (CS), and (c) bacterial cellulose (BC) XRD. The black line corresponds to the experimental result and the red line to data fit using the Fourier function.

Figure 5

X-ray diffraction spectra recorded from banana rachis cellulose samples (BR): (a) unmilled (film BR), and (b) milled for 10 min (P_BR_BM_10 m) and 6.5 h (P_BR_BM_6.5 h). The indexation is that defined in [40].

Figure 6

X-ray diffraction spectra recorded from commercial sample cellulose (CS): (a) unmilled (film CS), and (b) milled for 10 min (P_CS_BM_10 m) and 6.5 h (P_CS_BM_6.5 h). The indexation is that defined in [40].

Figure 7

X-ray diffraction spectra recorded from bacterial cellulose (BC): (a) unmilled (film BC), and (b) milled for 10 min (P_BC_BM_10 m) and 6.5 h (P_BC_BM_6.5 h). The indexation is that defined in [40].