On the role of tannins and iron in the Bogolan or mud cloth dyeing process

Abstract

We have investigated the chemistry of the Bogolan or mud cloth dyeing process, a traditional technique of coloring cotton cloths deeply rooted in Mali. Textiles produced by the traditional Bogolan process, using tannin-rich plant extract and iron-rich clay-based mud, were compared using infrared (IR) spectroscopy, scanning electron microscopy (SEM) and X-ray absorption near-edge spectroscopy (XANES) with cotton fibers that were impregnated with tannin and iron salt solutions. IR spectroscopy in both reflective mode on the cloth and cotton and in transmission mode on single fibers, together with SEM, showed that gallic and tannic acid adsorb and precipitate onto the cotton fiber surface. IR spectroscopy and comparison with tannin and iron solution-impregnated cotton showed that the black color of the traditional Bogolan cloth is dominated by the formation of iron-tannin complexes. The presence of iron in the Bogolan cloth was confirmed using XANES data, supporting the notion that iron has been transferred from the iron-rich clay-based mud to the cloth. The chemistry of Bogolan cloth is not only historically and culturally significant and of importance in textile conservation, but may also inspire future research on sustainable dyeing and processing techniques based on natural products.

Keywords

Bogolan dyeing tannins clay cotton mud cloth

Bogolan or mud cloth is a traditional, handmade African textile indigenous to the Bamana Tribe of Mali, where it has been produced and worn for generations.^1,2 Bogolan is also known as bogolanfini, bogo meaning “mud”, lan meaning “with” and fini meaning “cloth”.³ Bogolan is unique both in technique and in style, which has made the cloth appealing also in recent times.^1,4

The Bogolan dyeing follows a specific and unique procedure that utilizes natural products: textile, plants (rich in tannins) and clay-based mud (rich in iron).^3,5 The mud, which contains organic matter, is collected from still ponds or parts of the Niger river and stored in covered jars for up to a year prior to use. The textile consists of white cotton strips that are stitched together into a cloth of desired shape and size. Leaves and branches from the evergreen tree known as African birch or n’gallama (Anogeissus leiocarpa) are mashed and soaked in water for 24 hours or boiled for a few minutes. The textile is impregnated with this brown-colored leaf extract and dried in the sun. The process is repeated until the textile acquires a deep yellow color, which stems from some of the extracts released by the soaking or boiling of the leaves. Patterns are then drawn with a pointy object on the impregnated cloth using the blackish clay-based mud paste. After drying in the sun, the patterned textile is washed with water to remove any excess mud, leaving black or brown designs on a yellow background.⁶ This process can be repeated several times to obtain increasingly darker shades of color. Finally, the yellow background is bleached using a solution of millet bran, caustic soda and ground peanuts to render it white. This process yields a dyed cloth that has a high fastness and retains its dark color for a long time.

There are only a few reports describing the Bogolan dyeing process in more detail, primarily from handicraft or artistic viewpoints.¹^–⁵ Donne⁷ was the first to investigate this “cumbersome” process from a chemical perspective, succeeding in identifying the importance of the tannins and iron oxide to produce the brown or black color. Recently, Blanchart et al.⁶ presented a thorough investigation of two of the main components in the Bogolan dyeing process: Balengué clay and n’gallama leaves, showing that the Balengué clay is iron rich and that the n’gallama leaves are rich in tannins, primarily ellagic, gallic acid (GA) and tannic acid (TA).

Useful information on how black pigments can form through reactions between iron salts and tannins can be obtained from the numerous studies on iron-gall inks,⁸^–¹⁷ which was the dominating writing inks used in Europe since the 12th century until the introduction of synthetic inks in the late 19th century. Iron-gall inks were generally prepared by mixing iron(II) sulfate with a solution of fermented oak galls, which are rich in GA, and gum Arabic, which provides the desired rheology and also acts as a binder. It is interesting to note that iron-gall inks tend to slowly become darker after application, an effect that has been connected to the oxidation of the iron ion from the Fe²⁺ to the Fe³⁺ state.^11,12 Unfortunately, iron-gall inks can result in a degradation of the paper or vellum (skin) they are applied to, a challenge that has motivated many studies on, for example, paper degradation.¹¹^–¹⁴ Although the acidity of the ink and a possible excess of Fe²⁺ ions has been identified as possible causes for the degradation of iron-gall ink documents,¹² the mechanisms are complex and many ancient documents do not show any signs of damage or degradation by the iron-gall inks.

This study aims to elucidate the chemistry of the Bogolan dyeing process by characterizing both cloth dyed using the traditional process and cotton treated with only some of the main components, that is, GA and TA, and Fe(II) or Fe(III) solutions, which is referred to as model Bogolan cotton. The traditional and the model textiles have been characterized by a combination of infrared (IR) spectroscopy, scanning electron microscopy (SEM) and X-ray absorption near-edge spectroscopy (XANES). The interaction between the tannins and the cellulose and the formation of color pigments on the cotton fibers has been demonstrated. The oxidation state and the transfer of iron from iron-rich clay-based mud to the cotton cloth are discussed based on the XANES data.

Experimental details

Materials

Traditional Bogolan or mud cloth, n’gallama leaves and Balengué clay were obtained from Mali, Africa. The cloth was prepared in Mali using the traditional Bogolan dyeing process described earlier by treating a hand-woven textile with n’gallama leaves and Balengué clay-based mud.

Layered cotton was used as obtained. GA (C₇H₆O₅), TA (C₇₆H₅₂O₄₆), FeCl₃·6H₂O, FeCl₂·4H₂O and FeSO₄·7H₂O were purchased from Sigma Aldrich and used as received.

Cotton fibers were treated with GA and TA. A small piece (around 1 cm³) of cotton was soaked for 5 minutes in an aqueous solution containing concentrations of 0.005 M and 0.001 M of GA and TA, respectively (M = mol/dm³). The treated cotton (hereafter referred to as acid-treated cotton) was dried under ambient conditions. For the sake of comparison, cotton fibers were also treated with n’gallama leaf extract. The GA and TA-treated cotton were impregnated with different iron solutions (FeCl₃/FeCl₂/FeSO₄) of concentration 0.025 M and 0.005 M, respectively, and then dried under ambient conditions. The acid and iron salt solution-treated cotton are referred to as model Bogolan cotton.

Characterization

A Varian 610-IR Fourier transform infrared (FTIR) spectrometer was used to probe the molecular interactions of the starting materials and the dyed cotton and Bogolan cloth. The FTIR spectrometer was equipped with an attenuated total reflection (ATR) accessory (Specac) with a single-reflection diamond ATR element. Measurements were normally performed by accumulating 64 scans in the spectral region of 4000–390 cm⁻¹ with a spectral resolution of 4 cm⁻¹. IR spectra of the black and white regions of traditional Bogolan cloth were obtained by pressing the cloth against the diamond ATR element without destruction of the cloth. IR spectra of the model Bogolan cotton were also obtained following this procedure, together with a technique where a single fiber (around 3–5 mm long and 10 µm diameter) was extracted from the traditional and model Bogolan cloth and placed in a diamond anvil cell. Approximately a 60 × 60 µm² area can be investigated using a diamond anvil cell. The fiber section was examined by setting the aperture of a Varian 610-IR microscope in transmission mode (see Supplementary data Figure S1).

The morphological analysis was performed using a JEOL 7000 field emission gun scanning electron microscope. The samples were prepared by placing some fibers from the acid-treated and model Bogolan cotton on aluminum stubs using carbon double-sided tape and coating with a thin layer of amorphous carbon. The secondary electron images were recorded using accelerating voltage of 1 kV and with a medium probe current.

Room temperature Fe K-edge X-ray absorption near-edge spectra (XANES) were recorded at the Max lab beamline I811 in Lund, Sweden. The intensity of the X-ray beam with a sample spot size of 0.5 × 0.5 mm² was measured with three ionization chambers. A metallic Fe foil was used as a reference during acquisition. The data were recorded in transmission mode and fluorescence mode. The Bogolan sample for XANES measurements was prepared by scraping off a small amount (a few micrograms) of fibers from the surface of the black section of a traditional Bogolan cloth. The sample was glued onto Kapton tape and mounted in between the first and second ionization chambers and positioned at 45° with respect to the incident photon beam. The reference metallic Fe foil was inserted in between the second and third ionization chambers. The absorption spectra were recorded in the range of ± 150 eV with respect of the Fe K-edge (7112 eV). The data were acquired with a varying step size, that is, for the range (−150 to −50 eV) a step size of 5 eV was used, whereas for the ranges (−50 to 30 eV) and (30 to 150 eV) step sizes of 0.25 eV and of 1 eV were used, respectively. The acquisition time for the XANES data was ∼45 min for each spectrum. The short measurement time and sufficiently large spot size makes photon-induced changes unlikely.^12,17

Results and discussion

We have characterized traditional Bogolan cloth and model Bogolan cotton by a combination of IR spectroscopy, SEM and XANES. Figure 1 exemplifies the distinct dark patterns on a white background that are typical for a traditional Bogolan cloth. The IR spectrum recorded from a black region of the textile (Figure 2) shows the typical bands (in the regions 1200–900 cm⁻¹, 1500–1200 cm⁻¹ and 790–580 cm⁻¹) for cotton and an intense broad band in the range of 1760–1500 cm⁻¹. Tannins, such as GA or TA, have the characteristic carbonyl (C = O) band around 1700 cm⁻¹ and aromatic ring C = C stretching around 1600 cm⁻¹.^18,19 Impregnation of tannins on the cotton results in superimposition and broadening of the bands.¹⁹ The spectrum of the bleached, white part of the textile looks similar to that of untreated cotton. The carbonyl band of the bleached part is less intense compared to the black part, indicating that most of the tannins have been removed. However, features still present in the 1760–1500 cm⁻¹ region suggest that some tannins remain. The distinct and narrow OH bands at 3620 and 3700 cm⁻¹ characteristic for the Balengué clay are present in both the dark and white (bleached) regions of the traditionally dyed Bogolan cloth. Interestingly, spectroscopic analysis carried out on historic manuscripts written using iron-gall inks also showed an intense broad carbonyl band in the 1750–1500 cm⁻¹ region compared to pure cellulose.^14,20 This similarity between the two processes may already suggest a similar chemistry of iron-gall inks and Bogolan dyeing.

Figure 1.

Photograph of traditional Bogolan or mud cloth displaying the typical black and white patterns.

Figure 2.

Infrared (IR) spectra of cotton retrieved from the (a) black section and (b) white (bleached) section of a traditional Bogolan or mud cloth. The IR spectra of untreated cotton and Balengué clay are shown in (c) and (d), respectively. The inset figure display the respective sampling areas of the black and white regions of the traditional Bogolan cloth.

We have also used another sampling technique that allows IR spectra to be obtained from single fibers of the traditional Bogolan cloth. Placing a single cotton fiber in a diamond anvil cell yields a well-defined, sufficiently thin section of the fiber (see Supplementary data Figure S1) that allowed IR spectra to be retrieved in the transmission mode. The measurements on the single fiber shown in Figure 3 confirm the features observed from the ATR-measurements shown in Figure 2, with a prominent contribution from the cotton and intense absorption bands related to carbonyl groups on the black fiber. The absence of distinct and narrow OH bands at 3620 and 3700 cm⁻¹ indicates that the contribution from the clay is less pronounced in the single fiber measurements.

Figure 3.

Transmission infrared spectra of single fibers of (a) untreated cotton, (b) cotton treated with n’gallama leaf extract, (c) the white (bleached) part of the traditional Bogolan cloth and (d) the black part of the traditional Bogolan cloth.

Figure 4 shows the IR spectra of the n’gallama leaf and the cotton treated with n’gallama extract. The spectrum of a leaf native to Mali shows typical bands of cellulose, which of course relates to the matrix of the leaf. In addition, we can also identify intense bands for -CH₂- fragments at 2920 and 2851 cm⁻¹, characteristic for long chain alkanes, a C = O band at 1723 cm⁻¹, and a C = C aromatic ring stretching at 1600 cm⁻¹ typical for the tannins present in these leaves.²¹ The cotton treated with solutions of n’gallama leaf extract shows a C = O and C = C stretching region that is nearly identical to the n’gallama leaf, indicating that the tannins from the leaves are dissolved and attached to the surface of the cotton. The very broad band between 3300 and 2500 cm⁻¹ can be attributed to H-bonded OH groups.

Figure 4.

Infrared spectra of (a) n’gallama leaf, (b) untreated cotton and (c) cotton treated with n’gallama leaf extract.

We have treated cotton with two different tannins – GA and TA – which are found in n’gallama leaves and n’gallama leaf extract (Figure S2 in Supplementary data). Subsequently, we have treated the cotton with iron solutions to elucidate the chemistry of the Bogolan dying process in detail. Figure 5 shows that the treatment with GA and Fe(II) salt solutions produces a deep black color of the treated cotton, whereas combination with Fe(III) salt solution produces less intense brown or gray colors. Interestingly, the color of the cotton impregnated with TA displays much smaller differences in blackness after reaction with Fe(II) or Fe(III) salt solutions.

Figure 5.

Photographs of cotton treated with (a) gallic acid (GA) and FeCl₃, (b) GA and FeCl₂, (c) GA and FeSO₄, (d) tannic acid (TA) and FeCl₃, (e) TA and FeCl₂ and (f) TA and FeSO₄.

The SEM images of the cotton fibers shown in Figure 6 show that treatment with GA results in the formation of small particles on the fiber surface. The particles have an angular shape and the size is of the order of a few micrometers. The microscopic images of the cotton fibers impregnated with GA (0.005 M) and FeSO₄ (0.025 M) also show the presence of some particles (Figure 6(c)), suggesting that the formation of GA precipitates during the first step of the dying process, which is important for the subsequent in situ formation of the iron-gall pigments on the cotton fibers.

Figure 6.

Scanning electron microscopy images of (a) and (b) cotton treated with gallic acid (GA) and (c) and (d) cotton treated with GA and FeSO₄. The inset shows a magnified region of (d). The images were modified using GIMP 2 software.

The concentrations of GA and TA used to impregnate the cotton were adjusted (0.005 M and 0.001 M, respectively) for the interpretation of the IR spectra. When acid is in excess (0.070 M GA and 0.025 M TA), the bands observed in the IR spectra of the acid-treated cotton samples are dominated by the free acid (Supplementary data Figure S3). The concentrations of the acids were adjusted in order to observe the changes in the carbonyl region, which corresponds only to the acid molecules adsorbed on the cotton. Figure 7 shows IR spectra of cotton treated with dilute (0.005 M GA and 0.001 M TA) solutions of acids. Detailed assignation of the bands in the GA spectrum can be found elsewhere;¹⁸ here we have concentrated on the carbonyl stretching region. The untreated cotton has a carbonyl band at 1637 cm⁻¹ (Figure 7(a)) and pure GA shows a characteristic carbonyl band at 1698 cm⁻¹ and C = C aromatic ring stretching at 1610 cm⁻¹ (Figure 7(d)). The GA-treated cotton shows a broad band in the region 1711–1576 cm⁻¹ (Figure 7(b)), indicating that the treatment of GA with cotton causes superimposition and broadening of the bands. The difference spectrum obtained by subtracting the contribution of unmodified cotton from the spectrum of cotton treated with GA is a convenient way to visualize differences between the two spectra. Indeed, the similarity between the difference spectra (Figure 7(c)) and the spectrum of the pure GA (Figure 7(d)) confirms that GA adsorbs onto the cotton fibers. It can also be observed that the C = O band present at 1698 cm⁻¹ in pure GA was shifted to 1686 cm⁻¹ in the difference spectrum. The explanation for the shift is not straightforward, but suggests that the carbonyl group of the acid (at least partially) interacts with the cellulose. A possible explanation for the shift can be the participation of the carbonyl group in hydrogen bonding with functional groups on the cotton surface. Unfortunately, it is not possible to identify conclusively the changes in the OH stretching region from the complex difference spectra.

Figure 7.

Infrared spectra of (a) cotton, (b) cotton treated with gallic acid (GA) (cotton+GA), (c) the difference spectrum ((cotton+GA)–cotton) and (d) GA. The magnified region of the spectra between 1800 and 1500 cm⁻¹ is shown on the top right-hand side. Infrared spectra of (e) cotton, (f) cotton treated with tannic acid (TA) (cotton+TA), (g) the difference spectrum ((cotton+TA)–cotton) and (h) TA. The magnified region of the spectra between 1800 and 1500 cm⁻¹ is shown on the bottom right-hand side.

The IR spectrum of the cotton treated with TA is shown in Figure 7(f). The TA-treated cotton sample shows two absorption bands at 1610 and 1706 cm⁻¹, which correspond to the aromatic ring C = C stretching and carbonyl (C = O) stretching, respectively, of TA.¹⁹ The shift of the C = O band present at 1696 cm⁻¹ in pure TA (Figure 7(h)) to 1706 cm⁻¹ in the difference spectrum (Figure 7(g)) suggests that the carbonyl group of the TA (at least partially) interacts with the cellulose.

The IR spectra of the model Bogolan cotton first impregnated with GA or TA and then treated with FeSO₄ are shown in Figure 8. The spectra of model Bogolan cotton treated with both acids and all three iron salts are shown in the Supplementary data Figure S4. The broad band in the carbonyl region, which is characteristic for the cotton treated with GA or TA (see Figure 7), becomes broader after treatment with FeSO₄. The intensity of the carbonyl band for the FeSO₄-treated samples also increases compared to the acid-treated samples, using the most intense band of the cotton in the 1200–900 cm⁻¹ region as an internal reference. The similarity between the broad, intense carbonyl band found in the model Bogolan cotton samples and the traditional Bogolan cloth, and the previously studied iron tannates²² and iron gallates²³ indicates the presence of these species on the surface of the treated cotton. However, a detailed analysis of the IR spectra is not possible, as the iron complex has a similar spectrum in the carbonyl region to that of the adsorbed acids on the surface of the cotton.

Figure 8.

Infrared spectra of (a) cotton treated with gallic acid (GA) and (b) cotton treated with GA and FeSO₄. The magnified region of the spectra between 1800 and 1500 cm⁻¹ is shown on the top right-hand side. Infrared spectra of (c) cotton treated with tannic acid (TA) and (d) cotton treated with TA and FeSO₄. The magnified region of the spectra between 1800 and 1500 cm⁻¹ is shown on the bottom right-hand side.

XANES is a sensitive tool for the determination of the oxidation state of iron. Figure 9 shows the Fe K-edge XANES spectra of Bogolan cloth, Balengué clay and Fe reference foil. The Bogolan cloth and Balengué clay display a pre-edge (1 s → 3 d transition) at 7115 eV, which is characteristic of Fe(III). An edge (1 s → 4 p transition) is observed at 7133.7 eV for both the Bogolan cloth and Balengué clay. In the clay, a small shoulder is observed at 7147 eV, which indicates the presence of iron oxides or iron oxyhydroxides.^24,25 This corresponds well with previous observations,⁶ which suggested that Balengué clay contains akaganeite (β-FeOOH). The Fe K-edge XANES data clearly shows that the Bogolan cloth also contains iron. This observation suggests that the iron originally present in the clay is transferred at least partially to the cloth during the process of dyeing, as no other material except the clay contains iron. The XANES data shows that the transfer of iron occurs without change of oxidation state.

Figure 9.

Fe K-edge X-ray absorption near-edge spectroscopy spectra of (a) Fe foil, (b) traditional Bogolan cloth and (c) Balengué clay.

Conclusions

We have studied the chemistry of the traditional Bogolan or mud cloth and the interaction between cotton, tannins and iron salts. Studies on cotton fibers treated with GA and TA and iron solutions by mainly IR spectroscopy showed that the GA and TA adsorb on the cotton surface. The IR measurement of a single fiber is a promising technique to characterize small quantities of samples and it show similar features observed from the ATR measurements. The similarity of the IR spectra for the black regions of the traditional Bogolan cloth and cotton treated with tannins and iron solution suggests that the dying process is dominated by the formation of iron-tannin complexes. SEM confirmed the formation of precipitates on the cotton fibers after treatment with GA and FeSO₄. The unusually high color fastness of old Bogolan cloth suggests that the iron originally present in the clay is transferred to the cloth where it interacts with tannins, resulting in dark pigments strongly bound to the cotton fiber surfaces.

Footnotes

Acknowledgements

The Knut and Alice Wallenberg Foundation and Max lab, Lund, Sweden, are acknowledged for the electron microscopy facilities at Stockholm University and the allocation of beam time, respectively. We also thank Katarina Norén and Tom Willhammar for assistance and support during the XANES experiments and taking photos of the Bogolan samples respectively.

Funding

The work was supported by Wallenberg Wood Science Center (WWSC). MP and AD were supported by the International Science Programme, Uppsala University.

References

Hilu S and Hersey I. Bogolanfini mud cloth. Atglen, PA: Schiffer Publishing Ltd, 2005.

Imperato

Shamir

. Bokolanfini: mud cloth of the Bamana of Mali. Afr Arts 1970; 3: 32–41.

Toerien

. Mud cloth from Mali: its making and use. J Family Ecolo Consumer Sci 2003; 31: 52–56.

Rovine VL. Bogolan: shaping culture through cloth in contemporary Mali. Bloomington, IN: Indiana University Press, 2008.

Ouedraogo Z. On a Technical note: Bogolan a traditional dye. Baobab, http://www.ired.org/modules/infodoc/cache/files/pdf/anglais/doce168.pdf (1997). Accessed: January 25, 2012.

Blanchart

Dembelé

. Mechanism of traditional Bogolan dyeing technique with clay on cotton fabric. Appl Clay Sci 2010; 50: 455–460.

Donne

. Bogolanfini: a mud-painted cloth from Mali. Man 1973; 8: 104–107.

Havlínová

Babiaková

Brezová

. The stability of offset inks on paper upon ageing. Dyes Pigments 2002; 54: 173–188.

Burgaud

Rouchon

Refait

. Mössbauer spectrometry applied to the study of laboratory samples made of iron gall ink. Appl Phys A 2008; 92: 257–262.

10.

Kongdee

Bechtold

. In-fibre formation of Fe(OH)₃—a new approach to pigment coloration of cellulose fibres. Dyes Pigments 2004; 60: 137–142.

11.

Rouchon-Quillet

Remazeilles

Bernard

. The impact of gallic acid on iron gall ink corrosion. Appl Phys A: Mater Sci Processing 2004; 79: 389–392.

12.

Rouchon

Duranton

Burgaud

. Room-temperature study of iron-gall ink impregnated paper degradation under various oxygen and humidity conditions: time-dependent monitoring by viscosity and X-ray absorption near-edge spectrometry measurements. Anal Chem 2011; 83: 2589–2597.

13.

Lee

Mahon

Creagh

. Raman analysis of iron gall inks on parchment. Vib Spectrosc 2006; 41: 170–175.

14.

Remazeilles C, Quillet V and Bernard J. FTIR techniques applied to iron gall inked damaged paper. In: proceedings of the 15th world conference on non-destructive testing, Rome, 2000.

15.

Senvaitiene

Beganskiene

Kareiva

. Spectroscopic evaluation and characterization of different historical writing inks. Vib Spectrosc 2005; 37: 61–67.

16.

Poggi

Giorgi

Toccafondi

. Hydroxide nanoparticles for deacidification and concomitant inhibition of iron-gall ink corrosion of paper. Langmuir 2010; 26: 19084–19090.

17.

Wilke

Hahn

Woodland

. The oxidation state of iron determined by Fe K-edge XANES—application to iron gall ink in historical manuscripts. J Anal At Spectrom 2009; 24: 1364–1364.

18.

Mohammed-Ziegler

Billes

. Vibrational spectroscopic calculations on pyrogallol and gallic acid. J Mol Struct THEOCHEM 2002; 618: 259–265.

19.

Bicchieri

Monti

Piantanida

. Non-destructive spectroscopic characterization of parchment documents. Vib Spectrosc 2011; 55: 267–272.

20.

Bicchieri

Monti

Piantanida

. All that is iron-ink is not always iron-gall!. J Raman Spectrosc 2008; 39: 1074–1078.

21.

Jansen PCM and Cardon DPCM (eds). Plant resources of tropical Africa 3. Dyes and tannins. Wageningen, Netherlands: PROTA Foundation/Leiden, Netherlands: Backhuys Publishers/Wageningen, Netherlands: CTA, 2005.

22.

Iglesias

Saldaña

EGDE

Jaén

. On the tannic acid interaction with metallic iron. Hyperfine Interact 2001; 134: 109–114.

23.

Jaén

González

Vargas

. Gallic acid, ellagic acid and pyrogallol reaction with metallic iron. Hyperfine Interact 2003; 148/149: 227–235.

24.

Sánchez del Río

Sodo

Eeckhout

. Fe K-edge XANES of Maya blue pigment. Nuclear Instrum Methods Phys Res B 2005; 238: 50–54.

25.

Manceau

Gatest

. Surface structural model for ferrihydrite. Clay Clay Miner 1997; 45: 448–460.