Effect of Solvent Exchange on the Solid Structure and Dissolution

Dissolution behavior was observed as follows: 3 parts of the cellulose samples ...... Light-Scattering Analysis of Native Wood Holocelluloses Totally ...
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Biomacromolecules 2003, 4, 1238-1243

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Effect of Solvent Exchange on the Solid Structure and Dissolution Behavior of Cellulose Daisuke Ishii, Daisuke Tatsumi,* and Takayoshi Matsumoto Division of Forest and Biomaterials Science, Graduate School of Agriculture, Kyoto University, Kyoto 606-8502, Japan Received March 10, 2003; Revised Manuscript Received June 2, 2003

Effects of solvent exchange and milling on the solid structure of cellulose were investigated, using smalland wide-angle X-ray scattering and solid-state NMR. The solvent exchange facilitated the dissolution of cellulose in LiCl/DMAc with no change of the crystalline structure of cellulose. In contrast, the milling never facilitated the dissolution of cellulose, though the crystalline structure was almost destroyed. These facts show that the crystalline structure of cellulose hardly affects the dissolution in LiCl/DMAc. The fractal dimensions determined by the small-angle X-ray scattering measurements were increased by the solvent exchange, suggesting that the aggregation state of the cellulose microfibril is affected. It was also suggested by the NMR 1H spin relaxation time measurements that the solvent exchange enhances the molecular mobility of cellulose and shortens the characteristic length along the microfibril, which allows easier access of the solvent molecule to cellulose. 1. Introduction The dissolution of cellulose is one of the most important processes for the production of fibers, films, and other materials made of cellulose. The conventional viscose process has environmental disadvantages intrinsically, so that the exploring of alternative solvent systems has been attempted. Lithium chloride/N,N-dimethylacetamide (LiCl/DMAc) is one of the most efficient solvent systems among those newly attempted. Cellulose dissolves in LiCl/DMAc molecularly without degradation.1,2 This feature makes the solvent system suitable for the processing,3 characterization,4 or derivatization5 of cellulose. The dissolution of cellulose in LiCl/DMAc at room temperature requires a pretreatment of cellulose.1,2 Several different methods for the pretreatment of cellulose have been proposed. One of them is a kind of solvent exchange that typically consists of the sequential immersion of cellulose in water, acetone, and DMAc. Compared to other methods for the dissolution of cellulose, such as refluxing in DMAc, the solvent exchange method has the advantage of less degradation of cellulose. The mechanism with which the solvent exchange works for cellulose is still unknown. Some researchers6,7 have discussed it in terms of the changes in the supra-molecular order of cellulose; however, no experimental proofs have been shown. The supramolecular structure of cellulose on the submicron scale has been characterized by microfibrils with a lateral dimension of 3-30 nm.8,9 Both solid-state NMR and smallangle X-ray scattering (SAXS) can be used to investigate structures in such a dimension. Solid-state NMR has been utilized for the investigation of the structure and the * To whom correspondence should be addressed. E-mail: daiske9@ kais.kyoto-u.ac.jp.

morphology of cellulose;10-12 however, fewer reports have been made on the investigation of the fibril structure of cellulose. Newman13 investigated the lateral dimension of cellulose microfibril by the measurement of proton rotatingframe relaxation time and obtained the values between 2 and 10 nm. However, the characteristic values for the fibril structure of cellulose, typically on the scale of 10-100 nm determined by electron microscopic studies, have never been obtained yet using the NMR approach. SAXS measurements also cover the spatial scale from 1 to 100 nm and complement the NMR spin relaxation measurement.14 In addition, it can be used for an investigation of local heterogeneity such as surface roughness. Lenz15 evaluated the surface roughness of cellulose crystallite by estimating the surface fractal dimension from the scattering exponent in theregion where the scattering angle is relatively large (0.2 < (2 sin θ/0.154)/ nm-1 < 0.6; θ, scattering angle). However, the aggregated structures of cellulose microfibril, which is also likely to be a fractal, have not been investigated by SAXS. In this paper, we report the changes in the nanometerscale heterogeneity and the molecular mobility of cellulose caused by the solvent exchange, using solid-state NMR and SAXS measurements. We also discuss the relation of these changes to the dissolution behavior of cellulose in LiCl/ DMAc. The effect of the milling of cellulose is also investigated and compared with that of the solvent exchange. 2. Material and Methods 2.1. Materials. The cellulose material employed was a softwood sulfite dissolving pulp (DP, Nippon Paper Industries Co. Ltd.) consisting of cellulose with a weight-average molecular weight of 9.82 × 105.4 At first, the cellulose sample was dried in a vacuum for 24 h at 60 °C. We refer

10.1021/bm034065g CCC: $25.00 © 2003 American Chemical Society Published on Web 06/27/2003

Structure and Dissolution Behavior of Cellulose

to the cellulose in this stage as “untreated”. Then, it was treated in two different methods: one was the solvent exchange and the other was the milling. The solvent exchange was performed as follows: first, the cellulose was immersed in water for 2 days. Then the excess water was removed by filtration. Afterward, the immersion in acetone (twice, for 1 day) and in DMAc (twice, for 1 day) followed. Finally, the cellulose was dried in a vacuum for 40 h at 60 °C. The milling was performed using a Cryogenic Sample Crusher JFC-300 (Japan Analytical Industry Co.) That is, the cellulose was packed into a stainless cell, preliminarily cooled in liquid nitrogen for 10 min, and then milled under the frozen condition with a stainless ball for 20 min. All of the cellulose samples after the treatments were reserved in a desiccator before use. For the preparation of LiCl/DMAc solvent, commercially available LiCl and DMAc of guaranteed reagent levels (Nacalai Tesque, Inc.) were used without further purification. 2.2. Experimental Methods. Dissolution of Cellulose. Dissolution behavior was observed as follows: 3 parts of the cellulose samples were mixed with 97 parts of 8 wt % LiCl/DMAc, and the mixture was kept to stand at ambient temperature. Extinction of turbidity and heterogeneity visible with naked eyes was regarded as the complete dissolution of cellulose. Wide Angle X-ray Diffraction (WAXD). WAXD measurements were performed with a Rigaku RINT 2200V. The diffracted intensity of Cu KR radiation (wavelength of 0.1542 nm, under a condition of 40 kV and 30 mA) was measured in a 2θ range between 5° and 40°. Small-Angle X-ray Scattering (SAXS). SAXS profiles were obtained using a 6-m-SAXS camera in the High-Intensity X-ray Laboratory, Kyoto University.16 The scattered intensity of Cu KR radiation (40kV, 50mA) was detected by a twodimensional Ar gas-filled position-sensitive proportional counter. The distance between the sample cell and the detector was set to 1.6 m, covering the scattering angle up to ca. 2° (in 2θ). Acquired data were corrected for transmittance and background air scattering and then circularly averaged. In that way, one-dimensional profiles were obtained. CP/MAS 13C Solid State NMR. Cross polarization/magic angle spinning (CP/MAS) 13C solid-state NMR experiments were performed using a Chemagnetics CMX300 spectrometer operating under a static field strength of 4.7 T at ambient temperature (ca. 20 °C). The contact time for CP was 1 ms, and the MAS speed was 3 kHz. The delay time after the acquisition of the FID signal was 8-10 s. The chemical shifts were determined by using the crystalline methylene peak (at 33.6 ppm12 relative to tetramethylsilane) of linear polyethylene used as an internal standard. Under these conditions, the relaxation behavior of cellulose proton magnetization was observed via 13C nuclei using CP.17 The 1H spin-spin relaxation time (T2H) measurement was performed using the spin-echo18 method. The 1H spin-lattice relaxation time measurement was performed both in the laboratory frame (T1H) and in the rotating frame (T1FH). T1H was measured using the inversion-recovery method. T1FH was measured

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Figure 1. Wide-angle X-ray diffraction profile of celluloses.

Figure 2. Small-angle X-ray scattering profile of celluloses.

varying the spin lock time in which the magnetization is fixed along the y direction in the rotating frame. 3. Results and Discussion 3.1. Dissolution Behavior and Crystallinity. The solventexchanged cellulose dissolved in LiCl/DMAc in a few hours. On the other hand, it takes several years for the untreated or the milled cellulose to dissolve in the solvent. Figure 1 shows the WAXD profiles of these cellulose samples. Both the untreated and the solvent exchanged cellulose gave almost the same profiles. This fact suggests that the solvent exchange has no effects on the crystallinity of cellulose, though it affects the dissolution of cellulose remarkably. On the other hand, the milled cellulose alone gave a typical amorphous one. This shows that the crystallinity of cellulose was decreased by the milling, but it hardly affects the dissolution as described above. Therefore, it can be said that there is almost no relation between the crystallinity evaluated by WAXD and the dissolution of cellulose in LiCl/DMAc. 3.2. Investigation of the Nanometer-Scale Heterogeneity of Cellulose by SAXS. SAXS profiles of the cellulose samples are shown in Figure 2. The logarithm of the scattered intensity, I, is plotted versus the logarithm of the magnitude of the scattering wave vector, q ) (4π/λ) sin(θ/2), where θ and λ denote the scattering angle and the wavelength of irradiated X-ray (0.1542 nm), respectively. In these profiles, the relation between I and q obeys a power law in the q range between 0.16 and 0.34 nm-1, corresponding to the length scales between 18 and 40 nm. It is known that the scattered intensities from a mass fractal and a surface fractal are proportional to q-Dm and q-(6-Ds), respectively.19 Here Dm and Ds are the fractal dimensions of

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Figure 3. CP/MAS

13C

Ishii et al.

solid-state NMR spectra of celluloses.

mass and surface, respectively. In Euclidean space, their ranges are 1 e Dm e 3 and 2 e Ds < 3. Thus, when the scattering exponent is larger than -3, the object is a mass fractal. In like manner, when the exponent is less than -3, the object is a surface fractal. The slopes of the line fitted to the plot of the untreated, the solvent-exchanged, and the milled cellulose in Figure 2 are -3.47, -2.86, and -3.69, respectively. Therefore, the untreated and the milled cellulose have surface fractal dimensions, and the solvent-exchanged has a mass fractal one. The fractal dimensions of each samples are calculated as Ds ) 2.53, Ds ) 2.31, and Dm ) 2.86, respectively. The values of the fractal dimension of the untreated and the solvent-exchanged cellulose show that the solvent exchange causes a change from a surface fractal to a mass fractal. Considering that the spatial scale of the fractal regime lies outside the lateral dimension of the cellulose microfibril (ca. 15 nm for our samples - shown in the later section), it is supposed that the change in fractal nature reflects the change in the aggregation state of the cellulose microfibril. In general, scattering from surface fractal occurs only at the surface of the substance, whereas that from the mass fractal does at the inner part as well as the surface. One reason for this is that the mass fractal objects contain a more complex pore system than the surface fractal objects: the pore network penetrates more deeply inside the mass fractal objects than that of the surface fractal one. The complexity of the pore system depends on the aggregation state of the structural unit comprising the aggregate (microfibril as for cellulose solid). Therefore, it is supposed that the solvent exchange loosens the surface-fractal aggregate of microfibril, expanding the pore between the microfibrils, and consequently transforms the geomerty of the aggregate into mass fractal. The access of solvent molecule to the cellulose moiety may be facilitated by such a morphological transition. On the other hand, the milled sample has the smoothest surface among the three samples because of its smallest fractal dimension. This suggests that the milling breaks the cellulose microfibril into dense and smooth particles. 3.3. CP/MAS 13C Solid-State NMR Spectra. Figure 3 shows the NMR spectra of the cellulose samples. The reason the milled sample gives a different spectrum from the other samples is that the resonance lines for crystalline components (for example, sharp peaks around 90 ppm (C4) and 66 ppm (C6)) were not observed. This suggests that the conformational regularity of the cellulose molecule is lost in the milled sample. The former work13 used the C4 resonance lines for

Figure 4. 1H spin-spin relaxation behavior for the C1 proton of celluloses. Filled symbol, observed intensity; open symbol, fastrelaxing component subtracted; dotted line, T2H1 decay; solid line, T2H2 decay.

the investigation of the crystallinity of cellulose, but this approach cannot be applied in our case. In contrast, C1 resonance around 106 ppm was observed in all of the samples, so that the intensity of C1 resonance peak was used for the relaxation measurements. Figure 3 also shows that the solvent exchange makes no significant effect on the conformation of the cellulose molecule, because the spectra of the untreated and the solvent-exchanged samples are almost the same. 3.4. 1H Spin-Spin Relaxation. Figure 4 shows the relaxation behavior of the transverse magnetization of the cellulose C1 proton.17 The observed data (filled marks) suggest that there are two different relaxation modes in each system. In a solid polymer system with the components of different molecular mobility, the magnitude of the magnetic dipole-dipole interaction of protons differs in each component. In this case, the total transverse magnetization of the proton is expressed as the summation of the magnetization of each component.20 As for the two-phase system, the expression is as follows:21 M(t) ) M1 exp{-(1/2)(t/T2H1)2} + M2 exp(-t/T2H2)

(1)

where M(t), Mi, and T2Hi denotes the intensity of transverse magnetization at time t after the excitation, the intensity of magnetization at the thermal equilibrium of the ith component, and the spin-spin relaxation time of the ith component, respectively. The first Gaussian term and second exponential

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Structure and Dissolution Behavior of Cellulose Table 1. 1H Spin Relaxation Parameters and Maximum Diffusion Path Length of Cellulose. untreated

T2H/µs T1FH/ms T1H/s T1FH L/nm T1H

solvent-exchanged

rigid

mobile

rigid

mobile

6.0 29.7 2.9 16.0

44 7.1

7.7 27.0 1.8 13.0

83 5.8

153

107

milled rigid 6.4

mobile 387 4.0

2.8 0.7 146

term correspond to the rigid component and mobile component, respectively. Thus, the overall relaxations shown in Figure 4 are decomposed into an exponential (straight line) and a Gaussian (dotted curve) components. The T2H values calculated using eq 1 for the cellulose samples are listed in Table 1. The results well explain the dissolution behavior of cellulose samples in LiCl/DMAc. As for the rigid component, the solvent-exchanged cellulose has the largest T2H. This shows that the solvent exchange enhances the molecular mobility of cellulose. It is known that T2H reflects the libration of the molecule.22 Therefore, it can be said that solvent exchange facilitates the libration in any part of cellulose molecule. The T2H of the rigid component of the milled cellulose is fairly the same as that of the untreated cellulose, though that of the mobile component is remarkably increased by the milling process. This shows that the milling does not enhance the molecular mobility of cellulose, though it disturbs the crystalline order. These results suggest that the molecular mobility in the crystalline region is the most effective for the dissolution. 3.5. 1H Spin-Lattice Relaxation in the Laboratory Frame. The results of 1H spin-lattice relaxation measurements in the laboratory frame are shown in Figure 5. The longitudinal relaxation of proton magnetization is essentially composed of a single process, except for the untreated sample with the small amount of fast-relaxing component. The existence of two relaxation processes in the untreated sample shows that the exchange of the spin energy between the components with the different molecular mobility is inactive. Such a situation holds when the size of the rigid component is too large to transfer the spin energy to the mobile component.20 The values of T1H were calculated using eq 2 as follows and are listed in Table 1. As for the untreated sample, eq 2 was applied only for the slow-relaxing component. Mz ) M0{1 - 2exp(-t/T1H)}

(2)

where Mz denotes the intensity of longitudinal magnetization (subscript 0 designates the equilibrium). The solvent-exchanged cellulose has the shortest T1H as shown in Table 1. As for a solid macromolecular system like cellulose, T1H becomes shorter as the molecular mobility is increased. This means that the solvent-exchanged cellulose has the largest molecular mobility.23 This agrees with the result of the T2H measurements, though the molecular motion that modulates each relaxation is different. As T1H reflects the segmental motion in the molecule or the rotational motion

Figure 5. Laboratory-frame 1H spin-lattice relaxation behavior for the C1 proton of celluloses. Filled symbol, observed intensity; solid line, fitted line.

of side groups,24 it can be said that solvent exchange facilitates also these types of molecular motion. Using the T1H value, we can calculate a characteristic value of the spatial heterogeneity of cellulose. The spatial scale over which spin diffusion propagates, called the maximum diffusive path length, L, is used as the characteristic value of the heterogeneity of materials and defined by the equations below:25 L = (6Dt)1/2

(3)

where D is the coefficient of spin diffusion. D is related to T2H by the following equation:20 D ) 0.13a2/T2H

(4)

where a is the mean distance between protons. In the case of cellulose, a is 0.25 nm, calculated using MOLDA26 software. In eq 3, T1H or T1FH can be used for t, the characteristic time of diffusion. The values of L calculated using T1H listed in Table 1 are on the order of 100 nm and are shortened by the solvent exchange. L is comparable to the length of the hydrolytic residue of cellulose.27 As the length of the residue reflects the characteristic length of heterogeneity along cellulose microfibril,27-29 it can be said that the solvent exchange shortens the characteristic length of heterogeneity along cellulose microfibril.30 Such heterogeneity seems to have the structural origin other than crystalline order, because it is apparent from WAXD experiments that the crystalline order is retained in the solvent-exchanged sample and destroyed in the milled one.

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This shows that the crystalline order is broken in the milled cellulose. On the other hand, the relaxations in the untreated and the solvent-exchanged sample are composed of two processes (i ) 2). These relaxation components can be assigned to the cellulose moiety with different molecular mobility. This two-component relaxation demonstrates that the spin diffusion between the rigid and the mobile components in the time scale of T1FH is not operative. Therefore, the maximum diffusive path length in the time scale of T1FH characterizes the sizes of each components. The values of L calculated using the longer T1FH listed in Table 1 are comparable to the thickness of the cellulose microfibril.8,9 They do not show such a significant difference between the untreated and the treated samples. It follows that the thickness of cellulose microfibril is not so much affected by the solvent exchange. Therefore, it can be said that the thickness of cellulose microfibril does not affect the dissolution of cellulose in LiCl/DMAc. 4. Conclusion

Figure 6. Rotating-frame 1H spin-lattice relaxation behavior for the C1 proton of celluloses. filled symbol, observed intensity; open symbol, fast-relaxing component subtracted; solid line, fitted line for the slow-relaxing component; dotted line, fitted line for the fast-relaxing component.

As the solvent exchange involves no degradation process of cellulose molecules such as hydrolysis, the above-mentioned change must be caused not by the chemical degradation of cellulose molecules but by the increase in the molecular mobility of cellulose within the microfibril. The significance of the 100-nm-scale heterogeneity for the dissolution of cellulose has also been mentioned by Isogai and Atalla.31 On the other hand, L of the milled cellulose is almost the same as that of the untreated cellulose. This shows that the milling can hardly shorten the characteristic length along the cellulose microfibril. 3.6. 1H Spin-Lattice Relaxation in the Rotating Frame. The results of the 1H spin-lattice relaxation measurements in the rotating frame are shown in Figure 6. T1FH were obtained using the following equation: M(t) )

∑i Mi(0)exp(-t/T1FH )(i ) 1, 2, ...) i

(5)

where M(t) denotes the intensity of magnetization at the spin lock time t. i depends on the number of the relaxation processes observed. The T1FH values listed in Table 1 show that the untreated and the solvent-exchanged samples have large T1FH values but the milled one does not. This tendency can be correlated with the crystallinity evaluated from WAXD profiles. The relaxation in the milled cellulose is composed of single process (i ) 1) and occurs almost as fast as the noncrystalline component of the other samples.

The solvent exchange enhances the molecular mobility of cellulose and shortens the characteristic length along the cellulose microfibril. It is also suggested that the aggregation state of the cellulose microfibril is affected by the solvent exchange. These changes facilitate the access of solvent molecules to the cellulose and accelerate the dissolution of cellulose in LiCl/DMAc. On the other hand, the milling does not affect the above-mentioned factors, although it destroys the crystalline order of cellulose. Therefore, the refining does not facilitate the dissolution of cellulose in LiCl/DMAc. Acknowledgment. The authors thank Prof. T. Yoshizaki at the Graduate School of Engeneering, Kyoto University, for his kind support in the SAXS measurements. This work was supported by a Grant-in-Aid for Scientific Research (No. 12460076) from the Ministry of Education, Science, Sports and Culture of Japan and by a Grant-in Aid for Encouragement of Young Scientist (No. 11760123) from the Japan Society for the Promotion of Science. References and Notes (1) Turbak, A. Tappi J. 1984, 67, 94. (2) McCormick, C. L.; Callais, P. A.; Hutchinson Jr., B. H. Macromolecules 1985, 18, 2394. (3) Nishio, Y.; Roy, S. K.; Manley, R. J. Polymer 1987, 28, 1385. Nishio, Y.; Manley, R. J. Macromolecules 1988, 21, 1270. (4) Matsumoto, T.; Tatsumi, D.; Tamai, N.; Takaki, T. Cellulose 2002, 8, 275. (5) Heinze, T.; Liebert, T. Prog. Polym. Sci. 2001, 26, 1689. (6) Johnson, D. C. In Cellulose Chemistry and Its Applications; Nevell, T. P., Zeronian, S. H., Ed.; Ellis Horwood: Chichester, U.K., 1985; p 185. (7) Klemm, D.; Philipp, B.; Heinze, T.; Heinze U.; Wagenknecht, W. In ComprehensiVe Cellulose Chemistry; Wiley-VCH: Weinheim, Germany, 2001; Volume 1, pp 150. (8) Preston, R. D.; Nicolai, E.; Reed, R.; Millard, A. Nature 1948, 162, 665. (9) Frey-Wyssling, A. Science 1954, 119, 80. (10) Earl, W. L.; VanderHart, D. L. Macromolecules 1981, 14, 570. (11) VanderHart, D. L.; Atalla, R. H. Macromolecules 1984, 17, 1465. (12) Horii, F.; Hirai, A.; Kitamaru, R. Macromolecules 1987, 20, 2117. (13) Newman, R. H. Solid State Nucl. Magn. Reson. 1999, 15, 21. (14) Clauss, J.; Schmidt-Rohr, K.; Spiess, H. W. Acta Polymer. 1993, 44, 1.

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Structure and Dissolution Behavior of Cellulose (15) Lenz, J.; Schultz, J. Holzforsch. 1990, 44, 227. (16) Hayashi, H.; Hamada, F.; Suehiro, S.; Masaki, N.; Ogawa, T.; Miyaji, H. J. Appl. Crystallogr. 1988, 21, 330. (17) We consider that the observed intensity of the proton magnetization originates from the cellulose methyne (or methylene) proton. The reason is that the dipole-dipole interaction mediates the transfer of the magnetization from 1H to 13C in the CP process. It is quite likely that the interaction is active between 13C and methyne (or methylene) proton of solid cellulose. (18) Carr, H. Y.; Purcell, E. M. Phys. ReV. 1954, 94, 630. (19) Schmidt, P. W. In The Fractal Approach in Heterogeneous Chemistry; Avnir, D., Ed.; John Wiley & Sons: New York, 1989; p 67. (20) Tanaka, H.; Nishi, T. Phys. ReV. 1986, B33, 32. (21) Axelson, D. E.; Russell, K. E. Prog. Polym. Sci. 1985, 11, 221. (22) Leisen, J.; Beckham, H. W.; Benham, M. Solid State Nucl. Magn. Reson. 2002, 22, 409. (23) It is known that, in solid state, longitudinal relaxation of proton magnetization is affected by the proton spin diffusion.20 As the spin diffusion smears out the difference in the intrinsic spin-lattice relaxation time of the components with different molecular mobility, the apparent relaxation behavior of longitudinal magnetization is expressed by a single-exponential function. In such a case, the overall relaxation rate (reciprocal of observed T1H) is expressed by the sum of the relaxation rate of each of the components weighed by the mass fraction of them.22 Though we have not quantitatively investigated in this aspect, however, the shortened T1H of the solvent-exchanged cellulose shows that the amount of the mobile component is increased

(24) (25) (26) (27) (28) (29) (30)

(31)

or that the molecular motion that modulates T1H relaxation of mobile and/or rigid components is activated. In any case, it can be said that the solvent exchange enhances the molecular mobility of the cellulose material as a whole. Axelson, D. E.; Nyhus, A. K. J. Polym. Phys. Part B: Polym. Phys. 1999, 37, 1307. Cheung, T. T. P.; Gerstein, B. C.; Ryan, L. M.; Taylor R. E.; Dybowski, D. R. J. Chem. Phys. 1980, 73, 6059. http://www.molda.org/ Morehead, F. F. Text. Res. J. 1950, 20, 549. Philipp, H. J.; Nelson, M. L.; Ziifle, H. M. Text. Res. J. 1947, 17, 585. Battista. O. Ind. Eng. Chem. 1950, 42, 502. In eq 3, we assumed the isotropic spin diffusion. In this assumption, the effect of the shape of the cellulose microfibril on the spin diffusion is not considered. Therefore, whether the spatial size calculated by eq 4 reflects the characteristic length of the crystalline region in the cellulose microfibril leaves some ambiguity. However, even if the proton spin diffusion occurs only within a thread of microfibril (in this case, L is approximated by (2Dt)1/2), L is still near 100 nm, which is much larger than the thickness of microfibil. Therefore, it can be said that the proton spin diffusion in the time scale of T1H reflects the characteristic length along the cellulose microfibril. Isogai, A.; Atalla, R. H. Cellulose 1998, 5, 309.

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