The Structures of Cellulose - American Chemical Society

Chapter 14

Fractal Analysis of Cotton Cellulose as Characterized by Small-Angle X-ray Scattering 1

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J. S. Lin , Ming-Ya Tang , and John F. Fellers 1

National Center for Small Angle Scattering Research, Oak Ridge National Laboratory, Oak Ridge, TN 37830 Materials Science & Engineering, University of Tennessee, Knoxville, TN 37996-2200

Downloaded by UNIV OF ARIZONA on January 17, 2013 | http://pubs.acs.org Publication Date: June 22, 1987 | doi: 10.1021/bk-1987-0340.ch014

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Complete small-angle x-ray scattering (SAXS) curves are reported and analyzed by conventional and fractal theories in this study of Valonia and eleven cotton cellulose samples. The scattering source i s identified as voids in a solid matrix. The void volume fraction ranges from 0.7% to 3.4% in the various cotton samples and i s 17% in Valonia. Modifications such as dewaxing, scouring, and bleaching improve the packing efficiency within aggregates, and additionally increase the void fraction. NaOH mercerization and NH treatment destroy the packing efficiency slightly and decrease the void fraction. Two types of power-law decay were observed for the SAXS intensity I(s). Hydrocellulose II and Valonia follow Porod's inverse fourth power law. Conventional SAXS analysis then determines the average pore sizes to be 8.5 nm and 12.5 nm, and specific inner surfaces of 15.3 and 45.2 m /cm , respectively. The other ten cotton samples follow a power law decay with the exponent ranging from -2.7 to -2.1. The non-integer exponent is referred to as the Hausdorff dimension and suggests a fractal structure for the microcrystallites constituting the cellulose. The compliance of Hydrocellulose II and Valonia to Porod's law carries with it a model structure of a three dimensional void bounded by a smooth two dimensional surface. The other samples that have their fractal or Hausdorff dimension less than the Euclidian dimension implies there i s a unit of measure small enough to sense discontinuities of the structure. The Hausdorff dimensions measured here suggest that native cellulose i s a cluster aggregate of microcrystallites modified by 3

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0097-6156/87/0340-0233$06.25/0 © 1987 American Chemical Society

In The Structures of Cellulose; Atalla, R.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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subsequent rearrangement. Such s p e c u l a t i o n s may s t i m u l a t e some new i n s i g h t t o the growth mechanism of c o t t o n .


Structure In the l a s t s i x t y y e a r s , the morphology o f c e l l u l o s e has r e c e i v e d much a t t e n t i o n but has remaining u n r e s o l v e d f e a t u r e s . C e l l u l o s e i s a l i n e a r polymer composed o f anhydroglucose u n i t s j o i n e d by 14 β-Glycosidic bonds. I t forms the p r i n c i p a l c o n s t i t u e n t o f p l a n t c e l l w a l l s where i t o c c u r s as t h i n t h r e a d s o f i n d e f i n i t e l e n g t h c a l l e d m i c r o f i b r i l s . In w i d t h , m i c r o f i b r i l s vary from 7 to 30 nm, depending upon the source o f the c e l l u l o s e ( 1 ) . I t i s g e n e r a l l y agreed t h a t c o t t o n c e l l u l o s e i s arranged i n t h i n f i b r i l s forming the r a t h e r i r r e g u l a r o u t e r o r primary c e l l w a l l , and the h i g h l y ordered i n n e r o r secondary w a l l o f the hollow t u b u l a r s t r u c t u r e o f the c o t t o n f i b e r ( 2 ) . The e x i s t e n c e o f an o r d e r e d s t r u c t u r e i n c e l l u l o s e i s shown c o n c l u s i v e l y by wide-angle x-ray d i f f r a c t i o n (WAXD) and e l e c t r o n d i f f r a c t i o n s t u d i e s ( 3 ) . The d i f f r a c t i o n p a t t e r n s e x h i b i t r e a s o n a b l y w e l l - d e f i n e d r e f l e c t i o n s f o r which u n i t c e l l s have been d e f i n e d . There are f o u r b a s i c r e c o g n i z e d c r y s t a l l i n e m o d i f i c a t i o n s , namely, c e l l u l o s e I , I I , I I I and IV. By the WAXD method as proposed by Hermans (4,5) i t has been found t h a t n a t i v e c e l l u l o s e s o f d i f f e r e n t b i o l o g i c a l o r i g i n vary i n c r y s t a l l i n i t y o v e r wide l i m i t s , from 40% i n b a c t e r i a l c e l l u l o s e t o 60% i n c o t t o n c e l l u l o s e and 70% i n V a l o n i a c e l l u l o s e . The f i n e s t r u c t u r e o f c e l l u l o s e i s g e n e r a l l y i n t e r p r e t e d i n terms o f a two-phase c r y s t a l l i n e - a m o r p h o u s model ( 6 ) . A c c o r d i n g to t h i s concept c e l l u l o s e m i c r o f i b r i l s are regarded as a s s e m b l i e s of c r y s t a l l i n e and amorphous r e g i o n s . However, i n c o n t r a s t t o most s y n t h e t i c s e m i c r y s t a l l i n e polymers, n a t i v e o r r e g e n e r a t e d c e l l u l o s e f i b e r s do not show a m e r i d i o n a l s m a l l - a n g l e x-ray o r neutron r e f l e c t i o n (7-27), a l t h o u g h i n some s p e c i a l cases a v e r y weak long s p a c i n g r e f l e c t i o n c o u l d be d e t e c t e d f o r r e g e n e r a t e d c e l l u l o s e (12,13,24,27). T h i s o b s e r v a t i o n i s e x p l a i n e d by the assumption *(T3,25y~that the d i f f e r e n c e o f e l e c t r o n d e n s i t y between the "amorphous" and " c r y s t a l l i n e " r e g i o n s i s too weak t o g i v e r i s e t o a d i s c r e t e s m a l l - a n g l e r e f l e c t i o n , but the d i s t i n c t i o n i n c h a i n o r d e r i s r e a l i n the sense t h a t i t i s t h e b a s i s f o r s e l e c t i v i t y with r e s p e c t t o chemical d e g r a d a t i o n . Meanwhile the d i f f u s e s m a l l - a n g l e x-ray s c a t t e r i n g o f c o t t o n has been i n t e r p r e t e d as e i t h e r due t o m i c r o f i b r i l s having n e g l i g i b l e i n t e r p a r t i c u l a r i n t e r f e r e n c e (7-10, 22,25,26) o r due to a " d i l u t e " system o f m i c r o v o i d s o r pores i n a dense system (12, 14-19). The f i r s t view i s a p p a r e n t l y supported by t h e o b s e r v a t i o n o f Haase e t a l . (21,22) and Heyn (7-10, 26) t h a t the s m a l l e s t dimension r e v e a l e d from the d i f f u s e s c a t t e r i n g agrees w i t h the r e s u l t s o f the l i n e width a n a l y s i s o f WAXD and t h a t o f e l e c t r o n microscopy s t u d i e s . However t h i s a n a l y s i s i s dependent on the range o f s c a t t e r i n g a n g l e s ( 2 Θ ) , i . e . a d i f f e r e n t s ( s = 4 π sine/λ, λ = wavelength) range w i l l lead t o a d i f f e r e n t v a l u e o f f i b r i l d i a m e t e r s . The second view i s supported by S t a t t o n


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(12,18,19), Hermans e t a l . (14-16), and Kratky and Sekora (17) who found t h a t the mass d e n s i t y can be s a t i s f a c t o r i l y c o r r e l a t e d with the s c a t t e r i n g i n v a r i a n t measurement. Here a g a i n the d e t e r m i n a t i o n of v o i d s i z e i s dependent on the range o f s c a t t e r i n g a n g l e s . Thus one has t o extend the range o f s c a t t e r i n g angles as f a r as p o s s i b l e . T h i s c o n t r o v e r s y can be p a r t i a l l y overcome by a p p l y i n g the technique c a l l e d c o n t r a s t v a r i a t i o n (28). C o n t r a s t v a r i a t i o n can be o b t a i n e d by changing the e l e c t r o n d e n s i t y of one of the phases s i n c e SAXS i n t e n s i t y i s p r o p o r t i o n a l to the square of the d i f f e r e n c e between the mean s c a t t e r i n g d e n s i t y (number of e l e c t r o n s per u n i t volume) o f each phase i n the s c a t t e r i n g system. Downloaded by UNIV OF ARIZONA on January 17, 2013 | http://pubs.acs.org Publication Date: June 22, 1987 | doi: 10.1021/bk-1987-0340.ch014

I m p l i c a t i o n s of S t r u c t u r e from the Growth Process C o n s i d e r i n g the c o t t o n growth process may help d i s p e l ambiguity about the s t r u c t u r e o f c o t t o n . The growth of c o t t o n can be c o n s i d e r e d as a d e p o s i t i o n or a g g r e g a t i o n of c e l l u l o s e s u b u n i t s . Many o b j e c t s grow by random a d d i t i o n o f s u b u n i t s t o form l a r g e c l u s t e r s , i n c l u d i n g soot and smoke (29), d r o p l e t n u c l e a t i o n and growth (30), and c o l l o i d s . The r e s u l t a n t s t r u c t u r e s are c h a r a c t e r i z e d by t h e i r tenuous, c h a i n l i k e s t r u c t u r e . However, o n l y r e c e n t l y has i t been r e a l i z e d t h a t there i s a geometric f e a t u r e which c h a r a c t e r i z e s many o b j e c t s generated by i r r e v e r s i b l e growth: they seem to be s c a l e - i n v a r i a n t f r a c t a l s . The s u b j e c t of f r a c t a l s i s t r e a t e d i n c o n s i d e r a b l e d e t a i l i n the l i t e r a t u r e (31,32). F r a c t a l o b j e c t s are c h a r a c t e r i z e d by the s c a l e dependence o f t h e i r t o t a l mass when a c h a r a c t e r i s t i c l e n g t h s c a l e i s used t o examine the f r a c t a l . That i s [ M a s s l j o t a l - (Length)D,

(1)

where D, the f r a c t a l or Hausdorff dimension i s l e s s than d, the E u c l i d i a n dimension o f space, and i s u s u a l l y n o n - i n t e g r a l . A l s o the p o i n t to p o i n t d e n s i t y c o r r e l a t i o n f u n c t i o n c ( x ) w i t h i n a f r a c t a l m a t e r i a l has a power-law b e h a v i o r : d

c ( x ) = < P ( r ) · r p ( r + x) > - l / r " m

m

D

(2)

Thus, changing a l l l e n g t h s c a l e s m u l t i p l i e s c ( x ) by a c o n s t a n t ; t h i s means (33) the o b j e c t " l o o k s " the same on any l e n g t h s c a l e . The i d e a t h a t d i s o r d e r l y growth can lead to s c a l e i n v a r i a n c e was f i r s t p o i n t e d out by Witten and Sander (33) who were attempting to e x p l a i n e a r l i e r o b s e r v a t i o n s of F o r r e s t and W i t t e n (34) of smoke aggregates. Computer s i m u l a t i o n s (33, 35-38) have a l s o suggested t h a t the r e s u l t a n t s t r u c t u r e s e x h i b i t s c a l e i n v a r i a n c e and can be d e s c r i b e d as f r a c t a l s . Two g e n e r a l c l a s s e s o f i r r e v e r s i b l e a g g r e g a t i o n have emerged from the s i m u l a t i o n s . The f i r s t of these c l a s s e s i n v o l v e s c l u s t e r f o r m a t i o n by the s u c c e s s i v e a d d i t i o n o f s i n g l e randomly walking ( d i f f u s i o n ) p a r t i c l e s onto a seed p a r t i c l e r e p r e s e n t i n g a n u c l e a t i o n c e n t e r at a f i x e d p o i n t (33,35) ( d i f f u s i o n - l i m i t e d a g g r e g a t i o n , DLA) and the r e s u l t a n t s t r u c t u r e has D « 1.7 (d = 2) and 2.5 (d = 3 ) .



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C e r t a i n r e a l systems seem t o be d e s c r i b e d by DLA, n o t a b l y e l e c t r o d e p o s i t i o n on a sharp p o i n t (39) and d i e l e c t r i c breakdown (33,40). The second c l a s s i n v o l v e s c l u s t e r f o r m a t i o n by t h e homogeneous a g g r e g a t i o n o f a c o l l e c t i o n o f two c l u s t e r s o f comparable s i z e (37,38) ( c l u s t e r - c l u s t e r a g g r e g a t i o n , CA) and t h e r e s u l t a n t aggregate has a more open s t r u c t u r e and lower f r a c t a l dimension, D 1.4 ( d = 2) and 1.8 (d = 3 ) . Real smoke (34) and c o l l o i d s (41) seem t o have D = 1.8; t h i s i s a s a t i s f y i n g v e r i f i c a t i o n o f the model. A p r o c e s s t h a t has n o t , however, been i n c l u d e d i n t h e s i m u l a t i o n s i s rearrangement w i t h i n t h e c l u s t e r s . T h i s would lead t o denser s t r u c t u r e s w i t h h i g h e r H a u s d o r f f dimensions ( 4 2 ) . More r e c e n t l y , s c a t t e r i n g t e c h n i q u e s (SAXS, Small Angle Neutron S c a t t e r i n g (SANS) and l i g h t s c a t t e r i n g ) were employed t o c h a r a c t e r i z e t h e f r a c t a l s t r u c t u r e o f aggragates o f s i l i c a p a r t i c l e s (42-44) and g o l d c o l l o i d s ( 4 5 ) . They r e p o r t e d a power law decay o f t h e s c a t t e r i n g i n t e n s i t y I ( s ) over some range o f s c a t t e r i n g v e c t o r , s: I (s) ~ s-D.

(3)

S c h a e f e r e t a l . (42, 43) r e p o r t e d t h a t t h e f r a c t a l dimension o f s i l i c a aggregates i s 2.12 + 0.05, independent o f t h e s t a g e o f a g g r e g a t i o n e x c e p t a t t h e e a r l y phase o f growth. S i n h a e t a l . (44) r e p o r t e d t h a t t h e f r a c t a l dimension o f resuspended C a b - o - s i l aggregates was 2.52 + 0.05 f o r samples p r e s s e d i n t o d i f f e r e n t d e n s i t i e s r a n g i n g from 0.05 gm/cm t o 0.2 gm/cm - Weitz and Huang (45) r e p o r t e d a f r a c t a l dimension o f 1.75 f o r aqueous g o l d c o l l o i d s . Thus t h e a p p l i c a t i o n o f f r a c t a l c o n c e p t s i n v o l v i n g a g g r e g a t i o n growth p r o c e s s e s may p r o v i d e some new i n s i g h t i n t o cotton structure. In t h e p r e s e n t paper we extend t h e range o f s c a t t e r i n g angles as f a r as f i v e degrees and combine SAXS measurement w i t h wide-angle x - r a y d i f f r a c t i o n measurements. We r e p o r t what we b e l i e v e t o be t h e f i r s t complete SAXS c u r v e s f o r c o t t o n and V a l o n i a c e l l u l o s e . We a l s o demonstrate how t h e f r a c t a l concept can be a p p l i e d t o e x p l a i n t h e m i c r o c r y s t a l 1 i t e s t r u c t u r e i n cellulose. 3

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Materials Eleven c o t t o n c e l l u l o s e s and one o f V a l o n i a were s t u d i e d . Among the twelve samples, t h e f i r s t n i n e c o t t o n samples a r e i n a randomly o r i e n t e d f i b r i l s t a t e ( c o t t o n s l i v e r ) , EHC I and H y d r o c e l l u l o s e II a r e powders, and V a l o n i a i s i n membrane p i e c e s . They a r e l i s t e d and d e s c r i b e d below. Cotton C e l l u l o s e . Three c l a s s e s o f c o t t o n c e l l u l o s e were s t u d i e d . They a r e Greige Cotton Series: Greige Cotton Dewaxed G r e i g e C o t t o n Scoured G r e i g e C o t t o n Scoured and Bleached G r e i g e C o t t o n


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Absorbent C o t t o n NaOH M e r c e r i z e d Absorbent C o t t o n NH3 T r e a t e d Absorbent C o t t o n , NH3 removed a t room temperature NH3 T r e a t e d Absorbent C o t t o n , NH3 removed a t 95°C NH3 T r e a t e d Absorbent C o t t o n , sample immediately immersed i n H2O a f t e r NH3 treatment H y d r o l y z e d Cotton S e r i e s : EHC I , c o t t o n c e l l u l o s e H y d r o l y z e d i n HC51 u n t i l t h e o p t i m a l c r y s t a l l i n i t y was obtained Hydrocellulose II, cotton treated w i t h NaOH f o r m e r c e r i z a t i o n and then h y d r o l y z e d w i t h HCJl t o provide a highly c r y s t a l l i n e c e l l u l o s e II powder


Absorbent Cotton S e r i e s :

Valonia Ventricosa Cellulose. This i s a u n i c e l l u l a r alga, the v e s i c l e s o f which may reach a volume as l a r g e as 30 c c . V a l o n i a v e n t r i c o s a was gathered o f f t h e e a s t e r n c o a s t o f F l o r i d a . B e f o r e use i t was s t o r e d i n i c e - c o l d , o r i g i n a l s e a water f o r 11 months, a f t e r which i t was c l e a n e d and scoured i n b o i l i n g 2% NaOH w i t h 0.5% Prechem 70 under Argon f o r 1 hour. I t was kept r e f r i g e r a t e d i n water, w i t h a small amount o f c h l o r o f o r m added t o p r e v e n t growth o f b a c t e r i a . I t was a i r - d r i e d a t 100°C f o r 3 hours. SAXS Sample P r e p a r a t i o n The samples were vacuum d r i e d a t room temperature f o r 12 hours b e f o r e SAXS measurement. Iodine embedded c o t t o n was p r e p a r e d a c c o r d i n g t o t h e i o d i n e s o r p t i o n t e s t procedure proposed by Nelson e t a l . ( 4 6 ) . Soaking w i t h g l y c e r i n e was c a r r i e d o u t a t room temperature f o r 24 hours. Small-Angle X-Ray S c a t t e r i n g S m a l l - a n g l e x-ray s c a t t e r i n g experiments were performed on t h e 10 meter SAXS f a c i l i t y a t t h e N a t i o n a l Center f o r Small Angle S c a t t e r i n g Research a t t h e Oak Ridge N a t i o n a l L a b o r a t o r y ( 4 7 ) . T h i s i n s t r u m e n t c o n s i s t s o f a r o t a t i n g anode x-ray s o u r c e , p i n h o l e c o l l i m a t i o n , a two d i m e n s i o n a l p o s i t i o n - s e n s i t i v e p r o p o r t i o n a l c o u n t e r ( 4 8 ) , and a mini-computer system f o r d a t a a c q u i s i t i o n and a n a l y s i s . The system was c o n s t r u c t e d i n such a way t h a t a change i n t h e a n g u l a r range can be a c h i e v e d by l e n g t h e n i n g o r s h o r t e n i n g t h e aluminum beam path between t h e sample chamber and t h e d e t e c t o r . Three sample t o d e t e c t o r d i s t a n c e s , namely 5 meters ( l o n g geometry, 2 θ = 1 t o 20 mrad), 2 meters ( s h o r t geometry, 2 θ = 3 t o 45 mrad) and 1 meter ( u l t r a s h o r t geometry, 2 θ = 5 t o 90 mrad) were used and i t was found the c o m b i n a t i o n o f 5 meter and 1 meter beam paths was s u f f i c i e n t to o b t a i n t h e complete SAXS i n t e n s i t y d i s t r i b u t i o n c u r v e . A l l



238

measurements were c a r r i e d out at room temperature under vacuum (< 15 urn Hg). CuKa r a d i a t i o n (λ = 0.54 nm) was used. The raw s c a t t e r i n g d a t a were f i r s t c o r r e c t e d f o r i n s t r u m e n t a l background and dark c u r r e n t counts and then c o r r e c t e d f o r non-uniform d e t e c t o r e f f i c i e n c y a t each d e t e c t o r channel element. Then the s e n s i t i v i t y c o r r e c t e d d a t a were p l o t t e d as a two-dimensional contour p l o t with contour l e v e l s i n c r e a s i n g by a f a c t o r o f 2 from the outermost one. Lupolen 23/7 was used as a c a l i b r a t i o n standard t o determine the a b s o l u t e SAXS i n t e n s i t y (49,50).


Wide-Anqle X-Ray D i f f r a c t i o n Wide-angle x-ray d i f f r a c t i o n (WAXD) measurements were performed with a Rigaku x-ray d i f f r a c t o m e t e r i n the t r a n s m i s s i o n mode. CuKa r a d i a t i o n was obtained by u s i n g a N i - f i l t e r and d e t e c t e d by a s c i n t i l l a t i o n counter and a p u l s e h e i g h t d i s c r i m i n a t o r . For the scan over 2 θ = 5° to 13°, the background of the empty beam was s u b t r a c t e d from the measured i n t e n s i t y . Results SAXS from Cotton Samples The two-dimensional i s o i n t e n s i t y c o n t o u r p l o t s of the n a t i v e G r e i g e c o t t o n , H y d r o c e l l u l o s e II and V a l o n i a v e n t r i c o s a are shown i n F i g u r e s 1,2 and 3 r e s p e c t i v e l y . The s p h e r i c a l l y symmetrical p a t t e r n s are the r e s u l t o f randomly o r i e n t e d f i b r i l s o r powder samples. By c o n v e r t i n g the r a d i a l l y averaged i n t e n s i t y v a l u e s i n t o a b s o l u t e u n i t s (namely, e l e c t r o n u n i t s , eu/nm^), the i n t e n s i t y (I) data o b t a i n e d from d i f f e r e n t sample t o d e t e c t o r d i s t a n c e s L can be superimposed, as shown i n F i g u r e 4 f o r n a t i v e G r e i g e c o t t o n . F i g u r e 5 p l o t s the l o g I versus l o g s f o r n a t i v e G r e i g e c o t t o n , H y d r o c e l l u l o s e I I , and V a l o n i a and F i g u r e 6 i s a G u i n i e r p l o t (51) of the t h r e e samples. The s c a t t e r i n g i n t e n s i t y c u r v e s of a l l of the c o t t o n samples and EHC I are q u a l i t a t i v e l y s i m i l a r t o t h a t of G r e i g e c o t t o n . SAXS from G l y c e r i n e Soaked and Iodine Embedded Samples The e l e c t r o n d e n s i t y c o n t r a s t i n c o t t o n was v a r i e d by two ways: d e c r e a s i n g i t by f i l l i n g the pores and v o i d s with g l y c e r i n e and i n c r e a s i n g i t by p u t t i n g i o d i n e i n t o the s o l i d phase. The r e s u l t i n g two-dimensional i s o i n t e n s i t y contour p l o t s are shown i n F i g u r e 7. The log I v e r s u s l o g s p l o t s f o r g l y c e r i n e soaked, scoured, and bleached G r e i g e c o t t o n and f o r i o d i n e embedded c o t t o n are shown i n F i g u r e s 8 and 9, r e s p e c t i v e l y . WAXD from Cotton Samples The s c a t t e r i n g i n t e n s i t y c u r v e s i n the 2 θ range o f 5° t o 13° f o r some of the c o t t o n samples are shown i n F i g u r e 10. The o r d e r of the curves i n F i g u r e 10 does not correspond to the o r d e r of the



LIN

ET

AL.


F i g u r e 1. Two dimensional i s o i n t e n s i t y cotton. (A) L = (B) L = (C) L =

239

contour plots of Greige 5 m, P 2 m, P 1 m, P

0 0 0

= 1.8 χ 1 0 = 2.5 χ 1 0 = 2.5 χ 1 0

F i g u r e 2. Two dimensional i s o i n t e n s i t y contour p l o t s o f H y d r o c e l l u l o s e II powder. (A) L = 5 m, P = 1.8 χ 1 0 (B) L = 1 m, P = 2.5 χ 1 0

6 6 6

6

0

6

0


cps; cps; cps.

cps; cps.


240

THE

F i g u r e 3. Two dimensional (A) (B)

STRUCTURES OF

CELLULOSE

i s o i n t e n s i t y c o n t o u r p l o t s of V a l o n i a , L = 5 m, P = 1.8 χ 1 0 cps; L = 1 m, P = 2.5 χ 10^ c p s . 6

0

0

s

1

(nm" )

F i g u r e 4. S u p e r p o s i t i o n of s c a t t e r i n g i n t e n s i t y data of n a t i v e G r e i g e c o t t o n o b t a i n e d a t d i f f e r e n t sample t o d e t e c t o r distances.



LIN

ET

AL.

241


ΙΟ"

2

ΙΟ"

1

10°

1

ΙΟ

- 1

s (nm )

F i g u r e 5. Log I (s) versus log s p l o t s f o r n a t i v e G r e i g e c o t t o n , H y d r o c e l u l o s e I I , and V a l o n i a .

F i g u r e 6. G u i n i e r p l o t s f o r n a t i v e G r e i g e c o t t o n , H y d r o c e l l u l o s e I I , and V a l o n i a .


242


2θ

(mrad)


(A)

F i g u r e 7. Two d i m e n s i o n a l i s o i n t e n s i t y c o n t o u r p l o t s o f (A) i o d i n e embedded c o t t o n (NH3 t r e a t e d absorbent c o t t o n w i t h NH3 removal a t 95°C), and (B) g l y c e r i n e soaked, scoured and bleached G e r i g e c o t t o n .

10" Glycerin soaked Scoured and bleached cotton

108

U

10°

\r

£ c LU

104

I0

J

IO

f c

10

μ

-2

10

10

s

10

1

(nm" )

F i g u r e 8. Comparison o f the s c a t t e r i n g i n t e n s i t y o f o r i g i n a l and g l y c e r i n e soaked, scoured and b l e a c h e d G r e i g e c o t t o n .



LIN ET

AL.


243

F i g u r e 9· Comparison o f t h e s c a t t e r i n g i n t e n s i t y o f o r i g i n a l and i o d i n e embedded c o t t o n (NH3 t r e a t e d a b s o r b e n t c o t t o n with NH3 removal a t 95°C)




244

0

2

6

4

10

8

-1

s (nm ) I

5°

ι

I

7°

I

I

9°

1 — ι — ι — ι

II

e

13

e

2 θ (degrees)

F i g u r e 10. WAXD d a t a o f c o t t o n samples i n the 2Θ range o f 5° t o 13°.


14.

LIN ET AL.


245

magnitude o f the r e a l s c a t t e r i n g i n t e n s i t y . ECH I and H y d r o c e l l u l o s e II are put on t h i s p l o t as the two extremes f o r comparing the e f f e c t of c e l l u l o s e c r y s t a l l i n e forms on the shape o f the i n t e n s i t y c u r v e s . Discussion


S c a t t e r i n g Source The q u e s t i o n o f whether SAXS a r i s e s from the m i c r o f i b r i l l a r s t r u c t u r e (7-10,22,25-26) o f c o t t o n or from m i c r o v o i d s (12,14-19) d i s p e r s e d through the c o t t o n i s approached here by the use o f s c a t t e r i n g c o n t r a s t e x p e r i m e n t s . Wadsworth and Cuculo (52) i n d i c a t e d t h a t i o d i n e p e n e t r a t e s both the amorphous and c r y s t a l l i n e r e g i o n s of c e l l u l o s e . By comparing the s c a t t e r i n g i n t e n s i t y of c o t t o n and i o d i n e embedded c o t t o n (see F i g u r e 9 ) , i t i s c l e a r t h a t the s c a t t e r i n g i s caused by the c o n t r a s t between the s o l i d phase i n c o t t o n and the v o i d s . While the e n t i r e curve o f the former s h i f t s up a t a c o n s t a n t r a t i o on the l o g I v e r s u s l o g s p l o t , the s l i g h t d i s c r e p a n c y at the t a i l p a r t may be due t o the s w e l l i n g o f the c e l l u l o s e caused by i o d i n e s o r p t i o n ( 5 3 ) . The s c a t t e r i n g b e h a v i o r of g l y c e r i n e soaked c o t t o n i s r e l a t i v e l y more d i f f i c u l t t o e x p l a i n . By t h e o r e t i c a l c a l c u l a t i o n , i f the g l y c e r i n e f i l l s the v o i d s c o m p l e t e l y then the i n t e n s i t y should drop t o 1/14.5 of t h a t o f the u n f i l l e d c o t t o n . However, t h i s i s t r u e o n l y f o r the f i r s t two d a t a p o i n t s . Three reasons are proposed f o r t h i s o b s e r v a t i o n : ( i ) o n l y b i g p o r e s , whose s i z e s exceed the lower r e s o l u t i o n l i m i t o f the SAXS instrument, are f i l l e d w i t h g l y c e r i n e ; ( i i ) some pores may be i s o l a t e d and t h e r e f o r e are not a c c e s s i b l e t o g l y c e r i n e ; ( i i i ) g l y c e r i n e a c t s as a s w e l l i n g agent t o c e l l u l o s e and causes a change i n m i c r o s t r u c t u r e . Nonetheless, combining the r e s u l t s from the i o d i n e embedded sample and the g l y c e r i n e soaked sample, the c o n c l u s i o n t h a t the s c a t t e r i n g a r i s e s from c o n t r a s t i n the e l e c t r o n d e n s i t y between c e l l u l o s e and d i s p e r s e d m i c r o v o i d s i n the c e l l u l o s e i s s t r o n g l y supported. Power Law

Behavior

I t i s observed i n F i g u r e s 5 and 10 t h a t the s c a t t e r i n g i n t e n s i t y curves of the c e l l u l o s e samples c o n t i n u o u s l y decrease from 2 θ = 0° to about 6 ° . The s h o r t - r a n g e atomic s t r u c t u r e i n the sample becomes s i g n i f i c a n t when 2 θ i s g r e a t e r than about 4 ° . In most samples the i n t e n s i t y f i r s t f a l l s and i s then n e a r l y c o n s t a n t between 2 0 = 6 ° and 7 ° . When 2 θ i s g r e a t e r than 9 ° , the i n t e n s i t y s t a r t s t o i n c r e a s e a g a i n and the change o f i t s shape with c r y s t a l l i n e form can be c l e a r l y seen. Two types o f power law b e h a v i o r are observed. For H y d r o c e l l u l o s e II and V a l o n i a , I ( s ) i s p r o p o r t i o n a l t o s a c c o r d i n g to Porod's i n v e r s e f o u r t h power law (54) f o r a wide i n t e r v a l of s. For the o t h e r t e n c o t t o n samples, the i n t e n s i t y i s p r o p o r t i o n a l t o s w i t h exponents l e s s n e g a t i v e than -4. These two cases w i l l be d i s c u s s e d s e p a r a t e l y .


246


Porod's Inverse Fourth Power Law. The t h e o r y o f s m a l l - a n g l e s c a t t e r i n g by i s o t r o p i c two-phase systems w i t h w e l l d e f i n e d smooth phase boundaries p r e d i c t s a decrease o f the i n t e n s i t y p r o p o r t i o n a l t o s ~ at l a r g e v a l u e s o f s. T h i s i s known as Porod's law ( 5 4 ) , 4

lim S

I -+

(s) = k / s

4

(4)

p

oo

where k i s known as the Porod c o n s t a n t . By a l e a s t - s q u a r e s f i t i t i s found t h a t f o r H y d r o c e l l u l o s e II the i n t e n s i t y I i s p r o p o r t i o n a l t o s-(3-93 + 0.02) = 0.4 t o 1.1 nnpl and f o r V a l o n i a I i s p r o p o r t i o n a l t o s - ( - ± 0.02) = 0.26 t o 2.2 nm" . The s l i g h t d e v i a t i o n o f the exponent from -4 may be the r e s u l t o f a d e n s i t y t r a n s i t i o n o f f i n i t e width between the phases and d e n s i t y f l u c t u a t i o n s w i t h i n the phases ( 5 5 ) , o r o f the s c a t t e r i n g from s p h e r i c a l pores w i t h a power-law dimension d i s t r i b u t i o n ( 5 6 ) , o r simply due to experimental e r r o r s . A t o m i c - s c a l e d e n s i t y f l u c t u a t i o n s can account f o r the l a r g e d e v i a t i o n from Porod's law at the o u t e r p a r t o f the s c a t t e r i n g c u r v e . Values f o r the Porod c o n s t a n t o f H y d r o c e l l u l o s e II and V a l o n i a are g i v e n i n T a b l e I . p


o v e r 4

s

0 7

1

o v e r

s

T a b l e I.

Estimated S t r u c t u r a l Parameters f o r H y d r o c e l l u l o s e II and V a l o n i a

Sample

kp

R

I**

s/v

2

3

(eu/nm ) 22800 + 200

(nm) 8.8

(nm) 8.5

(m^/cm ) 15.3

67400 + 800

13.5

12.5

45.2

7

Hydrocellulose II Valonia

min*

K

min = 3 . 5 / s **H = 8ïïQ/k

m i n

p

D e v i a t i o n From Porod's Law. Except f o r V a l o n i a and H y d r o c e l l u l o s e II the i n t e n s i t y o f the o t h e r t e n c o t t o n samples d e c r e a s e s w i t h s w i t h a n o n - i n t e g e r exponent. Values o f the exponent f o r the v a r i o u s samples are g i v e n i n T a b l e I I . Note they range from -2.7 t o -2.1. Non-integer e x p o n e n t i a l b e h a v i o r has been observed by P e r r e t and Ruland (57,58) f o r carbon f i b e r s . By p r e p a r i n g a p l o t o f I - s v e r s u s "s* " ( s l i t c o l l i m a t i o n system), they o b t a i n e d a l i n e a r relation 3

I(s)

=

k -s" p

3

+ b-s"

1

(5)

and suggested the b * s ~ l term i s d i r e c t l y r e l a t e d t o the f l u c t u a t i o n i n the e l e c t r o n d e n s i t y i n the 00H d i r e c t i o n o f the carbonaceous m a t e r i a l . In another paper ( 5 5 ) , Ruland suggested


14. LIN ET AL.

Table I I .

Sample


247


Greige Cotton Dewaxed G r e i g e Cotton Scoured G r e i g e Cotton Sco & B l e Greige Cotton Absorbent Cotton NaOH M e r c e r i z e d NH3 removed at R.T. NH3 removed at 90OC H2O immersed EHC I H y d r o c e l l u l o s e II Valonia

Power Law Parameters f o r C e l l u l o s e Samples s Range f o r Power Law F i t (nm" )

Power Law Exponent

1

Slope o f I*s vs. s p l o t (eu/nm ) 2

4

-2.13

+

0.02

0.54

t o 2.0

-2.24

+

0.02

0.50

t o 3.2

-2.48

+

0.02

0.47

to 3.1

-2.52 -2.72 -.244

+ + +

0.01 0.03 0.02

0.40 0.60 0.47

t o 3.2 t o 2.8 to 3.1

2950 + 50 3080 + 90

-2.73

+

0.03

0.70

t o 2.5

890 + 30

-2.54 -2.50 -2.48 -3.93 -4.07

+ + + + +

0.03 0.03 0.02 0.02 0.02

0.60 t o 2.5 0.57 t o 2.8 0.67 to 2.9 0.40 to 1.1 0.26 t o 2.2

2270 + 60 2760 + 90

t h a t d e n s i t y f l u c t u a t i o n s w i t h i n the phases produce p o s i t i v e d e v i a t i o n s from Porod's law and can be d e t e c t e d by I - s v e r s u s s p l o t s . Such a p l o t i s shown i n F i g u r e 11 f o r the absorbent c o t t o n s e r i e s and the s l o p e s determined from t h i s p l o t are g i v e n i n Table I I . If Ruland's p r o p o s a l (55) i s t r u e i n the case o f c o t t o n c e l l u l o s e , then we should observe a c o r r e l a t i o n between the value of the s l o p e of the I * s v e r s u s s p l o t and the degree of d i s o r d e r of c o t t o n ; t h a t i s , the h i g h e r the d i s o r d e r , the h i g h e r the v a l u e of the s l o p e . I t i s w e l l known t h a t NaOH m e r c e r i z a t i o n and the l i q u i d amonia treatment i n c r e a s e the degree of d i s o r d e r i n c o t t o n (3,59). However, the v a r i a t i o n o f s l o p e s with these samples does not f o l l o w the c o r r e l a t i o n t h a t Ruland proposed (55,57,58). Thus, f l u c t u a t i o n s i n the dense phase cannot e x p l a i n the d e v i a t i o n from Porod's law s a t i s f a c t o r i l y . A d i f f e r e n t model w i l l be proposed i n a l a t e r s e c t i o n to e x p l a i n this deviation. 4

4

2

I n v a r i a n t and V o i d F r a c t i o n The general t h e o r y developed by Porod (54) as w e l l as by Debye and Buche (60) s t a r t s from the f a c t t h a t the small angle s c a t t e r i n g depends o n l y on v a r i a t i o n s of the e l e c t r o n d e n s i t y . The i n t e n s i t y i s determined by the mean s c a t t e r i n g power o f the system which i s g i v e n the d e s i g n a t i o n η o r mean square e l e c t r o n d e n s i t y f l u c t u a t i o n . For a two-phase system of volume V w i t h volume f r a c t i o n s x\ and x and w i t h the r e s p e c t i v e e l e c t r o n d e n s i t i e s p\ and p , i t can be shown t h a t 2

2

2

American Chemical Society Library 1155 16th St., N.W. In The Structures of Cellulose; R.; Washington, O.C.Atalla, 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

2


248

THE

F i g u r e 11. I · s

4

STRUCTURES OF

CELLULOSE

versus s^ p l o t s f o r absorbent c o t t o n s e r i e s .


14.

LIN

ET

249


AL.

(

P l

-

·

p ) 2

χ

·

χ

x

(6)

2

A d d i t i o n a l l y , Porod (54) d e r i v e d an i n t e g r a l over a l l s c a t t e r i n g space, the s o - c a l l e d i n v a r i a n t , which i s d i r e c t l y r e l a t e d t o the mean square f l u c t u a t i o n o f e l e c t r o n d e n s i t y , i r r e s p e c t i v e o f the g e o m e t r i c a l f e a t u r e s of the s t r u c t u r e , /~[I(s)dVs]/(2TT)

3

2

=

η ν

(7)


For an i s o t r o p i c s c a t t e r i n g system, Eq. (6) reduces t o 2

/^[4ïïs -I(s)ds]/(2ïï)

3

=

2

n V

(8)

The i n v a r i a n t v a l u e s t o g e t h e r w i t h the volume f r a c t i o n o f pores f o r c e l l u l o s e samples are l i s t e d i n T a b l e I I I . For the G r e i g e c o t t o n s e r i e s , dewaxing f o l l o w e d by s c o u r i n g and b l e a c h i n g , i n c r e a s e s the pore volume f r a c t i o n a t each s t e p , but has no s i g n i f i c a n t i n f l u e n c e on the shape o f the SAXS c u r v e . For the absorbent c o t t o n s e r i e s , m e r c e r i z a t i o n treatment w i t h e i t h e r sodium hydroxide o r l i q u i d ammonia d e c r e a s e s the pore volume f r a c t i o n t o a s i m i l a r l e v e l . The c o n d i t i o n s f o r ammonia removal e s s e n t i a l l y do not a f f e c t the pore volume f r a c t i o n . However, h y d r o l y z e d c o t t o n c e l l u l o s e has a much h i g h e r pore volume f r a c t i o n than the o t h e r c o t t o n samples. The e f f e c t s due t o the chemical p r o c e s s o f h y d r o l y z i n g need f u r t h e r study. T a b l e I I I . I n v a r i a n t and Pore Volume F r a c t i o n i n C e l l u l o s e Samples Sample Greige Cotton Dewaxed G r e i g e C o t t o n Scoured G r e i g e Cotton Sco & G l e G r e i g e Cotton Absorbent Cotton NaOH M e r c e r i z e d NH3 Removed a t R. T. NH3 Removed a t 95°C Η 0 Immersed EHCI H y d r o c e l l u l o s e II Valonia 2

Invariant (eu/nmô) 1790 1960 2490 2530 2620 1780 1790 1620 1900 3680 7730 33490

Pore V o l . Frac. m

0.76 0.83 1.06 1.12 1.12 0.76 0.76 0.69 0.81 1.58 3.37 17.02

The e s t i m a t e d u n c e r t a i n t y i n the d e t e r m i n a t i o n o f the i n v a r i a n t i s about f i v e p e r c e n t . The e r r o r i n v o l v e s the


250

THE

STRUCTURES OF CELLULOSE

e s t i m a t i o n o f sample t h i c k n e s s , d e t e r m i n a t i o n o f i n c i d e n t x-ray power, d e n s i t y , and s t a t i s t i c a l e r r o r i n d e t e c t o r c o u n t s . A l s o s i n c e some o f t h e pore s i z e s a r e b i g g e r than can be measured with the ORNL 10m SAXS i n s t r u m e n t , t h e i n v a r i a n t and t h e v o i d volume f r a c t i o n a r e c o n s i d e r e d t o be underestimated. Pore S i z e Two methods a r e employed t o e v a l u a t e t h e s i z e o f pores i n samples which f o l l o w Porod's law. The f i r s t i s a rough e s t i m a t e o f t h e average pore dimension R o b t a i n e d from s * , t h e s m a l l e s t v a l u e o f s a t which Porod's law s c a t t e r i n g i s observed. U s u a l l y one expects s i -R>> 1. As a c o n s e r v a t i v e e s t i m a t e , s j -R> 3.5 can be assumed (54, 6 1 ) . The average dimension o f t h e pores must then be a t l e a s t 3.5/s - . The second method i n v o l v e s t h e c a l c u l a t i o n o f t h e so c a l l e d average chord l e n g t h I ( 6 2 ) , mi


m

n

n

m

mi

n

n

Ï=Q ïïQ/k (9) T h i s I i s a measure o f t h e s i z e o f t h e i n h o m o g e n e i t i e s . Q i s the i n v a r i a n t and k i s Porod's c o n s t a n t . Due t o t h e r e s o l u t i o n l i m i t , t h e c a l c u l a t e d i n v a r i a n t Q i s underestimated and thus i i s underestimated i n t h i s study. Table I compares t h e pore dimensions i n H y d r o c e l l u l o s e II and V a l o n i a . I t appears t h a t t h e s i z e s determined by t h e two methods a r e comparable. The pores i n V a l o n i a a r e much b i g g e r than those i n H y d r o c e l l u l o s e I I . I t i s r e a s o n a b l e t o p o s t u l a t e t h a t t h e pores i n the o t h e r c o t t o n samples a r e about t h e same as those i n H y d r o c e l l u l o s e . p

p

S p e c i f i c Inner S u r f a c e The s p e c i f i c i n n e r s u r f a c e i s d e f i n e d as t h e r a t i o o f t h e a r e a o f the phase i n t e r f a c e S t o t h e volume o c c u p i e d by t h e d i s p e r s e phase V . When i t can be v e r i f i e d e x p e r i m e n t a l l y t h a t t h e i n t e n s i t y o f a two-phase s c a t t e r i n g system f o l l o w s t h e i n v e r s e f o r t h power law, t h e s p e c i f i c i n n e r s u r f a c e can be o b t a i n e d (54,62): 2

S/V

2

= 4 x

±

· x /l 2

(10)

The v a l u e s f o r H y d r o c e l l u l o s e II and V a l o n i a a r e l i s t e d i n T a b l e I. S i n c e Q i s underestimated, the c a l c u l a t e d s p e c i f i c i n n e r s u r f a c e tends t o be o v e r e s t i m a t e d . The t y p i c a l s u r f a c e area o f c o t t o n determined by s o r p t i o n o f n i t r o g e n and argon ranges between 0.3 t o 1.9 m /g ( 3 ) . The v a l u e determined by SAXS i s f i v e t o t e n time g r e a t e r than t h e l a t t e r . T h i s i s r e a s o n a b l e s i n c e SAXS can d e t e c t t h e i n a c c e s s i b l e pore s u r f a c e t o o . 2

Aggregate F r a c t a l s i n Cotton The p r o p e r t y o f s c a l e - i n v a r i a n c e i m p l i e s t h e power-law form f o r the d e n s i t y - d e n s i t y c o r r e l a t i o n f u n c t i o n :


14.

LIN ET

251


AL.

c(x) = < P U ) . r p ( r m

+ x) > - l / r

m

dD

(2)

The e l e c t r o n d e n s i t y - e l e c t r o n d e n s i t y c o r r e l a t i o n f u n c t i o n should have a s i m i l a r form:

p

el

(

r

)

1

~

d

/r "

D

and l e a d s t o a power-law dependence f o r t h e s c a t t e r i n g i n t e n s i t y which i s t h e F o u r i e r t r a n s f o r m o f p ^ ( r ) : 2

e


Ks)

= jf t P

2

r

e J l

D

(r)] r

s

~ /r -V - dV -

s"

(12)

s

D

The l o g I v e r s u s l o g s c u r v e s o f t h e G r e i g e c o t t o n s e r i e s , absorbent c o t t o n s e r i e s , and EHC I have t h e same o v e r a l l shape as the s c a t t e r i n g curve shown i n F i g u r e 4. The v a l u e s o f t h e exponents a r e between -2.12 + 0.02 t o -2.73 + 0.03 over t h e range 0.5 nm-1 < < 3 ηπτ*. Below s = 0.5 nm~l, t h e s l o p e becomes more n e g a t i v e . T h i s r e g i o n c h a r a c t e r i z e s t h e pore s t r u c t u r e and approaches Porod's law I ( s ) - s r a t h e r than G u i n i e r ' s a p p r o x i m a t i o n . The G u i n i e r treatment i n F i g u r e 6 c l e a r l y i n d i c a t e s t h e r e i s no simple s t r a i g h t l i n e r e l a t i o n s h i p , and r e v e a l s t h e r e i s no simple c h a r a c t e r i s t i c l e n g t h s c a l e d e d u c i b l e from t h e d a t a . S c a t t e r i n g c u r v e s o f t h i s kind have t r a d i t i o n a l l y been analyzed as s c a t t e r i n g from p a r t i c l e s w i t h a d i s t r i b u t i o n o f s i z e s . T h i s approach can be used t o r e p r e s e n t t h e p r e s e n t d a t a , but t h e parameters d e r i v e d i n t h i s f a s h i o n depend on t h e range o f s c a t t e r i n g angles and t h e i r r e l a t i o n s h i p t o t h e p h y s i c a l s t r u c t u r e i s dubious. I n s t e a d , we argue t h a t t h e power law b e h a v i o r f o r I ( s ) i s an i n d i c a t i o n o f t h e f r a c t a l s t r u c t u r e o f c e l l u l o s e m i c r o c r y s t a l l i n e a g g r e g a t e s . The power-law decay o f the SAXS i n t e n s i t y over t h e range 0.5 nm -1 < s s -1 > 2 nm. 0.3 nm i s about t h e s i z e o f one c e l l u l o s e monomer, 2 nm i s t h e s i z e o f m i c r o c r y s t a l l i t e s as measured by l i n e width a n a l y s i s o f WAXD (21,22) and e l e c t r o n microscopy ( 2 6 ) . We interprète t h e b e h a v i o r i n t h i s range t o mean t h a t w h i l e c e l l u l o s e monomer u n i t s form m i c r o c r y s t a l l i t e s w i t h t h e i r usual 3 dimensional o r d e r , t h e m i c r o c r y s t a l l i t e s form aggregated f r a c t a l s o f H a u s d o r f f dimension < 3. Computer s i m u l a t i o n s which may mimic a g g r e g a t i o n p r o c e s s e s i n 3 d space y i e l d v a l u e s o f D « 2.5 f o r DLA and D = 1.8 f o r CA (33, 35-38). C l e a r l y n e i t h e r t h e DLA o r CA model d e s c r i b e s t h e c o t t o n c e l l u l o s e system. A p o s s i b i l i t y t h a t so f a r has not been i n c l u d e d i n t h e s i m u l a t i o n s i s t h a t t h e aggregates might r e s t r u c t u r e a f t e r f o r m a t i o n . S c h a e f e r e t a l . (42,43) suggested t h a t a d d i t i o n a l attachments w i l l l e a d t o an i n c r e a s e d D so s

- 4

-1


THE


252

STRUCTURES OF CELLULOSE

r e s t r u c t u r i n g may e x p l a i n D > 1.8 f o r CA i n 3 d space. Another view has been expressed by V i c s e k and Family ( 6 3 ) . They e x p l o r e the p r o p e r t i e s o f a c l u s t e r s i z e d i s t r i b u t i o n f u n c t i o n and d i s c u s s t h e r e l a t i o n s h i p between D and t h e moments o f t h e d i s t r i b u t i o n f u n c t i o n . The mechanisms o f a g g r e g a t i o n p r o c e s s e s w i l l c o n t i n u e t o be o f i n t e r e s t t o those s t u d y i n g a v a r i e t y o f physical processes. The fundamental a s s e r t i o n we make here r e g a r d i n g t h e f r a c t a l n a t u r e o f c e l l u l o s e m i c r o c r y s t a l l i n e aggregates i s s p e c u l a t i v e . We view t h e w e l l e s t a b l i s h e d microporous and m i c r o f i b r i l l a r c h a r a c t e r o f c e l l u l o s e c o t t o n f i b e r s t o support o u r f r a c t a l i n t e r p r e t a t i o n . The b e h a v i o r o f t h e SAXS s c a t t e r i n g f u n c t i o n i s c o n s i s t e n t with t h i s f r a c t a l i n t e r p r e t a t i o n and does not conform t o t h e usual G u i n i e r and Porod methods o f a n a l y s i s . We hope t h e appoach used i n t h i s study i s s u f f i c i e n t l y p r o v o c a t i v e t o s t i m u l a t e t h e t h i n k i n g o f o t h e r r e s e a r c h e r s r e g a r d i n g t h e growth p r o c e s s o f c o t t o n c e l l u l o s e , whether i t be v i a a g g r e g a t i o n o f m i c r o c r y s t a l l i t e s f o l l o w e d by some rearrangement o r another process. Acknowledgments T h i s work was performed as p a r t o f S p e c i f i c C o o p e r a t i v e Agreement No. 58-7B30-3-560 between t h e U n i t e d S t a t e s Department o f A g r i c u l t u r e and The U n i v e r s i t y o f Tennessee. Portions of this work were performed a t t h e N a t i o n a l Center f o r Small Angle S c a t t e r i n g Research a t Oak Ridge N a t i o n a l L a b o r a t o r y which i s supported by NSF Grant No. QMR-77-24458 through i n t e r a g e n c y agreement No. 40-637-77 with t h e Department o f Energy.

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