Structural Units of Starch Determined by X-ray Crystal Structure Method

7/29/2019 Structural Units of Starch Determined by X-ray Crystal Structure Method

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S T R U C T UR A L U N I T S O F S T A RC H D E T E R M I N E D B YX - R A Y C R Y S T A L S T R U C T U R E M E T H O D .

BY O. L. SPON SLER,(From the University of California, Southern ~ranch, Los Angeles.)

(Received for publication, April 30, 1923.)Among the ear l ies t invest iga tors o f s ta rch the idea prevai led tha t

these minute , t ransparen t , spher ica l g ra ins were bu i l t o f un i formstruc t ura l un i ts , the na ture , s ize , shape , and ar ran geme nt o f whichhave b een the source of a num ber of theor ies and of much specula t ion .Raspai l ' s work ~ in 1825 led h im to th ink tha t the gra ins were no tcrysta l l iza t ion products . Mtin ter~ on the o ther hand dec ided tha tthe gra ins must be crysta ls . N~igeli conceived the gra in to be madeup of concentr ica l ly and rad ia l ly a r ranged par t ic les which he ca l ledat one t ime s molecules, and later 4 micell~e, and in one pla ce h e speaksof these smal l par t ic les as consis t ing of severa l thousand molecu les .In 1863 Kabsch~ considered starch grains to ha ve a ve ry definitear ran gem ent o f molecules , a l though no t suf f ic ien t ly un i form to haveopt ica l axes ascr ibed to them. Schimper6 dec ided tha t they consis tedof rad ia l ly a r ranged crysta l f ibers . In 1895 M eye r 7 comple ted th isidea of a spherocrysta l and conceived the gra ins to be bu i l t o f rad ia l lyar ranged needle- like branching crysta ls , which became more and moreb r an ch ed th e m o r e n ea r ly th ey ap p r o ach ed th e su r face o f t h e g r ain .These crysta ls he ca l led t r ich i tes . The vas t amo unt o f work tha thas been done s ince then has ne i ther conf i rmed nor d isproved thetheory of the t r ich i te o r mice l la r s t ruc ture , and of the la te r a r t ic leson s ta rch some favor and some oppose th is v iew.

1 Raspail, F. V., Annal. sc. natur., 1825, vi, series 1,387.2 Mtinter, J., Bot. Ztg., 1845, iil, 194.3 N~geli, C., Die St~trkek6rner, Zttrich, 1858.4 N~tgeli, C., Bot. Ztg., 1881, xxxix, 637.5 Kabsch, W., Z. anal. Chem., 1863, i/, 216.6 Schimper, A. F. W., Bot. Ztg., 1881, xxxix, 223.7 Meye r, A., Untersu chungen fiber die St~rkek6rner, Jen a, 1895.757

The Journal of General Physiology


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75 8 STRUCTURAL UNITS OF STARCttP r o b a b l y a l l h a s b e e n d o n e w i t h t h e m i c r o s c o p e a n d t h e u l t r a m i -

c r o s c o p e t h a t c a n b e d o n e , a n d n o s t r u c t u r a l u n i t h a s b e e n f o u n d .I f o n e i s t o b e d i s c o v e r e d i t m u s t p r o b a b l y b e w i t h s o m e n e w t o ol ,a n d d u r i n g t h e p a s t fe w y e a r s s u c h a n e w t o o l h a s m a d e i t s a p p e a r a n c e ,n a m e l y t h e x -r a y . I t h a s b e e n u s e d t o i n v e st i g a t e t h e b u il d i ngu n i t s o f c r y s ta l s , a n d w i t h i t a g r e a t d e a l o f w o r k h a s b e e n d o n ei n d e t e r m i n i n g t h e s i z e a n d a r r a n g e m e n t o f t h e s e s t r u c t u r a l u n i t s i nm a n y in o r g a n i c c r y s ta l s . T h e s e u n i t s p r o v e t o b e t h e a t o m s o fw h i c h t h e c r y s t a ls a r e c o m p o s e d. F o r e x a m p l e , th e c u b i c a l c r y s t a lo f c o m m o n t a b l e s a l t c o n s i s t s o f s o d i u m a n d c h l o r i n e a t o m s a r -r a n g e d a l t e r n a t e l y i n t h r e e d i m e n si o n s. T h e p o s i t i o n w i t h r e l a t io nt o e a c h o t h e r a n d t h e d i s t a n c e f r o m c e n t e r t o c e n t e r o f t h e s e a t o m sh a v e b e e n v e r y a c c u r a t e l y d e t e r m i n e d . 8 A b o u t f i f t y c o m p o u n d s a n da c o n s i d e r a b l e n u m b e r o f m e t a l e l e m e n t s h a v e b e e n i n v e s t i g a t e d i nt h i s w a y , a m o n g t h e m t h e d i a m o n d , g r a p h i t e , c a r b o n a t e s , s u l f i d e s ,o x id e s, e t c . V e r y f e w o r g a n ic c o m p o u n d s , h o w e v e r , h a v e b e e ns t u d i e d .

W i t h t h e s e i n v e st i g a ti o n s i n m i n d i t s e e m e d f a i r ly p la u s ib l e t h a tt h e s t r u c t u r e o f t h e s t a r c h g r a i n m i g h t b e d e t e r m i n e d , e s p e c i a l l ys i n c e t h e g r a i n s b e h a v e t o w a r d s l i g h t a s t h o u g h t h e y w e r e b u i l tu p i n s o m e r e g u l a r w a y , a n d s i nc e x - r a y s a re o f t h e n a t u r e o f l i gh t .

T h e x - r a y m e t h o d o f d e t e r m i n i n g t h e a t o m i c s t r u c t u r e o f c r y s t a l si s d e s c r i b e d i n c o n s i d e ra b l e d e t a i l in a n u m b e r o f p l a c e s i n t h e l i t e r a -ture ,8 ,9 ,1 so on ly a ver y b r ie f resum 6 wi ll be g iven here . Fo r p roofsa n d e v i d e n c e c o n c e r n i n g t h e v a r i o u s s t e p s t h e r e a d e r i s r e f e r r e d t ot h e c i t a t i o n s j u s t m e n t i o n e d .

T h e m e t h o d c o n s is t s i n m e a s u r i n g t h e a n g l e a t w h i c h x - ra y s a r er e f l e c te d f r o m a c r y s t a l , a n d c o m p u t i n g f r o m t h a t m e a s u r e m e n t th ed i s t a n c e b e t w e e n t h e p l a n e s o f a t o m s w h i c h h a v e c a u s e d t h e r e f l e c ti o n .W h e n a n x - r a y w a v e i s i n c i d e n t o n t h e f a c e o f a c r y s t a l i t p a s s e st h r o u g h t h e s u rf a c e l a y e r o f a t o m s a n d t h r o u g h m a n y t h o u s a n d

s Bragg, W. H ., and Bragg, W. L., X-rays and crystal structure, New York andLondon, 1918.9 Hull, A . W., Phys. Rev., 1917, x, series 2, 661; 1921, xvii, series 2,5 71 . Dcby e,P., and Scherrer, P., Physik . Z . , 1916, xvii, 277. Ba in, E. C., Chem. and M etallurg.Eng., 1921, xxv, 657.10 S pons ler, O. L., Am . J . Bot . , 1922, ix, 471.


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O. L. SPONSLER 759

l a y e r s b e n e a t h . O n l y a m i n u t e p a r t o f t h e w a v e i s r e f l e c te d f r o me a c h p l a n e . T h e re a r e s e v e ra l m i l l i o n s o f th e s e p la n e s o r l a y e r su n i f o r m l y s p a c e d i n e a c h m i l l i m e t e r o f d e p t h i n a c r y s ta l . T h e d i s -t a n c e b e t w e e n t h e l a y e r s a n d a l so b e t w e e n t h e a t o m s i n t h e l a y e r ,v a r i e s w i t h t h e k i n d o f c r y s t a l f r o m o n e t o s ev e r a l A n g s t r 6 m

1u n i t s . An A n g s t r6 m u n i t i s 1 0 ,0 0 0 ,0 0 0 " m i l l i m e t e r . W h e n t h ed i s t a n c e b e t w e e n t h e p l a n e s i s s u c h t h a t a c r e s t o f t h e m i n u t e p a r to f t h e w a v e w h i c h is r e f l e c t e d f r o m o n e p l a n e c o i nc i d es w i t h a c r e s tf r o m t h a t o f th e n e x t p l a n e, t h e n t h e y w i l l r e i nf o r c e, a n d t h e s u m o fm a n y t h o u s a n d s u c h r e f l e c ti o n s w i ll c a r r y s u f f ic i e nt e n e r g y t o r e g i st e rv i s ib l y o n a p h o t o g r a p h i c p l a te . T h u s x - r a y r e f le c t io n d e p e n d su p o n r e i n f o r c e m e n t f r o m a d e p t h o f m a n y p l a n e s. T h e c r e s ts o ft h e w a v e s w i l l c oi n c id e o n l y w h e n t h e r e i s a c e r t a i n r e l a t i o n b e t w e e nt h e g l a n c i n g a n g l e , t h e w a v e l e n g t h o f t h e x - r a y s u s e d , a n d t h e d i s-t a n c e b e t we e n t h e p l a n e s . T h i s r e l a t i o n s h i p i s e x p re s s e d b y t h ef o r m u l a

X = 2d s in 0i n w h i c h X i s t h e w a v e l e n g t h, d t h e d i s t a n c e b e t w e e n p l a n e s, a n dO t h e g l a n c i n g a n g le . I f t h e g l a n c i n g a n g l e v a r i e s b y o n l y on e p a r ti n s e v e r a l th o u s a n d t h e t e n d e n c y i s to a n n u l i n s t e a d o f r e in f o r ce ,a n d c o n s e q u e n t l y , r e fl e c t io n c a n o c c u r o n l y a t a v e r y d e f i n i te a n g l efo r a g i v e n s e t o f p l a n e s a n d a g i v e n wa v e l e n g t h .

W h e n a n a r r o w b e a m o f x - r a y s, c o n s i s ti n g p r i m a r i l y o f on e w a v el e n g t h o f k n o w n v a l u e , i s a l l o we d t o p a s s t h ro u g h a s m a l l m a s s o fp o w d e re d c ry s t a l s , s o m e o f t h e c ry s t a l p a r t i c l e s w i l l r e f l e c t a t o n ea n g l e , s o m e a t a n o t h e r , s t i l l o t h e r s a t a t h i rd a n g l e , a n d s o o n , a c -c o r d i n g t o t h e r e l a t i o n m e n t i o n e d a b o v e b e t w e e n t h e w a v e l e n g t h ,t h e g l a n c i n g an g l e , a n d t h e d i s t a n c e b e t w e e n p l a n e s i n t h e c r y s t a lp a r t ic l e s . W h e n t h e s e r e f l e c ti o n s a r e r e c o r d e d o n a p h o t o g r a p h i cf i l m , t h e y w i l l a p p e a r a s d e n s e l i n e s w i t h a w i d t h c o r r e s p o n d i n g t ot h e s l it t h r o u g h w h i c h t h e b e a m o f x - r a y s is a l lo w e d t o p a s s b e f o r er e a c h i n g t h e p o w d e r . T h e a r c o f t h e r e f l e c t in g o r g l a n c in g a n g l ec a n b e m e a s u r e d i n m i l li m e t e r s d i r e c t l y o n t h e f il m , a n d si n ce ak n o w n w a v e l e n g t h is u s ed , t h e d i s t a n c e b e t w e e n p l a ne s c a n b e r e a d i l yc o m p u t e d . F o r a m o r e d e t a i le d a n d s im p l e r e x p l a n a t io n , a s w e l l a s


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76 0 S T R U C T U R A L UNITS O F STARCHfo r d i a g ra m s a n d d e s c r i p t i o n s o f t h e a p p a ra t u s u s e d i n t h i s wo rk ,t h e r e a d e r i s r e fe r r e d t o m y p a p e r i n t h e A m e r i c a n J o u r n a l o f B o ta n y . 1M a n y d e m o n s t r a ti o n s h a v e b e e n m a d e b y a n u m b e r o f i n ve s ti g a -t o r s t o s h o w t h a t t h e d e n s e l i n e s , a s i n F i g . 1 , a r e p ro d u c e d b y t h er e f le c t io n o f x - ra y s f r o m p l a n e s o f a t o m s . T h e s e d e m o n s t r a t i o n sc o n s i s t o f t wo p a r t s . F i r s t , t h a t t h e li n e s o n t h e p h o t o g r a p h a r ep r o d u c e d b y r e f le c t in g p o i n t s a r r a n g e d i n p l a n e s ; a n d s e c o n d, t h a tt h e s e r e f l e c t in g p o i n t s a r e a t o m s . T h e p ro o f o f t h e f i r s t p a r t c o n -s is ts i n o b t a i n in g a n a g r e e m e n t b e t w e e n t h e v a l u e s o f d ( d i s t a n c eb e t w e e n p l a ne s ) f r o m m e a s u r e m e n t s o f t h e p h o t o g r a p h , a n d t h ev a l u e s o b t a i n e d f r o m a m a t h e m a t i c a l c o n s i d e r a t i o n o f t h e t y p e o fc ry s t a l u s e d . T h e p ro o f o f t h e s e c o n d p a r t c o n s i s ts i n o b t a i n i n g a na g r e e m e n t b e t w e e n t h e v o l u m e o c c u p i e d b y a r e f l e c ti n g p o i n t a sc o m p u t e d f r o m t h e p h o t o g r a p h a n d t h e v o l u m e o f th e a t o m o r m o le -c u l e a s o b t a i n e d b y t h e u s e o f t h e m o l e c u l a r w e i g h t, t h e d e n s i t y ,a n d A v o g a d r o ' s n u m b e r . I t m a y b e w o r t h w h i le t o i l lu s t r a te t h e set wo p o i n t s b r i e f l y , s i n c e s i m i l a r m e t h o d s a r e u s e d l a t e r i n d e t e rm i n -i n g t h e s t r u c t u r a l u n i t s o f s t a r c h .

F i g . 1 is r e p ro d u c e d f ro m a n x - r a y p h o t o g ra p h o f t h e l i n e s r e f l e c t e db y t h e c r y s t a l p a r t ic l e s o f p o w d e r e d s o d i u m c h l o ri d e . A r h o d i u ma n t i c a t h o d e w a s u s e d , a n d t h e r a y s w e r e f il t e re d t h r o u g h a r u t h e n i u ms c r e e n s o t h a t t h e b e a m w a s p r a c t i c a l ly m o n o c h r o m a t i c . T h eb l a n k s p a c e i n t h e m i d d l e o f t h e p h o t o g r a p h i s t h e s h a d o w o f a l e a ds h ie l d u s e d t o a b s o rb t h a t p a r t o f t h e m a i n b e a m w h i c h w a s n o td i v e r t e d w h e n p a s s in g t h r o u g h t h e p o w d e r . T h e r i g h t a n d l e f th a n d s id e s a r e m i r r o r i m a g e s , a n d t h e d i s t a n c e s b e t w e e n l in e s 1 a n d 1 ,2 a n d 2 , 3 a n d 3 , e tc . , m e a s u re t h e a r c o f 4 0 i n e a c h c a s e , wh e re Oi s t h e g la n c i n g a n g le . B y u s i n g t h e s e m e a s u r e m e n t s a n d t h e r h o d i u mK a wa v e - l e n g t h 0.6 14 A .u . , t h e d i s t a n c e b e t we e n t h e p l a n e s o fr e f l ec t i n g p o i n t s w a s c o m p u t e d f r o m t h e f u n d a m e n t a l f o r m u l a ,~, = 2 d s i n O . T h e r e s u l t s sh o w t h a t l i n e 1 wa s r e f l e c t e d f ro m p l a n e swh ich we re 2 .81 2~ .u . apa r t ; l ine 2 , b y p la nes 1 .99 .A. .u . ap ar t ands o o n a s r e c o r d e d i n T a b l e I .A s t r ik i n g a g r e e m e n t is o b t a i n e d w h e n t h e s e f i gu r e s a r e c o m p a r e dw i t h t h o s e w h i c h w e r e c o m p u t e d f r o m a c u b i c a l s p a c e l a t t i c e s u c ha s B r a v a i s ' o l d t h e o r y p r o p o se d f or th e a t o m s i n a c r y s t a l. K n o w -i n g t h a t s o d i u m c h l o r i d e f o r m s c u b i c a l c r y s t a l s , w e m a y t h i n k o f a


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o. L. SI'ONSLER 761u n i t c u b e a s h a v i n g a n a t o m a t e a c h c o r n e r a n d o f t h e l a r g e c r y s t a la s b e in g b u i l t u p o f m a n y o f th e s e u n i t c u b e s w i t h t h e a t o m s s h a r e db y t h e a d j a c e n t cu b e s. T h e a t o m s t h e n w o u l d f o r m a sp a c e l a t t ic ei n w h i c h t h e y w o u l d o c c u r i n m a n y s e ts o f p a r a ll e l p l a ne s . T h ep l a n e s c o i n c i d in g w i t h t h e f a c e s o f t h e c u b e s w o u l d b e f a r t h e s t a p a r t ,a n d t h e d i s t a n c e s b e t w e e n t h e d i a g o n a l p l a n e s w o u l d b e a r d e f i n i t er e l a t i o n s t o t h i s w i d e s t s p a c i n g . W h e n t h e s id e s o f t h e c u b e a r e

T A B L E I .Sodium Chloride.

Line No. Distance betwee n planes.

2 . 8 11 . 9 91 . 6 21 . 4 11 . 2 61 . 1 4

T A B L E I I .Sodium Chloride.

Line No. Distance computed from Computed from cubicl a t t i c e b a sed o n R a t i o o f p l a n e s in acublc lattlce.ngle and wave-length . 2.81 A.u.

2 . 8 11 . 9 91 . 6 21 . 4 11 . 2 51 . 1 4

2 . 8 11 . 9 91 . 6 21 . 4 11 . 2 51 . 1 4

1 . 0 0 00 . 7 0 70 . 5 7 70 . 5 0 00 . 4 4 70 . 4 0 8

1 .0 0 u n i t a p a r t t h e v a r i o u s s e t s o f d i a g o n a l p l a n e s a r e s p a c e d 0 .7 07u n i t , 0 .5 7 7 , 0 . 50 0 , e t c . N o w i f w e a c c e p t l i n e 1 a s b e i n g r e f l e c t e db y t h e p l a n e s w h i c h h a v e t h e w i d e s t s p ac i n g , t h e n i f a c u b i c a l a r r a n g e -m e n t e x is ts , l in e 2 w o u l d b e r e f l e c t e d b y p l a n e s w h i c h a r e s p a c e d0 .707 X 2 .81 ; l ine 3 , 0 .577 X 2 .81, e tc . Ta b le I I g ives the ra t io o fs p a c in g s o f p la n e s i n a c u b i c l a t t i c e a n d t h e d i s t a n c e b e t w e e n p l a n e sb a s e d o n 2 .8 1 ~ .u . a s t h e p o s s i b le d i s t a n c e b e t w e e n c u b e f a c e s .Ta b l e I i s i n c o rp o ra t e d i n i t f o r c o m p a r i s o n .


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762 STRUCTURAL UNITS OF STARCttS u c h c l os e a g r e e m e n t b e t w e e n t h e s e t w o s e t s o f f ig u r es n e c e s s a r il y

l e a d s o n e t o c o n c l u d e t h a t t h e " r e f l e c t i n g p o i n t s " m u s t b e a r r a n g e di n a c u b i c s p a c e l a t t i c e .T h e s e c o n d p a r t o f t h e d e m o n s t r a t i o n , s h o w i n g t h a t t h e r e fl e c ti n g

p o i n t s a r e a t o m s , i s g i v e n b r i e f l y i n t h e f o l l o w i n g p a r a g r a p h s .I t i s a w e l l e s t a b l i s h e d f a c t t h a t t h e m o l e c u l a r w e i g h t o f a n y c o m -

p o u n d i n g r a m s c o n t a i n s a d e f i n it e n u m b e r o f m o l e c ul e s ; th e a c c e p t e df i g u re i s 6 .0 6 2 1 02 3. T h i s is c a l l e d A v o g a d r o ' s n u m b e r . S o d i u mc h l o r i d e c o n t a i n s t h a t n u m b e r o f m o l e c u l e s fo r e a c h 5 8 .5 g i n. o f t h es a l t . T h e v o l u m e o f 5 8 .5 g m . o f N a C 1 i s 26.95 cc . , s i nce i t s spec i f i cg r a v i t y i s 2.17.

58.5 - 26.952.17

T h a t v o l u m e th e n c o n t a i n s 6. 0 62 X 1 02 3 m o l e c u l e s , a n d t h e v o l u m e o f26.951 m o l e c u l e o f s o d i u m c h l o r i d e w o u l d b e 6 .0 6 2 X 1 0~s or 44 .4 X 1 0 - 2 4 ,

o r 4 4 . 4 c u . . ~ . u .T h e p h o t o g r a p h s h o w s t h a t i n t h e u n i t c u b e t h e f a c e s a r e s p a c e d

2 .8 1 . ~ .u . a p a r t . E a c h p o i n t, th e n , m i g h t b e c o n s i d e r e d a s h a v i n g av o l u m e o f 2.8 18 c u . ~ ,. u ., a n d i f w e a s s u m e e a c h t o b e a n a t o m ,t h e n t h e v o l u m e o f t w o o f t h e m s h o u l d b e t h e v o l u m e o f a m o l e c u l eo f s o d i u m c h l o r i d e .

2.8 1' 2 -- 44.4 cu. A. u.

A g r e e m e n t a s c lo s e a s t h a t b o t h i n s p a c i n g a n d i n v o l u m e m a k e si t d i f f ic u l t t o b e l i e v e a n y t h i n g e l s e t h a n t h a t t h e r e f l e c t io n s a r e d u et o a t o m s a r r a n g e d i n a c u b i c s p a c e la t ti c e .

In terpre ta t ion o f the S tarch Spec trum .I n a n e a r li e r a r t ic l O i t w a s s h o w n t h a t a n x - r a y s p e c t r u m c a n

b e o b t a i n e d f r o m a m a s s o f s t a r c h g r a i n s s o m e w h a t s im i l a r t o t h a to b t a i n e d f r o m t h e c r y s t a l p o w d e r o f s o d i u m c h l or id e . I n l a t e r w o r k ,w h i c h i s d e s c r i b e d i n t h e p r e s e n t p a p e r , t h e n a t u r e a n d t h e s i ze o ft h e r e f l e c t i n g u n i t h a v e b e e n d e t e r m i n e d a n d a d e f i n i t e s t r u c t u r e h a sb e e n a s c r i b e d t o th e s t a r c h g ra i n. T h e d e m o n s t r a t i o n o f th e s ec o n c l u s i o n s f o l l o w i n g s o m e w h a t t h e s a m e l i n e s o f r e a s o n i n g a s j u s tu s e d f o r s o d i u m c h l o r i d e , i n v o l v e s t h e s e v e r a l s t e p s w h i c h a r e n o wt o b e p r e s e n t e d .


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O. L . SPONSLER 763

Nature of Reltected Lines.When compared with a line photograph of a common crystalline

substance such as sodium chloride, the negatives from starch exhibitseveral striking features (Figs. 1 and 2). The backgr ound isvery dense and the lines are only slightly denser, consequently thedefinition of the lines is poor; they seem to blend in with the back-ground instead of being clear cut, and wherever they occur close

FIG. 1. Sodiu m chloride.

Fio. 2. Top section, potato starch; middle section, cassava starch; bottom sec-tion, corn starch.together they often overlap so much that two lines make a broadband in which the y are scarcely separable. These features tend tomake measurements, both of distance and of comparative densitybetween lines, very difficult. The y also militat e against a satis-factory reproduction of the photographs by means of half-tones.

About a dozen negatives were made from three different kindsof sta rch --p ota to, corn, and cassava. On all of them two or threeof the lines are noticeably prominent and can be measured with a


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764 STRUCTURAL UNITS OF STARCHfair degree of accuracy, several more are visible only when carefullystudied in properly adjusted light, and still two or three more canbe detec ted only with a photome ter. The first two lines are some-times blended into a single broad band, but on several negatives theyappear clearly separated and there they can be readily measured.Line 4 (Table I I I ) , the third prominent line from the center of thenegative is by far the most sharply defined and has yielded consis-tent me asurement s on all of the ten or eleven negatives. Of theother lines, 6, 7, 8, 9, 11, and 12 are distinct enough on a half dozenor more negatives to be fairly consistently measured. The actualexistence of some of the lines was often questioned on account oftheir faintness, but several months after this paper was written anopportunity was presented for having an energy curve made on arecording micro photometery and the position of the lines as shownby the curve agreed so well with the measurements of the negativesth at fu rthe r doubt of their existence was dispelled. The curves, inaddition to verifying the visual location of the lines, brought out twolines, 3 and 5, which had been predicted but had no t been distingui shedby the unaided eye.

The fact that lines are present on the negatives indicates theexistence of reflecting points arranged in some regular way forminga space lattice. In a space latti ce the units form ma ny differentsets of parallel planes. Each set, having its own partic ular value ofd, the dist ance between planes, produces one of the lines on the photo-graphic film. The value of that d may be determined by using theformula ), = 2d sin O, in which the value used for O is obtained frommeasurements of the lines on the negative. In this way the valueof d for every line found on the negatives was obtained and listed inTable I I I , Columns 2 and 3. The value of X used in these computa-tions was 0.614 A.u., the wave length of the Ka line of rhodium.The figures, then, in the table represent the distances betweenthe parallel planes of the various sets for an unknown space lattice.

n Through the courtesy and kind assistance of Mr. Edison Petti t of the MountWilson Observatory at Pasadena, California, the energy curves referred to weremade on the registering micro photometer described in a paper by Pettit and Nich-olson (Pettit, E., and Nicholson, S. B.,J. Optical Soc. Am. a~M Rev. Scient. [nsiru-~m'.nts, 1923, vii, 187).


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O. L. S P O N S L E R 76 5T h e p r o b l e m n o w i s to d e t e r m i n e t h e t y p e o f th i s u n k n o w n s p a c e

l a t t ic e a n d t h e d i m e n s i o n s o f i t s e l e m e n t a r y c e ll . T h e s o l u t io n w a si n f l u e n c e d b y t h e o n e w e l l e s t a b l i s h e d f a c t c o n c e r n i n g t h e f o r m a t i o no f t h e s t a r c h g r a i n in t h e p l a n t c e ll ; t h a t i s, t h a t t h e s t a r c h s u b s t a n c ei s d e p o s i t e d o n t h e g r a i n a t t h e i n t e r f a c e b e t w e e n t h e g r a i n a n d t h ep r o t o p l a s m . TM S i n c e t h e g r a i n a s s u m e s a m o r e o r l e s s s p e r i c a l f o r mi t s e e m s p r o b a b l e t h a t t h e p a r t ic l e s a r e d e p o s i t e d a t e q u a l l y s p a c e dp o i n t s o n t h e s u r fa c e o f t h e g r ai n . T h i s w o u l d m a k e t w o d i m e n s i o n so f t h e l a t t ic e e q u a l a n d t h e v a l u e w o u l d b e t h e l a r g e s t o b t a i n -

TABLE 11I.Starc h .

L i n e o .

101112

f r o m p h o t o m e t e rCurves.

. u . $ . u .5.94 5.945.05 5.054.253.87 3.873 .28 . . . .2.92 2.982.61 2.652.50 2.53

2.332.05 2.101 . 9 0 1 . 9 4

d f r o m v i s u a lm e a s u r e m e n t .d e a l c u l a t e d froml a t t i c e ,

5 . 9 4 X 5 .9 4 X 5 . 0 5 .,tu .5.945.054.173.853.202.972.642.532.552.302.091.93

Indicesof p l a n e s .

001, 100010101I10, 011111001, 100 2nd ord er2 0 1 , 1 0 20 1 0 2 n d o r d e r.2 1 0 , 0 1 2

120, 021101 2nd ord er.110, 011 2nd order.a b l e f r o m t h e n e g a t i v e s ; t h a t is , 5 . 9 4 / ~ .u . T h e t h i r d d i m e n -s i o n w o u l d b e l i k e l y t o b e t h e n e x t l a r g e r s p a c i n g , 5 .0 5 ~ . u . a n d t h ee l e m e n t a r y c e l l o f t h e l a t t ic e t h e n w o u l d h a v e t h e d i m e n s io n s ,5 . 9 4 X 5 . 9 4 5 . 0 5 . I f t h i s c el l i s a r e c t a n g u l a r f i g ur e , a s q u a r ep r i s m , t h e n i t w o u l d h a v e f o r i t s v a r i o u s p l a n e s t h e v a l u e s o f d a sg i v e n i n C o l u m n 4 o f T a b l e I I I . T h e i n d i c e s o f t h e p l a n e s a reg i v e n i n C o l u m n 5 a n d t h e p o s i t i o n o f th e p l a n e s i n t h e c e ll i s s h o w nin F ig . 3 .

1~ Salte r, J . H ., J ahrb . w i s se nsc h . Bot . , 1898, xxxii, 164 . Criiger, H., Bot . Z tg . ,1854, xii, 41. Schim per, A. F. W., B o t . Z t g . , 1880, xxxviii, 88 4. Strasburger, Iv..,t3ber den Bau u nd das W achstum der Zellhitute, Jena, 1882, 154-159.


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76 6 S T R U C T U R A L U N I T S O F STARCHT h e a g r e e m e n t b e t w e e n t h e s e v a lu e s a n d t h o s e o b t a i n e d f r o m

t h e m e a s u r e m e n t s o f t h e n e g a t i v e s i s s u f f i c i e n t l y c l o s e t o j u s t i f yo u r a c c e p t a n c e o f t h e s h a p e a n d t h e s i ze o f th e e l e m e n t a r y c e ll a sa s s u m e d a b o v e , a n d w e m a y n o w s a y t h a t t h e l i n e s o n t h e n e g a t i v e si n d i c a t e t h a t p l a n e s o f r e f l e c t in g u n i t s a r e s p a c e d 5 .9 4 / ~ .u . a p a r t ,a n d t h a t o t h e r p l a n e s a t r i g h t a n g l e s t o t h o s e a r e s p a c e d 5 .0 5 f it .ua p a r t , f o r m i n g e l e m e n t a r y c e ll s o f t h e s iz e m e n t i o n e d i n t h e l a s tp a r a g r a p h . T h e l a t t ic e w o u l d l oo k s o m e w h a t l ik e F i g . 4 .

PLAN'3 ~ PLANE5

L~ PLANE ~ PZ-~~E ~ PLA~E L~ PL~ NE LLI PLANE

FIG. 3 . P osi t ion o f the mo re impor tan t p lanes in the e lem entary cel l.

Y J v/ / ,~ / -

it

trtt!tt!!t

iI

Ii: c

FIG. 4 . E lem enta ry cel ls f rom the FIG. 5 . E lem enta ry cel ls inlattic e of the starc h grain, two positions.

Size and Nature of the Reflecting Unit .T h e a t o m s w h i c h c a u s e t h e re f l e c ti o n f r o m s t a r c h g r a i n s a r e t h o s e

o f c a r b o n a n d o f o x y ge n . T h e f o r m e r a re 1 .5 0 A . u . i n d i a m e t e ra n d t h e l a t t e r , 1 .3 0 fi ~ .u . Th e r e f l e c t i o n f ro m h y d ro g e n i s t o ow e a k t o m a k e a n y a p p r e c i a b l e d if f e re n c e i n t hi s w o r k . I t s e e m sv e r y p r o b a b l e t h a t t h e u n it s w h i c h f o r m t h e l a t t ic e a r e n o ts i n g le a t o m s , f o r a s t r u c t u r e w i t h s o g r e a t a d i s t a n c e a s f i v e o r s ix


11/20

o. L. SPONSZE~ 767. ~ n g st r S m u n i t s b e t w e e n a t o m s , w h i c h a r e n o l a r g e r t h a n t h o s eo f c a r b o n a n d o x y g e n , w o u l d t a k e t h e f o r m o f s o m e o t h e r s t a t e o fm a t t e r t h a n t h a t o f a s ol id w i t h t h e d e n s i t y o f s t a r c h . I t f o l lo w st h e n t h a t t h e r e m u s t b e a group a r r a n g e m e n t o f t h e a t o m s a r o u n de a c h c o r n e r o f t h e e l e m e n t a r y ce ll . A n a r r a n g e m e n t o f t h is n a t u r ei s n o t u n u s u a l . V e r y c o n v i n c i n g e v i d e n c e h a s b e e n b r o u g h t f o r -w a r d t o s h o w t h a t t h e b e n z e n e r i n g a c ts a s a u n i t i n c r y s t a l s of a n -t h r a c e n e , n a p h t h a l e n e , a n d t h e i r c o m p o u n d s , 13 t h a t t h e C O8 g ro u pr e t a i n s i ts i d e n t i t y i n c r y s t a l s o f c a r b o n a t e s , a n d t h a t 3 m o l e c u le s ofs i l i c o n d i o x i d e a r e a s s o c i a t e d w i t h e a c h p o i n t i n t h e l a t t i c e o f q u a r t zcrys ta l s . 14

T h e g r o u p o f a t o m s i n s t a r c h , o f w h i c h o n e w o u l d n a t u r a l l y t h i n kf i r s t , i s t h a t i n d i c a t e d b y t h e e m p i r i c a l f o r m u l a , C 8 H I 0 0 5 . T h ev o l u m e o f t h a t g r o u p a s c o m p u t e d f r o m t h e d e n s i t y o f s t a r c h , 1 .5 0,t h e s u m o f t h e a t o m i c we i g h t s , 1 62 , a n d Av o g a d ro ' s n u m b e r , 6. 06 2 X102~, is 178.2 c ubi c ,~ng strS m units .

162 X 1 178.2 X 10"~4 or 178.2 cu. A . u.1.50 6.062 )< 10 ~3I f t h a t i s t h e g r o u p w h i c h i s a ss o c i a t e d w i t h t h e c o r n e r s o f th e

ce l l s , the n i t s vo lu me , 178.2 cu . ,~ .u . sh ou ld be eq ual to thev o l u m e o f t h e e l e m e n t a r y c el l. A l t h o u g h w e h a v e t h o u g h t o ft h e g ro u p s a s b e i n g i d e n t i f i e d w i t h t h e c o m e rs o f t h e c e l l s , t h a t i st h e p o i n t s o f t h e la t t ic e , t h e i m a g i n a r y b o u n d a r y l in e s m a y b e s h i f t e ds o t h a t a g r o u p w i l l b e s e e n t o o c c u p y a s p a c e e q u a l t o t h a t o f t h ec e ll . I n F i g . 5 t h e d o t t e d l i n e s i n d i c a t e t h e p o s i t io n s o f t h e n e wc e l ls a f t e r t h e s h i f t h a s b e e n m a d e . T h e v o l u m e o f t h i s c e ll i s a l m o s te x a c t l y t h a t o f t h e g ro u p , 1 7 8.2 c u . / ~ .u .

5 .94 X 5 .94 X 5 .05 = 178 .2T h i s a g r e e m e n t b e t w e e n t h e v o l u m e s o f t h e e l e m e n t a r y c e ll a n d

t h e g r o u p o f a t o m s i s p e r h a p s c l o s e r t h a n i s c o n s i s t e n t w i t h t h e d e -g r e e o f a c c u r a c y o f t h e m e a s u r e m e n t s ; o n t h e o t h e r h a n d , i t i s n o tl i k e ly t h a t i t i s m e r e l y c o i n c id e n t a l. I t s e e m s t o m e t h a t w e m a ya c c e p t t h e f i g u re s a s in d i c a t i n g t h e p r o b a b l e s t r u c t u r e a n d t h a t w e

1~ B r a g g , W . H . , Proc. Phys. Soc. London, 1 9 2 1 , x x x iv , 3 3 .14 B r a g g , W . H . , a n d B r a g g , W . L . , s p p . 1 1 7 a n d 1 6 4 .


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768 STRUCTURAL UNITS OF STARCHm a y c o n s i d e r t h e s t a r c h g r a i n a s b u i l t u p o f groups o f a t o m s , e a c hg r o u p b e i n g a s s o c i a t e d w i t h e a c h p o i n t i n t h e l a t t i c e , t h a t i s a g r o u pa c t i n g a s a u n i t o f t h e l a t ti c e ; a n d f u r t h e r , t h a t e a c h g r o u p c o n s i s t so f 6 c a r b o n , 5 o x y g e n , a n d 1 0 h y d r o g e n a t o m s .

I t i s h i g h l y p r o b a b l e t h a t e a c h g r o u p ( C 6 H I 0 0 ~ ) h a s a d e f i n i t e c o n -f i g u r a t io n , a n d f u r t h e r , t h a t a l l o f t h e g r o u p s , a t l e a s t a l a r g e p e r -c e n t a g e o f th e m , a r e o r ie n t e d i n t h e s a m e w a y w i t h r e s p e c t t o t h es u r f a c e o f t h e g ra i n. T h e s e a s s u m p t i o n s a r e b a s e d o n t h e d a r k c r o ss -e f f e c t w i t h p o l a r iz e d l ig h t , a c o m m o n p h e n o m e n o n p r o d u c e d b ys t a r c h g r a in s . W h a t t h e c o n f ig u r a t io n o f t h a t g r o u p i s w e h a v e n om e a n s o f k n o w i n g a t t h e p r e s e n t t i m e , b u t w e m a y a s s u m e a f o r mf o r i l l u s t r a t io n w h i c h h a s a s l i g h t b a s i s i n t h e c h e m i s t r y o f s ta r c h .T h e e n d - p r o d u c t o f m a n y s t a r c h r e a c t i o n s i s g l u c o s e ( C6 H 12 O e) .T h e s t r u c t u r a l f o r m u l a g e n e r a l l y a c c e p t e d f o r g lu c o s e sh o w s t h e3 r d a n d 6 t h c a r b o n a t o m s l i n k e d t o g e t h e r t h r o u g h a n o x y g e n a t o m .

C H ~ 0 Hi

C H O HI

C H

o r\ C H O H\ 1 CHOH

I n t h e s t a r c h g r o u p t h e 6 c a r b o n a t o m s a r e a t t a c h e d , w i t h o u t d o u b t ,i n t h e s a m e w a y a n d i t i s n o t i m p r o b a b l e t h a t t h e 3 r d a n d 6 t h c a r -b o n a t o m s a r e l i n k e d a l so t h r o u g h a n o x y g e n a t o m . O n t h a t a s -s u m p t i o n a m o d e l o f t h e s t a r c h g r o u p w a s m a d e t o s ca l e.

F i g . 6 g i v e s t w o v i e w s o f t h e m o d e l . T h e d a r k b a l l s r e p r e s e n t t h ec a r b o n a t o m s , t h e l i g h t o n e s t h e o x y g e n a t o m s , a n d t h e s m a l l l o o p si n d i c a te t h e p o s i t io n of t h e h y d r o g e n a t o m s . S o m a n y a r r a n g e m e n t so f t h e a t o m s a n d s o m a n y o r i e n t a t io n s o f th e w h o l e g r o u p i n s id e o ft h e e l e m e n t a r y c e l l a r e p o s s i b l e t h a t n o s p e c i f i c c o n c l u s i o n s c a n b em a d e , b u t n e v e r t h e l e s s c e r t a i n r a t h e r c o n v i n c i n g i m p r e s s i o n s a r el e f t w i t h o n e a f t e r a s h o r t s t u d y o f t h i s h y p o t h e t i c a l s t r u c t u r e .

T h e s iz e o f t h e s t r u c t u r e c o r r e s p o n d s t o t h e s i z e o f th e e l e m e n t a r yc e ll , th e b o u n d a r y l in e s o f w h i c h a r e r e p r e s e n t e d i n t h e m o d e l b yt h e r e c t a n g u l a r w i r e c a g e . T h e g r o u p f i t s i n t h e ce l l l o o s e l y e n o u g h


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O. L. SPONSLER 769

to suggest the low specific gravity of starch and at the same timeextends far enough towards each face of the cell to make the ratherweak cohesion, which is characteristic of the starch grain, seempossible.

In Fig. 6 the dia grams below the pictures of the model are inte ndedto help make clear the kind of reflection which occurs when a groupof atoms acts as a unit of the lattice. Parallel to each face of the

FIG. 6. Model of starch group. Principal and secondary planes indicated bylines below.cell there are several possible planes which contain atoms of theuni t group. In the 100 view the plane marked p in the diagram con-tains 4 atoms, the others marked s contain only 1 each, or in onecase, 2 atoms. In th e 010 view the principal plane, p, has 2 atomsin it and each of the second ary planes, s, has only 1. The reflectionwhich produces a line on the negative comes from the principalplane, but its reflecting power may be partially annulled by wavesfrom the secondary planes. The tendency of secondary planes in


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770 STRUCTURAL UNITS OF STARC/z[g e n e r a l i s t o a n n u l e a c h o t h e r , d e p e n d i n g u p o n t h e s p a c i n g a n d t h en u m b e r o f a t o m s o c c u r r i n g r e s p e c t i v e l y i n th e m . T h u s t h e re f le c t in gp o w e r o f a p a r t ic u l a r s e t o f p l a n e s d e p e n d s n o t o n l y o n t h e n u m b e r o fa t o m s i n a u n i t a r e a o f t h e p r i n c ip a l p l a n e , b u t a l s o u p o n t h e c o n d i -t io n s o f s p a c i n g a n d n u m b e r o f a t o m s o c c u r r in g i n t h e s e c o n d a r yp l a n e s. I t i s e v i d e n t f r o m t h is a n d t h e t w o v i e w s o f t h e m o d e l t h a tf o r t h e s a m e g r o u p o f a t o m s t h e r e f l e c t io n f r o m o n e s e t o f p l a n e s w i lln o t n e c e s s a r i i y b e a s s t r o n g a s t h a t f r o m a n o t h e r s e t . T h e r e f le c t i o nf r o m t h e 0 1 0 p l a n e s w o u l d p r o b a b l y b e v e r y w e a k , w h i l e t h a t f r o mt h e 1 0 0 p l a n e s w o u l d b e s t r o n g e r . C u r i o u s l y , t h a t i s e x a c t l y th ea p p e a r a n c e o f t h o s e tw o l in e s o n t h e n e g a ti v e s . T h e c o r e o f h e a v i e ra t o m s o c c u r r i n g n e a r t h e c e n t e r o f t h e c e l l w o u l d f a v o r s t r o n g r e -f l e c t io n s f o r th e 1 10 a n d 0 1 1 p l a n e s , a n d v e r y w e a k f o r t h e 1 11 p l a n e s ,w h i l e t h e s o m e w h a t f l a t t e n e d e f f e c t o f th e c o r e f a c i n g t h e 0 1 0 p l a n e sw o u l d f a v o r w e a k r e f l e c t i o n s f o r t h o s e p l a n e s a s w e l l a s f o r t h e 1 0 1p l a n e s , a n d s t r o n g e r r e f l e c ti o n s f o r t h e 1 0 0 p l a n e s . I t i s i n t e r e s t i n gt o s e e h o w f a v o r a b l e t h is p a r t i c u l a r s h a p e a n d p o s i t i o n o f th e m o d e li s t o t h e l i n e s a c t u a l l y o b t a i n e d o n t h e n e g a t i v e s , b u t s i n c e t h e d a t af r o m w h i c h t h e m o d e l w a s b u i l t a r e s o m e a g e r , t h e s t r u c t u r e m u s tn o t b e t a k e n t o o s e r io u s ly . T h e i m p o r t a n c e a t t a c h e d t o t h e m o d e ll i e s i n t h e f a c t t h a t a m o d e l c a n b e b u i l t w h i c h s e e m s t o f u l f i l l m o s to f t h e c o n d i t i o n s n e c e s s a r y f o r r e f l e c t i o n s s u c h a s t h o s e o b t a i n e df r o m t h e s t a r c h g r a i n s .

Concentric Layers.U p t o t h i s t i m e t h e d a t a h a v e b e e n u s e d a s t h o u g h s t a r c h w e r e

w i t h o u t q u e s t i o n a c r y s t a ll i n e s u b s t a n c e , w h i l e a s a m a t t e r o f f a c ts t a r c h d o e s n o t h a v e t h e a p p e a r a n c e n o r t h e p r o p e r ti e s o f c o m m o nc r y s t a l s . T h e g r a i n s a r e s p h e r i c a l b o d i e s w h i c h h a v e g r o w n b ya d d i t i o n s a t t h e i n te r f a c e b e t w e e n t h e g r a in a n d t h e p la s t i d , t h a t i st h e y a r e b u i l t u p o f c o n c e n t r ic l a y e r s ; t h e y h a v e n o o r d i n a r y c l e a v a g ep l a n e s ; a n d f u r t h e r , t h e p o l a r i z e d li g h t p h e n o m e n o n i s n o t t h a t o fo r d i n a r y c r y s t a l s. T h e s e s t a t e m e n t s i m m e d i a t e l y ra i se s e v e r a lq u e s t i o n s . H o w c o u l d s p h e r i c a l g r a i n s p r o d u c e li n e p h o t o g r a p h ss i m i l a r t o th o s e o f o r d i n a r y c r y s t a l s ? H o w c o u l d a l a t t i c e s u c h a st h a t a s c r i b e d t o s t a r c h o c c u r in a s p h e r e ?


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O. L. SPONSLER 771

T h e s e q u e s t i o n s m a y b e a n s w e r e d b e s t p e r h a p s b y c o m p a r i n g t h ep h o t o g r a p h s f r o m s t a r c h w i t h t h e r e s u l t s o f a n a s s u m p t i o n t h a t t h eg r a in s a r e b u i l t u p o f c o n c e n t r i c l a y e r s , e a c h l a y e r h a v in g t h et h i c k n e s s o f t h e C e H 10 05 g r o u p w h i c h , f r o m t h e l a t t ic e w o r k e d o u ta b o v e , w o u ld b e 5 . 0 5 /~ . u . t h i c k , a n d t h e g r o u p s i n e a c h l a y e rl o c a t e d 5. 94 A .u . a p a r t. I n o t h e r w o r d s t h e l a y e rs w o u l d b es h e e t s o f e l e m e n ta r y c el ls , o n e c el l t h i c k . O f co u r s e t h e i n n e rl a y e rs w o u l d h a v e t o c o n t a i n a s m a l l e r n u m b e r o f c el ls t h a n t h e o u t e ro n e s , a n d i n o r d e r t o r e t a i n t h e r e c t a n g u l a r l a tt i c e t h e r e w o u l d h a v et o b e s l i g h t r e a d j u s t m e n t s . T h e r e s u l t o f t h e s e r e a d j u s t m e n t s m a yb e t h e s o c a l l e d l a me l lm o f s t a r c h g r a in s .

T o g a i n a b e t t e r c o n c e p t i o n o f t h i s a r r a n g e m e n t o n e m a y i m a g i n et h e e l e m e n t a r y c e ll s to b e t h e s iz e o f c o m m o n b u i l d in g b r ic k s , a n dth e n b u i l d u p a s e t o f c o n c e n t r i c c i r c l e s t o r e p r e s e n t a c r o s s - s e c t i o no f a s t a r c h g r a in . N o w in t h e a v e r a g e s t a r c h g r a in th e r e a r e a b o u t2 0 ,0 0 0 e l e me n ta r y ce ll s a l o n g o n e d i a m e te r . ( T h e g r a in s a r e a b o u t100 ,000 A.u . in d iam ete r . ) So the con cent r ic c i r c le s of br icksw o u l d b e b u i l t o u t u n t i l t h e d i a m e t e r is 2 0,0 00 b r ic k s . T h i s w o u l dm a k e t h e o u t s i d e c i r cl e a b o u t 1 mi l e s i n d i a me te r .

O n e c a n s e e t h a t t h e r e a r r a n g e m e n t o f e l e m e n t a r y c e l l s i n t h ein n e r c i r c l e s , i n o r d e r t o k e e p a r e c t a n g u l a r l a t t i c e , w o u ld b e c o m-p a r a t i v e ly i n s ig n i f i c a n t ; a n d t h a t l a r g e r e g io n s w o u ld c lo s e ly a p p r o a c hth e p a r a l l e l l a y e r s o f a r e c t a n g u l a r l a t t i c e , s u c h a s t h a t o f o r d in a r yc r y st a ls . I t s e e m s t h e n n o t i m p r o b a b l e t h a t s t a r c h g r a i n s b u i l tp r o p o r t i o n a l l y i n a s o me w h a t s imi l a r w a y w o u ld r e f l e c t x - r a y s f r o mc e r t a in r eg io n s o f t h e g r a in . E a c h s p h e r i c a l g r a in , u n l i k e t h e p a r -t i c l e s o f a c r y s t a l p o w d e r , h o w e v e r , w o u ld r e f le c t f r o m a g r e a t m a n yr e g io n s . F r o m t h i s p o i n t o f vi e w i t is in t e r e s t i n g to e x a m i n e i n t oth e p o s s ib i li t ie s o f re f l e c ti o n f r o m a p o w d e r c o m p o s e d o f s u c h s p h e r i -ca l g ra ins .

I n F ig . 7 s u p p o s e t h e l a r g e c i r c l e t o b e a c r o s s - s e c t i o n o f o n e o ft h e s e s p h e r ic a l g r a in s p l a c e d i n t h e p a th o f a b e a m o f x - r a y s . T h er e g i o n s i n d i c a t e d b y t h e l e t t e r s a r e d r a w n t o s h o w f o u r e l e m e n t a r yc el ls . T h e r e fl e c t in g p l a n e s a r e m a d e s o m e w h a t h e a v i e r t h a n t h eo th e r l i n es . O f c o u rs e t h e c e ll s a r e e n o r mo u s ly o u t o f p r o p o r t i o nto t h e d i a me te r o f t h e c i r c l e .


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772 S T R U C T U R A L IT N I T S O F S T A R C HT h e s t r o n g e s t r e f l e c t i o n w o u ld b e t h a t f r o m th e 3 . 8 5 p l a n e s s i n c e

e v e r y g r a in w o u ld r e f l e c t f r o m a t l e a s t t h e fo u r r eg io n s C , C , C , C ,a n d m a n y o f t h e m w h i c h h a p p e n t o b e r e v o l v e d i n t o c e r t a i n p o s i t io n sw o u ld r e f l e c t f r o m f o u r a d d i t i o n a l r e g io n s , o n e a b o v e a n d o n e b e lo we a c h B . O n a l l o f t h e n e g a t i v e s t h i s l i n e i s a c tu a l l y t h e mo s t p r o mi -n e n t l i n e.

E v e r y g r a in w o u ld r e f l e c t a l so f r o m th e 5 . 0 5 p l a n e s f r o m tw o r e -g io n s , B , B . T h i s l i n e t o o sh o u ld b e a s t r o n g l i n e , a b o u t a s d e n se

W~ve ~cnl

f B"

594 5.94OH

FIG. 7. X -ray reflection rom a starch grain.a s t h e 3 .8 5 li n e . T h e n e g a t i v e s a c tu a l l y sh o w th e se tw o li n e s t o b ea b o u t e q u a l i n i n t e n s it y .

T h e 5 . 9 4 p l a n e s w o u ld b e i n t h e p r o p e r p o s i t i o n t o r e f l e c t i n o n lya c o m p a r a t i v e l y f e w g r a in s a n d o n t h a t a c c o u n t s h o u l d g i v e a m u c hw e a k e r l i n e t h a n t h e 5 . 0 5 p l a n e s ; b u t w h e n i n t h a t p o s i t i o n , t h er e f le c t i n g r e g io n w o u ld c o m p le t e ly e n ci r c le t h e g r a in p a s s in g t h r o u g hA , A , a n d c o n se q u e n t ly t h e d e n s i t y o f t h e r e f l e ct e d l i n e sh o u ld a p p r o a c hth a t o f t h e 5. 0 5 l i n e . T h i s is i n f a ir l y s a t i s f a c to r y a g r e e m e n t w i tht h e n e g a t iv e s .


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o. L. S~ONSLEI~ 773Th e 4 .1 7 p l a n e s w o u l d r e f l e c t i n s i m i l a r p o s i t io n s t o t h o s e o f t h e

5 .9 4 p l an e s a n d s h o u l d b e , a s i n o r d i n a r y c r y s t a ls , s o m e w h a t w e a k e r .O n t h e n e g a t i v e s t h e l i n e s a r e a c t u a l l y w e a k e r t h a n o n e i s l e a d t oe x p e c t f r o m t h e d i a g r a m .

Th e 3 .2 0 p l a n e s , w h i c h w o u l d r e f l e c t f r o m fo u r o r e i g h t p o s i t i o n sj u s t a s i t w a s s h o w n t h e 3 . 85 p l a n e s w o u l d d o, a c t u a l l y p r o d u c e m u c hw e a k e r li n e s t h a n w o u l d b e a n t i c i p a te d .

I n m a k i n g t h e s e c o m p a r i s o n s n o c o n s i d e r a t i o n w a s g i v e n t o t h ep ro b a b l e f a c t t h a t t h e p r i n c i p a l p l a n e s o f t h e d i f f e r e n t p o s i t i o n s a r en o t e q u a l i n r e f l e c t i n g p o w e r , n o r t o t h e p o s s i b le e f f e c t o f t h e s e c o n d -a r y p l a n e s i n r e d u c i n g t h e r ef l e ct io n . B o t h t h e p o s i t io n o f t h es e c o n d a r y p l a ne s a n d t h e n u m b e r o f a t o m s i n t h e m a r e v e r y i m p o r-t a n t f a c t o r s i n d e t e r m i n i n g t h e d e n s i t y o f t h e l i n e s , b u t t h e r e a r ea b s o l u t e l y n o d a t a s o f a r o b t a i n e d w h i c h c o u l d b e u s e d i n t h i s c o n -n e c t i o n . O n t h e w h o l e t h e a g r e e m e n t b e t w e e n t h e n e g a ti v e s a n dt h e e x p e c t a t i o n s f r o m t h e d i a g r a m i s f a ir l y s a ti s f a c t o r y .

T h e r e i s a n o t h e r f a c t o r w h i c h m a y t e n d t o m a k e t h e l in e s l es sd e n s e a n d s o d i m i n i sh t h e d i f f e r e n c e i n i n t e n s i t y b e t w e e n t h e l i n esa n d t h e b a c k g r o u n d . T h e 2 1 a t o m s o f t h e s t a r c h g r o u p , w h i l e t h e yo c c u p y a s p a c e e q u a l t o 1 78 c u b i c .~ n g s t r6 m u n i t s , u n d o u b t e d l y d on o t c o m p l e t e l y f il l t h a t s p a c e . O n t h e a s s u m p t i o n t h a t t h e c a r b o na n d o x y g e n a t o m s a r e t h e s a m e s iz e in s t a r c h t h a t t h e y a p p e a rt o b e i n m a n y c ry s t a l s , t h a t i s 1 .5 X .u . a n d 1 .3 ,~ .u . i n d i a m e t e rr e s p e c t i v e ly , a n d g u e s s in g t h a t t h e h y d r o g e n a t o m s a r e a b o u t1 A . u . in d i a m e t e r , t h e t o t a l s p a c e w h i c h t h e s e a t o m s w o u l df il l i s l e ss t h a n 5 0 c u b i c A n g s t r6 m u n i t s . Th e u n o c c u p i e d s p a c ei n t h e e l e m e n t a r y c el l w o u l d b e f o u r o r f i ve t i m e s a s m u c h a st h a t a c t u a l l y f i ll e d w i t h a t o an s . Th e g ro u p t h e n i s l o o s e l y c o n -s t r u c t e d a n d i s l i k e ly t o b e s t r o n g l y i n f l u e n c e d b y t e m p e r a t u r e .I n f a c t , a n i n c r e a s e o f a b o u t 1 50 C . o v e r r o o m t e m p e r a t u r e p r o d u c e sp r o f o u n d c h a n g e s in d r y s t a r c h , a n d i n w a t e r a t a b o u t 6 0 C . t h eg ra Lns u n d e rg o a k i n d o f d i s i n t e g ra t i o n . B a s e d o n t h a t , o n e m i g h te x p e c t c o n s i d e r a b l e t h e r m a l a g i t a t i o n i n d r y g r a i n s e v e n a t r o o mt e m p e r a t u r e . I t h a s b e e n s h o w n15 t h a t t h e r e i s a v e ry d e c i d e d r e -d u c t i o n i n i n t e n s i t y o f r e f l e c t i o n f r o m s o d i u m c h l o r i d e w h e n r a i s e d

15 Bra gg, W. H., .Phil. Mag., 1914, xxvii, 881.


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774 S T R U C T U R A L U N I T S O F S T A R C Hin temperature about half way up to its melting point. The experi-mental proof of the thermal effect in the case of starch seems com-paratively simple but has not yet been attempted.

Still another factor which should be mentioned in connectionwith the density of the reflected lines is one embodied in the sphericalshape of the grain. While certain large regions of the grain act asordinary crystal particles, there are other regions which just missthe exact angle for reflection and in which there are not enoughplanes to annul completely the reflection. This would produce abroadening of the reflected lines and increase the density of thebackground by blending into it.

S U M M A R Y .

A few brief sta tements summarizing the foregoing conclusions ma ymake a picture of the structure of the starch grain somewhat clearer.

1. The presence of lines on the negatives indicates a regular ar-rangement of the planes of atoms.

2. The lines are in close agreement with lines which would beproduced by a lattice of the t etragonal system, the elemen tary cell ofwhich is a square prism with the dimensions 5.94 5.94 X 5.05 .u.

3. The unit of the lat tice occupies a space equal to the volume ofthe starch group, C8H1005.

4. The large number of atoms in the un it makes it highly probablethat principal planes and secondary planes of atoms occur for everyreflecting position.5. The effect of the secondary upon the principal planes mayreadily account for the differences in the density of the lines pro-duced on the negatives.

6. From theoretical considerations, reflections, such as those ob-tained, would occur if starch grains were built up of concentric layersof units.7. Two other factors which might affect the density of the linesare thermal agitation and the curvature of the concentric layers.

8. A model of the starch group was constructed to scale based onthe accepted sizes of the atoms involved and upon rather meagerchemical evidence. The model apparen tly fulfills the requirementsnecessary to produce reflections such as were obtained.


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O. L. S P O N S L E R 775

9 . T h e m o d e l fi ts t h e e l e m e n t a r y c el l l o o se l y e n o u g h t o s u g g e s ta l o w d e n s i t y a n d t o a l l o w f o r c o n s i d e r a b l e t h e r m a l m o v e m e n t .A t t h e s a me t ime , p a r t s o f i t a p p r o a c h t h e f a c e s o f t h e c e l l c l o se lye n o u g h t o m a k e c o h e s io n s e em p o s s ib l e .

1 0. T h e m o d e l m a k e s c l e ar e r t h e b a s is f o r t h e a s s u m p t i o n t h a tr e fl e ct i o n fr o m c e r t a in p o s i t i o n s w o u l d b e s t r o n g e r t h a n f r o m o t h e r s.

I f t h e i n t e r p r e t a t i o n o f t h e d a t a i s c o r r e c t a n d i f t h e a s s u m p t i o n sm a d e a r e s o u n d , t h e n t h e s t a r c h g r a i n i s b u i l t u p o f u n i t s a r r a n g e din c o n c e n t r i c l a y e r s , a n d t h e u n i t s a r e g r o u p s o f a to ms , e a c h c o n -t a i n i n g 6 ca r b o n , 1 0 h y d r o g e n , a n d 5 o x y g e n a t o m s . S u c h a s t r u c -t u r e i s c e rt a i n l y n o t a n a m o r p h o u s s t r u c t u r e , a n d o n t h e o t h e r h a n di t is n o t c r y s t al l in e i n t h e c o m m o n s e n se o f t h e t e r m . P a r t s o f t h eg r a in , i t is t r u e , a c t a s c r y s t a l s i n t h a t f o r c e r t a in d i s t a n c e s t h e l a y e r so f u n i t s a r e i n p l a n e s, b u t t a k e n a s a w h o l e t h e l a y e rs a r e c u r v e d .A s t o t h e v a l i d i t y o f t h e c o n c lu s io n s , t h o s e p e r t a i n i n g t o t h e t y p eo f l a t t ic e a n d t o t h e s i z e o f t h e u n i t m a y b e a c c e p t e d a s s o u n d i n o u rp r e s e n t k n o w l e d g e o f x -r a y s a n d c r y s ta l s t r u c t u r e ; t h o s e , h o w e v e r,p e r t a i n i n g t o t h e n a t u r e a n d t h e s p h e r ic a l a r r a n g e m e n t o f t h e u n i t s,w h i l e t h e y s e e m c o n v i~ l c in g , n e e d t h e su p p o r t o f f u r th e r i n v e s t i g a -t i o n i n t o t h e v a r i o u s s t r u c t u r e s d e p o s i t e d b y l i v in g p r o t o p l a s m .

I n c o n c lu s i o n , t h e a s s u m p t i o n t h a t t h e u n i t s f o r m a s o r t o f sp h e r i-c a l sp a c e la t t i c e , g iv e s a p i c tu r e o f t h e s t a r c h g r a in w h ic h l e a d s u s t op o n d e r o v e r t h e n a t u r e o f t h e a c t i v i t y i n p r o t o p l a s m w h e n i t i sd e p o s i t i n g so l i d su b s t a n c e s . S t a r c h , c e l lu lo se, a n d p e c t i c b o d i e sa r e a b o u t t h e o n l y s o l id d e p o s i ts m a d e d i r e c t ly b y t h e l i v i n g s u b s t a n c eo f p l a n t s , a n d a l l t h r e e h a v e t h e s a m e p r o p o r t i o n a l f o r mu la , C 6H 1 00 5.I n v e s t i g a t i o n s , a s y e t i n c o mp le t e , i n d i c a t e t h a t c e l l u lo se a l so c o n -s i s t s o f a r e g u l a r a r r a n g e m e n t o f C 8 H 10 0 5 g r o u p s , e a c h a c t i n g a s aun i t , bu t the spac ing (5 .14 6 .14 5 .55) is s l igh t ly d i f fe ren t f romt h a t o f s t a rc h . P e c t i n h a s n o t b e e n s t u d i e d . P r o t o p l a s m m a y b eth o u g h t o f a s b e in g c o m p o se d o f mo le c u l e s o f m a n y d i f f e r e n t s iz es ,p o l y p e p t i d e s , o r e v e n p r o t e i n s f o r m i n g t h e l a r g e r , a n d a m i n o - a c i d sth e sm a l l e r, i f w a t e r a n d e l e c t ro ly t e s a re i g n o r e d . T h e sma l l e r mo le -c u l e s , su c h a s t h o se o f t h e a min o - a c id , l e u c in e , a r e a p p r o x ima te lye q u a l i n s iz e t o t h e C 6 H Io O 5 g r o u p o f s ta r c h . T h a t b e in g t h e c a se ,w h a t c a n b e t h e s t a t e o f a f f a i r s a t t h e i n t e r f a c e w h e n t h e s t a r c hp a r t ic l e s ar e b e i n g d e p o s i t e d ? I s i t p r o b a b l e t h a t p r o t o p l a s m i s


20/20

776 STRUCTURAL UNITS OF STARCHh o m o g e n e o u s t o t h e e x t e n t o f b e i n g a b l e t o d e p o s i t t h e se p a r t ic l e sa t 6 / ~ . u . i n t e r v a l s ?F r o m q u i t e a n o t h e r v i e w - p o i n t a c l e a r p i c t u r e o f t h e u n i t s o fs t r u c t u r e a n d t h e i r a r r a n g e m e n t i n c e ll u lo s e s h o u l d g i v e a n e w p o i n to f a t t a c k o n t h e m a n y p r o b l e m s c o n n e c t e d w i t h o sm o s i s . A n d fr o ms t i l l a d i f f e r e n t v i e w - p o in t , i t m ig h t l e a d p e r h a p s , t o a so lu t i o n o fp r o b l e m s c o n n e c t e d w i t h s w e ll in g .

A n o t h e r l in e o f t h o u g h t is s u g g e s t e d b y t h e u n i f o r m i t y o f t h eg r o u p s i n t h e s t a r c h g r a in . S in c e t h e C 8 H 10 0 5 g r o u p o c c u r s a s a nin d iv id u a l u n i t , o n e i s i n c l i n e d t o su sp e c t t h a t i t i s r e a l l y t h e mo le -c u l e. G e n e r a l l y t h e s t a r c h mo le c u l e i s c o n s id e r e d t o b e v e r y l a r g e ,t o b e c o m p o se d o f s e v e r a l d o z e n s o f su c h g r o u p s , a n d t o h a v e a mo le c -u l a r w e ig h t o f 7 ,0 0 0 o r m u c h mo r e . N o o n e f i g u re , h o w e v e r , s e emssa t i s f a c to r y t o t h e d i ff e r e n t a u th o r i t i e s . T h e r e is a l r e a d y a t h a n dc o n s id e r a b le e v id e n c e w h ic h w i l l b e a s se m b le d i n a l a t e r p a p e r f a v o r -in g t h e s i n g l e g r o u p , C 6 H 10 05 , a s t h e mo le c u l e .

F in a l l y , p r o b l e ms in p o l a r i z e d l i g h t ma y r e c e iv e mo r e s a t i s f a c to r ye x p l a n a t io n s t h r o u g h a c l ea r er n o t i o n o f t h e m o l e c u l a r s tr u c t u r e o ft h e c a r b o h y d r a t e s .

I t i s a p l e as u r e t o m e n t i o n h e r e m y a p p r e c i a t io n o f t h e s u g g e s t io n sa n d o f t h e h e lp k i n d l y g i v e n m e b y D r . D . L . W e b s t e r a n d D r . G e o r g eJ . P e i r c e a t S t a n f o r d U n iv e r s i t y .

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