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Thermodynamic functions of activation of viscous flow in NaI-water-amide systems

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A C T A U N I V E R S I T A T I S L 0 D Z I li N S I á _______ ___________ FOLIA CHIMICA 3 , 1984 ____ ______

S t e f a n i a T a n iew sk a-O siú sk a, A lin a P ie k a r s k a

THERMODYNAMIC FUNCTIONS OF ACTIVATION OF VISCOUS FLOW IN Nal-WATER-AMIDE SYSTEMS

The therm odynam ic p a ra m e te rs o f v is c o u s flo w , namely* AH, AS a t 29 8 .1 5 K and AG in 2 7 8 .1 5 -3 1 8 .1 ') K have been c a l c u l a t e d f o r t h e system s N a l-w ater-fo rm am id e ina ¡v¡I- -w a te r-N ,N -d im e th y lfo rm am id e.

The c a l c u l a t i o n s have been made on th e b a s i s o f o u r p re v io u s v i s c o s i t y d a t a .

In o u r e a r l i e r p a p e rs , [ 1 J we r e p o r t e d t h e r e s u l t s o f v i s - c o s im e U ic s t u d i e s o f N a l-w a te r-fo rm a m id e and Nal-water-DM F s y ­ stem s in th e te m p e ra tu re ran g e o f 2 7 8 .1 5 -3 1 8 .1 5 K. T aking ad­ v a n ta g e o f th o s e d a ta we have now c a l c u l a t e d th e therm odynam ic f u n c tio n s o f a c t i v a t i o n o f v is c o u s flo w i n th e two s y s te m s.

As i s w e ll known, u n d e r c o n s ta n t p r e s s u r e th e te m p e ra tu re f u n c tio n o f th e v i s c o s i t y o f m ost l i q u i d s can be p r e s e n te d as an A rh e n iu s e q u a tio n

w here Ey i s i s m olar a c t i v a t i o n e n e rg y o f v is c o u s flo w , w hich can be d e te rm in e d a s a s lo p e o f I n rj r e l a t i v e to 1 /T . A no ther form o f th e dependence u n d e r d is c u s s io n i s th e E y rin g equ- ion

[ 2 ] , w hich can be r e p r e s e n t e d a s :

R e s u lts and d is c u s s io n

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where h i s P l a n c k 's c o n s t a n t , V I s m olal volum e, N i s Avo- g a d ro ’ s num ber, and AG*, AH*, and AS* a r e a c t i v a t i o n f r e e e n e rg y , e n th a lp y and e n tr o p y r e s p e c t i v e l y . Assuming t h a t V and AS* a r e c o n s t a n t , eqn 2 c a n be re d u c e d t o e x p re s s io n (3 )8

rj - A exp f f i (3 )

whose form i s b a s i c a l l y i d e n t i c a l t o t h a t o f eqn ( 1 ) . In su ch a c a s e AH* can be compared to A d opting th e above assump­ t i o n we have c a l c u l a t e d AG*, AH* and AS* f o r a l l NaX s o ­ l u t i o n s in formamide and N ,N -dim ethylform am ide w ith w a te r in th e te m p e ra tu re ra n g e o f 2 7 8 .1 5 -3 1 8 .1 5 K. The r e s u l t s a r e c o l l ­

e c te d in Tab. 1 -4 . i

T a b l e 1 Form am ide-w ater m ix tu re a c t i v a t i o n p a ra m e te rs

Hoi % F AH* k J.m o i , AS* e . u . AG*/kJ • mol"1 2 7 8 .15K •2 8 8 .15K 2 9 8 .15K 3 0 8 .15K 318.15K 0 1 7 .1 6 26 .8 3 9 .7 7 9 .4 5 9 .1 6 8 .9 3 8 .7 4 10 1 5.92 2 0 .9 0 1 0 .17 9 .9 0 9 .6 9 9 .5 5 9 .3 7 20 1 5 .2 0 1 6 .6 0 10.61 1 0 .4 4 10.25 10.12 10.01 30 1 5 .00 14.15 1 1 .0 8 1 0.92 10.78 10 .68 1 0 .58 40 15.03 12.51 11 .56 1 1.43 11 .3 0 11.21 11.13 50 15.44 12.11 1 2.15 7 1 1 .9 4 11.83 1 1 .7 4 1 1.65 60 1 6.07 12.51 1 2 .6 0 •12.45 1 2.34 1 2 .2 5 .1 2 .1 6 70 1 6 .6 7 1 2 .8 4 1 3 .0 8 ,12.97 1 2 .8 4 12.76 1 2 .6 6 00 1 7.23 1 ^ .9 8 13.63 1 3 .46 1 3.36 1 3 .2 9 1 3.15 90 1 8 .2 7 1 4 .6 9 14.16 14.03 1 3 .8 9 13.81 1 3.63 100 19.66 1 8 .2 8 1 4 .7 7 14.56 14.41 1 4 .2 6 1 4 .1 0

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' f a b l e 2 A c t lv a t io o p a ra m e te rs o f N al-v rater-fo rm am id e system

N ala Mol AH* AS* AG */kJ • mol“ 1

F k J . mol e . u . 2 7 8 .15K 2 8 8 .15K 2 9 8 .15K 3 0 8 .15K 318.15K 0 1 6.77 2 5 .4 6 9 .7 6 9 .4 5 9 .1 8 8 .9 7 8 .7 8 10 1 5 .73 2 0 .0 9 1 0 .1 9 9.95 9 .7 4 9 .6 0 9.43 20 1 5 .1 0 16.03 1 0.66 1 0 .5 0 1 0 .32 1 0 .1 8 10.01 30 15.02 1 3.95 1 1 .1 5 11.01 10.86 10.72 1 0 .6 0 40 1 5.13 12.51 1 1.66 11.52 1 1 .4 0 11.31 11.23 0 .5 50 1 5.62 1 2 .3 8 1 2 .1 9 1 2 .0 6 1 1 .9 3 11.85 1 1.76 60 1 6.42 12.81 12.72 1 2 .5 8 1 2 .4 6 12.38 1 2.27 70 1 7 .0 2 1 2 .9 8 1 3 .2 4 1 3 .10 1 2 .97 1 2.87 1 2.78 80 1 7 .6 0 1 4 .2 9 1 3 .7 7 1 3 .6 0 1 3 .4 8 1 3 .37 1 3.27 90 1 8 .6 8 15.63 1 4 .2 4 1 4 .1 7 1 4.03 1 3 .93 13.75 100 2 0 .2 6 1 9.15 1 4 .8 6 14.71 1 4 .5 3 1 4 .3 8 14.22 0 1 6 .4 0 2 4 .1 8 9 .7 6 9 .4 5 ■ 9 .1 9 8 .9 9 8 .8 3 10 1 5 .4 0 18.95 10.21 9 .9 9 9 .7 9 9.67 9.1)0 20 14.95 15.46 10.73 1 0.56 1 0 .3 9 10.26 1 0 .1 0 30 14.95 1 3 .3 8 1 1.25 1 1 .1 0 1 0 .9 6 10.86 1 0 .7 5 40 15.27 12.61 1 1.7 8 1 1 .64 11.51 11.41 11.32 1 50 15.87 12.31 12.33 1 2 .1 9 1 2 .0 7 1 1 .9 8 11.86 60 16,64 12.71 1 2 .8 9 1 2.73 12.61 12.52 12.35 70 1 7.27 1 3.62 13.41 1 3 .2 7 13.14 13.03 12.75, 60 1 7 .9 0 1 5 .0 9 13.91 13.75 1 3 .6 0 1 3 .4 9 1 3 .3 ^ 90 1 8.94 16.64 1 4 .4 8 1 4.37 14.15 14.02 1 3.89 100 2 0 .5 4 2 0 .3 3 1 5 .0 6 1 4 .8 6 _ 14.66 1 4 .4 9 14.33 0 1 5 .7 8 2 1 .9 9 9 .7 6 9 .4 9 9 .2 2 9 .0 7 8 .9 2 10 1 5 .20 1 7.84 1 0 .29 1 0.05 9 .8 8 -9 .7 7 9 .62 20 14.93 14.76 10.85 1 0 .6 9 1 0.53 10.42 10.32 30 1 5 .1 0 1 3 .3 8 1 1 .4 0 1 1.25 11.11 1 1 .0 0 10.91 40 1 5 .5 0 1 2 .7 8 1 1 .9 7 11.83 1 1 .69 1 1 .5 5 1 1 .5 0 2 50 1 6 .1 8 13.11 1 2.55 12.41 1 2 .27 1 2 .1 3 1 2 .0 9 60 1 7 .0 6 1 3 .7 9 1 3.13 1 2 .9 8 12.85 12.74 12.65 70 17.77 1 4 .6 9 1 3 .69 1 3.54 1 3 .3 9 1 3 .2 8 13. .18 80 18.51 16.03 1 4 .2 0 1 4 .0 5 1 3.88 1 3 .7 6 15.63 90 19.57 1 7 .5 4 1 4 .7 7 14.61 14.41 1 4 .30 14.16 100 2 1 .3 0 2 1 .2 3 1 5 .4 0 1 5 .1 7 1 4 .9 7 14.79 1 4.62

a N al c o n c . in m oles o f N al in 100 mol m ixed s o l v e n t .

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N ,N -d im eth y lfo rra a m id e -w a te r m ix tu re a c t i v a t i o n p a ra m e te rs Hoi 56 DMF AH* 0 -1 k J.m o l

K

e . u . AGg/kJ . mol-1 2 7 8 .15K 2 8 8 .15K 2 9 8 .15K I 3 0 6 .15K 3 1 8 .15K O'. 17.16 2 6 .8 3 9 .7 7 9 .4 5 9 .1 6 8 .9 3 8 .7 4 5 1 9 .5 8 3 0.42 1 1 .1 6 1 0 .80 10.51 10.24 9 .9 8 10 2 1 .6 7 3 4 .1 7 12.22 1 1.85 1 1 .48 1 1 .1 9 1 0.93 , 15 2 3 .0 3 3 6 .3 9 13.01 1 2.63 1 2 .26 1 1.95 1 1.64 20 2 3 .6 3 3 6 ,4 2 1 3 .5 0 1 3 .1 5 1 2.77 1 2 .46 12 .14 ' 25 23.81 35 .8 5 1 3.85 .1 3 .4 7 1 3.12 1 2 .8 3 1 2 .5 0 30 2 3 .3 5 3 3 .6 0 14.01 13.67 1 3 .3 4 1 3 .06 12.75 35 2 2 .3 7 2 9 .92 _ 1 4 .0 2 1 3 .7 4 1 3 .4 5 1 3 .1 8 1 2.92 40 2 1 .0 0 2 5 .2 9 1 3.97 1 3 .6 4 1 3.46 13.25 13.02 50 1 8 .1 4 1 6 .1 0 1 3 .7 0 1 3 .4 4 1 3 .3 4 13.21 1 3 .1 3 60 1 5 .57 8 .1 8 1 3 .32 1 3 .1 9 1 3.13 13.07 1 3 .09 70 13.51 1 .9 8 1 2.96 12.91 1 2 .92 12.92 12.95 80 1 1.65 - 3 .5 9 1 2 .6 5 12.67 12.72 1 2 .7 8 1 2 .8 7 90 10.17 - 8 .1 2 12.41 12.51 1 2 .5 9 1 2 .6 8 1 2 .8 0 I 100 5.11 - 1 1 .3 0 1 2 .29 1 2 .3 6 | 1 2 .4 8 1 2 .67 .1 2.8 4

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T a b l e 4 'A c tiv a tio n p a ra m e te rs o f M al-w ater-N , N -dim ethylfurm a;nide

sy stem

N a la Mol % AH* AS* AG* k J . mol” 1

DMF k J.m o l” 1 e . u . 2 7 8 .15K 2 8 8 .15K 2 9 8 .15K 3 0 8 .15K 3 1 8 .15K 0 1 6 .77 2 5 .4 6 9 .7 6 9 .4 5 9 .1 8 8 .9 7 8 .7 8 5 19 .2 5 2 9 .2 5 1 1 ,16 10.82 10.53 10.27 10.03 10 2 1 .4 0 3 3 .1 7 12.23 1 1.87 11.51 11.27 10 .98 15 2 2 .8 3 3 5 .3 2 13.03 1 2.65 1 2 .30 1 2 .0 0 1 1.7 0 20 2 3 .4 0 3 5 .5 2 13.52 1 3 .1 9 12.81 12.52 1 2 .20 25 2 3 .5 9 3 4 .9 2 1 3 .9 0 13.52 1 3 .1 8 1 2 .9 0 1 2 .5 8 30 2 3 .3 3 3 3 .2 7 1 4 .0 8 13.74 13.41 1 3.15 12.84 0 .5 35 2 2 .4 6 2 9 .8 8 14.11 1 3.83 1 3 .5 5 1 3 .27 13 .01 40 2 1 .2 3 2 5 .6 9 1 4 .0 9 1 3.75 13.. 57 13.36 13.12 50 1 8 .4 6 1 6.77 13.84 1 3 .57 1 3 .4 6 1 3.34 1 3.24 60 1 5 .90 9.35- 13-31 - - 1 3 .0 7 13.11 1 3 .05 1 3 .2 0 70 1 3.85 2 .6 8 13.11 13.05 1 3.05 1 3 .0 5 13.08 80 1 2 .03 - 2 .7 8 1 2 .8 0 1 2.82 1 2 .86 1 2.94 1 3 .0 0 90 10.53 - 7 .3 5 12.55 12.65 1 2.72 1 2.85 12.92 100 9 .4 8 - 1 0 .5 0 1 2.44 1 2 .50 12.61 1 2 .7 8 12.95 0 1 6 .4 0 2 4 .1 8 S. 76 9 .4 5 9 .1 9 8 .9 9 B . ö j 5 1 8.95 2 8 .2 0 11.16 1 0 .8 3 1 0 .54 1 0 .3 0 1 0 .0 8 10 2 1 .1 3 3 2 .2 7 1 2 .2 0 1 1 .8 8 1 1.53 1 1.27 11.03 15 2 2 .6 8 34.71 1 3.07 1 2 ,6 5 ' 1 2 .33 12'. 04 1 1.75 20 2 3 .3 5 3 5 .1 8 1 3 .6 0 1 3 .2 0 1 2 .8 6 12.57 12*25 25 2 3 .5 8 .3 4 .6 8 1 3.95 1 3 .5 7 1 3 .24 1 2 .95 1 2 .6 3 30 2 3 .3 3 3 3 .0 4 1 4 .1 7 1 3 .7 9 1 3 .4 8 1 3.22 12.92 1 35 2 2 .6 8 3 0 .3 5 1 4.23 1 3 .8 9 1 3 .6 3 1 3.35 1 3 .0 9 40 2 1 .4 0 2 5 .9 6 1 4 .1 8 1 3.85 1 3 .6 6 1 3.44 13.2,9 - 50 1 8 .6 7 1 7.07 1 3.96 1 3 .70 1 3 .5 8 1 3 .44 1 3 .3 6 60 1 6 .2 3 9 .4 9 13.61 1 3 .4 7 1 3 .4 0 1 3.33 1 3 .32 70 1 4 .2 0 3 .3 8 Í 3 .2 6 1 3 .20 1 3 .1 9 1 3 .1 9 1 3 .2 0 80 1 2.32 - 2 .2 8 1 2.95 1 2 .9 6 1 3 .0 0 1 3 .0 5 13.11 90 1 0.83 - 6 .8 4 12.71 1 2 .8 0 12.87 1 2 .9 4 . 13.05 10Ó ,9 .7 7 - 1 0 .0 0 ■ - 1 2 .66 12.75 12.94 1 3 .0 9

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T a b le 4 c o n t.

Mala Mol % AH* AS* AG* k J * rao i"1

DMF ---0 «u* 2 7 8 .15K 2 8 8 .13K 2 9 8 .15K 3 0 3 .15K 313.15K 0 1 5 .7 3 2 1 .9 9 9 .7 6 9 .4 9 9 .2 2 9 .0 7 8 .9 2 5 18.32 2 5 .3 9 1 1 .1 7 10.8S 1 0 .6 0 1 0 .3 7 1 0 .1 7 10 2 0.62 30.25 1 2.27 1 1.92 1 1 .6 0 1 1 .3 5 1 1.1 4 15 2 2 .2 3 3 2 .9 7 1 3 .1 0 1 2 .7 5 1 2 .4 0 1 2.13 11.87 20 2 3 .0 8 3 5 .6 7 1 3 .6 4 1 3 .3 2 1 2.96 1 2 .6 8 1 2 .4 0 25 2 5 .3 7 3 3 .5 4 1 4 .06 1 3 .7 0 1 3 .3 7 1 3 .0 9 1 2 .8 0 50 23*12 3 1 .8 3 1 4 .2 9 1 3 .9 3 13.63 1 3 .3 6 13.11 2 35 2 2 .7 9 3 0 .1 5 1 4 .3 8 1 4 .1 0 1 3 .8 0 13.53 13.27 40 2 1 .7 3 2 6 .4 6 14.41 1 4 .0 5 1 3 .8 6 1 3 .6 4 13.41 50 1 9 .18 1 7 .9 4 1 4 .2 3 1 3 .9 5 13.83 1 3.64 1 3 .5 9 60 16.72 1 0 .2 3 1:5.89 1 3.75 1 3 .6 7 1 3 .5 9 1 3 .5 8 70 1 4 .70 4 .0 9 1 3 .5 6 13.49 1 3.48 1 3 .4 6 13.47 30 1 2 .7 9 , - 1 .6 3 13.26 1 3 .2 6 1 3 .2 9 1 3 .33 1 3 .4 0 90 1 1 .2 9 - 6 .2 7 1 3 .0 2 1 3 .1 0 13.16 1 3 .2 4 1 3.34 100 10.23 - 1 9 .3 9 1 2 .95 1 3 .03 1 3 .2 2 1 3 .3 8

a ¡4al conc In m oles o f Nal in 100 mol m ixed s o l v e n t .

A c t iv a t io n e n th a lp y o f v is c o u s flo w (AH*) o f w a te r-fo rm am id e m ix tu re s and o f Nal s o l u t i o n s i n th e s e m ix tu re s P ig . 1 d e c re a ­ s e s i n , t h e r a n ^ e o f 0* m ole t o 15-2056 m ole fon n am id e, w hich i s p r o b a b ly due to th e d e s t r u c t i v e e f f e c t o f form am ide on w a te r s t r u c t u r e : th e fo rm a tio n o f s m a ll an d homogeneous o r-m ix e d agg­ r e g a t e s f a c i l i t a t e s v is c o u s flo w . The minimum p o i n t (15-2056 mole F) p r o b a b ly c o rre s p o n d s t o t o t a l d e s t r u c t i o n o f th e t h r e e - . .»dim ensional H-bond l a t t i c e in -w ater. The f o rm a tio n o f l a r g e r m ixed iornr.araide-w ater a s s o c i a t e s p ro d u c e s an I n c r e a s e i n th e > a c t i v a t i o n e n th a lp y o f v is c o u 3 flo w i n th e ra n g e o f ~20?6- ~ 90 ^ mole f o r : M.cido. In th e 90 -1 0 0 # mole ra n g e a much f a s t e r i n ­ c r e a s e i n AH* is o b s e rv e d b o th i n H al s o l u t i o n s i n w a t e r - f o r - aatU ae m ix tu re s arid i n th e m ixed s o l v e n t . Q u ite l i k e l y , s o l u ­ tio n :; c o h t . Hing ao re th a n 90A mole form am ide d e v e lo p a form am ide

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s t r u c t u r e t y p i c a l o f p u re l i q u i d w h ich , in t u r n , makes v is c o u s flow more d i f f i c u l t and r e q u i r e s more e n e rg y . The a c t i v a t i o n e n e rg y o f v is c o u s flo w i n Nal s o l u t i o n s i n w ater-fo rm am id e Mix­ t u r e s i n th e ra n g e o f 0 -2 3 # m ole F i s lo w er th a n th ejt f o r p u re s o l u a a t . T his may be r e l a t e d to t h e s t r u c t u r e b re a k in g e f f e c t o f th e d o n s in tr o d u c e d on th e m ixed s o l v e n t . The o p p o s ite c o u r­ s e o f t h e two f u n c t i o n s i n th e ra n g e o f formarnide c o n te n ts ex­ c e e d in g *-2534 mole s u g g e s ts t h a t Hal h a s an o r d e r in g e f f e c t on th e s o lv e n t s t r u c t u r e .

F ig . 1 . A c t iv a t io n e n e rg y f o r v is c o u s flo w o f Nal s o l u t i o n s in w a te r-fo rm a m id e m ix tu re s a t 2 9 8 .15K, E l e d t r o l y t e c o n c e n t r a t io n

i n mole Mai p e r 100 mole o f m ixed s o lv a n t

j____ i_____i—,— i--- 1---- -—i

¿0 60 80 100

mo! F

A d i f f e r e n t c o u rs e o f th e AH* ■ f (56 mole amide) f u n c tio n i s o b s e rv e d b o th in th e c a s e o f DMF m ix tu re w ith w a te r and i n th e c a s e o f N al s o l u t i o n s in su c h m ix tu re s ( F i g , 2 ) . The a c ­ t i v a t i o n e n th a lp y o f v is c o u s flo w i n t h i s system e x h ib it's maxi­

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mum In th e a r e a c o rre s p o n d in g to maximum v i s c o s i t y o f th e s e sy ­ s te m s . The above f in d i n g seems to c o n firm t h e id e a - p u t f o r t h e a r l i e r [ 1 ] - t h a t in t h e ra n g e o f c o n te n t s u n d e r d i s c u s s io n th e fl-bonds have maximum d e n s i t y . S i m i l a r l y a s i n th e c a s e o f th e p r e v i o u s ly d is c u s s e d sy s te m , th e a c t i v a t i o n e n th a lp y o f v isc o u s flo w o f Nal s o l u t i o n s in th e ra n g e o f 0 -2 5 # m ole DMF i s lo w er th a n th e a c t i v a t i o n e n e rg y o f p u re s o l v e n t . T h is i s p r o b a b ly due to ^he d e s t r u c t i v e e f f e c t o f t h e io n s in tr o d u c e d on th e s o l v e n t a g g r e g a te s . In s o l u t i o n s c o n ta in in g more th a n 25% mole DMF, AH* o f t h e s o l u t i o n i s h ig h e r th a n AH* o f th e s o l v e n t , F ig . 2 . A c t i v a t i o n e n e rg y f o r v is c o u s flo w o f Nal s o l u t i o n s i n w a te r-ü 'îF ¡r x t u r e s a t 2 9 8 .1 5 K. E l e c t r o l y t e c o n c e n t r a t io n in

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p o s s i b l y due t o th e o r d e r in g e f f e c t o f Hal on th e s t r u c t u r e p f th e EMF-water m ix tu re .

A' d i f f e r e n t sh a p e o f t h e AH* » f (>6 mole amide) f u n c tio n i n EMF-water sy ste m in com pariso n to t h a t in fo rm am ide-w ater sy ste m , a s can be se e n i n F ig s . 1 and 2 i s p ro b a b ly due to th e h y d ro p h o b ic h y d r a tio n w hich can u ndergo two m ethyl g ro u p s in DMF m o le c u le . R e fe re n c e s [ 1 ] S . T a n i e w s k a - 0 s i r i s k a , A. P i e k a r s k a , A. K a c p e r s k a , J . S o l u ti o n Chem. 12 ( 1 0 ) , 71?

(1983).

[ 2 ] E, A. 0 u g g e n h e i m, J . E . M a y e r , F. C. T o m p -k i n s , The I n t e r n a t i o n a l E n c y c lo p e d ia o f P h y s ic a l Che­ m is tr y and Chem ical P h y s ic s , Pergamon P r e s s , y o l . I l l , p . 6 3 , 1963.

D epartm ent o f P h y s ic a l C h em istry U n i v e r s i ty o f Łódź

S t e f a n i a T a n iew sk a-O silisk a, A lin a P ie k a r s k a FUNKCJE TErtMODYNAMICZiNE AKTYWACJI LEPKIEGO PRZEPŁYWU

W UKŁADACH Nal-WODA-AMID

O b liczo n o term odynam iczne f u n k c je a k ty w a c ji le p k ie g o prZi- pływu AH*, AS* w te m p e ra tu rz e 2 9 8 .1 5 K o ra z AG* w z a k r e s ie te m p e ra tu r 2 7 8 .1 5 -3 1 8 .1 5 K d l a układów N al-w oda-form am id o ra z H al-w oda-N , U -dw uoetyloform am id. O b lic z e n ia wykonano na p o d sta w ie w c z e ś n ie js z y c h danych l e p k o ś c i . E n t a l p i a a k ty w a c ji le p k ie g o p r z e ­ pływ u, w z a le ż n o ś c i od z a w a rto ś c i am idu, w u k ła d z ie H al-w oda- -form am id p rz e c h o d z i p rz e z minimum w o b s z a r z e z a w a rto ś c i form a­ midu 15-20?* m ol. P r z e b ie g a n a lo g ic z n e j z a le ż n o ś c i w u k ia d z i Nal-woda-OMF w ykazuje maksimum w p r z e d z i a l e 2 5 -3 0 ^ mol W.F,

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C r e ia H H f l T a H e B C K a -O c K H b O K a , A jiH H a i l e K a p o i t a T EP :vt -iH W HA MVW ECK ü E vyHKUtfÜ AKIMBAUHM BJÖKOrO TiMEHUfl

B CHCTEMAX Nal-BOIA-A.WJI

Ha o c H O B e onyßjiHKOBainjx paHbme hahhux o bh3K0cth BU<tHOJieKU

TepMOÄHHaMHtieOKHe 4>yHKUIKH aKTHBąuHM BH3KOrO TetieHKA AH* H AS* npH teM neparype 29 8 .1 5 K h AG* b nnana30He T e x n e p a T y p 2 7 8 .1 5 - - 3 1 8 . 1 5 'K fljiH CHCT6M NaI-Bo^a-$opMaMHn h N a l-b o n a - ,!!»». ftHT&iib- nsła aKTHBauHU AH* icax <pynKUHH o ocłaB a paoiBopHianH« b ohctsmg NoI-Bona-śPopMaMm npoxo^HT «lepea uHHuuytt OTBenam»^ 15-20 moji %

(opuauiuia.

A H a . io r m i e c K a H ł y H K i i n a AJtfl c h c t e t u i N a I-B O ,n a -3 M X > n p o x o A H T h « - pe3 uaKcuMyu b paexBopax conep*anjHx 2 5 - 3 0 non % HMS.

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W części północnej natomiast, w pobliżu kulminacji wyniesienia odsłonię­ to zarysy dwóch niewielkich jam zawierających materiały ceramiczne późnej fazy kultury ceramiki

W powyższym utworze ujawnia się relacja Ja–Ty: „uwodzisz mnie promieniu słońca, dosięgasz (...)” oraz Ja–To w doświadczeniu świata przyrody według buberowskiej myśli:

The current flow rate determines the size of the weld nugget, which further affects the distribution of deformation in the joint and the load capacity of the

The main purpose of the Jagiellonian University Repository created in response to the Open Science demands is to collect, archive and disseminate information abo- ut the