Effects of Supercritical Solvents on the Rates of Homogeneous

Chapter 4

Effects of Supercritical Solvents on the Rates of Homogeneous Chemical Reactions Sunwook Kim and K. P. Johnston

Downloaded by UNIV OF TEXAS AT AUSTIN on October 4, 2017 | http://pubs.acs.org Publication Date: December 16, 1987 | doi: 10.1021/bk-1987-0329.ch004

Department of Chemical Engineering, University of Texas, Austin, TX 78712

Solvatochromic shift data have been obtained for phenol blue in supercritical fluid carbon dioxide both with and without a co-solvent over a wide range in temperature and pressure. At 45°C, SF CO2 must be compressed to a pressure of over 2 kbar in order to obtain a transition energy, ET, and likewise a polarizability per unit volume which is comparable to that of liquid n-hexane. The ET, data can be used to predict that the solvent effect on rate constants of certain reactions is extremely pronounced in the near critical region where the magnitude of the activation volume approaches several liters/mole. It is ironic that the large growth in SF extraction at the Max Planck Institute in Germany in the 1960f s was the result of a serendipitous discovery of the solvent power of supercritical ethylene during the "Aufbau" reaction of triethylaluminum with ethylene (1). A number of recent articles review supercritical fluid (SF) extraction (2_,.3,4) ; however, the literature contains relatively few examples where supercritical fluid solvents have been used to modify or control reaction rate constants Ç5,6^,7). Liquid phase reactions have been studied over wide pressure ranges, e.g. 1-10 kbar, to determine activation volumes, i.e. the pressure derivative of the rate constant. These studies essentially ignore the highly compressible near supercritical region where activation volumes can become infinite, either positively or negatively. Simmons and Mason (7) observed an abrupt decrease in the activation volume near the critical conditions for the cyclic dimerization of C2F3CI. Paulaitis et al. (6) measured activation volumes as low as -500 cc/mol for the Diels-Alder cycloaddition of isoprene and maleic anhydride in CO2. These examples provide an indication of the effects of supercritical solvents on the rate constants of homogeneous chemical reactions although a much larger data base is needed. Supercritical fluid solvents offer some potential advantages compared with liquids as an environment for chemical reactions. It 0097-6156/87/0329-0042$06.00/0 © 1987 American Chemical Society

Squires and Paulaitis; Supercritical Fluids ACS Symposium Series; American Chemical Society: Washington, DC, 1987.


4.

KIM AND JOHNSTON

Supercritical Fluid Solvents and Reaction Rates

43

w i l l be d e m o n s t r a t e d t h a t r e a c t i o n r a t e c o n s t a n t s o f c e r t a i n r e a c t i o n s may b e a l t e r e d m a r k e d l y b y s m a l l m o d i f i c a t i o n s i n t h e p r e s s u r e o f a SF s o l v e n t . R e a c t i o n p r o d u c t s c o u l d be separated efficiently using supercritical fluid extraction. Industrial applications of reactions in SF s o l v e n t s include: the detoxification of wastewater, ethylene polymerization, i s o m e r i z a t i o n o f η - p a r a f f i n s , s y n f u e l s p r o c e s s i n g , and t h e r e a c t i o n of ethylene w i t h t r i e t h y 1 a l u m i n u m ( 5 ) . S o l v e n t s t r e n g t h s c a l e s b a s e d on s o l v a t o c h r o m i s m , i . e . , shifts i n the a b s o r p t i o n w a v e l e n g t h o f i n d i c a t o r dyes caused by the s o l v e n t , a r e u s e d commonly t o c o r r e l a t e and t o p r e d i c t r a t e c o n s t a n t s f o r l i q u i d phase r e a c t i o n s ( 8 - 1 3 ) . L i n e a r s o l v a t i o n energy r e l a t i o n s h i p s based on s o l v a t o c h r o m i c p a r a m e t e r s have been used t o c o r r e l a t e and p r e d i c t s o l u b i l i t y phenomena, a b s o r p t i o n maxima i n I R , NMR, E S R , a n d U V - v i s i b l e s p e c t r o s c o p y , solvent effects on r e a c t i o n r a t e c o n s t a n t s and e q u i l i b r i u m c o n s t a n t s , f r e e energies and e n t h a l p i e s o f f o r m a t i o n o f a c i d - b a s e c o m p l e x e s , retention i n d i c e s i n g a s - l i q u i d chromatography and h i g h - p e r f o r m a n c e - l i q u i d chromatography, and f i n a l l y , p h y s i o l o g i c a l and toxicological quantitative structure-activity relationships (14). Although solvatochromic "solvent strength s c a l e s have such widespread a p p l i c a t i o n , t h e y a r e j u s t b e g i n n i n g t o become a v a i l a b l e f o r s u p e r c r i t i c a l f l u i d s o l v e n t s (15,16) f o r v e r y l i m i t e d p r e s s u r e and temperature ranges. Solvatochromic data are presented in this symposium i n t h e a r t i c l e by F r y e e t a l . 1 1

Solvatochromic data, s p e c i f i c a l l y absorption or transition energies ( E ^ / s ) , have been o b t a i n e d f o r the dye p h e n o l b l u e i n supercritical f l u i d s as a f u n c t i o n o f b o t h t e m p e r a t u r e and pressure. These d a t a w i l l be u s e d t o compare t h e "solvent strength" of these f l u i d s with l i q u i d solvents. We w i l l u s e t h e terms " s o l v e n t s t r e n g t h " and " E ^ " synonymously i n t h i s paper s u c h t h a t they i n c l u d e the magnitude o f the p o l a r i z a b i l i t y / v o l u m e as w e l l as t h e d i p o l e moment. The " s o l v e n t s t r e n g t h " h a s been c h a r a c t e r i z e d by the s p e c t r o s c o p i c s o l v a t o c h r o m i c p a r a m e t e r , E ^ , f o r numerous l i q u i d s o l v e n t s (9,11,17,18). R e a c t i o n r a t e c o n s t a n t s and a c t i v a t i o n v o l u m e s w i l l be p r e d i c t e d as a f u n c t i o n o f p r e s s u r e i n the h i g h l y c o m p r e s s i b l e near c r i t i c a l r e g i o n and i n t h e h i g h l y d e n s e , l e s s c o m p r e s s i b l e r e g i o n using Ε . In a d d i t i o n , the magnitude of the compression o f a s u p e r c r i t i c a l f l u i d about a s o l u t e i n the h i g h l y c o m p r e s s i b l e r e g i o n w i l l be d e t e r m i n e d q u a l i t a t i v e l y . These s p e c t r o s c o p i c d a t a , which describe i n t e r a c t i o n s at the m o l e c u l a r l e v e l , w i l l benefit s i g n i f i c a n t l y the understanding o f b o t h phase e q u i l i b r i a and s o l v e n t e f f e c t s on r e a c t i o n r a t e s i n the s u p e r c r i t i c a l f l u i d s t a t e . Experimental Phenol blue (benzoquinone N-[(4-dimethylamino) phenyl] imine, A l d r i c h >97%) w a s p u r i f i e d b y r e c r y s t a l l i z a t i o n a n d c h r o m a t o g r a p h i c separation (30). The p u r i t y was c h e c k e d b y t h e m e l t i n g p o i n t ( 1 6 1 - 1 6 2 ° C ) , a n d t h e a b s o r p t i o n maximum i n a c e t o n e ( 5 8 2 nm) a n d i n C C l ^ (565 nm). The dye was o f c h r o m a t o g r a p h i c p u r i t y as d e t e r m i n e d by t h i n - l a y e r c h r o m a t o g r a p h y o n s i l i c a g e l . T h e v o l u m e o f t h e c y l i n d r i c a l h i g h p r e s s u r e c e l l w a s 14 c m , and t h e p r e s s u r e and t e m p e r a t u r e r a n g e s were 0 t o 6000 p s i and - 3 0 3


SUPERCRITICAL FLUIDS

44

to 250°C, r e s p e c t i v e l y . The i n s i d e d i a m e t e r was 1.75 cm, and the w a l l t h i c k n e s s was 1.67 cm. Because o f the l a r g e 6 cm p a t h l e n g t h of t h e c e l l , t h e s p e c t r a l s h i f t can be measured f o r c o n c e n t r a t i o n s as low as 10 M a t 0.1 Absorbance u n i t s . Each 1 c m - t h i c k by 2.5 cm i n d i a m e t e r s a p p h i r e window was f l a t t o one w a v e l e n g t h o f y e l l o w l i g h t , and t h e o p t i c a l a x i s was p e r p e n d i c u l a r t o the f a c e . A t e f l o n o - r i n g was i n s e r t e d between t h e window and a f l a t s u r f a c e on the 316 s t a i n l e s s s t e e l v e s s e l . The c e l l was t h e r m o s t a t e d u s i n g a V copper heat exchange c o i l which was j a c k e t e d w i t h f i b e r g l a s s insulation. The temperature was i n d i c a t e d and c o n t r o l l e d t o ±0.1°C w i t h a p l a t i n u m r e s i s t a n c e probe w h i c h extended 1 mm i n s i d e the i n n e r s u r f a c e o f the c e l l . The p r e s s u r e was a d j u s t e d u s i n g a 100 cc Ruska s y r i n g e pump and was measured t o w i t h i n ±0.1% w i t h a 710A H e i s e d i g i t a l p r e s s u r e gauge w h i c h i s t r a c e a b l e t o an NBS s t a n d a r d . The p r e s s u r e v a r i e d l e s s than 0.15 b a r (2 p s i ) d u r i n g a s p e c t r a l scan. The w a v e l e n g t h a c c u r a c y was ±0.2 nm f o r t h e V a r i a n (Cary) 2290 s p e c t r o p h o t o m e t e r . The c e l l was l o a d e d w i t h 10 g p h e n o l b l u e , e v a c u a t e d , and p r e s s u r i z e d w i t h the s o l v e n t . A spectrum was o b t a i n e d a t a g i v e n p r e s s u r e a f t e r the temperature and absorbance e q u i l i b r a t e d . The a b s o r p t i o n band was scanned o v e r a range o f 450-600 nm 2-3 times t o o b t a i n t h e average λ . The r e p r o d u c i b i l i t y i n λ was ±0.2 nm max majx w h i c h c o r r e s p o n d s t o a p r e c i s i o n i n E^, o f ±0.02 k c a l / m o l .


6

5

R e s u l t s and D i s c u s s i o n S o l v e n t s t r e n g t h i n the c r i t i c a l r e g i o n . A l l o f the experiments were performed w i t h the dye p h e n o l b l u e w h i c h has been w e l l c h a r a c t e r i z e d b o t h e x p e r i m e n t a l l y and t h e o r e t i c a l l y i n l i q u i d s o l v e n t s (20,21,22). S i n c e t h e d i p o l e moment o f p h e n o l b l u e i n c r e a s e s 2.5 debye upon e l e c t r o n i c e x c i t a t i o n ( 8 ) , i t i s a s e n s i t i v e probe of the l o c a l s o l v e n t environment. F o r example the a b s o r p t i o n maxima o c c u r a t 550 and 608 nm i n n-hexane and m e t h a n o l , respectively. The e x c i t e d s t a t e i s s t a b i l i z e d t o a g r e a t e r e x t e n t than t h e ground s t a t e as t h e " s o l v e n t s t r e n g t h " i s i n c r e a s e d , w h i c h i s d e s i g n a t e d as a r e d s h i f t . The t r a n s i t i o n energy, E , o f p h e n o l b l u e i n CO2 i s p l o t t e d v e r s u s p r e s s u r e i n F i g u r e 1 a l o n g the s a t u r a t i o n c u r v e and a t s u p e r c r i t i c a l c o n d i t i o n s . The b e h a v i o r o f t h e E^ v e r s u s p r e s s u r e p l o t i s s i m i l a r t o t h a t o f d e n s i t y v e r s u s p r e s s u r e , such t h a t E i s f a i r l y l i n e a r i n d e n s i t y as shown i n F i g u r e 2. The e f f e c t ot temperature i s r e l a t i v e l y s m a l l a t a g i v e n d e n s i t y . I n the h i g h l y c o m p r e s s i b l e near c r i t i c a l r e g i o n , the E i s extremely s e n s i t i v e w i t h r e s p e c t t o p r e s s u r e a l o n g an i s o t h e r m , and l i k e w i s e w i t h r e s p e c t t o temperature a l o n g an i s o b a r (see F i g u r e 1 ) . At h i g h reduced p r e s s u r e s where t h e f l u i d i s r e l a t i v e l y i n c o m p r e s s i b l e , E^ i s o n l y a weak f u n c t i o n o f p r e s s u r e and temperature as i s t h e case f o r l i q u i d s n e a r the t r i p l e p o i n t . S u p e r c r i t i c a l f l u i d solvents e x h i b i t an i n t e r e s t i n g p r o p e r t y w h i c h i s not o b s e r v e d f o r pure l i q u i d s o l v e n t s i n t h a t t h e d e n s i t y and thus the " s o l v e n t s t r e n g t h " ( E ) may be a d j u s t e d o v e r a continuum u s i n g s m a l l changes i n temperature and p r e s s u r e . In T a b l e I , s e v e r a l SF s o l v e n t s a r e compared w i t h l i q u i d n-hexane a t a reduced temperature (Τ = T/T ) n e a r 1.05. F o r each T

T

T

T




KIM AND JOHNSTON

F i g u r e 2 . E o f p h e n o l b l u e i n CO2 v s . d e n s i t y (•= 31 Δ = 35 °C, 0 = 40 °C, 0= 45 °C, and i s calculated using Equation 5). T



46

f l u i d , t h e p r e s s u r e i s chosen t o match t h e Ε w i t h t h e v a l u e f o r n-hexane, so t h a t t h e comparison i s made a t c o n s t a n t "solvent strength". Many i n v e s t i g a t o r s have i m p l i e d t h a t t h e s o l v e n t s t r e n g t h o f a s u p e r c r i t i c a l f l u i d approaches t h a t o f a l i q u i d a t the p o i n t where t h e d e n s i t y approaches t h a t o f a l i q u i d . This i s c l e a r l y a m i s c o n c e p t i o n . A t 45°C (T = 1.05), t h e m o l a r d e n s i t y o f CO2 approaches t h a t o f n-hexane a t ^30 b a r , y e t i t i s a weaker s o l v e n t f o r a l i p h a t i c and a r o m a t i c h y d r o c a r b o n s a t t h e s e c o n d i t i o n s (2,3). The r e a s o n f o r t h i s d i f f e r e n c e i s t h a t t h g average p o l a r i z a b i l i t y p a r m o l e c u l e o f CO2 i s o n l y 26.5 χ 10 cm whereas i t i s 123 χ 10 cm f o r hexane. A t a g i v e n m o l a r d e n s i t y , t h e p o l a r i z a b i l i t y p e r u n i t volume i s much g r e a t e r f o r hexane. Iti s a l s o g r e a t e r f o r hexane a t a g i v e n mass d e n s i t y d e s p i t e t h e d i f f e r e n c e i n the molecular weights. 5

3


3

Table I.

Τ

Solvent

(°c) C Hi/

3 )

2

C0

2

CF C1

( 3 )

3

n-C Hm 6

(1) (2) (3)

Comparison o f SF S o l v e n t s at c o n s t a n t E ^

Τ = r T/T c

w i t h n-Hexane

6

(bar)

Ρ = r P/P c

(g/cc)

(cal/cc)^ 7.0

Ρ

Ρ

a/v

( 2 )

0.052

25

1.056

1700

33.8

0.57

45

1.046

2800

37.9

1.32

40

1.037

1300

33.2

1.95

6.9

0.051

25

-

-

0.66

7.3

0.057

1

10.3

0.048

H i l d e b r a n d s o l u b i l i t y parameter p o l a r i z a b i l i t y p e r volume r e f e r e n c e (19)

The Ε s o f t h e n o n p o l a r s o l v e n t s , C F 3 C I and 0 2 ^ , become e q u a l t o t n a t o f n-hexane a t a p r e s s u r e i n t h e range o f 1-2 kilobar. N o t i c e that the Hildebrand s o l u b i l i t y parameters of these three solvents are roughly equivalent at t h i s c o n d i t i o n of constant Ε · The same r e s u l t i s a l s o o b s e r v e d f o r t h e p o l a r i z a b i l i t i e s / volume o f t h e s e s o l v e n t s . A g a i n , t h e molar d e n s i t i e s o f t h e s e s u p e r c r i t i c a l f l u i d s a r e c o n s i d e r a b l y h i g h e r t h a n t h a t o f n-hexane at t h i s equivalence point i n solvent strength, since the p o l a r i z a b i l i t i e s / m o l e c u l e a r e lower. The E o f CO2 a t 45°C r e a c h e s t h a t o f n-hexane a t 2.8 k b a r . At t h i s p r e s s u r e , t h e p o l a r i z a b i l i t y / v o l u m e o f SF CO2 i s a l i t t l e l e s s t h a n t h a t o f n-hexane, w h i c h s u g g e s t s t h a t t h e r e a r e o t h e r m o l e c u l a r i n t e r a c t i o n s between CO2 and p h e n o l b l u e i n a d d i t i o n t o d i s p e r s i o n and i n d u c t i o n . The l i k e l y p o s s i b i l i t i e s i n c l u d e e l e c t r o n d o n o r - a c c e p t o r f o r c e s and d i p o l e - q u a d r u p o l e i n t e r a c t i o n s . The E ' s o f C O 2 , C2Ht+, and CHF3 a r e compared v e r s u s reduced d e n s i t y a t c o n s t a n t reduced temperature i n F i g u r e 3. The c u r v e s f

τ

T

T



4.

KIM A N D JOHNSTON

47


f o r CO2 and e t h y l e n e c o i n c i d e even though t h e p o l a r i z a b i l i t y / m o l e c u l e o f e t h y l e n e i s 1.6 times t h a t o f C O 2 . The p r i m a r y r e a s o n f o r t h i s i s t h a t t h e m o l a r d e n s i t y o f CO2 i s 1.4 times t h a t o f e t h y l e n e a t c o n s t a n t r e d u c e d d e n s i t y and t e m p e r a t u r e . The s e c o n d a r y f a c t o r i s t h a t CO2 i s s l i g h t l y a c i d i c and h a s a q u a d r u p o l e moment o t h e r w i s e i t would g i v e a s m a l l e r r e d s h i f t . F o r nonpolar s o l u t e s t h a t do n o t e x h i b i t d i p o l a r and a c i d - b a s e i n t e r a c t i o n s , t h e s o l v e n t s t r e n g t h o f CO2 would be l e s s than t h a t o f e t h y l e n e a t c o n s t a n t reduced temperature and d e n s i t y . I n a d d i t i o n , a t a g i v e n r e d u c e d temperature and d e n s i t y , t h e reduced p r e s s u r e s a r e s i m i l a r ( e . g . , see F i g u r e 3 and T a b l e 1) t h u s t h e a c t u a l p r e s s u r e f o r CO2 i s about 1.5 t i m e s t h a t f o r C2Hi+. The s o l u b i l i t y d a t a f o r n a p h t h a l e n e i n e t h y l e n e and i n CO2 a r e c o n s i s t e n t w i t h t h e E,j, d a t a i n F i g u r e 3. The p r o p e r way t o make the comparison i s t o u s e t h e enhancement f a c t o r i n s t e a d o f t h e solubility. The enhancement f a c t o r e q u a l s > which i s simply the a c t u a l s o l u b i l i t y d i v i d e d by t h e s o l u b i l i t y i n an i d e a l g a s . The enhancement f a c t o r removes t h e e f f e c t o f v a p o r p r e s s u r e w h i c h i s u s e f u l f o r comparing f l u i d s a t c o n s t a n t reduced temperature b u t at d i f f e r e n t a c t u a l temperatures. I n terms o f t h e f u g a c i t y c o e f f i c i e n t o f t h e s o l u t e , Φ2, t h e enhancement f a c t o r i s g i v e n by

S

Ε = exp(v P/RT)/2

(1)

2

s where V2 i s t h e molar volume o f t h e s o l i d . I f a comparison i s made a t c o n s t a n t reduced temperature and reduced d e n s i t y b u t a t d i f f e r e n t p r e s s u r e s , t h e enhancement f a c t o r removes t h e P o y n t i n g e f f e c t o f p r e s s u r e on t h e condensed phase. I n summary, t h e enhancement f a c t o r i s a measure o f t h e s o l v e n t s t r e n g t h i n t h e SF phase. The enhancement f a c t o r f o r n a p h t h a l e n e i n e t h y l e n e a t 25°C (T = 1.05) i s about 3 t i m e s t h a t i n C 0 a t 45°C (T = 1.05) f o r a wiSe range i n reduced d e n s i t y . The l a r g e r s o l u b i l i t y i n e t h y l e n e i s c o n s i s t e n t w i t h t h e above d i s c u s s i o n c o n c e r n i n g F i g u r e 3, s i n c e n a p h t h a l e n e i s n o t a v e r y s t r o n g Lewis base compared w i t h p h e n o l blue. 2

S o l v e n t e f f e c t on r a t e c o n s t a n t s . In this section, the rate c o n s t a n t w i l l be p r e d i c t e d q u a l i t a t i v e l y i n CO2 f o r t h e D i e l s - A l d e r c y c l o a d d i t i o n o f i s o p r e n e and m a l e i c a n h y d r i d e , a r e a c t i o n w h i c h has been w e l l - c h a r a c t e r i z e d i n t h e l i q u i d s t a t e (23,24). In a p r e v i o u s p a p e r , we used E_ d a t a f o r p h e n o l b l u e i n e t h y l e n e t o p r e d i c t the r a t e constant o f the Menschutkin reaction of t r i p r o p y l a m i n e and m e t h y l i o d i d e ( 1 9 ) . The r e a c t i o n mechanisms a r e q u i t e d i f f e r e n t , y e t t h e s o l v e n t e f f e c t on t h e r a t e c o n s t a n t o f b o t h r e a c t i o n s c a n be c o r r e l a t e d w i t h Ε o f p h e n o l b l u e i n l i q u i d solvents. The d i p o l e moment i n c r e a s e s m t h e M e n s c h u t k i n reaction g o i n g from t h e r e a c t a n t s t a t e t o t h e t r a n s i t i o n s t a t e and i n p h e n o l b l u e d u r i n g e l e c t r o n i c e x c i t a t i o n , so t h a t t h e two phenomena a r e correlated. I n t h e above D i e l s - A l d e r r e a c t i o n , t h e r e a c t i o n c o o r d i n a t e i s i s o p o l a r w i t h a n e g a t i v e a c t i v a t i o n volume ( 8 , 2 3 ) ,

Δν

Φ " W

R

*B - - T W l n k / d P ) x

American Chemical Society Library 1155 16th St., N.W. Washington, D.C. 20036 Squires and Paulaitis; Supercritical Fluids ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

(2)


48

where M

i s the t r a n s i t i o n

s t a t e , A and

Β a r e t h e r e a c t a n t s and

k χ i s t h e r a t e c o n s t a n t based on mole f r a c t i o n u n i t s . Using Regular S o l u t i o n T h e o r y , i t was demonstrated t h a t t h e r a t e c o n s t a n t i n c r e a s e s w i t h the c o h e s i v e energy d e n s i t y ( δ ) o f t h e s o l v e n t f o r t h i s r e a c t i o n as was o b s e r v e d e x p e r i m e n t a l l y ( 2 3 ) . Since there i s l i t t l e d i f f e r e n c e i n t h e d i p o l e moment o f the t r a n s i t i o n s t a t e v e r s u s the r e a c t a n t s , t h e s o l v e n t e f f e c t on t h e r a t e c o n s t a n t i s s m a l l compared w i t h the M e n s c h u t k i n r e a c t i o n . The r a t e c o n s t a n t d a t a f o r the D i e l s - A l d e r r e a c t i o n o f i s o p r e n e and m a l e i c a n h y d r i d e (23,24) may be c o r r e l a t e d w i t h Ε of p h e n o l b l u e a t 35°C by 2


In k χ

= -a E_ + b Τ

(3)

where the c o n s t a n t s a and b a r e -1.053 and 43.70, r e s p e c t i v e l y . U s i n g Eqs. 2 and 3, the a c t i v a t i o n volume may be e x p r e s s e d as Δ ν * = +aRTPk

T

(3E /3p) T

(4)

T

where k i s the i s o t h e r m a l c o m p r e s s i b i l i t y , 1 / ρ ( 9 ρ / 3 Ρ ) and i t i s assumed t h a t a and b a r e p r e s s u r e independent. The d e n s i t y d e r i v a t i v e of E i s r e l a t i v e l y c o n s t a n t compared t o pk^, e s p e c i a l l y i n the h i g h l y c o m p r e s s i b l e r e g i o n , and i s s i m i l a r f o r "both l i q u i d s and s u p e r c r i t i c a l f l u i d s . S i n c | phenol blue e x h i b i t s a red s h i f t , ( 3 E ^ / 3 p ) i s n e g a t i v e , as i s Δν which r e a c h e s a minimum a t the same d e n s i t y where the c o m p r e s s i b i l i t y i s a maximum. The l o g a r i t h m o f the r a t e c o n s t a n t of the above D i e l s - A l d e r r e a c t i o n i s p r e d i c t e d v e r s u s p r e s s u r e i n F i g u r e 4 a t 35°C. The r a t e c o n s t a n t i n c r e a s e s by a f a c t o r o f t e n f o r t h i s p r e s s u r e range w h i c h c o r r e s p o n d s t o a d e n s i t y range o f 6.7 t o 21 m o l / £ . The nega t i v e o f the s l o p e of t h i s p l o t , o r the a c t i v a t i o n volume becomes l a r g e l y n e g a t i v e i n the h i g h l y c o m p r e s s i b l e n e a r c r i t i c a l r e g i o n as shown i n T a b l e I I . ξοτ example, Δν r e a c h e s -4000 a t 75 b a r . At 35°C and 300 b a r , Δν i s o n l y m o d e r a t e l y n e g a t i v e , i . e . , -55 cc/mol compared w i t h -37.4 cc/mol i n l i q u i d e t h y l a c e t a t e a t 35°C. At each p r e s s u r e i n F i g u r e 4, the a c t i v a t i o n volume i s n e g a t i v e s i n c e the magnitude o f v ^ i s l e s s than t h a t o f the sum o f ν and v ^ f o r t h i s c y c l o a d d i t i o n r e a c t i o n (see Eq. 2 ) . In the h i g h l y c o m p r e s s i b l e r e g i o n , the v . s become l a r g e l y n e g a t i v e s i n c e the s o l u t e causes a compression or the f l u i d s o l v e n t as was e x p l a i n e d i n d e t a i l b o t h e x p e r i m e n t a l l y and t h e o r e t i c a l l y (26,2^7» 2 8 ) . As a r e s u l t , the a c t i v a t i o n volume i s a l s o an e x t r e m e l y l a r g e n e g a t i v e number. T

τ>

T

T

1

T a b l e I I . P r e d i c t i o n of the A c t i v a t i o n volume of D i e l s - A l d e r r e a c t i o n between i s o p r e n e and m a l e i c a n h y d r i d e i n s u p e r c r i t i c a l carbon d i o x i d e a t 35°C Pressure (bar) AV* (cc/mol)

75

80

-4000

-2000

the

85

100

200

300

-950

-225

-70

-55


4.

KIM AND JOHNSTON


56

• ι

...

Ί

Δ Δ Ο

°*

54h


• 52

50'

•

•

ι

1

1.0

2.0

Reduced

Density

F i g u r e 3. E-j- o f p h e n o l b l u e i n s e v e r a l f l u i d s v s . reduced d e n s i t y (Δ = C0 - 45 °C, Ο = C H - 25 °C ( 1 9 ) , and • = CHF - 40 °C ( 1 9 ) . 2

2

4

3

-5.6

* -5.8

&0 ο -6.2

100 200 300 Pressure (bar)

F i g u r e 4. P r e d i c t e d r a t e c o n s t a n t f o r the D i e l s - A l d e r of i s o p r e n e and m a l e i c anhydride, i n CO2 a t 35 °C.

reaction


49


50

The e x t r e m e l y pronounced s o l v e n t e f f e c t i n the n e a r c r i t i c a l r e g i o n can a l s o be e x p l a i n e d u s i n g Eq. 4. As mentioned above, (3E /3p) i s s i m i l a r f o r b o t h l i q u i d s and s u p e r c r i t i c a l f l u i d s . However, the magnitude o f a c t i v a t i o n volume can be much l a r g e r i n s u p e r c r i t i c a l f l u i d s because o f the much h i g h e r c o m p r e s s i b i l i t y . T h i s a n a l y s i s can a l s o be a p p l i e d t o the M e n s c h u t k i n r e a c t i o n of t r i p r o p y l a m i n e and m e t h y l i o d i d e , w h i c h has an a c t i v a t i o n volume of -65 cc/mol i n l i q u i d C C l ^ a t 30°C. In e t h y l e n e a t 66 b a r and 25°C, Δν i s p r e d i c t e d t o be -5000 c c / m o l . Both of t h e s e r e a c t i o n s e x h i b i t an e x t r e m e l y pronounced s o l v e n t e f f e c t i n the n e a r c r i t i c a l r e g i o n s i n c e the r e a c t i o n s have r e l a t i v e l y l a r g e ( i n magnitude) a c t i v a t i o n volumes even i n l i q u i d s . The s o l v e n t e f f e c t on the M e n s c h u t k i n r e a c t i o n would be even more pronounced i n a s u p e r c r i t i c a l f l u i d w i t h a d i p o l e moment where the " s o l v e n t s t r e n g t h " would be even more s e n s i t i v e t o d e n s i t y . These p r e d i c t i o n s suggest t h a t f u t u r e measurements o f r a t e c o n s t a n t s i n s u p e r c r i t i c a l f l u i d s c o u l d p o t e n t i a l l y demonstrate a s o l v e n t e f f e c t of o r d e r s of magnitude.


T

T

L o c a l s o l v e n t compression. The next a p p l i c a t i o n o f the s o l v a t o chromic d a t a w i l l be to d e t e r m i n e the magnitude of the l o c a l c o m p r e s s i o n of a s u p e r c r i t i c a l f l u i d s o l v e n t i n the immediate environment of the s o l u t e . The E^ of a dye such as p h e n o l b l u e can be p r e d i c t e d i n l i q u i d s where no s p e c i f i c i n t e r a c t i o n s are p r e s e n t by t r e a t i n g the s o l v e n t as a homogeneous p o l a r i z a b l e d i e l e c t r i c (22,29). The i n t r i n s i c " s o l v e n t s t r e n g t h " , Ε ^ ° , d e s c r i b e s d i s p e r s i o n , i n d u c t i o n , and d i p o l e - d i p o l e f o r c e s and i s g i v e n by ( 2 2 ) .

T

D

2n2 l

+

2

n2

+

+ 2

where η i s the r e f r a c t i v e i n d e x and D i s the d i e l e c t r i c c o n s t a n t . The c o n s t a n t s A, Β and C a r e f u n c t i o n s o f the p r o p e r t i e s of the dye such as the d i p o l e moment and o s c i l l a t o r s t r e n g t h o f t h e ground and e x c i t e d s t a t e s and the c a v i t y r a d i u s . The f i r s t term i n Eq. 5 i n c l u d e s d i s p e r s i o n and s o l u t e permanent d i p o l e - s o l v e n t i n d u c e d d i p o l e f o r c e s , thus i t i s a f u n c t i o n o f the r e f r a c t i v e i n d e x of the solvent. The second term d e s c r i b e s the e f f e c t s of permanent d i p o l e - d i p o l e f o r c e s ( o r i e n t a t i o n ) . The Ε^° of p h e n o l b l u e was c o r r e l a t e d s u c c e s s f u l l y w i t h Eq. 5 f o r 21 non-hydrogen b o n d i n g l i q u i d s o l v e n t s (20,22,29). The measured t r a n s i t i o n energy, Ε , i n c l u d e s the i n t r i n s i c " s o l v e n t s t r e n g t h " g i v e n by Eq. 5 and the s p e c i f i c " s o l v e n t strength", Ε , w h i c h d e s c r i b e s an e x a g g e r a t e d s o l v e n t e f f e c t such as hydrogen B o n d i n g such t h a t

E

T

( e x p e r i m e n t a l ) = E°

+ E^

(6)

g F o r p h e n o l b l u e , the Ε i s z e r o f o r e t h y l e n e and C F C 1 , but non z e r o f o r the Lewis a c i d s C F H and C 0 . One of the a t t r a c t i v e f e a t u r e s of s o l v a t o c h r o m i c s c a l e s i s t h a t the n o n - s p e c i f i c and s p e c i f i c i n t e r a c t i o n s may be s e p a r a t e d s i n c e the former can be c a l c u l a t e d s t r a i g h t f o r w a r d l y u s i n g Eq. 5. The E^ i s not i n f l u e n c e d by f a c t o r s such as r e p u l s i v e f o r c e s 3

3

2



4.

51


KIM AND JOHNSTON

between the s o l u t e and s o l v e n t s i n c e they a r e i d e n t i c a l i n the ground and e x c i t e d s t a t e s . The l o c a t i o n s of the m o l e c u l e s do not change d u r i n g the time frame o f e l e c t r o n i c e x c i t a t i o n . The theory f o r s o l u b i l i t y phenomena i s much more c o m p l i c a t e d ; f o r example, i t i n c l u d e s r e p u l s i v e f o r c e s . As a r e s u l t , s o l u b i l i t y d a t a g i v e l e s s i n f o r m a t i o n about the p r o p e r t i e s of the s o l v e n t , o r the l o c a l s o l v e n t environment about the s o l u t e . In o r d e r t o a n a l y z e the b e h a v i o r of p h e n o l b l u e i n CO2> i t i s u s e f u l t o r e v i e w the r e s u l t s f o r e t h y l e n e s i n c e i t has a s p e c i f i c " s o l v e n t s t r e n g t h " o f z e r o (19, see F i g u r e 5 ) . The dashed l i n e was c a l c u l a t e d u s i n g Eq. 5 where the c o n s t a n t s A and Β were o b t a i n e d from the l i t e r a t u r e (20,30) and C was chosen t o f o r c e agreement w i t h experiment i n the dense i n c o m p r e s s i b l e r e g i o n . The dashed l i n e f i t s the d a t a at h i g h d e n s i t y where e t h y l e n e i s r e l a t i v e l y incompressible. At a lower d e n s i t y , e.g. 7 mol/1, e t h y l e n e i s h i g h l y c o m p r e s s i b l e so t h a t i t " c l u s t e r s " about the s o l u t e due t o a t t r a c t i v e f o r c e s . E c k e r t e t a l (27,28) measured s o l u t e p a r t i a l m o l a r volumes on the o r d e r of -10 1/mol i n C0« and i n e t h y l e n e i n the h i g h l y c o m p r e s s i b l e r e g i o n . T h i s c l u s t e r i n g or l o c a l c o m p r e s s i o n phenomenon which i n c r e a s e s the number of s o l v e n t m o l e c u l e s n e a r the s o l u t e causes an a d d i t i o n a l r e d s h i f t o f 1 k c a l / m o l a t a d e n s i t y of 7 mol/1. The a d d i t i o n a l r e d s h i f t i s the d i f f e r e n c e between the e x p e r i m e n t a l p o i n t and t h a t w h i c h i s p r e d i c t e d u s i n g the t h e o r y f o r a homogeneous l i q u i d shown by the dashed l i n e . T h i s d i f f e r e n c e becomes s m a l l as the isothermal c o m p r e s s i b i l i t y d i m i n i s h e s as e x p l a i n e d below. The l o c a l d e n s i t y of s o l v e n t about the s o l u t e may be d e t e r m i n e d by comparing the e x p e r i m e n t a l and c a l c u l a t e d c u r v e s . C o n s i d e r p o i n t s A and Β i n F i g u r e 5 a t a c o n s t a n t v a l u e of E^, i . e . , 55 k c a l / m o l . A h y p o t h e t i c a l homogeneous f l u i d a t p o i n t Β g i v e s the same " s o l v e n t s t r e n g t h " as £he a c t u a l f l u i d a t p o i n t A.^ The l o c a l d e n s i t y about the s o l u t e exceeds the b u l k d e n s i t y P^ due t o c o m p r e s s i o n , such t h a t

P p B

i

A

r

=VT

(7)

ij

J

o

where g . . ( r ) i s the u n l i k e p a i r r a d i a l d i s t r i b u t i o n f u n c t i o n . U s i n g K i i k w o o d - B u f f s o l u t i o n t h e o r y ( 3 1 ) , i t was shown t h a t the d i f f e r e n c e between the l o c a l and b u l k d e n s i t i e s i s (19) 1 P l 2

Pk

"

p

=

-1ΪΓ

Tk (1

"

V 2

/ k

T

B V

( 8 )

where V12 i s a measure o f the volume of the f i r s t c o o r d i n a t i o n shell. Based on p r e v i o u s r e s u l t s ( E c k e r t e t a l . , 27, 28), i t i s r e a s o n a b l e t o assume

_ 00 V2

= al^

+ b


(9)

52


56


\

\

\

\

\

53 6

10

15

Density

(mol/L)

F i g u r e 5. E of phenol b l u e i n e t h y l e n e v s . d e n s i t y ( O = 25 °C, Δ = 10 °C, and i s c a l c u l a t e d E using Equation 5). T

T

U s i n g Eqs. 8 and 9, t h e f i n a l r e s u l t i s 1 (Pl

!

2

- P)/P = a k

T

+ b

f

(10)

?

where a and b* a r e f u n c t i o n s o f temperature and V . The l i n e a r i t y suggested by Eq. 10 has been o b t a i n e d from t h e d a t a i n Figure 5 (19). 1 2

The C 0 d a t a i n F i g u r e 2 a r e more d i f f i c u l t t o a n a l y z e because of t h e a c i d - b a s e i n t e r a c t i o n s . The dashed l i n e i s t h e c a l c u l a t e d r e s u l t f o r E^° o f a homogeneous p o l a r i z a b l e d i e l e c t r i c ( E q . 5) u s i n g t h e same v a l u e s o f t h e c o n s t a n t s A, B, and C as o b t a i n e d above f o r e t h y l e n e . A t h i g h d e n s i t y , where t h e l o c a l compression e f f e c t d i s a p p e a r s , the s p e c i f i c " s o l v e n t s t r e n g t h " which i s the d i f f e r e n c e between t h e d a t a and Ε^° i s about 0.7 k c a l / m o l . To p u t t h i s i n p e r s p e c t i v e , t h e s p e c i f i c " s o l v e n t s t r e n g t h s " a r e 6.3, 1.6, 1.3 f o r p h e n o l b l u e i n t h e l i q u i d s o l v e n t s m - c r e s o l ( s t r o n g Lewis a c i d ) , m e t h a n o l , and c h l o r o f o r m , r e s p e c t i v e l y ( 2 0 , 3 0 ) ) . In the h i g h l y c o m p r e s s i b l e r e g i o n , t h e r e d s h i f t exceeds t h e dashed l i n e due t o two c o u p l e d e f f e c t s , a c i d - b a s e f o r c e s , and l o c a l s o l v e n t compression. 2

The f i n a l s e t o f s o l v a t o c h r o m i c d a t a a r e shown i n F i g u r e 6 f o r p h e n o l b l u e i n SF C 0 doped w i t h v a r i o u s amounts o f t h e c o - s o l v e n t o r entraîner, m e t h a n o l . C o n s i d e r a p r e s s u r e o f 100 b a r where t h e E of phenol blue i n C 0 i s 54 k c a l / m o l . The r e d s h i f t i s i n c r e a s e d more by t h e a d d i t i o n o f 3.5 mole p e r c e n t methanol a t c o n s t a n t p r e s s u r e t h a n by an i n c r e a s e i n t h e p r e s s u r e o f p u r e C 0 of o v e r 200 b a r . The l a r g e s p e c i f i c " s o l v e n t s t r e n g t h " o f methanol causes t h i s b e h a v i o r . The r e d s h i f t caused by t h e c o - s o l v e n t i s i n 2

T

2

2


KIM AND JOHNSTON


53


4.

F i g u r e 6. E-p o f p h e n o l b l u e i n C0 -methanol m i x t u r e s C0 , Δ = C0 - 1% CH OH, 0 = C0 - 3.5% CH OH). 2

2

2

3

2

(•=

3


pure


54

e x c e s s o f t h e amount c a l c u l a t e d i f i t i s assumed t h a t the m i x t u r e i s random. T h i s i n d i c a t e s t h a t the dye i s s o l v a t e d p r e f e r e n t i a l l y by methanol such t h a t methanol's l o c a l c o n c e n t r a t i o n exceeds i t s b u l k c o n c e n t r a t i o n . A l a r g e number o f s o l u b i l i t i e s o f s o l i d s were measured i n C 0 w i t h and w i t h o u t c o - s o l v e n t by J o h n s t o n and co-workers (32,33). I n many o f these systems, s m a l l amounts o f c o - s o l v e n t s produced a g r e a t e r i n c r e a s e i n t h e s o l u b i l i t y t h a n p r e s s u r e i n c r e a s e s o f hundreds o f atmospheres. The r e l a t i o n s h i p between t h e s p e c t r o s c o p i c d a t a and t h e s o l u b i l i t y d a t a i s t h e s u b j e c t o f ongoing r e s e a r c h . 2


Acknowledgment s T h i s m a t e r i a l i s based on work supported by the N a t i o n a l S c i e n c e F o u n d a t i o n under Grant No. CPE-8306327. Any o p i n i o n s , f i n d i n g s , and c o n c l u s i o n s o r recommendations expressed i n t h i s p u b l i c a t i o n do not n e c e s s a r i l y r e f l e c t t h e v i e w s o f the N a t i o n a l S c i e n c e Founda tion. Acknowledgment i s made t o t h e Donors o f t h e P e t r o l e u m R e s e a r c h Fund, a d m i n i s t e r e d by the American C h e m i c a l S o c i e t y , f o r p a r t i a l support o f t h i s work. F u r t h e r support i s acknowledged from the Dow C h e m i c a l Company F o u n d a t i o n and t h e S e p a r a t i o n s Research Program a t The U n i v e r s i t y o f Texas.

Literature Cited 1. Zosel, K. Angew. Chem. Int. Ed. 1978, 17, 702. 2. Paulaitis, M. E.; Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Rev. in Chem. Eng. 1983 1(2), 179. 3. Johnston, K. P. "Kirk-Othmer Encyclopedia of Chemical Technology," John Wiley & Sons: New York, 1984. 4. McHugh, M. A. "Extraction with Supercritical Fluids," in "Recent Development in Separation Science," Li, Ν. N. and Carlo, J. Μ., Eds., CRC Press: Boca Raton, 1984; Vol. IX. 5. Randall, L. G. Sep. Sci. Technol. 1982, 17(1), 1. 6. Alexander, G.; Paulaitis, M. E. AIChE Annual Meeting, #140d, San Francisco, 1984. 7. Simmons, G. M.; Mason, D. M. Chem. Eng. Sci. 1972, 27, 89. 8. Reichardt, C. "Solvent Effects in Organic Chemistry," Verlag Chemie, Weinheim, New York, 1979. 9. Dack, M.R.J., "Solutions and Solubilities Part II," John Wiley & Sons: New York, 1976. 10. Tamura, K.; Imoto, T. Bull. Chem. Soc. of Japan 1975, 48(2), 369. 11. Reichardt, C. Angew. Chem. Int. Ed. 1979, 18, 98. 12. Kamlet, M. J.; Hall, T. N.; Taft, R. W. J. Org. Chem. 1979, 44, 2599. 13. Kamlet, M. J.; Abboud, J. L.; Taft, R. W. J. Amer. Chem. Soc. 1981, 103(5), 1080. 14. Taft, R. W.; Abraham, M. C.; Doherty, R. M.; Kamlet, M. J. Nature 1985, 313(31), 384. 15. Hyatt, J. A. J. Org. Chem. 1984, 49, 5097. 16. Sigman, M. E.; Lindley, S. M.; Leffler, J. E. J. Amer. Chem. Soc. 1985, 107, 1471. 17. Kamlet, M. J.; Abboud, J. L.; Taft, R. W. J. Amer. Chem. Soc. 1977, 99(18), 6027.



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18. Kamlet, M. J.; Abboud, J. L.; Abraham, M. H.; Taft, R. W. J. Org. Chem. 1983, 48, 2877. 19. Kim, S.; Johnston, K. P. "Molecular Interactions in Dilute Supercritical Fluid Solutions," Submitted to Ind. Eng. Chem. Fund. 1985. 20. Figueras, J. J. Amer. Chem. Soc. 1972, 93(13), 3255. 21. Kolling, O. W. Anal. Chem. 1981, 53, 54. 22. McRae, E. G. J. Phys. Chem. 1957, 61, 562. 23. Grieger, R. Α.; Eckert, C. A. Trans. Faraday Soc. 1970, 66, 2579. 24. Eckert, C. Α.; Hsieh, C. R.; McCabe, J. R. AIChE J. 1974, 20(1), 20. 25. Silber, E. Ph.D. Thesis, Texas Tech. Univ, 1971. 26. Eckert, C. Α.; Paulaitis, M. E.; Johnston, K. P. J. Phys. Chem. 1981, 85, 1770. 27. Eckert, C. Α.; Ziger, D. H.; Johnston, K. P.; Ellison, T. K. Fluid Phase Equilib. 1983, 14, 167. 28. Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J. Phys. Chem. 1986 (in press). 29. Mataga, N.; Kubota, T. "Molecular Interactions and Electronic Specta," Marcel Dekker, Inc.: New York, 1970. 30. Kolling, O. W.; Goodnight, J. L. Anal. Chem. 1973, 45(1), 160. 31. Kirkwood, J. C.; Buff, F. P. J. Chem. Phys. 1951, 19(6), 774. 32. Johnston, K. P.; Dobbs, J. M.; Wong, J. M.; Lahiere, R. J. Ind. Eng. Chem. Fund. 1986 (in press). 33. Johnston, K. P.; Dobbs, J. M.; Wong, J. M. J. Chem. Eng. Data 1986 (in press). RECEIVED June

25, 1986


Effects of Supercritical Solvents on the Rates of Homogeneous

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