Sorption and Diffusion of Monocyclic Aromatic Compounds Through

Chapter 19

Sorption and Diffusion of Monocyclic Aromatic Compounds Through Polyurethane Membranes 1

1

2

U. Shanthamurthy Aithal , Tejraj M.Aminabhavi ,and PatrickE.Cassidy 1

Department of Chemistry, Karnatak University, Dharwad, 580003, India Department of Chemistry, Southwest Texas State University, San Marcos, TX 78666

Downloaded by UNIV LAVAL on July 12, 2016 | http://pubs.acs.org Publication Date: May 9, 1990 | doi: 10.1021/bk-1990-0423.ch019

2

Sorption and transport of a number of monocyclic aromatics through a polyurethane membrane have been investigated at 25, 44 and 60°C based on an immersion/weight gain method. Activation parameters for the process of diffusion, permeation and sorption are found to follow the conventional wisdom that larger molecules exhibit lower diffusivities and higher activation energies. From a temperature dependence of the sorption constant, the standard enthalpy and entropy have been determined. The molar mass between c r o s s l i n k s has been determined by using the Flory-Rehner theory. Furthermore, results have been discussed in terms of the thermodynamic interactions between the polymer and penetrants. P o l y u r e t h a n e e l a s t o m e r s a r e known t o e x h i b i t unique mechanical p r o p e r t i e s , p r i m a r i l y as a r e s u l t of two p h a s e m o r p h o l o g y (_1 ). These m a t e r i a l s a r e alternating b l o c k copolymers made of h a r d segments of a r o m a t i c groups from t h e d i i s o c y a n a t e / c h a i n e x t e n d e r and soft segments of a l i p h a t i c c h a i n s from t h e d i o l ( e t h e r o r e s t e r ) . The h a r d and soft segments a r e c h e m i c a l l y i n c o m p a t i b l e and m i c r o p h a s e s e p a r a t i o n of t h e h a r d segments into domains d i s p e r s e d i n a m a t r i x of soft segments c a n occur i n v a r y i n g d e g r e e s . In v i e w of the i m p o r t a n c e of p o l y u r e t h a n e as a b a r r i e r m a t e r i a l i n s e v e r a l e n g i n e e r i n g areas (_2»_3), i t i s i m p o r t a n t t o know i t s t r a n s p o r t characteristics w i t h r e s p e c t to common o r g a n i c s o l v e n t s . Thus, k n o w l e d g e of t h e t r a n s p o r t mechanisms as m a n i f e s t e d b y s o r p t i o n , diffusion and permeation of o r g a n i c liquids (penetrants) i n a polyurethane matrix i s helpful f o r establishing the relationships between structures and p r o p e r t i e s under severe application c o n d i t i o n s . A l t h o u g h some p r e v i o u s s t u d i e s (4 -10) have been made on s o l v e n t t r a n s p o r t t h r o u g h p o l y u r e t h a n e , more e x p e r i m e n t a l data a r e s t i l l needed f o r a b e t t e r u n d e r s t a n d i n g of t h e t h e r m o d y n a m i c interactions between t h e polymer and solvents. The p r i n c i p a l o b j e c t i v e of t h i s paper i s to f o l l o w t h e t r a n s p o r t p r o p e r t i e s of

0097-6156/90/0423-0351$07.50/0 © 1990 American Chemical Society

Koros; Barrier Polymers and Structures ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

352

BARRIER POLYMERS AND STRUCTURES

monocyclic aromatic liquids through a commercially available p o l y u r e t h a n e membrane. I t i s e x p e c t e d t h a t a s y s t e m a t i c change i n s o l v e n t power would l e a d to r e s u l t s w h i c h c o u l d be i n t e r p r e t e d by c o n s i d e r i n g t h e p o s s i b l e i n t e r a c t i o n s w i t h soft and h a r d segments of the polymer. Transport properties v i z . , diffusivity, D, permeability, P, and s o r p t i o n , S, have been s t u d i e d o v e r an i n t e r v a l of t e m p e r a t u r e from 25 to 60°C, to p r e d i c t t h e A r r h e n i u s p a r a m e t e r s f o r each of t h e t r a n s p o r t p r o c e s s e s i n v o l v e d . F u r t h e r more, t h e r e s u l t s have been d i s c u s s e d i n terms of t h e r m o d y n a m i c i n t e r a c t i o n s between p o l y u r e t h a n e and t h e l i q u i d p e n e t r a n t s . Molar mass, M^, between c r o s s l i n k s have been e s t i m a t e d b y u s i n g t h e F l o r y - R e h n e r model (11,12).


EXPERIMENTAL REAGENTS AND MATERIALS. P o l y u r e t h a n e ( P U ) used was o b t a i n e d from PSI, A u s t i n , T e x a s i n s h e e t s of 0.250 cm t h i c k n e s s . T h e base p o l y m e r i s a V i b r a t h a n e B600 ( U n i r o y a l ) w h i c h was o b t a i n e d from the r e a c t i o n of p o l y p r o p y l e n e o x i d e and 2,6-toluene d i i s o c y n a t e (TDI). T h e base p o l y m e r was c u r e d w i t h 4, 4 ' - m e t h y l e n e - b i s ( o - c h l o r o a n i l i n e ) i . e . , MOCA, to g i v e t h e p o l y u r e t h a n e . T h u s , t h e t w o - p h a s e m o r p h o l o g y of PU c o n s i s t e d of p o l y e t h e r d i o l as t h e soft segment and t h e a r o m a t i c d i i s o c y n a t e a c t i n g as t h e h a r d segment. The d r i v i n g f o r c e f o r t h e phase s e p a r a t i o n i s t h e i n c o m p a t i b i l i t y of t h e h a r d and soft segments. A s c h e m a t i c a l d e s c r i p t i o n of t h e m o l e c u l a r s t r u c t u r e of t h e p o l y u r e t h a n e used i s g i v e n below : V^A/W-

AC — A B A B A B A B A B A — ι

J—ι

soft where,

1

CA — i

hard

_

soft

A : +-CM- C H 4 j 4 2

i

BABABAB-vvwvw, ι

ι

hard Β : —f- O — f C H 4 y 4 2

Some r e p r e s e n t a t i v e e n g i n e e r i n g p r o p e r t i e s of PU a r e t e n s i l e s t r e n g t h , 387 k g / s q . cm ( 5500 p s i ) ; maximum p e r c e n t elongat i o n , 430; modulus f o r 300% e l o n g a t i o n , 155 k g / s q . cm ( 2200 p s i ) ; tear s t r e n g t h , 5 kg/sq.cm(70 p s i ) (ASTM D- 470) and s p e c i f i c g r a v i t y 1.101. T h e Τ of t h e p o l y m e r was found to be -43.27°C w i t h a heat f l o w of - 1.420 Watts/g as d e t e r m i n e d by differential scanning c a l o r i m e t r y , duPont model 951. The s o l v e n t s g i v e n i n T a b l e I a r e of reagent grade and d o u b l e d i s t i l l e d b e f o r e u s e . DIFFUSION E X P E R I M E N T S : P o l y u r e t h a n e e l a s t o m e r s were cut into u n i f o r m s i z e c i r c u l a r p i e c e s ( d i a m e t e r = 1.9 cm) u s i n g a s p e c i a l l y designed, sharp-edged, s t e e l d i e and d r i e d o v e r n i g h t i n a d e s i c c a t o r b e f o r e use. T h e t h i c k n e s s of t h e sample was measured at s e v e r a l points using a micrometer ( p r e c i s i o n ± 0.001 cm) and t h e mean v a l u e was taken as 0.250 cm. D r y w e i g h t s of t h e cut s a m p l e s were taken b e f o r e i m m e r s i o n into t h e a i r t i g h t , m e t a l - c a p p e d test b o t t l e s c o n t a i n i n g t h e l i q u i d . A f t e r i m m e r s i o n into t h e r e s p e c t i v e l i q u i d s , t h e b o t t l e s were p l a c e d i n a t h e r m o s t a t i c a l l y c o n t r o l l e d oven (± 0.5°C).


19.

AITHAL ET AL.

Sorption and Diffusion Through Polyurethane Membranes 353


At p e r i o d i c i n t e r v a l s , the samples were r e m o v e d from the b o t t l e s , the wet s u r f a c e s were d r i e d between f i l t e r paper w r a p s and w e i g h e d i m m e d i a t e l y to the nearest 0.05 mg by p l a c i n g i t on a c o v e r e d w a t c h g l a s s w i t h i n the chamber of the balance. The samples w e r e p l a c e d back into test b o t t l e s and were t r a n s f e r r e d to the oven. The e x p e r i m e n t s were p e r f o r m e d at 25, 44 and 60°C. A p o s s i b l e source of e r r o r i n t h i s method i s t h a t the sample has to be removed from the l i q u i d to a l l o w w e i g h i n g ; i f t h i s i s done q u i c k l y (say w i t h i n 30-50 sees) c o m p a r e d to the time a sample spent i n the l i q u i d i n between c o n s e c u t i v e w e i g h i n g s , the sample r e m o v a l e x e r t s a n e g l i g i b l e e f f e c t . F o r those l i q u i d s whose d e n s i t y i s g r e a t e r than the p o l y m e r i t s e l f , the sample was k e p t submerged i n the l i q u i d by a g l a s s - p l u n g e r a t t a c h e d to the s c r e w cap. RESULTS AND SORPTION

DISCUSSION

KINETICS.

Room

temperature

sorption curves

expressed 1

as p e r c e n t penetrant u p t a k e , Q ( t ) , v e r s u s s q u a r e root of t i m e , t are d i s p l a y e d i n F i g u r e s 1 and 2. A p e r u s a l of the s o r p t i o n c u r v e s g i v e n i n F i g u r e 1 suggests a s y s t e m a t i c t r e n d i n the s o r p t i o n behavior of methyl substituted benzenes. For instance, the s o r p t i o n of benzene i s h i g h e r than o t h e r homologues; a l s o , benzene reaches sorption equilibrium more quicker than toluene, px y l e n e and m e s i t y l e n e . T h i s may be due to the presence of more b u l k i e r -CH^ groups r e n d e r i n g a s l u g g i s h movement of the s o l v e n t w i t h i n the p o l y m e r m a t r i x . The s o r p t i o n c u r v e s of o t h e r a r o m a t i c s , namely, bromobenzene, o-dichlorobenzene, nitrobenzene, chlorobenzene and a n i s o l e are p r e s e n t e d i n F i g u r e 2. Here, bromobenzene e x h i b i t s a maximum Q(t) of about 147% (the maximum of a l l the p e n e t r a n t s ) w h e r e a s a n i s o l e has o n l y about 80%. T h u s , i t i s c l e a r that c h l o r o , bromo, n i t r o and methoxy s u b s t i t u t i o n s on the benzene moiety tend to i n c r e a s e the extent of s o r p t i o n w i t h the p o l y u r e t h a n e membrane. The maximum s o r p t i o n of a l l the penetrants follow the sequence : Bromobenzene > o - d i c h l o r o b e n z e n e > c h l o r o b e n z e n e κ n i t r o b e n z e n e > a n i s o l e > benzene > toluene > p - x y l e n e > m e s i t y l e n e . S o r p t i o n data a l s o s e r v e as a guide to s t u d y the e f f e c t of t e m p e r a t u r e on the o b s e r v e d transport behavior. Temperature v a r i a t i o n of s o r p t i o n c u r v e s f o r some r e p r e s e n t a t i v e penetrants namely, benzene, m e s i t y l e n e , a n i s o l e , bromobenzene and o - d i c h l o r o benzene a r e i n c l u d e d i n F i g u r e s 3-7. In almost a l l c a s e s , the s h a p e s of s o r p t i o n c u r v e s at 25°C a r e s i m i l a r to those at the two h i g h e r t e m p e r a t u r e s , a l t h o u g h the change i n s l o p e i s more pronoun ced between 25 and 44°C than between 44 and 60°C. F o r a l l the penetrants except benzene and bromobenzene, the maximum s o r p t i o n v a l u e s at 44 and 60°C seem to be more or l e s s i d e n t i c a l . 2

F o r a F i c k i a n b e h a v i o r , the p l o t s of Q(t) v e r s u s t should increase linearly up to about 50% sorption. Deviations from the F i c k i a n s o r p t i o n a r e a s s o c i a t e d w i t h the time t a k e n by the p o l y m e r segments to r e s p o n d to a s w e l l i n g s t r e s s and r e a r r a n g e


354


BARRIER P O L Y M E R S AND STRUCTURES

]

Figure 1 Percentage mass uptake Q(t) of the polymer versus square root of time t for polyurethane (PU) + solvent pairs at 25 C. β



AITHAL ET AL.

0


15

30

45 v 1 (min) 7

60

75

90

•

Figure 2 Percentage mass uptake Q(t) of the polymer versus square root of time t for polyurethane (PU) + solvent pairs at 25 C. β


1/2

356



0

15

30

45

60

J t (min) Figure 3 Temperature dependence of percentage mass uptake Q(t) of the polymer versus t for polyurethane + Benzene system. 1/2




AITHAL E T

Figure 4 Temperature dependence of percentage mass uptake Q(t) versus t polyurethane + Mesitylene system.


1/2

for



358




AITHAL ET AL.




360


19.

AITHAL ET AL.

Sorption andDiffusion Through Polyurethane Membranes 361

themselves to accommodate the solvent molecules. This usually r e s u l t s i n t h e s i g m o i d a l s h a p e s f o r t h e s o r p t i o n c u r v e s : T h u s , nonFickian diffusion involves the tension between swollen (soft segments) and the u n s w o l l e n ( h a r d segments) p a r t s of polyurethane as the l a t t e r tend to r e s i s t f u r t h e r s w e l l i n g . However, during early stages of s o r p t i o n , the s a m p l e s may not r e a c h the t r u e e q u i l i b r i u m c o n c e n t r a t i o n of the penetrant and t h u s , t h e r a t e of s o r p t i o n b u i l d s up s l o w l y to p r o d u c e s l i g h t c u r v a t u r e s as shown i n F i g u r e s 1-7. T h i s i s i n d i c a t i v e of the d e p a r t u r e from the F i c k i a n mode and i s further confirmed from an a n a l y s i s of s o r p t i o n data by u s i n g the f o l l o w i n g e q u a t i o n (JJ^.J^) :


log

(M

/M ) œ

= log k + η log t

(1)

Here, the constant k d e p e n d s on the structural characteristics of the p o l y m e r i n a d d i t i o n to i t s i n t e r a c t i o n w i t h the s o l v e n t ; and a r e r e s p e c t i v e l y , the mass u p t a k e at time t and at e q u i l i b r i u m , t . The magnitude of η d e c i d e s t h e t r a n s p o r t mode; f o r i n s t a n c e , a v a l u e of η = 0.5 suggests the F i c k i a n mode and f o r η = 1, a n o n - F i c k i a n d i f f u s i o n mode i s p r e d i c t e d . H o w e v e r , the intermediate values ranging from η = 0.5 to u n i t y suggest the p r e s e n c e of anomalous t r a n s p o r t mechanism. F r o m a l e a s t - s q u a r e s a n a l y s i s , t h e v a l u e s of η and k have been e s t i m a t e d and these are included in Table I, and F i g u r e 8 r e p r e s e n t s a t y p i c a l p l o t f o r benzene and toluene. The a v e r a g e u n c e r t a i n t y i n the e s t i m a t i o n of η i s around ±0.007. The v a l u e of η do not i n d i c a t e any s y s t e m a t i c v a r i a t i o n w i t h t e m p e r a t u r e H o w e v e r , a general v a r i a t i o n of η from a minimum v a l u e of 0.53 to a maximum of 0.74 i n d i c a t e s t h a t the anomalous t y p e t r a n s p o r t mechanism is operative and the diffusion is slightly deviated from the F i c k i a n t r e n d . T h i s f a c t can be further substantiated 3

from the c u r v a t u r e d e p e n d e n c i e s of Q(t) v s . t p l o t s shown i n Figures 1-7. Such o b s e r v a t i o n s a r e a l s o e v i d e n t from the work of N i c o l a i s et a l . (_15) f o r n-hexane t r a n s p o r t i n g l a s s y p o l y s t y r e n e A t e m p e r a t u r e dependence of k suggests t h a t i t i n c r e a s e s w i t h a r i s e i n t e m p e r a t u r e f o r a l l the p e n e t r a n t s e x c e p t j D - x y l e n e and bromobenzene. F u r t h e r m o r e , k a p p e a r s to d e p e n d on s t r u c t u r a l characteristics of the penetrant molecules i.e., it decreases successively from benzene to mesitylene; this decrease in k parallels the decrease i n the values of sorption equilibrium. S i m i l a r l y , f o r c h l o r o b e n z e n e to n i t r o b e n z e n e via o-dichlorobenzene k d e c r e a s e s s u c c e s s i v e l y . T h u s , i t a p p e a r s t h a t k not o n l y depends on the structural characteristics of the p o l y m e r and penetrant molecules, but a l s o on s o l v e n t i n t e r a c t i o n s w i t h the polyurethane c h a i n s . At any r a t e , the g r e a t e r tendency f o r n o n - F i c k i a n c o e f f i cients in Equation (1) seen f o r 60°C, may r e f l e c t some a s p e c t of s w e l l i n g of i n t e r p h a s e r e g i o n s between the h a r d and soft domains.

—

TRANSPORT

COEFFICIENTS:

portion

the

of

sorption

From curves

the

slope

i . e . , Q(t)

j

initial

t ,

the

θ , of the vs.


linear

diffusion

362


Table

I

Analysis o f Penetrant Transport at Various

Molecular


Penetrant

Volume χ 1 0

Temperatures

Exponent 2 3

(g/g-hr)102 Q(t) (Eq 1) (X o f d r y sample wt)

Temp

η

(cm3/molecule)

(°C)

(Eq 1)

Benzene

14.85

25 44 60

0.554 0.593 0.599

2.809 3.295 3.975

71.01 72.15 74.14

Toluene

17.75

25 44 60

0.567 0.600 0.599

2.602 3.207 3.874

60.17 59.09 60.08

£-xylene

20.48

25 44 60

0.561 0.557 0.595

2.295 3.334 3.021

49.68 49.95 49.31

Mesitylene

23.19

25 44 60

0.532 0.571 0.602

1.261 2.203 2.444

40.15 41.52 41.99

Anisole

18.16

25 44 60

0.566 0.585 0.581

2.166 2.765 3.227

80.25 83.89 82.80

Nitrobenzene

17.14

25 44 60

0.602 0.584 0.618

1.134 1.797 1.839

106.32 107.17 114.81

Chlorobenzene

16.98

25 44 60

0.588 0.569 0.584

2.371 3.597 3.739

105.52 109.08 108.84

o-Dichlorobenzene

18.78

25 44 60

0.583 0.565 0.589

1.658 2.441 2.625

131.36 131.17 131.52

Bromobenzene

17.53

25 44 60

0.575 0.586 0.736

2.300 2.790 1.600

147.50 150.06 151.58

m a x


AITHAL E T A L .


Γ

1


τ

J 1.2

I

I

L

1.5

1.8

2.1

log t Figure 8 Log

•

versus log t for polyurethane + Benzene and polyurethane +

Toluene systems.


364


c o e f f i c i e n t s D, h a v e been c a l c u l a t e d

b y using (16,17)

D = π(ηθ/4Μ

)

2

(2)

00 Here, M has t h e same meaning as b e f o r e and h i s t h e i n i t i a l sample t h i c k n e s s ; t h e s l o p e Q , i s u s u a l l y o b t a i n e d b e f o r e 50% completion of s o r p t i o n . The values of D d e t e r m i n e d in this manner can be r e g a r d e d as independent of c o n c e n t r a t i o n , and a r e t h u s , a p p l i c a b l e f o r t h e F i c k i a n mode of t r a n s p o r t . A t r i p l i c a t e evaluation of D from sorption curves gave us D v a l u e s with an e r r o r of ±0.003 u n i t s at 25°C and ±0.005 u n i t s at 60°C f o r a l l polymer-penetrant systems. These uncertainty estimates regarding diffusion coefficients suggest that the half times were very r e p r o d u c i b l e ( t o w i t h i n a f e w tens of s e c o n d s ) . T h e v a l u e s of D are compiled i n T a b l e II f o r each p o l y u r e t h a n e - s o l vent pair. I n c l u d e d i n t h e same t a b l e a r e t h e v a l u e s of s o r p t i o n c o e f f i c i e n t s , S, as computed from t h e p l a t e a u r e g i o n s of t h e s o r p t i o n c u r v e s and permeability coefficient, Ρ as c a l c u l a t e d from the simple relation U 8 ) : Ρ = D.S (3)


œ

In a l l c a s e s , both p e r m e a b i l i t y and d i f f u s i v i t y of m e t h y l - s u b s t i t u t e d benzenes v a r y i n an i n v e r s e manner w i t h t h e i r m o l e c u l a r volumes (as c a l c u l a t e d b y d i v i d i n g t h e m o l e c u l a r w e i g h t by d e n s i t y and A v o g a d r o number to y i e l d t h e volume p e r m o l e c u l e ) . For o t h e r p e n e t r a n t s , namely, a n i s o l e , n i t r o b e n z e n e , c h l o r o b e n z e n e , o-dichlorobenzene and bromobenzene, t h e volume p e r molecule v a r i e s i n t h e range 17-19. However, t h e i r d i f f u s i o n t r e n d s a r e q u i t e d i f f e r e n t . F o r i n s t a n c e , though n i t r o b e n z e n e and c h l o r o b e n z e n e 2 3

3

h a v i n g almost t h e same m o l e c u l a r volume ( ~ 1 7 x l 0 ~ cm /molecule), y i e l d w i d e l y d i f f e r e n t d i f f u s i v i t y and p e r m e a b i l i t y ; h o w e v e r , t h e maximum S v a l u e s of both t h e penetrants a r e almost identical. Similarly, f o r bromobenzene, the diffusive trends are higher whereas, jo-dichlorobenzene exhibits somewhat intermediatory transport behavior between c h l o r o - and bromobenzene. However, a n i s o l e e x h i b i t s d i f f u s i v e t r e n d s that a r e i n between m e s i t y l e n e and _p-xylene. When our r e s u l t s a r e compared with the literature data, a good agreement c o u l d be seen. F o r e x a m p l e , i n a s t u d y by S c h n e i d e r and c o w o r k e r s (10) f o r t h e t r a n s p o r t of o - d i c h l o r o benzene in a segmented polyurethane elastomer at 25°C, a -7 2 v a l u e of D = 0.95 χ 10 cm /s agrees w i t h our data at 25°C -7 2 ( i . e . , 2.01 χ 10 cm fs). S i m i l a r l y , f o r benzene, toluene, and chlorobenzene at 30°C i n a p o l y u r e t h a n e , Hung (_5) found t h e -7 -7 -7 2 v a l u e s of D as 1.29 χ 10 , 1.43 χ 10 and 1.37 χ 10 cm /s respectively, which agree somewhat w i t h our v a l u e s , 2.90, 2.60 -7 2 and 3.42 χ 10 cm /s r e s p e c t i v e l y , at 25°C.


19.

AITHAL ET AL.


Table

II.

S o r p t i o n and T r a n s p o r t Data of P o l y u r e t h a n e - P e n e t r a n t Systems 7

Temp


Penetrant

/

χ ( C) β

Λ

S , , * (g/g)

*

7

DxlO

v

PxlO

s

,

/ ( mmol/g)

2. . (cm /s) E q . (2)

,

2, . (cm /s) E q . (3)

Benzene

25 44 60

0. 710 0. 721 0. 741

9. 09 9. 24 9. 49

2. 90 5. 23 8. 09

2. 06 3. 73 6. 00

Toluene

25 44 60

0. 602 0. 591 0. 601

6. 53 6. 41 6. 52

2. 60 5. 71 7. 52

1. 56 3. 37 4. 52

p-Xylene

25 44 60

0. 497 0. 500 0. 493

4.,68 4.,71 4.,64

2. 34 4. 33 7. 02

1. 16 2.,16 3.,46

Mesitylene

25 44 60

0. 402 0. 415 0. 420

3.,34 3.,45 3.,49

0. 86 2. 24 3. 76

0.,34 0.,93 1.,58

Anisole

25 44 60

0. 803 0. 839 0. 828

7.,42 7,.76 7,.66

1. 66 3. 57 4.82

1.,33 2,,99 3..99

Nitrobenzene

25 44 60

1. 063 1. 071 1. 148

8,.64 8,.71 9..23

0. 87 1. 57 2.,47

0,.92 1..68 2,.83

Chlorobenzene

25 44 60

1. 055 1. 091 1. 088

9,.38 9,.69 9,.67

3.,42 5.,41 6.,90

3,.61 5,.90 7,.50

o-Dichlorobenzene

25 44 60

1.,314 1.,312 1.,315

8,.94 8,.92 8,.95

2.,01 2.,87 4.,39

2,.64 3,.77 5,.77

Bromobenzene

25 44 60

1,,475 1.,501 1.,516

9 .39 9 .56 9 .65

2.,81 4..56 7,.19

4,.14 6 .85 10 .90


366


The d i f f u s i o n c o e f f i c i e n t s as c a l c u l a t e d from E q u a t i o n 2 have been used i n E q u a t i o n 4 to generate t h e t h e o r e t i c a l s o r p t i o n c u r v e s (19-22) :

oo

= 1 - (Α) π

M /M

η

Σ "

— 5 - exp [ - D ( 2 n + l ) (2η+1)

υ

2

2 ï ï

2

t/h l

(4)


Equation 4 d e s c r i b e s t h e F i c k i a n d i f f u s i o n mode. The s i m u l a t e d sorption curves are compared i n Figures 9 and 10 w i t h t h e experimental profiles f o r some r e p r e s e n t a t i v e penetrants. The o v e r a l l agreement i s o n l y f a i r . During e a r l y stages of s o r p t i o n the agreement i s not so good and t h e e x p e r i m e n t a l curves show s l i g h t c u r v a t u r e s ; t h i s suggests that t h e t r a n s p o r t i s not s t r i c t l y of F i c k i a n t y p e . TEMPERATURE E

D

and E

p

EFFECTS.

The A r r h e n i u s

f o r the processes

activation

parameters v i z . ,

of d i f f u s i o n and permeation

computed from a c o n s i d e r a t i o n of t h e t e m p e r a t u r e D and Ρ r e s p e c t i v e l y , b y u s i n g t h e r e l a t i o n : log

X = log X

- ( E / 2 . 3 0 3 RT)

X

refers

to D

or Ρ

been of

(5)

v

O

where

have

variation

A

and X

q

i s a constant

representing

D

Q

and P ; E ^ denotes t h e a c t i v a t i o n energy f o r t h e p r o c e s s under c o n s i d e r a t i o n and RT has t h e c o n v e n t i o n a l meaning. The e s t i m a t e d parameters Ε and E a r e g i v e n i n T a b l e I I I . The A r r h e n i u s p l o t s q

β

p

are g i v e n i n F i g u r e 11. The E and E D

for

t h e penetrants

under

p

values

vary

study.

As

from regards

about 16 to 35 k J / m o l the effect

s u b s t i t u t i o n on t h e benzene molecule ( i . e . , on going from to m e s i t y l e n e ) t h e r e i s a s y s t e m a t i c i n c r e a s e i n E ^ and E

of CH^-

p

benzene values.

These r e s u l t s c o u l d be e x p l a i n e d on t h e b a s i s of E y r i n g ' s h o l e t h e o r y (_23), a c c o r d i n g to w h i c h , t h e energy r e q u i r e d to "open a h o l e " i n t h e p o l y m e r m a t r i x to accommodate a d i f f u s i n g molecule bears a d i r e c t r e l a t i o n s h i p w i t h E^. Thus, t h e l a r g e r molecules in

a

related

series

will

have

larger

E^

and

smaller

diffusion

coefficients. This i s i n conformity with the experimental obser vations r e p o r t e d here. A t t e m p t s have a l s o been made to c a l c u l a t e t h e e q u i l i b r i u m s o r p t i o n c o n s t a n t s , K^, from c o n s i d e r a t i o n s on t h e e q u i l i b r i u m process occurring i n the l i q u i d pressure (5). Thus,

phase

at constant

number of moles of penetrant

temperature

sorbed

unit mass of t h e p o l y m e r


and

AITHALETAK



19.



368


0

10

20

30

40

50

60

I

1

1

1

1

1

Γ

7 t (min )

•

Figure 10 Comparison between experimental and simulated sorption curves for polyurethane + solvent systems.



19.

Table III.

369

Sorption and Diffusion Through

AITHALETAL.

A c t i v a t i o n P a r a m e t e r s and T h e r m o d y n a m i c F u n c t i o n s f o r P o l y u r e t h a n e - P e n e t r a n t Systems E

D

E

p

AS

0

ΔΗ°

Penetrant

Benzene Toluene p-Xylene Mesitylene Bromobenzene Anisole Chlorobenzene o-Dichlorobenzene Nitrobenzene

kJ/mol

kJ/mol

J/mol.K

24. 17 25.43 25.83 34.95 22.04 25.42 16.64 18.20 24. 54

25.,13 25..40 25..72 35.,90 22..67 26.,24 17.,40 18..23 26,.21

21.6 15.3 12.3 13.7 20.8 19.4 21.2 18.3 23.7


kJ/mol 0.99 - 0.08 -0.17 1.08 0.64 0.79 0.76 0.02 1.74

370



π

1

1 Ο

Benzene

Δ

Toluene

Ο

Mesitylene

•

Bromobenzene

•

o-Dichlorobenzene

φ

Nitrobenzene

3

Anisole

•

Chlorobenzene

•

p-Xylene

3.0

3.1

3.2 3

3.3

3.4

1

±χ10 (Κ" ) τ Figure 11 Arrhenius plots for diffusivity.


19.


AITHALETAK

_

m moles of penetrant g membrane

S Figure

12

weights

shows

at

25,

the

44

dependence

and

60°C;

of

a

Kg

on

systematic

penetrant decrease

molecular

in

Kg with


molecular weight can be seen for benzene to mesitylene an inverse dependence of Kg on molecular weight of the

suggesting penetrant.

This may be more logical because larger molecules tend to occupy more free volume in the amorphous regions of PU chains than smaller molecules. On the other hand, anisole, nitrobenzene, bromobenzene, chloro- and o-dichlorobenzene show positive devia tions ( i . e . , higher solubility) from linearity. This could be a t t r i buted to the structural and polarity similarities of the solvents. Another factor might be the affinity of these solvents towards polyurethane. Following the generalization "like absorbs like", this explanation is consistent with our experimental results. Using the data of Kg we have estimated change in standard enthalpy ( i . e . , heat of sorption) Δ Η ° , and standard entropy of by using van't Hoff relationship (24) :

log Κ

=

ς

s

The

plots

within the of

of

log

Kg versus

AS°

estimated error in about ±1 J / m o l / K . For vely

decreases

(1)

2 . 303R

temperature

ΔΗ° and

-J*l 2. 303 R

1/T as

interval of

are

also

Δ Η ° is

benzene,

shown

AS° is

in

±4 J/mol about

(7)

13,

are linear

The estimated

Table

III.

whereas

The

for

AS° is

about

values average

A S ° , it

22 J/mol. Κ and it

for which

AS°,

Τ

in Figure

25 to 6 0 ° C .

included

about

up to p-xylene

sorption

is

progressi 12

J/mol.K;

A S ° for mesitylene is slightly higher than j?-xylene. However, for the remaining penetrants we could not observe any systematic trend in A S ° values because cal sizes and interact This further confirms not involve polymeric essentially from the movement within the

these penetrants possess more or less identi differently with the polyurethane segments. that the diffusive portion of absorption does cooperation to a greater extent, but results positioning of penetrant molecules during pre-existing available sites of the polymer

matrix (21). The ΔΗ° values are small and positive excepting toluene and p-xylene for which negative values are observed. THERMODYNAMIC

ANALYSIS.

For

a

comprehensive

understanding

of the structure-property relationships of the elastomeric materials in the presence of a solvent, it is necessary to know the magnitude of polymer-solvent interaction parameter χ , and hence the molar mass between crosslinks, M^. The criterion for swelling equilibrium



372


1

1

1

1

C H Br6

5

cx

9 H

C

X6 6

H

N0

6 5 2 ©

C H Cl 6

C

Ό

\ 6 5 3 H

6

4

2

C,H OCH, c

CH

Κ

6

(0)-25*C

Ν. C H (CH ) ^\ 6

4

3

2

(Δ) - 60"C C H (CH )3^ 6

3

.. . 1

3

1 110

90

Mol.Wt.

1 130

1

150

>

Figure 12 Dependence of sorption constant (K ) on molecular weight of the solvents at (O) 25 * C; (•) 44 C; and ( Δ ) 60 C. β

β


19.


AITHAL ET A K

was f i r s t r e c o g n i z e d by F r e n k e l (25) and was l a t e r d e v e l o p e d by F l o r y and Rehner (11,12) i n t o a general t h e o r y . F o r a s u c c e s s f u l c a l c u l a t i o n of M by t h i s t h e o r y we must have i n hand r e l i a b l e data c

of χ f o r t h e s o l v e n t - p o l y m e r p a i r . A number of methods of d e t e r mining χ h a v e been suggested i n t h e l i t e r a t u r e and these h a v e been r e c e n t l y r e v i e w e d by T a k a h a s h i ( 2 6 ) . A l l t h e s e methods a r e e m p i r i c a l and r e q u i r e t h e use of s o l u b i l i t y parameter of t h e s o l v e n t . I n s t e a d , we suggest an a l t e r n a t i v e phenomenological treatment f o r the c a l c u l a t i o n of χ. T h i s a p p r o a c h i s based on e x p r e s s i n g t h e F l o r y - R e h n e r e q u a t i o n into a d e r i v a t i v e of volume f r a c t i o n of the polymer, φ , i n the c o m p l e t e l y s w o l l e n state w i t h r e s p e c t to temperature. Thus,


(

di, d

χφ

=

T

2ΧΦ -

-^-r

-

(-ί Ν = —

where

(

so t h a t

χ =

W/dT)

( 8 )

(1-φ)

- -

+

Φ + Χ Φ

3 Ν

(9)

1 / 3

-

Φ

fi)

(άφ/άΊ)

2

-

2

)

[{ φ / ( 1 - φ ) } + Ν In (1-φ)

[2φ

The

Un

2 / τ

φ Ν

-

+ Νφ

]

( 1 Q )

2

φ /Τ]

volume f r a c t i o n of t h e s w o l l e n p o l y m e r i s c a l c u l a t e d as :

φ = [1

Here,

and

are

after

p

M

=

(

(11)

i ) - —^- ]

respectively,

the

mass

of

polymer

before

i s s o l v e n t d e n s i t y and ρ i s d e n s i t y of b ρ polyurethane. Computation of the c o e f f i c i e n t of volume fraction (ά(\>/άΊ) can be done from a l e a s t - s q u a r e s f i t of t h e φ data v e r s u s t e m p e r a t u r e , T. The molar mass between c r o s s l i n k s can then be o b t a i n e d from a m o d i f i c a t i o n of F l o r y - R e h n e r r e l a t i o n as :

and

swelling,

+ — Β

C

P v p

(φ)

1 / 3

(12) [In (1-φ)

+ φ+

Χ

2

φ ]

w h e r e V i s molar volume of s o l v e n t and t h e parameter χ t o be used here has been o b t a i n e d from Equation 10. The estimated q u a n t i t i e s a r e c o m p i l e d i n T a b l e IV. Wide d i s p a r i t y i n χ and


374


1

1-0

1

1

I

C^Cl

Γ P C

H

6 5

N 0

=

I

& C H Br 6

5

= ·— *-

2*

o—

C H OCH 6

5

—A

C

H

6 6

3

—m C


•

H

6 5

C H

3

C

W

Δ

H

}

3 2

/\

0-6 C H (CH ) 6

0

3

3

3

—Λ

1

1

3-0

3.1

Ο 1

3.2 3

1

1X10 (K' )

1

1

3.3

3.4

•

τ

Figure 13 van't HofFs plots for polyurethane + solvent systems. Symbols:

(I)

Chloro- and Bromobenzene;

(0)

Benzene; (•)

(Δ)

^-xylene; and (o) Mesitylene;

Table IV.

Anisole; (•)

Toluene; (A)

Nitrobenzene.

Results of Flory-Rehner Theory

Penetrant Benzene Toluene p-Xylene Mesitylene Bromobenzene Anisole Chlorobenzene o-Dichlorobenzene Nitrobenzene

X 0.47 0.29 0.23 0.37 0.36 0.41 0.39 0.24 0.58

M c 860 551 469 517 1018 886 1017 848 1793


19. AITHAL ET AL. Sorption and Diffusion Through Polyurethane Membranes 375 values are observed w h i c h depend on t h e nature of t h e s o l v e n t s u s e d . F o r toluene, p - x y l e n e and o - d i c h l o r o b e n z e n e , both χ and respectively,

vary

from

:χ =

0.23 to 0.29 and M

c

= 470 to 850.

T h i s suggests that t h e r e i s a c o n s i d e r a b l e s o l v e n t i n t e r a c t i o n w i t h the p o l y u r e t h a n e segments. F o r benzene χ = 0.47 and M = 860, c

whereas

nitrobenzene

e x h i b i t s χ = 0.58 and M

c

= 1793, t h e h i g h e s t

among t h e l i q u i d s c o n s i d e r e d . On t h e o t h e r hand, m e s i t y l e n e , a n i s o l e , c h l o r o - and bromobenzene e x h i b i t almost i d e n t i c a l v a l u e s of χ i . e . , 0.36 to 0.41; among t h e s e , the latter two e x h i b i t higher (

~

1020) than


respectively,

either

mesitylene

517 and 886. Such

or

anisole

variations

in

for which data

are

indicate the

s e r i o u s l i m i t a t i o n s of t h e F l o r y - R e h n e r t h e o r y to s t u d y polymer swelling. However, the complexity of s o l v e n t interactions may p r o b a b l y a f f e c t i n v a r i o u s degrees, t h e h a r d and t h e soft segments of PU. T h i s will alter the overall swelling behavior thereby contributing to t h e v a r i a b i l i t y of M^ r e s u l t s . T h i s i s further i n d i c a t i v e of t h e s u b t l e the s o l v e n t - p o l y u r e t h a n e

n o n - F i c k i a n e f f e c t s as o b s e r v e d pairs.

f o r most of

ACKNOWLEDGMENTS The a u t h o r s a p p r e c i a t e t h e f i n a n c i a l s u p p o r t from t h e Robert A. Welch Foundation (Grant AI-0524); TMA and USA thank t h e U n i v e r s i t y Grants C o m m i s s i o n , New D e l h i , I n d i a f o r t h e a w a r d of a t e a c h e r f e l l o w s h i p to Mr. A i t h a l to s t u d y at Karnatak U n i v e r s i t y .

LITERATURE CITED 1. Cooper, S. L . ; Tobolsky, Α. V. J. Appl. Polym. Sci. 1966, 10, 1837. 2. Gibson, P. E. Properties in Polyurethane Block Copolymers in Developments in Block Copolymers; Goodman, I., Ed.; Elsevier : London, 1982. 3. Trapps, G. In Advances in Polyurethane Technology; Buist, J. M . ; Gudgeon, H . , Eds.; Interscience : New York, 1968 ; p 63. 4. Hung, G. W. C.; Autian, J. J. Pharm. Sci. 1972, 61, 1094. 5. Hung, G. W. C. Microchem. J. 1974, 19, 130. 6. Hopfenberg, Η. B . ; Schneider, N. S.; Votta, F. J. Macromol. Sci.-Phys. 1969, B3(4), 751. 7. Nierzwicki, W.; Majewska, Z. J. Appl. Polym. Sci. 1979, 24, 1089. 8. Sefton, M. V . ; Mann, J. L. J. Appl. Polym. Sci. 1980, 25, 829.


376 BARRIER POLYMERS AND STRUCTURES

Yokoyama, T.; Furukawa, M. In International Progress in Urethanes; Ashida, K.; Frisch, K. C., Eds.; Technomic Publishing Co., Inc., 1985; Vol. 4, Chapter 1. 10 Schnieder, N. S.; Illinger, J. L . ; Cleaves, M. A. Polym. Eng. Sci. 1986, 26, 1547. 11. Flory, P. J . ; Rehner, Jr, J. J. Chem. Phys. 1943, 11, 521. 12. Flory, P. J. J. Chem. Phys. 1950, 18, 108. 13. Lucht, L. M.; Peppas, N. A. J. Appl. Polym. Sci. 1987, 33, 1557. 14. Chiou, J. S.; Paul, D. R. Polym. Eng. Sci. 1986, 26, 1218. 15. Nicolais, L . ; Drioli, E . ; Hopfenberg, Η. B.; Apicella, A. Polymer 1979, 20, 459. 16. Britton, L. N.; Ashman, R. B.; Aminabhavi, T. M.; Cassidy, P. E. J. Chem. Educ. 1988, 65, 368. 17. Aminabhavi, T. M.; Cassidy, P. E. Polym. Commun. 1986, 27, 254. 18. Cassidy, P. E . ; Aminabhavi, T. M.; Thompson, C. M. Rubb. Chem. Technol., Rubb. Revs. 1983, 56, 594. Downloaded by UNIV LAVAL on July 12, 2016 | http://pubs.acs.org Publication Date: May 9, 1990 | doi: 10.1021/bk-1990-0423.ch019

9.

19.

24.

Crank, J. The Mathematics of Diffusion; 2nd Ed; Clarendon Press : Oxford, 1975. Gent, A. N.; Tobias, R. H. J. Polym. Sci. Polym. Phys. Ed. 1982, 20, 2317. Enscore, D. J . ; Hopfenberg, H. B.; Stannett, V. T. Polym. Eng. Sci. 1980, 20, 102. Garrido, L . ; Mark, J. E . ; Clarson, S. J . ; Semlyen, J. A. Polym. Commun. 1984, 25, 218. Zwolinski, B. J . ; Eyring, H.; Reese, C. E. J. Phys. Colloid Chem. 1949, 53, 1426. Golden, D. M. J. Chem. Educ. 1971, 48, 235.

25. 26.

Frenkel, J. Rubb. Chem. Technol. 1940, 13, 264. Takahashi, S. J. Appl. Polym. Sci. 1983, 28, 2847.

20. 21. 22. 23.

RECEIVED

December 5, 1989


Sorption and Diffusion of Monocyclic Aromatic Compounds Through

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