Relaxation Studies of Adsorbed Water on Porous Glass - American

19 Relaxation Studies of Adsorbed Water on Porous Glass Varying Temperature and Pore Size at Constant Coverages GEORGES BELFORT

1

Downloaded by RUTGERS UNIV on March 7, 2016 | http://pubs.acs.org Publication Date: August 19, 1980 | doi: 10.1021/bk-1980-0127.ch019

Rensselaer Polytechnic Institute, Troy, NY 12181 NAOMI SINAI University of Utah, Salt Lake City, UT 84112

Recent studies using Infrared Spectrocopy IR to characterize the state of water in desalination membranes have concluded that the water sorbed in these membranes has a low degree of association and that bonds between water and the membrane are considerably weaker than those in liquid water (1,2). These conclusions have been made for widely differing membrane materials such as cellulose acetate (1,2),polyimide, and porous glass (1) and appear to contradict the conclusions obtained from pNMR (3-8), differential scanning calorimetry (9-11) and transport (12,13) studies. These latter studies suggest that water molecules in the vicinity of the membrane are motionally restricted with respect to free bulk water. Several investigators have thus proposed multi-state models to characterize the occluded water in the porous media (3-8,10-13). The terms "phase" and "exchanging fractions" are sometimes used. To minimize confusion, since a thermodynamic phase is not what is being considered, "environmental state" should and will be used here. An explanation of the mechanism of solute selectivity and water transport in desalination membranes clearly depends on a resolution of the above apparent contradiction. A qualitative model of the state of water inside desalination membranes considering both the IR and pNMR results (including those presented here) will be proposed. This study i s a d i r e c t c o n t i n u a t i o n of our previous work i n which pNMR was used to measure the proton r e l a x a t i o n times of water adsorbed on four powdered porous glasses ranging i n pore s i z e from 29 to 189 Åas a f u n c t i o n of coverage a t room temperature ( 8 ) . I n t e r p r e t a t i o n of pNMR data f o r adsorbed systems i s To whom correspondence should be sent.

1

The research reported here was conducted at the School of Applied Science and Technology, Hebrew U n i v e r s i t y of Jerusalem, I s r a e l . 0-8412-0559-0/ 80/47-127-323S05.75 / 0 © 1980 A m e r i c a n Chemical Society

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.


324

W A T E R IN P O L Y M E R S

d i f f i c u l t at best. T h u s , i n d e p e n d e n t v a r i a b l e s s u c h as t e m p e r a t u r e ( 6 ) , degree o f l o a d i n g (or coverage) of the adsorbed s p e c i e s ( 1 4 , 1 5 ) , o p e r a t i n g f r e q u e n c y ( 1 6 , 1 7 ) and i s o t o p i c s u b s t i t u t i o n (16) a r e u s u a l l y used t o a s s i s t and c l a r i f y t h e i n t e r p r e t a t i o n o f the r e s e a r c h e r . A c c o r d i n g t o R e s i n g (18) " v a r i a t i o n o f t h e t e m p e r a t u r e o v e r as b r o a d a range as p o s s i b l e f o r a g i v e n s y s t e m o f f e r s the g r e a t e s t p r o b a b i l i t y of s u c c e s s f u l i n t e r p r e t a t i o n of NMR r e l a x a t i o n d a t a . " For t h i s reason, the research r e p o r t e d here was c o n d u c t e d as a c o m p l i m e n t a r y s t u d y t o t h a t r e p o r t e d e a r l i e r (8). Here we r e p o r t r e s u l t s o f t h e pNMR r e l a x a t i o n t i m e s o f w a t e r a d s o r b e d on t h e s m a l l e s t (29 Â) and t h e l a r g e s t (189 Â) p o r e s i z e p o r o u s g l a s s d e s a l i n a t i o n membranes s t u d i e d e a r l i e r (8) as a f u n c t i o n o f t h r e e coverages f o r the t e m p e r a t u r e range -80 t o +90°C. A l t h o u g h t h e a p p r o a c h and t h e r e l a x a t i o n model used h e r e i s s i m i l a r t o t h a t used by B e l f o r t e t aj_ ( 6 j t o s t u d y w a t e r a d s o r p t i o n a t two c o v e r a g e s on t h r e e d i f f e r e n t p o r e s i z e porous g l a s s d e s a l i n a t i o n membranes, t h e f o l l o w i n g d i f f e r e n c e s s h o u l d be e m p h a s i z e d . (i) The V y c o r - t y p e (96% s i l i c a ) p o r o u s g l a s s used h e r e was p r e p a r e d by t h e same p r o c e d u r e as t h e c a p i l l a r y p o r o u s g l a s s d e s a l i n a t i o n membranes used by S c h n a b e l ( 1 9 ) . C a r e was t a k e n t o p r e v e n t t h e i n t r o d u c t i o n o f p a r a magnetic centers i n t o the g l a s s melt d u r i n g p r o d u c t i o n (Schnabel, p r i v a t e communication). W i t h t h e two l a r g e p o r e s i z e p o r o u s g l a s s e s ( d e s i g n a t e d CPG-10-125 and C P G - 1 0 - 2 4 0 ) used by B e l f o r t e t a l ( 6 ) , t h i s was n o t t h e c a s e and t h e r e l a x a t i o n model c o u l d n o t be f i t t e d to the d a t a . ( i i ) C o v e r a g e s a t 100% RH and 50% RH w e r e a r b i t r a r i l y c h o s e n f o r the e a r l i e r study ( 6 ) , w h i l e d e t a i l e d adsorption i s o t h e r m s and a s s o c i a t e d BET r e s u l t s r e p o r t e d e a r l i e r ( 8 ) a r e used h e r e t o r a t i o n a l l y c h o o s e t h e d e s i r e d coverages. ( i i i ) P o r o u s g l a s s f r o m t h e same p r o d u c t i o n b a t c h was d i v i d e d i n t o two l o t s by t h e m a n u f a c t u r e r . One l o t was used i n t h i s s t u d y w h i l e t h e o t h e r l o t was used by Luck ( M a r b u r g , West Germany) f o r t h e IR i n v e s t i g a t i o n s (1). A p r o p o s e d model w o u l d t h e r e f o r e have t o be c o n s i s t e n t w i t h the r e s u l t s from both s t u d i e s , ( i v ) The c o m p u t e r f i t t i n g p r o c e d u r e was i m p r o v e d o v e r t h a t p r e v i o u s l y used ( 6 j r e s u l t i n g i n s i g n i f i c a n t t i m e savings. Methods Samples and W a t e r S o r p t i o n D e t a i l s o f t h e p r e p a r a t i o n and c l e a n i n g procedures o f t h e porous g l a s s o b t a i n e d from J e n a e r G l a s w e r k S c h o t t , M a i n z , Germany, have a l r e a d y been d e s c r i b e d ( 8 ) .


19.

Relaxation

B E L F O R T A N D SINAI

325

Studies

C o n s t a n t t e m p e r a t u r e a d s o r p t i o n i s o t h e r m s and BET r e s u l t s f o r t h e two p o r o u s g l a s s e s u s e d h e r e a r e r e p r o d u c e d i n T a b l e I f r o m R e f . 8 . N u c l e a r M a g n e t i c R e s o n a n c e - A p p a r a t u s and P r o c e d u r e The n u c l e a r m a g n e t i c r e l a x a t i o n t i m e s J\ and T and t h e m o b i l e f r a c t i o n f were measured w i t h a S p i n - l o c k p u l s e - s p e c t r o m e t e r (model C P S - 2 , P o r t C r e d i t , O n t a r i o , Canada) a t 33 Mhz. Tempera t u r e was c o n t r o l l e d w i t h a B r u c k e r T e m p e r a t u r e C o n t r o l l e r ( B r u c k e r , Germany). The magnet was 15 i n c h e s i n d i a m e t e r ( V a r i a n V 3 8 0 0 , P a l o A l t o , CA, U S A ) . The l o g i c f o r t h e c o n t r o l o f t h e p u l s e s p e c t r o m e t e r was f u l l y a u t o m a t e d and t h e d a t a was a c c u m u l a t e d , s t o r e d and a v e r a g e d by a C o n t r o l D a t a M i n i - C o m p u t e r . Hard c o p i e s ( p a p e r - t a p e s ) f o r e a c h r u n was s u p p l i e d a u t o m a t i c a l l y t o g e t h e r w i t h x - t p l o t o f the averaged r e l a x a t i o n d a t a . The t r a n s v e r s e r e l a x a t i o n t i m e s T were measured by " s p i n e c h o " method (2 p u l s e s : 9 0 - t - 1 8 0 ° ) . The " e c h o " s i g n a l s ( t ) , appearing a t t = 2 t , s a t i s f i e d the e q u a t i o n : 2


m

2

S(t) = s ( 0 )

exp

(-t/T )

(1)

2

The l o n g i t u d i n a l r e l a x a t i o n t i m e s Ti o f t h e p r o t o n s were measured by s a t u r a t i n g t h e l i n e w i t h a "comb" o f 1 8 0 ° p u l s e s , f o l l o w e d by a s e q u e n c e o f 2 p u l s e s 9 0 - t - 1 8 0 ° . The i n t e n s i t y Μ, ( t ) o f t h e " e c h o " a p p e a r i n g a f t e r t h e 180° p u l s e i s a f u n c t i o n o f t h e t i m e t between t h e "comb" and t h e s e q u e n c e ( 9 0 - t - 1 8 0 ° - t echo w h e r e t i s c o n s t a n t ) , and s a t i s f i e d t h e e q u a t i o n :

M

Q

- M

z

( t ) = M exp (-t/Ti)

(2)

where M = M (°°) and M7 ( 0 ) = 0 . T and Ti a r e o b t a i n e d a c c o r d i n g t o E q u a t i o n s (1) and (2) f r o m a c o m p u t e r n o n - l i n e a r l e a s t - s q u a r e s - f i t program. The m o b i l e f r a c t i o n f [=(I ,yT)/(I ,2g8' )] obtained f o r e a c h sample as f o l l o w s . The i n t e r c e p t s i n a m p l i t u d e s on t h e v e r t i c a l a x i s ( a t u n i t g a i n ) , I , y and Im,298 measured by e x t e n d i n g t h e f r e e i n d u c t i o n d e c a y c u r v e êack t o t h e z e r o t i m e a t T°K and 2 9 8 ° K , r e s p e c t i v e l y . 0

z

2

2 9 8

m

m

w

a

s

m

w

e

r

e

m

Experimental

Results

M a g n e t i c R e l a x a t i o n Measurements The l o n g i t u d i n a l T and t r a n s v e r s e T r e l a x a t i o n d a t a f o r t h e two p o r o u s g l a s s e s ( s a m p l e s 2 and 5) d e s c r i b e d i n T a b l e I a t 88 and 100% a r e p r e s e n t e d i n F i g u r e 1 as a f u n c t i o n o f r e c i p r o c a l t e m p e r a t u r e . The 88% RH was c h o s e n so as t o compare t h e e f f e c t o f r e m o v i n g t h e l o n g component f r o m t h e p o r o u s f o r g l a s s s a m p l e 5. The amounts o f w a t e r a d s o r b e d i n g H 0 / g g l a s s a t 100 and 88% RH f o r s a m p l e s 2 and 5 were 0.184 and 0 . 1 8 2 , and 0.33 and 0 . 0 5 , r e s p e c t i v e l y . B a s e d on t h e i r r e s p e c t i v e m o n o l a y e r volumes as d e t e r m i n e d by t h e BET a n a l y s i s o f w a t e r s o r p t i o n ( s e e column 6 i n T a b l e I ) , t h e x

2

2



a

197(189)

5

0.330(0.331)

0.186(0.149)

3 -1 cm g

67(70)

100(210)

BET 2 -1 m g

S

Surface a r e a ,

0.316

0.207

-

Porosity^, ε

0.016

0.024

3 -1 cm g

Monolayer Water Volume, V

(8)

4

Q

2

4

1

1

Λ

2

m

d

ρ

= 1 g/ce.

ε = v o i d f r a c t i o n a l volume = 1/[1 + ρ /Vp ], ρ =1.4 w g g

c Assuming

g/cc, ρ = 1.0 w

g/cc.

d = (4V/S ) χ 1 0 , A f o r t h e c y l i n d r i c a l model. S i n c e S = V / t χ 1 0 , where t = s t a t i s t i c a l l a y e r t h i c k n e s s f o r adsorbed water β 2.39 A. The BET method i s b e s t s u i t e d to adsorbed i n e r t gases such as N s i n c e problems a r i s e as to a s u i t a b l e c h o i c e of t f o r the hydrogen-bonding H 0. In t h i s study a v a l u e of t = 2.39 A was d e r i v e d from the s u r f a c e area of a water molecule adsorbed on amorphous air — " °A s i'" l•i*c a , where -12.5 was used

b

A l l v a l u e s shown i n b r a c k e t s were o b t a i n e d from the porous g l a s s s u p p l i e r , Dr. Roland Schnabel, Jenaer Glaswerk S c h o t t , Mainz, Germany, who used n i t r o g e n a d s o r p t i o n isotherms to o b t a i n d from the BET method.

74(29)

Â

2

Sample No.

pore at

RH,V

volume

diameter^, d

100%

Average

pore

Average

3

MEMBRANE CHARACTERISTICS DETERMINED BY ADSORPTION ISOTHERMS "

TABLE I


H

κ 2 w

g

< >

Relaxation

Studies

327



Figure 1. Proton relaxation times vs. 10 /T of adsorbed water in porous glass samples 2 and 5 at (a) P/P = 0.88 and (b) P/P = 1.00; (—) indicates the experimental trends. S

0

0


328

WATER IN POLYMERS

r e l a x a t i o n d a t a was a l s o measured a t a c o v e r a g e o f two l a y e r s f o r each g l a s s sample. This corresponded to a r e l a t i v e humidity o f 62 and 40% f o r t h e s a m p l e s 5 and 2 r e s p e c t i v e l y . The two l a y e r c o v e r a g e r e s u l t s a r e p r e s e n t e d i n F i g u r e 2 as a f u n c t i o n o f r e c i p r o c a l t e m p e r a t u r e . R e s u l t s f o r t h e two sample g l a s s e s have been e x t r a c t e d f r o m F i g u r e s 1 and 2 and a r e summarized in Table II. A t y p i c a l e x a m p l e o f t h e p r i m a r y r e l a x a t i o n d a t a was g i v e n i n F i g u r e 2 o f R e f e r e n c e 8 where one component e x p o n e n t i a l p l o t s f o r T ! and T were o b s e r v e d a t room t e m p e r a t u r e a t c o v e r a g e s above 30% RH. The l o n g i t u d i n a l and t r a n s v e r s e r e l a x a t i o n t i m e s f o r b o t h s a m p l e s 2 and 5 show i n F i g u r e s 1 and 2 i n v e r s e t e m p e r a t u r e p r o f i l e s t y p i c a l o f adsorbed systems f o r a l l the coverages except t h e 100% RH f o r sample 5. T h i s i m p l i e s a s h a l l o w Τχ minimum, a d r a s t i c s p r e a d i n g o u t o f t h e J c u r v e , and may i n c l u d e a s h o u l d e r e f f e c t o r maximum as T i n c r e a s e s w i t h t e m p e r a t u r e ( 2 0 , 2 1 ) . L o g a r i t h m i c G a u s s i a n t e m p e r a t u r e - i n d e p e n d e n t (B = c o n s t a n t ) d i s t r i b u t i o n s have been u s e d t o model t h e s e s y s t e m s and i s d i s c u s s e d below. Because o f the s i m i l a r i t y o f t h e s e p r o f i l e s , the m o t i o n a l c h a r a c t e r i s t i c s o f the adsorbed water i s probably s i m i l a r f o r the d i f f e r e n t c o n d i t i o n s l i s t e d i n F i g u r e s 1 and 2 . The d a t a i n T a b l e II s u p p o r t t h i s v i e w s i n c e ( e x c e p t f o r s a m p l e 5 a t 100% RH) ( i ) T i ^ - j p v a r i e s between 20 and 30 msec f o r a l l t h e c a s e s l i s t e d ( i i ) the temperature a t which T j o c c u r s , Θ ^ π i s also i n a very n a r r o w r a n g e and v a r i e s o n l y f r o m 210 t o 2 3 0 ° K . F o r sample 5 a t 100% RH, t h e T minimum i s deep and t h e T d r o p s p r e c i p i t o u s l y between a b o u t - 8 and - 2 0 ° C i n d i c a t i n g f r e e z i n g (23). This implies l i q u i d - l i k e behavior of a dominating water f r a c t i o n w i t h a l i q u i d - l i k e s i n g l e c o r r e l a t i o n t i m e as p r e d i c t e d by t h e t h e o r y o f B l o e m b e r g e n , P u r e e ! ! , and Pound (BPP) ( 2 2 ) . B e c a u s e o f t h e symmetry o f t h e T v e r s u s 1 0 / T ° K c u r v e s even a t low t e m p e r a t u r e s where p a r a m a g n e t i c i m p u r i t i e s c o u l d d o m i n a t e t h e r e l a x a t i o n p r o c e s s c a u s i n g t h e r i g h t arm o f t h e Ίι p r o f i l e t o d r o p ( s e e F i g u r e l e and I f i n R e f e r e n c e 6 ) , i n t r a m o l e c u l a r p r o t o n - p r o t o n i n t e r a c t i o n i s assumed t o d o m i n a t e . The BPP t h e o r y p r e d i c t s a T i / T a t ©min o f 1.6 and i s a p p l i c a b l e f o r one e n v i r o n m e n t a l s t a t e w i t h a s i n g l e c o r r e l a t i o n time. From T a b l e I I , t h e T i / T r a t i o a t Omin f o r sample 2 i s l o w e s t a t 100% RH, when t h e most b u l k - l i k e w a t e r i s p r o b a b l y p r e s e n t . I t i n c r e a s e s a t i n t e r m e d i a t e c o v e r a g e when more t h a n one s t a t e o f w a t e r i s p r e s e n t and d e c r e a s e s a g a i n a t low c o v e r a g e when another s t a t e dominates. Another i n t e r e s t i n g r e s u l t i s t h a t the T i / T r a t i o at Q ^ f o r b o t h s a m p l e s 2 and 5 a t 2 - l a y e r c o v e r a g e i s i n d e n t i c a l . In f a c t b o t h t h e T i and T c u r v e s shown i n F i g u r e 2 a r e s u p e r i m p o s a b l e i m p l y i n g a d s o r b e d w a t e r w i t h t h e same motional c h a r a c t e r i s t i c s . Thus, a t low c o v e r a g e s , the average p o r e s i z e d i a m e t e r has l i t t l e e f f e c t on t h e m o t i o n a l b e h a v i o r o f the w a t e r i n the porous g l a s s s t u d i e d h e r e . The l a r g e v a l u e s f o r T ! / T a t 0 i t o g e t h e r w i t h t h e


2

x

2

m

n

r

2

3

t

2

2

2

m

n

2

2

m

n




Relaxation

329

Studies

Figure 2. NMR relaxation times for water adsorbed on porous glass: (a) sample 2 at P/P = 0.4; (b) sample 5 at P/P = 0.62; (· · ·) experiment; (—) theory; curves a and b; least-squares fit to the Resing model (21); curve c obtained by using the parameters derived from the least-squares fit to adjust the T behavior at high temperatures to produce a shoulder effect caused by the presence of high energy sites (21) 0

0

2



74(29)

2

Assumed to be two-layer coverage.

197(189)

ο A

a

230

227

0.88 0.40

226

1.00

230

210

0.88 0.62

254

°K

θ . mm

1.00

a

P/Po

d

Ρ

R e l a t i v e Humidity

Mean Pore Diameter

5

Porous G l a s s

PULSED NMR EXPERIMENTAL PARAMETERS FOR WATER ADSORBED IN POROUS GLASS

TABLE I I


l

28

20

26

22

40

5

22

70

30

-

-

28

/

T

m

2

at θ

T

320

msec

T^in

19.

Relaxation


Studies

331

s h a l l o w n e s s o f t h e J minimum and t h e f a l l - o f f o f t h e m o b i l e f r a c t i o n a t l o w e r t e m p e r a t u r e s ( d i s c u s s e d l a t e r ) , c a n a l l be a c c o u n t e d f o r by a s s u m i n g a b r o a d d i s t r i b u t i o n o f c o r r e l a t i o n ( i n m o l e c u l a r jump) t i m e s ( 2 4 ) . In t e r m s o f t h e s i m p l e model o f a d s o r b e d w a t e r ( 8 ) , e n v i r o n m e n t a l s t a t e Β ( b u l k - l i k e w a t e r ) i s f i r s t removed f r o m t h e p o r e d u r i n g d e h y d r a t i o n l e a v i n g b e h i n d t h e two bound s t a t e s A i and A ( o r t h e combined s t a t e A ) . The combined s t a t e A i s assumed t o o c c u p y two l a y e r s o f w a t e r and i s i n d e p e n d e n t o f p o r o u s g l a s s p o r e d i a m e t e r . See T a b l e II i n R e f e r e n c e ( 8 ) . x

2


Initial

A m p l i t u d e ( o f F r e e I n d u c t i o n Decay)

Measurements

In t h e above model t h e m o b i l e o r s l o w d e c a y f r a c t i o n , f i s s t a t e B, and t h e l e s s m o b i l e f r a c t i o n ( l - f ) i s t h e combined bound s t a t e A . The i n t e r c e p t o f a f r e e i n d u c t i o n d e c a y w i t h the y - a x i s i s p r o p o r t i o n a l t o the paramagnetic s u s c e p t i b i l i t y o f t h e s p e c i m e n , and hence t h e number o f p r o t o n s i n t h e s p e c i m e n is p r o p o r t i o n a l to i n v e r s e temperature. Since the l e s s mobile f r a c t i o n has d e c a y e d b e f o r e t h e i n s t r u m e n t has r e c o v e r e d f r o m i t s 9 0 ° p u l s e ( i n < 20 μ s e c ) t h e m a g n i t u d e o f t h e i n t e r c e p t I a t z e r o t i m e f o r t h e f r e e i n d u c t i o n d e c a y r e f l e c t s t h e number of protons i n the mobile f r a c t i o n o n l y . T h u s , as t h e t e m p e r a t u r e , Τ i s v a r i e d , the product I T, i s p r o p o r t i o n a l o n l y t o the m o b i l e water molecules. The p l o t o f f = I T / ( I 2 9 8 ° K ) versus r e c i p r o c a l temperature f o r 100% RH and f o r 2 - l a y e r c o v e r a g e f o r p o r o u s g l a s s s a m p l e s numbers 2 and 5 a r e shown i n F i g u r e s 3 and 4 . F o r s a m p l e number 2 (mean p o r e d i a m e t e r 29 Â) a t 100% RH f i s constant at temper a t u r e s above about - 1 6 ° C . Below t h i s t e m p e r a t u r e t h e m o b i l e w a t e r f r a c t i o n s t e a d i l y d i m i n i s h e s w i t h o u t a sudden d r o p e x p e c t e d f r o m a f r e e z i n g phenomena. T h i s s l o w t r a n s i t i o n f r o m a m o b i l e t o l e s s m o b i l e f r a c t i o n i s e i t h e r due t o s u p e r - c o o l i n g and s l o w f r e e z i n g o r t h e a p p a r e n t phase t r a n s i t i o n e f f e c t ( 2 ^ 5 ) . F o r s a m p l e 5 a t 100% RH on t h e o t h e r hand f drops p r e c i p i t o u s l y a r o u n d 0 ° C . T o g e t h e r w i t h t h e r e s u l t s p r e s e n t e d i n F i g u r e 1 and T a b l e I I , t h i s drop i n f a p p e a r s t o be due t o f r e e z i n g o f t h e s l o w d e c a y f r a c t i o n o r s t a t e B. B o t h c u r v e s a p p e a r t o be s i m i l a r f o r b o t h p o r o u s g l a s s s a m p l e s a t 2 - l a y e r c o v e r a g e as shown i n F i g u r e 4 . T h i s , once a g a i n , c o n f i r m s t h a t t h e a d s o r b e d w a t e r on b o t h g l a s s s a m p l e s i s motionally s i m i l a r at 2 - l a y e r coverage. m

m

m

m

m

m

m

m

m

m

Interpretation of

Results

The N u c l e a r M a g n e t i c Resonance Model In t h i s s e c t i o n a n u c l e a r m a g n e t i c r e s o n a n c e m u l t i s t a t e model i s f i t t e d t o t h e e x p e r i m e n t a l r e l a x a t i o n d a t a shown i n F i g u r e s 1 and 2 . A f i t i s n o t a t t e m p t e d f o r s a m p l e 5 a t 100% RH b e c a u s e o f t h e anomolous Τ i , T v e r s u s 1 0 / T ° K p r o f i l e s p r o d u c e d by f r e e z i n g ( s e e F i g u r e 1 ) . 3

2


WATER IN


332

Figure 3.

Plot of mobile fraction t

(=

m

water at P/P

0

r

(293/- 298 Κ

'

}

VS

W

°

/

T

°

f

a

d

POLYMERS

s

o

r

b

e

d

= 1.00 for porous glass: (a) sample 2; and (b) sample 5

60

Figure 4. Plot of the mobile fraction (f ) vs. reciprocal temperature of adsorbed water on: (a) sample 2 at P/P = 0.40 and (b) sample 5 at P/P = 0.62; (-··) experiment; (—) theory

21

-35

ΊΟ

-56

-73

-88

-101

m

n

0

30

34

38

42

46

50

I0 /T°K 3


54

58

19.

Relaxation


333

Studies

F o r d e t a i l s o f t h e l o g - n o r m a l d i s t r i b u t i o n model and t h e a p p r o p r i a t e a c t i v a t i o n law, the reader i s r e f e r r e d to References 6 and 21_. In t h e s e r e f e r e n c e s d e t a i l s a r e p r o v i d e d as t o t h e method o f c a l c u l a t i o n . T h r e e c o m p u t e r programs w e r e used s e q u e n t i a l l y t o f i t t h e model t o t h e e x p e r i m e n t a l d a t a i n F i g u r e s 1 and 2. The t o t a l number o f p a r a m e t e r s i n t h e model a r e f i v e : t h r e e ( τ , Η, To) t o f i t t h e a c t i v a t i o n l a w f o r τ * , one t o c h a r a c t e r i z e t h e d i s t r i b u t i o n w i d t h B, and σ ο t h e s e c o n d moment. The f i r s t program ( o b t a i n e d f r o m D r . Leo J . L y n c h , D i v i s i o n o f T e x t i l e P h y s i c s Wool R e s e a r c h L a b s . , 338 B l a x l a n d R d . , R y d e l S y d n e y , NSW A u s t r a l i a . ) uses t h e model t o p r e d i c t σ and Β a t Om-jp as e s t i m a t e s f o r t h e s e c o n d p r o g r a m . The s e c o n d program ( o b t a i n e d f r o m D r . Henry A. R e s i n g , D e p t . o f C h e m i s t r y , Code 6 1 7 3 , N a v a l R e s e a r c h L a b s . , W a s h i n g t o n , DC 20390) uses n u m e r i c a l i n t e g r a t i o n techniques to c a l c u l a t e the parameters f o r the best l e a s t s q u a r e s f i t [ s e e F i g u r e 2 s o l i d l i n e s f o r T i and T curves ( a ) and ( b ) ] . These p a r a m e t e r s a r e summarized i n T a b l e I I I . The t h i r d program ( a l s o o b t a i n e d f r o m D r . Henry A. R e s i n g ) u s e s t h e parameters d e r i v e d from the l e a s t squares f i t t o a d j u s t T b e h a v i o r a t h i g h t e m p e r a t u r e s as t o p r o d u c e a s h o u l d e r e f f e c t (see F i g u r e 2 s o l i d l i n e f o r T c u r v e ( c ) ) . The f o l l o w i n g comments r e g a r d i n g t h e p a r a m e t e r s can be made: (i) The c r i t e r i a f o r an a c c e p t a b l e f i t was b a s e d f i r s t on t h e v a l u e o b t a i n e d f o r t h e s e c o n d moment σ and t h e n on t h e reasonableness of the other parameters. A l s o see f o o t n o t e d i n Table III. Three of the f i v e cases produced a c c e p t a b l e f i t s without f i x i n g σ a t i t s p h y s i c a l minimum o f 1.57 χ 1 0 rad sec~2. The p r o t o n - p r o t o n d i s t a n c e r c a l c u l a t e d from σ (see footnote c i n Table III) f o r s a m p l e s 5 and 2 a t 2 - l a y e r c o v e r a g e s ( p / p = 0.62 and 0 . 4 0 r e s p e c t i v e l y ) a r e v e r y c l o s e t o r = 1.54 Â f o r a f r e e w a t e r m o l e c u l e , i m p l y i n g an open r a t h e r t h a n dense packing. On a d d i n g w a t e r a d e n s e r p a c k i n g ( r = 1.47 Â ) i s o b s e r v e d f o r s a m p l e 2 a t 88% RH, w h i l e r e l a t i v e l y l a r g e r are c a l c u l a t e d f o r s a m p l e 5 a t 88% RH and s a m p l e 2 a t 100%. The s e c o n d moment v a l u e s σ f o r s a m p l e 5 a t 62% RH and sample 2 a t 40% RH a r e c l o s e t o t h e v a l u e s o b t a i n e d f o r w a t e r a d s o r b e d on b a c t e r i a l c e l l w a l l s (26J and z e o l i t e 1 3 - X . ( 2 7 ) . (ii) A t l o w e s t c o v e r a g e (2 l a y e r s ) t h e a c t i v a t i o n e n t h a l p y Η i s l e s s f o r s a m p l e 5 t h a n f o r sample 2 . For sample 2 a t 88% RH where r = 1.47 Â was t h e s m a l l e s t , t h e Η - v a l u e was t h e h i g h e s t (=1836 c a l m o l e " ) . (iii) For sample 2, a l l the preexponents τ l i e w i t h i n the range 1 0 ~ ' > τ > 1 0 " ' s e c i n accordance with the a c t i v a t e d s t a t e t h e o r y . The τ v a l u e s f o r s a m p l e 5 a p p e a r t o be o u t o f t h i s r a n g e maybe due t o t h e p r e s e n c e o f r e s i d u a l f r e e w a t e r . (iv) The B - v a l u e s a r e a b o u t t h e same f o r t h e t w o - l a y e r c o v e r a g e and i n c r e a s e as expected to the highest spread a t the 0

2

2


0

2

2

2

2

0

2

1 0

2

0

2

p p

0

0

p p

p p

p p

2

0

p p

1

0

2

5

0

0



"

(2

0

1.00 law was Τ

2. 301 =

140°K.

0.163

0.029 0.256

2.572

layer)

1.882

1.089 (0.966)

1.618

2.144 (2.034)

0.88

d

T

".

sec

10

Pre-exponent

1.570 (1.327)

2.093

1.570 :i.268)

,2 °-2 rad sec

a

-10 2

10

i n

Second moment

1.00

6 2

α (ζ 9 l a·y e rν)

0.88

P/Po

Relative humidity

f o r the a c t i v a t i o n

b

SUMMARY

2

2

f o r water

1645

1406

1836

1290 (1336)

968

784 (892)

c a l mole

Η 1

Activation enthalpy

Parameter

2 χ

10" 10 sec 2

rad ί

σ

2 7

r

A

PP

e r g s e c and

2

were t h e r e s u l t o f t h e b e s t f i t Where σ < 1.57 ο and t h e b e s t f i t f o r t h e o t h e r p a r a m e t e r s was o b t a i n e d .

1.59 1.54 1.55 1. 53 - 1.49 1.46 1.42

= 1.054 χ 1 θ "

I s o l a t e d molecule 1 57 F r e e water molecule 1 93 B a c t e r i a l c e l l s walls 1 83 Z e o l i t e 13X 2.00 -- 2. 29 Ice 2. 63 Wool 98.5% RH 3. 20

1

1

sec" , Π

i n other surfaces a i d the proton-proton distance

χ 10

1

surface

2

|Gauss |

Other

2

Gauss

adsorbed

Y = 2.675 χ 10

ξ 7.137 χ 1 0 ~

in Gauss\

Irad s e c I

is

moment σ

P o r e d i a m e t e r s f r o m t h e n i t r o g e n a d s o r p t i o n i s o t h e r m and BET a n a l y s i s .

Second

1.57 χ 10

C

(from R e f . 6,

v

g l a s s temperature

AG-39

a . The

m

29

2

Ρ

189

A

d

Mean p o r e diameter

m

5

Porous g l a s s sample no.

PARAMETER

TABLE H I

3

c

P

b

P

= W

0.174

~

0.2730

0.1955

0.6600 (0.6783)

0.2248

0.2419 (0.2880)

Β

Spread parameter


2

Â

PP

where σ

1.50

1.55

1.47

1.59 (1.64)

1.52

1.59 (1.65)

r

Proton-Proton distance

2

3 >

4^

Relaxation


19.

Studies

335

h i g h e s t % RH. F o r t h e c a s e s where t h e model f i t s t h e d a t a b e s t , i . e . w i t h o u t f o r c i n g σ t o i t s minimum v a l u e o f 1.570 χ 1 0 r a d s e c " , and p r o v i d i n g T « 1 the proton-proton d i s t a n c e s , rpp a t 2 l a y e r c o v e r a g e s gave v a l u e s ( 1 . 5 2 and 1.55A) e s s e n t i a l l y e q u a l to t h a t o f f r e e water molecules ( 1 . 5 4 Â ) . F o r p o r o u s g l a s s sample 2 , i n c r e a s i n g t h e c o v e r a g e t o 99% o f c o m p l e t e f i l l i n g a t 88% RH, without i n t r o d u c i n g s i g n i f i c a n t bulk water, the r value drops s i g n i f i c a n t l y t o l . 4 7 Â v e r y n e a r t h a t o f i c e and t h e a c t i v a t i o n e n t h a l p y H a l s o i n c r e a s e s t o a h i g h a t 1836 c a l m o l e " 2

1 0

2

2

29

C

p p

1


Relaxation

Analysis

Assuming t h a t proton i n t e r a c t i o n w i t h both paramagnetic i m p u r i t i e s and s u r f a c e h y d r o x y ! g r o u p s a r e n e g l i g i b l e , t h e above e x p e r i m e n t a l r e s u l t s c o u l d i n p r i n c i p a l be e x p l a i n e d by e a c h o r both p o s s i b i l i t i e s (28): (i) A d i s t r i b u t i o n o f c o r r e l a t i o n times f o r the adsorbed waters. T h u s , a t w o - f r a c t i o n f a s t exchange model (TFE) w i t h r a p i d e x c h a n g e between t h e m o l e c u l e s o f w a t e r i n r e g i o n B ' ( = A + B ) and r e g i o n Αχ c o u l d be p o s t u l a t e d . T h i s model g i v e s t h e f o l l o w i n g e q u a t i o n f o r s p e c i a l c a s e o f a sample w i t h a v e r y s m a l l (P/^ « P i ) b u t e f f i c i e n t (TT^ » T i g , ) r e g i o n ( a d s o r b e n t w i t h 2

B

a small f r a c t i o n o f high energy

ι\

or f o r T ^

Relaxation Studies of Adsorbed Water on Porous Glass - American

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